Editor(s)
Dr. Xingting Wang
Assistant Professor,
Department of Mathematics, Howard University, Washington, USA

ISBN 978-93-5547-326-4 (Print)
ISBN 978-93-5547-328-8 (eBook)
DOI: 10.9734/bpi/ramrcs/v6

This book covers key areas of Mathematical Research and Computer Science. The contributions by the authors include planar steady-state, evaporation, motion – filtration, radial fin, Frobenius method, improved classical method, finned electric motor, Harmonic and analytical functions, one radius theorem, mean value theorem, Laplace equation, time series, fuzzy time series, fuzzy sets, fuzzy logical relationships, fuzzy observations, spectral density function, period gram, Taylor theorem, congruent number, cybercrimes, cybercriminals, high-temperature superconductivity, vector optimization problem, saddle points,  total domination number, chromatic number and total dominator chromatic number, smarandachely k-dominator coloring, smarandachely k-dominator chromatic number, relation’s degree, connection, set ordering, trivial and proper equivalences, Quasi-differential expressions, Regular and singular equations, Minimal and maximal operators, Regularly solvable operators, J-self-adjoint extension. This book contains various materials suitable for students, researchers and academicians in the field of Mathematical Research and Computer Science.

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### Chapters

##### Study on Modeling the Movement of Groundwater in a Rectangular Jumper with a Screen

E. N. Bereslavsky

Recent Advances in Mathematical Research and Computer Science Vol. 6, 1 January 2022, Page 1-8
https://doi.org/10.9734/bpi/ramrcs/v6/3177F

The present work gives an exact solution of the filtration problem in a rectangular cofferdam with a screen in the presence of evaporation from the free surface of groundwater. Within the framework of planar steady-state filtration of incompressible fluid according to Darcy's law, an exact analytical solution of the problem of flow in a rectangular cofferdam with a screen in the presence of evaporation from the free surface of groundwater is given. The limiting cases of the considered motion - filtration in unconfined reservoir to imperfect gallery, as well as the flow in the absence of evaporation - are noted. The investigation shows that the filtration scheme in a rectangular cofferdam with impermeable screen, firstly, is very similar to the previously considered problem about movement of ground waters to the imperfect gallery, one of them being limiting with respect to the other.

##### Generalized Solution of One-Dimensional Radial Fin by Frobenius Method with Application on Finned Electric Motor

Elcio Nogueira

Recent Advances in Mathematical Research and Computer Science Vol. 6, 1 January 2022, Page 9-21
https://doi.org/10.9734/bpi/ramrcs/v6/1568B

An industrial application of extended surfaces occurs in electric motors, which are critical in the industry because they are used in machines of all types. To specify physical and thermal characteristics applied to extended surfaces, generalized one-dimensional models are used in this study. To compare the one-dimensional radial fin model, "Frobenius Method," with the mathematical model already created and validated, named "Improved One-dimensional Classic Radial Fin" in the literature, results for temperature, heat transfer rate, efficacy, and efficiency are produced. The findings of the two-dimensional model for the radial fin were numerically compared to the results of the generalized one-dimensional models for effectiveness and efficiency. The finned electric motor provides numerical and graphical effects with a 5.82 aspect ratio. When the Reynolds number range and aspect ratio value are considered, the equivalence of one-dimensional models is obvious.

##### Study on Harmonic Function Theory and One Radius Theorem

Dimitra Alexiou, Evlampia Athanailidou

Recent Advances in Mathematical Research and Computer Science Vol. 6, 1 January 2022, Page 22-28
https://doi.org/10.9734/bpi/ramrcs/v6/14381D

The present paper deals with the study of harmonic and analytical functions. It deals with well-known and powerful theorems of the Complex Analysis and has as its central theme the One-Radius Theorem, somehow reversing the Mean Value theorem of harmonic functions. These considerations are set out in Mark A. Pinsky’s article [Mean Values and the Maximum Principle: A Proof in Search of More Theorems].

##### Effect of Fuzzy Time Series Technique on Estimators of Spectral Analysis

Abd El-Moneim A. M. Teamah, Hasnaa M. Faied , Mohammed H. El-Menshawy

Recent Advances in Mathematical Research and Computer Science Vol. 6, 1 January 2022, Page 29-38
https://doi.org/10.9734/bpi/ramrcs/v6/1506B

In this chapter, we study the estimation of the spectral density function as well as the properties of the resulting estimator, known as the periodogram. The statistical properties of this periodogram for actual and forecasted observations of the fuzzy time series are investigated. The periodogram results in both cases can be compared based on MSEs, which are based on these statistical properties. A programme that converts observed time series to fuzzy time series with large sizes is created for this purpose.

Study Objective: Using the fuzzy time series technique to improve the estimation of the spectral density function while retaining its statistical properties.

##### Elliptical Curves are Reducible: A Mathematical Approach

Andri Lopez, Enfer Diez

Recent Advances in Mathematical Research and Computer Science Vol. 6, 1 January 2022, Page 39-45
https://doi.org/10.9734/bpi/ramrcs/v6/3080E

In this paper I present a way to reduce the elliptical curves and, thus we will can know if they have a y2 integer or more of one.

##### Comprehensive Study on Cybercrimes and Cyber Security: A Recent Approach

Pinaki Pratim Acharjya, Subhankar Joardar, Mihir Baran Bera

Recent Advances in Mathematical Research and Computer Science Vol. 6, 1 January 2022, Page 46-55
https://doi.org/10.9734/bpi/ramrcs/v6/3093E

In the course of recent years' crime has been quickly advancing into the universe of data and innovation. Today, Cybercrime has made part of harms people, associations and surprisingly the Government. Cybercrime recognition strategies and grouping techniques have concocted fluctuating degrees of achievement for forestalling and shielding information from such assaults. A few laws and techniques have been acquainted all together with forestall cybercrime and the punishments are set down to the hoodlums. Nonetheless, the review shows that there are numerous nations dealing with this issue even today and United States of America is driving with most extreme harm because of the cybercrimes throughout the long term. This chapter portrays about the normal regions where cybercrime generally happens and the various sorts of cybercrimes that are carried out today.

##### Numerical Approach in Superconductivity: An Advanced Study

V. A. Kizka

Recent Advances in Mathematical Research and Computer Science Vol. 6, 1 January 2022, Page 56-63
https://doi.org/10.9734/bpi/ramrcs/v6/1634A

The dependence of the critical temperature Tc of high-temperature superconductors of various families on their composition and structure is proposed. A clear dependence of the critical temperature of high-temperature superconductors (hydrides, Hg- and Y-based cuprates) on the serial number of the constituent elements, their valence and crystal lattice structure has been revealed. For cuprates, it is shown that it is possible to obtain even higher temperatures of superconducting transitions at normal pressure by implanting mercury atoms into the crystal lattice of cuprate.

##### Study on "Weak" Efficiencies in Vector Optimization

Cristina Stamate

Recent Advances in Mathematical Research and Computer Science Vol. 6, 1 January 2022, Page 64-81
https://doi.org/10.9734/bpi/ramrcs/v6/1536B

It is a well-known fact that efficient points enjoy special attention in vector optimization given that numerous applications in areas as mathematical economics, game theory, geometry of normed spaces.

Following the various types of efficient points introduced and studied overtime by many authors (see  [1-7], [8])  we propose an unified approach concerning the "weak" efficient points (efficient points defined by respect to cones that have some interiority properties).

These generalized weak efficient points will be called -efficient points and we will present conditions of existence, domination properties and comparative results for them. As application, we will study a generalized vector optimization problem defined with the -efficient points. The definition of the notion of solution generated some difficulties given that the usual notion of solution would have reduced the study of the generalized problem to a classical problem, the MIN problem. Finally, the solution for this problem will be a net of approximate efficient points which is closely related with the notion of asymptotically weakly Pareto optimizing sequence used in [9].

In order to obtain conditions on existence and properties of these solutions, we introduce the INFSUP problem, a generalization of MINMAX problem. Following the studies for the MINMAX problem (see for example [10-14], [15,16], [17-19], some saddle points theorems and duality results using a suitable lagrangian adapted for the INFSUP problem, a generalization of the MINMAX problem are obtained.

Also, we’ll present the links between our problems and two special problems, the scalar and the linear approximate problems.

##### Determination of Total Dominator Colorings in Caterpillars

A. Vijayalekshmi

Recent Advances in Mathematical Research and Computer Science Vol. 6, 1 January 2022, Page 82-88
https://doi.org/10.9734/bpi/ramrcs/v6/1642A

In this chapter we determine total dominator chromatic number in caterpillars. Let  be a graph without isolated vertices. A total dominator coloring of a graph  is a proper coloring of  with the extra property that every vertex in  properly dominates a color class. The smallest number of colors for which there exists a total dominator coloring of  is called the total dominator chromatic number of  and is denoted by

##### Study of Relations’ Properties Compatibility

Mikhail A. Mikhaylov

Recent Advances in Mathematical Research and Computer Science Vol. 6, 1 January 2022, Page 89-96
https://doi.org/10.9734/bpi/ramrcs/v6/1632A

This article is a sequel of my earlier paper [1]. In the 1st section the conditions for emergence of tolerance are considered – the uncertainty in definition of diagonal for such sets leads to it. Furthermore it was shown that relations’ property manifestations described earlier cannot appear accidentally and independently on each other. Also it was shown that just reflexive antisymmetric transitive relations may be applicable to make set ordering. Further an ambiguity in definition of idempotent element amongst relations was presented. General definitions of set theory (such as ordered and unordered pairs, set union and intersection etc.) are detailed in the works [6 – 14].

##### Cluster Based MapReduce Technique for Predicting Heart Disease -: A Modelling Approach

J. Sukanya, K. Rajiv Gandhi, V. Palanisamy

Recent Advances in Mathematical Research and Computer Science Vol. 6, 1 January 2022, Page 97-110
https://doi.org/10.9734/bpi/ramrcs/v6/4961F

Classification is the process of grouping the data elements with the class labels. It is the supervised learning technique. It is also the process of finding the model that describes and distinguishes data classes and its values. MapReduce provides a programming paradigm for performing distributed computation on computer clusters. In a MapRe-duce system such as hadoop, the user program forks a Master controller process and a series of Map tasks  and Reduce tasks .This paper describes the prediction system for heart disease based on  the MapReduce method with Relief feature selection and semi naive Bayes Classification Algorithms.

##### Studies on the Domains of Regularly Solvable Operators in the Direct Sum Spaces

Sobhy El-Sayed Ibrahim

Recent Advances in Mathematical Research and Computer Science Vol. 6, 1 January 2022, Page 111-131
https://doi.org/10.9734/bpi/ramrcs/v6/13558D

Given a general quasi-differential expressions $$\tau$$,$$\tau$$2 ,...,$$\tau$$each of order n with complex coefficients and their formal adjoint are $$\tau$$1+ ,$$\tau$$2+ ,...,$$\tau$$non the interval [a,b) respectively, we give a characterization of all regularly solvable operators and their adjoints generated by a general ordinary quasi-differential expressions $$\tau$$jp  in the direct sum Hilbert spaces L2w(ap,bp),p = 1,...,N. The domains of these operators are described in terms of boundary conditions involving L2w(ap,bp)- solutions of the equations $$\tau$$jp [y] = $$\lambda$$ wy and its adjoint $$\tau$$+jp[Z] = $$\lambda$$ wy ($$\lambda$$$$\in$$$$\not\subset$$) on the intervals [ap,bp). This characterization is an extension of those obtained in the case of one interval with one and two singular end-points of the interval (a, b), and is a generalization of those proved in the case of self-adjoint and J- self-adjoint differential operators as special case, where J denotes complex conjugation.