Analysis and Mathematical Physics最新文献

The algorithm for inverting covariant exterior derivative is provided. It works for a sufficiently small star-shaped region of a fibered set - a local subset of a vector bundle and associated vector bundle. The algorithm contains some constraints that can fail, giving no solution, which is the expected case for parallel transport equations. These constraints are straightforward to obtain in the proposed approach. The relation to operational calculus and operator theory is outlined. The upshot of this paper is to show, using the linear homotopy operator of the Poincare lemma, that we can solve the covariant constant and related equations in a geometric and algorithmic way. The considerations related to the regularity of the solutions are provided.

In this work, higher-order rogue wave solutions in the three-component local and nonlocal Gross-Pitaevskii equations are investigated. The first-order rogue wave solution for the three-component local and nonlocal Gross-Pitaevskii equations is derived using the Darboux transformation combined with a variable separation technique. In order to efficiently construct higher-order rogue wave solutions for the three-component local and nonlocal Gross-Pitaevskii equations, we establish a relationship between the three-component and the one-component versions of the nonlinear Schrödinger equation. Then using this relationship, we obtain the higher-order rational solutions for the three-component local and nonlocal Gross-Pitaevskii equations, which describe the rogue wave patterns. Moreover, the main characteristics of these rogue waves are graphically examined by varying the free parameters. In particular, these results show that rogue waves in the three-component nonlocal Gross-Pitaevskii equations may exhibit a much richer variety than those in the corresponding local equations.

In this paper, we define the concept of a cosmological time function on Lorentzian length spaces. We prove that a Lorentzian length space is globally hyperbolic if and only if the cosmological time function of a Lorentzian length space within its conformal class is regular. Additionally, we establish an ordering in the space of Lorentzian length spaces on a proper metric space and investigate stable causality in its fundamental form. Furthermore, we show that this definition of stable causality implies the existence of a time function inspired by the cosmological time function.

In this paper, we present new results on holomorphically accretive mappings and their resolvents defined on the open unit ball of a complex Banach space. We employ a unified approach to examine various properties of non-linear resolvents by applying a distortion theorem we have established. This method enables us to prove a covering result and to establish the accretivity of resolvents along with estimates of the squeezing ratio. Furthermore, we prove that under certain mild conditions, a non-linear resolvent is a starlike mapping of a specified order. As a key tool, we first introduce a refined version of the inverse function theorem for mappings satisfying so-called one-sided estimates.

Our first aim of this article is to establish several new versions of refined Bohr inequalities for bounded analytic functions in the unit disk involving Schwarz functions. Secondly, we obtain several new multidimensional analogues of the refined Bohr inequalities for bounded holomorphic mappings on the unit ball in a complex Banach space involving higher dimensional Schwarz mappings. All the results are proved to be sharp.

In [55] Weisz investigated strong convergence of partial sums (S_{m,n}) of the two-dimensional Walsh-Fourier series in the martingale Hardy spaces, but under the condition when (2^{-alpha }<m/nle 2^{alpha }). In this paper we investigate strong convergence of the two-dimensional Walsh-Fourier series in the martingale Hardy spaces ({H_p^{square }left( G^2right) }) for (0<p<1,) without any restriction on the indices. Moreover, we also prove sharpness of our result.

This paper is devoted to Opial-type inequalities involving the Riemann-Liouville fractional derivatives. We give continuous versions of certain inequalities that are generalizations of some known results related to Opial-type inequalities.

We prove a degenerate Sobolev inequality of the form

where Q is a matrix function whose smallest eigenvalue is bounded below by a constant multiple of (K^{-frac{2}{p'}}). As an application, we prove the exponential integrability of solutions of the Dirichlet problem for (-K^{-1}{{,textrm{div},}}(Q{{,mathrm{nabla },}}u)=f), (fin L^infty (K,Omega )), building upon recent results in Cruz-Uribe, MacDonald, and Rodney (2024).

Using the zero curvature representation within the framework of Yang-Mills theory, this paper is devoted to exploring geometric properties of the Mikhailov-Lenells system, which was constructed from Lax pairs of two linear (3times 3) matrix spectral problems. The Landau-Lifshitz type model of Sym-Pohlmeyer moving curves evolving in the reductive homogeneous space (GL(3,mathbb C)/({mathbb {C}}^*)^3) with initial data being suitably restricted is gauge equivalent to the Mikhailov-Lenells system. This gives a geometric realization of the Mikhailov-Lenells system.

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.