Tuesday, December 24, 2019

A Reflection On Learning Theories And Assessment Strategies

In Nursing, to provide and maintain high quality care to our population, nurses are required to have a continuous development of knowledge and skills based on evolving knowledge based practice. Great part of this learning can be developed in clinical practice, under supervision, from a person with sufficient skills to facilitate learning. Therefore, as part of pre-registration nursing students development process, the Nursing and Midwifery Council (NMC) (2008a) declares the requirement of a mentor for their clinical placements. The aim of this essay is to provide a critical reflection on learning theories and assessment strategies and how they were used to facilitate learning. The workplace setting was in an intensive care unit and the student used as a focus for this reflection was a second year student. This essay will be developed under the NMC Code of Practice (2015) to maintain privacy and confidentiality of the persons involved in this process. The role of the mentor emerged as a result of evidence that student nurses were not being prepared with the essential skills required for nursing practice (DoH, 1999. UKCC (1999) cited by Gopee, 2015). Therefore, the development of the Project 2000 in 1989 emphasized the mentor role in develop and assess students learning needs in clinical environment (Vinales, 2015). In this order, it is fundamental that mentors achieve learning outcomes described under eight domains by the NMC in order to support learning and assessment inShow MoreRelatedEssay about Assessment of Critical Thinking976 Words   |  4 Pages Assessment of learning can be a meaningful tool for teachers and students during a course to provide feedback to the student about the type and quality of work that is being completed in the course and for the instructor to find areas where the student is having difficulties and so additional materials can be provided or the course modified. The aim of this paper is to define assessment and critical thinking skills, and then review a State University course and suggest different assessments thatRead MoreThe Importance Of Critical Reflection On Teaching1270 Words   |  6 PagesImportance of reflection: Reflection on practice has different meanings, in my view it means constructive criticism: being honest with myself, becoming aware of and understanding my own strengths, and being able to review activities and constantly test assumptions related to our work. These have been my approach to critical reflection throughout the year. This is supported by Brookfield, he says that Critically reflective teaching happens when we identify and scrutinise the assumptions that undergirdRead MoreHow Constructivist Theory Changed My Transition From A Beginning Classroom Teacher954 Words   |  4 Pagesthe constructivist theory affected my transition from a beginning classroom teacher to an instructional school leader, I must admit that I didn’t really understand the process until it became a reality for me. I woke up one day and realized that things that were very difficult for me suddenly became second nature to me. Upon further reflection, I now realize that this was the culmination of past experiences, new knowledge, investigation, and synthesis producing genuine learning. Constructivism allowedRead MoreAcademic And Clinical Aspects Of The Curriculum846 Words   |  4 Pagesdifference between nursing theory and practice (Johns, 2009; Stuart, 2013). Reflection helps the student to observe, understand, learn and make sense of their daily experiences and also play a major role in student learning process (John, 2009). Schon (1992) stated that to succeed, the knowledge and skills from previous course work and clinical experiences must be built on by the student. Furthermore Plack et,al. (2008), affirm that to facilitate the process of reflection, the mentor is often requiredRead MoreTeaching And Learning Process Faculty1191 Words   |  5 PagesTo maximize the teaching and learning process faculty must make conscious multiple teaching methods to assist with the development of critical thinking. The use of multiple assessment techniques to monitor and evaluate the learning process support both formative and summative assessment. Evidence-based decisions will dramatically improve the learning outcomes. 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It is through such process that students gain in-depth learning and thus discover their values, abilities, passions as well as responsibilities in learning situations that provide adventure. In most school lessons, students undertake tasks that require them to use their creativity, self-discipline and craftsmanship.Read MoreReflective Practice in the Classroom1629 Words   |  7 PagesReflective practice – A tool for learning Introduction/Rationale When something goes wrong or something unexpected happens during a lesson or activity, we ask ourselves questions such as, could I have done something to avoid it? These experiences usually make us grow and we learn from experience, and we will be better prepared to face the situation if it happened again. This introspection is generally called â€Å"reflection†, and all professionals have adopted it in order to improve their practiceRead MoreEssay on Student Assessment Reflection1402 Words   |  6 Pagesbest by carrying out assessments or diagnostic meetings to identify their preferred learning styles, abilities and interests. Neil Flemming developed the VARK system in 1987 to determine whether a student is a visual, auditory, reading/writing or kinaesthetic learner. From there, students and teachers are able to formulate new strategies based on which category they learn efficiently. Instead of doing the 16-point questionnaire, I chose to determine my students’ learning styles through play andRead MoreEvents Of Instruction And Evaluating The Learners764 Words   |  4 Pagesdefine what s effectively working, or not working. This evaluation process defines value about learning and training program, so they can make improvements (Rossett, 2001). Events of Instruction Brown Green (2016) stated that students using the correct learning behavior skills in order to learn skills proficiently. Once students use the correct behaviors skills, they will be successful in learning. For this assignment the learners will complete an outline for the task. The students will create

Monday, December 16, 2019

Short Story Esay †on the Side Walk Bleeding Free Essays

A short story in which a material object becomes important is â€Å"On the Side walk Bleeding† by Evan Hunter. With reference to the text I will identify the object and explain it’s significance. In the opening paragraph the author gives a detailed description of a jacket which is worn by the victim of an attack. We will write a custom essay sample on Short Story Esay – on the Side Walk Bleeding or any similar topic only for you Order Now â€Å"The boy’s name was Andy, the name was delicately scripted in black thread on the front of the jacket, just over the heart. On the back of the jacket it has the slogan ‘THE ROYALS’† this is the gang he is associated with. The Royals’ are rivals to The Guardians. Being a Royal lead to Andy’s death. When he goes out for a pack of cigarettes he is violently assaulted by a member of The Guardians. The gang member said, with volume, â€Å"That’s for you Royal! †. This tone insinuates that he had a vendetta with the gang as he emphasises the word ‘Royal’. If Andy wasn’t wearing the Royal’s jacket he wouldn’t have been attacked. As the story progresses there are two young love birds strolling down the pavement. They duck into the ally where Andy lay after he’d been attacked. They didn’t realise that Andy was only a few feet away. Freddie, one of the couple, saw Andy and knelt down beside him, that was when he had seen the jacket and said â€Å"He’s a Royal. † The couple are afraid to help him in case The Guardians attack them. This further reveals the significance of the jacket; a material object which caused him to be targeted and is stopping people from helping him. When Laura, Andy’s girlfriend, goes searching for him she find him in the ally, dead. He was found 58 minutes after he had been stabbed but before he bleed to death he mustered up all his strength to try and take his dreaded jacket off in the hope that someone would attempt to help him. The jacket meant fear to any one and everyone if he had managed to take it off before, he would have been saved but he didn’t do it earlier. ‘A Royal, huh? were the first words the police officer said when he had found the jacket only a foot away from his cold body. Laura tried to tell him that his name was ‘Andy’ but the officer only saw a Royal and nothing else. The jacket was a label and his identity was lost whilst he wore it. The significance of a material object in the text is important because it symbolises his dedication to the gang. This not only resulted in him being targeted; it made people afraid to help him and ultimately because of the jacket, he was left to die. Jamie Blair How to cite Short Story Esay – on the Side Walk Bleeding, Papers

Saturday, December 7, 2019

Syllable Formal Ion free essay sample

Thus a meaningful language unit phonetically may be considered from the point of view of syllable formation and syllable division. The syllable is a complicated phenomenon and like a phoneme it can be studied on four levels articulatory, acoustic, auditory and functional. The complexity of the phenomenon gave rise to many theories. We could start with the so-called expiratory (chest pulse or pressure) theory by R. H. Stetson. This theory is based on the assumption that expiration in speech is a pulsating process and each syllable should correspond to a single expiration. We will write a custom essay sample on Syllable Formal Ion or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page So the number of syllables in an utterance is determined by the number of expirations made in the production of the utterance. This theory was strongly criticized by Russian and foreign linguists. G. P. Torsuyev, for example, wrote that in a phrase a number of words and consequently a number of syllables can be pronounced with a single expiration. This fact makes the validity of the theory doubtful. Another theory of syllable put forward by O. Jespersen is generally called the sonority theory. According to O. Jespersen, each sound is characterized by a certain degree of sonority which is understood us acoustic property of a sound that determines its perceptibility. According to this sound property a ranking of speech sounds could be established: voiceless plosives ( voiced fricatives (voiced plosives ( voiced fricatives ( sonorants ( close vowels (open vowels . In the word plant for example we may use the following wave of sonority: [pla:nt]. According to V. A. Vasssilyev the most serious drawback of this theory is that it fails to explain the actual mechanism of syllable formation and syllable division. Besides, the concept of sonority is not very clearly defined. Further experimental work aimed to description of the syllable resulted in lot of other theories. However the question of articulatory mechanism of syllable in a still an open question in phonetics. We might suppose that this mechanism is similar in all languages and could be regarded as phonetic universal. In Russian linguistics there has been adopted the theory of syllable by LV Shcherba. It is called the theory of muscular tension. In most languages there is the syllabic phoneme in the centre of the syllable which is usually a vowel phoneme or, in some languages, a sonorant. The phonemes preceding or following the syllabic peak are called marginal. The tense of articulation increases within the range of prevocalic consonants and then decreases within the range of postvocalic consonants. Russian linguist and psychologist N. I. Zhinkin has suggested the so-called loudness theory which seems to combine both production and perception levels. The experiments carried out by N. I. Zhinkin showed that the arc of loudness of perception level is formed due to variations of the volume pharyngeal passage which is modified by contractions of its walls. The narrowing of the passage and the increase in muscular tension which results from it reinforce the actual loudness of a vowel thus forming the peak of the syllabic. So the syllable is the arc Ð ¾f loudness which correlates with the arc of articulatory effort on the speed production level since variations in loudness are due to the work of all speech mechanisms. It is perfectly obvious that no phonetician has succeeded so far in giving an adequate explanation of what the syllable is. The difficulties seem to arise from the various possibilities of approach to the unit. There exist two points of view: 1. SÐ ¾me linguists consider the syllable to be a purely articulatory unit which lacks any functional value. This point of view is defended on the ground that the boundaries of syllables do not always coincide with those of morphemes. 2. However the majority of linguists treat the syllable as the smallest pronounceable unit which can reveal some linguistic function. Trying to define the syllable from articulatory point of view we may talk about universals. When we mean the functional aspect of the syllable it should be defined with the reference to the structure of one particular language. The definition of the syllable from the functional point of view tends to single out the following features of the syllable: a) a syllable is a chain of phonemes of varying length; b) a syllable is constructed on the basis f contrast of its constituents (which is usually of vowel consonant type); c) the nucleus of a syllable is a vowel, the presence of consonants is optional; there are no languages in which vowels are not used as syllable nuclei, however, there are languages in which this function is performed by consonants; d) the distribution of phonemes in the syllabic structure follows by the rules which are specific enough fo r a particular language. 2. The structure and functions of syllables in English Syllable formation in English is based on the phonological opposition vowel consonant.

Saturday, November 30, 2019

Poetry Unit 2000 Essays - American Cuisine, Connacht, Galway

Poetry Unit 2000 Poetry Unit 2000 LIMERICK There once was a kid named Darren, Who's room was surprisingly barren, He had no toys, Like all normal boys, But he did believe in sharing. There once was an old man named Esser, Whose knowledge grew lesser and lesser, It at last grew so small He knew nothing at all, And now he's a college professor. HAIKU Morning light appears The new day has awoken Nature stirs and sighs Spirits haunt my dreams Skeletons muffle my screams Night as black as death EPIGRAM The days become months and those become years, Only memories remain of both joy and tears. The screams the cries and the pain, All of this goes on in one's brain. PARODY Galway Bay Maybe some day I'll go back again to Ireland If my dear old wife would only pass away She nearly has my heart broke with all her naggin She's got a mouth as big as Galway Bay See her drinking sixteen pints of pabst blue ribbon And then she can walk home without a sway If the sea were beer instead of salty water She'd live and die in Galway Bay See her drinking sixteen pints at Padgo Murphey's The barman says I think it's time to go Well she doesn't try to speak to him in Gaelic In a language that the clergy do not know On her back she has tattooed a map of Ireland And when she takes her bath on Saturday She rubs the sunlight soap around by Claddagh Just watch the suds flow down by Galway Bay. IMITATION Happy and Gay May one day I'll go back again to my homeland, If only faster time will pass away, It's been many years and now its dragging, That's the only time I'll be happy and gay. See myself drinking six doses of bourbon And then I linger about and sway If instead I could have plain water That's when I'll be happy and gay. See myself drinking doses after doses The doctor says to take it slow Well I try to speak to him about this In any possible way I know. On my back is a map of my homeland And when the day will finally arrive Ill be running and dancing and singing Knowing only the right place to survive. BALLAD Who Threw The Golf Balls In My. Friends Chowder? My friends gave a party just about a week ago, Everything was plentiful because they're not too slow, They treated us like guests and we tried to act the same, And only what happened next was an awful shame. Who threw the golf balls in their chowder? Nobody spoke so we shouted all the louder, It's a little trick but we'll catch the guys that threw, The golf balls in my friends chowder. When they were cleaning the dish of chowder, they fainted on the spot. They found a set of golf balls at the bottom of the pot. The neighbors got very mad with their eyes bulging out. They stood upon the stand and loudly did they shout. They took the balls from out of the soup and laid them on the floor. Each of us swore that we'd ne'er seen them before. They were packed up with morter and were worn to the knee. Only for what happened then it was just too sad to see. When they came to, they began to cry and shout. They had put them in the wash that day and forgot to take them out. The fellow neighbors excused themselves for what they said that night So we put music to the words and sang with all our might. Poetry Essays

Tuesday, November 26, 2019

The Beheading of Precious Doe

The Beheading of Precious Doe On April 28, 2001, the nude, decapitated body of a 3-year-old girl was found near an intersection in Kansas City, Missouri. Two days later her head was found nearby in a plastic garbage bag. It would be more than four years before the girl, given the name Precious Doe by police, would be identified as Erica Green. Sketches, computer drawings and busts of the child were distributed nationwide and on several television crime programs before a relative came forward and identified the victim on May 5, 2005. Mother, Stepfather Charged in Case The Precious Doe case had frustrated police for four years and had been featured on several television crime shows, including Americas Most Wanted.   In the end, police say, it was a tip from a family member that finally helped authorities identify the child and also those responsible for her death. Press reports said a grandfather of one of the principles involved came forward and provided police with photographs of Erica as well as hair samples from the child and the mother. On May 5, 2005, Michelle M. Johnson, the 30-year-old mother of Erica, and Harrell Johnson, 25, her stepfather, were arrested and charged with murder. Police said Johnson told them he was under the influence of alcohol and PCP when he became angry with Erica when she refused to go to bed. He kicked her, threw her on the floor, and left her there unconscious. Erica remained on the floor unconscious for two days, because the couple refused to seek medical help because they both had warrants out for their arrest, police said. After Erica died the Johnsons carried her to a church parking lot, then into a wooded area where the stepfather cut her head off with hedge clippers. Ericas body was found near an intersection and two days later her head was found nearby in a plastic trash bag. On December 3, 2005, prosecutors announced that they would seek the death penalty in the case against Harrell Johnson. Authorities believed that the child died while Johnson was decapitating her with hedge clippers. Cousin Sheds Light on the Abuse Suffered by Erica According to Harrell Johnsons cousin, Lawanda Driskell, The Johnsons moved in with Driskell in April 2001. Michelle Johnson helped her husband dispose of Erica by placing the dead child in a stroller as if she was asleep. Later, she told Driskell that she had given Erica to another woman to raise. She described Harrells treatment of Erica as abusive, stating that he beat her for small infractions such as crying or not wanting to eat. One day she heard a loud bang coming from childs room and for the next two days, Erica was kept in the room. The couple told Driskell that the child was sick. Michelle Johnson then told Driskell that she took Erica to live with the woman who first raised the child. Michelle Johnson Pleads Guilty   On September 13, 2007, Michelle Johnson pleaded guilty to second-degree murder of her 3-year-old daughter. In a plea deal, she agreed to testify against her husband, Harrell Johnson, who was charged with first-degree murder. In return, prosecutors agreed to recommend a 25-year-sentence for the mother of the murdered child. Precious Does Mom Testifies Against Husband Michelle Johnson told the jury that Harrell Johnson was on drugs when he kicked her daughter in the head and the child dropped to the floor unconscious. He just picked up his feet and kicked her on the side of the face. I said, What the (expletive) did you do? It shook him out of his high, Johnson said. She said she put the child in a tub of cold water, but she failed to come around. She then put her on the bedroom floor where she stayed for two days before she died. Fearing that she might be arrested on outstanding warrants, Johnson made the decision to not call for medical help. Guilty Verdict A Kansas City jury deliberated for about three hours before returning a guilty verdict. Harrell Johnson, 29, was charged with the death and the decapitation of three-year-old Erica Green, the daughter of his then-girlfriend who he married a year later.   Johnson was also convicted of endangering the welfare of a child and abuse of a child. During closing arguments, prosecutors told the jury that a guilty verdict would finally bring justice for Erica. This selfish coward made the decision to put himself before this 3-year-old childs life, said prosecutor Jim Kanatzar. Sentenced On November 21, 2008, Harrell Johnson was sentenced to life without parole.

Friday, November 22, 2019

-CER - French Spelling Change Verbs Examples

s Verbs that end in -cer, like lancer, have a spelling change before endings that begin with the hard vowels a or o. Because c followed by a or o would make a hard c sound (like in cold), the c has to change to à § (c with a cedilla) to keep the c soft (as in cell).In the present tense and the imperative, this c à § spelling change is found only in the nous conjugation: lanà §ons. It is needed in the present participle, lanà §ant, but not the past participle, lancà ©. And it occurs in the following tenses/moods: Imperfect - singular conjugations plus the third person pluralPassà © simple - all conjugations except the third person pluralImperfect subjunctive - all conjugations There is no spelling change in the conditional, future, or subjunctive.The table below summarizes just the spelling change conjugations, or you can see lancer conjugated in all tenses.All verbs that end in -cer undergo this spelling change, including  Ã‚  Ã‚  annoncer  Ã‚  Ã‚  to announce  Ã‚  Ã‚  avancer  Ã‚  Ã‚  to advance  Ã‚  Ã‚  commencer  Ã‚  Ã‚  to begin  Ã‚  Ã‚  dà ©noncer  Ã‚  Ã‚  to denounce  Ã‚  Ã‚  divorcer  Ã‚  Ã‚  to divorce  Ã‚  Ã‚  effacer  Ã‚  Ã‚  to erase  Ã‚  Ã‚  lancer  Ã‚  Ã‚  to throw  Ã‚  Ã‚  menacer  Ã‚  Ã‚  to threaten  Ã‚  Ã‚  placer  Ã‚  Ã‚  to put  Ã‚  Ã‚  prononcer  Ã‚  Ã‚  to pronounce  Ã‚  Ã‚  remplacer  Ã‚  Ã‚  to replace  Ã‚  Ã‚  renoncer  Ã‚  Ã‚  to renounce Present Imperfect Pass simple Imperfect subjunctive Participles je lance lanais lanai lanasse tu lances lanais lanas lanasses Present il lance lanait lana lant lanant nous lanons lancions lanmes lanassions vous lancez lanciez lantes lanassiez Past ils lancent lanaient lancrent lanassent lanc

Wednesday, November 20, 2019

Role in the meeting user needs in my placement Essay

Role in the meeting user needs in my placement - Essay Example Over time I have been able to witness that my role had been from accomplishing individual and group therapy that was set up by interdisciplinary treatment teams to carrying out assessments, revisions, as well as approval. I came to realize that for a practitioner to be successful, he or she must not only be aware of the agency policies that are applicable, the laws that are related to the intended philosophy, and the procedures of the institutions, but also the knowledge of those interventions that are the most suitable and fitting in the associated case. One such example is from my placement where the revolving door approach was tackled on a patient. In such a scenario, a user usually becomes stable for a while but then goes back at the same problem in some time. Basically, the user only gains a short term steadiness and then deteriorates to the same level as the beginning. The user in this scenario needed support as well as intervention of the highest level that tested my abilities of exhibiting the appliance of processes and techniques that were related to the required therapy. I came to realize that as a practitioner, my role was to provide my patients an approach that they can embody so that they could work towards a healthy mental treatment. A practitioner must also be aware of the biological model, the claim of which is supported by James (2009) that one must be able to understand the basic structure as well as the way a human body functions because of the fact that the human body is very important for becoming a health care professional. I also realized the importance of interpersonal relationships and was amazed to see that the main culture that is needed for treatments in the mental health is being able to make connection with various events. For example, one of my patients required a joined up approach of thinking that did the same. The treatment revolved around making sure that those events of the past that are directly related to the current situat ion of the user are brought in focus. In this way, experiences from childhood and adolescence were brought in picture that helped the user recognize the patterns forming the behavior. The whole idea behind this strategy could only be accomplished when a practitioner like me recognized the need to turn a mere treatment into a meaningful recovery. Therefore, one of the most important lessons that I have learned through my placements is that it is not just about dealing with a treatment that is presented to you, that could range from a bracket of drug abuse, depression, to stress and depression, it is also about understanding the meaning of a holistic approach that considers each individual as a person. In this way, both the practitioner as well as the individual gains a lot and thus identifying ways to recognize each action demonstrated by the user and thereby exploring the root cause. Utilizing the psychological techniques that need to be carried out must also be one of the biggest k nowledge and skill that must be used in order to meet the needs of the user. It is imperative that the professional actually listens to the user and assures them that they are being taken seriously. For example, it is being taught to us that the user must be able to recognize the presence of his or her internal world with which they would slowly learn to

Tuesday, November 19, 2019

Consumption of Natural Resources Essay Example | Topics and Well Written Essays - 4750 words

Consumption of Natural Resources - Essay Example The US tops consumption in natural gas, 2 oil, coffee, corn, zinc, lead, aluminum, rubber and many other resources. There are numerous ways in which this consumption rates can be illustrated. For example, a commodity like meat is consumed by almost all nations. However, consumption should be such that it corresponds with the overall population. China is therefore justified for being the largest overall consumer since they have the largest population. But when one examines the amount of meat consumed by individuals in each country, the US carries the day. It was found that this country exceeds the world average by three hundred percent. Southern Asian meat consumers fall below the world average by seventy five percent. African countries on the other hand fall below the world average consumption by fifty percent. Other products such as fish are consumed by populations depending on their availability. This is because fish is quite cheap if it is located near consumers. Maldives - which is a relatively poor country - has recorded high fish consumption rates. Even other rich nations such as Japan have high fish consumption rates because this has been part of their tradition ever since time immemorial. It should be noted that consumption rates normally indicate the extent of industrialization in any given country. Countries such as Taiwan, Korea and Malaysia are growing economies. Most of them are engaging in building projects since they are all trying to develop their infrastructure. Consequently, the latter three countries are the world's largest Cement consumers. Surveys found that these countries exceeded US cement consumption with a ratio of 2:1. On the other hand, industrialized nations like the UK consume about a quarter of the cement that the Asian countries mentioned above consume. 3 Water consumption largely depends upon the geographical location of a specific country. For instance Egypt gets most of its water from other countries that have large portions of fresh water from the Nile. Sudan is also faced with a similar situation. It does not have access to the River Nile and therefore gets most of its water from its neighbors. Other countries that also depend on their neighbors for water are Iraq and Syria. The latter countries depend on the Euphrates for survival. It should however be noted that water consumption mostly depends on the rate of development and the economic activities that go on in a country. For example, countries growing cash crops that require a lot of water are more likely to record high water consumption rates per person. On the other hand, countries that have poor infrastructural facilities are more likely to waste water resources and will therefore record higher levels of water consumption. Statistics comparing annually water consumption in a number of countries throughout the world found that a relatively under developed country such as Turkmenistan in the Soviet Union consumed five million liters per person as compared 1.8 million liters of water per person. France take up 0.65 million liters while the United Kingdom uses 0.2 million liters of water per person. 4 Some natural resources are taken up depending on the end products they can produce. One such resource is timber or forest resources. Finland has been recorded as the highest timber consumer because they are also the largest producers of paper. In light of this, it should be

Saturday, November 16, 2019

Consumer Purchase Decision Essay Example for Free

Consumer Purchase Decision Essay There are many reasons that a consumer chooses a certain product. It may be that it is environmentally friendly, a great design or it might be as simple as the price of the product. As a business organization we must be able to conduct our research and decipher what is most important to our target market. The consumer buying decision process is a systematic way of looking at how a consumer makes the decision to purchase a product (any product) in a product category. In our restaurant we will determine what products they want and develop a successful strategy on how to market our products and services. As a customer in our restaurant we will have many choices available to them at a low cost. There are five steps in the consumer purchase decision that I’ll explain. Step one is need recognition which simply means that we identify what the potential customers need in our market. What kind of foods do they like and what kind of experience do they want when they go to a restaurant? Step two is searching for the product that the customer wants. We will have many avenues, such as print ads and our website, in which to market our product and inform the public of our food and services. The third step is product evaluation where the consumer gathers information on our products and services. We will have the best menu and service in our market to gain a larger market share in our area. The fourth step is product choice and purchase so it is vital that we successfully advertise and market our restaurant. We will have the best menu, greatest service and the most updated restaurant within a hundred mile radius. The fifth step is the post purchase and evaluation step where the consumer will decide whether our food and  service is worth a return visit. We will make a great impression on our customers through our delicious menu and excellent dining experience. A consumer’s buyer behaviour is influenced by four major factors: 1) Cultural, 2) Social, 3) Personal and 4) Psychological. Cultural factors include a consumer’s culture, subculture and social class. These factors are often  inherent in our values and decision processes. Our target customers are mostly young families and lower to upper middle class. Social factors include groups (reference groups and member groups), family, roles and status. This explains the outside influences of others on our purchase decisions either directly or indirectly. Personal factors include such variables as age and lifecycle stage, occupation, economic circumstances, lifestyle (activities, interests, opinions and demographics), personality and self concept. These may explain why our preferences often change as our `situation changes. Psychological factors affecting our purchase decision include motivation (Maslows hierarchy of needs), perception, learning, beliefs and attitudes. Other peop le often influence a consumer’s purchase decision. Word of mouth can be one of our biggest allies or our greatest threat in the marketing of our restaurant. We will make sure that every customer will enjoy their experience from the moment that they walk through our doors. They will be greeted when they enter and when they exit and our servers will be courteous and knowledgeable. We need to know which people are involved in the buying decision and what role each person plays, so that marketing strategies can also be aimed at these people. Understanding these behaviours as they pertain to our restaurant will help us gain a competitive advantage against all competitors in our area. Market segment is defined as the process of defining and subdividing a large homogenous market into clearly identifiable segments having similar needs, wants, or demand characteristics. Its objective is to design a marketing mix that precisely matches the expectations of customers in the targeted segment. We have effectively indentified our market segment as having fewer than ten thousand potential customers in our area with an additional five thousand from outside our area such as truck drivers and customers passing through. Our town has consistently been moving to a younger crowd (Generation X) so our fresh new look and our website should appeal to this younger generation. This market also values environmentally friendly products so we will utilize environmentally safe products in our restaurant. The majority of our market are family oriented so our family style menu and restaurant will be very appealing to our customers. We understand that the  customer has a process that they u se to determine where they want to dine. With our excellent customer service, great new menu and low prices we will gain their loyalty and get them back through our doors. Our customers are always number one and our customer service will be second to none. There are many options to dine in our area but we will set ourselves apart from the competition.

Thursday, November 14, 2019

A Sistine Chapel of My Own :: Personal Narrative Religion Essays

A Sistine Chapel of My Own I was almost God, that day. I was away from the world, looking down upon it, or out at it, from a different place, a place not of it. The world looked peaceful, what I could see of it, lying there in the summer sun, but I saw it as one might see a distant galaxy through a telescope. A world was there, a complex world, perhaps a busy world, possibly even a world that could turn violent—but I was not of it. I was detached, beyond it, above it—an interested observer. The year was 1935, and I was eleven, a boy growing up on a South Dakota farm. This epiphany had an unpretentious setting—our outhouse, which was set back into some trees about a hundred feet northwest of the house. I was sitting there in the darkened interior when I noticed a nail hole through the door in front of my face. By putting my eye up close, I could squint through the hole and see outside. The scene itself was unremarkable—the nearby trees, our house, a large white structure with a hip roof, the garden, the hog yard and the road in the distance. But I was, strangely, not a part of it. It gave me a feeling of exhilaration—of awe. I was away, in some distant place. A higher place. I have tried to explain this experience to myself, but never with complete success. What I was looking at was something I saw every day, and something I could have seen better if I had just opened the door and stepped outside. The scene was as ordinary as anything could be, it would seem bleak to any modern viewer, just a typical summer day on an austere South Dakota farm in the Dust Bowl era. The feeling didn't even particularly relate to the scene itself; the view in another direction would have served as well, I think. But the nail hole was essential to the experience, as was the room, and being alone there. Being alone in that small, dark space allowed me to separate myself from the world. Perhaps no one knew I was there; perhaps no one even knew there was such a person as me; perhaps I really wasn't even a person of the ordinary world—my usual awareness of self seemed to diminish or disappear in there.

Monday, November 11, 2019

Black Panther Party during the 1960s Essay

The Black Panther Party was a left-wing organization founded in 1966 for the defense of African Americans (Katsiaficas, and Cleaver 3). It was founded in Oakland, California by Bobby Seale and Huey Newton and would go on to gain fame all over the United States for its deep commitment to defend the rights of the African American population as a minority group (Katsiaficas, and Cleaver 3). For the decade it lasted, the Black Panther Party was able to tackle one of the most pertinent issues of the time: Racism. In this essay, I seek to explain the role the Black Panther Party, whose initial objective was to defend African Americans from police brutality, played in American society in the 1960s. Black Panther Party began as a result of a prior history of activism where African American opinion leaders were pushing for equality and an end to racial prejudices and police brutality (Katsiaficas, and Cleaver 71). African Americans had for long demanded that authorities address the issues that were affecting them as a minority in the American society. The Black Panther Party the discipline and calmness preached by renown African American activist Malcolm X to become the heroes of the African American cause (Smethurst 21). The party symbolized self determination and pride, and initiated programs aimed at educating African Americans politically as an attempt to achieve a revolution in diction, the free spirit and commitment to the cause. It became a symbol of African American culture and even had an impact on fashion. The Black Panther Party, through its Ten Point Program, was able to grasp the attention of the authorities and the American public about the issues that were affecting the African American community (Katsiaficas, and Cleaver 76). It gave an outcry about the oppression that was perpetuated against members of its target community and their lack of control in the political and social institutions that were meant to serve them. The party also petitioned the government and demanded it honors its obligation to provide employment or guarantee an income for all people (Katsiaficas, and Cleaver 76). The other demands in the Ten Point program included a call to end economic exploitation of the African American and other minority communities and the honor of the promise for forty acres of land and a mule that had been made 100 years earlier as reparation for slavery (Jones 177). The party also demanded better housing to be made available in African American neighborhoods failure to which the land should be made cooperative land so that African Americans could build their own decent housing. The Black Panther Party managed to petition authorities about the poor quality of educational infrastructure in African American neighborhoods as well as pushing the agenda for free healthcare for impoverished Americans (Jones 179). Police brutality was rampant in those days, targeting African American and Hispanic men. The Black Panther Party wanted an end to all this; and through sensitizing the public, it helped create an awareness and knowledge of human rights which was later to become instrumental in later activism (Smethurst 26). The Black Panther Party followed the ideals of Chinese revolutionary leader Mao Zedong as he outlined them in his manual, The Little Red Book, to orchestrate economic and social awareness campaigns among African American people through what it called Survival Programs (Katsiaficas, and Cleaver 81). Through these programs, it fought drug abuse and rehabilitated drug addicts, organized free medical clinics and offered emergency response and ambulance services. In addition it founded the Inter-communal Youth Institute with Ericka Huggins as the director to demonstrate how African American youth must be educated so that they would be empowered politically and economically (Katsiaficas, and Cleaver 81). There were also other programs, most of which had an impact on live in areas where the party was operational. The Black Panther Party had an impact on the political landscape during the time it existed. The party assumed the role of teaching African Americans their political rights and their guarantees as legal American citizens to basic human rights, individual freedoms and liberties (Jones 178). To be more effective, it briefly combined efforts with the Student Non-violent Coordinating Committee which was headed by Stokely Carmichael who later renamed himself Kwame Ture in line with his Pan African ideals (Jones 178). This was just after it was founded. In the year 1967, the Black Panther Party organized a street march in which many African Americans were involved in a procession to the California State Capital to oppose a proposed directive to ban the carrying of loaded weapons to public places (Katsiaficas, and Cleaver 81)). The panthers (members of the party) had already begun exercising that right; and on this procession they all carried rifles. The Black Panther Party sought to empower African Americans politically; and having garnered widespread support from African Americans and other sympathizers, its Minister of Information, Eldridge Cleaver ran for president in the 1968 presidential elections (Katsiaficas, and Cleaver 85). The party made a bigger impact than its opposite, the White Panther Party. Its biggest role was perhaps in the human rights movement. Even though the party lasted for only 14 years, it left a lasting impression on the struggle for rights and equality, and its ideals of community service are still present in many African American communities today. Works cited Jones, Charles. The Black Panther Party (Reconsidered). Baltimore, MD: Black Classic Press, 1998. Katsiaficas, George, and Cleaver, Kathleen. Liberation, Imagination and the Black Panther Party: A New Look At The Panthers and Their Legacy. New York: Rutledge, 2001. Smethurst, James. The Black Arts Movement: Literary Nationalism in the 1960s and 70s. Chapel Hill, NC: University of North Carolina Press, 2005.

Saturday, November 9, 2019

Critical Book Review of “Fast Food Nation” Essay

In this essay, an attempt is made to critically review the book, â€Å"Fast Food Nation† which deals with the process of emergence of fast food culture in America leading to significant social changes. Analysis The meticulously researched book â€Å"Fast Food Nation† is written by the journalist Eric Schlosser. The author devotes much attention to unhealthy fast food, labor violations, and many cases of food poisoning. The author gives information regarding the process of emergence of fast food culture in America; the health issues related to fast food culture, and the government regulations regarding the fast food. In this book, the author demonstrates the ugly side of American food culture. According to the author of this book Americans spend more on fast food than on books, movies, etc. In 2001, Americans have spent $110 billion on fast food. There are 43000 meatpacking workers. Fast food industry spends $3 billion to attract the young people to the fast food centers. The author states that every American consumes three hamburgers and four orders of French fries every week. He says that the social price of fast food has neglected the traditional American values. The attempt of the author is to argue against the consumption of fast food by the Americans. He obtained information through fieldwork and by interviewing different categories of workers involved in fast food production. The author argues that the main reason for opening so many fast food centers was to attract large number of people to the fast food culture. This is a part of the capitalist agenda since the fast food centers have increased the capital of the owners of these centers. Due to this, few corporations have dominated the fast food business in America. The author does not hide his distrust regarding the fundamental principles of the capitalist system. He has given information regarding the economic strategies of the capitalists in popularizing the consumption of fast food among the American youth and other sections of American society. The book also gives information regarding the problems faced by the teen-aged workers who were paid low wages. The author mentions that one out of every eight worker in America is employed in McDonald. McDonald’s hire nearly million people a year. However, they work under dangerous working conditions. It is mentioned that three companies master 80 percent of US demand for frozen fries. The author visited the slaughterhouses and comprehended the potential health hazards both to the workers and the consumers. He mentions that each year one in three workers go to doctor due to problem with their stomach. The author gives the information that two thirds of fast food workers are under 20 and most of them work 12 hours shift. To demonstrate his argument the author has used the examples, logos from the companies such as MacDonald’s. The fast food culture has few negative impacts on the health and society of America. For instance, this has increased the problem of obesity. These restaurants use items such as potatoes and cattle to produce the popular food. The use of items such as oil and method of production of meat has increased the problem of obesity in America. Obesity in the recent years has emerged as the one of the most severe social and health problems among the American youth. Thus, fast food culture can be considered as one factor leading to this problem of obesity in America. However, the author has neglected the role of consumer while discussing the growth of fast food culture. The author points out the need for government regulations to curb the freedom of multi national companies in imposing their capitalist agenda on the people. The fast food mostly produced and consumed by the younger generation are not healthy. Regarding the health hazard, the author refers to E. coli and salmonella infection. The author blames the politicians for taking money from agri business capitalists, which has increased the number of fast food restaurants throughout America. The author has urged the readers that they should run away from the fast food in order to maintain their health. The fact that fast food culture is becoming popular indicates the emergence of significant changes in the American society. The fast food centers have on the one hand created health problems, and, on the other, they have led to changes in the social values among the American youth. The author says that everyday one-quarter of adult population in America visit fast food centers. Although people are aware of the bad effects of the fast food, still fast foods have not lost their popularity. Thus, the author does not give clear explanation regarding the reasons for the popularity of these fast food centers. However, the author, by the use of statistics, symbols, and examples has succeeded in arguing against the monopoly of few companies in fast food business. He has demonstrated the negative impact of fast food on health and society of America. Those who read this book would not send their children to the fast food centers. Conclusion The book â€Å"Fast Food Nation† has convincingly proved that fast food culture has led to problem of obesity and affected the workers and health of consumers of fast food. This also demonstrates that the nature of changes that would emerge in the future American society.

Thursday, November 7, 2019

Tom Cruise Essay Example

Tom Cruise Essay Example Tom Cruise Essay Tom Cruise Essay Tom Cruise was born on 3 July 1962, Syracuse, New York, USA.Originally, Cruise wanted to become a Priest at the age of 14, an ironic concept, compared to what his true career was to become.If you were to hear the name Tom Cruise, two words would generally come to mind, these words being Small and Scientology.Fortunately for Cruise, the latter term brought his fame up a level, not altogether in a positive way however.An example of this is in 1992, where, in an interview, Cruise claimed that Scientology has cured his dyslexia. More information on Cruises fame through Scientology can be found in Chapter 2.In 2006, Cruise, married Katie Holmes (his 3rd wife), however after finding his new love, he appeared to become deluded into thinking he had more public power than he actually did, shown in the Oprah scene. More information on the Oprah scene can be found in Chapter 3.2 ANALYSIS OF FAMECruises recognition came at the age of 21, in the film Risky Business.From then, he went on to Top Gu n where he came to fame in 1986. See Chapter 4.1 for in-depth analysis of Top Gun.Just 2 years later, Cruise appeared in the light-hearted drama Cocktail, where Cruise received his first nomination for a Razzie award in 1989. This will have boosted his fame furthermore, and, just at the age of 27, Cruise had appeared in 3 big hits.In 1992, Cruise appeared in A few good men, where he received a Golden Globe and MTV nominations. The Golden Globe would have brought Cruise massive respect from fellow actors, and, critics. Once more, Cruises fame was rising.12 years later, Cruise appeared in Vanilla Sky, a film, different in genre, compared to the typical action related films he usually partook in.Overall, Cruises career as an actor brought him fame, fortune, fans and finally, formidable flagging in terms of his publicity.However, his fame, combined with good acting certified him to be nominated for 3 Oscars, and caused his to win an impressive 40 nominations.3 POWER OF PUBLICITYOver tim e, Cruise has displayed several ways of publicising himself, be it positively, negatively, on purpose or just by coincidence.An example of Cruises negative self advertisement is The Oprah Scene.In 2005, Cruise professed his love for Katie Holmes upon his appearance of the Oprah show. His behaviour of jumping up and down on the couch and repeatedly hitting the floor, in the way to express his devotion for his new partner, was seen by almost everyone, as over-the-top drama. This is a classic example of a celebrity overusing their power, of which Cruise imagined he had a great deal of.Onto another topic, Cruise, seemingly inadvertently, leaks a video of him talking about his passion for Scientology.The video released on January 15, 2008, shows Cruise being interviewed, with the ironically background music from Mission Impossible playing in the background, denoting his action filled persona.4 FILM TRAILER ANALYSISIn this Chapter, I will analyse two separate films.The two films I am goin g to analyse are Top Gun and Vanilla Sky.The images above show two very juxtaposing films where, between a period of time, Cruise differentiates his genres in acting From action in Top Gun, to romance in Vanilla Sky.4.1 TOP GUNIn May 1986, Cruises big hit was released. Top Gun became the highest grossing film of the year, taking in $354 million in worldwide.Cruise plays the heroic marine pilot, a seemingly Perfect Fit role for him. Personally I believe this to be rationalised by his real life cocky mind-set.The TrailerThe trailer creates an atmosphere of fast beating action, shown by the quick-burst cuts/edits.The aspect of romance is partly shown in two parts. Firstly it is shown in the silhouette image of Cruise and his partner kissing, and again, where his partner his helping him to decide upon a perceptibly important decision. This portrays the soft, romantic side Cruise plays, to attract the female audience, whereas the action scenes entice the male audience. This was helped b y Cruises age making him an apt choice for the film.Finally, emphasis is displayed in the way of the trailer narrative to confirm that Cruise is the protagonist in the film.4.2 VANILLA SKY15 years later after the release of Top Gun, romantic thriller Vanilla Sky was released.The word Romantic instantly stands out compared to his preceding films, where his roles took on more action related parts, such as in the films Mission Impossible and War of the Worlds.The films itself is itself a remake of the 1997 movie Abre Los Ojos (Open Your Eyes).Now at the age of 39, the difference in genre seems suitable; to portray the maturity Cruise has developed over time.The TrailerImmediately, the audience will realise that, compared to most other films Cruise has appeared in, the genre in Vanilla Sky is far different.It has a far more relaxed and surreal aspect to it and as the trailer continues, the romantic side is introduced.A clever device the studio uses when creating the trailer is the prese nting of 6 separate words, which sum up the films true light. These words are as follows:1. Life2. Work3. Play4. Hate5. Death6. RealityLife describes the films as a whole, basically concentrating on the life of the role Cruise plays David Aames.Play, cleverly used as an innuendo, links in with the affair Cruise takes part in, and then associating cleverly with the words Hate, Death and finally Reality. The latter word is yet another reminder of the surrealism of the film.5 FINAL ANALYSISIn general, I believe Cruises career has been a path of ups and downs. His life outside movies brought controversy with his multiple marriages, and stories of his love for Scientology.As with most actors and actresses, he had a big break, for Cruise, being in 1986 in the film Top Gun. From then on his fame took a high, with several big hit films, starring him, being released. Over time however, his fame somewhat faltered and shrunk.The infamous Oprah scene brought about some of this disapproval in hi s self-publicity stunts.Overall, I think that Tom Cruise has led the usual Hollywood life of fame and fortune and some unfortunate events of which he will probably wish to forget.His acting brought his true fame from the start, and tradition was only to be carried on by his publicity stunts. Yet I believe there are still some uncovered truths about this iconic actor, yet to be discovered. Undoubtedly they will be one day.

Monday, November 4, 2019

Brand Media Strategy for Integrated munications Planning

Integrated marketing munication is important for irrespective of the kinds of panies such as small sized panies and the multinational panies. However, the mode of munication differs in some regards. This is because of the fact that every promotional mode does require high-end investments, which is not feasible to every organization. Another point is that different panies have different levels for the same promotional mode, which is mainly because of their global presence that pels them to approach the market differently. Irrespective of the kinds of the munication campaigns, all the panies have some similarities, which is the usability of some mon campaigning mediums such as traditional and non-traditional modes (Ang 2014). The chosen product for this assignment is â€Å"Samsung Galaxy S6†, which is set to be presented in this assignment as a product for undergoing the market munication planning. The reason to choose Samsung Galaxy S6 is the dominance of the previous offering of the same series. However, the overwhelming success, which the Samsung pany had ever fetched with the Galaxy S3, was never repeated. Some of the recent offerings of the series felt miserably in petition from some other petitors such as Sony and HTC. The recent offerings of the same series such as S4 and S5 could not sustain the same performance as done by the S3. This is because of the fact it b es important that the pany does overwhelming promotion of the product, so that, it catches the minds of users (Belch et al. 2014). The main purpose of this assignment is to analyze the existing market situation of galaxy S6. Moreover, this assignment is set to provide some effective medium of promotions to help the brand dominating and recapturing the minds of customers even more than before. After the launch of the product, it has already steered the market with a sheer selling of approximately around 55 millions of unit’s sales. During the first three month of the launch of the product, it has already boosted the market share of the pany; however, it is finding stiff petition from some other petitors such as Iphone6 and HTC. Samsung is facing a direct petition from the Apple’s Iphone6 in respect to the cost of the product. The pany has always performed exceptionally well on paper when it es to the power packed inbuilt features. However, it fell short of every Apple’s product of the same generation when it es to the overall performance of the product. This is one such reason, which has kept Samsung engaged for producing something bigger than before and outplays its biggest rival Apple’s Iphone. The parative study of Galaxy S6 does very well indicate towards a fact that the irrespective of the kinds of offerings of the product is unmatchable fr om other. However, rest depends on the actual market responses and the customer’s feedbacks. The market petition is fierce because of the fact that both the Samsung and Iphone do brig their flagship handsets every year on a regular basis. However, this is also an undeniable fact that the market share of Samsung Smartphones has witnessed a dip of 57% whereas Apple has witnessed a rise of approximately around 40% (Inquirer, 6, Latest, & read, 2017). The main objective behind integrated market munication is to grab a maximum awareness of customers. Moreover, these marketing munication modes have now b e widely used tools for the irrespective kinds of panies. Nevertheless, the quality of integrated marketing munication does produce a resonant effect on the market. This is done by means of several promotional modes, which are highly important for generating the spaces in the market. Nevertheless, the main objective behind the integrated marketing munication tool is to capitalize a pre-release dominance on the market and cash on the hyped curiosity. This is very effective in making huge unit sales in the initial few days after the venturing of the product (Blakeman 2014). Another objective behind the integrated munications modes is the enhancement of brand appeal, which helps in generating enough buzz in the market. This helps the brand in providing a stiff petition to the other petitors in the market. Samsung has the same objective with the Galaxy S6 as they want to capitalise the minds of consumers to give its product enough of spaces to fill this gap with some gigantic unit sales. The planning for the integrated marketing munication would be to pronounce the effect of the product by giving it some modification to receive the attention and support the brand with some good sales (Boone and Kurtz 2013). At present, the product is lagging behind to its biggest rival Iphone6 and Samsung is finding no solution to outclass the presence of Iphone in the market. This is indeed very difficult to re-establish the buzz among the customers about an existing product but this is how integrated marketing munication works. Integrated marketing munication is a good weapon for panies before the launch of the product; however, it continues to provide beneficial ou es to its inhibitors. The execution of integrated marketing munication is to support the launched product with some innovative ideas to support its growth before the ultimate fall in graph happens. Following are two most important objectives behind an Integrated Marketing munications (Lin 2012): The best way to conduct the planning of the integrated marketing munication would be to use the Percentage of Sales method, which is widely used across most of the big multinational panies. This method includes the usage of the percentage of the past sales, which is the generated revenue. However, it is entirely up to the pany that how they plan for the usage of percentage. They can take percentage from the profit generated by some other products or they can also take percentage of the past sales of the same product. Following are some of the considerations, which managers can make before making decisions on ways to take percentage from the generated past sales (Percy 2014): Following are some of the examples, which show the advantages of using the Percentage of Sales method for planning the budget for the integrated marketing munication (Rogala and Kaniewska-S?ba 2013): However, the method has some disadvantages as well, which are as follows (Schultz, Patti and Kitchen 2013): The chosen mode for the integrated marketing munication is the Advertising and the Public Relations. However, it is very important to appropriately allocate the budgeting to the different kinds of integrated marketing munication modes. The chosen method for the integrated marketing munication is the Percentage of Sales Method, which makes this important for the planning team that they allocate minimal budget to the advertisements. This is because of the fact that the proposed method for the integrated marketing munication is best productive with the lower expenditures on the advertisements costs. The advertisement itself contains several of domains, which needs the allocation of budget but to a minimal degree. The advertisement may include but not limited to the factors mentioned such as printing, direct mailing, broadcasting and outdoor expenses. The budget may include several factors such as media costs, ads creation costs and conducting research to evaluate the success of the plan ning. Some of the panies do often pay approximately 15% of the costs involved in the purchasing of media to the advertising agency; however, some pay a set free. Nevertheless, some might also plan the advertising internally by hiring some copywriters and graphic designers on a contractual basis. They can efficiently handle the advertisement works. Hiring graphic designers and copywriters on a contractual basis looks very preferable choices for the chosen method, as the chosen method does not allow any higher expenditure on the advertisements (Shimp and Andrews 2012). Allocation of budgeting in PR involves the expenditures on all the necessary ponents of the PR activities. It includes the relationship making with the member of media through different functionalities such as press releases, free samples and media days. Some PR may also include the running of promotion such as conduction of a cause-marketing campaign. Some other effective ways to generate PR is to donate some funding of the pany to some of the non-profit organizations in the name of charity works and sponsoring for different kinds of sports (Thorson and Moore 2013). To develop an integrated marketing munication for Samsung Galaxy S6, it is required to follow some necessary steps that are widely important for the program. Following are some of the steps; which can be used to develop the integrated marketing munications for Galaxy S6: There are different modes of marketing munications available; however, it is necessary to identify the best possible and feasible modes of marketing munications. Different kinds of marketing munications are such as advertising, social media and sales promotions. However, in the development of marketing munication for the galaxy S6, it is best feasible to stick to the two most widely used and effective tools such as advertising and PR for the marketing munication. The advertising mode is selected as it consumes less expenditures and best feasible to the Percentage Sales method of Budgeting. The advertising mode of munication is controllable and can be reduced to lower expenditures on hiring some copywriters and graphic designers on a contractual basis.  Ã‚   PR is another very important aspect in developing the marketing munication strategies for a product. This is nothing but a close interaction with the media personals. This is one of the easiest ways to interact with media and mu nicated indirectly to the targeted customers. This is also useful in promoting products in media shows, which is very useful for highlighting the newly added features in the existing product. This helps increase the curiosity level in customers to some extents as they are being promised to get more out of the box (Yeshin 2012). The development of advertising can be done by hiring some copywriters and graphic designers on a contractual basis. They are cost-effective, which is important, as the chosen method is Percentage of Sales method. Some of the panies do spend a lot of amount on the expenditures; however, to Samsung Galaxy S6, it is best suited to stick to the hiring of required personal. This is cost-effective as well as deeply controlled approach, which provides firm support to the development management team. The development of PR can be done by making some investments on scheduling some interactions with media personals. However, the interactions should be monitored at regular intervals to check the profitability of the implemented program. This is enormously important as the measurement saves from over budgeting and unnecessary expenditures (Percy 2014). This is very important as the campaigning of different programs and relevant expenditures would be only helpful if these stunts are relevant to the customer’s needs. This is also necessary in saving the over budgeting. The different kinds of integrated marketing munications do only provide some ways to interact with customers, it never guarantees of success, which entirely depend on the customer’s perceptions. This is why it is very important to know the requirements of customers to best utilize the different kinds of munication modes. For example, if customers are wanting something on the display part of the screen and the pany unanimously came to a conclusion without having any thorough research on the problem and presented some other new addition to the existing offerings. This would simply be wastage of money and constraints on the management team. The development program would also be affected. It would be a total loss of budgeting, physical labours and time (Lin 2 012). The implementation of the chosen modes of campaigning should be done in accordance to the actual requirement of the customers. The advertisement in particular needs to be attractive and full of useful messages conveying the flow of changes in the existing offerings. This is very important in saving the campaigning from any kinds of failure. The PR related activities does not need any charming presentation, as quality is more important than just the words. The interaction with the media personals would be to show the highly incremented gratitude to their requirements and the counter actions from the pany. The message needs to be clearly delivered at the time of interaction with the media personals (Percy 2014). The evaluation and monitoring of the proposed marketing munications is very important to help pany save from unnecessary expenditures and over budgeting. This is because of the fact that a continuous evaluation is mandate to bring the maximum profitability to the selected product by implementing chosen IMC. Following are some of the ways, which are extremely helpful in evaluating the ou e of the implemented IMC program (Young 2014): KPIs are extensively useful in measuring the ou e of the proposed campaigning for the enhancement of existing sales of the Galaxy S6. The evaluation can be made by measuring the success of both the program on a scoring scale to check the level of success such as customer feedbacks with numbers of positives or negatives responses and the publishing media news, which help check the reflection of campaign on the media personals Return on investments is another method to check the profitability of the campaigning as it is a long term evaluation method, which would give results only when the units sales of the product are increased The first point of r mendation is related to the pricing of the galaxy S6, which is very much manageable than incepting some new features in the product. This is probably has b e a popular trend among the different Smartphone panies. This help grab and turn the attention of customers into their favour. A high number of populations living in the world do prefer a reasonable pricing tagged to the top-end offerings. Samsung has also mitted the same thing but their price reduction is not that much low, which could pete with some other brands such as Lenovo. However, the highlighted problem was related to the severe petition with the Iphone6, which means that a price reduction would certainly influence and change the perceptions of a group of customers that has less priority to high-end pricing. However, it would not help pany in winning the hearts of premium customers, as they have more concerns for quality product and less regards to the pricing. Indeed, the quality of Galaxy S6 is not poor but it is not as good as Iphone6. Integrated marketing munication is helpful in making some useful revenues; however, it is only an alternate solution, which could enhance the profitability of a venture to some extent. Organizations need not depend entirely on the integrated marketing munication campaigning as the quality of the product matters the most. However, the importance of marketing munications can never be ignored as it adds some important values to the credibility of the products. Ang, L., 2014.  Principles of integrated marketing munications. Cambridge University Press. Belch, G.E., Belch, M.A., Kerr, G.F. and Powell, I., 2014.  Advertising: An integrated marketing munication perspective. McGraw-Hill Education. Blakeman, R., 2014.  Integrated marketing munication: creative strategy from idea to implementation. Rowman & Littlefield. Boone, L.E. and Kurtz, D.L., 2013.  Contemporary marketing. Cengage learning. Inquirer, T., 6, S., Latest, I., & read, M. 2017. Samsung sheds market share as the Galaxy S6 fails to challenge Apple's iPhone 6 | TheINQUIRER. https://www.theinquirer.net. Retrieved 1 May 2017, from https://www.theinquirer.net/inquirer/news/2422775/samsung-sheds-market-share-as-galaxy-s6-fails-to-challenge-the-iphone-6 Lin, T.L., 2012. The Sparks When Integrated Marketing munications Meets Word-of-Mouth Marketing and Experience Marketing.  New York Science Journal,  5(5), pp.70-85. Percy, L., 2014.  Strategic integrated marketing munications. Routledge. Rogala, A. and Kaniewska-S?ba, A., 2013. Internal munication as a marketing munications tool. In  13th International Marketing Trends Conference, pod red. Franà §oise CONCHON-Pary?: ESCP-AEP European School of Management. Schultz, D., Patti, C.H. and Kitchen, P.J., 2013.  The evolution of integrated marketing munications: The customer-driven marketplace. Routledge. Shimp, T.A. and Andrews, J.C., 2012.  Advertising promotion and other aspects of integrated marketing munications. Cengage Learning. Thorson, E. and Moore, J., 2013.  Integrated munication: Synergy of persuasive voices. Psychology Press. Yeshin, T., 2012.  Integrated marketing munications. Routledge. Young, A., 2014.  Brand media strategy: integrated munications planning in the digital era. Springer. With a decade's experience in providing essay help,

Saturday, November 2, 2019

Unit IV Assessment#2 Sick Building Syndrome Essay

Unit IV Assessment#2 Sick Building Syndrome - Essay Example The agents coagulate in the rooftops and walls and people end up inhaling the particles in them (Wargocki et al., 2000; pg. 72). The biological contaminants inhibit respiratory activities thus causing SBS. SBS has been associated with several symptoms. The major symptom is a feeling of acute discomfort that results from throat, nose, and eye irritation, headaches, sensitivity to stenches, dizziness, fatigue, dry and/or itchy skin, and inability to concentrate. The occupants also have trouble in breathing, an inordinate feeling of weariness and tiredness. These symptoms fluctuate from person to person depending on the degree of exposure to the contaminants and the type of SBS (whether type 1 or type 2) (Gurjar et al., 2010; pg. 121). Though the symptoms are increasingly becoming prevalent due to occupants spending most of their time indoors, no medication for SBS has been discovered. The long lasting solution to SBS is improving the building techniques to improve structures and make them less problematic (Wargocki et al., 2000; pg. 104). This is attained by ensuring that buildings are fitted with ventilators and chimneys that absorb the contaminants and allow inflow of fresh air. The number and efficiency of HVAC ventilations should be improved. However, the short term and immediate solution to SBS is leaving the building (Gurjar et al., 2010; pg. 120). Those affected by SBS report feeling better after leaving the building, to acquire fresh air. Gurjar,  B.  R., Molina,  L.  T., & Ojha,  C.  S. (2010).  Air pollution: Health and environmental impacts. Boca Raton, FL: CRC Press. Retrieved from

Thursday, October 31, 2019

Discussing Julianne Moore's and Dennis Haysbert role in the movie Far Research Paper

Discussing Julianne Moore's and Dennis Haysbert role in the movie Far from heaven. Which Frame of Reference is most applicable t - Research Paper Example This is, then, a positive model. Were not certain facts about black existence in America so true and persistent, this model should help all resolve all consciousness of the responsibility of African Americans as citizens of the United States. But African Americans still remain at the bottom poll receiving American resources. Under the current economic crisis, black employment remains among the highest, and black education scores are still the lowest in the nation. Such evidence demonstrates that either something is not working or things are being done. One other solution, that nothing can be done, will be developed in the conclusion. The other three frames are not so hopeful. To an extent at least they are realistic, accepting the reality if there has been any advance in racial relations in the United States, it has indeed been very slow. They accept the view that elementary sticklers of racism remain. There is no advance for the black poor and there is continual racism for those who have obtained middle-class. The Colonial Model reflects the views of such as Frantz Fanon by seeing African Americans as forming an internal colony inside America that is ruled by 'colonialist' Americans (Hansen).This view is plausible since it reflects the ideal that the basic position of African Americans has not changed. It has only changed to the extent that Fanon's solution, that of revolution, is no longer tenable (Quellel). Blacks have integrated too much in the American social and economic system to support any kind of revolution. However this brings up another factor that is not acknowledged in any of the frames and which should be there. This is that the black cultural experience in American has become necessary for the heart of the country. And it stands and continues to be one of the major percolators of that heart, just as the cultural styles of black Americans have always been replicated in some form or other worldwide. The Pluralist Melting Pot frame offers the best positive thrust of this factor, and oddly the other frames may allow it but only in a negative way. The Dominant-Subordinate Group Model stands on the principle that black inferiority has been capsulated to always exist and never be removed (Doane Jr.). Hence African Americans will always be in power struggle with the dominant position of whites. This frame helps bring realism to the fact that we have never solved the problem of black poverty nor of low black education results. The model accepts the position that there will always be conflict. But what contradicts this model, or what it stands forth to look at is the immediate future. The fact is that the United States is becoming more diversified and that other ethnic groups will also obtain positions of power. Individuals may become experts in certain fields and secondarily they are members of ethnic groups. The belief to hold is that the experts will, instead of being appreciated as members of 'ethnic groups', will become appreci ated as expert members of a diversified America. The Colonial and Dominant-Subordinate Group Models then are based on conflict and upholding racial differences. Harris's Alternative Formulation also has this kind of racial or ethnic conflict tied in. To the extent that

Tuesday, October 29, 2019

Buddhism Before 1850 Essay Example | Topics and Well Written Essays - 500 words

Buddhism Before 1850 - Essay Example The three major sects of Buddhism are the Mahayana, Theravada, and Vajrayana. A schism at the second Buddhist Council in 443-379 BCE, led to the formation of the Mahayana sect. In addition to the Tipitaka, this sect also gives importance to the sutras as a precept for life and is relatively liberal in its beliefs. Emphasis is given to Bodhisattvas or living saints. At the third Buddhist Council of 247 BCE, a second schism resulted in the Theravada sect in which the Tipitaka is the main scripture. According to this school, total renunciation is the way to salvation. The Vajrayana school developed from 320-100 and is characterized by the use of mantras – incantations, and tantras – mystic symbols. In addition to the three main schools of Buddhism, there are two other contemporary lines of belief in China and Japan: Pure Land, or Jodo and Ch’an or Zen (Tamney, â€Å"Buddhism†). Buddhism spread during the reign of Emperor Asoka in 247 BCE. Asoka sent emissarie s to Sri Lanka Burma, Afghanistan and even Egypt and Greece. 65 CE witnessed the entry of Buddhism into China and Thailand. Vietnam was entered in the second century, followed by Korea in 372, Nepal in the fourth century, Java, Sumatra and Borneo in the fifth century, Cambodia in the fifth century and Japan in 552 CE. Buddhism spread to Tibet in 641 CE. In all the countries of its adoption, Buddhism experienced its highs and lows due to repression and persecution by some rulers, and violent encounters with Islam.

Sunday, October 27, 2019

Basics of Topological Solutons

Basics of Topological Solutons Research into topological solitons began in the 1960s, when the fully nonlinear form of the classical field equations, were being thoroughly explored by mathematicians and theoretical physicists. Topological solitons were first examined when the solutions to these equations were interpreted as candidates for particles of the theory [1]. The particles that were observed from the results were different from the usual elementary particles. Topological solitons appeared to behave like normal particles in the sense that they were found to be localised and have finite energy [4]. However, the solitons topological structure distinguished them from the other particles. Topological solitons carry a topological charge (also known as the winding number), which results in these particlelike objects being stable. The topological charge is usually denoted by a single integer, N; it is a conserved quantity, i.e. it is constant unless a collision occurs, and it is equal to the total number of partic les, which means as |N| increases, the energy also increases. The conservation of the topological charge is due to the topological structure of the target space in which the soliton is defined. The most basic example of soliton has topological charge, N = 1, which is a stable solution, due to the fact a single soliton is unable to decay. 3 If the solution to a nonlinear classical field equation has the properties of being particle-like, stable, have finite mass; and the energy density is localised to a finite region of space, with a smooth structure; then this solution is a topological soliton. In addition to solitons existing with topological charge, N, there also exist antisolitons with -N. In the event of a collision between a soliton and an antisoliton, it is possible for them to annihilate each other or be pair-produced [1]. It is also possible for multi-soliton states to exist. Any field composition where N > 1, is known as a multi-soliton state. Likewise, multi-solitons also carry a topological charge which again means they are stable. Multi-state solitons either decay into N well separated charge 1 solitons or they can relax to a classical bound state of N solitons [1]. The energy and length scale [1] (a particular length which is determined to one order of magnitude.) the constant in the Lagrangian and field equations which represents the strength of the interaction between the particle and the field, also known as the coupling constant. The energy of a topological soliton is equal to its rest mass in a Lorentz invariant theory. [5] [6] Lorentz invariant: A quantity that does not change due to a transformation relating the space-time coordinates of one frame of reference to another in special relativity; a quantity that is independent of the inertial frame. In contrast to the topological soliton, the elementary particles mass is proportional to Plancks constant, ~. In the limit ~ à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ 0, the elementary particles mass goes to zero where as the topological solitons mass is finite. The quantization of the wave-like fields which satisfy the linearized field equations [1] determines the elementary particle states, where the interactions between the particles are determined by the nonlinear terms A fundamental discovery in supporting the research of topological solitons is that, given the coupling constants take special values, then the field equations can be reduced from second order to first order partial differential equations.[1] In general, the resulting first order equations are known as Bogomolny equations. These equations do not involve any time derivatives, and their solutions are either static soliton or multi-soliton configurations. [1] In these given field theories, if the field satisfies the Bogomolny equation then the energy is bounded below by a numerical multiple of the modulus of the topological charge, N, so the solutions of a Bogomolny equation with a certain 4 charge will all have the same energy value. [1] The solutions of the Bogomolny equations are automatically stable [1] because the fields minimize the energy [1]. As well as this they naturally satisfy the Euler-Lagrange equations of motion, which implies the static solutions are a stationary point of the energy. [1] Kinks are solutions to the first-order Bogomolny equation which we shall see in the following chapter Figure 2.2 shows a model of an infinite pendulum strip, with the angle à Ã¢â‚¬   being the angle to the downward vertical [3]. The energy (with all constraints set to 1) is E = Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾Ãƒâ€šÃ‚   1 2 à Ã¢â‚¬   02 + 1 à ¢Ã‹â€ Ã¢â‚¬â„¢ cos à Ã¢â‚¬  Ãƒâ€šÃ‚   dx (2.1) where à Ã¢â‚¬   0 = dà Ã¢â‚¬   dx . For the energy density to be finite this requires à Ã¢â‚¬   à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ 2à Ã¢â€š ¬nà ¢Ã‹â€ Ã¢â‚¬â„¢ as x à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ and à Ã¢â‚¬   à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ 2à Ã¢â€š ¬n+ as x à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã… ¾, where n ± à ¢Ã‹â€ Ã‹â€  Z. To find the number of twists, N, this is simply N = n+ à ¢Ã‹â€ Ã¢â‚¬â„¢ nà ¢Ã‹â€ Ã¢â‚¬â„¢ = à Ã¢â‚¬   (à ¢Ã‹â€ Ã… ¾) à ¢Ã‹â€ Ã¢â‚¬â„¢ à Ã¢â‚¬   (à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾) 2à Ã¢â€š ¬ = 1 2à Ã¢â€š ¬ Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ à Ã¢â‚¬   0 dx à ¢Ã‹â€ Ã‹â€  Z This is the equation for the topological charge or the winding number. If we set nà ¢Ã‹â€ Ã¢â‚¬â„¢ = 0 and n+ = 1 then N = 1, this gives the lowest possible energy for a topological soliton. This is called a kink, and it is the term we use for the one spatial dimension soliton with a single scalar field. The name kink is due to the shape of the scalar field when plotted as a function of x [1]. Knowing that a kink gives the minimum of the energy, it is possible to apply the calculus of variations to derive a differential equation à Ã¢â‚¬  (x) and then solve it[3] to give the shape of the kink. Given a differentiable function on the real line, f(x), it is possible to find the minimum of f(x) by finding the solutions of f 0 (x) = 0, i.e. by finding the stationary points of f(x) [3]. It is achievable to derive this differential equation, f(x), by making a small change to x, i.e. x à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ x + ÃŽÂ ´x, and from this calculate the change in the value of the function to lea ding order in the variaton ÃŽÂ ´x [3]. ÃŽÂ ´f(x) = f(x + ÃŽÂ ´x) à ¢Ã‹â€ Ã¢â‚¬â„¢ f(x) = f(x) + ÃŽÂ ´xf0 (x) + à ¢Ã‹â€ Ã¢â‚¬â„¢ f(x) = f 0 (x)ÃŽÂ ´x + If f 0 (x) 0. If f 0 (x) > 0 then we can make ÃŽÂ ´f(x) The term [à Ã¢â‚¬   0 ÃŽÂ ´Ãƒ Ã¢â‚¬  ] à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ equates to zero on the boundary because it must satisfy ÃŽÂ ´Ãƒ Ã¢â‚¬  ( ±Ãƒ ¢Ã‹â€ Ã… ¾) = 0 as we cannot change the boundary conditions, so ÃŽÂ ´E = Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ {(à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ Ã¢â‚¬   00 + sin à Ã¢â‚¬  )ÃŽÂ ´Ãƒ Ã¢â‚¬  } dx (2.6) This equation can be minimised minimised further to the second order nonlinear differential equation, à Ã¢â‚¬   00 = sin à Ã¢â‚¬   (2.7) The solution of this differential equation with the boundary conditions, à Ã¢â‚¬  (à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾) = 0 and à Ã¢â‚¬  (à ¢Ã‹â€ Ã… ¾) = 2à Ã¢â€š ¬ is the kink. Therefore the kink solution is, à Ã¢â‚¬  (x) = 4 tanà ¢Ã‹â€ Ã¢â‚¬â„¢1 e xà ¢Ã‹â€ Ã¢â‚¬â„¢a (2.8) where a is an arbitrary constant. When x = a, this is the position of the kink (à Ã¢â‚¬  (a) = à Ã¢â€š ¬). It is clear to see à Ã¢â‚¬   = 0 is also a solution to the differential equation , however, it does not satisfy the boundary conditions. It is possible to find a lower bound on the kink energy without solving a differential equation [3]. First of all we need to rewrite the energy equation (2.1), using the double angle formula the equation becomes, E = 1 2 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾Ãƒâ€šÃ‚   à Ã¢â‚¬   02 + 4 sin2   à Ã¢â‚¬   2   dx (2.9) By completing the square the equation becomes, E = 1 2 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾Ãƒâ€šÃ‚   à Ã¢â‚¬   0 à ¢Ã‹â€ Ã¢â‚¬â„¢ 2 sin   à Ã¢â‚¬   2 2 + 4à Ã¢â‚¬   0 sin   à Ã¢â‚¬   2 dx (2.10) Therefore the energy satisfies the inequality, E > 2 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ à Ã¢â‚¬   0 sin   à Ã¢â‚¬   2   dx = 2 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ sin   à Ã¢â‚¬   2   dà Ã¢â‚¬   dxdx = 2 Z 2à Ã¢â€š ¬ 0 sin   à Ã¢â‚¬   2   dà Ã¢â‚¬   = à ¢Ã‹â€ Ã¢â‚¬â„¢4   cos   à Ã¢â‚¬   2 2à Ã¢â€š ¬ 0 = 8 (2.11) In order to obtain the solution which is exactly 8, the term à Ã¢â‚¬   0 à ¢Ã‹â€ Ã¢â‚¬â„¢ 2 sin à Ã¢â‚¬   2 2 would have to be exactly 0. Therefore the lower bound on the kink energy is calculated by the solution to the equation, à Ã¢â‚¬   0 = 2 sin   à Ã¢â‚¬   2   (2.12) This is a first order Bogomolny equation. Taking this Bogomolny equation and differentiating with respect to à Ã¢â‚¬   0 gives, à Ã¢â‚¬   00 = cos   à Ã¢â‚¬   2   à Ã¢â‚¬   0 = cos   à Ã¢â‚¬   2   2 sin   à Ã¢â‚¬   2   = sin à Ã¢â‚¬   (2.13) This shows that a solution of the Bogomo lny equation (2.12) gives the output of the kink solution (2.7). To calculate the energy density ÃŽÂ µ, equation (2.1), we need to use the fact that the Bogomolny equation shows that ÃŽÂ µ = à Ã¢â‚¬   02 . From equation (2.8) we have, tan à Ã¢â‚¬   4   = e xà ¢Ã‹â€ Ã¢â‚¬â„¢a , therefore 1 4 à Ã¢â‚¬   0 sec2   à Ã¢â‚¬   4 = e xà ¢Ã‹â€ Ã¢â‚¬â„¢a This equation gives, à Ã¢â‚¬   0 = 4 e xà ¢Ã‹â€ Ã¢â‚¬â„¢a 1 + tan2 à Ã¢â‚¬   4   = 4e xà ¢Ã‹â€ Ã¢â‚¬â„¢a 1 + e 2(xà ¢Ã‹â€ Ã¢â‚¬â„¢a) = 2 cosh (x à ¢Ã‹â€ Ã¢â‚¬â„¢ a) = 2 (x à ¢Ã‹â€ Ã¢â‚¬â„¢ a) (2.15) Therefore it can be seen that the energy density is given by ÃŽÂ µ = 42 (x à ¢Ã‹â€ Ã¢â‚¬â„¢ a) From this we get the solution of a lump with a maximal value of 4 when x = a. This maximal value is the position of the kink. The position of the kink is also the position of the pendulum strip when it is exactly upside down, this is due to the fact à Ã¢â‚¬  (a) = à Ã¢â€š ¬ [3]. Using this interpretation for the energy density, it can be verified that the energy is equal to the lower bound E = Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ ÃŽÂ µdx = 4 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ 2 (x à ¢Ã‹â€ Ã¢â‚¬â„¢ a) dx = 4 [tanh (x à ¢Ã‹â€ Ã¢â‚¬â„¢ a)]à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ = 8 (2.16) For N > 1 i.e. more than one kink, E > 8|N|. In order t o obtain the lower bound of N > 1 kinks, the kinks must be infinitely apart to create N infinitely separated kinks. This means there must be a repulsive force between kinks. We shall now look at applying Derricks theorem [3] to kinks to show that it does not rule out the existence of topological solitons. Derricks Theorem: If the energy E has no stationary points with respect to spatial rescaling then it has no solutions with 0 Derricks theorem can only be applied to an infinite domain. Firstly, the energy terms need to be split according to the powers of the derivative, E = E2 + E0 = Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ 1 2 à Ã¢â‚¬   02 dx + Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ (1 à ¢Ã‹â€ Ã¢â‚¬â„¢ cos à Ã¢â‚¬  ) dx (2.17) Now consider the spatial rescaling x 7à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ x ÃŽÂ » = X, so that à Ã¢â‚¬   (x) 7à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ à Ã¢â‚¬   (X), with dx = ÃŽÂ »dX, d dx = 1 ÃŽÂ » d dX . Under this rescaling the energy becomes E (ÃŽÂ »), E(ÃŽÂ ») = Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ 1 2 ( 1 ÃŽÂ » dà Ã¢â‚¬   dX ) 2ÃŽÂ »dX + Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ (1 à ¢Ã‹â€ Ã¢â‚¬â„¢ cos à Ã¢â‚¬  ) ÃŽÂ »dX = 1 ÃŽÂ » E2 + ÃŽÂ »E0 (2.18) It is now important to see whether E(ÃŽÂ ») has a stationary point with respect to ÃŽÂ », dE (ÃŽÂ ») dÃŽÂ » = à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 ÃŽÂ » 2 E2 + E0 = 0 (2.19) if ÃŽÂ » = qE2 E0 , where ÃŽÂ » equals the size of the soliton. From this we can see a stationary point exists, so by Derricks theorem we cannot rule out the possibility of a topological soliton solution existing. We already know this is the case due to already finding the kink solution earlier. If it is found that à Ã¢â‚¬  (x) is a solution then the stationary point corresponds to no rescaling [3], so ÃŽÂ » = 1, meaning E2 = E0. This is known as a virial relation. In order to extend the kink example to higher spatial dimensions, we will rewrite it using different variables. If we let à Ã¢â‚¬   = (à Ã¢â‚¬  1, à Ã¢â‚¬  2) be a two-component unit vector, where à Ã¢â‚¬    · à Ã¢â‚¬   = |à Ã¢â‚¬  | 2 = 1. By writing à Ã¢â‚¬   = (sin à Ã¢â‚¬  , cos à Ã¢â‚¬  ), the energy from (2.1) can be rewritten as E = Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ ( 1 2  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   dà Ã¢â‚¬   dx  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   2 à ¢Ã‹â€ Ã¢â‚¬â„¢ H  · à Ã¢â‚¬   + |H| ) dx (2.20) where H = (0, 1). [3] In this new formulation à Ã¢â‚¬   represents the direction of the local magnetization (restricted to the plane) in a ferromagnetic medium [3] and H represents the constant background magnetic field which is also restricted to lie within the same plane as à Ã¢â‚¬  . There is only one point in which the systems ground state is equal to zero in terms of à Ã¢â‚¬  , which is à Ã¢â‚¬   = H |H| = (0, 1 ). Any structure with finite energy has to approach this zero energy ground state at spatial infinity, therefore the boundary conditions are à Ã¢â‚¬   à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ (0, 1) as x à ¢Ã¢â‚¬  Ã¢â‚¬â„¢  ±Ãƒ ¢Ã‹â€ Ã… ¾. As à Ã¢â‚¬   takes the same value at x = à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ and x = +à ¢Ã‹â€ Ã… ¾, then these points can be identified so the target space, which is the real line R, topologically becomes a circle, S 1 of infinite radius. Therefore we have the mapping à Ã¢â‚¬   : S 1 7à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ S 1 between circles, because à Ã¢â‚¬   is a two-component vector so it also lies on a circle of unit radius. [3] The mapping between circles has a topological charge (winding number), N, which counts the number of times à Ã¢â‚¬   winds around the unit circle as x varies over the whole real line. [3] The topological charge is equal to the equation defined earlier in (2.2), but using the new variables it is given by the expression N = 1 2à Ã¢â€š ¬ Z à ¢ 蠁 ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾Ãƒâ€šÃ‚   dà Ã¢â‚¬  1 dx à Ã¢â‚¬  2 à ¢Ã‹â€ Ã¢â‚¬â„¢ dà Ã¢â‚¬  2 dx à Ã¢â‚¬  1   dx (2.21) If we consider a restricted ferromagnetic system in which there is the absence of a background magnetic field (H = 0); it is still possible for a topological soliton to exist if there is an easy axis anisotropy. [3] Magnetic anisotropy is the directional dependence of a materials magnetic property, and the easy axis is a energetically favorable direction if spontaneous magnetization occurs.[7] The energy for this system is E = Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ ( 1 2  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   dà Ã¢â‚¬   dx  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   2 + A 1 à ¢Ã‹â€ Ã¢â‚¬â„¢ (à Ã¢â‚¬    · k) 2   ) dx (2.22) where A > 0 is the anisotropy constant and k is the unit vector which specifies the easy axis. [3] For this type of system there are two zero energy ground states, à Ã¢â‚¬   =  ±k. The kink in t his system, also called a domain wall, interpolates between the two zero energy ground states and has boundary conditions à Ã¢â‚¬   à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ k as x à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ and à Ã¢â‚¬   à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã¢â‚¬â„¢k 15 as x à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ +à ¢Ã‹â€ Ã… ¾. Therefore the domain wall does not have a full twist of a kink and only has a half-twist. It is possible to map this system to our original kink example by a change of variables. If we set k = (0, 1) for convenience, and choose A = 1 2 . Setting à Ã¢â‚¬   = sin à Ã¢â‚¬   2   , cos à Ã¢â‚¬   2 , then the energy equation becomes E = 1 4 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾Ãƒâ€šÃ‚   1 2 à Ã¢â‚¬   02 + 1 à ¢Ã‹â€ Ã¢â‚¬â„¢ cos à Ã¢â‚¬  Ãƒâ€šÃ‚   dx (2.23) which is equal to the energy equation (2.1) but with a normalization factor of 1 4 . The domain wall boundaries are à Ã¢â‚¬   à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ (0,  ±1) as x à ¢Ã‹â€ Ã¢â‚¬Å" à ¢Ã‹â€ Ã… ¾ are exactly the kink boundary conditions à Ã¢â‚¬   (à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾) = 0 and à Ã¢â‚¬   (à ¢Ã‹â€ Ã… ¾) = 2à Ã¢â€š ¬. [1] This chapter will focus on topological solitons in (2+1) spatial dimensions. It would be incorrect to use the term soliton for these solutions due to their lack of stability, instead they are often referred to as lumps. The solutions for these lumps are given explicitly by rational maps between Riemann spheres. [1] For this chapter we shall be looking at one of the simplest Lorentz invariant sigma models in (2+1) spatial dimensions which renders static topological soliton solutions; the O(3) sigma model in the plane. [1] A sigma model is a nonlinear scalar field theory, where the field takes values in a target space which is a curved Riemannian manifold, usually with large symmetry. [1] For the O(3) sigma model the target space is the unit 2-sphere, S 2 . This model uses three real scalar fields, ÃŽÂ ¦ = (à Ã¢â‚¬  1, à Ã¢â‚¬  2, à Ã¢â‚¬  3), which are functions of the space-time coordinates (t, x, y) in (2+1) spatial dimensions. [2] The O(3) model is defined by the Lagrangia n density L = 1 4 (à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒÅ½Ã‚ ¦)  · (à ¢Ã‹â€ Ã¢â‚¬Å¡  µÃƒÅ½Ã‚ ¦)  with the constraint ÃŽÂ ¦  · ÃŽÂ ¦ = 1. For this equation the indices represent the space-time coordinates and take the values 0, 1, 2, and à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µ is partial differentiation with respect to X µ . [2] From (3.1), the Euler-Lagrange equation can be derived, which is à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒ ¢Ã‹â€ Ã¢â‚¬Å¡  µÃƒÅ½Ã‚ ¦ + (à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒÅ½Ã‚ ¦  · à ¢Ã‹â€ Ã¢â‚¬Å¡  µÃƒÅ½Ã‚ ¦) ÃŽÂ ¦ = 0 (3.2) Due to the dot product in à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒÅ½Ã‚ ¦  · à ¢Ã‹â€ Ã¢â‚¬Å¡  µÃƒÅ½Ã‚ ¦, this shows that the Euclidean metric of R 3 is being used, and this becomes the standard metric on the target space S 2 when the constraint ÃŽÂ ¦  · ÃŽÂ ¦ = 1 is being imposed. [1] For the sigma model we are exploring, the O(3) represents the global symmetry in the target space corresponding to the rotation s: ÃŽÂ ¦ 7à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ MÃŽÂ ¦ Where M à ¢Ã‹â€ Ã‹â€  O(3) is a constant matrix. [1] The sigma in the models name represents the fields (à Ã¢â‚¬  1, à Ã¢â‚¬  2, à Ã†â€™), where à Ã¢â‚¬  1 and à Ã¢â‚¬  2 are locally unconstrained [1] and à Ã†â€™ = p 1 à ¢Ã‹â€ Ã¢â‚¬â„¢ à Ã¢â‚¬   2 1 à ¢Ã‹â€ Ã¢â‚¬â„¢ à Ã¢â‚¬   2 2 is dependent on à Ã¢â‚¬  1 and à Ã¢â‚¬  2. The energy for the O(3) sigma model is E = 1 4 Z à ¢Ã‹â€ Ã¢â‚¬Å¡iÃŽÂ ¦  · à ¢Ã‹â€ Ã¢â‚¬Å¡iÃŽÂ ¦d 2x (3.3) where i = 1, 2 runs over the spatial indices. In order for the energy to be finite, ÃŽÂ ¦ has to tend to a constant vector at spatial infinity, so without loss of generality we are able to set the boundary condition ÃŽÂ ¦ à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ (0, 0, 1) as x 2 + y 2 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã… ¾. Topologically we have R 2 à ¢Ã‹â€ Ã‚ ª {à ¢Ã‹â€ Ã… ¾}, which is interpreted as a sphere S 2 via the stereographic projection. (The sphere itself has finite radius.) Therefore we are considering mapping between spheres ÃŽÂ ¦ : S 2 7à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ S 2 . Just like in our kink example, mapping between spheres means there exists a topological charge, which can be found using N = 1 4à Ã¢â€š ¬ Z ÃŽÂ ¦  · (à ¢Ã‹â€ Ã¢â‚¬Å¡1ÃŽÂ ¦ ÃÆ'- à ¢Ã‹â€ Ã¢â‚¬Å¡2ÃŽÂ ¦) d 2x (3.4) The topological charge represents the number of lumps in the field configuration [1], since generally there are N well-separated, localized areas where the energy density is concentrated and each area has one unit of charge. However, as the lumps approach each other this is no longer the case. In order to apply Derricks theorem to the energy (3.3), we would need to consider the scaling x 7à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ x ÃŽÂ » = X and y 7à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ y ÃŽÂ » = Y which would give E (ÃŽÂ ») = E. The energy is independent of ÃŽÂ », therefore any value of ÃŽÂ » is a stationary point since the energy does not change from spatial rescaling. If we integrate the inequality  (à ¢Ã‹â€ Ã¢â‚¬Å¡iÃŽÂ ¦  ± ÃŽÂ µijÃŽÂ ¦ ÃÆ'- à ¢Ã‹â€ Ã¢â‚¬Å¡jÃŽÂ ¦)  · (à ¢Ã‹â€ Ã¢â‚¬Å¡iÃŽÂ ¦  ± ÃŽÂ µikÃŽÂ ¦ ÃÆ'- à ¢Ã‹â€ Ã¢â‚¬Å¡kÃŽÂ ¦) à ¢Ã¢â‚¬ °Ã‚ ¥ 0 (3.5) over the plane and use the equations (3.3) and (3.4) for the energy density and the topological charge respectively [1], then we get the Bogomolny bound E à ¢Ã¢â‚¬ °Ã‚ ¥ 2à Ã¢â€š ¬ |N| (3.6) This Bogomolny bound is the lower bound of the energy in terms of lumps. [1] If the field is a solution to one of the first-order Bogomolny equations à ¢Ã‹â€ Ã¢â‚¬Å¡iÃŽÂ ¦  ± ÃŽÂ µijÃŽÂ ¦ ÃÆ'- à ¢Ã‹â€ Ã¢â‚¬Å¡jÃŽÂ ¦ = 0 (3.7) then the energy is equal to the Bogomolny bound. In order to analyse the Bogomolny equations it is best to make the following changes of variables. For the first change in variable let X = (X1, X2, X3) denote the Cartesian coordinates in R 3 and take X = ÃŽÂ ¦ to be a point on the unit sphere, (X2 1 , X2 2 , X2 3 ) = 1. Let L be the line going through X = (0, 0, à ¢Ã‹â€ Ã¢â‚¬â„¢1) and ÃŽÂ ¦ and set W = X1 + iX2 to be the complex coordinate of the point where L intersects the plane at X3 = 0. We then get W = (à Ã¢â‚¬  1 + ià Ã¢â‚¬  2) (1 + à Ã¢â‚¬  3) (3.8) where à Ã¢â‚¬  1 =   W + W 1 + |W| 2   , à Ã¢â‚¬  2 = i   W à ¢Ã‹â€ Ã¢â‚¬â„¢ W 1 + |W| 2   , à Ã¢â‚¬  3 = 1 à ¢Ã‹â€ Ã¢â‚¬â„¢ |W| 2 1 + |W| 2 ! (3.9) As ÃŽÂ ¦ tends to the point (0, 0, à ¢Ã‹â€ Ã¢â‚¬â„¢1) then L only intersects X3 = 0 at à ¢Ã‹â€ Ã… ¾, therefore the point (0, 0, à ¢Ã‹â€ Ã¢â‚¬â„¢1) maps to the point W = à ¢Ã‹â€ Ã… ¾. This method of assigning each point on the sphere to a point in C à ¢Ã‹â€ Ã‚ ª {à ¢Ã‹â€ Ã… ¾} is called stereographic projection as seen in Figure 3.1.[3] The next change in variable comes from using a complex coordinate in the (x, y) plane by letting z = x + iy. Using this formation it is possible to rewrite the Lagrangian density, from (3.1) L = 1 4 ( à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒ Ã¢â‚¬  1) 2 + (à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒ Ã¢â‚¬  2) 2 + (à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒ Ã¢â‚¬  3) 2   . Firstly we need to partially differentiate à Ã¢â‚¬  1, à Ã¢â‚¬  2, à Ã¢â‚¬  3, giving à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒ Ã¢â‚¬  1 = à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW + à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW 1 + |W| 2 à ¢Ã‹â€ Ã¢â‚¬â„¢ (à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW) W + W à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW   1 + |W| 2 2 W + W   (3.10) à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒ Ã¢â‚¬  2 = i à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW à ¢Ã‹â€ Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW 1 + |W| 2 à ¢Ã‹â€ Ã¢â‚¬â„¢ (à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW) W + W à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW   1 + |W| 2 2 W à ¢Ã‹â€ Ã¢â‚¬â„¢ W Finally, from simplifying (3.37) we get the equation for the topological charge in the new formulation to be N = 1 4à Ã¢â€š ¬ Z 4 1 + |W| 2 2 à ¢Ã‹â€ Ã¢â‚¬Å¡zW à ¢Ã‹â€ Ã¢â‚¬Å¡zW à ¢Ã‹â€ Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã¢â‚¬Å¡zW à ¢Ã‹â€ Ã¢â‚¬Å¡zW   d 2x = 1 à Ã¢â€š ¬ Z |à ¢Ã‹â€ Ã¢â‚¬Å¡zW| 2 à ¢Ã‹â€ Ã¢â‚¬â„¢ |à ¢Ã‹â€ Ã¢â‚¬Å¡zW| 2   1 + |W| 2 2 d 2x (3.38) In this formulation it is clear to see E à ¢Ã¢â‚¬ °Ã‚ ¥ 2à Ã¢â€š ¬ |N|, with equality if and only if Bogomolny equation is satisfied à ¢Ã‹â€ Ã¢â‚¬Å¡W à ¢Ã‹â€ Ã¢â‚¬Å¡z = 0 (3.39) This equation shows that W is a holomorphic function of z only. [4] Due to the requirement that the total energy is finite, together with the boundary condition [4] W à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ 0 as |z| à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã… ¾, this means that N is finite. [3] The simplest solution for the Bogomolny equation would be W = ÃŽÂ » z , where ÃŽÂ » is a real and positive constant. Applying this to the equation (3.9) yields the solution for t he N = 1 solution ÃŽÂ ¦ =   2 ÃŽÂ » 2 + x 2 + y 2 , à ¢Ã‹â€ Ã¢â‚¬â„¢2 ÃŽÂ » 2 + x 2 + y 2 , x 2 + y 2 à ¢Ã‹â€ Ã¢â‚¬â„¢ ÃŽÂ » 2 ÃŽÂ » 2 + x 2 + y 2 (3.40) If we change the negative sign in the second component to a positive sign then we get the solution of the anti-Bogomolny equation (3.7) (with the minus sign), which also has E = 2à Ã¢â€š ¬ but has N = à ¢Ã‹â€ Ã¢â‚¬â„¢1. This soliton is located at thee origin because W(0) = à ¢Ã‹â€ Ã… ¾. [3] The N = 1 general solution has 4 real parameters and is given by the Bogomolny solution W = ÃŽÂ »eiÃŽÂ ¸ z à ¢Ã‹â€ Ã¢â‚¬â„¢ a (3.41) where ÃŽÂ » is the size of the soliton, ÃŽÂ ¸ is the constant angle of rotation in the (à Ã¢â‚¬  1, à Ã¢â‚¬  2) plane and a à ¢Ã‹â€ Ã‹â€  C is the position of the soliton in the complex plane, z = x + iy. The O(3) sigma model can be modified to stabilise a lump, and the simplest way in doing this is by introducing extra terms into the Lagrangian which break the conformal invariance of the static energy. [1] These new terms must scale as negative and positive powers of a spatial dilation factor. [1] An example of this is the Baby Skyrme model which is given by the Lagrangian L = 1 4 à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒÅ½Ã‚ ¦  · à ¢Ã‹â€ Ã¢â‚¬Å¡  µÃƒÅ½Ã‚ ¦ à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 8 (à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒÅ½Ã‚ ¦ ÃÆ'- à ¢Ã‹â€ Ã¢â‚¬Å¡ÃƒÅ½Ã‚ ½ÃƒÅ½Ã‚ ¦)  · (à ¢Ã‹â€ Ã¢â‚¬Å¡  µÃƒÅ½Ã‚ ¦ ÃÆ'- à ¢Ã‹â€ Ã¢â‚¬Å¡ ÃŽÂ ½ÃƒÅ½Ã‚ ¦) à ¢Ã‹â€ Ã¢â‚¬â„¢ m2 2 (1 à ¢Ã‹â€ Ã¢â‚¬â„¢ à Ã¢â‚¬  3) (3.42) where the constraint ÃŽÂ ¦  · ÃŽÂ ¦ = 1 is implied. As we can see the first term in this Lagrangian is simply that of the O(3) sigma model. The second term in (3.42), is known as the Skyrme term and the final term in this Lagrangian is the mass term. The complete understanding of topological solitons is unknown and there are very limited experimental tests of many of the theories of topological solitons and their mathematical results. However, there is evidence of topological solitons existing in some physical systems, for example in one-dimensional systems they exist in optical fibres and narrow water channels. [1] Topological solitons can be applied to a range of different areas including particle physics, condensed matter physics, nuclear physics and cosmology. They also can be applied within technology, which involves using topological solitons in the design for the next generation of data storage devices. [3] In August 2016, a 7 million pound research programme, being led by Durham University, was announced into looking at how magnetic skyrmions can be used in creating efficient ways to store data. [10] Magnetic skyrmions are a theoretical particle in three spatial dimensions which have been observed experimentally in condensed matter systems. [11] This type of soliton was first predicted by scientists back in 1962, but was first observed experimentally in 2009. [10] In certain types of magnetic material it is possible for these magnetic skyrmions to be created,manipulated and controlled[10], and because of their size and structure it is possible for them to be tightly packed together. The structure inside the skyrmions [10] Due to this and the force which locks the magnetic field into the skyrmion arrangement, any magnetic information which is encoded by skyrmions is very robust. [10] It is thought that it will be possible to move these magnetic skyrmions with a lot less energy than the ferromagnetic domain being used in current data storage devices of smartphones and computers. Therefore, these magnetic skyrmions could revolutionise data storage devices, as the devices could be created on a smaller scale and use a lot less energy, meaning they would be more cost effective and would generate less heat. This project has given an insight into the very basics of topological solutons by analysing the energy and topological charge equations for kinks in one spatial dimension and lumps in (2+1) spatial dimensions. From the energy equation for a kink, we could derive the solution of a kink and find the lower energy bound. From the lump model, we successfully changed the variables for the energy, topological charge and the Lagrange equation for a lump to be able to analyse the Bogomolny equation. From this change of variables of the Lagrange equation we successfully solved the Euler-Lagrange equations of motion for the lump model. This research project has been captivating and has given me an insight into how the complex mathematics we learn is applied to real world situations. I first became interested in this topic after attending the London Mathematical Societys summer 33 school in 2016, where I had the privilege of attending a few lectures given by Dr Paul Sutcliffe, one of the authors of the book on Topological Solitons. It was in these few lectures where I first learnt about topological solitons and some of their applications, and this inspired me for my research project as I wanted to study the topic further. Although this project has been thoroughly enjoyable, it came with challenging aspects, due to its complex mathematics in such a specialised subject. As a result of this topic being so specific, I was very limited in the resources I had for my research, my main resource being the book on topological solitons by Dr Paul Sutcliffe and Dr Nicholas Manton. I have gained a lot of new skills from this research project and it has given me an opportunity to apply my current mathematical knowledge. There is an endless amount of research that can be continued within this subject. I, for example, would have liked to do some further research into the (2+1) spatial dimension model of the Baby Skyrmion and, like the lump example, solve the EulerLagrange equations motion . As well as this, I would have liked to input the equations of motion I solved for the lump model in Maple, so it was possible to simulate two lumps colliding and from this graph the energy density. It would have been really interesting to research further into topological solitons in three spatial dimensions, specifically Skyrmions, to learn further about their technological applications. However, the mathematics used for this model is very challenging and specialised, and goes beyond my understanding and knowledge.