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We prove a version of a general transfer theorem for random sequences with independent random indexes in the double array limit setting under relaxed conditions. We also prove its partial inverse providing the necessary and sufficient…

We give a proof of the uniform convergence of Fourier series, using the methods of nonstandard analysis.

In the spirit of the many recent simple models of evolution inspired by statistical physics, we put forward a simple model of the evolution of such models. Like its objects of study, it is (one supposes) in principle testable and capable of…

We will give a pure combinatorial proof of the Eisenbud-Goto conjecture for arbitrary monomial curves. Moreover, we will show that the conjecture holds for certain simplicial affine semigroup rings.

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

This short note provides a new and simple proof of the convergence rate for Peng's law of large numbers under sublinear expectations, which improves the corresponding results in Song [15] and Fang et al. [3].

We obtain a recursive formula for the Gotzmann threshold of a power of a variable. Consequently, we give an affirmative answer to a conjecture of Bonanzinga and Eliahou.

In this paper, we prove a conjecture of Schnell in the surface case.

I present a simple derivation of the de Gennes narrowing phenomenon.

We prove Fujita's spectrum conjecture on the discreteness of pseudo-effective thresholds for polarized varieties.

In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the…

We prove a Frobenius-type theorem for singular distributions generated by a family of locally Lipschitz continuous vector fields satisfying almost everywhere a quantitative finite type condition.

We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.

We present an elementary proof for Ljunggren equation

In this study, we give an alternative and elementary proof to Tsuji's criterion for a Cartier divisor to be numerically trivial.

We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the…

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

We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.

Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.

For basic discrete probability distributions, $-$ Bernoulli, Pascal, Poisson, hypergeometric, contagious, and uniform, $-$ $q$-analogs are proposed.