Oscillation Criteria for Higher Order Nonlinear Functional Difference Equations: Critical Study | Chapter 8 | Recent Studies in Mathematics and Computer Science Vol. 1

In this chapter some criteria for the oscillation of high order functional difference equation of the form ∆2(r(n)[∆(m−2)y (n)]α)+ q (n)f [y (g (n))] = 0,

where

∞ ∑s =n0

r− 1 α (s) < ∞ and m > 1 is discussed. Examples are given to illustrate the results.

Author(s) Details

S. Kaleeswari
Department of Mathematics, Nallamuthu Gounder Mahalingam College, Bharathiar University, Coimbatore, Tamil Nadu, India.

B. Selvaraj
Department of Science and Humanities, Nehru Institute of Engineering and Technology, T. M. Palayam, Coimbatore, Tamil Nadu, India.

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Approximation of the Modified Error Function by Using Perturbative and Sinc Collocation Methods | Chapter 7 | Recent Studies in Mathematics and Computer Science Vol. 1

This chapter deals with the evaluation of some integrals involving error-, exponential- and algebraic functions with an objective to present explicit expressions for the second and third order correction terms in the approximation of the modified error function in the perturbation approach. Over and above an approximation of the desired modified error function has been developed in sinc basis. The accuracy in the approximation (perturbation method and sinc basis) have been compared with the approximate value available in the literature. Results obtained by perturbation approximation and scheme based on sinc basis seem to be useful in the study of Stefan problem. The results obtained here appear to be new and resolve the lack of desired monotonicity property in the results derived earlier e.g. by Ceretania et al.

Author(s) Details
Supriya Mandal
Department of Mathematics, Visva-Bharati (A Central University), Santiniketan-731235, West Bengal, India.

Debabrata Singh
Department of Mathematics, Visva-Bharati (A Central University), Santiniketan-731235, West Bengal, India.

M. M. Panja
Department of Mathematics, Visva-Bharati (A Central University), Santiniketan-731235, West Bengal, India.

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A Nonstandard Approach to Cauchy’s Functional Equation | Chapter 11 | Recent Studies in Mathematics and Computer Science Vol. 1

In this short note we give a nonstandard proof of the well-known result that any Lebesgue measurable function :ℝ→ℝ which satisfies the functional equation (+)=()+() is continuous. 

Author(s) Details  
Grigore Ciurea
Department of Mathematics, Academy of Economic Studies, Piata Romana 6, Bucharest 010374, Romania.

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Generalized Power Transformation of Error Components of Multiplicative Time Series Model | Chapter 10 | Recent Studies in Mathematics and Computer Science Vol. 1

In this paper the author(s) present derivations for the mean and variance of the nth power transformation of the error component of the multiplicative time series model. As a general rule to any power transformation. Some of the published transformations like the square root and the inverse were used to validate the results obtained. The results showed that they conformed to the general rule, Also the cube transformation equally used to establish a practical illustration of the general rule. Data from federal road safety commission (FRSC) Nigeria on road accident were collected and analyzed by fitting the regression line of log mean (logmean) against log standard deviation (logstdev). This gave a slope =0.666977 which agrees with the required value of 0.6666 this gives a transformation of 1-0.666977= 0.333023 (1-) which is the cube root transformation. Data were later decomposed into time series components. Recommendations on areas of application of cube root transformation were equally given. 

Author (s) Details

A. O. Dike
Department of Mathematics and Statistics, Akanu Ibiam Federal Polytechnic, Unwana, P.M.B.1007, Afikpo, Ebonyi State, Nigeria.

E. L. Otuonye
Department of Statistics, Faculty of Biological and Physical Sciences, Abia State University, P.M.B.2000, Uturu, Nigeria.
D. C. Chikezie
Department of Statistics, Faculty of Biological and Physical Sciences, Abia State University, P.M.B.2000, Uturu, Nigeria.

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On the Donfagsiteli Conditional Function and Some Applications in Pure and Applied Sciences | Chapter 9 | Recent Studies in Mathematics and Computer Science Vol. 1

The Donfagsiteli conditional function ([Cdk]f) is a set of classes and families of mathematical functions which have been recently defined. [Cdk]f is related to a predefined function f in a way similar to that of a bijective function and its inverse . It is a generalization of both elementary and special functions. The function has many applications in pure and applied sciences, when makes it possible, to solve explicitly several models where as this is not possible with elementary and some special functions such as Lambert W functions. In this book chapter, definition and properties of Donfagsiteli conditional function, have been revisited with their extension to the conditional complex plan. Some transcendental equations and novel models were treated to solve certain problems in biology such as enzymatic kinetics and marginal value theorem. [Cdk]f is a tool to provide deeper insight and a new point of view when describing natural phenomena.

Author(s) Details

Nehemie Donfagsiteli Tchinda
Medicinal Plants and Traditional Medicine Research Centre, Institute of Medical Research and Medicinal Plants Studies (IMPM), Yaounde, Cameroon.

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Approximation Formulae for Phase Shifts of s–wave Schrödinger Equation Due to Binomial Potential and Their Applications: Recent Advancement | Chapter 4 | Recent Studies in Mathematics and Computer Science Vol. 1

In this paper, we derive the approximation formulae for phase shifts of s-wave Schrödinger equation on introducing binomial potential function and then make their applications to study the fluctuations in the phase shift difference from the s-wave with respect to different values of the arbitrary parameter occurring in a given binomial potential function. 

Author(s) Details
Dr. Hemant Kumar
Department of Mathematics, D. A-V. Postgraduate College, Kanpur, Uttar Pradesh, India.

Dr. Vimal Pratap Singh
Department of Mathematics, U.I.E.T. Building C.S.J.M. University, Kanpur, Uttar Pradesh, India.

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On Katugampola Fourier Transform: Critical Overview | Chapter 3 | Recent Studies in Mathematics and Computer Science Vol. 1

The aim of this article is to introduce a new definition for the Fourier transform. This new definition will be considered as one of the generalizations of the usual (classical) Fourier transform. We imploy the new Katugampola derivative  to obtain some properties of Katugampola Fourier transform, and find the relation between Katugampola Fourier transform and the usual Fourier transform. The inversion formula and the convolution theorem for Katugampola Fourier transform are considered. 

Author(s) Details
Tariq O. Salim
Department of Mathematics, Al-Azhar University, Gaza, Palestine.

Atta A. K. Abu Hany
Department of Mathematics, Al-Azhar University, Gaza, Palestine.

Mohammed S. El-Khatib
Department of Mathematics, Al-Azhar University, Gaza, Palestine.

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Derivatives Involving I-Function of Two Variables and General Class of Polynomials: Brief Overview | Chapter 2 | Recent Studies in Mathematics and Computer Science Vol. 1

This chapter presents some derivative formulas of I-function of two variables involving general class of polynomials. The special cases of our derivatives yield interesting results.

Author(s) Details

Dr. Y. Pragathi Kumar 
Department of Mathematics, College of Natural and Computational Sciences, Adigrat University, Adigrat, Ethiopia.

B. Satyanarayana 
Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar – 522 510, Andhra Pradesh, India

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Non-uniform Lossless Transmission Lines Terminated by L-Load in Series Connected to Parallel Connected GL-Loads | Chapter 1 | Recent Studies in Mathematics and Computer Science Vol. 1

The paper analyses non-uniform transmission lines terminated by nonlinear loads situated as follows: GC-loads are connected parallel and L-load is connected in series to them (Fig. 1). First, we formulate boundary conditions for a lossless transmission line system on the basis of the Kirchhoff’s law. Then, we reduce the mixed problem for the system in question to initial value problem for a neutral system on the boundary. We introduce an operator in a suitable function space whose fixed point is an оscillatory solution of the system on the boundary. The obtained conditions are easily verifiable. We demonstrate the advantages of our method in Numerical example.

Author(s) Details
Vasil G. Angelov 
Department of Mathematics, University of Mining and Geology “St. I. Rilski”, 1700 Sofia, Bulgaria.

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Vertical Cooperative Advertising with Substitute Brands: Brief Overview | Chapter 6 | Recent Studies in Mathematics and Computer Science Vol. 1

Cooperative (co-op) advertising is attracting more and more attention. This paper analyzes co-op advertising behavior based on a dual brands model with a single manufacturer and a single retailer and some interesting conclusions are achieved. Firstly, firm in the supply chain advertises both brands and the difference of advertising expenditure is not very large in equilibrium. Secondly, the retailer’s advertising and the manufacturer’s participation ratio depend on both the retailer’s and the manufacturer’s marginal profits. Thirdly, stimulating effect increases advertising investment while competition effect decreases it, but they have no effect on the manufacturer’s participation ratio. Fourthly, co-op advertising is more sensitive to the manufacturer’s marginal profits than that of the retailer. Lastly, total advertising investment and profit are greater under cooperative decision than under Stackelberg decision

Author(s) Details

You-Hua Chen
 College of Economics and Management, South China Agricultural University, Guangzhou, 510642, P. R. China.

Xiao-Wei Wen
College of Economics and Management, South China Agricultural University, Guangzhou, 510642, P. R. China.

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