Journal of Mathematics

The main purpose of this article is to use some identities of the classical Gauss sums, the properties of character sums, and Dedekind sums (modulo an odd prime) to study the computational problem of one-kind mean values related to Dedekind sums and give some interesting identities for them.

The Hyers–Ulam stability of multi-coefficients Pexider additive functional inequalities in Banach spaces is investigated. In order to do this, the fixed point method and the direct method are used.

This paper presents a three-dimensional continuous time dynamical system of three species, two of which are competing preys and one is a predator. We also assume that during predation, the members of both teams of preys help each other and the rate of predation of both teams is different. The interaction between prey and predator is assumed to be governed by a Holling type II functional response and discrete type gestation delay of the predator for consumption of the prey. In this work, we establish the local asymptotic stability of various equilibrium points to understand the dynamics of the model system. Different conditions for the coexistence of equilibrium solutions are discussed. Persistence, permanence of the system, and global stability of the positive interior equilibrium solution are discussed by constructing suitable Lyapunov functions when the gestation delay is zero, and there is no periodic orbit within the interior of the first quadrant of state space around the interior equilibrium. As we introduced time delay due to the gestation of the predator, we also discuss the stability of the delayed model. It is observed that the existence of stability switching occurs around the interior equilibrium point as the gestation delay increases through a certain critical threshold. Here, a phenomenon of Hopf bifurcation occurs, and a stable limit cycle corresponding to the periodic solution of the system is also observed. This study reveals that the delay is taken as a bifurcation parameter and also plays a significant role for the stability of the proposed model. Computer simulations of numerical examples are given to explain our proposed model. We have also addressed critically the biological implications of our analytical findings with proper numerical examples.

Suppose that is a Banach algebra and is its enveloping dual Banach algebra, we show that is approximately contractible (approximately amenable) if has the same property. Also, we study the relation between the pseudoamenability of and the pseudoamenability of the second dual and we also characterize approximate biflatness and approximate biprojectivity of associated with approximate biflatness and approximate biprojectivity of the second dual .

The influence of consumer psychological effects on customer needs has become a normal state of product sales models in the consumer goods supply chain field. The literature lacks systematic research on the mechanism through which consumer psychological effects affect customer needs. On the basis of analyzing and sorting out the literature and viewpoints, this paper establishes a mathematical model to investigate how manufacturers design and plan product supply strategies based on nonessential demand patterns under three different sales models. Finally, by solving the mathematical model, the optimal production volume, the optimal commodity price, and the maximum profit that can be obtained by the manufacturer are obtained, and the correctness of the model is verified via numerical calculation. The study results explain the relationships among commodity costs, demand, and commodity pricing, which are significant for the study of consumer psychology and can further provide a beneficial reference for manufacturers in various industries.

The objective of the current study is to provide a variety of families of soliton solutions to pseudo-parabolic equations that arise in nonsteady flows, hydrostatics, and seepage of fluid through fissured material. We investigate a class of such equations, including the one-dimensional Oskolkov (1D OSK), the Benjamin-Bona-Mahony (BBM), and the Benjamin-Bona-Mahony-Peregrine-Burgers (BBMPB) equation. The Exp (-)-expansion method is used for new hyperbolic, trigonometric, rational, exponential, and polynomial function-based solutions. These solutions of the pseudo-parabolic class of partial differential equations (PDEs) studied here are new and novel and have not been reported in the literature. These solutions depict the hydrodynamics of various soliton shapes that can be utilized to study the nature of traveling wave solutions of other nonlinear PDE’s.