相关论文: A solution to an open problem on the Mathieu serie…

We characterise those real analytic mappings between any pair of tori which carry absolutely convergent Fourier series to uniformly convergent Fourier series via composition. We do this with respect to rectangular summation. We also…

The main objective of the present paper is to solve the several long standing divergence problems related to the logarithmic means of Fourier series in context of general orthonormal systems.

In this paper, we construct a new integrable equation which is a generalization of $q$-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of the generalized $q$-Toda…

By solving an infinite nonlinear system of $q$-difference equations one constructs a chain of $q$-difference operators. The eigenproblems for the chain are solved and some applications, including the one related to $q$-Hahn orthogonal…

The proof of the inequalities for alternating Mathieu type series in Journal of Mathematical Inequalities (2008) by \v{Z}. Tomovski and R. Hilfer contains a mistake. Here we give the values of parameters for which these inequalities are not…

We introduce a modification of the linear sieve whose weights satisfy strong factorization properties, and consequently equidistribute primes up to size $x$ in arithmetic progressions to moduli up to $x^{10/17}$. This surpasses the level of…

We investigate the solutions of the second-order difference equation $u_{n+2}=(au_n)/(1+bu_nu_{n+1})$ using a group of transformations (Lie symmetries) that leaves the solutions invariant.

In the present paper, we are concerned with the tau function and its connection with the Kadomtsev-Petviashvili (KP) theory for the massive Thirring (MT) model. First, we bilinearize the massive Thirring model under both the vanishing and…

We give an explicit description of the basic solutions of max-linear systems with two inequalities.

We introduce the multivariate analogue of the well known inequality $1+x\leq \mathrm{e}^x$, for an abstract non negative real number $x$. The result emerges from the study of the blow up time of certain solutions of the Cauchy problem for a…

The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported.

The main aim of this article is to establish a sharp improvement of the classical Bohr inequality for bounded holomorphic mappings in the polydisk $\mathbb{P}\Delta(0;1_n)$. We also prove two other sharp versions of the Bohr inequality in…

A bilinear inequality of Geba, Greenleaf, Iosevich, Palsson, and Sawyer for the Fourier transform is shown to be equivalent to a simpler linear inequality, and the range of exponents is extended. Related mixed-norm inequalities are…

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

We consider an open question posed in \cite{Zhu-Baggio-17} on the uniqueness of the solution to a parametric spectral estimation problem.

We introduce a new -as far as we know- problem, according to which we are asked to match sequences of two digits in matrices having entries among those two digits (but others too) and prove that this problem is NP-complete

Given two real numbers $q_0,q_1>1$ satisfying $q_0+q_1\geq q_0q_1$ and two real numbers $d_0\ne d_1$, by a {double-base expansion} of a real number $x$ we mean a sequence $(i_k)\in \{0,1\}^{\infty}$ such that \begin{equation*}…

In this article we present method of solving some additive problems with primes. The method may be employed to the Goldbach-Euler conjecture and the twin primes conjecture. The presented method also makes it possible to obtain some…

Mathieu equation is widely used to study several natural phenomenon. In this paper, we show that replacing the sinusoid in the Mathieu equation with a phasor can lead to solutions that behave in a totally different way. Solutions of Mathieu…

We establish an analog Hardy inequality with sharp constant involving exponential weight function. The special case of this inequality (for n=2) leads to a direct proof of Onofri inequality on S^2.