Bulletin of the London Mathematical Society最新文献

We introduce the notion of radical preservation and prove that a radical-preserving homomorphism of left artinian rings of finite projective dimension with superfluous kernel reflects the finiteness of the little finitistic, big finitistic, and global dimension. As an application, we prove that every bound quiver algebra with quasi-uniform Loewy length, a class of algebras introduced in this paper, has finite finitistic dimensions. The same result holds more generally in the context of semiprimary rings. Moreover, we construct an explicit family of such finite-dimensional algebras where the finiteness of their big finitistic dimension does not follow from existing results in the literature.

We prove a novel four-variable character sum identity that serves as a twisted, non-Archimedean analog of Weber's integrals for Bessel functions. Using this identity and ideas from Venkatesh's thesis, we provide a short spectral proof of the Voronoi formulae for classical modular forms with character twists. A key aspect of this work is a new way of explicitly determining the root numbers, which entails delicate arithmetic considerations.

This paper proves the existence of a chiral map with alternating automorphism group for every hyperbolic type. Equivalently, for every pair of natural numbers $��(�m�,�n�)�$ such that , there is a finite alternating group generated by a pair of elements whose orders are $�m$ and $�n$ and whose product is an involution, where furthermore the group does not have an automorphism which inverts these generators. We call on previously known results for when both the valency $�n$ and the face-length $�m$ are odd, and present a set of new constructions using permutations for when at least one parameter is even.

In this paper, we analyze the Cauchy problem for the two-component Camassa–Holm (2CH) system in weighted Sobolev spaces, achieving two key results. First, we establish a new irregular Riemann–Hilbert (RH) problem, without the normalization conditions, for the associated Cauchy problem. Second, we identify six main asymptotic sectors in the space–time region and derive the leading-order asymptotics for these sectors using the $�\overline{\partial }$-nonlinear steepest descent method. This confirms the soliton resolution conjecture for the 2CH system. Notably, the 2CH system exhibits unique characteristics within the RH formalism, distinguishing it from the classical Camassa–Holm (CH) equation. We prove that the reconstruction process remains unique even when the RH problem lacks uniqueness. Additionally, numerical simulations are provided to validate these asymptotic results.

The purpose of this paper is to establish a connection between a one-dimensional random walk in a random sparse environment and the random pinning model. We show that the grand canonical partition function of the pinning model coincides with the mean number of returns to the origin for a random walk in a random sparse environment averaged over the randomness location. We obtain thereof some information on the integrability of the number of return times in the annealed and partially annealed setups.

A matrix $��A�\in �R^{�m�\times �n�}�$ is strictly sign regular (or sign regular) if for each $��1�⩽�k�⩽�\min �\{�m�,�n�\}�$, all (nonzero) $��k�\times �k�$ minors of $�A$ have the same sign. This class of matrices contains the totally positive matrices, and was first studied by Schoenberg in 1930 to characterize variation diminution, a fundamental property in total positivity theory. In this article, we classify all surjective linear mappings $��L�:�R^{�m�\times �n�}�\to �R^{�m�\times �n�}�$ that preserve: (i) sign regularity and (ii) sign regularity with a given sign pattern, as well as (iii) strict versions of these.

For any given set $��E�\subset �[�1�,�2�]�$, we discuss a fractal frequency-localized version of the $�L^p$ local smoothing estimates for the half-wave propagator with times in $�E$. A conjecture is formulated in terms of a quantity involving the Assouad spectrum of $�E$ and the Legendre transform. We validate the conjecture for radial functions. We also prove a similar result for fractal-time $��L^2�\to �L^q�$ and square function bounds, for arbitrary $�L^2$ functions and general time sets. We formulate a conjecture for $��L^p�\to �L^q�$ generalizations.

Stable envelopes, introduced by Maulik and Okounkov, provide a family of bases for the equivariant cohomology of symplectic resolutions. They are part of a fascinating interplay between geometry, combinatorics and integrable systems. In this expository article, we give a self-contained introduction to cohomological stable envelopes of type $�A$ bow varieties. Our main focus is on the existence and the orthogonality properties of stable envelopes for bow varieties. The restriction to this specific class of varieties allows us to illustrate the theory combinatorially and to provide simplified proofs, both laying a basis for explicit calculations.