Afrika Matematika最新文献

In this paper we are going to show that derivations satisfying some identity carry a certain form. To prove this, we assume (mathcal {R}) is a prime ring with (char(mathcal {R})ne 2), (mathcal {I}) is a nonzero ideal of (mathcal {R}), (mathcal {U}) is the Utumi quotient ring of (mathcal {R}) with extended centroid (mathcal {C}=mathcal {Z}(mathcal {U})) and (f(x_1,ldots ,x_n)) is any noncentral valued multilinear polynomial over (mathcal {C}). Suppose that (mathcal {F}) and (mathcal {G}) are two generalized derivations and d is any non-zero derivation of (mathcal {R}). If

for all (zeta =(zeta _1,ldots ,zeta _n)in mathcal {I}^n), then (mathcal {F}(x)=ax) or (mathcal {F}(x)=xa) for any (xin mathcal {R}), for some (ain mathcal {U}) along with (a^2 =0) and following one conclusion holds:

1. (1)

   (mathcal {G}=0);

2. (2)

   there exists (lambda in mathcal {C}) and a derivation h of (mathcal {R}) such that (mathcal {G}(x)= lambda x+h(x)) for all (xin mathcal {R}) with (f(zeta _1,ldots ,zeta _n)^2) is central valued on (mathcal {R});

3. (3)

   (mathcal {R}) satisfies (s_4).

In this article, we define a new operation on a graph, namely the u-graph and find a necessary and sufficient condition for the folded map to be a homomorphism. Also, we introduce the limit folded map on the u-graph. We deduce the relation between a special family of graphs and their folded maps. We construct a finite sequence of folded maps on a finite number of connected u-graphs. Under certain conditions, we derive the relationship between a u-graph and its subgraphs. Furthermore, we present some applications for new graph operations.

We study a coupled system of waves and strongly damped Petrovsky equations with internal fractional damping in a bounded domain. After demonstrating that the system is well-posed using the semigroup theory of linear operators and a conclusion established by Borichev and Tomilov, we analyze the systems stability.

In a space X, if for every countable open cover (mathcal {U} ={U_n:n in textbf{N}}) of X, we can find a subcover ({mathcal {V}} = {U_{m_k}:k in textbf{N}}) such that (delta ({m_k: U_{m_k} in {mathcal {V}} })=0) then the space is called a statistically compact space. Extending the recent works of Sarkar, Bal, and Rakshit on statistically compactness, we investigate statistically compactness of a topological space in the star-operator’s background. The concept of star statistically compactness is contrasted to other topological features. This study explains the attributes of star statistically compactness and its subspaces under diverse circumstances, especially under open continuous surjection.

In our experiment, we investigate a model of a three-species food chain that includes the predation-driven Allee effect. Within this framework, we propose and analyze an application of a Z-type control mechanism. Our findings reveal that the predation pressure exerted by the intermediate predator on the prey population induces chaos through period-doubling bifurcation. To confirm the presence of chaos, we compute the Lyapunov exponents. Subsequently, we introduce an indirect Z-control mechanism across different trophic levels of the food chain model. Specifically, we apply the Z-control method to the top predator to regulate the population fluctuations of the intermediate predator. Furthermore, we employ the Z-type controller on the intermediate predator population to govern the oscillations in the prey population, leading to the eradication of chaos from the system. Additionally, we observe that gestation delay in the top predator can trigger population oscillations within the system. We also find that implementing the indirect Z-controller to the top predator population can suppress population oscillations in the delayed system. Our research establishes the fundamental concept that the Z-type control method serves as the most efficient controller across various dynamical regimes of the uncontrolled system. It facilitates the regulation of all kinds of oscillations within the system and can replace population oscillation with a predefined stable steady-state, which is vital for promoting ecosystem stability. Our experiment emphasizes the importance of control mechanisms in managing population fluctuations and highlights the potential of Z-type control mechanisms in predator–prey interaction strategies.

We propose a new concept of stability, called here as “aggregated multi-stability”, which is based on multiple aggregation functions and also uses Mittag-Leffler and hypergeometric functions. This is inspired by the general framework of the Ulam, Hyers and Rassias types of stability, but differs in essence both in the multi-dependency of various aggregation functions and in choosing special functions to play the role of controllers. This notion is applied here to a class of (mathfrak {J})-Hilfer fractional differential equations for which we identify sufficient conditions to guarantee its aggregated multi-stability.

In this paper, we study the so called Kato-Rellich theorem. We prove a similar result for multi-subordinate perturbation. Moreover, we apply this result to study a perturbed operator of Nagy and (n times n) block matrices of linear operators. The obtained results are of importance to be applicated to study the Schrödinger operators. Finally, we give an application to a Gribov operator in Bargmann space.

We propose in this paper a tighter underestimator for (C^{2})-nonconvex bivariate functions. We show that it is tighter than the classical (alpha -)BB underestimator. A branch and bound algorithm with this tighter underestimator is developed to solve bivariate global optimzation problems. The triangulation is used as an exhaustive subdivision, and a convex/concave test is added to accelerate the convergence of our branch and bound algorithm.

In this research, we have derived a mathematical model for within human dynamics of COVID-19 infection using delay differential equations. The new model considers a ’latent period’ and ’the time for immune response’ as delay parameters, allowing us to study the effects of time delays in human COVID-19 infection. We have determined the equilibrium points and analyzed their stability. The disease-free equilibrium is stable when the basic reproduction number, (R_0), is below unity. Stability switch of the endemic equilibrium occurs through Hopf-bifurcation. This study shows that the effect of latent delay is stabilizing whereas immune response delay has a destabilizing nature.

In the present paper, sufficient conditions for the existence of bounded positive periodic solutions are established for a class of nonlinear neutral differential equations with iterative source term and nonlinear impulses. The form including an impulsive term of the equations in this paper is rather general and incorporates as special cases various problems which have been studied extensively in the literature. Transforming the considered equation to an equivalent integral equation, we prove the existence of positive periodic solutions using a Krasnoselskii fixed point theorem for the sum of a contraction and a compact mapping. Finally, we present an example to illustrate the effectiveness of our results.