Related papers: Inversion of adjunction for quotient singularities…

In this paper we present a novel algorithm for computing a congruence on an inverse semigroup from a collection of generating pairs. This algorithm uses a myriad of techniques from the theories of groups, automata, and inverse semigroups.…

We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential…

This paper mainly studies nonnegativity decision of forms based on variable substitutions. Unlike existing research, the paper regards simplex subdivisions as new perspectives to study variable substitutions, gives some subdivisions of the…

We prove that the forgetful functor from the category of Boolean inverse semigroups to inverse semigroups with zero has a left adjoint. This left adjoint is what we term the `Booleanization'. We establish the exact connection between the…

We construct an equivariant version of discrete Morse theory for simplicial complexes endowed with group actions. The key ingredient is a 2-categorical criterion for making acyclic partial matchings on the quotient space compatible with an…

We prove some statements of left- and right-continuous variants of generalized inverses of non-decreasing real functions.

The paper considers a universal approach that allows one to quite simply obtain nonlinear asymptotic estimates of various summation functions. It is shown the application of this approach to the asymptotic estimation of divergent Dirichlet…

We generalize the notion of length to an ordinal-valued invariant defined on the class of finitely generated modules over a Noetherian ring. A key property of this invariant is its semi-additivity on short exact sequences. As an…

We connect Dedekind sums and some formulas for numerical semigroups.

We give examples for existence and non-existence of categorical quotients for algebraic group actions in the categories of algebraic varieties and prevarieties. All our examples are subtorus actions on toric varieties.

This work presents the conjugacy classes of finite abelian subgroups of the Cremona group of the plane. Using a well-known theory, this problem amounts to the study of automorphism groups of some Del Pezzo surfaces and conic bundles. We…

We prove Shokurov's index conjecture for quotient singularities.

We establish sharp forms of Young's convolution inequality and its reverse on the discrete hypercube $\{0,1\}^d$ in the diagonal case $p=q$. As applications, we derive bounds for additive energies and sumsets. We also investigate the…

We study actions of connected algebraic groups on normal algebraic varieties, and show how to reduce them to actions of affine subgroups.

We show that there is a bijection between real-linear automorphisms of the multicomplex numbers of order $n$ and signed permutations of length $2^{n-1}$. This allows us to deduce a number of results on the multicomplex numbers, including a…

We examine a condition on a simply connected 2-complex X ensuring that groups acting properly on X are coherent. This extends earlier work on 2-complexes with negative sectional curvature which covers the case that G acts freely. Our…

We propose a variant of the effective adjunction conjecture for lc-trivial fibrations. This variant is suitable for inductions and can be used to treat real coefficients.

Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…

We find an explicit form of the inverse isomorphism from Shapiro's lemma in terms of inhomogeneous cocycles and apply it to construct special nonsplit coverings of groups with a unique conjugacy class of involutions.

We provide a survey of results concerning both the direct and inverse problems to the Cauchy-Davenport theorem and Erdos-Heilbronn problem in Additive Combinatorics. We prove a slight extension to an inverse theorem of Dias da…