Recent Studies in Mathematics and Computer Science Vol. 1

Non-uniform Lossless Transmission Lines Terminated by L-Load in Series Connected to Parallel Connected GL-Loads

Vasil G. Angelov — 2020-03-27

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.

Derivatives Involving I-Function of Two Variables and General Class of Polynomials: Brief Overview

Y. Pragathi Kumar — 2020-03-27

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.

On Katugampola Fourier Transform: Critical Overview

Tariq O. Salim — 2020-03-27

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.

Approximation Formulae for Phase Shifts of s–wave Schrödinger Equation Due to Binomial Potential and Their Applications: Recent Advancement

Hemant Kumar — 2020-03-27

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.

Identifying Time-varying Drivers for Social Media Issues and Conversations

Gurpreet Singh Bawa — 2020-03-27

Successfully understanding of social media conversation growth, dissemination and extinction is a challenging task that relies on identifying groups, group influence, diffusion models, forecast models, social dynamics and text analytics. In this problem, we concentrate on the description of a novel approach for identifying drivers of the direction and momentum of social conversations, including the spread of mood, sentiment and issues. The approach first groups potential drivers of conversation based on variability. The primary driver in each group is then selected. Finally, the relationship between the selected drivers and the topic outcome is calculated and displayed visually. This enables the quick identification of the form and structure of the conversation and allows us to predict momentum, direction, contagion risks, potential responses and interventions. There is a huge amount of data in the form of text available today in the internet across various channels – social media, news articles, blogs, e-commerce websites. Most of this data is a part of some “conversation” or the other where real-world entities discuss, analyze, comment, exchange information in the form of written expressions in textual format. Driver Modeling on textual data can be useful in observing the key drivers which are driving the “conversation” coupled with the associated sentiments and mood states for the observed key drivers. These insights about the key conversational drivers are often used in a variety of domains such as tracking news cycles, stock movements, legislation developments, brand image, viral breakouts and much more.

Vertical Cooperative Advertising with Substitute Brands: Brief Overview

You-Hua Chen — 2020-03-27

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.

Approximation of the Modied Error Function by Using Perturbative and Sinc Collocation Methods

Supriya Mandal — 2020-03-27

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.[1].

Oscillation Criteria for Higher Order Nonlinear Functional Dierence Equations: Critical Study

S. Kaleeswari — 2020-03-27

In this chapter some criteria for the oscillation of high order functional difference equation of the form

is discussed. Examples are given to illustrate the results.

On the Donfagsiteli Conditional Function and Some Applications in Pure and Applied Sciences

Nehemie Donfagsiteli Tchinda — 2020-03-27

The Donfagsiteli conditional function is a set of classes and families of mathematical functions which have been recently defined. 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. is a tool to provide deeper insight and a new point of view when describing natural phenomena.

Generalized Power Transformation of Error Components of Multiplicative Time Series Model

A. O. Dike — 2020-03-27

In this paper the author(s) present derivations for the mean and variance of the n^th 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 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.

A Nonstandard Approach to Cauchy’s Functional Equation

Grigore Ciurea — 2020-03-27

In this short note we give a nonstandard proof of the well-known result that any Lebesgue measurable function which satisfies the functional equation is continuous.

Handwritten Character Recognition from Digital Image: Recent Advancements

Abhishek Mehta — 2020-03-27

This paper presents an overview of feature extraction methods for off-line recognition of segmented (isolated) digit/chratchter. Selection of a feature extraction method is probably the single most important factor in achieving high recognition performance in character recognition systems. Different feature extraction methods are designed for different representations of the digit/characters, such as solid binary characters, skeletons (thinned digit /characters), or gray level sub images of each individual character. Latest research in this area has been able to grown some new methodologies to overcome the complexity of Guajarati digit writing style. The recognition of handwritten digits which are written in proper way to easily readable. The problem is human can write digit in different styles so it is not identified by the computer but the some feature extraction methodologies like end point, junction point; straight lines etc. For features identification and character classification studied different algorithm and technique.