数学
We consider closed contact manifolds $(M,\xi)$ with periodic positive equivariant symplectic homology. This is a very large class of contact manifolds and, to the best of our knowledge, includes all currently known examples admitting Reeb…
The optimal control of three-phase permanent-magnet synchronous motors (PMSMs) is challenging due to their nonlinearity and the discrete nature of the control set. Existing approaches either rely on mixed-integer trajectory optimization or…
In this paper, we prove a sign phenomenon first observed by Andrews for certain $q$-series from Ramanujan's Lost Notebook. For three of the series considered by Andrews, namely $v_2(q)$, $v_3(q)$, and $v_4(q)$, we show that the coefficients…
The greedy Tamari poset, inspired by the well-studied Tamari lattice, was recently defined by Dermenjian in the more general setting of greedy $\nu$-Tamari posets. Bousquet-M\'elou and Chapoton counted intervals of the greedy $m$-Tamari…
Towards developing the tools of geometric group theory for non-locally compact topological groups, we give one of the first complete classifications of a family of such groups up to coarse equivalence, and when possible, up to…
We present a Hopf algebraic generalization of the Abe-Kanno theorem on a correspondence between subgroups of an algebraic group and invariant subfields of the field of rational functions. It applies to residually finite-dimensional Hopf…
We establish sharp lower bounds for the Dirichlet character moments $\frac{1}{r-1} \sum_{\chi \; \text{mod} \; r} |\sum_{n \leq x} \chi(n)|^{2q}$, where $r$ is a large prime, $1 \leq x \leq r^{0.499}$, and $0 \leq q \leq 1$ is real. These…
V. Drinfeld and E. Lau introduced a ``decompletion'' of the ring of $p$-typical Witt vectors, following earlier work of T. Zink. The goal of this paper is to offer an exposition of this construction, which we call the sheared Witt vectors,…
We bound the dimension of the Prym-Brill-Noether variety for an open subset of the moduli space of \'{e}tale double covers of k-elliptic curves. We also obtain new bounds on the dimension of the Prym-Brill-Noether variety for general…
Let $F(N)$ denote the largest cardinality of a Sidon subset of $\{0, 1, \dots, N - 1\}$. We prove \[ F(N) \le N^{1/2} + 0.94601 N^{1/4} + O(1). \] This improves the recently announced coefficient $0.97633$ obtained by Carter, Georgiev,…
We introduce the notion of one-sided median porosity for subsets $E$ of $\mathbb{R}$. We prove that this condition is necessary and sufficient for the distance weight $d_E^{-\alpha}$ to belong to a one-sided Muckenhoupt $A_p$ class for some…
Let $\mathbb F$ be an algebraically closed field of characteristic $0$. Let $k\geq 2$ be an integer, and let $n\in \mathbb F[x]\setminus\{0\}$. We study generalized Diophantine tuples $A\subset \mathbb F[x]$ with property $D_k(n)$, meaning…
In this paper, we study blowup solutions of an important class of Chern-Simons systems. We first show that when blowup of mean-field type occurs, the corresponding blowup solution is unique under natural geometric assumptions. We also…
Very recently, using Meshulam's lemma, Blagojevi\'c proved a constrained version of the colorful Carath\'eodory theorem for joins of bipartite spanning trees and wedge of spheres. Our main contribution extends his result from joins of…
Loewner chains are ubiquitous in the theory of slit mappings, and hence in the study of bounded conformal maps. They have attracted new interest in the past decades through their applications to statistical physics and fractal geometry,…
In this paper, we investigate the combinatorial structure arising from the $(p, q)$-deformed generalized Weyl algebra generated by variables $X, Y$, and $Z_p$, satisfying the $(p, q)$-commutation relations $XY-qYX=h Y^sZ_{p}, XZ_p=pZ_pX$,…
We prove the Ashbaugh--Benguria reciprocal-gap conjecture for the Dirichlet Laplacian in every dimension $N\ge2$. Specifically, if $\Omega\subset\mathbb R^N$ is a bounded domain and $$…
The generalized honeymoon Oberwolfach problem (HOP) asks whether it is possible to seat $2n$ participants consisting of $n$ newlywed couples at a conference with $s$ tables of size $2$ and $t$ "round'' tables of sizes $2m_1, 2m_2, \ldots,…
Using modifications to work of Klagsbrun, Mazur, and Rubin, we study (assuming the Extended Riemann Hypothesis) the distribution of Selmer ranks of twist families of some given even-dimensional Galois modules satisfying some mild technical…
The theory of boundary quadruples and boundary triples is well-studied for symmetric and skew-symmetric operators and in general for dual-pairs. This paper adapts a suitable version for abstract Friedrichs operators and addresses the…