相关论文: Improvement on a Central Theory of PDEs
The notion of a symmetrically factorizable Lie group is introduced. It is shown that each symmetrically factorizable Lie group is related to a set-theoretical solution of the pentagon equation. Each simple Lie group (after a certain Abelian…
The article on the upper central series of infinite groups by M. de Falco, F. de Giovanni, C. Musella and Y.P. Sysak, proceedings of the american mathematical society, Volume 139, Number 2, February 2011, 385--389 consists of a quite long…
We establish analogues in the context of group actions or group representations of some classical problems and results in additive combinatorics of groups. We also study the notion of left invariant submodular function defined on power sets…
We prove a discretized Product Theorem for general simple Lie groups, in the spirit of Bourgain's Discretized Sum-Product Theorem.
A group is called capable if it is a central factor group. For each prime $p$ and positive integer $c$, we prove the existence of a capable $p$-group of class $c$ minimally generated by an element of order $p$ and an element of order…
An extension of an abstract argumentation framework, called collective argumentation, is introduced in which the attack relation is defined directly among sets of arguments. The extension turns out to be suitable, in particular, for…
We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of…
The method of preliminary group classification is rigorously defined, enhanced and related to the theory of group classification of differential equations. Typical weaknesses in papers on this method are discussed and strategies to overcome…
In this article, we study group theoretical embedding properties of subgroups in central products of finite groups. Specifically, we give characterizations of normal, subnormal, and abnormal subgroups of a central product of two groups.
We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of…
In combinatorics, P\'{o}lya's Enumeration Theorem is a powerful tool for solving a wide range of counting problems, including the enumeration of groups, graphs, and chemical compounds. In this paper, we present an extension of P\'{o}lya's…
We prove Roth type theorems in finite groups. Our main tool is the Triangle Removal Lemma of Ruzsa and Szemer\'edi.
Some superlinear fourth order elliptic equations are considered. Ground states are proved to exist and to concentrate at a point in the limit. The proof relies on variational methods, where the existence and concentration of nontrivial…
In this paper we give simple extension and uniqueness theorems for restricted additive and logarithmic functional equations.
The main result of [4] is that all finitely presented groups of p-deficiency greater than one are p-large. Here we prove that groups with a finite presentation of p-deficiency one possess a finite index subgroup that surjects onto . This…
Wei's celebrated Duality Theorem is generalized in several ways, expressed as duality theorems for linear codes over division rings and, more generally, duality theorems for matroids. These results are further generalized, resulting in two…
In this paper, we present a generalization of one of the theorems in [G. E. Andrews, Partitions with parts separated by parity, \textit{Annals of Combinatorics} \textbf{23}(2019), 241 - 248], and give its bijective proof. Further variations…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
A theorem is proved to verify incremental stability of a feedback system via a homotopy from a known incrementally stable system. A first corollary of that result is that incremental stability may be verified by separation of Scaled…
An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.