Arabian Journal of Mathematics最新文献

This paper presents a stochastic (mathsf {S_{h}V_{h}A_{h}C_{h}H_{h}R_{h}}) model to analyze the transmission dynamics of Hepatitis B virus (HBV) by incorporating random noise, time delays, and vaccination effects. The perturbations are modeled as linear, assuming that immunity wanes after a certain period post-vaccination. Initially, a deterministic model is developed to calculate the basic reproduction number (R_{h0}^D). This deterministic model is then extended to its stochastic counterpart. We prove the existence of a globally bounded and positive solution for the stochastic model, ensuring its mathematical and biological feasibility. Furthermore, we demonstrate that the model is ergodic and possesses a unique stationary distribution. Numerical simulations are performed to illustrate the theoretical findings, showing how stochastic perturbations can significantly influence HBV transmission dynamics. These simulations underscore the importance of effective control measures, such as vaccination and quarantine strategies, to mitigate the spread of HBV. The study provides valuable information for public health policymakers and contributes to designing more effective HBV control programs.

We propose a queueing-inventory system (QIS) that involves a single server who places a random order quantity ’R’ when stock is depleted completely and immediately takes a vacation. This variable R follows a discrete probability distribution, while the server’s vacation duration follows a phase-type (PH) distribution. Customers arriving during stock-out and vacation periods are turned away, resulting in lost sales. Inter-arrival times, service time, and lead times are all assumed as mutually independent and exponentially distributed random variables. Each customer is served a single unit of the product. Our research primarily examines the stability condition and the stationary distribution of the three-dimensional process encompassing queue length, inventory status, and server states. The stability condition is derived as a function of arrival and service rates. Additionally, we develop a cost model to determine the economic order quantity (EOQ) and provide numerical illustrations to trace EOQ values under various order policies and PH type vacations.

In this paper, we review Segal’s postulates for general Quantum Mechanics, updating and clarifying their mathematical formulation to simplify them. Our approach provides additional insights as well as a pathway to easily contribute new results to the body of knowledge on systems of observables. Moreover, we introduce the notion of complex system of observables, which arises naturally from the analysis carried out. As we show, these last systems of observables are related to the classical (real) ones through the process of complexification. Taking advantage of this, algebraic systems of observables are completely determined in both the real and complex cases.

This paper deals with the existence, uniqueness, the Ulam–Hyers (UH) and Ulam–Hyers–Rassias (UHR) Stability of the fractional stochastic integro-differential equations (FSIDEs) with non-instantaneous impulsive and nonlocal conditions in a Hilbert space. The results are obtained by using stochastic analysis techniques, fixed point theory and generalized Grönwall inequality. An example is given to illustrate the effectiveness of the proposed results.

Chaudhry and Qadir obtained new identities for the gamma function by using a “distributional representation” for it. Here we obtain new identities for the Riemann zeta function and its family by using that representation for them. This also leads to new identities involving the Dirichlet eta and Lambda functions.

In this work, we introduce the idea of (lambda )-central Musielak–Orlicz-BMO spaces and (lambda )-central Musielak–Orlicz–Morrey spaces. We obtain the boundedness of the Hardy operators on (lambda )-central Musielak–Orlicz–Morrey spaces.

In this paper, we examine a general model of Love-type damped wave equations that includes the p-Laplacian and a memory term. Firstly, by utilizing linearization techniques, the Faedo-Galerkin method, and arguments of compactness, we establish the existence and uniqueness of solutions for the problem. Next, the techniques and estimations presented in [Appl. Math. 68 (2) (2023) 209-254] are used to obtain the continuous dependence of solutions on relaxation functions and nonlinear components of the problem. Furthermore, under several appropriate assumptions, a finite-time blow-up of solutions with negative initial energy is also proved. Finally, we discuss some open problems that arise from our findings.

In this paper, an efficient method has been introduced for solving the generalized Burgers’ equation by combining Hermite interpolating polynomials and the nonstandard finite difference technique. Initially, the time derivative is discretized using the nonstandard finite difference method and the spatial derivatives are discretized using a (theta -) weighted scheme. The computation is further based on quintic Hermite polynomials, transforming the differential equations into algebraic equations which are then solved numerically using MATLAB. Stability analysis is conducted using the Von Neumann approach. An adequate investigation has been performed for test problems with higher order nonlinearities for demonstrating the application of the proposed method. The numerical solutions obtained for them closely match the exact solution and give better results than existing literature. The obtained rate of convergence is of nearly third order. This approach can be applied widely to various nonlinear physical models, as it is efficient in terms of easy implementation and high accuracy.

Considering a ({mathbb {Z}}_3)-graded 3-dimensional space, we develop ({mathbb {Z}}_3)-graded differential calculi on the algebra of functions defined on this space, which is a ({mathbb {Z}}_3)-graded Hopf algebra. We demonstrate that these differential calculi admit a (*)-operation. Additionally, we discover a new ({mathbb {Z}}_3)-graded upper triangular quantum group and explicitly define its ({mathbb {Z}}_3)-graded Hopf algebraic structure. We also show in detail that this quantum group is the symmetry group of one of these calculi.

Using properties of the generalised Zeckendorf decompositions, we study the extended Frobenius problem for sequences of the form ({p_a+p_n}_{nin {mathbb {N}}}), where ({p_n}_{nin {mathbb {N}}}) is an r-Fibonacci sequence and (p_a) is an r-Fibonacci number.