Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas最新文献

The main goal of this article is to study a Calderón type inverse problem for certain viscous nonlocal wave equations. We show that the partial Dirichlet to Neumann map uniquely determines on the one hand linear perturbations and on the other hand homogeneous nonlinearities f(u) whenever the latter satisfy a certain growth assumption. As a preliminary step we discuss the well-posedness in each case, where for the nonlinear setting we invoke the implicit function theorem after establishing the differentiability of the associated Nemytskii operator f(u). In the linear case we establish a Runge approximation theorem in $L^2(0,T;{\tilde{H}}^s\left(\Omega \right))$ , which allows us to uniquely determine potentials that belong only to $L^{\infty }(0,T;L^p\left(\Omega \right))$ for some $1<p\le \infty$ satisfying suitable restrictions. In the nonlinear case, we first derive an appropriate integral identity and combine this with the differentiability of the solution map around zero to show that the nonlinearity is uniquely determined by the Dirichlet to Neumann map. To make this linearization technique work, it is essential that we have a Runge approximation in $L^2(0,T;{\tilde{H}}^s\left(\Omega \right))$ instead of $L^2\left({\Omega }_T\right)$ at our disposal.

We deduce a new family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial from George Andrews' multi-series extension of the Watson transformation. A Karlsson-Minton type summation for very-well-poised basic hypergeometric series due to George Gasper also plays an important role in our proof. We put forward two relevant conjectures on supercongruences and q-supercongruences for further study.

We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called isosceles-free. In particular, we characterize all homogeneous isosceles-free spaces up to isometry as vector spaces over the two-element field, endowed with an injective norm. Using isosceles-free decompositions, we provide bounds on the maximal number of distances in arbitrary homogeneous finite metric spaces.

Let $C$ be a class of topological semigroups. A semigroup X is called absolutely $C$-closed if for any homomorphism $h:X\to Y$ to a topological semigroup $Y\in C$, the image h[X] is closed in Y. Let $T_{1}S$, $T_{2}S$, and $T_{z}S$ be the classes of $T_1$, Hausdorff, and Tychonoff zero-dimensional topological semigroups, respectively. We prove that a commutative semigroup X is absolutely $T_{z}S$-closed if and only if X is absolutely $T_{2}S$-closed if and only if X is chain-finite, bounded, group-finite and Clifford + finite. On the other hand, a commutative semigroup X is absolutely $T_{1}S$-closed if and only if X is finite. Also, for a given absolutely $C$-closed semigroup X we detect absolutely $C$-closed subsemigroups in the center of X.

Here we perform the univariate quantitative approximation, ordinary and fractional, of Banach space valued continuous functions on a compact interval or all the real line by quasi-interpolation Banach space valued neural network operators. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged function or its Banach space valued high order derivative or fractional derivatives. Our operators are defined by using a density function generated by the Richards curve, which is generalized logistic function. The approximations are pointwise and of the uniform norm. The related Banach space valued feed-forward neural networks are with one hidden layer.

In this paper, three parametric q-supercongruences for truncated very-well-poised basic hypergeometric series are proved, one of them modulo the square, the other two modulo the cube of a cyclotomic polynomial. The main ingredients of proof include a basic hypergeometric summation by George Gasper, the method of creative microscoping (a method recently introduced by the first author in collaboration with Wadim Zudilin), and the Chinese remainder theorem for coprime polynomials.

We prove that each Borel function $V:\Omega \to [-\infty ,+\infty ]$ defined on an open subset $\Omega \subset R^N$ induces a decomposition $\Omega =S\cup {\bigcup }_i{D}_i$ such that every function in $W_0^{1,2}\left(\Omega \right)\cap L^2(\Omega ;V^{+}dx)$ is zero almost everywhere on S and existence of nonnegative supersolutions of $-\Delta +V$ on each component $D_i$ yields nonnegativity of the associated quadratic form ${\int }_{D_i}{\left(\right|\nabla \xi |}^2+V{\xi }^2).$.

We prove the existence of free objects in certain subcategories of Banach lattices, including p-convex Banach lattices, Banach lattices with upper p-estimates, and AM-spaces. From this we immediately deduce that projectively universal objects exist in each of these subcategories, extending results of Leung, Li, Oikhberg and Tursi (Israel J. Math. 2019). In the p-convex and AM-space cases, we are able to explicitly identify the norms of the free Banach lattices, and we conclude by investigating the structure of these norms in connection with nonlinear p-summing maps.