数学

In this paper, we extend Stein's method to the symmetric matrix normal distribution. In particular, we obtain a Stein characterization of the symmetric matrix normal distribution involving the extended generator of the symmetric matrix…

Finite fields are important algebraic structures that have a wide range of applications in fields such as coding theory and cryptography. But the standard construction of finite field extensions through polynomial quotients is…

In a previous paper, we introduced the notion of hyper swap structures, a novel class of hyperalgebras that naturally generalizes swap structures semantics. In this paper we introduce the concept of hyper Boolean algebras based on Morgado…

We study the Fischer-Musz\'ely functional equation for the positive semidefinite and the positive definite cones of unital $C^*$-algebras. We show that any bijection between the positive semidefinite cones satisfying the Fischer-Musz\'ely…

In this partially expository paper, we present a novel construction of differentially closed fields of characteristic $0$: Let $\mathcal{K}_{\mathrm{dense}}$ be the differential ring of all meromorphic functions whose domain is a (not…

We prove an asymptotic formula for a weighted Riesz mean of Hurwitz class numbers and real quadratic class numbers. To do this, we introduce L-functions for weight $\frac {1}{2} $ sesquiharmonic Maass forms of moderate growth and prove a…

Electroelastic shells are widely used in soft actuators, sensors, and energy harvesters owing to their large electrically induced deformations. However, the accurate simulation of their complex nonlinear multiphysics coupling, including…

Let $\gamma \ge 1$. A set $A$ of nonnegative integers is a Sidon set if for each $d>0$ there is at most one pair $(a,b) \in A \times A$ with $d=a-b$. If there are at most $\gamma$ pairs, then $A$ is a $\gamma$-Golomb ruler. We prove that if…

We study the exponential rate $r(\alpha,\lambda)$ of the energy $\mathcal{E}_N$ needed to steer a far site, at distance $N$, of an Aubry--Andr\'e chain $H_\lambda$ via one boundary actuator with closed-loop margin $\alpha$. An exact…

Let $Q^{(k)}_N$ be an $N\times N$ matrices with entries satisfying CAR, normalized to have variance $1/\sqrt{N}$ with respect to the trace of the CAR algebra. We show that, although the operator norm of the real part of an individual matrix…

We study $[\phi_t , X]$, the maximal space of strong continuity for a semigroup of composition operators induced by a semigroup $\{\phi_t\}_{t\ge0}$ of analytic self-maps of the unit disk, when $X$ is BMOA, $H^\infty$ or the disk algebra.…

Considering pointwise and sup-norm estimation, we analyze the non-asymptotic behavior of local averaging estimators for Lipschitz regression functions. Building on a general deviation bound for estimators based on a VC family of localizing…

Our main result is a characterization of $g$ for which the operator $S_g(f)(z) = \int_0^z f'(w)g(w)\, dw$ is bounded below on the Bloch space. We point out analogous results for the Hardy space $H^2$ and the Bergman spaces $A^p$ for $1 \leq…

More than forty years ago, Andersen and Hoffman independently proved that every symmetric Latin rectangle can be extended to a symmetric Latin square with prescribed diagonal entries. We generalize this theorem as follows. Let $k\leq n^2$,…

Robust Markov decision processes provide a principled framework for protecting sequential decision-making against transition-law misspecification and have attracted substantial recent research interest. As in non-robust stochastic optimal…

We study the maximal displacement of a one-dimensional subcritical branching random walk with offspring distribution $\{p_k\}$ and step size $X$ such that $m := \sum_{k=1}^\infty k p_k \in (0,1)$. Let $M_n$ denote the maximal position of…

We study the family of complex rational functions known as Generalized McMullen maps, F(z) = z^n + a/z^n+b, for integer n at least 3 fixed, and complex parameters a, b with a nonzero. In prior work by the same authors, we provided a…

We calculate the first derivative of the Jacobi polynomials with respect to their order in explicit form. This derivative is not an elementary function, but contains elementary special cases. As an application, we use our result with a…

We construct a reduced planar convex body $R$ with thickness $\Delta(R)=1$ and \[\operatorname{area}(R)=0.786215\ldots>0.785398\ldots=\frac{\pi}{4}.\] Thus $R$ is a counterexample to Lassak's conjectured upper bound…

Cayley codes, introduced by Kaufman and Wigderson, are linear codes constructed from a Cayley graph and a smaller linear code. We explore general properties of the class of Cayley codes for finite groups. In particular we give a reduction…