Results 31 to 40 of about 108,393 (45)

A Multidimensional Central Sets Theorem [PDF]

Combin. Probab. Comput., 15, 2006, 807-814, 2008
The Theorems of Hindman and van der Waerden belong to the classical theorems of partition Ramsey Theory. The Central Sets Theorem is a strong simultaneous extension of both theorems that applies to general commutative semigroups. We give a common extension of the Central Sets Theorem and Ramsey's Theorem.
arxiv  

How the Quantum Sorites Phenomenon Strengthens Bell's Argument [PDF]

arXiv, 2014
Recently, Colbeck and Renner (2011) [arXiv:1005.5173] published a theorem that appears to be stronger than the Bell (1964) theorem in a way that is more significant than the other variations of Bell's theorem that have been published in the 50 years since Bell's theorem.
arxiv  

Generalizations of Wei's Duality Theorem [PDF]

arXiv, 2009
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 Wei-type duality theorems for new combinatorial structures that are introduced and named {\em demi-matroids ...
arxiv  

On Fabry's Gap Theorem [PDF]

Arch. Math. (Brno) 38 (2002), no. 4, 307--309, 2011
By combining Tur\'an's proof of Fabry's gap theorem with a gap theorem of P. Sz\"usz we obtain a gap theorem which is more general then both these theorems.
arxiv  

A unified proof of Brooks' theorem and Catlin's theorem [PDF]

Discrete Mathematics, Volume 338, Issue 2, 6 February 2015, Pages 272-273, 2014
We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.
arxiv  

The modified Poynting theorem and the concept of mutual energy [PDF]

arXiv, 2015
The goal of this article is to derive the reciprocity theorem, mutual energy theorem from Poynting theorem instead of from Maxwell equation. The Poynting theorem is generalized to the modified Poynting theorem. In the modified Poynting theorem the electromagnetic field is superimposition of different electromagnetic fields including the retarded ...
arxiv  

Some ergodic theorems over $k$-full numbers [PDF]

arXiv
In 2022, Bergelson and Richter established a new dynamical generalization of the prime number theorem. Later, Loyd showed a disjoint form with the Erd\H{o}s-Kac theorem. Recently, the author and his coauthors proved some ergodic theorems over squarefree numbers related to these results.
arxiv  

A Survey on Universal Approximation Theorems [PDF]

arXiv
This paper discusses various theorems on the approximation capabilities of neural networks (NNs), which are known as universal approximation theorems (UATs). The paper gives a systematic overview of UATs starting from the preliminary results on function approximation, such as Taylor's theorem, Fourier's theorem, Weierstrass approximation theorem ...
arxiv  

Some extensions from famous theorems for $h$-mid-convex function [PDF]

arXiv
In this paper, we prove that every continuous $h$-mid-convex with suitable conditions on $h$ is $h$-convex function. Also, we extend Ostrowski theorem, Blumberg-Sierpinski theorem, Bernstein-Doetsch theorem, Mehdi theorem.
arxiv  

Variants of Łoś's Theorem [PDF]

arXiv
We study \L o\'s's theorem in a choiceless context. We introduce some variants of \L o\'s's theorem. These variants seem weaker than \L o\'s's theorem, but we prove that these are equivalent to \L o\'s's theorem.
arxiv