Airo national research journal



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Objective

The main objective of this thesis is to get the current global acceptance of British and American English in the international context of communication mainly in corporate world. Through this work we understand the major differences and the way of acceptance and understand both the languages. Through review we got to know how and where with the differences these languages are being implemented and accepted with the lee.

Hypothesis

At present, the English language situates itself at a transitional point between two worlds: o the old world where all other usages than standard – informal speech, regional dialect – were considered to be inferior or corrupt, and thus excluded from serious consideration, and o the new world where informal and nonstandard usage is achieving a new presence and respectability within society.

American English is increasingly becoming a minority dialect of world English, and, although it has exercised a greater influence on world English than any other variety, it seems to slowly lose its status as the dominant version. A good example in this direction is the situation of the Internet.

Conclusion  

The conclusions are drawn in the theory and last chapters. The summary of the findings comes first, focusing on the fact that British English has been influenced by American English since the 17th century. Our research shows that this influence has been present in different fields of activity. In order to provide a detailed view of the Americanisms that entered the British English vocabulary, we classified the 793 words and phrases under two headings: everyday vocabulary (480 terms) and functional varieties (313 terms).

In our opinion the whole world witnesses the increasing unification of English towards the status of a world language, as English has some kind of special administrative status in over seventy countries, it achieves a special role when it is made a priority in a country’s foreign-language teaching policy, and communication in the worlds of business and education is expected to be conducted in English. The final conclusion is that the influence of American English on British English was much greater in the beginning, but nowadays words and phrases are filtered and everything useless, pompous, or simply fashion is to be eliminated. The more necessary an item proves to be, the more quickly it will be absorbed into the language and it will accommodate in such a manner that will not be perceived as an intruder anymore

References  


  Airo Article Series 2006

  Airo Article Series 2007

Airo Article Series 2008

AIEER Research Press 2009

Aruna & Archana: Communication Realities.

Chapman, James A. Grammar and Composition IV. 3d ed. Pensacola: A Beka Book, 2002.

 "The names of sports teams, on the other hand, are treated as plurals, regardless of the form of that name.

The American Heritage Dictionary of the English Language: Fourth Edition. 2000

http://www.perfectyourenglish.com/writing/american-and-british-usage-2.htm "Conditional would is sometimes used in both clauses of an if-sentence. This is common in spoken American English."  

 
An Introduction to Grobner Bases

      Submitted by Rajwinder Kaur      Research Scholar Mathematics

Introduction

One of the purposes of research paper is to show that, in many cases Gröbner bases can be used to find solutions for formal verification problems. In this way, this forms a good complement to existing techniques, like simulators and SAT-solver, which are suited for identification of counter examples (falsification).

A significant advantage is, that Gröbner bases provide a mathematically proven systematic and very flexible tool while many engineering solutions inside commercial verification tools rely on ad hoc heuristics for special cases. However, the success of Gröbner basis methods, reported in this paper, could not be achieved with existing generic Gröbner basis algorithms and implementations.

A new efficient algorithm for computing Gröbner bases which is to avoid as much intermediate computation as possible, the algorithm computes successive truncated Gröbner bases and it replaces the classical polynomial reduction found in the Buchberger algorithm by the simultaneous reduction of several polynomials. This powerful reduction mechanism is achieved by means of a symbolic precomputation and by extensive use of sparse linear algebra methods. Current techniques in linear algebra used in Computer Algebra are reviewed together with other methods coming from the numerical field. Some previously untractable problems (Cyclic 9) are presented as well as an empirical comparison of a first implementation of this algorithm with other well known programs. This comparison pays careful attention to methodology issues. All the benchmarks and CPU times used in this paper are frequently updated and available on a Web page. Even though the new algorithm does not improve the worst case complexity it is several times faster than previous implementations both for integers and modulo p computations. a new efficient algorithm for computing Gröbner bases.

 

Review of literature

All operations related to Gröbner bases require the choice of a total order on the monomials, with the following properties of compatibility with multiplication. For all monomials MNP,

1.     m<n \longleftrightarrow mp<np

2.     m<mp .

A total order satisfying these condition is sometimes called an admissible ordering.

These conditions imply Noetherianity, which means that every strictly decreasing sequence of monomials is finite.

Although Gröbner basis theory does not depend on a particular choice of an admissible monomial ordering, three monomial orderings are specially important for the applications:

        Lexicographical ordering, commonly called lex or plex (for pure lexical ordering).

        Total degree reverse lexicographical ordering, commonly called degrevlex.

        Elimination orderinglexdeg.

Gröbner basis theory was initially introduced for the lexicographical ordering. It was soon realised that the Gröbner basis for degrevlex is almost always much easier to compute, and that it is almost always easier to compute a lex Gröbner basis by first computing the degrevlex basis and then using a "change of ordering algorithm". When elimination is needed, degrevlex is not convenient; both lex and lexdeg may be used but, again, many computations are relatively easy with lexdeg and almost impossible with lex.

Once a monomial ordering is fixed, the terms of a polynomial (product of a monomial with its nonzero coefficient) are naturally ordered by decreasing monomials (for this order). This makes the representation of a polynomial as an ordered list of pairs coefficient–exponent vector a canonical representation of the polynomials. The first (greatest) term of a polynomial p for this ordering and the corresponding monomial and coefficient are respectively called the leading termleading monomial and leading coefficient and denoted, in this article, lt(p), lm(p) and lc(p).



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