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, Edem Kwedzo Bankas, Mohammed Muniru Iddrisu
Journal of Advances in Mathematics and Computer Science pp 72-90; https://doi.org/10.9734/jamcs/2021/v36i930405

Abstract:
In this research paper, a Redundant Residue Number System (n,k) code is introduced to enhance Cloud ERP Data storage. The research findings have been able to demonstrate the application of Redundant Residue Number System (RRNS) in the concept of Cloud ERP Data storage. The scheme contributed in addressing data loss challenges during data transmission. The proposed scheme also addressed and improved the probability of failure to access data compared to other existing systems. The proposed scheme adopted the concept of Homomorphic encryption and secret sharing whiles applying Redundant Residue Number System to detect and correct errors.The moduli set used is {2m, 2m + 1, 2m+1 - 1, 2m+1 + 1, 2m+1 + k, 22m - k, 22m + 1} where k is the number of the information moduli set used. The information moduli set is {2m, 2m + 1, 2m+1 - 1} and the redundant moduli is {2m+1 + 1, 2m+1 + k, 22m - k, 22m + 1}. The proposed scheme per the simulation results using python reveals that it performs far better in terms of data loss and failure to access data related concerns. The proposed scheme performed better between 41.2% for data loss to about 99% for data access based on the combination of (2, 4) and (2, 5) data shares respectively in a (k, n) settings.
Shiyu Li
Journal of Advances in Mathematics and Computer Science pp 91-108; https://doi.org/10.9734/jamcs/2021/v36i930406

Abstract:
In this paper, we are concerned with the existence and uniqueness of global weak solutions for the weakly dissipative Dullin-Gottwald-Holm equation describing the unidirectional propagation of surface waves in shallow water regime: ut − α2uxxt + c0ux + 3uux + γuxxx + λ(u − α2uxx) = α2(2uxuxx + uuxxx).Our main conclusion is that on c0 = − γ/α2 and λ ≥ 0, if the initial data satisfies certain sign conditions, then we show that the equation has corresponding strong solution which exists globally in time, finally we demonstrate the existence and uniqueness of global weak solutions to the equation.
, Duncan Kioi Gathungu
Journal of Advances in Mathematics and Computer Science pp 56-71; https://doi.org/10.9734/jamcs/2021/v36i930404

Abstract:
The aim of this paper is to analyse thermal elastohydrodynamic lubrication (TEHL) line contact of rolling a bearing using a non-Newtonian uid that is described by the power law model. The performance characteristics of the rolling bearing are determined for various index for dilatant, Newtonian and pseudo plastic uids. The one-dimensional Reynolds and energy equations are both modied to incorporate the non-Newtonian nature of the lubricant. The coupled system of governing equations are discretized using the finite difference method and solved simultaneously. The results show that the pressure, film thickness and temperature for dilatant uids increased with increase in the ow index as compared to pseudo plastic uids. The in uence of thermal effects on pressure and lm thickness is more significant compared with that under isothermal elastohydrodynamic lubrication especially on the case of dilatant uids. The viscosity of the lubricant increases with increase in pressure and reduces with increment in temperature. The surface roughness in the bearing surface increases the lm thickness of the lubricant. The uid pressure, film thickness and temperature increases with increase in the bearing speed. To truly re ect the characteristics of EHL models, thermal effects should be considered.
Bing Cheng, Guangbin Wang, Fuping Tan
Journal of Advances in Mathematics and Computer Science pp 48-55; https://doi.org/10.9734/jamcs/2021/v36i930401

Abstract:
In this paper, we construct two-step tensor splitting iteration method for multi-linear systems. Moreover, we present convergence analysis of this method. Finally, we give two numerical examples to show that this new method is more ecient than the existing methods.
D. Samaila, G. N. Shu’Aibu, B. A. Modu
Journal of Advances in Mathematics and Computer Science pp 37-47; https://doi.org/10.9734/jamcs/2021/v36i930400

Abstract:
A long-standing problem is how to create a short-length presentation for finite groups of degree n. This paper aimed at presenting a concrete method for generating presentations for the groups Sm+n, S2m and Smn for all m,nÎZ+ with fewer relations than the existing literature from the presentations of Sm and Sn. The aim is achieved by considering finite groups acting on sets and Cartesian product of groups which lead to the construction of multiple transformations as representatives of some finite groups.
Journal of Advances in Mathematics and Computer Science pp 30-36; https://doi.org/10.9734/jamcs/2021/v36i930399

Abstract:
In this article, it is assumed that the distribution of the error terms is the Birnbaum-Saunders distribution in the process of one-way ANOVA. The Birnbaum-Saunders distribution has been widely used in reliability analysis especially in fatigue-life models. In reliability analysis, nonnormal distribution is much more common than the normal distribution. We obtain the estimation of the parameters og interest by maximum likelihood method. We also propose new test statistics based on these estimators . The efficiencies of the maximum likelihood estimators and the Type I errors obtained by using the proposed estimators are compared with normal theory via Monte Carlo simulation study. At the end of the study, the real life example is given just for the illustration of the method.
D. Samaila, G. N. Shu’Aibu, B. A. Modu
Journal of Advances in Mathematics and Computer Science pp 17-29; https://doi.org/10.9734/jamcs/2021/v36i930398

Abstract:
The use of finite group presentations in signal processing has not been exploit in the current literature. Based on the existing signal processing algorithms (not necessarily group theoretic approach), various signal processing transforms have unique decomposition capabilities, that is, different types of signal has different transformation combination. This paper aimed at studying representation of finite groups via their actions on Signal space and to use more than one transformation to process a signal within the context of group theory. The objective is achieved by using group generators as actions on Signal space which produced output signal for every corresponding input signal. It is proved that the subgroup presentations act on signal space by conjugation. Hence, a different approach to signal processing using group of transformations and presentations is established.
D. N. Ojua, J. A. Abuchu, E. O. Ojua, E. I. Enang
Journal of Advances in Mathematics and Computer Science pp 1-16; https://doi.org/10.9734/jamcs/2021/v36i930397

Abstract:
Calibration approach adjusts the original design weights by incorporating an auxiliary variable into it, to make the estimator be in the form of a regression estimator. This method was employed to propose calibration product type estimators using three distance measures namely; chi-square distance measure, the minimum entropy distance measure and the modified chi-square distance measure using double constraints. The estimators of variances of the proposed estimators were also obtained. An empirical study to ascertain the performance of these estimators using a secondary data set and simulated data under underlying distributional assumptions of Gamma, Normal and Exponential distributions with varying sample sizes of 10%, 15%, 20% and 25% were carried out. The result with the real life data showed that the calibration product type estimator from chi-square distance measure estimated the population mean with minimum bias than and obtained from the other distance measures. The result from real life data also revealed that the estimator obtained from chi-square distance measure under two constraints was more efficient than the other three estimators. The result from simulation studies showed that the proposed calibration product type estimators outperform the conventional product type estimator in term of efficiency, consistency and reliability under the Gamma and Exponential distributions with the exponential distribution taking the lead. The conventional product type estimator however was found to be better under normal distribution. It was also observed that as sample size increases there was no significant change in the performance of these proposed estimators which justifies the preference with small sample size.
, Maurice Oduor Owino, Moses Ndiritu Gichuki
Journal of Advances in Mathematics and Computer Science pp 137-154; https://doi.org/10.9734/jamcs/2021/v36i830396

Abstract:
In this paper, R is considered a completely primary finite ring and Z(R) is its subset of all zero divisors (including zero), forming a unique maximal ideal. We give a construction of R whose subset of zero divisors Z(R) satisfies the conditions (Z(R))5 = (0); (Z(R))4 ̸= (0) and determine the structures of the unit groups of R for all its characteristics.
Journal of Advances in Mathematics and Computer Science pp 120-136; https://doi.org/10.9734/jamcs/2021/v36i830395

Abstract:
Some fundamental mathematical researches have been carried out about mathematical certainties based on ancient Egyptian mathematical sources and their problems following ancient Egyptian Wisdom set of knowledge building the new scientific paradigm following the rediscovery of the true value of PI and following the new approach of Global Dimensional Mathematics [1]. Some fundamental mathematical researches on the foundations of Egyptian mathematics covering the mathematical problem of The Akhmin wooden tablets [2], the tenth and the fourteenth problem of The Moscow Mathematical Papyrus [3] as well as the forty-first and fiftieth problem from The Rhind Mathematical Papyrus [3] have been carried out, without forgotten, the resolution of the fundamental question of the quadrature of the circle which is now effective. In the disclosure of Egyptian mathematics, the new approach to fundamental mathematical notions is established, adding the cornerstone to building the core of the new approach to Egyptian mathematics, mathematics and science in general. The Egyptian mathematics disclosure solves, following the Egyptian approach to mathematics and following ancient Egyptian Wisdom set of knowledge, unsolved ancient Egyptian mathematical problems, such as finding the complete solution and decoding the glyph of the eye of Horus, as well as the problem of the truncated pyramid which has found a solution like the half basket problem found one. The question of the quadrature of the circle shatters the mathematical conceptions with all the consequences that we can only begin to understand. The Egyptian mathematics disclosure forms the basis for building the new scientific approach based on ancestral Egyptian mathematical problems, the true rediscovered value of PI and the new original Global Dimensional Mathematics opening up a still unknown perspective on the world of science in general.
Journal of Advances in Mathematics and Computer Science pp 70-119; https://doi.org/10.9734/jamcs/2021/v36i830394

Abstract:
In this paper intuitionistic set theory INC#∞# in infinitary set theoretical language is considered. External induction principle in nonstandard intuitionistic arithmetic were derived. Non trivial application in number theory is considered.The Goldbach-Euler theorem is obtained without any references to Catalan conjecture. Main results are: (i) number ee is transcendental; (ii) the both numbers e + π and e − π are irrational.
, Steady Mushayabasa
Journal of Advances in Mathematics and Computer Science pp 52-69; https://doi.org/10.9734/jamcs/2021/v36i830393

Abstract:
To understand the effects of animal movement on transmission and control of brucellosis infection, a reaction diffusion partial differential equation (PDE) brucellosis model that incorporates wild and domesticated animals under homogeneous Neumann boundary conditions is proposed and analysed. We computed the reproductive number for the brucellosis model in the absence of spatial movement and we established that, the associated model has a globally asymptotically stable disease-free equilibrium whenever the reproductive number is less or equal to unity. However, if the reproductive number is greater than unity an endemic equilibrium point which is globally asymptotically stable exists. We performed sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. For the model with spatial movement the disease threshold is studied by using the basic reproductive number. Additionally we investigate the existence of a Turing stability and travelling waves. Our results shows that incorporating diffusive spatial spread does not produce a Turing instability when the reproductive number R0ODE associated with the ODE model is less than unity. Finally the results suggest that minimizing interaction between buffalo and cattle population can be essential to manage brucellosis spillover between domesticated and wildlife animals. Numerical simulations are carried out to support analytical findings.
Journal of Advances in Mathematics and Computer Science pp 44-51; https://doi.org/10.9734/jamcs/2021/v36i830391

Abstract:
Sarason did pioneer work on the reflexivity and purpose of this paper is to discuss the reflexivity of different class of contractions. Among contractions it is now known that C11 contractions with finite defect indices, C.o contractions with unequal defect indices and C1. contractions with at least one finite defect indices are reflexive. More over the characterization of reflexive operators among co contractions and completely non unitary weak contractions with finite defect indices has been reduced to that of S (F), the compression of the shift on H2 ⊖ F H2, F is inner. The present work is mainly focused on the reflexivity of contractions whose characteristic function is constant. This class of operator include many other isometries, co-isometries and their direct sum. We shall also discuss the reflexivity of hyponormal contractions, reflexivity of C1. contractions and weak contractions. It is already known that normal operators isometries, quasinormal and sub-normal operators are reflexive. We partially generalize these results by showing that certain hyponormal operators with double commutant property are reflexive. In addition, reflexivity of operators which are direct sum of a unitary operator and C.o contractions with unequal defect indices,is proved Each of this kind of operator is reflexive and satisfies the double commutant property with some restrictions.
Yakubu Abdul-Wahab Nawusu, Alhassan Abdul-Barik, Salifu Abdul-Mumin
Journal of Advances in Mathematics and Computer Science pp 27-43; https://doi.org/10.9734/jamcs/2021/v36i830388

Abstract:
Transmission errors are commonplace in communication systems. Wireless sensor networks like many other communication systems are susceptible to various forms of errors arising from sheer noise, heat and interference in sensor circuitry and from other forms of distortions. Research efforts in WSN have attempted to guarantee reliable and accurate data transmission from a target environment in the midst of these unwanted exposures. Many techniques have appeared and employed over the years to deal with the issue of transmission errors in communication systems. In this paper we present a new approach for single and multiple error control in WSN relying on the inherent fault tolerant feature of the Redundant Residue Number System. As an off shoot of Residue Number System, RRNS's fault tolerant capabilities help in building robust systems required for reliable data transmission in WSN systems. The Chinese Remainder Theorem and the Manhattan Distance Heuristics are used during the integer recovery process when detecting and correcting error digit(s) in a transmitted data. The proposed method performs considerably better in terms of data retrieval time than similar approaches by needing a smaller number of iterations to recover an originally transmitted data from its erroneous form. The approach in this work is also less computationally intensive compared to recent techniques during the error correction steps. Evidence of utility of the technique is illustrated in numerical examples.
Changwang Xiao
Journal of Advances in Mathematics and Computer Science pp 10-26; https://doi.org/10.9734/jamcs/2021/v36i830387

Abstract:
We obtain a blowup result for solutions to a semilinear wave equation with scale-invariant dissipation. We perform a change of variables that transforms our starting equation into a Generalized Tricomi equation, then apply Kato’s lemma, we can prove a blowup result for solutions to the transformed equation under some assumptions on the initial data. In the critical case, we use the fundamental solutions of the Generalized Tricomi equation to modify Kato’s lemma to deal with it.
Journal of Advances in Mathematics and Computer Science pp 1-9; https://doi.org/10.9734/jamcs/2021/v36i830386

Abstract:
Associated with every commuting m-tuples of operators on a complex Hilbert space X is its Aluthge transform. In this paper we show that every commuting m-tuples of operators on a complex Hilbert space X and its Aluthge transform have the same joint essential spectrum. Further, it is shown that the joint essential spectrum of Aluthge transform is contained in the joint essential numerical range of Aluthge transform.
K. W. Bunonyo, C. U. Amadi
Journal of Advances in Mathematics and Computer Science pp 66-79; https://doi.org/10.9734/jamcs/2021/v36i730385

Abstract:
In this research, we investigated the effect of tumor growth on blood flow through a micro channel by formulated the governing model with the assumption that blood is an incompressible, eclectrially conducting fluid which flow is caused by the pumping action of the heart and suction. The governing model was scaled using some dimensionless variables and the region of the tumor was obtained from Dominguez [1] which was incorporated in our model. The model is further reduced to an ordinary differential equation using a perturbation condition. However, the ordinary differential equation was solved using method of undermined coefficients, and the constants coefficients obtained via matrix method. Furthermore, the simulation to study the effect of the pertinent parameters was done suing computation software called Mathematica. It is seen in our investigation that the entering parameters such as magnetic field parameter, the Reynolds number, womersley number, oscillatory frequency parameter, and permeability parameter affect the blood velocity profile in decreasing and increasing fashion.
K. C. Nwankwo, I. S. Onyeagu, C. H. Nwankwo, G. A. Osuji, C. K. Onyekwere
Journal of Advances in Mathematics and Computer Science pp 52-65; https://doi.org/10.9734/jamcs/2021/v36i730384

Abstract:
In this article, we study the mathematical characteristics of the inverse power Pranav distribution. The proposed distribution has three special cases namely Pranav, inverse Pranav and inverse power Pranav distributions. In addition with the basic properties of the distribution, the maximum likelihood method was employed in computing the parameters of the distribution. The 95% confidence interval was estimated for each of the parameters and finally, the distribution was applied to 128 bladder cancer patients to illustrate its applicability, and compared to Pranav distribution, inverse power Lindley distribution and inverse Ishita distribution. However, the inverse power Pranav distribution proved superiority over the competing models.
, A. A. Malle, C. Chibuisi, M. Z. Idris
Journal of Advances in Mathematics and Computer Science pp 45-51; https://doi.org/10.9734/jamcs/2021/v36i730383

Abstract:
The conjugacy classes of the Metabelian group G, plays an important role in defining the conjugate graph, whose vertices are non-central elements of G, and two vertices are connected if and only if they are conjugate. The constructions of conjugate graphs of all non abelian metabelian groups of order less than 24 are the basis for this paper. And the obtained results are then used to calculate the energy of the aforementioned group. This is aided by specialized programming software (maple).
Journal of Advances in Mathematics and Computer Science pp 38-44; https://doi.org/10.9734/jamcs/2021/v36i730382

Abstract:
In this paper, we give some application of scalar type operators to Decomposibility. In particular, we show that if H is of (α, α + 1) type R and that it generates a strongly continuous group on a Banach space, then its resolvent is Decomposable hence scalar type.
Journal of Advances in Mathematics and Computer Science pp 30-37; https://doi.org/10.9734/jamcs/2021/v36i730381

Abstract:
Nowadays, video sharing websites are becoming more and more popular, such as YouTube, Tiktok. A good way to analyze a video’s sentiment would greatly improve the user experience and would help with designing better ranking and recommendation systems [1,2]. In this project, we used both acoustic information of a video to predict its sentiment levels. For audio data, we leverage transfer learning technique and use a pre-trained VGGish model as a features extractor to analyze abstract audio embeddings [6]. We then used MOSI dataset [5] to further fine-tune the VGGish model and achieved a test accuracy of 90% for binary classification. For text data, we compared traditional bag-of-word model to LSTM model. We found that LSTM model with word2vec outperformed bag-of-word model and achieved a test accuracy of 84% for binary classification.
Journal of Advances in Mathematics and Computer Science pp 21-29; https://doi.org/10.9734/jamcs/2021/v36i730380

Abstract:
Like the optical prism to break white light up into its constituent spectral colors, the machine to show a prime as a single spectrum is proposed. From the theoretical analysis, it can be shown that the machine to recognize the prime number as a single spectrum can be realized by using the correlation function of Riemann zeta function. Moreover, this method can be used for a factorization of the integer consisted of two primes.
Patrick Mwangi Kimani, Daniel Adicka
Journal of Advances in Mathematics and Computer Science pp 11-20; https://doi.org/10.9734/jamcs/2021/v36i730379

Abstract:
Most researchers consider the action of projective general group on the cosets of its maximal subgroups leaving out non-maximal subgroups. In this paper, we consider the action of centralizer of an elliptic element which is a non maximal subgroup . In particular, we determine the subdegrees, rank and properties of the suborbital graphs of the action. We achieve this through the application of the action of a group by conjugation. We have proved that the rank is q and the subdegrees are and .
Journal of Advances in Mathematics and Computer Science pp 1-10; https://doi.org/10.9734/jamcs/2021/v36i730378

Abstract:
Here we build the fundamentals of global dimensional mathematics in order to build the new basis of the new theoretical scientific paradigm. Research on the foundations of mathematics covering the definition of fundamental mathematical concepts such as point, line, direction, dimension, addition, multiplication, division, zeros, infinities, limits, factorization, integers and prime numbers, were carried out and further still the resolution of the Goldbach conjecture is now effective. New original fundamental mathematical notions are established building the core of global dimensional mathematics based on the decomposition of integers into an addition of prime numbers terms and on fundamental geometric concepts such as the concept dimension based on the notion of direction and point, as well as research on set theory and work on the notion of limits and infinity. The termization as a decomposition of integers into an addition of prime number terms by a python program, breaks the unique factorization theorem, the fundamental theorem of arithmetic while the geometric notions developed break Euclidean geometry leading to a new mathematical framework, geometry, topology and metrics leading to a total change of theoretical scientific paradigm. Global dimensional mathematics forms the basis for the construction of the new scientific paradigm of the 21st century and beyond, opening up a still unknown perspective on the world of science in general.
Jiajun Hua,
Journal of Advances in Mathematics and Computer Science pp 97-109; https://doi.org/10.9734/jamcs/2021/v36i630377

Abstract:
In this paper, by using the general discrete Halanay inequalities, the techniques of inequalities and some other properties, we study the ultimate boundedness of a class of the discrete-time uncertain neural network systems and obtain several sufficient conditions to ensure the ultimate boundedness of discrete-time uncertain neural networks with leakage and time-varying delays. Finally numerical examples are given to verify the correctness of the conclusion.
M. Jeyaraman, S. Sowndrarajan, A. Ramachandran
Journal of Advances in Mathematics and Computer Science pp 88-96; https://doi.org/10.9734/jamcs/2021/v36i630374

Abstract:
In this paper, we consider generalized fuzzy metric spaces and provide existence and uniqueness fixed point results. First, we use compatible maps of type (β) to prove fixed point results, then we introduce weakly compatible maps to approximate common fixed point results by using an implicit relation.
Journal of Advances in Mathematics and Computer Science pp 63-74; https://doi.org/10.9734/jamcs/2021/v36i630372

Abstract:
In this work, the stability properties of damped gyroscopic systems have been studied using Lyapunov direct method. These systems are generally stable because of the presence of gyroscopic effect. Conditions for determining the stability of the damped gyroscopic systems have been developed. Solution bounds of amplitude and velocity have been obtained for both homogeneous and inhomogeneous cases. An example is given to show how the stability conditions are applied to systems to determine its stability status.
, Bhausaheb R. Sontakke
Journal of Advances in Mathematics and Computer Science pp 75-87; https://doi.org/10.9734/jamcs/2021/v36i630373

Abstract:
The intention behind this paper is to achieve exact solution of one dimensional nonlinear fractional partial differential equation(NFPDE) by using Adomian decomposition method(ADM) with suitable initial value. These equations arise in gas dynamic model and heat conduction model. The results show that ADM is powerful, straightforward and relevant to solve NFPDE. To represent usefulness of present technique, solutions of some differential equations in physical models and their graphical representation are done by MATLAB software.
Journal of Advances in Mathematics and Computer Science pp 30-62; https://doi.org/10.9734/jamcs/2021/v36i630371

Abstract:
In this paper, closed forms of the sum formulas ∑n k=0 xkWmk 2 +j for generalized Fibonacci numbers are presented. As special cases, we give sum formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered. Of course, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery.
Journal of Advances in Mathematics and Computer Science pp 24-29; https://doi.org/10.9734/jamcs/2021/v36i630370

Abstract:
In this work, the effect of perturbation on linear fractional differential system is studied. The analysis is done using Riemann-Liouville derivative and the conclusion extended to using Caputo derivative since the result is similar. Conditions for determining the stability and asymptotic stability of perturbed linear fractional differential system are given.
, B. O. John
Journal of Advances in Mathematics and Computer Science pp 11-23; https://doi.org/10.9734/jamcs/2021/v36i630369

Abstract:
Across different sections of life, physical and chemical sciences, differential equations which could be ordinary differential equations (ODEs) or partial differential equations (PDEs) are used to model the various systems as observed. Some types of ODEs, and a few PDEs are solvable by analytical methods with much difficulties. However, the great majority of ODEs, especially the non-linear ones and those that involve large sets of simultaneous differential equations, do not have analytical solutions but require the application of numerical techniques. This work focused on exemplifying numerical approximations (Adams-Bashforth-Moulton, Bogacki-Shampine, Euler) of ODEs Initial value Problem in its simplest approach using a case study of gluconic acid frementation by Psuedonomas Ovalis. The performance of the methods was checked by comparing their accuracy. The accuracy was detrermined by the size of the discretization error estimated from the difference between analytical solution and numerical approximations. The results obtained are in good agreement with the exact solution. This work affirms that numerical methods give approximate solutions with less rigorous work and time as there is room for flexibility in terms of using different step sizes with the Euler solver as most accurate.
, Joseph Folake Lois
Journal of Advances in Mathematics and Computer Science pp 1-10; https://doi.org/10.9734/jamcs/2021/v36i630368

Abstract:
MATLAB is a high level programming tool for technical computing, its application cuts across different sphere of science, engineering, finance, communication, music etc. With the current increase in the use of non-integer order derivatives, there is a need to have tools that handle them for effective applications. In this paper, we present a brief comparative review of 2 expressions of fractional derivative. MATLAB functions for approximating Riemann-Liouville and Caputo fractional derivatives are presented alongside. Numerical simulations with test examples are implemented and results compared. To effectively handle non-polynomial function, Taylor series expansion is employed to convert the function into a form that can be easily handled.
, Gukat G. Bitrus, Chibuisi Chigozie
Journal of Advances in Mathematics and Computer Science pp 107-119; https://doi.org/10.9734/jamcs/2021/v36i530367

Abstract:
An 8 dimensional Walker manifold (M; g) is a strict walker manifold if we can choose a coordinate system fx1; x2; x3; x4; x5; x6; x7; x8g on (M,g) such that any function f on the manfold (M,g), f(x1; x2; x3; x4; x5; x6; x7; x8) = f(x5; x6; x7; x8): In this work, we dene a Non-strict eight dimensional walker manifold as the one that we can choose the coordinate system such that for any f in (M; g); f(x1; x2; x3; x4; x5; x6; x7; x8) = f(x1; x2; x3; x4): We derive cononical form of the Levi-Civita connection, curvature operator, (0; 4)-curvature tansor, the Ricci tensor, Weyl tensorand study some of the properties associated with the class of Non-strict 8 dimensionalWalker manifold. We investigate the Einstein property and establish a theorem for the metric to be locally conformally at.
Journal of Advances in Mathematics and Computer Science pp 98-106; https://doi.org/10.9734/jamcs/2021/v36i530366

Abstract:
Meta-heuristic techniques are important as they are used to find solutions to computationally intractable problems. Simplistic methods such as exhaustive search become computationally expensive and unreliable as the solution space for search algorithms increase. As no method is guaranteed to perform better than all others in all classes of optimization search problems, there is a need to constantly find new and/or adapt old search algorithms. This research proposes an Infrasonic Search Algorithm, inspired from the Gravitational Search Algorithm and the mating behaviour in peafowls. The Infrasonic Search Algorithm identified competitive solutions to 23 benchmark unimodal and multimodal test functions compared to the Genetic Algorithm, Particle Swarm Optimization Algorithm and the Gravitational Search Algorithm.
, David Angwenyi, Kevin Midenyo
Journal of Advances in Mathematics and Computer Science pp 84-97; https://doi.org/10.9734/jamcs/2021/v36i530365

Abstract:
There are several functional forms for non-linear dynamical filters. Extended Kalman filters are algorithms that are used to estimate more accurate values of unknown quantities of internal dynamical systems from a sequence of noisy observation measured over a period of time. This filtering process becomes computationally expensive when subjected to high dimensional data which consequently has a negative impact on the filter performance in real time. This is because integration of the equation of evolution of covariances is extremely costly, especially when the dimension of the problem is huge which is the case in numerical weather prediction.This study has developed a new filter, the First order Extended Ensemble Filter (FoEEF), with a new extended innovation process to improve on the measurement and be able to estimate the state value of high dimensional data. We propose to estimate the covariances empirically, which lends the filter amenable to large dimensional models. The new filter is derived from stochastic state-space models and its performance is tested using Lorenz 63 system of ordinary differential equations and Matlab software.The performance of the newly developed filter is then compared with the performances of three other filters, that is, Bootstrap particle Filter (BPF), First order Extended Kalman Bucy Filter (FoEKBF) and Second order Extended Kalman Bucy Filter (SoEKBF).The performance of the FoEEF improves with the increase in ensemble size. Even with as low number of ensembles as 40, the FoEEF performs as good as the FoEKBF and SoEKBF. This shows, that the proposed filter can register a good performance when used in high-dimensional state-space models.
, U. G. I. G. K. Udagedara, Erik M. Bollt
Journal of Advances in Mathematics and Computer Science pp 66-83; https://doi.org/10.9734/jamcs/2021/v36i530364

Abstract:
Full-waveform inversion (FWI) is a non-destructive health monitoring technique that can be used to identify and quantify the embedded anomalies. The forward modeling of the FWI consists of a simulation of elastic wave equation to generate synthetic data. Thus the accuracy of the FWI method highly depends on the simulation method used in the forward modeling. Simulation of a 3-D seismic survey with small-scale heterogeneities is impossible with the classic finite difference approach even on modern super computers. In this work, we adopted a mesh refinement approach for simulation of the wave equation in the presence of small-scale heterogeneities. This approach uses cubic smoothing spline interpolation for spatial mesh refinement step in solving the wave equation. The simulation results for the 2-D elastic wave equation are presented and compared with the classic finite difference approach.
T. O. Akinwumi, , A. O. Adesanya, M. O. Alabi
Journal of Advances in Mathematics and Computer Science pp 35-51; https://doi.org/10.9734/jamcs/2021/v36i530362

Abstract:
In this paper, a mathematical model for the transmission of HIV/AIDS with early treatment is developed and analyzed to gain insight into early treatment of HIV/AIDS and other epidemiological features that cause the progression from HIV to full blown AIDS. We established the basic reproduction number which is the average number of new secondary infection generated by a single infected individual during infectious period. The analysis shows that the disease free equilibrium is locally and globally asymptotically stable whenever the threshold quantity is less than unity i.e. Numerical analysis shows that the early treatment of latently infected individuals reduces the dynamical progression to full blown AIDS. The result also showed that immunity boosted substances increase the red blood cells, sensitivity analysis of basic reproduction number with respect to parameters showed that effective contact rate must not exceed 0.3 to avoid endemic stage.
, Amina E. Abo-Hussien, Salwa A. Mousa, Magda M. Ismail
Journal of Advances in Mathematics and Computer Science pp 52-65; https://doi.org/10.9734/jamcs/2021/v36i530363

Abstract:
In this paper, an odd generalized exponential Lomax (OGEL, in short) distribution has been considered. Some mathematical properties of the distribution are studied. The methods of maximum likelihood and maximum product of spacing are used for estimating the model parameters. Moreover, 95% asymptotic confidence intervals for the estimates of the parameters are derived. The Monte Carlo simulation is conducted for the two proposed methods of estimation to evaluate the performance of the various proposed estimators. The proposed methods are utilized to find estimates of the parameters of OGEL distribution for the daily recovery cases of COIVD-19 in Egypt from 12 May to 30 September 2020.The practical applications show that the proposed model provides better fits than the other models.
Journal of Advances in Mathematics and Computer Science pp 1-5; https://doi.org/10.9734/jamcs/2021/v36i530360

Abstract:
Let R be a commutative ring with identity 1 and I is an ideal of R. The zero divisor graph of the ring with respect to ideal has vertices defined as follows: {u ∈ Ic | uv ∈ I for some v ∈ Ic}, where Ic is the complement of I and two distinct vertices are adjacent if and only if their product lies in the ideal. In this note, we investigate the conditions under which the zero divisor graph of the ring with respect to the ideal coincides with the zero divisor graph of the ring modulo the ideal. We also consider a case of Galois ring module idealization and investigate its ideal based zero divisor graph.
Journal of Advances in Mathematics and Computer Science pp 6-34; https://doi.org/10.9734/jamcs/2021/v36i530361

Abstract:
Empirical evidence in support of generalizations of Fermat’s equation is presented. The empirical evidence consists mainly of results for the p = 3 case where Fermat’s Last Theorem is almost false. The empirical evidence also consists of results for general p values. The \pth power with respect to" concept (involving congruences) is introduced and used to derive these generalizations. The classical Furtw¨angler theorems are reformulated. Hasse used one of his reciprocity laws to give a more systematic proof of Furtw¨angler’s theorems. Hasse’s reciprocity law is modified to deal with a certain condition. Vandiver’s theorem is reformulated and generalized. The eigenvalues of 2p x 2p matrices for the p = 3 case are investigated. (There is a relationship between the modularity theorem and a re-interpretation of the quadratic reciprocity theorem as a system of eigenvalues on a finite-dimensional complex vector space.) A generalization involving generators and \reciprocity" has solutions for every p value.
Journal of Advances in Mathematics and Computer Science pp 90-112; https://doi.org/10.9734/jamcs/2021/v36i430359

Abstract:
In this paper intuitionistic set theory INC# ∞# in infinitary set theoretical language is considered. External induction principle in nonstandard intuitionistic arithmetic were derived. Non trivial application in number theory is considered.The Goldbach-Euler theorem is obtained without anyreferences to Catalan conjecture.
Journal of Advances in Mathematics and Computer Science pp 79-89; https://doi.org/10.9734/jamcs/2021/v36i430358

Abstract:
Groundwater is the main source of fresh water available for human beings. The surface water groundwater interaction affects the quantity and quality of groundwater. Hence the study of surfacewater-groundwater interaction is the emerging topic in this new era. In this paper, the analytical approximation of water table fluctuation in the aquifer is presented. The aquifer is subjected to the recharge and withdrawal activity through multiple basins and wells in the domain. The time dependent multiple recharge is considered. The flow is approximated by a non linear partial differential equation called Boussineq equation. The solution of Boussineq equation is developed using Finite Fourier cosine transform. Response of the solution to using numerical examples has been tested. Effect of aquifer parameters on the fluctuation of water table formation mainly water mound and cone of depression due to recharge and withdrawal are presented. The effect of permeability of aquifer base on the water table is also discussed.
Lanxi Zhang,
Journal of Advances in Mathematics and Computer Science pp 54-61; https://doi.org/10.9734/jamcs/2021/v36i430356

Abstract:
Forecasting gasoline consumption is of great significance for formulating oil production, foreign trade policies, and ensuring the balance of domestic refined oil supply. Based on grey system theory, a fractional accumulation operator is constructed to optimize the accumulation method of the traditional discrete grey model, and the Particle Swarm Optimization algorithm is used to solve the fractional nonlinear parameters. This model was used in the prediction of gasoline consumption in Chongqing, China, and compared with the existing 7 models. The results show that the fractional discrete grey model optimized by PSO has better prediction accuracy. The fractional discrete grey model optimized by PSO can be used as a quantitative method in the field of energy forecasting.
Journal of Advances in Mathematics and Computer Science pp 62-78; https://doi.org/10.9734/jamcs/2021/v36i430357

Abstract:
In this paper, we extend the Bernardi-Raugel element [1] to convex polygonal meshes by using the generalized barycentric coordinates. Comparing to traditional discretizations defined on triangular and rectangular meshes, polygonal meshes can be more flexible when dealing with complicated domains or domains with curved boundaries. Theoretical analysis of the new element follows the standard mixed finite element theory for Stokes equations, i.e., we shall prove the discrete inf-sup condition (LBB condition) by constructing a Fortin operator. Because there is no scaling argument on polygonal meshes and the generalized barycentric coordinates are in general not polynomials, special treatments are required in the analysis. We prove that the extended Bernardi-Raugel element has optimal convergence rates. Supporting numerical results are also presented.
, A. M. Abd Al-Fattah, G. R. Al-Dayian, A. A. El-Helbawy
Journal of Advances in Mathematics and Computer Science pp 30-53; https://doi.org/10.9734/jamcs/2021/v36i430355

Abstract:
Statistical prediction is one of the most important problems in life testing; it has been applied in medicine, engineering, business and other areas as well. In this paper, the exponentiated generalized xgamma distribution is introduced as an application on the exponentiated generalized general class of distributions. Bayesian point and interval prediction of exponentiated generalized xgamma distribution based on dual generalized order statistics are considered. All results are specialized to lower records. The results are verified using simulation study as well as applications to real data sets to demonstrate the flexibility and potential applications of the distribution.
Fangyu Zhang, Yuqin Zhang,
Journal of Advances in Mathematics and Computer Science pp 23-29; https://doi.org/10.9734/jamcs/2021/v36i430354

Abstract:
Let T be a unit regular tetrahedron. A diminished copy of T is the image of T under a homothety with positive ratio smaller than 1. Let m be a positive integer and let γm(T) be the smallest positive number r such that T can be covered by m translates of rT. Zong gave the results of γ4(T) = 3/4and γ5(T) = 9/13. However, the values of γ6(T) , γ7(T) and γ8(T) were not given then. In this article we give the upper bounds of γ6(T), γ7(T) and γ8(T).
Xu Yifan,
Journal of Advances in Mathematics and Computer Science pp 15-22; https://doi.org/10.9734/jamcs/2021/v36i430353

Abstract:
By using the properties of Euler function, an upper bound of solutions of Euler function equation is given, where is a positive integer. By using the classification discussion and the upper bound we obtained, all positive integer solutions of the generalized Euler function equation are given, where is the number of distinct prime factors of n.
, Winifred N. Mutuku
Journal of Advances in Mathematics and Computer Science pp 1-14; https://doi.org/10.9734/jamcs/2021/v36i430352

Abstract:
Aims: Develop and analyze a mathematical model of the effect of inpatient rehabilitation of tobacco smokers on tobacco smoking using Kenya as a case study. Perform stability analysis on the smoking free equilibrium point and endemic equilibrium point of the model. Use numerical simulation to investigate the impact of inpatient rehabilitation of tobacco smokers on smoking. Place and Duration of Study: Department of Mathematics and Actuarial Science, School of Pure and Applied Sciences (SPAS), Kenyatta University, Kenya, between May 2019 and September 2020. Tobacco smoking is a serious burden in Kenya and the world at large. Smoking harms nearly every organ of the body and affects the overall health of a person. Despite the overwhelming facts about the consequences of tobacco smoking, it remains a bad wont which is socially accepted and widely spread. In this research we numerically analyze the dynamics of smoking incorporating the impact of inpatient rehabilitation to curb the smoking habit. We first present a three-compartment model incorporating inpatient rehabilitation, then develop the system of ordinary differential equations governing the smoking dynamics. The basic reproduction number is determined using next generation matrix method. The model equilibria were computed and the stability analysis carried out. The results of stability analysis indicate that the disease-free equilibrium (DFE) is both locally and globally asymptotically stable for RS < 1 while the endemic equilibrium is both locally and globally asymptotically stable for RS > 1. Numerical simulations of model carried out with the help of MATLAB shows that, when rehabilitation is implemented effectively, it helps in minimization of smoking in the community.
, Lucas S. F. de Araujo
Journal of Advances in Mathematics and Computer Science pp 97-117; https://doi.org/10.9734/jamcs/2021/v36i330349

Abstract:
Based on the SIR model that divides the population into susceptible, infected and removed individuals, data about the evolution of the pandemic compiled by the Johns Hopkins University Center for Systems Science and Engineering (JHUCSSE) are integrated into the numerical system solution. The system parameters Rate of Contact β, Basic Reproduction Number R0 and Removal Rate γ, also named Rate of Decay, are determined according to a ridge regression approach and a mobile statistical scheme with different averages. Data is automatically downloaded from https://raw.githubusercontent.com/CSSEGISandData/COVID-19. The main Python libraries used are Numpy, Pandas, Skit-Learn, Requests and Urllib.
Journal of Advances in Mathematics and Computer Science pp 118-131; https://doi.org/10.9734/jamcs/2021/v36i330350

Abstract:
A quantum field theory has been constructed, in which leptons are bound by electromagnetic forces. Using severe boundary conditions, in particular several constraints on the rotation velocity, a precision test has been possible, in which the needed 7 parameters are determined by many more constraints. Since arbitrary adjustment parameters are excluded, absolute values of radii, rotation velocities and binding energies are obtained, possible only in a fundamental theory, which must be close to the final lepton theory. The resulting masses are obtained with uncertainties much smaller than 1 %. The results show a very special structure of charged and neutral leptons. 1. Charged leptons: The deduced radii due to electric and magnetic binding are different by many orders of magnitude. In particular, the large electric root mean square radius of the electron of about 103fm is almost of the same size as electron wave functions in light atoms, whereas the magnetic radius of 2.5 · 10−10 fm is consistent with a ”point” particle needed to describe electron hadron scattering. Neutrals: The acceleration term gives rise to dynamically generated neutral particles of ”hole” structure, which can be identified with neutrinos. Their masses are 2 · 10−8eV, 17 eV and 12 MeV for νe, νµ and ντ , respectively. The full calculations together with the underlying fortran source code can be viewed at https://h2909473.stratoserver.net or https://leptonia-etc.de.
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