Related papers: Schottky's theorem in $\mathbb{C}^n$

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

The famous Conway--Gordon--Sachs theorem for the complete graph on six vertices was extended to the general complete graph on $n$ vertices by Kazakov--Korablev as a congruence modulo $2$, and its integral lift was given by…

We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.

Approximation theory of entire functions has been used to demonstrate the construction of a map on $\mathbb{C}\times\mathbb{R}$ having wandering domains. We also present suitable modification to this construction that helps in obtaining…

This note is an (exact) copy of the report of Jaak Peetre, "Generalizing Ovchinnikov's Theorem". Published as Technical Report, Lund (1981). Some more recent general references have been added, some references updated though (in italics)…

In this paper we first extend a generalization of Ostrowski type inequality on time scales for functions whose derivatives are bounded and then unify corresponding continuous and discrete versions. We also point out some particular integral…

Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.

Derrick's theorem is an important result that decides the existence of soliton configurations in field theories in different dimensions. It is proved using the extremization of finite energy of configurations under the scaling…

In this paper, we study a so-called Condition C1 and a weaker Condition C2. For Druzkowski maps Condition C2 is equivalent to the Jacobian conjecture. Main results obtained: - Stating new equivalent formulations of the Jacobian conjecture.…

Simple argument in favour of unitarity, to all orders, of space-like noncommutative theory is given.

In this note, we present a simple proof of an analogue of the Cauchy-Schwarz inequality relevant to products of determinants. Specifically, we show that $$ |\det(A^*MB)|^2\leq \det(A^*MA)\cdot \det(B^*MB),\quad A,B\in \mathbb{C}^{m\times…

In this paper, we generalize the arithmetic Chern-Simons theory to regular flat separated schemes of finite type over rings of integers of number fields by applying the duality theorems for arithmetic schemes.

In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.

We give a short proof for the Hartogs's extension theorem on (n-1)-complete complex spaces.

In this paper we present a short and elementary proof for the error in Simpson's rule.

The Riemann Theorem states, that for any nontrivial connected and simply connected domain on the Riemann sphere there exists some its conformal bijection to the exterior of the unit disk. In this paper we find an explicit form of this map…

In measure theory, Steinhaus theorem is a result that deals with a property of the difference between two sets of positive measure. We give a simple elementary proof of the result.

We give an overpartition analogue of Bressoud's combinatorial generalization of the G\"ollnitz-Gordon theorem for even moduli in general case. Let $\widetilde{O}_{k,i}(n)$ be the number of overpartitions of $n$ whose parts satisfy certain…

In this short note, we briefly discuss the Borel-Cantelli lemma and propose a new generalization of the first part of it.

The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.