IT Case Study Essay

The Widget Wonders distribution center is the worldwide leader in widgets. Which they’re in the process of building a state of art facility to manufacture new generation of widgets. The SNHUConsulting group leads the way of consulting in information technology. SNHUConsulting has been hired to consult on new hardware that will last for at least the next three years for the different apartments. The sales department consists of 50 employees that requires mobility with access to the company’s resources while in the field with customers and presenting at sales meeting and conferences. The manufacturing department will have 45 employees and will need hardware that support word processing and spreadsheet programs and internet capable. The inventory control department will have 30 employees who would need mobility hardware as well with power to access database systems. The research and development department will consist of 20 employees that’s need hardware with graphics design and CAD programs. The MIS will consist of 5 employees who will need additional processors and memory requirements to support administration tasks. My recommendations for the sales department for mobility purposes is notebooks, smartphones, and tablets for visiting customers. For bigger presentations a digital projector that is interactive, with laser pointers that allows the sales team to talk and click on the computer to dictate its pace. Also USB drives that holds a large amount of storage that the sales team can upload from any computer systems. For the manufacturing department my recommendation are the new generation computer systems that support multi servers for the manufacturing needs. The manufacturing department will also need printers and connectivity capability to the internet as an additional resource tool to complete their job functions. The inventory department will need tablets with 32 or more GB of storage with direct access to the company’s database systems. The research and development department needs  notebooks, printers, and a docking station for automated systems backing up. Hardware that is able to compare and contrast data for the development of the company. The MIS department would need computer systems that is compatible with graphic adapters. Also the computer systems will have a multimedia screen capability for administrating tasks. In conclusion, the hardware that would be required for each department will have the durability and warranty that will last the company for at least 3 years, which will then require the company to revisit their strategic plan for any updates as needed. In purchasing the hardware, the company will included warranty and service agreement with the vendor to assist in any maintenance issues that may arrived regarding any of the hardware purchased. The hardware will have the most advance technology needed for each department efficient in their job duties.

Gentleman Of Rio En Medio Essay

Having a Family Don Anselmo is the protagonist of the short story â€Å"Gentleman of Rà ­o en Medio† written by Juan A. A. Sedillo. He is an old man descendent of Mexican Americans who born and lived up in Rà ­o en Medio, New Mexico. He is a respectable, humble and generous man who cares a lot of the people around him. The most important value that represents Don Anselmo is demonstrate through the development of the story is the importance of having a family. For Don Anselmo the family is a very important value. Its importance is present from the beginning to the end of the story. Don Anselmo has a particular form to introduce himself in the meeting he has with Senator Catron. Before considering a new offer proposed by the Americans, the ones who want to buy Don Anselmo’s house and property and the principal purpose of the meeting, the old man starts a conversation about his family. During this conversation, he emphasizes how proud he is for having a very big family in which he is like the â€Å"patriarca†. When Senator finally had the opportunity to make the new offer, Don Anselmo does not accept it immediately. It is possible to infer that the old gentleman does not respond because he was thinking in his family and community. He feels that he cannot accept this offer because he does not deserve more money for sell something that he consider a gift from nature to his family. At the end of the meeting Don Anselmo decided to reject the new offer in order to respect the value of nature and the love that he and his family feel for it. (By Nicole Ferrer) Other reason to say that the highest value of Don Anselmo is the family is that almost every person in Rio en Medio are they descendants. In several parts of the story â€Å"Gentleman of Rio en Medio† the author emphasizes using the characters the importance that the family has to Don Alselmo. Also he says in the story that the children of Rio en Medio are his sobrinos and  nietos, part of his family. Like the oldest man of the village, the people there belong to him. For this reason, he demonstrates the responsibility that has with his family that is the people in Rio en Medio. This show us why he don’t accept more money for the sale of his land or the reason to says that the trees aren’t of he, they belong to the children in Rio en Medio. Once more time we realize that the value best describe Don Alselmo is having a family because he has a responsibility with his descendants and a respect to them. (by Edrick Negron) The last reason to say that the most important value that guides Don Anselmo’s behavior in â€Å"Gentleman form Rio en Medio is having a family because every time a child was born in Rio en Medio, Don Anselmo planted a tree for that child (par.11). It was like a birth gift, so that tree belong to the child. When the Americans complain about the children trespassing the fence to play at the orchard after Don Anselmo sold it to them, they wanted him to stop the children for doing it. Since the children were part of Don Anselmo’s family they thought he had the power to stop it. When they confront Don Anselmo he said that he couldn’t do a thing about it because the trees belonged to the child and not to him (par. 12). When Don Anselmo didn’t sold the trees because he couldn’t; the Americans bought the trees from every single children. (By Bryanda Diaz) Don Anselmo’s biggest value is having a family. Three reasons why he is a family man are presented in the story. Been a family man includes being caring and Don Anselmo demonstrates this in the story when he say he gave every child in the city a tree as a birthgift. Also it says he is proud of his big family; every child in Rio en Medio is his niece or grandchild. Having a family includes being honest, caring, loving and have wisdom, and Don Anselmo have all of this.

Design Of The Tomba Brion Vega Architecture Essay

In my survey I intend to explicate carlo scarpas thought in his design of the Tomba brion Vega, his most visited work and analyze the design of each component separately and as a whole. It is a site of elegance and poesy and epitomises Carlo Scarpas usage of architecture to bring forth significance and feeling. Carlo Scarpa himself describes the grave as a tract ( Un'ora con Carlo Scarpa The Brion Tomb is situated in the North of Italy in the small town San Vito d'Altivole near Treviso. It was designed for the household Brion by Carlo Scarpa after the decease of Giuseppe Brion. It was commissioned by the married woman of Giuseppe, Onorina Brion ; together they co-founded the electronics steadfast Brion-Vega. Giuseppe was born in San Vito and the household owned a secret plan of land in the local graveyard every bit good as a funerary chapel which originally stood on the site. Scarpas original thought and his early work for the household was for a figure of seperate graves for different household members on the original graveyard secret plan. These early designs were to subsequently incorporated in to the concluding design. in 1969 the household bought an L shaped secret plan of land wrapped around the northern and eastern sides of the bing graveyard. Geting this secret plan of land allowed Scarpa to integrate all the household tombs into a individual maestro program for the Brion households resting topographic point. Not taking with the mainline tendency that with money and power when decease occurs a immense shrine or memorial should be erected in memorial Scarpa went the opposite manner. Scarpa states â€Å" I believe it is mistaken to see the Brion Cemetery the merchandise of a affluent capitalist. Rather it is rather the antonym † . â€Å" Of class I could hold merely made a big statue and left the remainder a lawn, but I enjoy doing things † making this he avoided the narrow dictates of rationalism, taking instead to emphasize interior deepness, dreams, and nostalgia. In this he creates a poetic resting topographic point every bit much as a sculptural commemoration in a green, quieting garden. In March 1970 the Plans for the site had reached their concluding signifier and planning permission was given for building. The Cemetery was completed in 1978 and is regarded by many as Scarpas chef-d'oeuvre. Below is a quotation mark from Scarpa on his design of the Brion Tomba. â€Å" I consider this work, if you permit me, to be instead good and ( something ) which will acquire better over clip. I have tried to set some poetic imaginativeness into it, though non in order to make poetic architecture but to do a certain sort of architecture that could emanate a sense of formal poesy. I mean an uttered signifier that can go poesy, though, as I said before, you can non deliberately do poesy. The deceased has asked to be near to ( the ) Earth since he was born in this small town – So I decided to construct a little arch, which I will name Arcosolium. Arcosolium is a Latin term from the clip of the early Christians in the Catacombs. Important individuals or sufferers were buried in them. ) I used a more dearly-won version†¦ I thought it ( was ) a good thought for two people who had loved each other to be put in such a manner as to be able to recognize one another, after decease. Soldiers stand vertical, motions are human. The Arcosolium became an arch, a span span, an arch of strengthened concrete and would still hold looked like a span if I had n't had it illustrated, I mean decorated. But alternatively of painting we used mosaics, A Venetian tradition that I interpreted in a different manner † The statement above merely shows how much thought went in to the design of his lifes chef-d'oeuvre. The organic structure of the graveyard The L shaped site has 5 chief focal points ; the arcosolium which was of great importance was placed on the north eastern corner to in Scarpas words â€Å" benefit from the best position and sunniest exposure † . The arcosolium acts as a sort of ocular flexible joint on the L shaped site fall ining the north and eastern sides of the site. The household Gravess are situated on the north wall of the site sheltered underneath a canopy which shelters them from the elements. On the south side of the L form is a marquee which floats over a Lilly pool. To the western terminal he designed square chapel which leads to a private entombment land for local priests. Another entryway manner to the site was constructed near to the marquee where the original funerary chapel stood. The site is enclosed by a 2.3m high wall. Internally the positions out from the site about go a portion of the design and Looking towards the site the 60deg incline of the wall directs sight over the graveyard doing minimal obstructor of the positions out from the town whilst besides dissembling its internal parts. Scarpa acknowledged that he â€Å" had captured the sense of the countryside, as the Brions wished † ( Scarpa 1978-84 ) The Arcosolium The Arcosolium in history has been situated within a Catholic burial chamber. A individual catacomb would incorporate multiple arcosolium for of import people and sufferer. They are arched deferrals carved from solid stone with a solid rock casket sarcophagus to the underside. The arch and around it were frequently decorated with symbolic frescoes. In the image to the left is the arcosolium which is situated in Via Latina, Cubiculum E, a catacomb in Rome. You can clearly see the arched deferral to the rear and the sacredly painted walls. Scarpas arcosolium is the chief focal point for the whole grave, moving as a flexible joint between the two perpendicular countries of the site. The two caputs of the household are buried here and is hence sited with importance and was built on the north east corner of the site. Unlike the solid arch of the historic Catholic arcosolium the arch Scarpa designed is sleek and slender and is made out of concrete and bows over the deep-set land on which sit the two burial chambers. The asymetical arch has four constituents or ocular niceties which make the whole. The arch itself is visually two parts with the perpendicular chief arch or the anchor crossing the burial chambers and below this sits a drifting plane which shelters the crypts. The anchor has four fives which run the length of the arch. These fives are closed to their bottom so to shelter the residents. The two natation planes are decoratively layered to their topside instead like the arcosolium ornament of old. These are connected to the 3rd and 4th constituents of the arch by pin articulations and are the two concrete pedestals which sit at the two terminals of the arch and land the design and besides convert the otherwise compressional construction of an arch in to a tensile construction. The plinths themselves are split in to two parts with a solid mass cresting the arch and a more dynamic signifier stoping the completed arch. The pedestals are decorated non with pictures or stuffs but with the z ag zig signifier which dominates the cemetary. The two concerete pedestals are orthogonally stepped three dimensionally decreasing with weight the farther off from the arch they are. Below the arch the two burial chambers sit in a deep-set handbill bowl which is sheltered by the arch above. Originally this round base home base was to be surrounded by a H2O channel emanating from the north pool. The tombs themselves are made out of two tone marble with the sides facing each other being coal black, the top bed a speckled, black marble and the bottom bed a more grained white marble. The ebony boards on the facing planes of the caskets give them a softer touch. The two crypts are sat side by side underneath the arch and thin to each other as though they were seeking to touch. This is besides reiterated on the bottom of the multitudes. Scarpa non desiring to anchor the two objects excessively much curved the bottom of them doing them seem movable and non stuck to the land. Scarpa described it like this â€Å" It is as it should be that the two people who loved each other in life to flex toward each other in recognizing after decease † . A sense of Scarpas love affair can be seen here. In Yutak Saito ‘s book Carlo Scarpa, he describes how the two burial chambers are perceived to â€Å" drift like two boats beneath the arch. † This is evocative of the edifices of Scarpas beloved Venice. Whilst under the arch the colored glass tiles can be seen. Yutak Saito says â€Å" The ceiling of the arch is covered in glass tiles, giving the sense of heavenly glare † The glass tiles run either side of an onyx strip which runs down the center of the four fives of the arch, these â€Å" omit a milklike white translucency † . Brion Tomba cemetery entryway The entryway lies down an avenue of trees which run the old Village Cemetery. Upon attack the first thing noticed is the two intersecting circles which lay at the terminal of the little corridor and their framed image of the lawn and the Hedera helix covered wall beyond. The entryway is sat beside other bing graves and its graduated table is as those of the bing grave. This gives the Brion Tomb a tardis like feel one time inside holding entered through here. The entryway is decorated with a zigzag design like the arcosolium with horizontal pieces through the mass in which the sky or in Scarpas oculus the celestial spheres can be seen. On come ining the square entryway opens up like a cave and upon talking unusual reverberations resile off the zigzagged indoors. Again horizontal pieces allow the sight of the celestial spheres whilst inside this dark entryway manner. Four stairss lead up to the corridor beyond. These are somewhat offset to the left manus side giving you a sense of way in which 1 should go. This little gesture The intersecting circles at the terminal of the corridor are rimmed with ruddy and bluish glass tiles. They signify the Earth and the celestial spheres and the Earth and the intersected subdivision signifies the religious universe which may lie in between. You can besides see this looking through the two circles with the green grass meaning the Earth the sky the oasiss and the Grey concrete wall which splits the two the religious universe. With these two intensions Scarpa wanted to instil a sense of how close the three universes are and how they intersect with each other. The corridor splits left and right now. The left manus side is brighter and beckons you down, another way index of which Scarpa is good known for. Looking down the corridor the left manus side of the arcosolium can be seen with the countryside in the backgr ound and the corridor opens a few meters down. It opens to the right with the left manus side go oning farther. At the transitional point between unfastened and closed a H2O class continues the line of the construction which runs down in to the arcosolium adjacent to the paseo. Along this paseo are a set of beginning stairss which lead up to the grazed country above. These stairss are of different thicknesses with each possessing a different sound when treaded upon. If you turn right at the corridor the way leads you down a darkened corridor which opens up onto a drifting way which leads to the raised marquee, the marquee sits on the pool that feeds the watercourse. The Pavillion The marquee sits on the north side of the site above a shallow organic structure of H2O. At a distance it seems to drift above the H2O. It is supported by a set of slender steel columns which rise out of the H2O. The thought behind the marquee was to make a canopy under which the psyche of the dead may come in to intercede. It is accessed via the chief entryway manner along a thin dark corridor and so through a glass door which is opened with an luxuriant system of blocks which are seeable on the other side of the wall to the glass door. The top of the marquee is clad in lumber and Yutaka Saito in his book Carlo Scarpa notes the similarities in the deepness and accent of the design associating to the series of torri Gatess of the fushimi Inari Shrine in Kyoto. Below the weather-beaten lumber box sits a thin metallic modesty panel painted green and is textured with a form of nails which softens the strong stuff doing the infinite more comfy. From its exterior the marquee looks like a solid construction and a sense of weight is felt on sight but the visceras are hollow which lets light go through down in to the infinite where underneath sits a bench on which Scarpa imagined the liquors could rest after they have had their playday in the environing gardens of the graveyard. Its openness gives a connexion between the spirit universe and ours leting passageway of psyches in to it. Underneath the marquee a little seating country is found for the liquors and this sits on a little breakwater which seems to drift a few centimeters above the pool. This may non be a piece of aesthetic design but a great cognition of how H2O and building stuffs respond over clip with staining and corrosion. This can besides be seen on the back wall of the marquee with it looking to drift merely above the H2O degree. Use of H2O Carlo Scarpa was of Venetian beginning and this influenced his designs in that H2O and the effects it caused were frequently cardinal elements of his designs. Bodies of H2O and/or H2O classs were elemental. He spent most of his life in Venice, rolling down its narrow gangways with edifices either drifting on or reflected in H2O ; a universe altering with the wane and flow of the tides. The brion grave is no exclusion with Scarpa planing two pools at opposing terminals of the site which were to be connected by thin watercourses that would weave inbetween the grave linking them with a sense of life or motion of the streamlined H2O. A relationship between the laguna and the canal can be envisioned here. The construct was non to the full designed in but can still be seen in the signifier of a channel running between the marquee and the arcosolium. Bing from Venice Scarpa knew the consequence of the tide and how this could consequence stuffs and sometimes whole constructions, submersing their lower floors on some occasions and the H2O class and pool in the graveyard were designed to debar deluging the next infinites when it rains. The pools themselves are instead shallow being merely half a meter in deepness at their deepest point with the zigzag form taking down to the lowest point giving the H2O a sense of volume and a topographic point for the Sun to play in, making traveling shadows and contemplations of the environing constructions during daytime hours. There are a figure of H2O channels on the site. They all flow to the arcosolium and narrow as they get nearer. This narrowing of the channels give the feeling of a sense of impulse and in kernel, life. Brion Family Tomb The little household grave is situated on the south side of the site and sits against the exterior wall giving a sense of shadiness for its residents. It is a triangular molded construction with a little entryway to the West. The entryway is little and was designed so that to come in one must bow as a mark of regard to the asleep residents. Internally the infinite is little yet the horizontal slits in the signifier allow the external openness to fall in with the internal infinite. The roof of the grave narrows towards the top with a piece taken out at its extremum. This was once more the thought that the liquors could roll freely around the site and come back to their resting topographic points for rest. The chapel and Sacristy The chapel sits on the E of the site and its importance is emphasised by the continual perpendicular planes that cut through the horizontal plane of the level lawn. This accent shows its hierarchy and label the construction as being the edifice of most importance. There are two entrywaies to the chapel, one through the gardens and the 2nd which is used for more formal occasions such as church mass. The entryway through the gardens shows this hierarchy the most, the tall walls create a strong perpendicular volume to go down. Two little stairss are at the entryway and act as a passage between the less formal garden infinite and the more formal chapel beyond. On the left manus side wall a grid form of concrete lines was formed with 10mm deferrals in which beds of plaster were trowelled and so polished which reflects light down the corridor. On this wall the door to the private vestry can be found and follows the same grid clog as the walls somewhat camouflaging it to place its privateness. At the terminal of the corridor stands a big steel and plaster skiding lattice door reminiscent of the manner of Otto Wagner of whom Scarpa was a fan and the traditional Nipponese screen. Beyond the doors stands the chapel and the Chinese manner threshold that leads in to it which allows for the easy transition of caskets and on juncture to get by with a big Numberss of people. The prevailing stuff used in the building of the chapel was once more superimposed concrete. The floor is made of little cobble like rocks which run at a 45deg angle to the room towards the alter. Two marble stairss lead up to the alter and junctions between the stuffs was planned meticulously. The Conclusion-The Journey The journey was really of import in the planning of the site and all the senses were thought of when planing. Although the site is made up of tonss of separate elements they are all portion of the whole and are linked by tracts sometimes physical and sometimes psychological. hypertext transfer protocol: //www.greatbuildings.com/buildings/Brion-Vega_Cemetery.html

The Great Awakening Essay Example | Topics and Well Written Essays - 1500 words

The Great Awakening - Essay Example The Puritans gained ascendency as a reaction to the perceived corruption and worldliness of the Church of England, while Catholics were a small minority. In 1670, Charles 11, followed by James 11, reestablished Catholic control. The Glorious Revolution of 1688 saw William and Mary put an end to Catholicism, repress other minority religious groups and unequivocally reinstate the Church of England as the dominant religion. The Anglican clergy shunned doctrinal extremes and adopted a moderate path. Religious belief was confined to mere nominal participation in church services. At the beginning of the eighteenth century, Charles and John Wesley, along with others like George Whitefield, â€Å"reacted against the coldness of religion and the deistic rationalism which prevailed† and revived the personal significance of the gospels (Great-Awakening.com, n.d.). These were the seeds of the Great Awakening. ... The political scene in England, described above, engendered an atmosphere of uncertainty in the colonies. These economic and political changes diverted the populace from religious concerns. Orthodox Calvinism was also challenged by the rationalism of the Enlightenment, which rejected the Puritan emphasis on the â€Å"inherent depravity† of human nature. The Enlightenment’s emphasis on logic and reason led to the study of theology being superseded by the introduction of math, science, law, and medicine into the college curriculums. Economic success and rational thought took precedence over religion and led to a laxity of morals. This weakening of religious commitment was further exacerbated by compromise within the Congregational Church. In order to stop the sharp decline in church congregations, the Congregational Churches of Connecticut and Massachusetts adopted the Halfway Covenant in 1662, by which churches baptized the second generation of Puritans as infants, with the assumption that they would be converted later in life. Again, the churches ignored the failure of this generation to adhere to this conversion stricture. The children of unregenerate Puritans were baptized but forbidden communion. By thus isolating the third generation of Puritans from the traditional means of receiving God's grace, this Covenant furthered the degeneration of the church. In 1690, the â€Å"halfway members† of the church were allowed to receive Communion. In effect, â€Å"the second and third generations of Puritans failed to demonstrate the same devotion and discipline that the original Puritans had practiced† (Valkenburg, 2011).  In 1708, the Saybrook Platform, or fifteen â€Å"Articles for the Administration of Church Discipline,† attempted to

Hemorrhage Research Paper Example | Topics and Well Written Essays - 1000 words

Hemorrhage - Research Paper Example In many cases, tissues and vessels are scarred and damaged during the delivery process. This presents a situation where blood continuously flows after the delivery (Anderson, 2007). The uterus is also at risk of losing its ability to contract. This leads to the flow of blood without the ability to self contain itself and stop. In other instances, some tissues and vessels may be retained in the uterus causing the bleeding to occur. This is also made quite difficult if the woman is suffering from a blood disorder (Knight, 2009). The disorder affects the entire body’s clotting system. This will then inhibit the body’s ability to stop any bleeding. This data has created a scenario where there is an urgent need to find the most effective and efficient way to prevent and treat hemorrhage. This is with the aim of reducing all the PPH related complications and deaths that occur all over the world (Anderson, 2007). There have been very many studies that have been conducted to de al with the PPH issue. They all aim to identify the best procedure to deal with the issue of PPH. In one study, it was observed that there are trends that can be monitored and observed in many of the cases of PPH. The International PPH which is a Collaborative Group conducted studies in some countries. The countries included the US, Belgium, France, UK, Canada and Australia. They observed that there was a very close connection between PPH patients in the countries. The research did not highlight on the criteria used to select the above mentioned case study countries (Miller, 2004). It is also important to note that they were observing trends from developed countries. This had the sole aim of identifying the observations arrived at from the research. It would have been essential to observe some developing countries. This would have provided a great contrast for the study. Research of prevention and management of PPH shows high chances of problem identification and correction. Once da ta has been collected, it is easy to observe the trends. They offer a healthy basis to understand very many factors that have been previously ignored. Some factors include the effect of the environment on the pregnant woman. Another trend includes the effect of prolonged labour on her reproductive system. There is an obvious conclusion that there are some issues that are arrived at based on observations. The research concludes that there is a need to insist on prevention of PPH. This is as compared to treating it once it has occurred (Anderson, 2007). Doctors should be very observant of their patients before and after the delivery process. It is crucial for doctors to observe the patients general weight and anaemic tendencies. This will ensure that some of the possible causes of PPH are eliminated. The doctor should then find out the patient’s history in respect to previous births (Bhau, 2008). Historical information is very important as it will help identify if there are cha nces for the hemorrhage to occur. In all the researches conducted, there is an agreement of the two distinct methods to deal with PPH. They include all the medical procedures as well as surgical ones. In many cases, patients receive both treatments. This is with the aim of reversing the amount and levels of hemorrhage experienced by the patients. The most common medicinal component used to cure PPH is the drug Oxytocin. It is very common because unlike Misoprostol it has no side

Play with Alexander Hamilton, John Adams, and Abigil Adams Essay

Play with Alexander Hamilton, John Adams, and Abigil Adams - Essay Example At any rate, I am an American, as are many of you. We’re here today talk about America, world events, and to get the impressions and thoughts and ideas of people who are historically significant to America. On my right, is one of those historically significant people, Samuel Adams. Thank you, and thank ye all for that warm welcome. I am humbled. And knowing what I do about modern day round tables, I have to admit that I was just a little bit reluctant to be here, but I have reconciled myself that it is a good thing. A necessary thing. Thank you, Mr. Adams. We are all certainly glad for your decision to be here. Seated to my left is the former First Lady, Abigail Adams, wife of the second president of the United States, John Adams. Mrs. Adams, welcome, and I want to thank you for agreeing to be here today. Mrs. Adams, you’re probably even better known for your writing of letters during the American Revolutionary War; they stand out as both great writing in American history, and as one of the earliest collection of thoughts on women’s rights. And we’ll talk with you a little more about that in a few minutes here. But, again, thank you for joining us. And seated in the middle, between Mrs. Adams and Mr. Adams, is Alexander Hamilton. Mr. Hamilton might best be known for his duel with Aaron Burr, during which he was mortally wounded; but before that, he served with the Continental Congress militia under General George Washington, and later served in the president’s cabinet. An accomplished lawyer, and a signature on the United States Constitution. Welcome, Mr. Hamilton. Not a chance, haven’t you heard, you’re emancipated? Good Gawd, woman, have you seen what they’re wearing these days? There you sit buttoned up to the neck, and you was the one that started all this stuff. Are you a material girl? That’s untrue, Alex. I advocated for women’s rights, not women’s

Is the UK economy out of recession Essay Example | Topics and Well Written Essays - 2000 words - 1

Is the UK economy out of recession - Essay Example The financial crisis that emerged from sub prime-mortgage crisis in 2007 in the United States transformed into a global recession. The financial and economic activities of about all the countries have been severely affected by this sub prime-mortgage crisis. The industrialised economies have been hit hard in this crisis. The UK economy underwent the impact of this crisis in the second quarter of 2008. During this period, UK faced the largest contraction in economy on record. However, the latest statistics of UK are predicting that era of soaring borrowing and economic downturn is over. At the end of year 2008, British economy could not come out of recession, showing the lagging position of economy and everyone was afraid of the potential relapse in the following year. Although the recession emerged from sub-mortgage crisis in the United States, however, UK economy was at disadvantage because it was highly dependent on the financial sector. The poor performance of UK financial sector along with the increasing levels of consumers debt, were keeping the state at a lag behind the other industrialised states, thereby, preventing UK economy to recover from global recession. The official statistics that have been published in January 2010 reveal that British economy is out of recession. While we cannot answer this question exactly, unless there have been some visible trends in the economic conditions. Before analysing whether UK is out of recession or not, looking into what has happened to UK during the last few years (particularly before recession) will be very significant. During the last ten years, the investment and growth in UK has remained passive however, the economy has faced high levels of FDI. The financial sector has become stronger both domestically and internationally whereas; the manufacturing sector has gone down. Moreover, the growth of financial

Finals Assignment Example | Topics and Well Written Essays - 750 words

Finals - Assignment Example Malthus identified the substance wage, with foodstuff the workers’ wages is what workers eat. Rapid increase of food crops is not possible because supply of fertile land is limited and technical improvements do not come fast enough. To Ricardo, economic rent is paid to the owner of the land for the use original and indestructible power of the soil. This rent is not the same as returns derived from improvements made on the land that result to rise of the profit rather than rents. Malthus considered higher rents for landowners as salutary thing. Ricardo believed rent to be unearned income. Landowners who have to work longer hours for the bushel of wheat, sell it at same price as farmers who own the richest delta land. Rent does not determine the prices of grain rather than grain decides the amount of the rent. Answer to question 5. Both contemporary and modern critics have very often regarded Malthus, as an eminently inconsistent writer. Not only was he accused of not reasoning well (Ricardo himself wrote for instance, His arguments are not very cogent; indeed, I am often puzzled to find any connection between the premises and conclusions of his propositions’ Ricardo’s was highly influenced by sparked spare abstraction of English economy of parliamentary debate than proposed corn laws which prohibited importation of grain until the price of domestic grain increased to a specific amount. The central conflict arose from industrialist against landowners who had expanded cultivated acreage. Corns laws had favored only a few at expense of their own capital accumulation thus higher prices meant industrialists had to pay for higher wages. Since most of landowners were parliamentary, thus Corn Law passed easily, debate on these law defined interest of various economic units (groups).Malthus lavished praise on land lords and Ricardo attached the consequences, thus legislative issues become context in economic analysis and revelation of class conflict- how national income to be distributed among landlords manufacturer and workers. Malthus argued that taxation reduces disposable income thus are left worse off. Thus, Corns laws are unfavorable. Answer to question 6. Mill turns economics into a viable philosophical area of inquiry by exploring what people really want and what economics can measure and assess. Mill’s approach to economics is based on his belief in the superiority of socialism, in which economic production would be driven by cooperatives owned by the workers. To this end, Mill argues that the laws of production may be natural laws, but the laws of distribution are created and enacted by human beings. In other words, wealth is the natural product of labor, but the distribution of wealth is determined by the decisions and the will of actual people (the elite) and is not simply part of the order of nature. Mill carries this view quite far, maintaining that human laws and institutions can and should determine how w ealth is distributed. Thus, for Mill, economics is closely tied to social philosophy and politics. Private property being assumed as a fact, we have next to enumerate the different classes of persons to whom it gives rise; whose concurrence, or at least whose permission, is necessary to production, and who are therefore able to stipulate for a share of the produce. We have to inquire, according to what laws the produce distributes itself among these classes, by the spontaneous

Creative Problem Solving Essay Example | Topics and Well Written Essays - 750 words

Creative Problem Solving - Essay Example Since the experts blame alcohol advertising for alcohol consumption among teens, then they take it as truth. Alcohol adverts are not aimed at teenagers or for alcohol consumption increase. Rather, advertising of alcohol is targeted for those who take alcohol to switch alcohol brands. Most commercials will take a minute or so and do not really reveal what they are about. Usually, only those who understand them are old and mature enough to take alcohol. This I say from experience when I first look at an advert I rarely know what the advert is talking about at first. For instance, most Smirnoff adverts require one to understand alcohol and know that they are talking about it. While alcohol ads are highly visible in sports magazines, most people who watch sport agree that liquor and sport are not compatible. Most teens who read sports magazines will know that should they have an interest in sport when they grow up, then they are aware that alcohol will destroy or stop their dreams. Alcoh ol ads are not meant to increase consumption but to get people to take the specific brand instead. While people think that these ads are targeted at consumption of alcohol, the truth is that they are not bad intentioned. The reason why these adverts are on the magazine is to increase market share. The adverts are not intended for young people since the advertisers are only out to increase brand awareness. While advertisement of alcohol may be high coupled to high abuse of alcohol among teens, evidence is not conclusive that young people are led to increase alcohol consumption by the adverts. Not only do alcohol adverts not target consumption of alcohol, there is no evidence that it leads to increased consumption either. ... However, it is also true that some underage drinking is caused by alcohol adverts on magazines aimed at teenagers. This is because it can be proven that young people are more vulnerable to persuasion from magazines with higher readership since they feel part of something bigger. The possibility that delayed effect from adverts on magazines with high circulation among teenagers has an effect on alcohol consumption among them is very high (Rand Health 1). It is obvious that the younger generation does spend a lot of time reading magazines and, in the process, take in a lot of alcohol adverts. It is quite clear that these magazines have to do with sport and being chic. These sorts of magazines also have a very high proportion of their adverts dedicated to alcohol. In fact, most of the teenagers read twice as many magazines as the older generations who have extra pressing issues at hand. Since these magazines have a very high proportion of their adverts linked to alcohol, it is highly po ssible that their readers are the major target. While children at a younger age who do not read these magazines have a low knowledge of alcohol, the generation right ahead of them seems to know a lot more (Rand Health 1). In short, the average sixteen year old knows more about alcohol than the average nine year old. This, in my opinion, implicates the magazine adverts. The social cost of adolescent drinking is very high on most economies in the world with alcohol fuelled accidents and alcohol aided crime being the most obvious. Combating drivers who are underage and drunk involves multiple systems of approach (Rand Health 1). With emphasis on advertising of alcohol in magazines, several policies

Content of Tabloids and Sensationalism Essay Example | Topics and Well Written Essays - 750 words

Content of Tabloids and Sensationalism - Essay Example Stereotyping is very common in several communities especially towards women, minorities, physically or mentally challenged. As expressed in many tabloids, there are issues concerning attitudes towards persons and groups ‘cultures, the way of life, and their capabilities. Some myths and misconceptions about the minorities and the mentally or physically challenged persons are simply stereotypes (Deal, 2007). People tend to place people with disabilities, women, and the minorities in categories that undermine their natural capacities. For instance, notions such as people with disabilities are different from other human beings are issues of stereotyping. Some communities simply categorize such persons as ‘others’ and that any successful handicapped person or woman is superhuman. Other people consider people with disabilities as a source of sorrow to the family members and the community and think that the disability is kind of an illness. According to other forms of ste reotypes, people with disability are a menace to others and the society especially those with mental disability. The pictures of disability portray the minority and people with disability as social and cultural misfits who should not feature in the public. The other attitudes that are expressed in the tabloids concerning the minority groups, women, and the physically or the mentally challenged persons is discrimination. Discrimination is in several forms such the stigmatization of and negative attitudes towards the minority, women, and physically or mentally handicapped. Some depictions of people with mental illnesses in drama and entertainment give them a picture of persons without a normal life. Stigma is a mark of shame or degradation that can affect the psychological well-being of an individual. Stigma and discrimination may bring shame and distress to individuals and make them have low self-esteem. In fact, stigma is one of the greatest

The Nature vs. Nurture Debate Essay Example for Free

The Nature vs. Nurture Debate Essay The nature versus nurture debate is of constant discussion amongst psychologists today. In the 17th century the French philosopher Rene Descartes set out views which held that people possess certain inborn ideas that enduringly underpin peoples approach to the world (Bee, p.3). On the other hand, the British philosopher John Locke took a more empirical approach emphasizing the role of experience as fully contributing to behavioral development (Bee, p.3). Since the days of Descartes and Locke, the empirical nurture approach has possibly tended to have the best of the argument but the debate is far from being settled. Nature is our genetic gift; it determines our basic physical layout, hair and eye color. It determines the types of emotions and motivations we can experience like happiness, sadness, and fear. A person maintains his mental ability only based on what he is born with genetically on the nature side of the debate; therefore stating the environment plays no role in determining his mental aptitude. Nurture is the experience during our lifetime; the assumption that what makes children turn out the way they do, aside from their genes, the environmental part of child development, is the experiences they have at home in particular the experiences they have with their parents and society. This side argues that the environment and surroundings of a person affect their mental ability and are influential in the development of that person. A nature-nurture debate is concerned with what causes something to develop. The debates of nature vs. nurture tend to be historical rather than current. Today, most psychologists see development differently: they believe biological predispositions guide development in certain directions, but experience as influencing how that development manifests itself. The two sources are seen as interconnected, not as opposing alternatives, and it is the way that they interact which is the focus of interest.

The Welcome Table vs Country Lovers Essay Example for Free

The Welcome Table vs Country Lovers Essay Have you ever experienced discrimination and/or racism? It is my belief that, sadly, most of us have; for this paper I have chosen to compare and contrast the literary works, â€Å"The Welcome Table† by Alice Walker, and â€Å"Country Lovers† by Nadine Gordimer. Both of these literary pieces give the reader awareness of the pain and suffering endured by the two African-American characters that were subject to racial discrimination and the superior mentality of those that participated in the discrimination. Discrimination and racism is the core issue in both of these short stories; I will address the subject of racism in various ways. A similarity of both short stories is that the narrator reveals the characters through observation which means both stories are told in the third-person omniscient point of view. I will explore how the narrator drew me in when reading each of the stories. I can relate to to each through experiences in my lifes journey, and will explore those emotions a bit as well. The stories authors will also be compared and contrasted and compared. â€Å"The Welcome Table† Storyline â€Å"The Welcome Table† story was intriguing to me because the author describes the old woman as one who does not have emotional ties with the people around her. â€Å"The Welcome Table† theme is racism. I was moved deeply by The Welcome Table, in which an old, dying black woman is evicted by bodily force from a white church, but then meets-up with Jesus on the highway. I believe the old woman is bitter from the days she was a slave to the white people. Because of this, it appears she has focused only on Jesus for some time now; she knows it will soon be time to join Him. The old woman in the story is a spiritual woman, but bitter, and is so looking forward to her day of meeting with her Lord Jesus Christ, it appears she cares little about anything else at this point in her life. For example, in â€Å"The Welcome Table†: â€Å"The old woman stood with eyes uplifted in her Sunday–go–to–meeting clothes: high shoes polished about the tops and toes, a long rusty dress adorned with an old corsage, long withered, and the remnants of an elegant silk scarf as head rag stained with grease from the many oily pigtails underneath. Perhaps she had known suffering. There was a dazed and sleepy look in her aged blue–brown eyes. But for those who searched hastily for reasons in that old tight face, shut now like an ancient door, there was nothing to be read. And so they gazed nakedly upon their own fear transferred; a fear of the black and the old, a terror of the unknown as well as of the deeply known. Some of those who saw her there on the church steps spoke words about her that were hardly fit to be heard, others held their pious peace; and some felt vague stirrings of pity, small and persistent and hazy, as if she were an old collie turned out to die.†. â€Å"Country Lovers† Storyline The â€Å"Country Lovers† storyline was captivating as well; the theme is racism also. In this story the characters are young; â€Å"Country Lovers† follows the evolving relationship between a white, well to do farm-owners son, Paulus, and the black daughter of a farm-worker, Thebedi. â€Å"Country Lovers† is set in South Africa, and focuses greatly on the product of the star-crossed lovers union. Example in â€Å"Country Lovers†: â€Å"For the first time since he was a small boy he came right into the kraal. It was eleven oclock in the morning. The men were at work in the lands. He looked about him, urgently; the women turned away, each not wanting to be the one approached to point out where Thebedi lived.† Apartheid Regime At the time this story happens, South Africa was under a strict apartheid regime. The white population of South Africa was in charge of the country, and even though they were the minority they oppressed the rest of the inhabitants, mostly the black population. In â€Å"Country Lovers†, we see how distinct the differences between blacks and white were. The fact that Paulus was found ‘not guilty’ of murder, even though there was enough evidence against him, shows how the white people protected each other at all costs. The story also tells how the white children get to go to school, while the black children are not considered when it comes to education. In my opinion, you have to know something about the apartheid period in South Africa in order to understand the short story fully. The educational value is definitely present. And TodayDiverse Opinions â€Å"In post-apartheid South Africa we speak about race extensively. It permeates our workplace, weaves a thread through the fabric of our professional and personal lives, as well as our private conversations and public interactions with others. From within psychoanalytic theory, the thread weaves through the unknown content of our radicalized unconscious. When there is a focus on race in the South African psychoanalytic context it largely takes the form of the struggle to articulate the complexities of working with difference, as Swartz notes, or the struggle to map out issues of race. Such struggles are not localized in South Africa, but strongly reflect a much broader struggle within the global psychoanalytic community, as mirrored in the expanding focus on race.† (Knight, Z. G. (2013)) â€Å"Fourteen years after apartheid, is the ideal of a rainbow nation fading? Not at all. South Africa has come a long way since the days of institutional racism. Its transition to democracy has been remarkably smooth, set against the countrys bitter past. You hear of few incidents of racially motivated violence. The vast majority of South Africans want a non-racial democracy that respects peoples differences. There are laws to punish unfair discrimination, and black economic empowermenta positive-discrimination policyseeks to redress past injustice.† (Knight, Z. G. (2013)) Theme and Characters As you can see already, there are many differences, but there is but one meaningful theme in both stories, racism. In â€Å"The Welcome Table† the main character is an old woman, ready to meet her maker; it is apparent the pain the woman has endured throughout her life just by the description of the condition of her appearance, â€Å"beaten by king cotton and the extreme weather†, the condition of her clothing items â€Å"a long rusty dress adorned with an old corsage, long withered, and the remnants of an elegant silk scarf as head rag stained with grease from many oily pigtails underneath†, and the emptiness conveyed by her to the outsiders â€Å"a dazed and sleepy look in her aged blue brown eyes.†. The descriptiveness, the symbolism drew me in when reading this story. Racism and Spirituality Black liberation theology is a theological perspective found in some Christian churches in the United States which contextualizes Christianity in an attempt to help African-Americans overcome oppression. Black liberation theology seeks to liberate people of color from multiple forms of political, social, economic, and religious subjugation and views Christian theology as a theology of liberation- a rational study of the being of God in the world in light of the existential situation of an oppressed community, relating the forces of liberation to the essence of the Gospel, which is Jesus Christ, writes James Hal Cone, one of the original advocates of the perspective. African-American theology has come from biblical faith to cultural captivity dogmatic texts from the patristic period to the Reformation. Dogma is a principle or set of principles laid down by an authority as incontrovertibly true Theme and Characters In â€Å"Country Lovers†, the main characters are young, and see the beauty in life for a time. I sympathize more with Thebedi throughout the story; I believe she leaves herself vulnerable when she chooses to give herself to Paulus; I believe him to know more what the outcome of their relationship will be; I believe she secretly wants for her lover to be with her and their child. I see women to be more unrealistic because of their deep emotional attachments. I believe Paulus was a bit full of himself as well. He is heartless to call the baby it, and then to kill her himself? In both stories, there is the knowledge of racism by the characters, but in â€Å"The Welcome Table†, although the old woman is aware, she does not consider what others will think at this point, and in â€Å"Country Lovers†, the threat of what others may think means very much. Heart-breaking Realities In both stories I see the reality of broken-hearts. In â€Å"The Welcome Table† the old woman has been through much because of racism in her day; in â€Å"Country Lovers†, the heart-break is just beginning. Both stories are culturally rich, but in diverse ways. While â€Å"Country Lovers† tells of how it is acceptable to test the waters to see if your wife to be is able to bare your fruit, â€Å"The Welcome Table† implies that the old woman was accepted as grandma or auntie when raising a white mans children, but when it came to entering their church there was no acceptance what-so-ever. To me, these short stories have very different endings. The ending in â€Å"Country Lovers† was absolutely heart-breaking compared to the ending of â€Å"The Welcome Table†, which had a rather happy ending in my way of thinking. Authors Many authors have written essays, stories, and poems about negative judgmental and biased views of people in hopes to understand unfair treatment towards mankind and promote changes in human behavior that will bring solutions of peace. These authors are no different; both authors have been rewarded many honorary awards for promoting peace. Ironically, Nadine Gordimer is a white woman born and raised in South Africa and Alice Walker is an African-American from Eatonton, Georgia, but both authors have kindred spirits and are celebrated for their commitments to fight racism. These authors have a twenty year age difference, and have experienced racism in very diverse ways, in their very diverse lives. Nadine Gordimer grew-up in a privileged family, while Alice Walker grew-up poor. Her mother worked as a maid to help support the familys eight children, while Nadine Gordimer is an only child, whose mother imagined her to be ill, weak, throughout her childhood. Both authors began writing at an early age, each for different reasons I believe. Alice Walker started writing age eight, and Nadine Gordimer at nine. Alice Walker, who also wrote The Color Purple, started writing after listening to her grandfathers stories, who was the inspiration for Mr. in The Color Purple; With my family, I had to hide things, she said. And I had to keep a lot in my mind.. Nadine Gordimers first writings were that of apartheid on the lives of South Africans; Gordimer witnessed government repression firsthand when still a teenager; the police raided her family home, confiscating le tters and diaries from a servants room. Personal Thoughts and Feelings on Racism I have had mostly bi-racial amorous relationships in my lifetime; I am Caucasian, and my romantic relationships have been with African-American and Hispanic men. Even in this day and age I believe many people frown on this. Many of the people of either race whole-heartily approves of this in my opinion. The struggle to eliminate racism from our world is an important one. Understanding what it is, understanding the key role it plays in dividing people, and how to challenge it, in ourselves and others, is central to our understanding of how oppression works and how, ultimately, we can free all humanity from it. Racism is ignorance. There are no rational conflicts of interest between any peoples on this planet. There is not rational need for the artificial borders that have been erected over the years to separate different groups of humans. All people deserve an equal share in and access to food, shelter, education, health care and the other necessities of life. The false divisions created by racism only serve the short-term interests of systems which constantly try to divide us and distract us from seeing the underlying economic exploitation that feeds greed. Some have minds that are full of misinformation and confusions about people who have a skin color that is different to our own. Many have been left with irrational fears about countless aspects of other peoples’ and their cultures. The Solution? Nadine Gomier and Alice Walker both wrote what they lived; both stories are laced with racism and discrimination. Where does the solution to this basic human problem lie? The simple answer is in helping people consider an alternate course of action. How? Here is where it gets complex. Let me present several complementary models. First, a basic premise: Racism in its essence is the refusal to accept the other as an equal. To do so, one will have to share in the societal rewards of social wealth, political power, and structural privilege. If racism has nothing to do with biology, but has everything to do with socially structured beliefs and behavior, then it can also be socially unlearned and unstructured. How people proceed, however, depends on how they see themselves when confronted with evil. The great Karl Marx spoke of â€Å"the haves and the have nots†; I see that to be very accurate still today. In â€Å"The Welcome Table and â€Å"country Lovers We cannot change yesterday, and we cannot predict tomorrow, but we can live today. So, do not allow anyone to make you feel less than or hurt you.

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.

Essay --

Child Abuse and its Prevalence in Modern Society In our day and age when people are busy living their everyday lives, a child is being abused behind a closed door. According to Bryan Calo, supervisor of child protective services, â€Å"Child abuse is if a child’s physical, mental, or emotional condition is impaired. The child’s basic needs are not being met, and they are not being provided a safe environment to live in† (Telephone Interview). Most often children that are abused, whether it is physical, sexual, emotional, or neglect abuse, will keep their home lives to themselves. This is not because the child is embarrassed but usually because he or she is frightened of how the abuser will react toward him or her. Although it is not often shared with friends and even other family members, so it is still not being taken into consideration that it does exist. Unfortunately, child abuse is a real occurrence that happens every day. Children are being beaten, being sexually abused, being spoken poorly too, not being given daily needs, and being rejected by a parent or guardian all the time. Today’s society should be more aware of child abuse because when a situation is reported it helps benefit the child that is suffering by placing him or her in a safer environment (Telephone Interview). (PP) Being able to recognize physical, behavioral, and mental indicators are ways in which today’s society can help prevent child abuse from happening to children all throughout the world. Physical abuse must be prevented in today’s society because children deserve to be in a safe environment. A significant factor when it comes to child abuse is being able to notice indicators that would fall under the category of abuse (What is Child Abuse and Neglect? 5)... ... familiar with. However, child abuse does not only happen to certain children but can occur with both sexes throughout all regions of the world. (The Children’s Center para. 15) (SUM) Therefore, physical, behavioral, and mental indicators need to be accounted for wherever an individual might encounter them. These indicators include bruises, burns, fractures, aggressiveness, and doubtful thinking. Child abuse must be prevented because children are defenseless; therefore, they need someone to take care of them (Telephone Interview). (PP) Although today’s society cannot eliminate child abuse from the world, it can be prevented. About half a million children are abused across the United States ever year (Telephone Interview). (PP) These children do not deserve to be treated poorly, and people should help by being more aware of what is happening all around them. Essay -- Child Abuse and its Prevalence in Modern Society In our day and age when people are busy living their everyday lives, a child is being abused behind a closed door. According to Bryan Calo, supervisor of child protective services, â€Å"Child abuse is if a child’s physical, mental, or emotional condition is impaired. The child’s basic needs are not being met, and they are not being provided a safe environment to live in† (Telephone Interview). Most often children that are abused, whether it is physical, sexual, emotional, or neglect abuse, will keep their home lives to themselves. This is not because the child is embarrassed but usually because he or she is frightened of how the abuser will react toward him or her. Although it is not often shared with friends and even other family members, so it is still not being taken into consideration that it does exist. Unfortunately, child abuse is a real occurrence that happens every day. Children are being beaten, being sexually abused, being spoken poorly too, not being given daily needs, and being rejected by a parent or guardian all the time. Today’s society should be more aware of child abuse because when a situation is reported it helps benefit the child that is suffering by placing him or her in a safer environment (Telephone Interview). (PP) Being able to recognize physical, behavioral, and mental indicators are ways in which today’s society can help prevent child abuse from happening to children all throughout the world. Physical abuse must be prevented in today’s society because children deserve to be in a safe environment. A significant factor when it comes to child abuse is being able to notice indicators that would fall under the category of abuse (What is Child Abuse and Neglect? 5)... ... familiar with. However, child abuse does not only happen to certain children but can occur with both sexes throughout all regions of the world. (The Children’s Center para. 15) (SUM) Therefore, physical, behavioral, and mental indicators need to be accounted for wherever an individual might encounter them. These indicators include bruises, burns, fractures, aggressiveness, and doubtful thinking. Child abuse must be prevented because children are defenseless; therefore, they need someone to take care of them (Telephone Interview). (PP) Although today’s society cannot eliminate child abuse from the world, it can be prevented. About half a million children are abused across the United States ever year (Telephone Interview). (PP) These children do not deserve to be treated poorly, and people should help by being more aware of what is happening all around them.

Bradstreets The Author to Her Book :: Bradstreet Author to Her Book Essays

In Anne Bradstreet's poem "The Author to Her Book," the controlling metaphor is the image of a baby being born and cared for. This birth imagery expresses the complex attitude of the speaker by demonstrating that the speaker's low regard for her own work and her actions are contradictory. The first effect of the birth imagery is to present the speaker's book as a reflection of what she sees in herself. Unfortunately, the "child" displays blemishes and crippling handicaps, which represent what the speaker sees as deep faults and imperfections in herself. She is not only embarrassed but ashamed of these flaws, even considering them "unfit for light". Although she is repulsed by its flaws, the speaker understands that her book is the offspring of her own "feeble brain", and the lamentable errors it displays are therefore her own. When the speaker's book is returned by the publisher, the speaker's attempt to "wash (the) face" of her child only worsens the image of herself that she sees in it. Washing the child, rubbing off a blemish, and stretching its joints but failing to improve his imperfections all contribute to an image of the speaker rewriting her book, desperately trying to raise its quality up to her high standards, but discovering in the process that its imperfections and errors run too deep to be corrected, as do her own. In the second half of the poem, a new facet of the speaker's attitude is displayed. In line 17, she wants to improve the ugliness of her "child" by giving him new clothes; however, she is too poor to do so, having "nought save homespun cloth" with which to dress her child. In the final stanza, the speaker reveals poverty as her motive for allowing her book to be sent to a publisher (sending her "child" out into the world) in the first place. This makes her attitude seem to contradict her actions.

Economy of Cote DIvoire (Ivorycoast) :: essays research papers

Once a stable and relatively prosperous country, CÃ ´te d’Ivoire has suffered from continued political instability and economic stagnation since 1999. The current crisis, which began in September 2002, has further aggravated the country’s already difficult social and economic conditions. The civil conflict cut short the incipient economic recovery in 2002. GDP is estimated to have declined by 1.6% in 2002 and 3.8 % in 2003. Inflationary pressures intensified temporarily after the crisis, but decreased subsequently, with 2003 inflation estimated to have averaged 3.8 %. The current account of the balance of payments moved into surplus in 2002 and 2003, as export revenues rose on the strength of international cocoa prices. Public finances deteriorated in the second half of 2002 and in 2003, reflecting a combination of expenditure overruns, tax revenue stagnation, and a decline in foreign financing. Domestic and external arrears reached 13,5% of GDB by end-2003. An improvement in security and political normalization are indispensable for economic recovery. However, a coherent economic policy framework and transparent and efficient management of public finances are critical to consolidate the gains from the return to stability, and to restore private sector confidence. Given the uncertainty about availability of external resources and the need to address the problem of large stock of domestic and external arrears, the authorities should target a higher primary budget surplus in 2004 than the currently envisaged 2,8% GDP. With little room for additional tax revenue mobilization, the authorities need to mobilize more resources from the oil and gas sector and scale down domestically-financed investment and recruitment plans for 2004. The authorities should be more vigilant and proactive in responding to the fragile state of the commercial banking system and imposing corrective actions on banks in distress. In particular, the financial position of the state-owned Caisse Autonome d’Amortissement (CAA) remains very weak, and options for a resolution of its problems need to be considered, in close consultation with the World Bank. The structural reform agenda should be revived with a focus on the cocoa, financial, and energy sectors. Most urgently, an action plan and timetable for addressing the institutional weaknesses in the cocoa sector should be developed in close consultation with the World Bank and other donors. The authorities have requested a resumption of World Bank fund assistance. A credible program of fiscal consolidation and structural reform would facilitate. Fund support, which could initially take the form of post-conflict emergency assistance. Such support would be possible in a framework of concerted support of CÃ ´te d’Ivoire’s development partners, and could pave the way for a move to supported programs.