Editor(s)

Dr. Xingting Wang
Assistant Professor, Department of Mathematics, Howard University, Washington, USA.

ISBN 978-93-90888-20-7 (Print)
ISBN 978-93-90888-28-3 (eBook)
DOI: 10.9734/bpi/tpmcs/v9

This book covers key areas of mathematics and computer science. The contributions by the authors include integrating factor, operator D method, variational iteration method, radiation reaction force, 1-D electron motion, damping motion, Kalman filter, steady state relationship, velocity, generalized penrose transforms, coherent g-quasi-equivariant D-modules, hecke sheaf, moduli stacks, moduli spaces, reliability and validity studies, sequential probability ratio test, Bland Altman analysis, paradoxical parameter space, Bayesian statistics, bank stability, bank performance, architectural troubles, linear differential equations, circumcoronene series of benzenoid, molecular graph, lattice, triangle benzenoid, interpenetrating model, difference scheme, energy estimation, Brinkman model, transmuted power Gompertz distribution, tatistical properties, estimation of parameters, application and performance, incompressible MHD equations, Riccati auxiliary equation, travelling wave solutions, deductive system, residuated lattices, database security, database watermarking, multi-place watermarking. This book contains various materials suitable for students, researchers and academicians in the field of mathematics and computer science.

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### Chapters

##### Recent Study on the Computation of the Lagrange Multiplier for the Variational Iteration Method (VIM) for Solving Differential Equations

N. Okiotor, F. Ogunfiditimi

Theory and Practice of Mathematics and Computer Science Vol. 9, 4 May 2021, Page 1-22
https://doi.org/10.9734/bpi/tpmcs/v9/2423E

In this chapter, the Variational Iteration Method (VIM) is applied in finding the solution of differential equations with emphasis laid on the choice of the Lagrange multiplier used while employing VIM. We apply restricted variation only to the non-linear term in the correction functional. Building on existing methods and variational theories, the operator D-Method and integrating factor are employed in certain aspects in the determination of exact Lagrange multiplier for VIM. When results of the computed exact Lagrange multiplier were compared with results of approximate Lagrange multiplier, it was observed that the computed exact Lagrange multiplier reduced significantly the number of iterations required to get a good approximate result, and in some cases the result converged to the exact solution after a single iteration. Evaluations are carried out using MAPLE Software.

##### Dynamics of 1-D Electron Motion with Radiation Reaction Effect under a Periodic Electric Field

Gustavo V. López, Jorge Lizarraga

Theory and Practice of Mathematics and Computer Science Vol. 9, 4 May 2021, Page 23-29
https://doi.org/10.9734/bpi/tpmcs/v9/6157D

We consider the 1-D motion of an electron under a periodic force and take into account the effect of radiation reaction dissipation force on its motion, using the formulation of novel radiation reaction force as a function of the external force expression. Two cases are considered: A simple sinusoidal time depending force and sinusoidal electromagnetic force with position and time dependence. The purpose of the study of these cases is to bring about a way to find an experimental study to determine the validity of this novel approach for the radiation reaction force. We found that the difference of the normalized (with respect the speed of light) velocities, with and without radiation reaction, is quite small between 10-31 to 10-14 for intensities on the electric field of 10-8 to 1 Dynes/ues, which may represent some concern to measure experimentally.

##### Position, Velocity and Acceleration Tracking Using Kalman Filter

G. Tziallas, M. Adam, N. Assimakis, A. Polyzos

Theory and Practice of Mathematics and Computer Science Vol. 9, 4 May 2021, Page 30-47
https://doi.org/10.9734/bpi/tpmcs/v9/2441E

Constant acceleration movement in one, two and three dimensions can be modeled using time invariant models. Position, velocity and acceleration tracking is obtained using time invariant Kalman filter and steady state Kalman filter. The derived estimation and prediction are reliable.

##### Penrose Transform on Induced DG=H-Modules and Their Moduli Stacks in the Field Theory II

Francisco Bulnes

Theory and Practice of Mathematics and Computer Science Vol. 9, 4 May 2021, Page 48-60
https://doi.org/10.9734/bpi/tpmcs/v9/4004D

We look at generalizations of the Radon-Schmid transform on coherent DG=H -Modules with the aim of obtaining equivalence between geometric objects (vector bundles) and algebraic objects (D-Modules) that characterize conformal groups in the space-time that determine a moduli space on coherent sheaves for the purpose of obtaining solutions in field theory. Elements of derived categories such as D-branes and heterotic strings are regarded in a significant sense. Similarly, a moduli space is obtained for equivalence between some geometrical pictures (non-conformal worldsheets) and physical stacks using the geometric Langlands programme (derived sheaves). This provides equivalences between several theories of field supersymmetries of a Penrose transform that generalises the Langlands program’s implications. Extensions of a cohomology of integrals for a major class of field equations to the corresponding Hecke group are obtained with it.

##### Application of Sequential Probability Ratio Test for Reliability and Validity Studies

Jeffrey O. Wand, Steven B. Kim

Theory and Practice of Mathematics and Computer Science Vol. 9, 4 May 2021, Page 61-75
https://doi.org/10.9734/bpi/tpmcs/v9/7792D

Suppose that a new blood pressure cuff has been created. Before this device can be accepted in the medical community, doctors would need to be sure that the new device is fairly consistent in its measurements and as accurate as the old blood pressure cuff. Likewise, to compare an old (standard) device with a new device, reliability and validity studies are performed in practice. In reliability and validity studies, a device is said to be reliable when it has low variance and a device is said to be valid when it has zero or small bias. Among many approaches for comparing two devices in the literature, the method of Bland and Altman analysis has been popular due to its simple calculation and interpretation under the assumption of normal distribution for the difference between two devices’ measurements. Note that researchers often collect data sequentially. In this chapter we present alternative statistical approaches to save researchers’ resources if possible. First, we present the application of a statistical method called the sequential probability ratio test which allows an early conclusion before reaching a fixed sample size. Next, we relax the normality assumption (which is not guaranteed to be satisfied in practice) by transforming an observed difference between two devices’ measurements into a Bernoulli random variable, and it provides a slightly different interpretation than the original Bland Altman analysis.

##### Relationship between Credit Risk and Bank Stability of Vietnam Commercial Bank: A BK Approach

Sang Tang My

Theory and Practice of Mathematics and Computer Science Vol. 9, 4 May 2021, Page 76-87
https://doi.org/10.9734/bpi/tpmcs/v9/7774D

Through the secondary data collected from 2005 to 2019, we used the BK approach in which, Pooled OLS, FEM, REM, and GMM methods and Sobel’s test are used to check the relationship between bank credit risk and bank stability of Vietnam commercial bank system. The results show that bank credit risk, profitability, and bank stability have a direct relationship and have a partial indirect relationship. The size and profitability of the previous period have a positively correlated with bank profitability, nonperforming loan, loan loss provision, non-interest income, efficiency, and bank credit growth have a negative impact on bank profitability, bank profitability has no impact on bank credit risk. Profitability and bank stability of the previous period have an impact on current bank stability. Nonperforming loans, non-interest income hurt bank stability, loan loss provision and bank stability of the previous period have a positively correlated with current bank stability. Finally, banks need to build and perfect the risk management system to comply with Basel II standards. Identifying and forecasting credit risks are one of the areas that need to be improved and carried out regularly and continuously.

##### Note on Practical Troubles Appear on Computer Architecture on the Interface User (Desktop) Operations

Zahir Alhashami

Theory and Practice of Mathematics and Computer Science Vol. 9, 4 May 2021, Page 88-93
https://doi.org/10.9734/bpi/tpmcs/v9/1706F

This paper describes the troubles and problems appear by indication of what are occurring on the Graphic User Interface (GUI). Any operation happen indication for system case and the Architectural case for the users. During use operations and the usual programs are used speed and response could see the global case of machine system. Every peripheral storage device (main or secondary) also could be indication for system state need troubleshooting or not. Opening and closing some programs and type of operation could check what is problem and trouble what is. Practical operations in a network or not could appear the irregularity of this proposal. The Used Methodology is checking operations users use like storage, inputting and outputting, data transferring, doing equations and connect the peripherals devices. These operations are done with considering global computer system case and another conditions regard system controlling of other units.

Aims and Objectives: Every computer has its independent system, with its OS. This Operating System has set of instruction must follow to do specific function within and with limits of the peripherals and attached input and output of the computer.

Based on that the computer system architecture is defines the conceptual structure and functional behavior of a computer system, it is necessitating to check the system risks and troubles that cause to unorganized and non-synchronized operations that they done every day by the clients.

The GUI is appearing and clear screen for the user to see and check if there are any risks or there are problems or irregular in the system work.

It is very easy to see irregularity in the computer system just by notify the Graphic User Interface alarms, or troubles appear, or even disruption in the desktop usual operations notified by the user.

After understand of the conceptual architecture of the computer system, it is very easy to note that there are some specific operations disturbed are not work properly or precisely.

The aims of this project study can be concise in these points:

• Studying the signs of system irregularity
• To make easy know what happen for the user about the system troubles by note the GUI by testing some system operations on the desktop
• Know the architectural work flow of the computer system and to be familiar

Identify the computer system troubles and disruptions abstractly on the desktop.

##### Hyers-Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order: A Scientific Explanation

Yongjin Li, Yan Shen

Theory and Practice of Mathematics and Computer Science Vol. 9, 4 May 2021, Page 94-99
https://doi.org/10.9734/bpi/tpmcs/v9/2940D

The aim of this paper is to prove the stability in the sense of Hyers-Ulam of differential equation of second order $$y^{\prime\prime}+p(x)y^{\prime}+q(x)y+r(x)=0$$. That is, if f is an approximate solution of the equation $$y^{\prime\prime}+p(x)y^{\prime}+q(x)y+r(x)=0$$, then there exists an exact solution of the equation near to f.

##### Computation of Molecular Descriptors for Chemical Graph Structure Using Python Program

S. Manimekalai

Theory and Practice of Mathematics and Computer Science Vol. 9, 4 May 2021, Page 100-114
https://doi.org/10.9734/bpi/tpmcs/v9/7715D

Many researchers proved that the newly defined, essential parameters like degree and eccentricity based indices of molecular graph is very much useful in QSPR and QSAR study. It is also advisable to do further investigations in this index. Many drug discovery procedures are based on the design of molecular similarity. Bridge molecular graph is one of the most essential structures in medicine industry to discover drugs.

##### Some Stable Difference Schemes to Describe the Flow in the Combined Region

U. Dalabaev

Theory and Practice of Mathematics and Computer Science Vol. 9, 4 May 2021, Page 115-126
https://doi.org/10.9734/bpi/tpmcs/v9/1652C

In many environmental, industrial and biological processes, flows occur in a saturated porous fluid medium. The transport of substances between surface water and groundwater is a very serious problem. The basis of the mathematical model is based on the interpenetrating model (Rahmatullin model) of two-phase media. The proposed equations make it possible to study the flow of a liquid in and outside the porous region in a uniform manner. In this case, the Navier-Stokes equation is obtained in the liquid region. In the porous region, the equations are close to the Brinkman model. In connection with the description of the flow from the standpoint of a single equation for the entire region, there is no need to set boundary conditions in the separation region (such as Beavers – Joseph – Saffman). Cross-border conditions arise if the energy estimation is used for the porous region. In this case, the order of the systems of equations in each area is different. On the basis of the proposed model, the energy estimation for the equation of Rahmatullin is derived using energy inequalities. The difference scheme of the equation of Rahmatullin is constructed and the stability of the constructed scheme is obtained.

##### A Transmuted Power Gompertz Distribution: Properties and Applications

Innocent Boyle Eraikhuemen, Terna Godfrey Ieren, Adana’a Felix Chama, Abraham Iorkaa Asongo, Bassa Shiwaye Yakubu, Abdul Haruna Bala

Theory and Practice of Mathematics and Computer Science Vol. 9, 4 May 2021, Page 127-145
https://doi.org/10.9734/bpi/tpmcs/v9/2394E

This work introduces and studies a new probability distribution called “Transmuted Power Gompertz distribution”. The work studied the properties of the new model. The estimates of the four parameters model were carried out using the method of maximum likelihood estimation. The work further evaluates the goodness-of-fit of the proposed distribution compared to other distributions by means of applications of the model to two real life datasets and the result show that the proposed distribution is more flexible than the fitted existing distributions.

##### Studies on Travelling Wave Solutions for Three Dimensional Incompressible MHD Equations

M. Aldhabani, S. M. Sayed

Theory and Practice of Mathematics and Computer Science Vol. 9, 4 May 2021, Page 146-153
https://doi.org/10.9734/bpi/tpmcs/v9/6458D

In this paper, the solutions of three dimensional incompressible magnetohydrodynamics (MHD) equations are obtained by using sin (k$$\mathrm{\xi}$$)- cos (k$$\mathrm{\xi}$$)($$\mathrm{\xi}$$=$$\mathrm{\xi}$$(x,y,z,t),k$$\geq$$0) method and Riccati auxiliary equation. This paper obtains the soliton solutions by the aid of software Mathematica. These stabilized soliton solutions are focused at incompressible fluids and the main technological applications in mind are those related with material processing techniques.

##### Deductive System on CL-Algebra

Safiqul Islam

Theory and Practice of Mathematics and Computer Science Vol. 9, 4 May 2021, Page 154-160
https://doi.org/10.9734/bpi/tpmcs/v9/8488D

In this paper, we introduce the concept of deductive system on CL-algebra. It is proved that this concept generalizes the notion of deductive system on Residuated Lattices. It has been shown that quotient algebra, corresponding to CL-algebra, formed with the help of deductive system is also a CL-algebra.

##### Study on Watermarking Relational Databases

Mayuree K. Rathva, G. J. Sahani

Theory and Practice of Mathematics and Computer Science Vol. 9, 4 May 2021, Page 161-171
https://doi.org/10.9734/bpi/tpmcs/v9/8227D

The use of digital watermarking to secure the content of database systems is a new research direction in information security. Until now, the majority of the work has been based on image, video and audio. However, because of the growing use of relational database systems, database watermarking has become a research subject. Which addresses the legal issue of database system copyright protection. In this paper, we have focused on the review of four relational database watermarking techniques proposed by researchers [R. Agarwal & Jerry Kiernan, ZHU Qin, Brijesh B. Mehta, A. Al-Haj and Ali Hamadou]. The security of relational databases has been a great concern since the expanded use of these data over the Internet. Digital watermarking for relational databases emerged as a candidate solution to provide copyright protection, tamper detection, traitor tracing and maintaining integrity of relational data.