Thursday, November 28, 2019

25 Quotes to Inspire Thoughtful Written Sentiments

25 Quotes to Inspire Thoughtful Written Sentiments Sometimes its easy to take friends and family for granted, which is why showing appreciation is so important. As philosopher Voltaire said, Appreciation is a wonderful thing: It makes what is excellent in others belong to us as well. When you take the time to express thanks and gratitude, you help build and strengthen bonds of trust and love. It doesnt matter whether you send a card or make a phone call. Appreciation, however you express it, builds bridges and fosters healthy relationships. Of course, appreciation should always be sincere. For example, when you praise a family member for their cooking, mention what you specifically liked about the dish, and thank them for preparing it so well. If a friend has thrown you a surprise birthday party, offer your sincere thanks. Remember to say what you enjoyed most about the celebration. Everyone loves a thoughtful thank-you card, but finding the right words to show your appreciation is not always easy. The following is a list of quotes on the subject of appreciation and gratitude from well-known artists, writers, world leaders, and others to help you create your own special sentiments. You could also include the entire attributed quote if it makes sense. Maya Angelou: When we give cheerfully and accept gratefully, everyone is blessed. Guillaume Apollinaire: Now and then it’s good to pause in our pursuit of happiness and just be happy. Thomas Aquinas: There is nothing on this earth more to be prized than true friendship. Marcus Aurelius: Dwell on the beauty of life. Watch the stars, and see yourself running with them. Leo Buscaglia aka Dr. Love: Too often we underestimate the power of a touch, a smile, a kind word, a listening ear, an honest compliment, or the smallest act of caring, all of which have the potential to turn a life around. Henry Clay: Courtesies of a small and trivial character are the ones which strike deepest in the gratefully and appreciating heart. Ralph Waldo Emerson: A friend may well be reckoned the masterpiece of nature. Helen Keller: Words are never warm and tender enough to express ones appreciation of a great kindness. Dalai Lama aka Tenzin Gyatso: The roots of all goodness lie in the soil of appreciation for goodness. Washington Irving: Sweet is the memory of distant friends! Like the mellow rays of the departing sun, it falls tenderly, yet sadly, on the heart. President John F. Kennedy: As we express our gratitude, we must never forget that the highest appreciation is not to utter words, but to live by them. Steve Maraboli: Forget yesterday - it has already forgotten you. Dont sweat tomorrow - you havent even met. Instead, open your eyes and your heart to a truly precious gift - today. Willie Nelson: When I started counting my blessings, my whole life turned around. Marcel Proust: Let us be grateful to the people who make us happy; they are the charming gardeners who make our souls blossom. Albert Schweitzer: At times our own light goes out and is rekindled by a spark from another person. Each of us has cause to think with deep gratitude of those who have lighted the flame within us. Mark Twain aka Samuel Langhorne Clemens: To get the full value of joy you must have someone to divide it with. Kindness is a language which the deaf can hear and the blind can see. Voltaire: Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well. William Arthur Ward: Flatter me, and I may not believe you. Criticize me, and I may not like you. Ignore me, and I may not forgive you. Encourage me, and I may not forget you. Booker T. Washington: Any mans life will be filled with constant and unexpected encouragement if he makes up his mind to do his level best each day. Mae West aka Mary Jane West: Too much of a good thing can be wonderful! Walt Whitman: I have learned that to be with those I like is enough. Oscar Wilde: The smallest act of kindness is worth more than the grandest intention. Thornton Wilder: We can only be said to be alive in those moments when our hearts are conscious of our treasures. Oprah Winfrey: Be thankful for what you have; youll end up having more. If you concentrate on what you dont have, you will never, ever have enough.

Sunday, November 24, 2019

Calculating the Mean Absolute Deviation

Calculating the Mean Absolute Deviation There are many measurements of spread or dispersion in statistics. Although the range and standard deviation are most commonly used, there are other ways to quantify dispersion.  We will look at how to calculate the mean absolute deviation for a data set.   Definition We begin with the definition of the mean absolute deviation, which is also referred to as the average absolute deviation. The formula displayed with this article is the formal definition of the mean absolute deviation. It may make more sense to consider this formula as a process, or series of steps, that we can use to obtain our statistic. We start with an average, or measurement of the center, of a data set, which we will denote by m.  Next, we find how much each of the data values deviates from m.  This means that we take the difference between each of the data values and m.  After this, we take the absolute value of each of the difference from the previous step. In other words, we drop any negative signs for any of the differences.  The reason for doing this is that there are positive and negative deviations from m.  If we do not figure out a way to eliminate the negative signs, all of the deviations will cancel one another out if we add them together.Now we add together all of these absolute values.Finally, we divide this sum by n, which is the total number of data values.  The result is the mean absolute deviation. Variations There are several variations for the above process.  Note that we did not specify exactly what m is. The reason for this is that we could use a variety of statistics for m.  Typically this is the center of our data set, and so any of the measurements of central tendency can be used. The most common statistical measurements of the center of a data set are the mean, median and the mode.  Thus any of these could be used as m in the calculation of the mean absolute deviation. This is why it is common to refer to the mean absolute deviation about the mean or the mean absolute deviation about the median. We will see several examples of this. Example:  Mean Absolute Deviation About the Mean Suppose that we start with the following data set: 1, 2, 2, 3, 5, 7, 7, 7, 7, 9. The mean of this data set is 5.  The following table will organize our work in calculating the mean absolute deviation about the mean.   Data Value Deviation from mean Absolute Value of Deviation 1 1 - 5 = -4 |-4| = 4 2 2 - 5 = -3 |-3| = 3 2 2 - 5 = -3 |-3| = 3 3 3 - 5 = -2 |-2| = 2 5 5 - 5 = 0 |0| = 0 7 7 - 5 = 2 |2| = 2 7 7 - 5 = 2 |2| = 2 7 7 - 5 = 2 |2| = 2 7 7 - 5 = 2 |2| = 2 9 9 - 5 = 4 |4| = 4 Total of Absolute Deviations: 24 We now divide this sum by 10, since there are a total of ten data values.  The mean absolute deviation about the mean is 24/10 2.4. Example:  Mean Absolute Deviation About the Mean Now we start with a different data set: 1, 1, 4, 5, 5, 5, 5, 7, 7, 10. Just like the previous data set, the mean of this data set is 5.   Data Value Deviation from mean Absolute Value of Deviation 1 1 - 5 = -4 |-4| = 4 1 1 - 5 = -4 |-4| = 4 4 4 - 5 = -1 |-1| = 1 5 5 - 5 = 0 |0| = 0 5 5 - 5 = 0 |0| = 0 5 5 - 5 = 0 |0| = 0 5 5 - 5 = 0 |0| = 0 7 7 - 5 = 2 |2| = 2 7 7 - 5 = 2 |2| = 2 10 10 - 5 = 5 |5| = 5 Total of Absolute Deviations: 18 Thus the mean absolute deviation about the mean is 18/10 1.8.  We compare this result to the first example.  Although the mean was identical for each of these examples, the data in the first example was more spread out. We see from these two examples that the mean absolute deviation from the first example is greater than the mean absolute deviation from the second example. The greater the mean absolute deviation, the greater the dispersion of our data. Example:  Mean Absolute Deviation About the Median Start with the same data set as the first example: 1, 2, 2, 3, 5, 7, 7, 7, 7, 9. The median of the data set is 6.  In the following table,  we show the details of the calculation of the mean absolute deviation about the median. Data Value Deviation from median Absolute Value of Deviation 1 1 - 6 = -5 |-5| = 5 2 2 - 6 = -4 |-4| = 4 2 2 - 6 = -4 |-4| = 4 3 3 - 6 = -3 |-3| = 3 5 5 - 6 = -1 |-1| = 1 7 7 - 6 = 1 |1| = 1 7 7 - 6 = 1 |1| = 1 7 7 - 6 = 1 |1| = 1 7 7 - 6 = 1 |1| = 1 9 9 - 6 = 3 |3| = 3 Total of Absolute Deviations: 24 Again we divide the total by 10 and obtain a mean average deviation about the median as 24/10 2.4. Example:  Mean Absolute Deviation About the Median Start with the same data set as before: 1, 2, 2, 3, 5, 7, 7, 7, 7, 9. This time we find the mode of this data set to be 7.  In the following table,  we show the details of the calculation of the mean absolute deviation about the mode. Data Deviation from mode Absolute Value of Deviation 1 1 - 7 = -6 |-5| = 6 2 2 - 7 = -5 |-5| = 5 2 2 - 7 = -5 |-5| = 5 3 3 - 7 = -4 |-4| = 4 5 5 - 7 = -2 |-2| = 2 7 7 - 7 = 0 |0| = 0 7 7 - 7 = 0 |0| = 0 7 7 - 7 = 0 |0| = 0 7 7 - 7 = 0 |0| = 0 9 9 - 7 = 2 |2| = 2 Total of Absolute Deviations: 22 We divide the sum of the absolute deviations and see that we have a mean absolute deviation about the mode of 22/10 2.2. Fast Facts There are a few basic properties concerning mean absolute deviations The mean absolute deviation about the median is always less than or equal to the mean absolute deviation about the mean.The standard deviation is greater than or equal to the mean absolute deviation about the mean.The mean absolute deviation is sometimes abbreviated by MAD.  Unfortunately, this can be ambiguous as MAD may alternately refer to the median absolute deviation.The mean absolute deviation for a normal distribution is approximately 0.8 times the size of the standard deviation. Common Uses The mean absolute deviation has a few applications.  The first application is that this statistic may be used to teach some of the ideas behind the standard deviation. The mean absolute deviation about the mean is much easier to calculate than the standard deviation. It does not require us to square the deviations, and we do not need to find a square root at the end of our calculation. Furthermore, the mean absolute deviation is more intuitively connected to the spread of the data set than what the standard deviation is. This is why the mean absolute deviation is sometimes taught first, before introducing the standard deviation. Some have gone so far as to argue that the standard deviation should be replaced by the mean absolute deviation.  Although the standard deviation is important for scientific and mathematical applications, it is not as intuitive as the mean absolute deviation. For day-to-day applications, the mean absolute deviation is a more tangible way to measure how spread out data are.

Thursday, November 21, 2019

Assignment One Essay Example | Topics and Well Written Essays - 1500 words

Assignment One - Essay Example As the utilization of ICT increases with the creation of new applications, the governments continue to adopt these services. The implementation of the ICT technologies by governments matches the millennium development goals (MDG’s) that focus on digitizing government services. Although embracing some of the ICT technologies strains the financial budgets of countries, all governmental stakeholders agree that it is immensely critical in facilitating public services. Evidently, there has been an evolution of modern communication methods. The methods through which citizens interact with the government have changed remarkably from counter transactions to digital channels, for example, government websites. Rwanda is one of the countries that are currently incorporating ICT technologies in their governance structures (Watkins, 2008). This entails public sector services such as healthcare, license acquisition, taxation and education. Due to this, the government will be able to provide better services. The adoption of ICT solutions by various countries is in coherence with the globalization objective of computerizing administration procedures. The digitization processes are within the millennium development goals (MDG’s) of developing counties. ICT enhancement addresses Rwanda’s MDGs. The Rwandan government acknowledges the rising utilization of ICT in daily lives of its citizens. Consequently, the enhancement of government services through the ICT will be highly beneficial. It will assist the governance process in achieving exemplary echelons of performance. Furthermore, ICT adoption will increase the interaction of the authorities and citizens, further enhancing responsiveness of Rwanda’s government to their citizens’ concerns. For example, the Rwandan health ministry can create websites that focus on the needs of the citizens (Watkins, 2008). This means the citizens can apply health services online and share information. Additionally, the

Wednesday, November 20, 2019

Bush's War (PBS) Analasys Essay Example | Topics and Well Written Essays - 750 words

Bush's War (PBS) Analasys - Essay Example Cheney advocated the use of controversial interrogation techniques to obtain information that would link Saddam Hussein to the 9/11 attacks. In the documentary, Cheney and Rumsfeld supported a pentagon (military) led alternative that led to the decision to invade Iraq. Cheney was also involved in securing controversial secret legal opinions from the Justice Department that would grant President Bush unrestricted broad authority to wage 'war' without the consent of the U.S congress. Cheney also supported the use of 'enhanced combat and interrogation techniques' against captured combatants. President Bush's fixation on invading Iraq was borne out of his distrust of Saddam Hussein. Bush stated in the documentary that Saddam was "an evil man who gassed his own people" In reference to Saddam Hussein, Bush declared after the 9/11 attacks, that his administration would hunt down the Islamic fundamentalists and "those who harbour them." Bush believed that Saddam Hussein was providing support for Al-Qaeda. The intelligence information that was used as a predicate to the invasion was manipulated in order to justify the war. This invasion 'policy' was hatched and promoted chiefly by Cheney and Rumsfeld although there was a lack of substantial evidence that linked Saddam to Al-Qaeda. The Central Intelligence Agency (CIA) Director, George Tenet did not initially support the Iraq invasion on account of the lack of credible intelligence evidence available. Instead of relying and heeding to CIA intelligence reports, Cheney and Rumsfeld formed a parallel and secretive intelligence unit in the Pentagon to analyse evidence that would hitherto link Saddam Hussein to Al Qaeda (Chapter 12). Cheney also pressured CIA analysts who were preparing a National Intelligence Estimate, to include language that would support the invasion policy. The CIA analysts have since reported that Cheney and his staff wanted the report to indicate that Saddam had or was seeking to acquire Weapons of Mass Destruction ( WMD). This attempts led the administration to use "highly dubious" and un-corroborated evidence that stated that Saddam Hussein had attempted to purchase 'yellow cake' Uranium (a key component for producing a nuclear weapon) from Niger (Chapter 12). Why was the press unable to bring this story to light earlier Although some sections of the press were critical of the plans, President Bush had a 90% popularity rate. The national press were therefore weary and feared a public backlash if they did not seem to be supporting the President in war time. How would you assess Rumsfeld's role in this issue Donald Rumsfeld was the one of the Architects of the invasion of Iraq. Rumsfeld first succeeded in taking the lead role in the 'war on terror' from the CIA in Afghanistan and subsequently in the Iraq invasion plans. He wanted to be the solely in charge, "100% responsible" and determined to go to war with Saddam at all cost. He continued to claim that Saddam Hussein had WMD (Chapter 13). Rumsfeld also withheld critical information form the White House and undermined both the State Department and the CIA all in a bid to ensure that the invasion took

Monday, November 18, 2019

Audit of Panera Bread Company Quality Service and Market Share Process Research Paper

Audit of Panera Bread Company Quality Service and Market Share Process - Research Paper Example This is because, few customers subscribe to this company and, therefore, the expenses incurred by the company compared to the revenue generated from the services rendered is relatively high. In order to decrease its liabilities, and hence portray a positive image of the company, managers may attempt to take the losses into a different account especially the expenses accounts. In addition, when customers are disappointed in the orders they make, there is a higher possibility of them demanding that their order be remade or refunded. This environment provides the possibility of pilfering by employees as they can always say they had to remake an order with no hint of plausibility. Increased customer returns and higher rates of pilfering by the employees increases the costs of goods sold by the company. Another risk is that Panera Bread is in the provision of services it offers on a national, regional, and local level, and this reduces its revenues and market share. When customers get poo r services, it increases their chances of shifting to another competing company offering the same services. This reduces the amount of revenue and the company incurs expenses such as, in advertising and improving its services to be better than those offered by their competitors. However, the company must make sure not to increase its prices since the customers will again shift to the competing companies. Since advertising is necessary, the managers then tend to hide the expenses behind the advertising expense in the statement of account. Controls To alleviate the risks coming from poor services, Panera Bread should put into practice several controls. The company, to alleviate the risk of accounts payable being understated, as a result of increased expenses and, therefore, managers resulting to understating the expenses, should require proper authorisation of orders and entry of these orders in its ledger. The company should establish regular receipt book control, and ledger book to help reduce the irregularities. In a bid to entice customers, advertising is done. A control on this should also be enacted where the company should ensure that there are supporting documents any time a manager books an advertising expense. It should also provide an appropriate division of duties such that a manager does not fake any advertising expenses. The company, to deal with the risks of losing its customers, can offer differentiated services from those that it normally offers. This can be done through, introducing offers, for example, ‘buy one get two’. Also, the maintenance of a serene environment can also be an advantage. This increases the influx of customers thereby solving the problem of managers faking expenses to reduce the liabilities since the revenue will increase in the long run. Audit Objectives During this audit, I plan to test the accuracy and the valuation of the contingent liability for losses associated with poor services, the completeness of pur chases and accounts payable and the existence of advertising expenses. Risk Assessment As a result, many emerging enterprises, especially in the food service industry, restaurants are always searching for ways of increasing their profits: Therefore, I assessed natural risk throughout all financial assertions. Moreover, the contingent liability is an estimation and, therefore, at a high risk of manipulation by the managers. The controls around the accounts payable

Friday, November 15, 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.

Wednesday, November 13, 2019

Capote/Krakauer Comparison :: essays papers

Capote/Krakauer Comparison Essay The most important thing any writer can do is to give their characters a feel of dimension to make them seem real. Although Capote and Krakauer do that in very different ways in In Cold Blood and Into Thin Air, they both reached the same end result: characters you believe. They give them thoughts, faces and personalities. They don’t portray everyone as flawless, they display the faults and the little quirks. They give them life through words, making these stories believable. Despite the fact both incidents happened years before each book was written, the use of detailed facts and personality profiles make each story seem incredibly realistic. But while Capote chooses to write an entirely objective piece, Krakauer relies heavily on personal opinion and experience, creating two very distinct frames of mind and causing the reader too see the characters in each book very differently. In 1959 the Clutter family was murdered in a tiny Kansas town called Holcomb. Six years later Truman Capote wrote a very detailed book about the whole case, from the day of the murder to the court case prosecuting the two murderers, Dick and Perry. Although he wasn’t there when the four murders happened, through word choice, description and characterization he creates an accurate portrait of the many intense events surrounding such a tragic story. In comparison, in 1996 esteemed climber Rob Hall led an expedition of moderately experienced climbers attempting to climb Mt. Everest, only to result in disaster and the loss of nine people’s lives. Jon Krakauer was a member of that expedition, and wrote a piece about the misadventure for Outside magazine. Feeling there was more to be said, soon after he wrote a book. Krakauer takes a similar approach as Capote, yet inserting more opinions and less of a feeling of objectiveness to his characters. This is most likely since Krakauer was living Everest first hand, as opposed to Capote who put himself into the environment years later, picking up details here and there instead of relying solely on memory and friends. One of Capote’s greatest strengths is to create thought for his characters, making it almost appear as if he knows what they are thinking. All summer Perry undulated between half-awake stupors and stickly, sweat-drenched sleep. Voices roared through his head; one voice persistently asked him, â€Å"Where is Jesus? Where?† And once he woke up shouting, â€Å"The bird is Jesus! The Bird is Jesus!† (381) This selection almost creates a feeling that Capote is talking about himself as opposed to a man he never met. Capote/Krakauer Comparison :: essays papers Capote/Krakauer Comparison Essay The most important thing any writer can do is to give their characters a feel of dimension to make them seem real. Although Capote and Krakauer do that in very different ways in In Cold Blood and Into Thin Air, they both reached the same end result: characters you believe. They give them thoughts, faces and personalities. They don’t portray everyone as flawless, they display the faults and the little quirks. They give them life through words, making these stories believable. Despite the fact both incidents happened years before each book was written, the use of detailed facts and personality profiles make each story seem incredibly realistic. But while Capote chooses to write an entirely objective piece, Krakauer relies heavily on personal opinion and experience, creating two very distinct frames of mind and causing the reader too see the characters in each book very differently. In 1959 the Clutter family was murdered in a tiny Kansas town called Holcomb. Six years later Truman Capote wrote a very detailed book about the whole case, from the day of the murder to the court case prosecuting the two murderers, Dick and Perry. Although he wasn’t there when the four murders happened, through word choice, description and characterization he creates an accurate portrait of the many intense events surrounding such a tragic story. In comparison, in 1996 esteemed climber Rob Hall led an expedition of moderately experienced climbers attempting to climb Mt. Everest, only to result in disaster and the loss of nine people’s lives. Jon Krakauer was a member of that expedition, and wrote a piece about the misadventure for Outside magazine. Feeling there was more to be said, soon after he wrote a book. Krakauer takes a similar approach as Capote, yet inserting more opinions and less of a feeling of objectiveness to his characters. This is most likely since Krakauer was living Everest first hand, as opposed to Capote who put himself into the environment years later, picking up details here and there instead of relying solely on memory and friends. One of Capote’s greatest strengths is to create thought for his characters, making it almost appear as if he knows what they are thinking. All summer Perry undulated between half-awake stupors and stickly, sweat-drenched sleep. Voices roared through his head; one voice persistently asked him, â€Å"Where is Jesus? Where?† And once he woke up shouting, â€Å"The bird is Jesus! The Bird is Jesus!† (381) This selection almost creates a feeling that Capote is talking about himself as opposed to a man he never met.

Sunday, November 10, 2019

Adam Capital Management

Adams Capital Management: Fund IV Joel Adams, founder and general partner of Adams Capital Management (ACM), a $700 million early-stage venture capital firm investing in the information technology, networking infrastructure, and semiconductor industries, glanced up as his fellow general partners trooped into his office on a brisk December morning in 2005 for their annual retrospective and planning meeting. The main topic on the agenda was a new one, ?would 2006 be the right time to launch their fourth fund?Since late 2000, ACM had been deploying its $420 million third fund, using its â€Å"markets first† strategy, an approach that identified and sought to take advantage of discontinuities within the three industry segments it targeted. Having invested in a company exploiting such a change, the general partners then guided the investment through a five-point structured navigation system. In November 2005, ACM Ill sold a portfolio company and made its first distribution to its l imited partners (Lips).The fund's portfolio also had 18 other operating companies that were showing steady growth, ND two new investments were in the due diligence phase and preparing for final negotiations. â€Å"The question as I see it,† said Adams to his partners, â€Å"is whether we need to exit more companies and generate additional distributions to our Lips before we start raising ACM Since Scam's first fund had closed in 1997, the investment environment had gone from robust to hysterical to deflated and now, finally, to what appeared to be a modest recovery. Likewise, Scam's performance had been whipped about.Fund I was almost top-quartile, Fund II could return capital with a few breaks, ND Fund Ill, a 2000 vintage fund was â€Å"too new to tell, â€Å"Adams noted (see Exhibit 1 for performance data). The firm had adopted its strategy in part to differentiate itself for potential Lips. But the partners also believed that the pure opportunistic approach of many vent ure firms?where each general partner was often given wide leeway in determining which, and how many, markets and business models to invest in?could cause the firm to lose sight of the portfolio as a whole.Without a â€Å"markets first† strategy, through which the entire firm agreed upon the markets of interest before engendering individual companies, the partners felt that firms would invest more on the basis of the fashion of the moment than on business fundamentals or market analysis. In Fund Ill, ACM had taken more significant ownership positions than in the past?typically 35% or more?led every deal, and held a seat on every board. In 85% of the fund's investments, it was the first institutional money in the company.Adams believed that this was the only way to respond to the sharply reduced volatility of the venture capital market: â€Å"build a collection of really good companies and own enough f them to matter. † Associate Ann Lemon wrote the original version of t his case, â€Å"Adams Capital Management: March 2002,† HOBS Case No. 803-143 which is being replaced by this version prepared by Professor Field Harmony and Senior Research Associate Ann Lemon. HOBS cases are developed solely as the basis for class discussion.Cases are not intended to serve as endorsements, sources of primary data, or illustrations of effective or ineffective management. Copyright 2006 President and Fellows of Harvard College. To order copies or request permission to reproduce materials, call -800-545-7685, write Harvard Business School Publishing, Boston, MA 02163, or go to http://www. Hobs. Harvard. Due. No part of this publication may be reproduced, stored in a retrieval system, used in a spreadsheet, or transmitted in any form or by any meaner?electronic, mechanical, photocopying, recording, or otherwise?without the permission of Harvard Business School.This document is authorized for use only in FINDINGS Alternative Asset Classes – SSL/2013 by Jas on Zen at University of New South Wales from March 2013 to September 2013. 806-077 ACM knew this strategy was not without its risks. Fund Oil's portfolio contained some rinsing companies, but, Adams said, â€Å"When you own a significant chunk of the company and it doesn't do well, that hurts the fund. † Going to market with a good small early fund, a struggling second fund and a yet unproven third fund might not be easy. â€Å"The Lips may want to know why we don't go back to taking smaller positions in more companies,† he noted. L have to be able to give them an answer. † Venture Investing in 2005 The first half of the 21st century had truly witnessed the Dickens best and worst of times. The final years of the sass had seen an unprecedented run-up in venture activity. Everything had increased?the amounts of capital raised, the management fees paid, the amounts invested, the prices that companies could command, the exit valuations received, and the speed with wh ich investments became liquid. As the century changed, so did the venture environment.The NASDAQ reached its peak in March 2000 and by 2001, the party had come to a grinding halt. After a decade marked by continuously rising amounts of capital flowing into venture funds, 2001 raised half of sass's record of $71. 7, and 2002 and 2003 raised barely 10% ($7 billion and $8 billion, respectively). L (See Exhibit 2 for fundraising data). By 2005, the numbers of deals, their price levels, and the size of the rounds had all fallen considerably from their peaks in 1999 and 2000. Since the precipitous drop, though, they had steadied (see Exhibit 3 for trends).The initial decline, termed a â€Å"train wreck,† reflected the fact that almost three years of record-breaking venture activity had funded too many companies chasing too few customers in almost all technology customers had cut their capital expense budgets, and on top of that, were suffering from a backlog of earlier technology i nvestments that had not yet been fully implemented. Spending on technology fell off sharply. As a result, portfolio companies significantly underperformed expectations, often forcing their investors to resort to inside rounds for continued financing because all firms were trying to fix their own troubled portfolios.Thereafter, activity had resumed albeit at a lower level. A further complication for the venture capital (PVC) industry was the longer path to liquidity. The Initial Public Offering (PIP) market dried up in 2001, only to revive?at least to a degree–in 2004 and 2005. The number of venture-backed mergers and acquisitions had stayed reasonably steady in the vicinity of 300 transactions from 000 through 2004 and even looked likely to continue for 2005 based on first-half data, the number of Ipso had plummeted from 264 in 2000 to 41 in 2001 and a mere 24 and 29 in 2002 and 2003.Although this number had tripled in 2004, to 93, sass's first half saw an uninspiring 20 Ipso , a number nonetheless close to the total for all of 2002. 2 By mid-2005, though, glimmers of recovery pierced the gloom. PVC fund- raising for 2004, at $1 5 billion, equaled the sum of the previous two years' total. Firms had triages the worst of their problem companies, by selling them for the intellectual repertory, merging them with other weak companies, or shutting them down.Technological evolution provided market opportunities for young companies and some older ones, weaned off the easy-money of the bubble, had brought their products to market and were profitable. Disclosed prices for mergers and acquisitions rose to the highest average since 1 Abstracted from data from Private Equity Analyst and Asset Alternatives. 2 Thomson Financial/Venture Economics, Venture Backed M&A Volume Holds Steady,† www. Nava. Org, accessed December 8, 2005. 2 IQ 2002. 3 The door to the PIP market, blown off its hinges in 2004 by PVC-backedGoogle's debut, reopened, with new companies pricing their offerings almost every week. The pace and valuations of deals had risen, and with it, investor confidence. â€Å"It's not that PVC has become hard,† said one veteran venture capitalist. â€Å"It's Just gotten back to normal. † Adams Capital Management Joel Adams, founder of ACM, grew up in Phelps, New York, a small town between Rochester and Syracuse. â€Å"My dad owned a dairy farm,† recalled Adams, â€Å"and his and doing chores. † Adams was 15 when his mother passed away, leaving his father with no choice but to delegate most of his wife's responsibilities to the three children.Looking back on those days, Adams said: â€Å"At the time the confluence of events was a hell of a wake-up call for a teenager, but I learned invaluable lessons about money and time management. † After graduating from the University of Buffalo in 1979, Adams Joined nuclear submarine manufacturer General Dynamics, where he became a test engineer, the lead engineer re sponsible for starting and testing a sub's nuclear reactor and representing General Dynamics during the Navy's sea trials of the new boats. In 1984 he moved to Pittsburgh to attend the business school at Carnegie Mellon University (UCM), lured by its strong program in entrepreneurship.During Adams' second year at UCM, he worked part-time for Foisting Capital, a small PVC firm that invested on behalf of the Foster's, a wealthy Pittsburgh family. Adams Joined Foisting after graduation as a Junior partner, with the firm's new $14 million fund. Shortly thereafter, the firm and Adams became involved with PAP/Foisting l, a Joint venture formed with Patricia ; Co. To manage the $40 million fund that the state of Pennsylvania wanted to invest in PVC. In 1994 after nine years with Foisting, Adams, SCOFF Andrea Joseph, longtime secretary Lynn Patterson, and former partner Bill Hulled armed Adams Capital Management, Inc. O handle the Foisting portion of the $60 million PAP/Foisting II, raised in 1992. In 1997, ACM raised its first fund, the $55 million ACM l, with its markets-first investment strategy. Discontinuity-based investing Ever since he had Joined Foisting, Adams had been dissatisfied with what he considered a lack of focus and discipline in the firm's investment strategy. â€Å"Here's a nuclear engineer, walking into this industry, with a very small fund in Pittsburgh whose strategy was to be diversified by stage, by industry, and by geography,† Adams recalled. After about a year, I said, ‘This isn't a strategy at all? you could do anything. He was especially nonplussed by the method of developing deal flow. Rather than learning about markets and then targeting specific deals within them, he said, â€Å"The approach at Foisting was to open the mail in the morning† to see what business plans had arrived. Two of Adams' experiences at Foisting acquainted him with the power of targeted investing. The first was his involvement with Sharper Corpor ation, a developer of software applications for engineering product data management. â€Å"l understood the issues of engineering data management from my says at General Dynamics,† Adams said. L was a much smarter investor looking at an industry that I knew. † Not only was he a better investment manager and board member, he realized, 3 Ibid. 3 but he was also a better negotiator. â€Å"Entrepreneurs are passionate and biased about their businesses,† he said. â€Å"If the first time I hear about a market is from the entrepreneur, I'm at a big disadvantage. † His second revelation was even more powerful. Seeking a computer in 1987, Adams happened to learn about a mail-order operation in Texas called PC's Limited that custom-built personal computers and undercut retail prices.After speaking with the company's CEO, Adams invested $750,000 in the future Dell Computer's first outside venture round. Had the firm held this position, it would have been worth $382 m illion as of the end of September 2005. Adams realized that Dell had created such an explosion of value by exploiting a discontinuity ? a dramatic and sudden change in a large and established market. In this instance, the discontinuity involved distribution. The rise of direct distribution surprised the large personal computer manufacturers, which had highly entrenched outworks of retail dealers.These networks, Adams noted, â€Å"couldn't be unwound overnight. † Dell could build a multi-billion dollar business from scratch because his large and sleepy competitors could not respond to this distribution discontinuity in time. As ACM expanded, Adams resolved that any new partners would be engineers, and thus bring their technical training to bear in thorough examinations of a few promising markets (see Exhibit 4 for partner biographies). Scam's strategy evolved to focus on investments in markets that the partners already knew well and had already identified as attractive.A few i nitial prerequisites had developed over time. The first was that the companies in which ACM invested would sell to businesses, not consumers, and their value propositions would be driven by return on investment (ROI). â€Å"That's ROI for the customers, not us,† said Adams. â€Å"Our first question is, ‘If somebody is going to buy this company's product, what does the Chief Financial Officer's recommendation look like? † The second criterion was that the business was fragmentation applied technology,' or one of the first companies to use a specific technology for a specific application.Given the partners' engineering backgrounds, the firm focused on the information technology (IT) and telecommunication/ semiconductor industries, areas that were, in their view, experiencing significant discontinuities. The most important criterion was that, as in the case of Dell, Scam's portfolio companies would exploit discontinuities in existing markets, shifts that would creat e opportunities for start-up companies to become market leaders. In the IT industry, the partners anticipated that the need to create virtual enterprises on a global scale would force companies to look for highly adaptable systems.The telecommunications industry, faced with global expansion in bandwidth requirements for data, seemed to be faced with an entire rethinking of the existing technology and infrastructure, while reaching the limits of current silicon technology appeared likely to revolutionize the semiconductor industry. Within these areas, Scam's partners sought to identify four primary causes of discontinuities (see Exhibit 5 for more on discontinuities): 1 . Standards. Despite the emergence of a technology technologies in an attempt to preserve their captive customer base.Even as customers demented the standard, the existing manufacturers perceived it as a threat to their oligopolies market positions, and were reluctant to adopt it. One such example was FORE Systems, wh ich built communications devices that conformed to the ATM (asynchronous transfer mode) standard for communications in wide-area networks. The big players at the time, AT&T/Lucent and Northern Telecoms, each had proprietary protocols for those communications. These manufacturers clearly had the technical prowess and market muscle to 4 exploit ATM as well, but they were slow to do so for fear of cannibalizing their own racket shares.In April 1999, FORE was acquired by GEE Pl for $4. 5 billion. 2. Regulation. Unexpected regulatory changes could force market players to adapt quickly to a new market reality. An example of such a dislocation had occurred in the U. S. Cellular market where a host of new opportunities and networks had emerged after the government's creation of the PC'S spectrum. From a technology point of view, the new spectrum provided a chance for GSM, the cheaper and more easily-deployed base station technology popular in the rest of the world, to gain ground on the unw ieldy proprietary technology dominant in the United States.GSM equipment manufacturers and the upstart carriers who provided their services used their agility in the new regulatory environment to challenge the giants. 3. Technology. A technology-based discontinuity could take two forms. In one, it could appear as a whiz-bang package that took big competitors months or years to duplicate, such as Apple's Macintosh operating system. Alternatively, it could involve the convergence of technologies that had hitherto been separate, requiring innovation to allow these once-disparate systems to interact.An example here was the rise of corporate remote access, which forced companies to buy technology that would connect the public carrier telephone networks to the corporations' internal local area networks. 4. Distribution. Dell Computer in the earlier example provided the ultimate example of a distribution-based discontinuity?the rise of mail-order completely surprised existing personal comp uter manufacturers, to the great enrichment of Dell and its shareholders. This top-down approach to identifying markets was crucial in helping ACM achieve consensus about and control over where its partners would invest.Adams firmly believed, â€Å"Market due diligence is the only due diligence you can do independent of a transaction. If you present the partners with the industry and market dynamics ahead of time, then we can all talk about each other's prospective investment. † Scam's approach to identifying discontinuities included its Discontinuity Roundtable, a group of advisors that met periodically with the ACM partners to identify and discuss market discontinuities that could lead to fruitful investment theses. The 20-person Roundtable comprised industry experts and observers who attended meetings depending on the topic at hand.Among their number had been Clayton Christensen of the Harvard Business School known for his research on how innovation affected markets; Georg e Symmetry, inveterate entrepreneur and founder and backer of over 200 companies; Attic Razz, former CEO of MAD, the chip-maker that competed against Intel; and Mike Maples, former COT of Microsoft. The process required partners to write discontinuity white papers that advanced the investment thesis and to present them to a Roundtable of appropriate experts drawn from the pool.The group would discuss the merits of the thesis under consideration, usually greening to pursue two or three of the eight to ten papers presented in a meeting. The meetings would also identify other avenues for future exploration. Once an investment thesis was thoroughly vetted by the Discontinuities Roundtable, the ACM partners would systematically search for deals in that domain. Sometimes this took the form of identifying pockets of excellence in the appropriate technology and supporting entrepreneurs in forming a company.In other cases, it was a matter of identifying and sorting through several existing p otential investments. This process eve the partners deep knowledge of these companies' opportunities and therefore made ACM more attractive as an investment partner. 5 Structured Navigation In addition to a systematic approach for identifying markets, ACM also developed a system for managing its investments, called â€Å"structured navigation. † The system was born out of the observation that early-stage technology companies shared many of the same benchmarks and needed many of the same elements to succeed.Jerry Sullivan, who had Joined the firm from MAC, Tektronix and Phillips, explained: Our investments typically have high development costs coupled with the direct sales Orca characteristic of companies at these stages. The majority of our investments? 90%?are software-based, so resource planning and allocations are well understood by all of our general partners. We feel that our structured navigation strategy applies to all companies within the model. Aspects of the structu red navigation included : 1 . Round out the management team.Like most other PVC firms, ACM was deeply involved in helping its entrepreneurs complete their management teams. â€Å"Almost 85% of the management team without capital,† Martin Neat, a former executive vice president with IBM and now ACM general partner, said. People are going to Join a company that has some capital behind it, so we fundamentally believe that if you've got a great opportunity that's well-funded, you're going to attract a lot of talent. † ACM devoted significant resources to the creation of its Services Group, which helped its portfolio companies in this area. . Obtain a corporate partner or endorsement. The notion that an early stage company, hoping to exploit a sea change in a large existing market, could forge a partnership (an endorsement, a distribution deal, or an equity investment) with one of the very players from whom it hoped to steal market share mimed entirely contradictory. But the ACM partners believed that this should almost always be possible. From Scam's perspective, forging these relationships early would often create other exit opportunities. . Gain early exposure to industry and investment banking analysts. Industry analysts such as Garner, Gaga, and Forrester often created the first wave of market interest in a new technology. This group's validation could speed the acceptance or application of a new technology. While industry analysts could help create a market for the technology, analysts at investment banking firms could create an exit for the company, and ACM tried to make sure they met the portfolio companies early. First of all, the good analysts really do understand the businesses of these little companies,† N. George Sugars, a general partner in the Silicon Valley office, said. â€Å"But the second thing is, [bankers are] in the fee business, and they need to put marriages together. [Introducing the two parties early] is a tactic that w ill set you up for deals later on. † 4. Expand the product line. A first-generation applied technology company would be confronted by sigh initial costs of development and sales.In such a case, Bill Freeze, a general partner in Scam's Boston office, observed, â€Å"The marginal cost of the development for subsequent products or the next sale is much lower. † Once a new technology product had been developed and a base of customers secured, the costs of leveraging that technology into another, similar product and selling it into a base of existing accounts was comparatively small. But â€Å"sometimes the entrepreneur hasn't thought that out yet,† he noted. Our approach ensures that the companies are adequately focused on this value creation opportunity. 5. Implement best practices. Scam's partners felt that their entrepreneurs should focus on developing products and selling them to customers, not on structuring stock option packages or compensation 6 plans. After w orking with dozens of companies with similar structures, the partners felt that they should be able to provide boilerplate versions of plans that worked. ACM used these five â€Å"steps† (in no particular order) to manage its investments, complete.The process, the partners felt, not only made their investments more successful, but also provided the partners in four offices across the U. S. With a molly understood internal barometer of a company's progress (see Exhibit 6 for offices). â€Å"If ten months into a deal you can't attract talented people, corporations don't care, and you can't get the bankers interested?you're learning something,† observed Sullivan. â€Å"And maybe you ought to get out. † Defending the Strategy Was it really necessary to formulate such a rigorous strategy for investing in early- stage businesses?Adams admitted that, to a certain extent, the strategy was motivated by the practical necessities faced by a small firm based in Pittsburgh r aising a $55 million fund in 1997. We had to get ourselves above the muck, and the way you do that is with a well-defined, market-centric strategy that you execute in a disciplined manner,† he said. It had also given a small partnership, scattered among offices in Pittsburgh, Philadelphia (later Boston), and Austin, Texas (Silicon Valley was added in 1999) a common language and approach that facilitated communication.Adams balked at the conventional wisdom about PVC and venture capitalists?namely, that PVC was a personality-driven business, and that successful venture capitalists were all genius dealers whose vision turned everything they touched into gold. L just don't buy the ‘rock star' model that many venture firms promote,† Adams said. Instead, he wanted to build a venture firm in the same way that most businesses were built ? with a structure in which any of its employees were, in principle, replaceable. â€Å"We wanted to develop a system where you could th row anybody out of here and the thing will still cook along,† he said. We wanted to build a system for executing this business. We're engineers, we think that way. We're not rock stars. We have a system for finding areas that are of interest, getting deals, and making them valuable. That's what we do. † The Funds Since 1997, the partners felt that strict adherence to strategy, combined with the systematic portfolio management that navigation provided, had served the firm well. They had grown from a $55 million fund to managing $700 million and from one office in Pittsburgh to four in areas in which 68% of all PVC activity in the U.S. Occurred. Each fund had been invested according to plan, although the results had not been entirely anticipated. ACM I had invested in 15 companies for a total cost basis of $55 million. Information technology accounted for 49% of the portfolio; electrification for 30%, medical devices for 11% and networking infrastructure for 10%. As of Sep tember 2005, the fund was fully invested and had exited all but one company, distributing stock valued at $122. 7 million for a net IR to its Lips of 46% Oust below the upper quartile).The general partners hoped to achieve at least $140 million in total proceeds by the end of Fund Xi's contractual life. With its smaller size, ACM I had aimed for percentage ownership in the low teens. The firm had held a board seat in 67% of its original 15 companies, and its positions could get diluted if it as 7 unable to participate fully in subsequent rounds. However, as Adams said, â€Å"This was the home-run era of early stage PVC investing?significant returns were almost the norm. We had our share, with three acquisitions and three Ipso. That was a good fund. Based on the early success of Fund I and the frenzy around PVC, ACM had closed the $1 50 million ACM II at the end of 1999, followed quickly by the $420 million ACM Ill at the end of 2000 (see Exhibit 7 for fund statistics). In the over- heated environment of 1999 and early 2000, though, the partners found that the game had changed. At first it seemed that home-runs were still possible,† said Adams: †¦ Putting money to work was paramount. Unfortunately, this meant that we had less time to investigate new markets and we therefore had less diversification in the portfolio.If the big companies were looking for drop-add-multiplex-switches, that was what we backed as all of them were being bought because every big company needed its own drop-add-multiplicities. We ended up with a lot of similar companies. Our goal was to own around 20%, and we usually had enough money to keep our position, which was not always the best thing in retrospect. Fund II had stayed the strategic course. Of the 14 companies in the portfolio, three had been acquired, five written off, and six were still active and showing strong revenue growth.The firm had moved away from investing in medical devices though. Information technology made up 45% of the portfolio, semiconductors 38%, and telecommunications 17%. Although Fund Sis's value currently stood at a 40% discount to cost, Adams hoped that, with a few breaks, it could return the Lips' capital. Fund Oil's approach of taking larger position had been adopted in response to the changes that the partners noted in the market in particular, a reduction in volatility. As Adams explained,: The days of the consistent home-runs are gone.Reduced volatility meaner that we need to build portfolios that are more balanced and consistent in their performance. We're not looking for xx returns, although we certainly wouldn't refuse them. I Just don't think that's the norm anymore. Instead, we're looking to build a solid portfolio that yields xx to xx returns based on operating success?positive cash flow and net income. We look to own enough of each company that every deal is an impact deal, both for us and for the company. And here, because outcome volatility has fallen so substa ntially, we need to have diversity among our companies.You might say that beta has fallen so we must increase alpha. We had to assemble an interesting collection of really good companies that addressed significant discontinuities in the market and own enough of them to matter. We've done that. We've also added value to them through the ACM Services Group, which provides corporate partnering, recruitment and financial management guidance. By September 30, 2005, Fund Ill had called 74% of its committed capital. Information technology accounted for 59% of

Friday, November 8, 2019

British South Africa Company (BSAC)

British South Africa Company (BSAC) The British South Africa Company (BSAC) was a mercantile company incorporated on 29 October 1889 by a royal charter given by Lord Salisbury, the British prime minister, to Cecil Rhodes. The company was modeled on the East India Company and was expected to annex and then administer territory in south-central Africa, to act as a police force, and develop settlements for European settlers. The charter was initially granted for 25 years, and was extended for another 10 in 1915. It was intended that the BSAC would develop the region without significant cost to the British tax payer. It was therefore given the right to create its own political administration supported by a paramilitary force for protection of settlers against local peoples. Profits form the company, in terms of diamond and gold interests were reinvested in the company to allow it to expand its area of influence. African labor was exploited partially through the application of hut taxes, which required Africans to look for wages. Mashonaland was invaded by a Pioneer Column in 1830, then the Ndebele in Matabeleland. This formed the proto-colony of Southern Rhodesia (now Zimbabwe). They were stopped from spreading further to the north west by King Leopolds holdings in Katanga. Instead they appropriated lands which formed Northern Rhodesia (now Zambia). (There were failed attempts to also incorporate Botswana and Mozambique.) The BSAC was involved in the Jamison Raid of December 1895, and they faced a rebellion by the Ndebele in 1896 which required the aid of British to quell. A further rising of Ngoni people in Northern Rhodesia was suppressed in 1897-98. Mineral resources failed to be as large as implied to settlers, and farming was encouraged. The charter was renewed in 1914 on the condition that settlers be given greater political rights in the colony. Towards the end of the last extension of the charter, the company looked towards South Africa, which was interested in incorporating Southern Rhodesia into the Union. A referendum of the settlers voted for self-government instead. When the charter came to an end in 1923, white settlers were allowed to take control of the local government as a self-governing colony in Southern Rhodesia and as a protectorate in Northern Rhodesia. The British Colonial Office stepped in 1924 and took over. The company continued on after its charter lapsed, but was unable to generate sufficient profits for shareholders. Mineral rights in Southern Rhodesia were sold to the colonys government in 1933. Mineral rights in Northern Rhodesia were retained until 1964 when they were forced to hand them over to the government of Zambia.

Wednesday, November 6, 2019

Essay on Greece and Greek Philosopher

Essay on Greece and Greek Philosopher Essay on Greece and Greek Philosopher The Ancient Greek contribution ranged by the 1900-133 BC, however its influence on the Western Literate Society lasts to this day. As the Greeks expanded their empire, they spread their ideas to other countries, while also borrowing from other cultures. During this period of time, the Greeks made many significant and long-lasting contributions to our modern culture in Philosophy, Art, Democracy, Drama, Math, and Science. These giving of important ideas, inventions, and structures have had an extraordinary influence on the surrounding environment, society, and in the future. The essential contributions of Greeks to the Western Civilization are Democracy, Art, and Philosophy. One thing that the ancient Greek affected western civilization is politics. It was the Greeks who developed a democracy, they were the very first. Pericles stated that he wanted all citizens to have an equal opportunity to serve the public. In both the US democracy and the Greeks democracy, political privilege can be use by citizens. An example of a political privilege can be use by citizens in Greek was that laws were voted upon and to able to nominate by the assembly of all citizens. In the US when citizens are 18 and older they are granted the right to vote. In the US most of the democratic system that the government uses is either identical or very similar to the Ancient Greek system. Perhaps the most famous piece of ancient Greek art work is Myron’s famous marble sculpture of The Discus Thrower. Myron’s art represents an Olympic event called Discus. The marble sculpture is notable because it reveals the ancient Greek value of athletics. The ancient Olympics were made up of a series of athletic matches that the people of the city-states within Greece would participate in. The city-states would put aside all differences to participate in these events to show their victory. The Olympics, that the ancient Greeks held, inspired other civilizations to hold an Olympics to test their athletes as well. A world Olympics is still held

Monday, November 4, 2019

Chinese Women and Culture Essay Example | Topics and Well Written Essays - 1750 words

Chinese Women and Culture - Essay Example The recent developments on China portray a comparatively liberal image of the women than was possible some decades ago. Not too far off in history, in fact if a critical analysis is made for the 1980`s and the 1990`s both the authorities in China as well as the traditional Chinese society were resistant to the growth of feminist attitudes.The traditional ancient Chinese rituals and belief systems though still prevalent to some extent in China adds to the limitations that women have to face to contribute significantly to the Chinese cultures and traditions. 1990`s however opened doors towards acceptance to the fact that women can also significantly contribute to the cultural development in China.To understand China in the modern context, it is crucial to analyze the role of women in the ancient century as well so that patterns in evolution can be drawn.China is always perceived as a culturally isolated and a backward society, and the image of the state is that of an authoritarian tyra nnical one. Modern elements of change like modern art, modern music, internet evolution and social networking seems to be absent and highly controlled. The beginning of the new century saw an immense increase in modernization. With the opening of market in the late 1990`s, China`s economy started to boom as markets expanded and modernized. Cultural values, however, didn’t saw as immense of a change but some level of change was inevitable and 12 Girls Band is the product of this change. Thus, 12 Girls Band is symbolic for women empowerment, the ability for Chinese to preserve their traditional legacies, portraying a liberal yet sophisticated image of Chinese woman throughout the world. All members of the 12 Girls Band are thus Ambassadors to China who have positively affected the cultural variables in China at home and abroad. To understand China in the modern context, it is crucial to analyze the role of women in the ancient century as well so that patterns in evolution can b e drawn. In the ancient China women were considered to be inferior to men, and all their lives they were expected to obey the male members of the family, thus they had no freedom of their own and their role towards cultural community development was absent. The practice of binding women`s feet is symbolic for the control over women during that century. However, with time when the People`s Republic of China was found the role of women started to change, at least rhetorically and a significant level of independence was gained by the women. It wasn’t until 1979 that the government enacted reforms which enabled women to seek jobs in the market. This was the beginning of the initiation of the contribution of women to art; however the role was still very limited. However, with the cultural revolutions more and more opportunities were produced for the women and the process of evolution began to speed up (Wales 1967). Until the 1990`s the women were significantly contributing economi cally as well as culturally to the Chinese legacy. During this period, women poetry groups and arts clubs began to emerge and their activities began to enhance rapidly (Descoteaux 2008). The beginning of the new century saw an immense increase in modernization, and thus 12 Girls Band is a product of the modernization and cultural fusion. The band was selected in an audition in 2001, and twelve members later constituting of thirteen members, this band was a unique blend of girls who knew to play diverse range of instruments both modern and traditional in nature. All band members have gone through rigorous trainings in the field, and all of them belong to the conservatories groups which include the China`s Academy of Music, Central Conservatory of Music and the Chinese National Orchestra. The idea behind the concept belongs to Wang Xio-Jing who wanted twelve members for a band and his aim was to promote folk music however make it appealing by adding a modern touch to it. Thus, the wom en were inspired by the work of Yue

Friday, November 1, 2019

Carmen by Georges Bizet - Report Essay Example | Topics and Well Written Essays - 750 words

Carmen by Georges Bizet - Report - Essay Example The costumes of the opera singers were typically in the character of a Spanish Seville setting. At one point we saw actual Toreador clothing. PERFORMANCE SETTING According to the Grove Music Online the opera was chosen after a French book. A distant cousin of Bizet was one of the two people who wrote the libretto. The librettist were Henri Meilhac and Ludovic Halevy. (Grove 2011)They wrote for other French composers. Bizet chose the subject himself. He wanted to use melodrame as it had been used since 1850 in opera comique . (Grove 2011) An opera where there was dialogue accompanied by music was a technique that came from Italy in the opera buffa. TYPE(S) OF MUSIC . The opera was an opera comique taking after the opera buffa in the classical period. There were spoken parts. Carmen, the provocative bohemiane gypsy was a mezzo- soprano. Don Jose was a tenor which is higher than a bass. Before the opera began there was a short spoken introduction. I did not listen. I was too excited to hear the performance begin. Carmen is a gypsy who provokes men into loving her. A soldier, Don Josee, sees her kill another women and takes her to the police. He falls in love and lets her go. When he finds her again, she is already married to someone else. He becomes a bandit. He kills Carmen out of jealousy or madness because she won't come back to him. This soldier is Don Josee. Carmen, Don Josee, Micaella, and Escamillo are the principal characters. It was so different seeing the opera on stage than seeing it on a screen; the sounds of hearing the whole hall were amazing. Knowing that Bizet never had been to Spain makes one wonder how he could have written such Spanish sounding music. The Grove's said his opera changed the Spaniard's conception of their own music. The two parts of the opera chosen were. Carmen's Fate aria, and the Duet in Act IV before Don Josee kills Carmen. Carmen's Habanara "aria" is using all of Bizet's use of musical genres. 1. It starts with the use of voi ce as if were spoken drama with music being played under the voice. Please note the music is not accompanying the voice at certain points where it is at others. 2. The voice is used in dialogue with the chorus answering 3. The voice is used as an accompaniment to the chorus 4. The voice is used as a solo without any instrumental accompaniment. 5. The full orchestra with the full chorus begins the Fate "aria" The second part chosen is in Act IV of the opera. It is the final duet which ends the opera. The duet between Carmen an Don Josee is exquisitely beautiful. It is long for a duet of the Romantic Era. Bizet uses many techniques to change the emotions and the color of the aria. In the beginning there is very little instrumental intervention and the voices are calm. He is singing of how he loved her and she is saying she doesn't anymore. There is a build up of emotions when she says in the bottom of her soul she doesn't love him. The percussion and strings are playing and there is a change of attitude of Don Josee. He starts to beg and she sings in duet that she cannot go away with him. At one moment we hear the chorus and orchestra playing the Toreador theme. Don Josee knows Escamillo is coming and starts to sing more quickly. When he sings he is going to kill her, the key (tone ) changes to minor and the bass instruments play to show the gravity of the situation. He does kill her and the Toreador, Escamillo comes. This is a duet with