Related papers: A local Jordan-Brouwer separation theorem

The aim of the present paper is to make some notes to the newly introduced conformable derivative as a type local fractional derivative and to present a surprising result about the relation between the conformable derivatives and the usual…

We prove a Jordan decomposition theorem for minimal connected simple groups of finite Morley rank with non-trivial Weyl group. From this, we deduce a precise structural description of Borel subgroups of this family of simple groups. Along…

Consideration of the Noether variational problem for any theory whose action is invariant under global and/or local gauge transformations leads to three distinct theorems. These include the familiar Noether theorem, but also two equally…

We classify simple finite Jordan conformal superalgebras and establish preliminary results for the classification of simple finite Jordan pseudoalgebras.

We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.

The main purpose of this short note, on the one hand, to is rigorize some part of the proof of Theorem 1.3 in [11] in a simple way, and on the other hand, to give an alternative argument from local inequalities to global ones.

In this paper, we mainly study the derivation algebras of semi-simple Jordan algebras over a field of characteristic $0$ and give sufficient and necessary conditions that the derivation algebras of them are simple. As an application, we…

The author surveys the problem of piecing together integral or rational solutions to Diophantine equations (global structure) from solutions modulo congruences and real solutions (local structure).

A thought experiment with the path-entangled photon pairs is suggested. Its analysis predicts elimination of local coherence even at infinitesimally weak entanglement. Local coherence turns out to be totally incompatible with entanglement.…

In this note, we prove that any Jordan derivation on the generalized matrix ring $T_n(R,M)$ is a derivation. This extends some well-known results of this branch due to Bre\v{s}ar et al. in the cited literature.

We first establish a general random Sperner lemma by presenting a completely new approach for the theory of $L^{0}$-simplicial subdivisions of $L^{0}$-simplexes. Based on this, we are able to achieve a new complete proof of the random…

In this work, we present a result on the local existence and uniqueness of solutions to nonlinear Partial Differential-Algebraic Equations (PDAEs). By applying established theoretical results, we identify the conditions that guarantee the…

We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.

In this paper, we mainly study Jordan derivations of dual extension algebras and those of generalized one-point extension algebras. It is shown that every Jordan derivation of dual extension algebras is a derivation. As applications, we…

We present a short and self-contained proof of the choosability version of Brooks' theorem.

The theory of complete generalized Jordan sets is employed to reduce the PDE with the irreversible linear operator $B$ of finite index to the regular problems. It is demonstrated how the question of the choice of boundary conditions is…

This note is a short introduction to the Julia-Wolff-Carath\'eodory theorem, and its generalizations in several complex variables, up to very recent results for infinitesimal generators of semigroups.

We study local existence for the Boltzmann equation near a global Maxwellian.

We provide a simple proof of a computable analogue to the Jayne Rogers Theorem from descriptive set theory. The difficulty of the proof is delegated to a simulation result pertaining to non-deterministic type-2 machines. Thus, we…

We adapt the method of solution regions to prove new existence and localization results for systems of discontinuous differential equations. Some assumptions concerning the definition of a solution region are relaxed and thus our results…