Journal of Computational Mathematics and Applied Mathematics

Authors:-Farhana Alam, M. H. Rashid

Abstract:-In the present paper, we are interested to study the following generalized equation by secant-type method 0∈f(x)+g(x)+H(x),                                                                                       (*) where X and Y are real or complex Banach spaces, the function f:X→Y is a Frechet differentiable on neighborhood of a point x ̅ (which is the solution of (*)), g is differentiable at x ̅ but may not differentiable on the neighborhood of x ̅ and H:X⇉Y is a set-valued mapping with closed graph. We prove the existence of the sequence generated by the secant-type method and establish local convergence of the sequence generated by this method for generalized equation (*). Basically, we show the existence of the sequence generated by the secant-type method and establish the local convergence results of the sequence which is linearly convergent when the Frechet derivative of f, denoted by ∇f, is continuous, g admits first order divided deference and the set-valued mapping (f+ g+ H)^-1 is pseudo-Lipschitz. Furthermore, if ∇f satisfies Holder continuity property, g admits first order divided deference satisfying p-Holder continuity property and the set-valued mapping               (f+ g+ H)^-1 is pseudo-Lipschitz, we prove the existence of sequence generated by the secant-type method and prove the local convergence results of the sequence which converges super linearly to the solution of (*). In particular, our results extend and improve the corresponding ones Geoffroy and Pietrus (2004), and fix a gap in the sense of numerical computations in the proof in (Geoffroy and Pietrus (2004), Theorem 3.1).

Authors:-Dr. P. K. Mishra*, Debasis Gountia

Abstract:-

In this paper, we have estimated bounds of the number of level crossings of the
random algebraic polynomials 
 
n
k
k
n k f x a t x
0
( ,1) ( ) 0 where
ak (t) ï‚£ t,0 ï‚£ t ï‚£1, are dependent random variables assuming real values
only and following the normal distribution with mean zero and joint density
function M ï° ï› ï¤ Mï¤ ï a s (2 ) exp ( 1/ 2) ' 1/ 2 /
 
. There exists an integer n0 and a set
E of measure at most A/(log n0log log log n0) such that, for each n>n0
and all not belonging to E, the equations (1.1) satisfying the condition (1.2),
have at most (log log n) log n 2 ï¡ roots where α and A are constants.
1991 Mathematics subject classification (Amer. Math. Soc.): 60 B 99.

Authors:-Raghvendra Singh, Vandana Gupta, S. K. Tiwari

Abstract:-Neural network is an important area of research due to its usage in various fields of engineering and sciences. Orthogonal neural network is a special kind of neural network where basis functions are orthogonal to each other. In this paper, orthogonal neural network is discussed and its important properties are detailed. It is found that its properties very much resemble with the Fourier series properties.

Author: Dr. P.K. Mishra

Abstract: We study the expected number of level crossings of an algebraic polynomial of degree n, whose coefficients are independent distributed random variables. We present a formula for the expected number, which has the advantage of being easy to use numerically. This approach shows that the error term involved in the asymptotic estimate for the expected number of real zeros with this class of distribution for the coefficients is 0(1).

Authors: Purvi J Naik, Dr Sandeep Rai

Abstract: In this article, Taguchi method is used to theoretically optimize the various reaction parameters and their interactions that may affect the end properties of Guar Gum Grafted copolymers made in a laboratory glass reactor. In the present study, an attempt has been made to assess and predict the effect of temperature, monomer (Acrylonitrile) concentration and Guar Gum concentration on % efficiency. With the use of Taguchi method, orthogonal experimental design and analysis technique; the performance of this process was analyzed with more objective conclusion with only a small number of simulation experiments. Analysis of variance (ANOVA) was performed to identify the significant factors affecting the response and the best possible factor level combination was determined.

Authors:  S K Dadhich, Arun Kumar, Ram Dayal Pankaj

Abstract: In the paper, the coupled 1D Zakharov equation is considered as the model equation for wave-wave interaction in ionic media. A finite difference scheme is derived for the model equations. A new six point scheme, which is equivalent to the multi-symplectic integrator, is derived. The numerical simulation is also presented for the model equations.

Author: S.N.R.G. Bharat Iragavarapu 

Abstract: 

In this paper, using computer programming C language, we determine the Pythagoras heptagon  for any six natural numbers p, q, r, s, t, u  and this Pythagoras heptagon satisfies the extension of the Pythagoras theorem i.e the sum of the squares of the first six side lengths is equal to the sum of the square of the remaining side length.

 Keywords: Pythagoras theorem, Pythagoras heptagon

Authors: Sangita Saha, Santanu Roy

Abstract: In this article, the concept of statistically pre-Cauchy sequence of fuzzy real numbers having multiplicity greater than two defined by Orlicz function is introduced. A characterization of the class of bounded statistically pre-Cauchy triple sequences of fuzzy numbers with the help of Orlicz function is presented. Then a necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be statistically pre-Cauchy is proved. Also a necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be statistically convergent is derived. Further, a characterization of the class of bounded statistically convergent triple sequences of fuzzy numbers is presented and linked with Cesáro summability.

Authors: R.K. Mishra, Avtar Chand

Abstract: In this communication we have investigated various cosmological consequences along with a new class of cosmological models in f(R, T) modified theory of gravity as proposed by Harko et al.(Phy. Rev. D. 024020), where the gravitational Lagrangian is replaced by an arbitrary function of Ricci scalar R and trace T of stress energy tensor. We have also studied the string cosmological models by considering the time dependent deceleration parameter with and without presence of magnetic field. In the last section of the paper the behavior of some cosmological parameters have been represented in pictorial form.

Author: R. Panneerselvi

Abstract: This study examines the flow of an unsteady, incompressible, viscous electrically conducting fluid with suction/blowing. The lower porous boundary is assumed to be heated by the presence of a heat source. The effect of magnetic field in case of suction/blowing and acceleration/ deceleration are obtained. The effect of various dimensionless parameters on the velocity and temperature distributions are depicted graphically and analyzed in detail.

Author: Munmun Nath, Bijan Nath, Santanu Roy 

Abstract: In this article, the notion of different types of statistically convergent and statistically null fuzzy real-valued sequences having multiplicity greater than two are introduced. We make an effort to prove some algebraic and topological properties of these spaces such as solid, monotone, symmetric, convergence free, sequence algebra etc. Also fuzzy real-valued Cesáro summable triple sequence space is introduced. Moreover a relation between strongly p-Cesáro summability and bounded statistically convergent triple sequences has been established.

Authors: Anwar A. Patel , Rukhsar K. Pathan

Abstract: Since we can calculate slope of two dimensional object and equation of Tangent and Normal of the any two dimensional curve. Slope (m) is change in Y-coordinates with respect to X-coordinate. But in three dimensional three axis should be considered. dx, dy, dz this changes in X, Y & Z are measured and slope can be calculated. Normal and Tangent equation in three dimensional has three points and three different distances. In two dimensional there is only one Tangent at one point to the curve but in three dimensional Cartesian three tangents at a point. One is parallel to X-axis, second is parallel to Y-axis and third one parallel tozaxis. radius of curvature or sphere can be easily calculated with the help of slope equation. The Cartesian plane is a two-dimensional mathematical graph. When graphing on it, a line may not start at zero as in the ski slope examples. In fact, a line goes on forever at both ends. The slope of a line, however, is exactly the same everywhere on the line. So, you can choose any starting and ending point on the line to help you find its slope. It is also possible that you might be given a line segment , which is a section of a line that has a beginning and an end. Or, you might be given two points and you are expected to draw (or imagine) the line segment between them. In all these situations, finding the slope works the same way. Just like with the ski slope, the goal is to find the change in height and the change in width. For the line segment in the image, you can simply count the squares on the grid. Three dimensional slope is useful to civil engineering in designing heavy structure of dam, bridge and constructive parts. Also this is helpful for mechanical industry and safety management. Radius of curvature is the radius of approximating sphere or elliptical shape elements. When engineers design train track, curve road they will need to ensure the curvature of track, bridge & tunnel to provide a comfortable ride for given speed of trains.

Authors: S.N.R.G. Bharat Iragavarapu, Kota Vidhya Sagar

Abstract: In this paper, using a computer programming language, we determine the number of equilateral, isosceles and right angled triangles having sides of positive integer length by breaking a stick of length n where n being a positive integer greater than 3.

Authors: S.N.R.G. Bharat Iragavarapu, M. Anuraag Chandra

Abstract: In this paper, using a computer programming language, we determine the number of triangles that can be formed by using a stick of a given length, say n units, n being a positive integer greater than 3.