iosr-Jm   Volume-3 ~ Issue-4

Abstract :Presently angular measurements are made using protractors having a normal accuracy of 1 or at the most ½ . The scale of chords, as linear scale, can be constructed for measurement and construction of angles having accuracy equal to that of a normal protractor. This paper presents a new concept of construction of a diagonal scale of chords that can have an accuracy of 10 or less, and thus, using diagonal scale of chords, angles can be constructed or measured to a higher accuracy which is not possible using normal size protractors.
Keywords - Angle measurements, Protractor, Scale of chords, Diagonal scale of chords

[1] A. M. Chandra and Satish Chandra, Engineering Graphics (Narosa Publishing House, New Delhi, 2003)

Abstract :Let G = (V, E) be a simple graph. A set S  V is a dominating set of G, if every vertex in V-S is adjacent to atleast one vertex in S. Let 2 n C be the square of the Cycle n C and let 2 ( , ) n D C i denote the family of all dominating sets of 2 n C with cardinality i. Let 2 ( , ) n d C i = | 2 ( , ) n D C i |. In this paper, we obtain a recursive formula for 2 ( , ) n d C i . Using this recursive formula, we construct the polynomial, 2 ( , ) n D C x = 2 5 ( , ) n i n i n   d C i x      , which we call domination polynomial of 2 n C and obtain some properties of this polynomial.
.Keywords:domination set, domination number, domination polynomials.

[1]. S.Alikhani and Y.H.Peng, Introduction to domination polynomial of a graph. arXiv:0905.2251v1[math.CO] 14 May 2009.
[2]. S.Alikhani and Y.H.Peng, 2009, Domination sets and Domination Polynomials of paths, International journal of Mathematics and
Mathematical Sciences. Article ID 542040.
[3]. G.Chartand and P.Zhang, Introduction to Graph Theory, McGraw-Hill, Boston, Mass, USA, 2005.
[4]. T.W.Haynes ,S.T.hedetniemi,and P.J.Slater, Fundamental of Domination in graphs,vol.208 of Monographs and Textbooks in Pure
and Applied Mathematics, Marcel Dekker, New York,NY,USA,1998.
[5]. S.Alikhani and Y.H.Peng, Domination sets and Domination Polynomials of cycles, arXiv: 0905.3268v [math.CO] 20 May 2009.
[6]. A.Vijayan and K.Lal Gipson, Domination sets and Domination Polynomials of Square paths, accepted in "Open Access journal of
Discrete Mathematics." – USA.

Abstract: This paper is concerned with the determination of the distribution of temperature and displacement in a thin semi-infinite elastic rod when its free end is subjected to periodic heating. It has been pointed out by P.Chadwick(1960) that the rigorous approach,i.c. the approach by way of the coupled equations, to the thermal boundary value problem. In this paper the one dimensional problem of the periodic heating of the free surface of a semi-infinite rod has been solved by a perturbation procedure, approximations upto the first order being retained.

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Abstract :In this paper we prove two fixed point theorems in topological vector space valued cone metric spaces (briefly TVS-CMS). To that end we introduce the concept of complete topological algebra cone (briefly CTA cone). Our theorems are generalizations of corresponding theorems in [8] and [13]. The paper also gives answers to the open problems posed in [15]. Finally we give an application of our first theorem. AMS Mathematics Subject Classification (2010): 47H10, 54H25, 46A40
Keywords -topological vector space, ordered topological vector space, algebra over a field, topological algebra over a field, topological vector space valued cone metric space, scalarization function, CTA cone

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Abstract :By using the generalized Hirrota bilinear operators a kind of bilinear differential equations is established and examined when the linear super position principle can apply to the resulting generalized bilinear differential equations. Examples of generalized bilinear differential equations together with an algorithm using weights are computed using a 1+1 and 2+1 dimensional equations in order to shed more lights on the presented general scheme for the construction of the bilinear differential equations which posses linear subspaces of solutions.

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Abstract :Neutrosophy has been introduced by Smarandache [7, 8] as a new branch of philosophy. The purpose of this paper is to construct a new set theory called the neutrosophic set. After given the fundamental definitions of neutrosophic set operations, we obtain several properties, and discussed the relationship between neutrosophic sets and others. Finally, we extend the concepts of fuzzy topological space [4], and intuitionistic fuzzy topological space [5, 6] to the case of neutrosophic sets. Possible application to superstrings and   space–time are touched upon.
Keywords -Fuzzy topology; fuzzy set; neutrosophic set; neutrosophic topology

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Abstract :Operator regularization is one of the excellent prescriptions for studying gauge theories. Among the many regularization prescriptions Dimensional regularization and Pre-regularization are the best methods for evaluating loop diagrams perturbatively. On the other hand Operator regularization can also be said one of the best methods for studying gauge theories because of its two-fold use. With this prescription one can adopt pathintegral method with the combination of background field quantization and Schwinger expansion to find the result of the required problem without considering any Feynman diagrams. Also from this prescription one can consider Feynman diagrams and evaluating these diagrams using the Operator regularization prescription. In this paper we have shown how one can use both the options of Operator regularization method to evaluate Feynman diagrams in QED in (3+1) dimensional space-time.
Keywords-Operator regularization, Dimensional regularization, Feynman diagrams in QED, Path-integral method, Background field quantization and Generating functional..

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