Analysis and Mathematical Physics最新文献

We extend the theory of exterior differential systems from manifolds and their tangent bundles to Lie algebroids. In particular, we define the concept of an integral manifold of such an exterior differential system. We support our developments with several examples, including an application to dynamical systems with a symmetry group and to the invariant inverse problem of the calculus of variations.

We study the inverse problem of reconstructing symmetric m-tensor fields in (mathbb {R}^n) from generalized Radon transforms, which arise naturally in areas such as medical imaging, seismology, and tomography. We introduce longitudinal and transversal Radon transforms, along with their momentum variants, which extend classical Radon transforms to tensor fields. We provide explicit kernel characterizations and establish invertibility modulo these kernels. Furthermore, we show that symmetric m-tensor fields can be uniquely recovered from suitable combinations of introduced transforms. Our results provide a mathematical foundation for imaging of tensor-valued physical quantities, going beyond scalar tomography.

In this paper, we present new fixed point theorems for sets that are endowed with a quasi-metric, which is a generalization of a metric space, where the triangle inequality is modified into a less restrictive form known as the relaxed triangle inequality: (mathfrak {D}_{q}(x,y) le s[mathfrak {D}_{q}(x,z) + mathfrak {D}_{q}(z,y)]), (s ge 1.) Furthermore, we apply our results to iterated function system theory to generate fractals, showcasing their usefulness in fractal construction. At the end, we discuss how sensitivity on maps carry over to their products and same for iterated function systems in the framework of quasi-metric spaces.

This paper investigates a p-Laplace higher-order hyperbolic equation with strong and weak damping terms and a superlinear source:

in (Omega times (0,T_{textrm{max}})), subject to null Navier boundary conditions. Here, (Omega subset {mathbb {R}}^n) is a bounded open domain. By using the Banach contraction mapping principle, we establish the well-posedness of weak solutions. When (q + 1 le p), we prove that all the weak solutions remain globally bounded. For (q + 1 > p), within the potential well framework, we derive the global existence of solutions for both critical and subcritical initial energy cases, accompanied by distinct decay estimates for global solutions when (q+1 > p), initial energy (E(0) le d) and Nehari functional (I(u_0)ge 0). Additionally, under specific exponent conditions (e.g., (2le m+1< p < q+1) for negative initial energy, (max {p, m+1}<q+1) for non-negative initial energy), we characterize finite-time blow-up of solutions under both positive and negative initial energy conditions. Using an auxiliary function method, we further demonstrate finite-time blow-up for linear weak damping with subcritical initial energy, and derive the bounds for the blow-up time.

This paper deals with developing a general spectral theory for only metrizable fuzzy normed algebras, whose topology is determined by functionals that may lack subadditivity. There are introduced the notions of fuzzy spectral radius, fuzzy boundedness radius, and fuzzy regular elements, and classical spectral results from Banach and locally convex algebras to this setting are extended. There are described fuzzy normed algebras induced by two strict t-norms and provide explicit examples, for which it is computed the fuzzy spectral radius and it is established the domain of fuzzy convergence for the Neumann series. A characterization of the fuzzy Waelbroeck resolvent set of regular elements is also given. As an application, the fuzzy Fourier transform on these algebras is investigated, proving to be a generalization of the classical transform to contexts governed by fuzzy rather than classical constraints.

We consider complete Horn hypergeometric series in two variables and present an algorithm for the determination of their domains of convergence. To this end, we start from the fundamental results due to Horn and we investigate the properties and geometry of the rational algebraic curves delimiting the Reinhardt image of the domain of convergence. Under natural restrictions on the geometry of these curves, we provide an algorithm that iteratively enumerates special subsets of the boundary of the domain of convergence. In particular, we note that the provided algorithm can be efficiently applied to determine the domains of convergence of the analytic continuations of complete hypergeometric series in two variables.

In this paper, we consider the inverse scattering problem for one-dimensional Schr(ddot{o})dinger operator on the half-line ([0,infty )) with spectral parameter dependent on boundary condition and interior discontinuous conditions. The scattering data of the problem is defined and the modified Marchenko main equation is derived. With the help of the obtained integral equations, it is shown that the potential is uniquely recovered by the given scattering data.

By utilizing constrained variational methods and analytical techniques, we investigate the existence of normalized solutions to a class of (p, q)-Laplacian equations with (L^p)-constraint, where the nonlinearity satisfies distinct weak mass supercritical conditions. Our results generalize and complement several known results in the literature. In particular, this work extends the existing results of Chen and Tang (J. Differ. Equ. 386 (2024) 435-479) and Jin and Tang (Appl. Math. Lett. 160 (2025) 109329) to the (p, q)-Laplacian setting.

The existence of weighted nontangential limits and growth rates near a polar set E of positive superharmonic functions satisfying a nonlinear inequality (-Delta u(x)le cd(x,E)^{-beta } u(x)^p) and having singularities on E are investigated. A main result extends Lions’ result (1980) regarding the asymptotic behavior near an isolated singularity of a positive solution of the Lane–Emden equation to the case of non-isolated singularities, and complements the author and Ono’s result (2014) regarding removable singularities of solutions of semilinear elliptic equations.

The paper is devoted to quadratic Poisson structures compatible with the canonical linear Poisson structures on (necessarily) trivial 1-dimensional central extensions of semisimple Lie algebras. In particular, we develop the general theory of such structures and study related families of functions in involution. We also show that there exists a 10-parametric family of quadratic Poisson structures on (mathfrak {gl}(3)^*) compatible with the canonical linear Poisson structure and containing the 3-parametric family of quadratic bivectors introduced in 2017 by Vladimir Sokolov, who showed that the corresponding involutive family of functions contains the hamiltonian of the polynomial form of the elliptic Calogero–Moser system. We also explicitly write the normal forms of the Poisson pencils in the 10-parametric family and related integrable systems. They correspond to normal forms of ternary cubic forms (degenerations of normal elliptic curve in (mathbb {P}^2)).