75 reads in the past 30 days

M-Polynomial and NM-Polynomial Methods for Topological Indices of PolymersFebruary 2024

·

379 Reads

Published by Wiley

Online ISSN: 1687-0425

Disciplines: Mathematics & statistics, general & introductory mathematics

75 reads in the past 30 days

M-Polynomial and NM-Polynomial Methods for Topological Indices of PolymersFebruary 2024

·

379 Reads

52 reads in the past 30 days

Bernoulli Poisson Moment Exponential Distribution: Mathematical Properties, Regression Model, and ApplicationsOctober 2024

·

52 Reads

36 reads in the past 30 days

Effects of Thermal Radiation and Chemical Reaction on Hydromagnetic Fluid Flow in a Cylindrical Collapsible Tube with an ObstacleMarch 2023

·

284 Reads

·

7 Citations

33 reads in the past 30 days

A Mathematical Model for the Within-Host Dynamics of Malaria Parasite with Adaptive Immune ResponsesOctober 2024

·

56 Reads

31 reads in the past 30 days

M− Prime Ideals in Lattices and Their M− Prime SpectrumOctober 2024

·

31 Reads

International Journal of Mathematics and Mathematical Sciences is an open access journal publishing research across all fields of mathematics and mathematical sciences, such as pure and applied mathematics, mathematical physics, probability and mathematical statistics.

As part of Wiley’s Forward Series, this journal offers a streamlined, faster publication experience with a strong emphasis on integrity. Authors receive practical support to maximize the reach and discoverability of their work.

November 2024

·

1 Read

Ramdé Nestor

·

Traoré Amidou

·

Simporé Yacouba

·

Nakoulima Ousseynou

We consider a linear system based on a population dynamics model dependent on age, space and nonlocal boundary conditions. Note that our population dynamics model is a four-step model with a second derivative with respect to the age variable and a second derivative with respect to the space variable. Population growth at each stage depends on time and space. We prove the uniqueness and existence of a positive solution by combining the Galerkin’s variational method and the Banach’s fixed point theorem.

November 2024

·

20 Reads

In this paper, the concept of centrally extended α,β-higher derivations is studied. It is shown to be additive in a ring without nonzero central ideals. Also, we prove that in semiprime rings with no nonzero central ideals, every centrally extended α,β-higher derivation is an α,β-higher derivation. Some examples are given to show that our theorems’ assumptions cannot be relaxed. The invariance problem of the center of the ring is also investigated.

October 2024

·

11 Reads

We provide in this note a different refinement of Jensen’s inequality obtained via superquadratic functions. A refinement of Minkowski’s and Hölder’s inequalities is also established as an application of our refined Jensen’s inequality.

October 2024

·

52 Reads

We introduce a new flexible count distribution by combining Bernoulli and Poisson moment exponential (PMEx) distributions. The new model named the Bernoulli PMEx distribution. Some mathematical properties are studied, including the hazard rate function, moments, moment generating function, probability generating function, and dispersion index. A count regression model is also proposed based on this distribution. The maximum likelihood estimation method is used to estimate the model parameters. In the end, three datasets from different fields are utilized for application purposes. The findings show that the new model efficiently analyzed these datasets as compared to Poisson, discrete Pareto, discrete Rayleigh, discrete Burr-Hatke, and discrete inverted Topp–Leone distributions.

October 2024

·

31 Reads

In this paper, we explore various characteristics and attributes of M− prime ideals, minimal M− prime ideals, and weakly M− prime ideals in a lattice. We demonstrate that the image and inverse image of an M− prime ideal (or weakly M− prime ideal) also qualify as an M− prime ideal (or weakly M− prime ideal). Additionally, we investigate the relationship between M− prime ideals and weakly M− prime ideals. Finally, we introduce the concept of the space of M− prime ideals and discuss their characterizations.

October 2024

·

56 Reads

Mathematical analysis of epidemics is crucial for long-term disease prediction and helps to guide decision-makers in terms of public health policy. In this study, we develop a within-host mathematical model of the malaria parasite dynamics with the effect of an adaptive immune response. The model includes six compartments, namely, the uninfected red blood cells, infected red blood cells, merozoites, gametocytes, cytotoxic T cells immune response, and antibodies immune response, which are activated in the host to attack the parasite. We establish the well-posedness and biological feasibility of the model in terms of proving the non-negativity and boundedness of solutions. The most important threshold value in the epidemiological model known as the basic reproduction number, R0, which is used to determine the stability of the steady state, is investigated. Furthermore, the parasite-free equilibrium is locally and globally stable if the basic reproduction number, R0<1, otherwise, if R0>1, then there exist four parasite-persistence equilibria. The stability conditions of these parasite-persistence equilibria are presented. Sensitivity analysis of the basic reproduction number shows that parameters representing the recruitment rate of uninfected red blood cells, infection rate of red blood cells by merozoites, and the average number of merozoites per ruptured infected red blood cells are the most influential ones in affecting the dynamics. Finally, several numerical simulations of the model are presented to supplement the theoretical and analytical findings. It has been observed that numerical simulations and theoretical results are coherent. The response of cytotoxic T cells and antibodies has a significant impact on suppressing infected cells and malaria parasites in the host’s body.

September 2024

·

23 Reads

This paper offers an in-depth investigation into pure ideals within the Hurwitz series ring. Specifically, by focusing on the Hurwitz series ring, denoted as HR over a ring R, we present a comprehensive characterization of differential ideals. In this paper, we prove that these differential ideals can be expressed in the form HI, where I represents an ideal in the underlying ring R. Through this analysis, a comprehensive understanding of the structure and properties of pure ideals within the Hurwitz series ring is achieved.

September 2024

·

46 Reads

Hybrid metaheuristics is one of the most exciting improvements in optimization and metaheuristic algorithms. A current research topic combines two algorithms to provide a more advanced solution to optimization problems. The present study applies a new approach called HWOA-TTA which means a hybrid of the whale optimizer algorithm (WOA) and tiki-taka algorithm (TTA). The hybrid WOA-TTA combines the exploitation phase of WOA with the exploration phase of TTA. Two stages in the hybridized model are suggested. First, the WOA exploitation phase incorporates the TTA mechanism. Second, a new approach is included in the research phase to enhance the result with each iteration to a set of unconstrained benchmark test functions and engineering design applications. To verify the performance of the improved algorithm, thirteen benchmark functions have been used to compare HWOA-TTA with the classical intelligent population algorithms (PSO, TTA, and WOA). The hybrid algorithm is applied to two well-known engineering mathematical models. The experiments show that the HWOA-TTA outperforms other algorithms.

September 2024

·

49 Reads

The morbidity of children under five years due to diarrhea is very prevalent in Nairobi County. Mathematical models can be used to study the dynamics of infections and suggest possible control strategies in the process. In this study, a deterministic model has been developed to investigate the impact of hygiene and treatment as control strategies, on the dynamics of diarrhea in children under five years of age in Nairobi County. In the analysis of the model, it was shown that the disease-free equilibrium of the model was locally and globally asymptotically stable if the effective reproduction number was less than unity, while the endemic equilibrium point was locally and globally asymptotically stable if the effective reproduction number was greater than unity. From the sensitivity analysis of the effective reproduction number, it was observed that the sensitivity indices of the effective contact rate, the fraction of children joining the infected classes and modification parameters, are positive, while the indices of the rate of being born five years ago, hygiene compliance, natural death rate, rate of gaining symptoms, death rates due to diarrhea, treatment rates for infected children, recovery rates for treated children, and discharge rate are negative. From scenario simulations of the model, it was observed that when hygiene compliance strategy is increased, the disease is decreased and when it is equal to one, that is, when it is fully embraced, the disease is completely eradicated. It was observed that by increasing the treatment rate for mildly infected and treatment rate for severely infected children, the disease is controlled. It was lastly found that by increasing both the treatment rate for mildly infected children and hygiene compliance, the disease dies out and by increasing both the treatment rate for severely infected children and hygiene compliance, the disease is also eradicated completely. From the results, it was noted that by increasing hygiene compliance, the disease is completely wiped out as compared to treatment. It was also noted that for the two strategies combined, the disease is wiped out after 20 days if increased, while for the hygiene compliance strategy alone, the disease is wiped out after 40 days if fully embraced. Thus, it was concluded that both hygiene compliance and treatment are the best control strategies if fully embraced for the complete eradication of the disease within a shorter period of time.

August 2024

·

50 Reads

·

2 Citations

In this article, a uniformly convergent numerical scheme is developed to solve a singularly perturbed convection-diffusion equation with a small delay having a boundary layer along the left side. A priori bounds of continuous solution and its derivatives are discussed. To solve the problem, the Crank–Nicolson scheme in the time direction and the exponentially fitted finite difference scheme in the space direction are used. The stability of the method is analyzed. It is proved that the developed scheme converges uniformly with first order in space and second order in time. To validate the applicability of the theoretical finding of the developed scheme, numerical experiments are carried out by considering two test examples.

August 2024

·

76 Reads

The aim of this research is to investigate certain problems of differential subordination and superordination of analytic univalent functions in an open unit disk. Furthermore, the universal by-product operator and geometric properties such as coefficient inequalities are investigated. Remarkable results on the differential subordination and superordination of analytic univalent functions and results using higher derivative operator for differential subordination are obtained. Some interesting applications of subordination in the unit disk are obtained using convolution and convexity.

August 2024

·

40 Reads

This paper derives and evaluates the reliability measures for a model pumping system composed of six subsystems linked in series: subsystems 1, 2, and 6, each comprising one unit, while subsystems 3 and 5 each contain three units operating in parallel. Subsystem 4 contains three units effectively operating in series. Unit failure rates are assumed to be constant, while repair rates are modeled by either a general distribution or, in the event of system failure, a Gumbel–Hougaard copula. The Laplace transform and additional supplementary variable approaches are employed to solve the system. The conventional measures of reliability are computed for a range of parameter values and as functions of time. In addition, tables are presented containing parameters for different cases, accompanied by a discussion of how they were chosen and their impact on the results.

August 2024

·

16 Reads

In this article a nonlinear Volterra integral equation is studied in the space of functions of the bounded variation in the Shiba sense on the plane. A series of conditions is established for the functions and the kernel involved in this equation which guarantee the global existence and uniqueness of the solution in this space.

August 2024

·

103 Reads

Trigonometric functions have gained considerable attention in recent studies for developing new lifetime distributions. This is due to their parsimonious framework, mathematical tractability, and flexibility of the newly developed distributions. In this paper, the Sine-generated family is used to create a new bounded lifetime distribution, known as Sine-Marshall–Olkin Topp–Leone distribution, for modeling data defined on the unit interval. Some statistical properties of the new bounded distribution, including quantile function, ordinary moments, incomplete moments, moment-generating functions, inequality measures, Rényi entropy, and probability weighted moments are derived. Seven methods of parameter estimation, including maximum likelihood, ordinary least squares, weighted least squares, moment product spacing, Anderson–Darling, and Cramér–von Mises estimators are used to estimate the parameters of the new distribution. The behavior of the estimators obtained from the estimation methods are investigated using Monte Carlo simulation studies. The results show that the estimation methods are asymptotically efficient and consistent. The flexibility of the new bounded distribution is examined via data fitting using two proportional datasets. The results of the fittings show that the new bounded distribution performs significantly better than the competing bounded lifetime distributions. Finally, Sine-Marshall–Olkin Topp–Leone regression model is presented as an alternative to the beta and Kumaraswamy regression models.

July 2024

·

75 Reads

Every field in mathematics has made significant progress in research with fuzzy sets. Numerous application fields were discovered in both empirical and theoretical investigations, ranging from information technology to medical technology, from the natural sciences to the physical sciences, and from technical education to fine arts education. However, it has limitations of its own and has not been able to function in real-world situations. An interdisciplinary approach of fuzzy theory with number theory, especially Diophantine equations, needs to be accomplished to overcome this problem. A thorough literature study of the Diophantine equations, fuzzy sets, and the combination known as the linear Diophantine fuzzy set (LDFS) is accomplished in the present study. New forms of LDFSs have been added recently, and these additions have found use in a variety of fields, including the disciplines of pharmacology, power, healthcare, goods, and finance. The genesis of these expansions is also examined in this study of the literature. Hence, in the present work, some applications of LDFS are described in detail. Further in the present study, the existing primary constraints in the research on LDFS are highlighted. Also, the last section of the review is dedicated to outlining some future directions for the study of LDFS.

July 2024

·

24 Reads

July 2024

·

51 Reads

Some boundedness and convergence properties of generalized Fibonacci’s-type recurrences and their associated iterated recurrence ratios between pairs of consecutive terms are discussed under a wide number of initial conditions. Also, a more general, so-called k,q Fibonacci’s recurrence and the associated Fibonacci’s ratio recurrences are investigated, where the constants k and q are the prefixed gains used to generate each new member of the recurrences from the two preceding ones. Some oscillation and periodicity conditions are also discussed depending on the initial conditions, while convergence and stability properties are also dealt with. The initial conditions of the recurrences can be fixed arbitrarily, so that both the well-known standard Fibonacci recurrence and the Lucas recurrence are just particular cases. In the most general case, the initial conditions can be integer or real and of alternate signs. Later on, the manuscript deals with some further boundedness, oscillation, convergence, and stability properties of generalized Fibonacci recurrences and associated Fibonacci ratio recurrences being generated under, in general, recurrence-dependent gain sequences.

July 2024

·

79 Reads

In this work, we introduce a new concept called the tripotent divisor graph of a commutative ring. It is defined with vertices set in a ring R, where distinct vertices r1 and r2 are connected by an edge if their product belongs to the set of all nonunite tripotent in R. We denote this graph as 3I ΓR. We utilize this graph to examine the role of tripotent elements in the structure of rings. Additionally, we provide various findings regarding graph-theoretic characteristics of this graph, including its diameter, vertex degrees, and girth. Furthermore, we investigate the size, central vertices, and distances between vertices for the tripotent divisor graph formed by the direct product of two fields.

July 2024

·

158 Reads

In this article, a one-parameter probability mass function called Poisson XRani is proposed by combining the Poisson and the XRani distributions. A wide range of distributional properties such as the shape of the probability mass function, probability generating function, factorial moments, moment generating function, characteristic function, raw moments, dispersion index, mean, variance, coefficient of skewness, and coefficient of kurtosis are investigated. It is proven that the proposed probability mass function can easily handle overdispersed and right-skewed count observations with heavy tails. Both maximum likelihood and Bayesian estimation techniques are used to estimate the unknown parameter of the proposed distribution and a simulation study was conducted to examine and analyze the performance of the maximum likelihood estimation procedure based on sample size, absolute bias, relative absolute bias, and root mean square error. The usefulness of the proposed distribution is assessed using two distinctive real datasets. These applications reveal that the new distribution provides an adequate fit compared to the other eight discrete distributions.

July 2024

·

24 Reads

In this paper, we investigate a reflected backward stochastic differential equation (RBSDE) with jumps, focusing on cases where the mean reflection is nonlinear. Unlike traditional RBSDEs, this particular type of RBSDE imposes a constraint defined by the mean of a loss function that does not follow the continuous condition. We start by deriving an a priori estimate of the solution, followed by establishing the uniqueness and existence of the solution. Theoretical results are illustrated by way of an example of the application of super-hedging to the reinsurance and investment problem under a risk constraint.

June 2024

·

69 Reads

The Poisson regression model (PRM) is a widely used statistical technique for analyzing count data. However, when explanatory variables in the model are correlated, the estimation of regression coefficients using the maximum likelihood estimator (MLE) can be compromised by multicollinearity. This phenomenon leads to inaccurate parameter estimates, inflated variance, and increased mean squared error (MSE). To address multicollinearity in PRM, we propose a novel Kibria–Lukman hybrid estimator. We evaluate the performance of our estimator through extensive Monte Carlo simulations, assessing its accuracy using mean absolute percentage errors (MAPE) and MSE. Furthermore, we provide empirical applications to illustrate the practical relevance of our proposed method. Our simulation results and empirical applications demonstrate the superiority of the proposed estimator.

June 2024

·

47 Reads

This paper aims to introduce a novel variation of almost Hardy–Rogers ψ,ϕ-type multivalued contraction and ϑ-type contraction mappings. The main focus is on proving new fixed point (FP) results in M℘-metric space (M℘-MS). Additionally, several consequences are derived from our main findings. To elucidate the recency of our outcomes, various examples are provided. Finally, we utilize the obtained results to scrutinize the existence of solutions for nonlinear fourth-order differential equations (NFODEs).

June 2024

·

46 Reads

To obtain the links between the incomplete gamma function and the two copulas (independent and Gumbel). We went through some integral function transformations. The transformations used are Laplace, Fourier, and Mellin. Our work can be seen as a bridge between the notion of copula in probability and Euler’s gamma function which has a lot of application in mathematical modeling. In short, a wide range of possibilities is offered to us thanks to these links that we have established.

June 2024

·

74 Reads

·

2 Citations

This research paper introduces the novel subclass ϒΣϑ,β,μq˜ of bi-univalent functions that are connected to Fibonacci numbers. Our main contributions in this study involve establishing constraints on the absolute values of the second coefficient a2 and the third coefficient a3 for functions within this specific subclass. In addition, we provide solutions to Fekete–Szegö functional problems. Furthermore, our investigation reveals intriguing outcomes resulting from the specific parameter values used in our main findings.

May 2024

·

17 Reads

A boundary value problem for a nonhomogeneous heat equation with a load in the form of a fractional Riemann–Liouville integral of an order β∈0,1 is considered. By inverting the differential part, the problem is reduced to an integral equation with a kernel with a special function. The special function is presented as a generalized hypergeometric function. The limiting cases of the order β of the fractional derivative are studied: it is shown that the interval for changing the order of the fractional derivative can be expanded to integer values β∈0,1. The results of the study remain unchanged. The kernel of the integral equation is estimated. Conditions for the solvability of the integral equation are obtained.

Journal Impact Factor™

Acceptance rate

CiteScore™

Submission to first decision

Article processing charge

Sergey Evgenievich Barykin

Academic Editor

Peter the Great St. Petersburg Polytechnic University, Russia

Bilal Bilalov

Academic Editor

Institute of Mathematics and Mechanics, Ministry of Science and Education Republic of Azerbaijan, Azerbaijan

Fernando Bobillo

Academic Editor

University of Zaragoza, Spain