Related papers: A note on the Tikhonov theorem on an infinite inte…

We provide a Kingman-like Theorem for arbitrary finite measures and a version of Birkhoff's Theorem for bounded observable. As an application, we show that Birkhoff's limit exists for some continuous observable, in an example of Bowen.

A simple proof of Egorov's theorem for infinite measure is given

We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.

In this note we give a detailed proof of a theorem of Aubin.

In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.

In this paper we provide an application to the Neumann problem of a recent three critical points theorem.

The paper considers impulsive systems with singularities. The main novelty of the present research is that impulses (impulsive functions) are singular. This is beside singularity of differential equations. The Lyapunov second method is…

We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.

In this letter, by regarding finite-time stability as an inverse problem, we reveal the essence of finite-time stability and fixed-time stability. Some necessary and sufficient conditions are given. As application, we give a new approach…

We survey the classical results of the Dirichlet Approximation Theorem.

We furnish an explicit bound for the prime number theorem in short intervals on the assumption of the Riemann hypothesis.

This note gives results on the existence of semi-continuous solutions of a Fredholm integral equation of the second kind using Tarski's fixed point theorem.

The note contains the proof of the uniqueness theorem for the inverse problem in the case of $n$-th order differential equation.

By the example of the proof of Minkowski's conjecture on critical determinant we give a category theory framework for interval computation.

The purpose of this note is to consider a number of straightforward generalizations of the Pirogov-Sinai theory which can be covered by minor additions to the canonical texts. These generalizations are well-known among the adepts of the…

In a present note we give a new proof of Etingof-Kazhdan quantization theorem.

We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.

Discrete-time counterpart of thermodynamic uncertainty relation (conjectured in P. Pietzonka, et.al., arXiv:1702.07699 (2017)) with finite time interval is considered. We show that this relation do not hold by constructing a concrete…

We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.

This is a new version of our previous work. In this version, we fill a gap included in the original proof of Theorem 1.1 in our previous paper entitled "An iterative method for Kirchhoff type equations and its applications".