**Vol. 4, No. 2, June 2011**

**Contents**

**Title:** **An Integer Solution of Fractional Programming Problem**

**Authors:** S.C. Sharma and Abha Bansal

**Abstract:** The present paper describes a new method for solving the problem in which the objective function is a fractional function, and where the constraint functions are in the form of linear inequalities. The proposed method is based mainly upon simplex method, which is very easy to understand and apply. This can be illustrated with the help of numerical examples.

**PP.** 1-9

**Title:** **On Strictly Convex and Strictly Convex according to an index Semi-Normed Vector Spaces**

**Author:** Artur Stringa

**Abstract:** The purpose of this paper is giving the notion of strictly convex semi–normed vector spaces according to an index and the notion of an extreme point of a convex set C in a vector space X, according to the semi-norm p in the space X. We extend to semi-normed vector spaces, via semi–pre-inner–products, some known results on strictly convex normed vector spaces, which are characterized in terms of semi-inner-products.

**PP. **10-22

**Title:** **On Relative Order and Relative Type of an Entire Function Represented by Dirichlet Series**

**Author:** Bibhas Chandra Mondal

** Abstract:** In this paper we have introduced relative type *T*_{g}(*f*) of an entire function *f *represented by Dirichlet Series relative to another entire function *g*represented by Dirichlet series. We obtained formulas for *T*_{g}(*f*) in terms of maximum modulus function as well as in terms of coefficients and exponents of the series. We have also found out a property of the relative type of sum and difference of two functions. We obtained a relation between *T*_{g}(*f*), *T*(*f*) and *T*(*g*)* *where T(f)* *and *T*(*g*) are classical type of *f *and *g *respectively. We have established a relation connecting *T*_{g}(*f*), *ρ*_{g}(*f*), *ρ*(f), *ρ*(g) where *ρ*_{g}(*f*) is the relative order of *f *relative to *g *and *ρ*(f), *ρ*(g) are classical orders of *f *and *g *respectively.

**PP.** 23-36

**Authors:** Bijan Rahimi, Mohammad mordad, Leyla Rahmani and Esmaeil Babolian

**Abstract:** In this paper, Block Pulse Functions and their operational matrices are used to solve Volterra-Fredholm integro-differential equation (VFIDE). First the equation is integrated over interval [0, x] and then Block Pulse functions are used to obtain numerical solution. Some theorems will prove convergence of the method. Some numerical examples are included to illustrate accuracy of the method.

**PP.** 37-48

**Title:** **Solution of the Time-Fractional Navier-Stokes Equation**

**Authors:** V.B.L. Chaurasia and Devendra Kumar

**Abstract:** In this paper we obtain the solution of a time-fractional Navier-Stokes equation. The solution is derived by the application of Laplace and finite Hankel transforms. The results are obtained in compact and elegant forms in terms of the Mittag-Leffler and Bessel functions, which are suitable for numerical computation. The results derived here are quite general in nature and capable of yielding a very large number of known (may be new also) results, hitherto scattered in the literature.

**PP. **49-59

**Title:** **On the Number of Minimum Neighbourhood Sets in Paths and Cycles**

**Authors:** M. P. Sumathi and N.D. Soner

**Abstract:** This paper is concerned with total number of minimum neighbourhood sets in paths and cycles. We establish the relation between minimum number of neighbourhood sets in paths and cycles and the blocks of partial balanced incomplete block design with *m*-association scheme.

**PP.** 60-70

**Title:** **The Application of the Variational Method to Optimize a Snowboard Course**

**Authors:** Feroz shah Syed, Xue-Yuan Zhang,Song Huang and Xiao Sun

**Abstract:** In this paper, by using the variational method, we obtain the optimal design on the “halfpipe” shape for a skilled player to maximize the production of “vertical air”. The main idea is that we make the halfpipe shape such that the player can get maximalkinetic energy. Neglecting the air resistance, friction drag, and so on, we formulate the variation for the steepest descent curve so that the player gets a maximum velocity at the bottom of the halfpipe. Then, we consider the bottom plane of the halfpipe to continue optimization. Having the aid of the obtained maximum velocity together with the optimizations in the bottom plane, the player can obtain more kinetic energy to jump up and twist as higher and better as possible. We also make some numerical simulation to verify the theoretical analysis. Finally, according to above analysis, we design a better halfpipe for players to use in practice. Our conclusion is that, based on our design with the standard sizes, the maximum vertical air and the time for twist in the air can exceed the known best results obtained by the world class players.

**PP. **71-86

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