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‚¬ ’ 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 †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€ ’à ¢Ã‹â€ Ã… ¾Ãƒâ€šÃ‚ 1 2 à †02 + 1 à ¢Ã‹â€ ’ cos à †Â dx (2.1) where à †0 = dà †dx . For the energy density to be finite this requires à †à ¢Ã¢â‚¬ ’ 2à ₠¬nà ¢Ã‹â€ ’ as x à ¢Ã¢â‚¬ ’ à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾ and à †à ¢Ã¢â‚¬ ’ 2à ₠¬n+ as x à ¢Ã¢â‚¬ ’ à ¢Ã‹â€ Ã… ¾, where n ± à ¢Ã‹â€ ˆZ. To find the number of twists, N, this is simply N = n+ à ¢Ã‹â€ ’ nà ¢Ã‹â€ ’ = à †(à ¢Ã‹â€ Ã… ¾) à ¢Ã‹â€ ’ à †(à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾) 2à ₠¬ = 1 2à ₠¬ Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾ à †0 dx à ¢Ã‹â€ ˆZ This is the equation for the topological charge or the winding number. If we set nà ¢Ã‹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 †(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‚¬ ’ 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€ ’ f(x) = f(x) + ÃŽÂ ´xf0 (x) + à ¢Ã‹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 †0 ÃŽÂ ´Ãƒ †] à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾ equates to zero on the boundary because it must satisfy ÃŽÂ ´Ãƒ †( ±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€ ’à ¢Ã‹â€ Ã… ¾ {(à ¢Ã‹â€ ’à †00 + sin à †)ÃŽÂ ´Ãƒ †} dx (2.6) This equation can be minimised minimised further to the second order nonlinear differential equation, à †00 = sin à †(2.7) The solution of this differential equation with the boundary conditions, à †(à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾) = 0 and à †(à ¢Ã‹â€ Ã… ¾) = 2à ₠¬ is the kink. Therefore the kink solution is, à †(x) = 4 tanà ¢Ã‹â€ ’1 e xà ¢Ã‹â€ ’a (2.8) where a is an arbitrary constant. When x = a, this is the position of the kink (à †(a) = à ₠¬). It is clear to see à †= 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€ ’à ¢Ã‹â€ Ã… ¾Ãƒâ€šÃ‚ à †02 + 4 sin2Â à †2 dx (2.9) By completing the square the equation becomes, E = 1 2 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾Ãƒâ€šÃ‚ à †0 à ¢Ã‹â€ ’ 2 sinÂ à †2 2 + 4à †0 sinÂ à †2 dx (2.10) Therefore the energy satisfies the inequality, E > 2 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾ à †0 sinÂ à †2 dx = 2 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾ sinÂ à †2 dà †dxdx = 2 Z 2à ₠¬ 0 sinÂ à †2 dà †= à ¢Ã‹â€ ’4 cosÂ à †2 2à ₠¬ 0 = 8 (2.11) In order to obtain the solution which is exactly 8, the term à †0 à ¢Ã‹â€ ’ 2 sin à †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 †0 = 2 sinÂ à †2 (2.12) This is a first order Bogomolny equation. Taking this Bogomolny equation and differentiating with respect to à †0 gives, à †00 = cosÂ à †2Â à †0 = cosÂ à †2 2 sinÂ à †2 = sin à †(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 †02 . From equation (2.8) we have, tan à †4 = e xà ¢Ã‹â€ ’a , therefore 1 4 à †0 sec2Â à †4 = e xà ¢Ã‹â€ ’a This equation gives, à †0 = 4 e xà ¢Ã‹â€ ’a 1 + tan2 à †4 = 4e xà ¢Ã‹â€ ’a 1 + e 2(xà ¢Ã‹â€ ’a) = 2 cosh (x à ¢Ã‹â€ ’ a) = 2 (x à ¢Ã‹â€ ’ a) (2.15) Therefore it can be seen that the energy density is given by ÃŽÂ µ = 42 (x à ¢Ã‹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 †(a) = à ₠¬ [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€ ’à ¢Ã‹â€ Ã… ¾ ÃŽÂ µdx = 4 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾ 2 (x à ¢Ã‹â€ ’ a) dx = 4 [tanh (x à ¢Ã‹â€ ’ a)]à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ ’à ¢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€ ’à ¢Ã‹â€ Ã… ¾ 1 2 à †02 dx + Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾ (1 à ¢Ã‹â€ ’ cos à †) dx (2.17) Now consider the spatial rescaling x 7à ¢Ã¢â‚¬ ’ x ÃŽÂ » = X, so that à †(x) 7à ¢Ã¢â‚¬ ’ à †(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€ ’à ¢Ã‹â€ Ã… ¾ 1 2 ( 1 ÃŽÂ » dà †dX ) 2ÃŽÂ »dX + Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾ (1 à ¢Ã‹â€ ’ cos à †) 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€ ’ 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 †(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 †= (à †1, à †2) be a two-component unit vector, where à †Â · à †= |à †| 2 = 1. By writing à †= (sin à †, cos à †), the energy from (2.1) can be rewritten as E = Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾ ( 1 2    dà †dx    2 à ¢Ã‹â€ ’ H  · à †+ |H| ) dx (2.20) where H = (0, 1). [3] In this new formulation à †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 †. There is only one point in which the systems ground state is equal to zero in terms of à †, which is à †= 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 †à ¢Ã¢â‚¬ ’ (0, 1) as x à ¢Ã¢â‚¬ ’  ±Ãƒ ¢Ã‹â€ Ã… ¾. As à †takes the same value at x = à ¢Ã‹â€ ’à ¢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 †: S 1 7à ¢Ã¢â‚¬ ’ S 1 between circles, because à †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 †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 ₠¬ Z à ¢ 蠁 ¾ à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾Ãƒâ€šÃ‚ dà †1 dx à †2 à ¢Ã‹â€ ’ dà †2 dx à †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€ ’à ¢Ã‹â€ Ã… ¾ ( 1 2    dà †dx    2 + A 1 à ¢Ã‹â€ ’ (à †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 †=  ±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 †à ¢Ã¢â‚¬ ’ k as x à ¢Ã¢â‚¬ ’ à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾ and à †à ¢Ã¢â‚¬ ’ à ¢Ã‹â€ ’k 15 as x à ¢Ã¢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 †= sin à †2 , cos à †2 , then the energy equation becomes E = 1 4 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾Ãƒâ€šÃ‚ 1 2 à †02 + 1 à ¢Ã‹â€ ’ cos à †Â 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 †à ¢Ã¢â‚¬ ’ (0,  ±1) as x à ¢Ã‹â€ â€Å" à ¢Ã‹â€ Ã… ¾ are exactly the kink boundary conditions à †(à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¾) = 0 and à †(à ¢Ã‹â€ Ã… ¾) = 2à ₠¬. [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 †1, à †2, à †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€ ‚ µÃƒÅ½Ã‚ ¦)  · (à ¢Ã‹â€ ‚  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€ ‚ 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€ ‚ µÃƒ ¢Ã‹â€ ‚  µÃƒÅ½Ã‚ ¦ + (à ¢Ã‹â€ ‚ µÃƒÅ½Ã‚ ¦  · à ¢Ã‹â€ ‚  µÃƒÅ½Ã‚ ¦) ÃŽÂ ¦ = 0 (3.2) Due to the dot product in à ¢Ã‹â€ ‚ µÃƒÅ½Ã‚ ¦  · à ¢Ã‹â€ ‚  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‚¬ ’ MÃŽÂ ¦ Where M à ¢Ã‹â€ ˆO(3) is a constant matrix. [1] The sigma in the models name represents the fields (à †1, à †2, à ƒ), where à †1 and à †2 are locally unconstrained [1] and à ƒ = p 1 à ¢Ã‹â€ ’ à †2 1 à ¢Ã‹â€ ’ à †2 2 is dependent on à †1 and à †2. The energy for the O(3) sigma model is E = 1 4 Z à ¢Ã‹â€ ‚iÃŽÂ ¦  · à ¢Ã‹â€ ‚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‚¬ ’ (0, 0, 1) as x 2 + y 2 à ¢Ã¢â‚¬ ’ à ¢Ã‹â€ Ã… ¾. Topologically we have R 2 à ¢Ã‹â€  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‚¬ ’ 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 ₠¬ Z ÃŽÂ ¦  · (à ¢Ã‹â€ ‚1ÃŽÂ ¦ ÃÆ'- à ¢Ã‹â€ ‚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‚¬ ’ x ÃŽÂ » = X and y 7à ¢Ã¢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€ ‚iÃŽÂ ¦  ± ÃŽÂ µijÃŽÂ ¦ ÃÆ'- à ¢Ã‹â€ ‚jÃŽÂ ¦)  · (à ¢Ã‹â€ ‚iÃŽÂ ¦  ± ÃŽÂ µikÃŽÂ ¦ ÃÆ'- à ¢Ã‹â€ ‚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 ₠¬ |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€ ‚iÃŽÂ ¦  ± ÃŽÂ µijÃŽÂ ¦ ÃÆ'- à ¢Ã‹â€ ‚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€ ’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 †1 + ià †2) (1 + à †3) (3.8) where à †1 = W + W 1 + |W| 2 , à †2 = i W à ¢Ã‹â€ ’ W 1 + |W| 2 , à †3 = 1 à ¢Ã‹â€ ’ |W| 2 1 + |W| 2 ! (3.9) As ÃŽÂ ¦ tends to the point (0, 0, à ¢Ã‹â€ ’1) then L only intersects X3 = 0 at à ¢Ã‹â€ Ã… ¾, therefore the point (0, 0, à ¢Ã‹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€  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€ ‚ µÃƒ †1) 2 + (à ¢Ã‹â€ ‚ µÃƒ †2) 2 + (à ¢Ã‹â€ ‚ µÃƒ †3) 2 . Firstly we need to partially differentiate à †1, à †2, à †3, giving à ¢Ã‹â€ ‚ µÃƒ †1 = à ¢Ã‹â€ ‚ µW + à ¢Ã‹â€ ‚ µW 1 + |W| 2 à ¢Ã‹â€ ’ (à ¢Ã‹â€ ‚ µW) W + W à ¢Ã‹â€ ‚ µW 1 + |W| 2 2 W + W (3.10) à ¢Ã‹â€ ‚ µÃƒ †2 = i à ¢Ã‹â€ ‚ µW à ¢Ã‹â€ ’ à ¢Ã‹â€ ‚ µW 1 + |W| 2 à ¢Ã‹â€ ’ (à ¢Ã‹â€ ‚ µW) W + W à ¢Ã‹â€ ‚ µW 1 + |W| 2 2 W à ¢Ã‹â€ ’ W Finally, from simplifying (3.37) we get the equation for the topological charge in the new formulation to be N = 1 4à ₠¬ Z 4 1 + |W| 2 2 à ¢Ã‹â€ ‚zW à ¢Ã‹â€ ‚zW à ¢Ã‹â€ ’ à ¢Ã‹â€ ‚zW à ¢Ã‹â€ ‚zW d 2x = 1 à ₠¬ Z |à ¢Ã‹â€ ‚zW| 2 à ¢Ã‹â€ ’ |à ¢Ã‹â€ ‚zW| 2 1 + |W| 2 2 d 2x (3.38) In this formulation it is clear to see E à ¢Ã¢â‚¬ °Ã‚ ¥ 2à ₠¬ |N|, with equality if and only if Bogomolny equation is satisfied à ¢Ã‹â€ ‚W à ¢Ã‹â€ ‚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‚¬ ’ 0 as |z| à ¢Ã¢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€ ’2 ÃŽÂ » 2 + x 2 + y 2 , x 2 + y 2 à ¢Ã‹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 ₠¬ but has N = à ¢Ã‹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€ ’ a (3.41) where ÃŽÂ » is the size of the soliton, ÃŽÂ ¸ is the constant angle of rotation in the (à †1, à †2) plane and a à ¢Ã‹â€ ˆC 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€ ‚ µÃƒÅ½Ã‚ ¦  · à ¢Ã‹â€ ‚  µÃƒÅ½Ã‚ ¦ à ¢Ã‹â€ ’ 1 8 (à ¢Ã‹â€ ‚ µÃƒÅ½Ã‚ ¦ ÃÆ'- à ¢Ã‹â€ ‚Π½ÃƒÅ½Ã‚ ¦)  · (à ¢Ã‹â€ ‚  µÃƒÅ½Ã‚ ¦ ÃÆ'- à ¢Ã‹â€ ‚ ÃŽÂ ½ÃƒÅ½Ã‚ ¦) à ¢Ã‹â€ ’ m2 2 (1 à ¢Ã‹â€ ’ à †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.
Friday, October 25, 2019
Clifford Olson: Canadian Serial Killer Essay -- Biography Biographies
Clifford Olson: Canadian Serial Killer Clifford Olson is one of Canada's well known serial killers. He showed no sign of sympathy for the public all throughout his life and would eventually end up killing many innocent people and spending a good portion of his life in jail. Clifford Olson was born on January 1st 1940, in Vancouver, British Columbia. While he was growing up he was always in trouble. Even as a child in school her was referred to as a bully and not a nice kid. Then as he grew up things didn't change for the better the just got worse. As a teenager and young adult Olson found himself in trouble with the law quite frequently. From the year of 1951 to 1981 ( ages 17-21) he had 94 arrests. He was put in jail for some of them and served time for cries ranging from fraud to armed robbery. While in prison Olson was known for two things. One was for being a homosexual rapist and the second was for being a snitch, and helping out the police. Olson helped the police by getting his friend named Garry Marcoux (also in jail), to give a detailed description and confession to raping and mutilating a nine year old girl. Somehow Olson was able to get Marcoux to write down his confession. Olson them gave this to police and it was used to convict Marcoux of that crime. Once Olson had served his time and was released he went to live with the mother of is son. One would have thought that he had learned his lesson and would try to turn his life around. However very unfortunately that was not the case. In November of 1980 A young girl, 12 years old, named Christine Weller went missing. She would later prove to be one of Olson's first murder victims. Christine was abducted from her home in Surrey, BC. Her mutilated body ... ...ack of his van, police found an address book containing the name of Judy Kozma. Along with this and other evidence the police were able to charge Clifford Olson with the murder of Judy Kozma 6 days later. Olson knew that he was going to be put back in jail and was suspected on some of the other murders that he had committed.. So Olson made a deal with the prosecution. In his deal Olson' s family, (wife and son) were to be paid $10,000 for each of his victims. This was very controversial. In exchange Olson would provide the information on the known murders and gave the police direction to 6 outstanding bodies. Olson kept his part of the deal and so did the prosecution. The money was paid to Olson's family on schedule. On January 11th 1982, Clifford Olson pleaded guilty to 11 counts of murder. For this he was sentenced to 11 concurrent life terms in prison.
Thursday, October 24, 2019
School Locker Search Persuasive Essay
School Locker Searches: Protecting Your Children â€Å"The National School Board estimates that more than 135,000 guns are brought to school each day†(Debate). Besides weapons, drugs like marijuana are reportedly used by up to 22. 6 percent of 12th graders (Drugabuse). With rising danger in schools, locker searches seem like the right thing to do. A locker is owned by the school and loaned to the student, therefore entry is always legal. With this legal authority, schools should flex their rights and protect their students. With rising crime rates and high-profile shootings, firearms are often stored in the schools’ lockers.If these are searched daily or even weekly, students would be in a much less dangerous setting. Finally, frisks can stop some of the biggest issues in school: drug dealing. A simple run-through can remove some of the most dangerous substances in school  In short, locker searches prove to be legal, cause a safer-feeling environment, and prevent cr imes. First off, lockers are school property, and therefore subject to any search. Although students are protected by the fourth amendment, lockers do not have to follow this guideline (Nytimes).This reasoning has been tested in numerous court cases, namely in the Supreme Court’s decision of New Jersey v TLO (Nytimes). In this ruling, a it was stated that School officials do not have to follow the strict Fourth Amendment guidelines in school. Furthermore, lockers must also be maintained. This means that they require entrance for regular maintenance and custodial problems, like rotting food. If this isn’t done, health hazards could be a massive problem for students in the building. Finally, in every Lakeville South handbook, students agree to locker searches when they start school.It is written that locker searches will be conducted at random. This gives a very civil warning for the students. For these reasons, locker searches are not only legal, but fair. Next, locker frisks can provide a peace of mind for individuals in the building. According to one New York Newspaper, 200 students were evacuated after a shooting threat was found in the women’s bathroom (Smithtown). Acts like this terrorize students, and disrupt the daily learning. Martha Kaufeldt, an established author and educator states, â€Å"The brain gives priority to processing incoming data that poses threat to survival. (Dialogueonlearning) This means that in threatening habitats, students will perform worse than average. To combat this issue, locker searches could help provide a feeling of safety, thus allowing students to fully apply themselves to school. Simply put, locker searches will create a safe and enjoyable atmosphere. Lastly, schools must protect against the use of lockers in serious crimes. In January 1999, a bomb explosion in a Kansas High School locker sent 11 students to the hospital (Schoolsecurity).If a search had discovered the bomb, students could have been e vacuated to a safe area and protected from the blast. Adding to the issue, a half pound of marijuana was found in a 13 year old’s locker (Thenewsdispatch). He later confessed to police that he intended to sell the drug. In both these cases, the school became a dangerous environment and disrupted daily learning. Had the school regularly frisked lockers, students could be confiscated of dangerous materials or even discouraged from bringing them in the first place. Actions like this can increase safety and student involvement in class.In short, locker checks create a safer, more efficient environment for everyone in school. All in all, there is no reason a school shouldn’t search lockers. As its property, an institution can search anything it owns, without a reason. While removings drugs and firearms, these searches protect students and faculty alike, creating a safe and efficient workplace. Finally, locker frisks will promote a safer feeling environment, preventing unnec essary absences by students. With the dangerous crime rates, it only endangers students to skip much-needed locker frisks.
Wednesday, October 23, 2019
A Portrait of the City of Mumbai
City that never sleeps. Iambi, capital of Maharajah's and financial capital of India, home to Plywood film industry and home to people from all over the country. The local language spoken here is Amaranth but English and Hindi are also spoken fluently. So a new visitor will not have much trouble.Temperature varies throughout he year. March- June is summer months with temperature reaching almost degree . June- October monsoon season with rain in full force. November to February is mainly winter months but being a coastal city the winters are mild here and pleasant weather. The Places to see here are the : colonial architecture from the Victorian times , the Gateway of India, the Cathartic Shiva Terminus building, the Hajji all mosque , film city . The famous Tag Mall hotel is located Just opposite the Gateway of India.The Iambi University buildings and the High Court are also excellent examples of colonial architecture in the city. Nehru science center and Nehru planetarium are very g ood place to visit as they have museum and planetary views shown at both centers Iambi has a few beaches, at Juju, Psychopath, Marvel. In addition to this, Iambi is also known for its own lip-smacking pap abaci, belle purr and kebabs. Iambi is a shopper's delight with bargain buys, exclusive boutiques, ethnic markets and mini bazaars.The Iambi city also has a flourishing cultural life. Being the seat of the Indian (Hindi) film industry, Iambi stages regular performances in music, dance and drama. The Hindi film industry, also known as Plywood, produces the largest number of films in the world. Iambi caters to the needs of almost all sections through sporting activities, nightclubs, pubs, theaters, beaches, shopping Malls and restaurants. Old and new, rich and poor, classical and modern- Iambi is truly a melting pot! A Portrait of the City of Iambi By Misunderstanding
Tuesday, October 22, 2019
Free Essays on Internet Censorship
Internet Censorship The debate over whether the government should censor the Internet is intense. In 1995 the senate passed the Communications Decency Act written by Senator Jim Exon. The act â€Å"outlaws ‘obscene, lewd, lascivious, filthy or indecent’ communications on the Internet,†(Exon 130). Americans on both sides of the issue are asking some very pertinent, yet difficult to answer, questions. Does censorship of the Internet violate our First Amendment rights? Is regulation of the Internet even possible? Will censoring the Internet protect children from inappropriate material or will it hinder those searching for legitimate information? As a mother, I am concerned about my child having access to pornographic or otherwise inappropriate material on the Internet. However, my personal belief is that it is impossible to regulate the Internet without infringing on the liberties of the First Amendment. Simply put: one person’s definition of inappropriate or pornographic material may be totally different from another’s. It must be made clear that although I am neither totally for nor against censorship, I do not wish to have a limit set on what I can and cannot access determined by someone else’s values. Those who support censorship of Internet materials feel that applying obscenity laws to the internet will protect children from pornography without â€Å"significantly†infringing upon our First Amendment rights (Exon 125). Supporters of this view argue that we live with restrictions on our freedom of speech everyday, such as: libel laws and laws against false advertising. These people submit that the â€Å"anti-pornography laws that exist for U.S. mail, broadcast and telephone communications,†should also apply to computers (Exon 126). These people suggest the use of blocking software in libraries and support the required use of â€Å"a verified credit card, debit account, adult access code or personal identification number... Free Essays on Internet Censorship Free Essays on Internet Censorship Thesis: Government Censorship would damage the atmosphere of the freedom to express ideas on the Internet; therefore, government should not encourage censorship. Introduction I. In the Internet community, there is a large volume of technical terms. For this reason, it is first necessary to examine the terminology specific to Internet. 1.The internet is a world wide computer network. 1.Electronic mail (email), which is one component of the Internet, approximates person to person letters, memoranda, notes and even phone calls. 2.Another term that is often used is electronic news (enews/Usenet), enews is a broadcast, free to the Internet medium. 3.The term FTP is also frequently used. File transfer protocol (FTP) started as an Internet archival and retrieval medium, somewhat analogous to traditional libraries. 4.The world-wide web (WWW), which is another component of the Net, can be used to "publish" material that would traditionally appear in journals, magazines, posters, books, television and even on film. 2.It is also essential to give a brief history on the internet. 3.The U.S. government is now trying to pass bills to prevent misuse of the Net. II. In order to understand the need for the ever-growing body of legislation, it is important to explore the controversy, and the current problems involved with the Net as it exists must be introduced. 1.The problem that concerns most people is offensive materials such as pornography. 2.Another crucial internet crime is the stealing of credit card numbers. III. One reaction to this inapplicability has been the "Censor the Net" approach (the censorship bill), we are now to compare its advantages and disadvantages. 1.First, the meaning of "Censoring the Net" must be explained. 2.However, many experts have pointed out that government censorship is not possible. 1.First, it is not fair to exclude the freedom and damage the atmosphere of... Free Essays on Internet Censorship Freedom of Speech: Censorship of the Internet Many of use it daily. We find it useful, and it has become part of our everyday lives. â€Å"It†is the Internet. The Internet has dramatically changed our society. It brings together people and their ideas from all around the world in a short amount of time. It is expanding daily to allow new ideas and thought s to be transmitted quickly and easily with the single click of a button. One can find information on almost any subject there. Yet many people are trying to censor it. The Internet is accessed by millions of people around the world each day. If the Internet is to considered a global resource it must remain uncensored. Is Internet Censorship Needed? Internet censorship seems to be the target of many debates nowadays in the U.S. due to the rising popularity of the Internet and the large amounts of pornography, warez, illegal drugs, and general threats to society. It is a very hard subject to handle, after all no individual is in charge of the internet, and in fact no one really owns it except perhaps the â€Å"millions of people throughout the world who contribute to it in various ways†(Burton). The argument for censorship has been going on for at least 5 years now and no one sees an answer being had anytime soon. Getting rid of all the offensive content on the Internet would perhaps make it more productive but is it legal to stifle the rights of others like that? The government thought so at one point and tried to pass a law to help filter the Internet only to have it found unconstitutional soon after To understand why the Internet is subject to such a controversial debate, we must first learn what it is and what it contains. The Internet is a method of communication and a source of information that is becoming more popular among those who are interested in, and have the time to surf the information superhighway. The Internet has been in universal use for many years. It... Free Essays on Internet Censorship Internet Censorship The debate over whether the government should censor the Internet is intense. In 1995 the senate passed the Communications Decency Act written by Senator Jim Exon. The act â€Å"outlaws ‘obscene, lewd, lascivious, filthy or indecent’ communications on the Internet,†(Exon 130). Americans on both sides of the issue are asking some very pertinent, yet difficult to answer, questions. Does censorship of the Internet violate our First Amendment rights? Is regulation of the Internet even possible? Will censoring the Internet protect children from inappropriate material or will it hinder those searching for legitimate information? As a mother, I am concerned about my child having access to pornographic or otherwise inappropriate material on the Internet. However, my personal belief is that it is impossible to regulate the Internet without infringing on the liberties of the First Amendment. Simply put: one person’s definition of inappropriate or pornographic material may be totally different from another’s. It must be made clear that although I am neither totally for nor against censorship, I do not wish to have a limit set on what I can and cannot access determined by someone else’s values. Those who support censorship of Internet materials feel that applying obscenity laws to the internet will protect children from pornography without â€Å"significantly†infringing upon our First Amendment rights (Exon 125). Supporters of this view argue that we live with restrictions on our freedom of speech everyday, such as: libel laws and laws against false advertising. These people submit that the â€Å"anti-pornography laws that exist for U.S. mail, broadcast and telephone communications,†should also apply to computers (Exon 126). These people suggest the use of blocking software in libraries and support the required use of â€Å"a verified credit card, debit account, adult access code or personal identification number... Free Essays on Internet Censorship The Internet is a wonderful place of entertainment and education but like all places used by millions of people, it has some murky corners people would prefer children not to explore. In the physical world society as a whole conspires to protect children, but there are no social or physical constraints to Internet surfing. The Internet Censorship Bill of 1995, also known as the Exon/Coats Communications Decency Act, has been introduced in the U.S. Congress. It would make it a criminal offense to make available to children anything that is indecent, or to send anything indecent with "intent to annoy, abuse, threaten, or harass" ("Stop the Communications ..." n.p.). The goal of this bill as written (though not as stated by its proponents) is to try to make all public discourse on the Internet suitable for young children. The issue of whether is it necessary to have censorship on the Internet is being argued all over the world. There are numerous homepages on the World Wide Web discussing this issue, or asking people to sign the petition to stop government censorship. The Internet was originally a place for people to freely express their ideas worldwide. It is also one of America's most valuable types of technology; scientists use email for quick and easy communication. They post their current scientific discoveries on the Usenet newsgroups so other scientists in the same field of study all over the world can know in minutes. Ordinary people use the Net for communication, expressing their opinions in the newsgroups, obtaining up-to-date information from the WWW, acquiring files by using FTP, etc. Censorship would damage the atmosphere of the freedom to express ideas on the Internet; therefore, government should not encourage censorship. In the Internet community, there is a large volume of technical terms. For this reason, it is first necessary to examine the terminology specific to Internet. The Internet is a world wide computer net...
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