Tuesday, August 6, 2019
Hurricanes in New York Essay Example for Free
Hurricanes in New York Essay Hurricanes are weather systems that have winds faster than 119 km/hr, brought by intense rotation, gaining momentum as it is formed in the sea. It originates and builds up over tropical oceanic regions. These hurricanes are relatively smaller than storms, usually having about 500km in diameter. When it is above a body of water, the air moves in a counterclockwise direction, but at the top of the storm, the winds are following a clockwise direction (What Is a Hurricane? ). Just recently, hurricanes devastated several states in the United States; including the great damage it brought to New Orleans and many more. Hurricanes are forces of nature that no man can stop. It is a great force of nature that no man can go against with. No matter how industrialized the place is, no matter how many high rising buildings you have, it a hurricane will hit you, it will. As studies show, the next place a hurricane could hit can be New York City. Unusual target. â€Å"Shortly before dawn on Friday, September 1st, weather services carried the news that everyone had been dreading major storm, Hurricane Ella, was off Cape Hatteras and heading for New York. At 6:30 A. M., an emergency-planning group convened at the command center in Robertsons office. †(MORGENSTERN) New York City, considered as one of Americas most developed urban area yet is not as safe as anyone thinks when it comes to a natural disaster like that of a hurricane. No one can imagine how a center of development and commerce, rich with large corporate enterprises and humungous buildings could be devastated by a natural phenomenon. History of Hurricanes in New York New York has a very â€Å"colorful†history when it comes to hurricanes, even though it rarely meets one. Way back in 1821, an enormous hurricane made its presence felt when it went head on with Manhattan, leaving residents in great shock when they saw the sea levels rising more than ten feet in less than an hour. Everything was trashed away by the hurricane, flooding may streets including Canal Street. Experts say that the only thing that stopped the hurricane from completely destroying the city was it happened during a low tide. If it happened on a high tide, it would have brought a lot of water and would have flooded the city more. In August of 1893, an entire island got wiped of the map of New York completely. It was the Hog Island, an island the shape of a pig, which runs for more than a mile in the coast south of the Rockaways. It was developed right after the Civil war, wherein many structures were built, like saloons, bathhouses and gambling areas. It was developed for some prominent people, a place where they can relax when they are away from work. Then, disaster struck. It was one big event, wherein it took a lot from the people. It destroyed and sunk boats on the dock or out on sea, killing hundreds of sailors. It destroyed a lot of residential areas, uprooted many trees, and literally wiped the entire Hog’s Island. It was as high as 30 feet, sweeping through Brooklyn, Queens, and other areas nearby destroying anything in its path. Hog’s Island was the first situation wherein a hurricane literally removed an entire island (Britt). New York Hurricane Statistics â€Å"His figures told him that such an event had a statistical probability of occurring as often as once every sixteen yearswhat meteorologists call a sixteen-year storm. †(MORGENSTERN) According to statistics, storms usually come to New York in a sixteen-year basis. Within 16 years, there is a chance that one hurricane would pass New York’s vicinity. But storms with the strength like that which swept Hog’s Island is said to hit New York in a span of 75 years or more. But after the incident on Hog’s, another massive hurricane swept the city, which is a lot sooner, not following the 75 year sequence. That hurricane was known as the Long Island Express. Long Island wasn’t populated that much yet, so if that same hurricane struck the place again; it would surely raise a lot of panic and fear, because of its strength, with winds that go for 183 miles per hour. A major hurricane in New York would surely stir things up. About 78. 5% of New Yorkers in the coastal areas have never experienced a major hurricane ever in their lives. It is deemed that in the next 50 years, there is a 73% chance that New York City will be hit by a hurricane. But when it comes to a major, greatly destructive hurricane, there is a 26 % chance that New York will get hit in the next 50 years. With these statistics, hopefully, it would help people in staying alert, being prepared if anything goes wrong, if ever another super hurricane would come their way (Mandia). Experts believe that New York City is one of the most dangerous cities that could get the next hurricane disaster. They say that New York is already in third place, following Miami, and New Orleans. These two were heavily devastated by hurricanes in the previous years. Engineering experts say that New York poses a potentially lethal features and characteristics. The bridges in New York are placed so high that it could easily get trashed by pre-hurricane winds, which means that these possible escape routes would be destroyed even before the hurricanes are actually in New York, trapping all the civilians in the city. This decreases the possibility of evacuation, thus a big possibility for a lot of lives to be lost. It is said that in a category 4 hurricane, JFK International Airport would be submerged in 20 feet of water. The cost of hurricane damages Experts say that if hurricanes of the past would happen today, the New York City regions would suffer great financial losses. It is an estimated $18 billion worth of damages if ever disasters like this would likely to happen. Hurricanes are to blame for about 70% of insure property loss in the United States. New York’s coastal state is second in terms of insured coastal property, following Florida, so this means that surely, hurricanes would put a great impact on the economy, not only for New York but also for America, and maybe, the world (Naparstek). Hurricanes and the economy. Experts warn that if ever a hurricane makes contact to or anywhere near New York, it would surely affect the economy, for New York is the largest, one of the most productive urban center in the United States. A hurricane attack, even a low category one, would already flood the runways of the JFK International Airport, thus causing a major stir in the flights, of possible investors or investments coming and going out of the area. It could also flood the streets of Manhattan, depending on how it formed and came, and the tides, whether it is high tide or low tide. It could also cause a lot of damages in the buildings and other infrastructure in the highly urbanized area. These losses are of great importance to marketing and finance, and could surely create an upset. New York is a worldwide center when it comes to finance, it is already an institution. It also has a very large effect on national and international commerce. If ever one hurricane would hit New York making its ports closed, the New York Stock exchange would really suffer. A week of closure would surely damage the economy of America, worse than hurricane Katrina’s effect (Drye). Conclusion From Tropical Storms, to low-category hurricanes, to major devastating hurricanes like hurricane Katrina and Long Island Express, they’re all the same. They could all bring bad things; the only difference is the intensity of the damage. They are forces of nature in which man cannot contend with, the only thing that we can do is to be prepared. It is the key for survival, and the key for the reduction of losses we could experience. References: Britt, Robert Roy. History Reveals Hurricane Threat to New York City. 2005. LiveScience. http://www. livescience. com/forcesofnature/050601_hurricane_1938. html. Drye, Willie. Hurricane Could Devastate New York, U. S. Economy, Experts Warn. 2006. National Geographic Society. http://news. nationalgeographic. com/news/2006/05/060519_hurricanes. html. Mandia, Scott A. Whats in Store for New Yorks Future? 2003. http://www2. sunysuffolk. edu/mandias/38hurricane/hurricane_future. html. MORGENSTERN, JOE. The Fifty-Nine-Story Crisis. 1995. http://www. duke. edu/~hpgavin/ce131/citicorp1. htm. Naparstek, Aaron. Storm Tracker. 2005. http://nymag. com/nymetro/news/people/columns/intelligencer/12908/. What Is a Hurricane? 2001. http://www.comet.ucar.edu/nsflab/web/hurricane/311.htm
Hopf Algebra Project
Hopf Algebra Project Petros Karayiannis Chapter 0 Introduction Hopf algebras have lot of applications. At first, they used it in topology in 1940s, but then they realized it has applications through combinatorics, category theory, Hopf-Galois theory, quantum theory, Lie algebras, Homological algebra and functional analysis. The purpose of this project is to see the definitions and properties of Hopf algebras.(Becca 2014) Preliminaries This chapter provides all the essential tools to understand the structure of Hopf algebras. Basic notations of Hopf algebra are: Groups Fields Vector spaces Homomorphism Commutative diagrams 1.Groups Group G is a finite or infinite set of elements with a binary operation. Groups have to obey some rules, so we can define it as a group. Those are: closure, associative, there exist an identity element and an inverse element. Let us define two elements U, V in G, closure is when then the product of UV is also in G. Associative when the multiplication (UV) W=U (VW) à ªÃ¢â‚¬Å" ¯ U, V, W in G. There exist an identity element such that IU=UI=U for every element U in G. The inverse is when for each element U of G, the set contains an element V=U-1 such that UU-1=U-1U=I. 2.Fields A field Ã’Å“ is a commutative ring and every element b à  µ Ã’Å“ has an inverse. 3.Vector Space A vector space V is a set that is closed under finite vector addition and scalar multiplication. In order for V to be a vector space, the following conditions must hold à ªÃ¢â‚¬Å" ¯ X, Y à  µ V and any scalar a, b à  µ Ã’Å“: a(b X) = (a b) X (a + b) X=aX + bX a(X+Y)=aX + aY 1X=X A left ideal of K-algebra is a linear subspace that has the property that any element of the subspace multiplied on the left by any element of the algebra produces an element of the subspace. We say that a subset L of a K-algebra A is a left ideal if for every x and y in L, z in A and c in K, we have the following: X +y is in L cx is in L zà ¢Ã¢â‚¬ ¹Ã¢â‚¬ ¦ x is in L If we replace c) with xà ¢Ã¢â‚¬ ¹Ã¢â‚¬ ¦ z is in L, then this would define a right ideal. A two-sided ideal is a subset that is both a left and a right ideal. When the algebra is commutative, then all of those notions of ideal are equivalent. We denote the left ideal as à ¢Ã…  ³. 4.Homomorphism Given two groups, (G,*) and (H, °) is a function f: Gà ¢Ã¢â‚¬ ’H such that à ªÃ¢â‚¬Å" ¯ u, v à  µ G it holds that f(u*v)=f(u) °f(v) 5.Commutative diagrams A commutative diagram is showing the composition of maps represented by arrows. The fundament operation of Hopf algebras is the tensor product. A tensor product is a multiplication of vector spaces V and W with a result a single vector space, denoted as V  W. Definition 0.1 Let V and W be Ã’Å“-vector spaces with bases {ei } and {fj } respectively. The tensor product V and W is a new Ã’Å“-vector space,  V  W with basis { ei fj }, is the set of all elements v  w= à ¢Ã‹â€ ‘ (ci,j ei  fj ). ci,j à  µÃƒâ€™Ã…“ are scalars. Also tensor products obey to distributive and scalar multiplication laws. The dimension of the tensor product of two vector spaces is: Dim(V W)=dim(V)dim(W) Theorem of Universal Property of Tensor products 0.2 Let V, W, U be vector spaces with map f: V x W à ¢Ã¢â‚¬ ’ U is defined as f: (v, w) à ¢Ã¢â‚¬ ’vw. There exists a bilinear mapping b: V x W à ¢Ã¢â‚¬ ’ V W , (v,w) à ¢Ã¢â‚¬ ’ v   w If f: V x W à ¢Ã¢â‚¬ ’ U is bilinear, then there exist a unique function, f: V Wà ¢Ã¢â‚¬ ’U with f=f °b  Extension of Tensor Products0.3 The definition of Tensor products can be extended for more than two vectors such as; V1 à ¢Ã… - V2à ¢Ã… -  V3 à ¢Ã… -Â à ¢Ã¢â€š ¬Ã‚ ¦..à ¢Ã… - VN = à ¢Ã‹â€ ‘( biv1à ¢Ã… - v2à ¢Ã… -Â à ¢Ã¢â€š ¬Ã‚ ¦.à ¢Ã… - vn ) (Becca 2014) Definition0.4 Let U,V be vector spacers over a field k and ÃŽÂ ½ à  µ Uà ¢Ã‚ ¨Ã¢â‚¬Å¡V. If ÃŽÂ ½=0 then Rank (ÃŽÂ ½) =0. If ÃŽÂ ½Ãƒ ¢Ã¢â‚¬ °Ã‚ 0 then rank (ÃŽÂ ½) is equal to the smallest positive integer r arising from the representations of ÃŽÂ ½= à ¢Ã‹â€ ‘ui à ¢Ã‚ ¨Ã¢â‚¬Å¡ vi à  µUà ¢Ã‚ ¨Ã¢â‚¬Å¡V for i=1,2,à ¢Ã¢â€š ¬Ã‚ ¦,r. Definition0.5 Let U be a finite dimensional vector space over the field k with basis {u1,à ¢Ã¢â€š ¬Ã‚ ¦.,un} be a basis for U. the dual basis for U*is {u1,à ¢Ã¢â€š ¬Ã‚ ¦.,un} where ui(uj)= ÃŽÂ ´ij for 1à ¢Ã¢â‚¬ °Ã‚ ¤I,jà ¢Ã¢â‚¬ °Ã‚ ¤n. Dual Pair0.6 A dual pair is a 3 -tuple (X,Y,) consisting two vector spaces X,Y over the same field K and a bilinear map, : X x Yà ¢Ã¢â‚¬ ’K with à ªÃ¢â‚¬Å" ¯x à  µ X{0} yà  µY: 0 and à ªÃ¢â‚¬Å" ¯y à  µ Y{0} xà  µX: 0 Definition0.7 The wedge product is the product in an exterior algebra. If ÃŽÂ ±, ÃŽÂ ² are differential k-forms of degree p, g respectively, then  Π±Ãƒ ¢Ã‹â€  §ÃƒÅ½Ã‚ ²=(-1)pq ÃŽÂ ²Ãƒ ¢Ã‹â€  §ÃƒÅ½Ã‚ ±, is not in general commutative, but is associative, (ÃŽÂ ±Ãƒ ¢Ã‹â€  §ÃƒÅ½Ã‚ ²)à ¢Ã‹â€  §u= ÃŽÂ ±Ãƒ ¢Ã‹â€  §(ÃŽÂ ²Ãƒ ¢Ã‹â€  §u) and bilinear (c1 ÃŽÂ ±1+c2 ÃŽÂ ±2)à ¢Ã‹â€  § ÃŽÂ ²= c1( ÃŽÂ ±1à ¢Ã‹â€  § ÃŽÂ ²) + c2( ÃŽÂ ±2à ¢Ã‹â€  § ÃŽÂ ²) ÃŽÂ ±Ãƒ ¢Ã‹â€  §( c1 ÃŽÂ ²1+c2 ÃŽÂ ²2)= c1( ÃŽÂ ±Ãƒ ¢Ã‹â€  § ÃŽÂ ²1) + c2( ÃŽÂ ±Ãƒ ¢Ã‹â€  § ÃŽÂ ²2).   (Becca 2014) Chapter 1 Definition1.1 Let (A, m, ÃŽÂ ·) be an algebra over k and write mop (ab) = ab à ªÃ¢â‚¬Å" ¯ a, bà  µ A where mop=mà „Α,Α. Thus ab=ba à ªÃ¢â‚¬Å" ¯a, b à  µA. The (A, mop, ÃŽÂ ·) is the opposite algebra. Definition1.2 A co-algebra C is A vector space over K A map Ά: Cà ¢Ã¢â‚¬ ’C à ¢Ã… - C which is coassociative in the sense of à ¢Ã‹â€ ‘ (c(1)(1) à ¢Ã… -  c(1)(2) à ¢Ã… - c(2))= à ¢Ã‹â€ ‘ (c(1) à ¢Ã… -  c(2)(1) à ¢Ã… - c(2)c(2) )Â Â à ªÃ¢â‚¬Å" ¯ cà  µC (Άcalled the co-product) A map ÃŽÂ µ: Cà ¢Ã¢â‚¬ ’ k obeying à ¢Ã‹â€ ‘[ÃŽÂ µ((c(1))c(2))]=c= à ¢Ã‹â€ ‘[(c(1)) ÃŽÂ µc(2))] à ªÃ¢â‚¬Å" ¯ cà  µC ( ÃŽÂ µ called the counit) Co-associativity and co-unit element can be expressed as commutative diagrams as follow: Figure 1: Co-associativity map ΆFigure 2: co-unit element map ÃŽÂ µ Definition1.3 A bi-algebra H is An algebra (H, m ,ÃŽÂ ·) A co-algebra (H, Ά, ÃŽÂ µ) Ά,ÃŽÂ µ are algebra maps, where Hà ¢Ã… - H has the tensor product algebra structure (hà ¢Ã… - g)(hà ¢Ã… - g)= hhà ¢Ã… -  gg à ªÃ¢â‚¬Å" ¯h, h, g, g à  µH. A representation of Hopf algebras as diagrams is the following: Definition1.4 A Hopf Algebra H is A bi-algebra H, Ά, ÃŽÂ µ, m, ÃŽÂ · A map S : Hà ¢Ã¢â‚¬ ’ H such that à ¢Ã‹â€ ‘ [(Sh(1))h(2) ]= ÃŽÂ µ(h)= à ¢Ã‹â€ ‘ [h(1)Sh(2) ]à ªÃ¢â‚¬Å" ¯ hà  µH The axioms that make a simultaneous algebra and co-algebra into Hopf algebra is à „: Hà ¢Ã… - Hà ¢Ã¢â‚¬ ’Hà ¢Ã… -H Is the map à „(hà ¢Ã… -g)=gà ¢Ã… -h called the flip map à ªÃ¢â‚¬Å" ¯ h, g à  µ H. Definition1.5 Hopf Algebra is commutative if its commutative as algebra. It is co-commutative if its co-commutative as a co-algebra, à „Î†=Ά. It can be defined as S2=id. A commutative algebra over K is an algebra (A, m, ÃŽÂ ·) over k such that m=mop. Definition1.6 Two Hopf algebras H,H are dually paired by a map : H H à ¢Ã¢â‚¬ ’k if, =à ˆ,Άh>, =ÃŽÂ µ(h) g >=, ÃŽÂ µ(à †)= = à ªÃ¢â‚¬Å" ¯ à †, à ˆÃ  µ H and h, g à  µH. Let (C, Ά,ÃŽÂ µ) be a co-algebra over k. The co-algebra (C, Άcop, ÃŽÂ µ) is the opposite co-algebra. A co-commutative co-algebra over k is a co-algebra (C, Ά, ÃŽÂ µ) over k such that Ά= Άcop. Definition1.7 A bi-algebra or Hopf algebra H acts on algebra A (called H-module algebra) if: H acts on A as a vector space. The product map m: AAà ¢Ã¢â‚¬ ’A commutes with the action of H The unit map ÃŽÂ ·: kà ¢Ã¢â‚¬ ’ A commutes with the action of H. From b,c we come to the next action hà ¢Ã…  ³(ab)=à ¢Ã‹â€ ‘(h(1)à ¢Ã…  ³a)(h(2)à ¢Ã…  ³b), hà ¢Ã…  ³1= ÃŽÂ µ(h)1, à ªÃ¢â‚¬Å" ¯a, b à  µ A, h à  µ H This is the left action. Definition1.8 Let (A, m, ÃŽÂ ·) be algebra over k and is a left H- module along with a linear map m: Aà ¢Ã… -Aà ¢Ã¢â‚¬ ’A and a scalar multiplication ÃŽÂ ·: k à ¢Ã… - Aà ¢Ã¢â‚¬ ’A if the following diagrams commute. Figure 3: Left Module map Definition1.9 Co-algebra (C, Ά, ÃŽÂ µ) is H-module co-algebra if: C is an H-module Ά: Cà ¢Ã¢â‚¬ ’CC and ÃŽÂ µ: Cà ¢Ã¢â‚¬ ’ k commutes with the action of H. (Is a right C- co-module). Explicitly, Ά(hà ¢Ã…  ³c)=à ¢Ã‹â€ ‘h(1)à ¢Ã…  ³c(1)à ¢Ã‚ ¨Ã¢â‚¬Å¡h(2)à ¢Ã…  ³c(2), ÃŽÂ µ(hà ¢Ã…  ³c)= ÃŽÂ µ(h)ÃŽÂ µ(c), à ªÃ¢â‚¬Å" ¯h à  µ H, c à  µ C.  Definition1.10 A co-action of a co-algebra C on a vector space V is a map ÃŽÂ ²: Và ¢Ã¢â‚¬ ’Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V such that, (idà ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã‚ ²) à ¢Ã‹â€ ËÅ"ÃŽÂ ²=(레 ¢Ã‚ ¨Ã¢â‚¬Å¡ id )ÃŽÂ ²;  id =(ÃŽÂ µÃƒ ¢Ã‚ ¨Ã¢â‚¬Å¡id )à ¢Ã‹â€ ËÅ"ÃŽÂ ². Definition1.11 A bi-algebra or Hopf algebra H co-acts on an algebra A (an H- co-module algebra) if: A is an H- co-module The co-action ÃŽÂ ²: Aà ¢Ã¢â‚¬ ’ Hà ¢Ã‚ ¨Ã¢â‚¬Å¡A is an algebra homomorphism, where Hà ¢Ã‚ ¨Ã¢â‚¬Å¡A has the tensor product algebra structure. Definition1.12 Let C be co- algebra (C, Ά, ÃŽÂ µ), map ÃŽÂ ²: Aà ¢Ã¢â‚¬ ’ Hà ¢Ã‚ ¨Ã¢â‚¬Å¡A is a right C- co- module if the following diagrams commute. Figure 6:Co-algebra of a right co-module Sub-algebras, left ideals and right ideals of algebra have dual counter-parts in co-algebras. Let (A, m, ÃŽÂ ·) be algebra over k and suppose that V is a left ideal of A. Then m(Aà ¢Ã‚ ¨Ã¢â‚¬Å¡V)à ¢Ã… †V. Thus the restriction of m to Aà ¢Ã‚ ¨Ã¢â‚¬Å¡V determines a map Aà ¢Ã‚ ¨Ã¢â‚¬Å¡Và ¢Ã¢â‚¬ ’V. Left co-ideal of a co-algebra C is a subspace V of C such that the co-product Άrestricts to a map Và ¢Ã¢â‚¬ ’Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V. Definition1.13 Let V be a subspace of a co-algebra C over k. Then V is a sub-co-algebra of C if Ά(V)à ¢Ã… †Và ¢Ã‚ ¨Ã¢â‚¬Å¡V, for left co-ideal Ά(V)à ¢Ã… †Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V and for right co-ideal Ά(V)à ¢Ã… †Và ¢Ã‚ ¨Ã¢â‚¬Å¡C. Definition1.14 Let V be a subspace of a co-algebra C over k. The unique minimal sub-co-algebra of C which contains V is the sub-co-algebra of C generated by V. Definition1.15 A simple co-algebra is a co-algebra which has two sub-co-algebras. Definition1.16 Let C be co-algebra over k. A group-like element of C is c à  µC with satisfies, Ά(s)=sà ¢Ã‚ ¨Ã¢â‚¬Å¡s and ÃŽÂ µ(s)=1 à ªÃ¢â‚¬Å" ¯ s à  µS. The set of group-like elements of C is denoted G(C). Definition1.17 Let S be a set. The co-algebra k[S] has a co-algebra structure determined by Ά(s)=sà ¢Ã‚ ¨Ã¢â‚¬Å¡s and ÃŽÂ µ(s)=1 à ªÃ¢â‚¬Å" ¯ s à  µS. If S=à ¢Ã‹â€ †¦ we set C=k[à ¢Ã‹â€ †¦]=0. Is the group-like co-algebra of S over k. Definition1.18 The co-algebra C over k with basis {co, c1, c2,à ¢Ã¢â€š ¬Ã‚ ¦..} whose co-product and co-unit is satisfy by Ά(cn)= à ¢Ã‹â€ ‘cn-là ¢Ã‚ ¨Ã¢â‚¬Å¡cl and ÃŽÂ µ(cn)=ÃŽÂ ´n,0 for l=1,à ¢Ã¢â€š ¬Ã‚ ¦.,n and for all nà ¢Ã¢â‚¬ °Ã‚ ¥0. Is denoted by Pà ¢Ã‹â€ Ã… ¾(k). The sub-co-algebra which is the span of co, c1, c2,à ¢Ã¢â€š ¬Ã‚ ¦,cn is denoted Pn(k). Definition1.19 A co-matrix co-algebra over k is a co-algebra over k isomorphic to Cs(k) for some finite set S. The co-matrix identities are: Ά(ei, j)= à ¢Ã‹â€ ‘ei, là ¢Ã‚ ¨Ã¢â‚¬Å¡el, j ÃŽÂ µ(ei, j)=ÃŽÂ ´i, j à ¢Ã‹â€ â‚ ¬ i, j à  µS. Set Cà ¢Ã‹â€ †¦(k)=(0). Definition1.20 Let S be a non-empty finite set. A standard basis for Cs(k) is a basis {c i ,j}I, j à  µS for Cs(k) which satisfies the co-matrix identities. Definition1.21 Let (C, Άc, ÃŽÂ µc) and (D, ΆD, ÃŽÂ µD) be co-algebras over the field k. A co-algebra map f: Cà ¢Ã¢â‚¬ ’D is a linear map of underlying vector spaces such that ΆDà ¢Ã‹â€ ËÅ"f=(fà ¢Ã‚ ¨Ã¢â‚¬Å¡f)à ¢Ã‹â€ ËÅ" Άc and ÃŽÂ µDà ¢Ã‹â€ ËÅ"f= ÃŽÂ µc. An isomorphism of co-algebras is a co-algebra map which is a linear isomorphism. Definition1.22 Let C be co-algebra over the field k. A co-ideal of C is a subspace I of C such that ÃŽÂ µ (I) = (0) and Ά(ÃŽâ„ ¢) à ¢Ã… †Ià ¢Ã‚ ¨Ã¢â‚¬Å¡C+Cà ¢Ã‚ ¨Ã¢â‚¬Å¡I. Definition1.23 The co-ideal Ker (ÃŽÂ µ) of a co-algebra C over k is denoted by C+. Definition1.24 Let I be a co-ideal of co-algebra C over k. The unique co-algebra structure on C /I such that the projection à ₠¬: Cà ¢Ã¢â‚¬ ’ C/I is a co-algebra map, is the quotient co-algebra structure on C/I. Definition1.25 The tensor product of co-algebra has a natural co-algebra structure as the tensor product of vector space Cà ¢Ã… -D is a co-algebra over k where Ά(c(1)à ¢Ã‚ ¨Ã¢â‚¬Å¡d(1))à ¢Ã‚ ¨Ã¢â‚¬Å¡( c(2)à ¢Ã‚ ¨Ã¢â‚¬Å¡d(2)) and ÃŽÂ µ(cà ¢Ã‚ ¨Ã¢â‚¬Å¡d)=ÃŽÂ µ(c)ÃŽÂ µ(d) à ¢Ã‹â€ â‚ ¬ c in C and d in D. Definition1.26 Let C be co-algebra over k. A skew-primitive element of C is a cà  µC which satisfies Ά(c)= gà ¢Ã‚ ¨Ã¢â‚¬Å¡c +cà ¢Ã‚ ¨Ã¢â‚¬Å¡h, where c, h à  µG(c). The set of g:h-skew primitive elements of C is denoted by Pg,h (C). Definition1.27 Let C be co-algebra over a field k. A co-commutative element of C is cà  µC such that Ά(c) = Άcop(c). The set of co-commutative elements of C is denoted by Cc(C). Cc(C) à ¢Ã… †C. Definition1.28 The category whose objects are co-algebras over k and whose morphisms are co-algebra maps under function composition is denoted by k-Coalg. Definition1.29 The category whose objects are algebras over k and whose morphisms are co-algebra maps under function composition is denoted by k-Alg. Definition1.30 Let (C, Ά, ÃŽÂ µ) be co-algebra over k. The algebra (Cà ¢Ã‹â€ -, m, ÃŽÂ ·) where m= 레 ¢Ã‹â€ -| Cà ¢Ã‹â€ -à ¢Ã‚ ¨Ã¢â‚¬Å¡Cà ¢Ã‹â€ -, ÃŽÂ · (1) =ÃŽÂ µ, is the dual algebra of (C, Ά, ÃŽÂ µ). Definition1.31 Let A be algebra over the field k. A locally finite A-module is an A-module M whose finitely generated sub-modules are finite-dimensional. The left and right Cà ¢Ã‹â€ --module actions on C are locally finite. Definition1.32 Let A be algebra over the field k. A derivation of A is a linear endomorphism F of A such that F (ab) =F (a) b-aF(b) for all a, b à  µA. For fixed b à  µA note that F: Aà ¢Ã¢â‚¬ ’A defined by F(a)=[a, b]= ab- ba for all a à  µA is a derivation of A. Definition1.33 Let C be co-algebra over the field k. A co-derivation of C is a linear endomorphism f of C such that 레 ¢Ã‹â€ ËÅ"f= (fà ¢Ã‚ ¨Ã¢â‚¬Å¡IC + IC à ¢Ã‚ ¨Ã¢â‚¬Å¡f) à ¢Ã‹â€ ËÅ"Ά. Definition1.34 Let A and B ne algebra over the field k. The tensor product algebra structure on Aà ¢Ã‚ ¨Ã¢â‚¬Å¡B is determined by (aà ¢Ã‚ ¨Ã¢â‚¬Å¡b)(aà ¢Ã‚ ¨Ã¢â‚¬Å¡b)= aaà ¢Ã‚ ¨Ã¢â‚¬Å¡bb à ªÃ¢â‚¬Å" ¯ a, aà  µA and b, bà  µB. Definition1.35 Let X, Y be non-empty subsets of an algebra A over the field k. The centralizer of Y in X is ZX(Y) = {xà  µX|yx=xy à ªÃ¢â‚¬Å" ¯yà  µY} For y à  µA the centralizer of y in X is ZX(y) = ZX({y}). Definition1.36 The centre of an algebra A over the field Z (A) = ZA(A). Definition1.37 Let (S, à ¢Ã¢â‚¬ °Ã‚ ¤) be a partially ordered set which is locally finite, meaning that à ªÃ¢â‚¬Å" ¯, I, jà  µS which satisfy ià ¢Ã¢â‚¬ °Ã‚ ¤j the interval [i, j] = {là  µS|ià ¢Ã¢â‚¬ °Ã‚ ¤là ¢Ã¢â‚¬ °Ã‚ ¤j} is a finite set. Let S= {[i, j] |I, jà  µS, ià ¢Ã¢â‚¬ °Ã‚ ¤j} and let A be the algebra which is the vector space of functions f: Sà ¢Ã¢â‚¬ ’k under point wise operations whose product is given by (fà ¢Ã¢â‚¬ ¹Ã¢â‚¬ g)([i, j])=f([i, l])g([l, j]) ià ¢Ã¢â‚¬ °Ã‚ ¤là ¢Ã¢â‚¬ °Ã‚ ¤j For all f, g à  µA and [i, j]à  µS and whose unit is given by 1([I,j])= ÃŽÂ ´i,j à ªÃ¢â‚¬Å" ¯[I,j]à  µS. Definition1.38 The algebra of A over the k described above is the incidence algebra of the locally finite partially ordered set (S, à ¢Ã¢â‚¬ °Ã‚ ¤). Definition1.39 Lie co-algebra over k is a pair (C, ÃŽÂ ´), where C is a vector space over k and ÃŽÂ ´: Cà ¢Ã¢â‚¬ ’Cà ¢Ã‚ ¨Ã¢â‚¬Å¡C is a linear map, which satisfies: à „à ¢Ã‹â€ ËÅ"ÃŽÂ ´=0 and (ÃŽâ„ ¢+(à „à ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã¢â€ž ¢)à ¢Ã‹â€ ËÅ"(ÃŽâ„ ¢Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡Ãƒ „)+(ÃŽâ„ ¢Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡Ãƒ „)à ¢Ã‹â€ ËÅ" (à „à ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã¢â€ž ¢))à ¢Ã‹â€ ËÅ"(ÃŽâ„ ¢Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã‚ ´)à ¢Ã‹â€ ËÅ"ÃŽÂ ´=0 à „=à „C,C and I is the appropriate identity map. Definition1.40 Suppose that C is co-algebra over the field k. The wedge product of subspaces U and V is Uà ¢Ã‹â€  §V = Ά-1(Uà ¢Ã‚ ¨Ã¢â‚¬Å¡C+ Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V). Definition1.41 Let C be co-algebra over the field k. A saturated sub-co-algebra of C is a sub-co-algebra D of C such that Uà ¢Ã‹â€  §Và ¢Ã… †D, à ªÃ¢â‚¬Å" ¯ U, V of D. Definition1.42 Let C be co-algebra over k and (N, à  ) be a left co-module. Then Uà ¢Ã‹â€  §X= à  -1(Uà ¢Ã‚ ¨Ã¢â‚¬Å¡N+ Cà ¢Ã‚ ¨Ã¢â‚¬Å¡X) is the wedge product of subspaces U of C and X of N. Definition1.43 Let C be co-algebra over k and U be a subspace of C. The unique minimal saturated sub-co-algebra of C containing U is the saturated closure of U in C. Definition1.44 Let (A, m, ÃŽÂ ·) be algebra over k. Then, Aà ¢Ã‹â€ ËÅ"=mà ¢Ã‹â€ 1(Aà ¢Ã‹â€ -à ¢Ã‚ ¨Ã¢â‚¬Å¡Aà ¢Ã‹â€ - ) (Aà ¢Ã‹â€ ËÅ", Ά, ÃŽÂ µ) is a co-algebra over k, where Ά= mà ¢Ã‹â€ -| Aà ¢Ã‹â€ ËÅ" and ÃŽÂ µ=ÃŽÂ ·Ãƒ ¢Ã‹â€ -. ÃŽÂ ¤he co-algebra (Aà ¢Ã‹â€ ËÅ", Ά, ÃŽÂ µ) is the dual co-algebra of (A, m, ÃŽÂ ·). Also we denote Aà ¢Ã‹â€ ËÅ" by aà ¢Ã‹â€ ËÅ" and 레 ¢Ã‹â€ ËÅ"= aà ¢Ã‹â€ ËÅ"(1)à ¢Ã‚ ¨Ã¢â‚¬Å¡ aà ¢Ã‹â€ ËÅ"(2), à ªÃ¢â‚¬Å" ¯ aà ¢Ã‹â€ ËÅ" à  µ Aà ¢Ã‹â€ ËÅ". Definition1.45 Let A be algebra over k. An ÃŽÂ ·:ÃŽÂ ¾- derivation of A is a linear map f: Aà ¢Ã¢â‚¬ ’k which satisfies f(ab)= ÃŽÂ ·(a)f(b)+f(a) ÃŽÂ ¾(b), à ªÃ¢â‚¬Å" ¯ a, bà  µ A and ÃŽÂ ·, ÃŽÂ ¾ à  µ Alg(A, k). Definition1.46 The full subcategory of k-Alg (respectively of k-Co-alg) whose objects are finite dimensional algebras (respectively co-algebras) over k is denoted k-Alg fd (respectively    k-Co-alg fd). Definition1.47 A proper algebra over k is an algebra over k such that the intersection of the co-finite ideals of A is (0), or equivalently the algebra map jA:Aà ¢Ã¢â‚¬ ’(Aà ¢Ã‹â€ ËÅ")*, be linear map defined by jA(a)(aà ¢Ã‹â€ ËÅ")=aà ¢Ã‹â€ ËÅ"(a), a à  µA and aà ¢Ã‹â€ ËÅ"à  µAà ¢Ã‹â€ ËÅ". Then: jA:Aà ¢Ã¢â‚¬ ’(Aà ¢Ã‹â€ ËÅ")* is an algebra map Ker(jA) is the intersection of the co-finite ideals of A Im(jA) is a dense subspace of (Aà ¢Ã‹â€ ËÅ")*. Is one-to-one. Definition1.48 Let A (respectively C) be an algebra (respectively co-algebra ) over k. Then A (respectively C) is reflexive if jA:Aà ¢Ã¢â‚¬ ’(Aà ¢Ã‹â€ ËÅ")*, as defined before and jC:Cà ¢Ã¢â‚¬ ’(C*)à ¢Ã‹â€ ËÅ", defined as: jC(c)(c*)=c*(c), à ªÃ¢â‚¬Å" ¯ c*à  µC* and cà  µC. Then: Im(jC)à ¢Ã… †(C*)à ¢Ã‹â€ ËÅ" and jC:Cà ¢Ã¢â‚¬ ’(C*)à ¢Ã‹â€ ËÅ" is a co-algebra map. jC is one-to-one. Im(jC) is the set of all aà  µ(C*)* which vanish on a closed co-finite ideal of C*. Is an isomorphism. Definition1.49 Almost left noetherian algebra over k is an algebra over k whose co-finite left ideal are finitely generated. (M is called almost noetherian if every co-finite submodule of M is finitely generated). Definition1.50 Let f:Uà ¢Ã¢â‚¬ ’V be a map of vector spaces over k. Then f is an almost one-to-one linear map if ker(f) is finite-dimensional, f is an almost onto linear map if Im(f) is co-finite subspace of V and f is an almost isomorphism if f is an almost one-to-one and an almost linear map. Definition1.51 Let A be algebra over k and C be co-algebra over k. A pairing of A and C is a bilinear map  Π²: AÃÆ'-Cà ¢Ã¢â‚¬ ’k which satisfies, ÃŽÂ ²(ab,c)= ÃŽÂ ² (a, c(1))ÃŽÂ ² (b, c(2)) and ÃŽÂ ²(1, c) = ÃŽÂ µ(c), à ªÃ¢â‚¬Å" ¯ a, b à  µ A and       c à  µC. Definition1.52 Let V be a vector space over k. A co-free co-algebra on V is a pair (à ₠¬, Tco(V)) such that: Tco(V) is a co-algebra over k and à ₠¬: Tco(V)à ¢Ã¢â‚¬ ’T is a linear map. If C is a co-algebra over k and f:Cà ¢Ã¢â‚¬ ’V is a linear map,à ¢Ã‹â€ Æ’ a co-algebra map F: Cà ¢Ã¢â‚¬ ’ Tco(V) determined by à ₠¬Ãƒ ¢Ã‹â€ ËÅ"F=f. Definition1.53 Let V be a vector space over k. A co-free co-commutative co-algebra on V is any pair (à ₠¬, C(V)) which satisfies: C(V) is a co-commutative co-algebra over k and à ₠¬:C(V)à ¢Ã¢â‚¬ ’V is a linear map. If C is a co-commutative co-algebra over k and f: Cà ¢Ã¢â‚¬ ’V is linear map, à ¢Ã‹â€ Æ’ co-algebra map F:C à ¢Ã¢â‚¬ ’C(V) determined by à ₠¬Ãƒ ¢Ã‹â€ ËÅ"F=f.                  (Majid 2002, Radford David E) Chapter 2 Proposition (Anti-homomorphism property of antipodes) 2.1 The antipode of a Hopf algebra is unique and obey S(hg)=S(g)S(h), S(1)=1 and (Sà ¢Ã‚ ¨Ã¢â‚¬Å¡S)à ¢Ã‹â€ ËÅ"Άh=à „à ¢Ã‹â€ ËÅ"레 ¢Ã‹â€ ËÅ"Sh, ÃŽÂ µSh=ÃŽÂ µh, à ¢Ã‹â€ â‚ ¬h,g à ¢Ã‹â€ ˆH.             (Majid 2002, Radford David E) Proof Let S and S1 be two antipodes for H. Then using properties of antipode, associativity of à „ and co-associativity of Άwe get S= à „à ¢Ã‹â€ ËÅ"(Sà ¢Ã… -[ à „à ¢Ã‹â€ ËÅ"(Idà ¢Ã… -S1)à ¢Ã‹â€ ËÅ"Ά])à ¢Ã‹â€ ËÅ"Ά= à „à ¢Ã‹â€ ËÅ"(Idà ¢Ã… - à „)à ¢Ã‹â€ ËÅ"(Sà ¢Ã‚ ¨Ã¢â‚¬Å¡Idà ¢Ã… -S1)à ¢Ã‹â€ ËÅ"(Id à ¢Ã… -Ά)à ¢Ã‹â€ ËÅ"Ά= à „à ¢Ã‹â€ ËÅ"(à „à ¢Ã‚ ¨Ã¢â‚¬Å¡Id)à ¢Ã‹â€ ËÅ"(Sà ¢Ã‚ ¨Ã¢â‚¬Å¡Idà ¢Ã… -S1)à ¢Ã‹â€ ËÅ"(레 ¢Ã… -Id)à ¢Ã‹â€ ËÅ"Ά= à „à ¢Ã‹â€ ËÅ"( [à „à ¢Ã‹â€ ËÅ"(Sà ¢Ã‚ ¨Ã¢â‚¬Å¡Id)à ¢Ã‹â€ ËÅ"Ά]à ¢Ã‚ ¨Ã¢â‚¬Å¡S1)à ¢Ã‹â€ ËÅ" Ά=S1. So the antipode is unique. Let Sà ¢Ã‹â€ -id=ÃŽÂ µs idà ¢Ã‹â€ -S=ÃŽÂ µt To check that S is an algebra anti-homomorphism, we compute S(1)= S(1(1))1(2)S(1(3))= S(1(1)) ÃŽÂ µt (1(2))= ÃŽÂ µs(1)=1, S(hg)=S(h(1)g(1)) ÃŽÂ µt(h(2)g(2))= S(h(1)g(1))h(2) ÃŽÂ µt(g(2))S(h(3))=ÃŽÂ µs (h(1)g(1))S(g(2))S(h(2))= S(g(1)) ÃŽÂ µs(h(1)) ÃŽÂ µt (g(2))S(h(2))=S(g)S(h), à ¢Ã‹â€ â‚ ¬h,g à ¢Ã‹â€ ˆH and we used ÃŽÂ µt(hg)= ÃŽÂ µt(h ÃŽÂ µt(g)) and ÃŽÂ µs(hg)= ÃŽÂ µt(ÃŽÂ µs(h)g). Dualizing the above we can show that S is also a co-algebra anti-homomorphism: ÃŽÂ µ(S(h))= ÃŽÂ µ(S(h(1) ÃŽÂ µt(h(2)))= ÃŽÂ µ(S(h(1)h(2))= ÃŽÂ µ(ÃŽÂ µt(h))= ÃŽÂ µ(h), Ά(S(h))= Ά(S(h(1) ÃŽÂ µt(h(2)))= Ά(S(h(1) ÃŽÂ µt(h(2))à ¢Ã‚ ¨Ã¢â‚¬Å¡1)= Ά(S(h(1) ))(h(2)S(h(4))à ¢Ã‚ ¨Ã¢â‚¬Å¡ ÃŽÂ µt (h(3))= Ά(ÃŽÂ µs(h(1))(S(h(3))à ¢Ã‚ ¨Ã¢â‚¬Å¡S(h(2)))=S(h(3))à ¢Ã‚ ¨Ã¢â‚¬Å¡ ÃŽÂ µs(h(1))S(h(2))=S(h(2))à ¢Ã‚ ¨Ã¢â‚¬Å¡ S(h(1)). (New directions) Example2.2 The Hopf Algebra H=Uq(b+) is generated by 1 and the elements X,g,g-1 with relations gg-1=1=g-1g and g X=q X g, where q is a fixed invertible element of the field k. Here ΆX= Xà ¢Ã‚ ¨Ã¢â‚¬Å¡1 +g à ¢Ã‚ ¨Ã¢â‚¬Å¡ X, Άg=g à ¢Ã‚ ¨Ã¢â‚¬Å¡ g, Άg-1=g-1à ¢Ã‚ ¨Ã¢â‚¬Å¡g-1, ÃŽÂ µX=0, ÃŽÂ µg=1=ÃŽÂ µ g-1, SX=- g-1X, Sg= g-1, S g-1=g. S2X=q-1X. Proof We have Ά, ÃŽÂ µ on the generators and extended them multiplicatively to products of the generators. ΆgX=(Άg)( ΆX)=( gà ¢Ã‚ ¨Ã¢â‚¬Å¡g)( Xà ¢Ã‚ ¨Ã¢â‚¬Å¡1 +gà ¢
Monday, August 5, 2019
Children rights of protection and participation
Children rights of protection and participation Introduction This research paper focuses on the childrens rights and the participation that the children have in their implementation. It is every childs right to have a say on the things that affects its life. However, some children are either too young or too truant to make solid decisions. This research paper discusses on these rights and to what extent that the children can decide on their way of life. Child Rights on decision making Children have the same rights as adults. As a vulnerable group, children have particular rights that recognize their special need for protection and also that help them develop their full potential. Children are not helpless objects of charity or a property of their parents. They are recognized as human beings and the subjects of their own rights. A child is an individual, a family and community member with rights and appropriate responsibilities for his or her age and development stage. Children should enjoy the basic qualities of life as rights rather than privileges accorded to them (CRC, 2006) Every child whether a boy or girl irrespective of age is unique and has value importance as a person with a right for their human dignity to be respected. It has a right to have a say in all decisions and matters that concern him or her, to be listened to and his or her opinion taken seriously (CRIN, 2002). This will enhance understanding and mutual respect between children and adults. The participation of children protects them more effectively from abuse and exploitation. When we understand and respect childrens own experiences, we are able to create better protection mechanisms and the children themselves can act as active agents in their own protection. This helps to develop and build recognition of children as independent bearers of rights with a sense of identity and a positive implication for their self esteem (CRIN, 2002). Childrens rights are defined in a wide spectrum of economic, civil, political and social rights. These rights have been labeled as the right to protection and right to empowerment. Some of these rights are: Right to provision: Children have a right to be provided with a good standard of living, education and services, health care and a right to play. These include access to schooling, a balanced diet and a warm bed to sleep in. They also have a right to be protected from neglect, abuse, discrimination and exploitation (CRC, 2006) Children also have a right to participation. They have a right to their own programs and services and to take part in them. This includes decision making and involvement in libraries. Some rights allow children to grow up healthy and free. This include; Freedom of speech, Freedom of thought, Freedom from fear, Freedom of choice and to make decisions and Ownership over ones body. The United Nations Convention on the Rights of the Child (CRC) provides a framework for addressing not only rights to child protection care and adequate provision, but also for participation. A child who is capable of making his or her own views shall be assured by the parties of the state a right to express them freely (CRC, 2006) The views of the child are given weight according to the maturity and age of the child. A child can participate in the sense of taking part or being present or participate in the sense of knowing that ones actions are taken note of and may be acted upon. The extent to childrens participation will vary between and within societies (CRC, 2006) There has been a clash between the childrens protection and participation rights. Protection rights protect the children against exploitation and abuse for the best interest of the child while in participatory rights; children take part in decisions concerning their lives and a right to freedom of conscious and to hold an opinion. Adults and their childrens views may not always coincide. Many childrens wishes and views are ignored by the adults for the best interest of the child. For instance; (CRC) Every child is entitled to acquire a name and a nationality. All children registration should be upon birth. The childs name, birth date and parents names are recorded. When a child is given a name at birth, he or she is not given an opportunity to choose a name for himself or herself. The parents do this for the best interests of the child (CRC). The child may however, decide to change its name upon reaching the age of maturity. In this case the child is denied a right to participate in choosing its name at first but at later stages of development; the same child can participate in the same by changing to its desired name (CRC). Â Â Â Â Â A child has a right to be protected from all forms of punishment or discrimination regardless of their age, race, sex, religion, status, their expressed opinions, activities and beliefs of the family members. As much as a child has a right to religion, to express their opinion, or equality regardless of their age, these are sometimes restricted by their parents or legal guardians. For instance, a child is not at liberty to join a religion cult without the parents interference. It is not because the child is denied its freedom to worship but its for the best interest of the child (CRC). Children also have a right to get and share information and to express them. In exercising this right, they are supposed to be careful not to damage themselves or the freedoms, rights and reputations of others. They may share information through talking, writing or drawing. A childs wishes may be ignored if it is for the best of the child. For instance, a child may be denied the right to express dislike or hatred towards a particular person by hauling insults at the person. On the same, the child may be restricted on the manner of expression. For instance through shouting or screaming or demanding instead of asking politely (CRC). Children have a right of association. They have a right to meet and to join groups and organizations. Not all groups joined by children are acceptable by their parents or guardians; this brings a clash between the childrens right of association and prevention of joining them. Children are also restricted from joining into these groups if they stop other people from enjoying their rights. For instance a rioting group which will probably cause peace disturbance to others, or an outlawed group will not be acceptable that the children join (CRC). Children have a right to privacy. They are protected from attacks in their way of life, their name, families and homes. However, their way of life can be invaded by their parents or guardians if its for their best interests, for instance, when parents suspect that the child may be involved in drugs or other unlawful activities they may be forced to ransack the childs room or personal effects (CRC). Its a right for the children to access information. This they get through the radio, newspapers, television, internet and childrens books. They have a right to choose what kind of information they would like to access and in which manner. However, not all information is suitable or helpful to them (CRC). Most of the information provided by the mass media especially the radio, television and internet is unsuitable to children. It may contain violence, obscenity or strong language. Since these are harmful to the children they dont have a right over them and so their parents or guardians have to protect the children from such by deciding on what is good or bad for them. The parents also have to protect on what their children browse on the internet since they can access pornography or sites with violence which are harmful to the child (CRC). It is a childs right to live with its parents. The child can however be separated from the parents when the conditions are not favorable for the child. Such conditions may be neglect or abuse by the parents or separation by the parents hence the state has to decide on which parent has to live with the child. If the child has no parents the state decides on a home or an institution for the child to live. In this case the child may not have much of a say in the choice of who to live with. Sometimes children run away from their birth homes to live with their relatives or even live on the streets. This may be as a result of poverty or rebellion. The best interests of the child are considered first before the child is taken back to its parents home (CRC). Conclusion Children have a right to participate in decisions that shape their life and therefore should be given a chance to express their own opinion. However, this right is only exercised considering the maturity and the best interest of the child. Not all decisions that a child makes will be supported by their parents or guardians. For instance, a child cannot make a decision not to go school. For the best interests of the child the child will be forced to attend school. References CRC (Convention on the Rights of the Child). (2006). Retrieved on February 25, 2010 from: http://www.unicef.org/crc/index_30168.html CRC (The Convention on the Rights of the Child). (n.d). Retrieved on February 23, 2010 from: http://www.unicef.org/crc/files/Participation.pdf CRIN (Child rights information networks). (2002). Retrieved on February 23, 2010 from: http://www.crin.org/docs/resources/publications/childrenaspartners/CAP-outcomes-Mtg%203.pdf
Sunday, August 4, 2019
An Examination of Factors Contributing to Identity Development and Adj
The process of adopting a child internationally is lengthy, costly, and both physically and emotionally exhausting.Since it takes so much to adopt, only a small number of Americans can and do; mostly middle- and upper-middle class couples.Therefore, many internationally adopted children grow up in an environment with ready access to resources, with adults who are able to support them financially and emotionally.In such narrow socioeconomic circumstances, the question then arises: What accounts for those internationally adopted children and youth who do not adjust well?What factors contribute to the normal, healthy development of these individuals?Examining international adoption also brings up this point:Is there really a significant difference between the development of trans-racial, internationally adopted children and their peers who are raised by their biological parents?In order to try and answer these questions, this essay will look at a number of studies from several countries , including America, which cover a range of influences: from secure attachment to the pre-adoption situation, to location, to patterns of normal cognitive development which may negatively impact the emerging identity of a trans-racial adoptee. In infancy, researchers study attachment patterns between mother and infant and determine if they are securely attached.Overall, infants who are securely attached tend to cry when their mother leaves, but are happy to see her when she comes back (Papalia, Olds, & Feldman, p. 212). How do internationally adopted, trans-racial infants compare?Juffer and Rosenbloom (1997)?s Netherlands study found that there was no significant difference in attachment between infant-adopted mother and infant-birth mother dyads (... ... passport and inability to speak their birth language. Their development is often accompanied by feelings of anger, frustration, and confusion, which they are confronted with in college, and subsequently address. The literature reviewed in this paper examines factors of attachment, the pre-adoption situation, parenting styles, normal development in middle childhood, the development of ethnic identity, place, and the search for birth origins, in the ways that they impact the adoptees? identity development. Further research could examine the influence of a sibling cohort adopted from the same country as the adoptee, long-term effects of an orphanage stay into adolescence and adulthood [using the People?s Republic as an example], and mono-zygotic, trans-racial twin pairs reared apart, in an effort to control the factors that contribute to a negative sense of identity.
Saturday, August 3, 2019
Acupuncture :: essays research papers
Acupuncture      Acupuncture is a Chinese medical practice that treats illness and provides local anesthesia by the insertion of needles at predetermined sites of the body. Acupuncture may also follow many other forms. The word acupuncture comes from the Latin word acus, meaning needle, and pungere, meaning puncture. The Chinese call acupuncture Chen Chiu.      On doing my research over acupuncture I used many different sources. I got most of my information from the Internet. I discovered a large acupuncture clinic in Houston and contacted them over the phone. I never really realized that acupuncture was used so much in this country, but there are many places acupuncture is used in the United States.      Acupuncture is used in the treatment of a wide variety of medical problems. It is used for ear, nose, and throat disorders, respiratory disorders, Gastrointestinal disorders, Eye disorders, and Neurological and Muscular disorders. The needles used in acupuncture are usually only inserted from 1/4 to 1 inch deep into the skin. There is usually no pain in acupuncture. Usually if any pain it is only mild. Most of the needles now used in acupuncture are disposable needles. Acupuncture does not always only involve needles. They may also use other methods such as moxibustion, cupping, electronic stimulation, magneotherapy and various types of massage. There are also many different styles of acupuncture practiced all over the world.      There are many things to consider when choosing an acupuncturist. Acupuncture is a licensed and regulated healthcare profession in about half the states in the United States. There are many acupuncture practices which are not certified, so when choosing one some research is required. If you get acupuncture usually between five to fifteen sessions are required, depending on the severity of the complaint. Many acute conditions only require a single treatment. The main thing to remember when receiving acupuncture is to simply relax. After acupuncture treatments much of the pain may be gone after the first treatment, or in some cases it takes more. In some cases the pain may become worse, this is known as the rebound effect.      The clinic I got most of my information from is a clinic in Houston. They specialize in Acupuncture Therapy for diseases and conditions such as acute and chronic pain, degenerative diseases, arthritis, M.S., post-stroke, migraine
Friday, August 2, 2019
Fairies :: essays research papers
FAIRIES ARE EVERYWHERE! Â Â Â Â Â Fairies are magical creatures, usually very much like human beings. But they can do many things that humans cannot do. Most fairies can make themselves invisible. Many can travel in an instant anywhere they want to go, even very great distances. Some can change their shapes; they might look like cats, or birds, or dogs, or any other animal. Some of them live for many hundreds of years; others (Like with Tinker Bell From Peter Pan) live forever. Many fairies like to play tricks on human beings; others like to help them. Fairies come in all sizes and shapes as well. They might be ugly, humpbacked little creatures, like the trolls or gnomes that the people tell about in Denmark, Sweden, and Germany. Both trolls and gnomes are supposed to guard treasures. Trolls live in dark caves, and gnomes make their homes underground. Some fairies are handsome, for example, the pixies of Wales, or the goldenhaired white elves of the Scandinavian countries. Some fairies are giants, others are less than two feet tall. Some have special shapes. Example are mermaids and mermen, human above the waist but with the lower part of their bodies like fish. They live in an underwater world of splendor. Beautiful mermaids often lure sailors to their destruction, or cause shipwrecks. The Scandinavians believed in a river spirit that looked like a man above the water and like a horse below. Â Â Â Â Â Most fairies live in fairyland, where some strange things are ALWAYS happening. They live together ruled by a king and queen, whose names are Oberon and Titania. Some people think that the ruler of Fairyland is Queen Mab. Â Â Â Â Â Not all fairies live in fairyland, however. Some live alone as the guardians of certain places. The Lorelei of Germany is a beautiful woman with long golden hair. She stays on a special rock on the right bank of the Rhine River. Â Â Â Â Â Many kinds of fairies like to play tricks on human beings. Sometimes they tie knots in the manes of horses at night, and ride them till the horses are tired out. A horseshoe nailed to the stable door will keep these fairies away. If the maid is lazy and does not clean the house carefully, the fairies will pinch her while she sleeps. The pixies of Wales are especially troublesome to human beings. Some pixies lead travelers the wrong way. Others call to a lost person in the voice of his friend. When he follows the voices, he finds nobody there. The pixies like to hid things in houses, and to blow out candles so that the people of the
Thursday, August 1, 2019
Archaeology Essays – Archaeological Excavation
Can archeological digging of sites non under immediate menace of development or eroding be justified morally? Explore the pros and cons of research ( as opposed to deliver and salve ) digging and non-destructive archeological research methods utilizing specific illustrations.Many people believe that archeology and archeologists are chiefly concerned with digging – with delving sites. This may be the common public image of archeology, as frequently portrayed on telecasting, although Rahtz ( 1991, 65-86 ) has made clear that archaeologists in fact do many things besides excavate. Drewett ( 1999, 76 ) goes farther, noticing that ‘it must ne'er be assumed that digging is an indispensable portion of any archeological fieldwork’ . Excavation itself is a dearly-won and destructive research tool, destructing the object of its research forever ( Renfrew and Bahn 1996, 100 ) . Of the present twenty-four hours it has been noted that instead than wanting to delve every site t hey know about, the bulk of archeologists work within a preservation moral principle that has grown up in the past few decennaries ( Carmichaelet Al. 2003, 41 ) . Given the displacement to excavation taking topographic point largely in a deliverance or salvage context where the archeology would otherwise face devastation and the inherently destructive nature of digging, it has become appropriate to inquire whether research digging can be morally justified. This essay will seek to reply that inquiry in the affirmatory and besides explore the pros and cons of research digging and non-destructive archeological research methods. If the moral justification of research digging is questionable in comparing to the digging of threatened sites, it would look that what makes deliverance digging morally acceptable is the fact that the site would be lost to human cognition if it was non investigated. It seems clear from this, and seems widely accepted that digging itself is a utile fact-finding technique. Renfrew and Bahn ( 1996, 97 ) suggest that digging ‘retains its cardinal function in fieldwork because it yields the most dependable grounds archeologists are interested in’ . Carmichaelet Al. ( 2003, 32 ) note that ‘excavation is the agencies by which we entree the past’ and that it is the most basic, specifying facet of archeology. As mentioned above, digging is a dearly-won and destructive procedure that destroys the object of its survey. Bearing this in head, it seems that it is possibly the context in which digging is used that has a bearing on whether or non it is morally justifiable. If the archeology is bound to be destroyed through eroding or development so its devastation through digging is vindicated since much informations that would otherwise be lost will be created ( Drewett 1999, 76 ) . If rescue digging is justifiable on the evidences that it prevents entire loss in footings of the possible informations, does this mean that research digging is non morally justifiable because it is non merely ‘making the best usage of archeological sites that must be consumed’ ( Carmichaelet Al. 2003, 34 ) ? Many would differ. Critics of research digging may indicate out that the archeology itself is a finite resource that must be preserved wherever possible for the hereafter. The devastation of archeological grounds through unneeded ( ie non-emergency ) digging denies the chance of research or enjoyment to future coevalss to whom we may owe a tutelary responsibility of attention ( Rahtz 1991, 139 ) . Even during the most responsible diggings where detailed records are made, 100 % recording of a site is non possible, doing any non-essential digging about a willful devastation of grounds. These unfavorable judgments are non entirely valid though, and surely the latter ho lds true during any digging, non merely research diggings, and certainly during a research undertaking there is likely to be more clip available for a full recording attempt than during the statutory entree period of a deliverance undertaking. It is besides debateable whether archeology is a finite resource, since ‘new’ archeology is created all the clip. It seems ineluctable though, that single sites are alone and can endure devastation but although it is more hard and possibly unwanted to deny that we have some duty to continue this archeology for future coevalss, is it non besides the instance that the present coevalss are entitled to do responsible usage of it, if non to destruct it? Research digging, best directed at replying potentially of import research inquiries, can be done on a partial or selective footing, without upseting or destructing a whole site, therefore go forthing countries for later research workers to look into ( Carmichaelet Al. 2003, 41 ) . Furt hermore, this can and should be done in concurrence with non-invasive techniques such as aerial picture taking, land, geophysical and chemical study ( Drewett 1999, 76 ) . Continued research digging besides allows the pattern and development of new techniques, without which such accomplishments would be lost, forestalling future digging technique from being improved. An first-class illustration of the benefits of a combination of research digging and non-destructive archeological techniques is the work that has been done, despite expostulations, at the Anglo-saxon graveyard at Sutton Hoo, in eastern England ( Rahtz 1991 136-47 ; Renfrew and Bahn 1996, 98-99 ) . Excavation originally took topographic point on the site in 1938-39 uncovering many hoarded wealths and the feeling in sand of a wooden ship used for a burial, though the organic structure was non found. The focal point of these runs and those of the sixtiess were traditional in their attack, being concerned with the gap of burial hills, their contents, dating and placing historical connexions such as the individuality of the residents. In the 1980s a new run with different purposes was undertaken, directed by Martin Carver. Rather than get downing and stoping with digging, a regional study was carried out over an country of some 14ha, assisting to put the site in its local context. Electr onic distance measurement was used to make a topographical contour map prior to other work. A grass expert examined the assortment of grass species on-site and identified the places of some 200 holes dug into the site. Other environmental surveies examined beetles, pollen and snails. In add-on, a phosphate study, declarative mood of likely countries of human business, corresponded with consequences of the surface study. Other non-destructive tools were used such as metal sensors, used to map modern trash. A proton gaussmeter, fluxgate gradiometer and dirt electric resistance were all used on a little portion of the site to the E, which was subsequently excavated. Of those techniques, electric resistance proved the most enlightening, uncovering a modern ditch and a dual palisade, every bit good as some other characteristics ( see comparative illustrations in Renfrew and Bahn 1996, 99 ) . Excavation subsequently revealed characteristics that had non been remotely detected. Electric re sistance has since been used on the country of the hills while soil-sounding radio detection and ranging, which penetrates deeper than electric resistance, is being used on the hills themselves. At Sutton Hoo, the techniques of geophysical study are seen to run as a complement to digging, non simply a preliminary nor yet a replacing. By trialling such techniques in concurrence with digging, their effectivity can be gauged and new and more effectual techniques developed. The consequences at Sutton Hoo suggest that research digging and non-destructive methods of archeological research remain morally justifiable. However, merely because such techniques can be applied expeditiously does non intend that digging should be the precedence nor that all sites should be excavated, but such a scenario has ne'er been a likely one due to the usual restraints such as support. Besides, it has been noted above that there is already a tendency towards preservation. Continued research digging at celebrated sites such as Sutton Hoo, as Rahtz notes ( 1991, 140-41 ) , is justified since it serves professedly to develop archeological pattern itself ; the physical remains, or forms in the landscape can be and are restored to their former visual aspect with the fillip of being better understood, more educational and interesting ; such alien and particular sites capture the imaginativeness of the populace and the media and raise the profile of archeology as a whole. There are other sites that could turn out every bit good illustrations of morally justifiable long term research archeology, such as Wharram Percy ( fo r which see Rahtz 1991, 148-57 ) . Progressing from a straightforward digging in 1950, with the purpose of demoing that the earthworks represented mediaeval edifices, the site grew to stand for much more in clip, infinite and complexness. Techniques used expanded from digging to include study techniques and aerial picture taking to put the small town into a local context. In decision, it can be seen that while digging is destructive, there is a morally justifiable topographic point for research archeology and non-destructive archeological techniques: digging should non be reduced merely to deliver fortunes. Research digging undertakings, such as Sutton Hoo, have provided many positive facets to the development of archeology and cognition of the past. While digging should non be undertaken lightly, and non-destructive techniques should be employed in the first topographic point, it is clear that every bit yet they can non replace digging in footings of the sum and types of informations provided. Non-destructive techniques such as environmental sampling and electric resistance study have, provided important complementary informations to that which digging provides and both should be employed. BibliographyCarmichael, D.L. , Lafferty III, R.H. and Molyneaux, B.L. 2003.Excavation.Walnut Creek and Oxford: Altamira Press.Drewett, P.L. 1999.Field Archaeology: An Introduction. London: UCL Press.Rahtz, P. 1991.Invitation to Archaeology. 2nd edition. Oxford: Blackwell.Renfrew, C. and Bahn, P.1996.Archeology: Theories, Methods and Practice. 2nd edition. London: Thames & A ; Hudson.
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