Analysis and Mathematical Physics最新文献

A novel asymptotic representation of the analytic solutions to a family of singularly perturbed (q-)difference-differential equations in the complex domain is obtained. Such asymptotic relation shows two different levels associated to the vanishing rate of the domains of the coefficients in the formal asymptotic expansion. On the way, a novel version of a multilevel sequential Ramis-Sibuya type theorem is achieved.

This work is devoted to discuss the existence of solutions for an abstract class of partial integro-differential inclusions without compactness or norm-continuity conditions. Therefore, we derive an existence theory for some problems of fractional differential inclusions, as well as, neutral differential inclusions with nonlocal conditions on Banach space. Our studies are achieved via fixed point techniques.

This study aims to investigate the intricate dynamics of the stochastic Hirota-Maccari system forced in the It(hat{o}) sense. First, we establish a dynamical system linked to the equation by employing the Galilean transformation. By employing the system of complete discriminant of the polynomial technique, we methodically develop single traveling wave solutions for the governing model. Our solutions encompass hyperbolic, rational, and trigonometric forms, Jacobian elliptic functions, and various solitary wave solutions, along with transitions of Jacobian elliptic functions to periodic and hyperbolic solutions. Furthermore, we investigate the bifurcation processes that are intrinsic to the derived system using concepts from the theory of planar dynamical systems. Additionally, the existence of chaotic behaviors in the governing model is investigated by adding a perturbed term into the resulting dynamical system and presenting various two and three dimensional phase pictures. We also conduct sensitivity analyses to understand how various initial conditions affect the governing model. The proposed bifurcation and sensitivity analyses provide a framework for predicting and managing soliton behaviour in noisy environments, with possible applications in optical communications, fluid dynamics, and quantum mechanics. To illustrate our findings, we include several graphics that vividly demonstrate the influence of noise. These graphics reveal distinct patterns of random fluctuations, demonstrating the tremendous impact of stochastic forces across different systems and scenarios.

Kirchoff’s matrix tree theorem of 1847 connects the number of spanning trees of a graph to the spectral determinant of the discrete Laplacian [22]. Recently an analogue was obtained for quantum graphs relating the number of spanning trees to the spectral determinant of a Laplacian acting on functions on a metric graph with standard (Neumann-like) vertex conditions [20]. This result holds for quantum graphs where the edge lengths are close together. A quantum graph where the edge lengths are all equal is called equilateral. Here we consider equilateral graphs where we perturb the length of a single edge (almost equilateral graphs). We analyze the spectral determinant of almost equilateral complete graphs, complete bipartite graphs, and circulant graphs. This provides a measure of how fast the spectral determinant changes with respect to changes in an edge length. We apply these results to estimate the width of a window of edge lengths where the connection between the number of spanning trees and the spectral determinant can be observed. The results suggest the connection holds for a much wider window of edge lengths than is required in [20].

Let f be a polynomial-like map with dominant topological degree (d_tge 2) and let (d_{k-1}<d_t) be its dynamical degree of order (k-1). We show that every ergodic measure whose measure-theoretic entropy is strictly larger than (log sqrt{d_{k-1} d_t}) is supported on the Julia set, i.e., the support of the unique measure of maximal entropy (mu ). The proof is based on the exponential speed of convergence of the measures(d_t^{-n}(f^n)^*delta _a) towards (mu ), which is valid for a generic point a and with a controlled error bound depending on a. Our proof also gives a new proof of the same statement in the setting of endomorphisms of (mathbb P^k(mathbb C)) – a result due to de Thélin and Dinh – which does not rely on the existence of a Green current.

In this paper, we develop an algebraic degeneracy theorem for meromorphic mappings from Kähler manifolds into complex projective manifolds provided that the dimension of target manifolds is not greater than that of source manifolds. With some curvature or growth conditions imposed, we show that any meromorphic mapping must be algebraically degenerate if it satisfies a defect relation.

We proved higher integrability (the Boyarsky–Meyers estimate) of solutions to nonlinear minimizing problems (i.e. for minimizers of nonlinear functionals) in domains perforated along the boundary.

We study the Fubini-Study currents and equilibrium metrics of continuous Hermitian metrics on sequences of holomorphic line bundles over a fixed compact Kähler manifold. We show that the difference between the Fubini-Study currents and the curvature of the equilibrium metric, when appropriately scaled, converges to 0 in the sense of currents. As a consequence, we obtain sufficient conditions for the scaled Fubini-Study currents to converge weakly.

We introduce and study a novel grand Lorentz space—that we believe is appropriate for critical cases—that lies “between” the Lorentz–Karamata space and the recently defined grand Lorentz space from Ahmed et al. (Mediterr J Math 17:57, 2020). We prove both Young’s and O’Neil’s inequalities in the newly introduced grand Lorentz spaces, which allows us to derive a Hardy–Littlewood–Sobolev-type inequality. We also discuss Köthe duality for grand Lorentz spaces, from which we obtain a new Köthe dual space theorem in grand Lebesgue spaces.

In this paper, we investigate the Bohr–Rogosinski radius for holomorphic mappings on the unit ball of a complex Banach space with values in a higher dimensional complex Banach space. First, we obtain the Bohr–Rogosinski radius for holomorphic mappings with values in the closure of the unit polydisc of the space ({mathbb {C}}^n), (nge 2). Next, we obtain the Bohr–Rogosinski radius for holomorphic mappings with values in the closure of the unit ball of a (hbox {JB}^*)-triple. Finally, we obtain the Bohr–Rogosinski radius for a class of subordinations on the unit ball of a complex Banach space. All of the results are proved to be sharp.