Related papers: Comparison theorems and some of their applications
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.
In this note a proof of a differential analog of Chevalley's theorem \cite{C} on homomorphism extensions is given. An immediate corollary is a condition of finitenes of extensions of differential algebras and several equivalent definitions…
This article is about the proof of the celebrated KAM theorem as sketched out in \cite{KOL} Kolmogorov's original presentation to the ICM. The proof presented here has been detailed as an effort to clarify if Kolmogorov's argument can be…
Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.
We survey some basic results on the Gromov-Prohorov distance between metric measure spaces. (We do not claim any new results.) We give several different definitions and show the equivalence of them. We also show that convergence in the…
In the present paper we introduce old and new results related to St\"ormer theorem about Pell equations. Moreover we give four types of applications of these results.
Measures on a non-Archimedean Banach space $X$ are considered with values in the real field $\bf R$ and in the non- Archimedean fields. The non-Archimedean analogs of the Bochner- Kolmogorov and Minlos-Sazonov theorems are given. Moreover,…
We generalize several comparison results between algebraic, semi-topological and topological K-theories to the equivariant case with respect to a finite group.
Some inequalities for different types of convexity are established.
This an expository article on Givental's axiomatic Gromov--Witten theory and some of its applications.
We discuss combinatorial conditions for the existence of various types of reductions between equivalence relations, and in particular identify necessary and sufficient conditions for the existence of injective reductions.
A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.
Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently co-exist for the first time and are here reviewed, ranging from dominant ones such as statistical lossless compression…
A comparison theorem is proved for a pair of solutions that satisfy in a weak sense opposite differential inequalities with nonlinearity of the form $f (u)$ with $f$ belonging to the class $L^p_{loc}$. The solutions are assumed to have…
We present a well-structured detailed exposition of a well-known proof of the following celebrated result solving Hilbert's 13th problem on superpositions. For functions of 2 variables the statement is as follows. Kolmogorov Theorem. There…
Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes.
We give a q-analogue of Gauss' divisibility theorem
By employing certain extended classical summation theorems, several surprising \pi and other formulae are displayed.
We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral…
Three generalizations of the well-known Ceva's Theorem are given in this paper and some applications.