Afrika Matematika最新文献

In the present article, we prove a Shapiro uncertainty principle for the directional short-time Fourier transform. Next, we introduce the notion of Toeplitz operators associated with the directional short-time Fourier transform. Particularly, we study the trace class properties of such operators and prove that they belong to the Schatten–von Neumann class. Next, we investigate the boundedness and compactness of these Toeplitz operators in the (L^{p})-spaces. Finally, we introduce and study the generalized spectrogram associated with these Toeplitz operators.

In this article, we discuss the geometry of gradient Ricci-Bourguignon solitons (GRB) and then we characterize the general relativistic space-time with Ricci-Bourguignon (RB) and GRB solitons. First, we obtain the expression for the scalar curvature of a compact GRB soliton. Then, we prove that the gradient of the potential function of GRB soliton is bounded if its scalar curvature satisfies a boundedness condition. Then the Riemannian curvature of a 4-dimensional GRB soliton and its derivative are investigated whenever the Weyl tensor is harmonic. It is proven that if the potential vector field is torse-forming, then a compact RB soliton becomes perfect fluid space-time. We also discuss the bounds of the first eigenvalue of Laplacian. A volume formula for GRB soliton is obtained. Further, we study the application of conformal vector field on a RB soliton and obtain the expression for the Ricci curvature. Next, we find when RB soliton is expanding, shrinking and steady, if relativistic perfect fluid space-time admits a RB soliton with conformal vector field. We also construct a non-trivial example of GRB soliton equipped with a conformal potential vector field.

First, we prove a new alternative fixed point theorem in generalized gauge (or generalized uniformizable) spaces. This is a generalization of a famous result of Diaz-Margoli. Next, using this theorem, we show the stability of a delay differential equation where the unknown mapping takes its values in a locally convex space (in particular into a Banach space). Examples are given to support our results. We also point out some gaps in the literature and fix them.

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.