Related papers: Two-radii theorem for solutions of some mean value…
The main results here are two Helly type theorems for the sum of (at most) unit vectors in a normed plane. Also, we give a new characterization of centrally symmetric convex sets in the plane.
We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
A generalized divergence theorem is established allowing for domains with inner boundaries. The normal trace of a rough integrand is not a Radon measure; rather, the boundary integral is expressed via a surface functional continuous with…
We derive some regularity estimates of the solution to a time fractional diffusion equation, that are useful for numerical analysis, and partially unravel the singularity structure of the solution with respect to the time variable.
We prove that non-trivial bounds for generalized Radon transforms imply correspondingly non-trivial discrete incidence theorems for manifolds and suitably regular point sets.
We introduce a {\it non-regular} generalisation of the N\"{o}rlund mean, and show its equivalence with a certain moving average. The Abelian and Tauberian theorems establish relations with convergent sequences and certain power series. A…
In order to investigate minimal sufficient conditions for an abstract integral to belong to the convex hull of the integrand, we propose a system of axioms under which it happens. If the integrand is a continuous $R^n$-valued function over…
We present a generalized notion of degree for rotating solutions of planar systems. We prove a formula for the relation of such degree with the classical use of Brouwer's degree and obtain a twist theorem for the existence of periodic…
The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a…
Preliminary results from Nathanson [5] are used to prove the Muirhead and Rado inequalities.
The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.
In this paper, we obtain an asymptotic formula for the number of integral solutions to a system of diagonal equations. We obtain an asymptotic formula for the number of solutions with variables restricted to smooth numbers as well. We…
The arithmetic function of two variables is defined. Some properties of the function are given along with the formula that is an analog of the so-called Mobius' inversion formula. A heuristic statement is suggested.
Several incidence theorems of planar projective geometry are considered. It is demonstrated that generalizations of Pascal theorem due to M\"obius give rise to double cross-ratio equation and Hietarinta equation. The construction…
We obtain simple proofs of certain inequalites for bivariate means.
We provide several characterizations of ring-shaped rotationally symmetric solutions to the Serrin problem in arbitrary dimensions.
Regularity of solutions is studied for backward stochastic parabolic Ito equations. An analog of the second energy inequality and the related existence theorem are obtained for domains with boundary.
We give description of rational solutions of polynomial-equations.
We give tight bounds for logarithmic mean. We also give new Frobenius norm inequalities for two positive semidefinite matrices. In addition, we give some matrix inequalities on matrix power mean.