Related papers: A counterexample to Feit's Problem VIII on decompo…
We discuss a construction that gives counterexamples to various questions of unique determination of convex bodies.
We propose upper bounds for the number of modular constituents of the restriction modulo $p$ of a complex irreducible character of a finite group, and for its decomposition numbers, in certain cases.
We establish bounds on a finite separable extension of function fields in terms of the relative class number, thus reducing the problem of classifying extensions with a fixed relative class number to a finite computation. We also solve the…
We continue to discuss the example presented in \cite{JarPfl2015}. In particular, we clarify some gaps and complete the description of the Shilov boundary.
Provides a counterexample to a long standing conjecture of A. Adem regarding the behaviour of the integral cohomology of a p-group.
We study the decomposition of central simple algebras of exponent 2 into tensor products of quaternion algebras. We consider in particular decompositions in which one of the quaternion algebras contains a given quadratic extension. Let $B$…
In this paper, we prove the finiteness of the number of integer solutions of the decomposable form inequalities. We also study the number of integer solutions of a sequence of decomposable form inequalities.
This paper gives the first explicit example of a finite separating set in an invariant ring which is not finitely generated, namely, for Daigle and Freudenburg's 5-dimensional counterexample to Hilbert's Fourteenth Problem.
Cox's well-known theorem justifying the use of probability is shown not to hold in finite domains. The counterexample also suggests that Cox's assumptions are insufficient to prove the result even in infinite domains. The same…
On compact Riemannian manifolds, we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.
A boundary value problem associated to the difference equation with advanced argument \begin{equation} \label{*}\Delta\bigl (a_{n}\Phi(\Delta x_{n})\bigr)+b_{n}\Phi(x_{n+p} )=0,\ \ n\geq1 \tag{$*$} \end{equation} is presented, where…
As a sequel to the paper [9], we study the existence and properties of Lipschitz solutions to the initial-boundary value problem of some forward-backward parabolic equations with diffusion fluxes violating Fourier's inequality.
In this paper, we establish lower bounds on Weil height of algebraic integers in terms of the low lying zeros of the Dedekind zeta-function. As a result, we prove Lehmer's conjecture for certain infinite non-Galois extensions conditional on…
The present paper is exclusively devoted to counterexamples about commutators and self commutators of unbounded operators on a Hilbert space. As a bonus, we provide a simpler counterexample than McIntosh's famous example obtained some while…
We consider partitions of the edge set of a graph G into copies of a fixed graph H and single edges. Let \phi_H(n) denote the minimum number p such that any n-vertex G admits such a partition with at most p parts. We show that…
We shall present an elementary approach to extremal decompositions of (quantum) covariance matrices determined by densities. We give a new proof on former results and provide a sharp estimate of the ranks of the densities that appear in the…
Recently, Keith investigated reciprocals of false theta functions and proved some interesting results such as congruences, asymptotic bounds, and combinatorial identities. At the end of his paper, Keith posed a conjecture on congruences…
In this paper we improve upon in terms of S the best known effective upper bounds for the solutions of S-unit equations and decomposable form equations.
We introduce a decoder for the 3D color code with boundaries, which is a variation of the restriction decoder introduced by Kubicka and Delfosse. Specifically, we adapt the lift procedure to efficiently find a correction on qubits adjacent…
A proof is given to the Dixmier's 5'th problem for the Weyl algebra.