数学

We consider the analytic index and spectral flow of Fredholm operators on Hilbert $C^*$-modules. Our spaces and algebras are equipped with a real structure, so the analytic index and spectral flow takes value in the real $K$-theory group of…

Let $X$ and $Y$ be locally compact Hausdorff spaces. We study order isomorphisms \[ T:C_0^+(X)\to C_0^+(Y), \] where $C_0(X)$ denotes the Banach space of all real-valued continuous functions on $X$ vanishing at infinity, and \[…

This paper is dedicated to Paul Butzer on the occasion of his 85th birthday. His work and example have strongly influenced not only the first author, but also generations of mathematicians working in approximation theory and Fourier…

We provide an upper estimate \`a la Pleijel on the asymptotic number of nodal domains for eigenfunctions corresponding to the cogenus eigenvalues $\{\lambda_k(p;\Omega)\}$ of the $p$-Laplacian in a bounded domain $\Omega$, and identify…

We present a comparison principle for unbounded viscosity solutions to Hamilton-Jacobi equations on Wasserstein spaces of probability measures over $R^d$ . In addition to the use of standard techniques of viscosity solutions, our approach…

We derive sufficient and almost necessary conditions for large sample and catalytic majorization between finite statistical experiments over standard Borel sample spaces. This work generalizes previous results, on one hand, in the bivariate…

A diffeomorphism of a $4$-manifold is said to be exotic if it is continuously isotopic to the identity but not smoothly isotopic to the identity. Ruberman constructed the first examples of exotic diffeomorphisms on simply-connected closed…

We derive a heat kernel lower bound estimate for symmetric pure jump processes on general volume doubling metric measure spaces with possible degenerate and/or singular jump kernels using averaged jump kernels. As an application, the main…

This paper investigates recovery operators in quasi-Nelson logic, the algebraizable logical counterpart of quasi-Nelson algebras. These form a variety of three-potent, distributive, but not necessarily involutive residuated lattices that…

We consider the one-phase free boundary problem for the incompressible Navier-Stokes equations in $\mathbb{R}^d$ ($d\ge2$). The surface tension is taken into account. The initial domain, which is the outside of a bubble, is an exterior…

Andrews and Dastidar (\textit{Ramanujan J. 69, Article Number 26, (2026)} ) introduced the $SOME(n)$ and $DSOME(n)$ functions that calculate the sum of all odd parts minus the sum of all even parts of ordinary partitions and distinct…

For each prime $p$ and each power $q=p^k$, we present two large classes of permutation polynomials over $\F_{q^2}$ of the form $X^r B(X^{q-1})$ which have at most five terms, where $B(X)$ is a polynomial with coefficients in the prime field…

This paper establishes a mathematical framework for nonlinear subwavelength resonances and bound states in the continuum (BIC) in an acoustic metascreen with a cubic Kerr nonlinearity. We first use the quasiperiodic Dirichlet-to-Neumann…

We construct closed manifolds with vanishing L^2-Betti numbers over every field) which do not virtually fibre over the circle. The class of fundamental groups that occurs is the largest possible, and in many cases the dimension may be taken…

We prove that the Rouquier dimension of the bounded derived category of finitely generated modules over a commutative noetherian ring is bounded below by the Krull dimension of the ring.

A total rainbow forest in an edge-colored graph is a forest that contains every edge color exactly once. Using a necessary and sufficient condition that a total rainbow forest exists, we demonstrate the existence of huge numbers of…

We develop a rigorous numerical analysis framework for a class of semilinear parabolic problems with nonsmooth initial data. We employ a linear Galerkin finite element method for spatial discretization coupled with a high-order explicit…

We develop an analytic construction of nowhere-vanishing harmonic $1$-forms on real loci of K3-fibred Calabi-Yau $3$-folds with collapsing Ricci-flat K\"ahler metrics. We apply our construction to examples whose real loci have connected…

We study the Diophantine equation $(a^n+1)(b^n+1)=x^2$, which belongs to the family of equations originating from the work of Szalay in 2000. If $a>1$, it is shown that the equation of the title has only one solution in positive integers,…

The isometry group of the bounded Urysohn space, $G = \mathrm{Iso}(\U{1})$ is a central object in the study of Polish groups and topological dynamics. It is known that generic sequences in $G$ generate algebraically free dense subgroups. In…