Related papers: Ludwig Bieberbach's "Remarks on Hilbert's Thirteen…
The classical Hermitian eigenvalue problem addresses the following question: What are the possible eigenvalues of the sum A+B of two Hermitian matrices A and B, provided we fix the eigenvalues of A and B. A systematic study of this problem…
This is an English translation of Felix Klein's paper "Ueber die Transformation elfter Ordnung der elliptischen Functionen" from 1879.
Formulating a Schubert problem as the solutions to a system of equations in either Pl\"ucker space or in the local coordinates of a Schubert cell typically involves more equations than variables. We present a novel primal-dual formulation…
In 1910 Einstein published a crucial aspect of his understanding of Boltzmann entropy. He essentially argued that the likelihood function of any system composed by two probabilistically independent subsystems {\it ought} to be factorizable…
In this paper, we study an additive model where the response variable is Hilbert-space-valued and predictors are multivariate Euclidean, and both are possibly imperfectly observed. Considering Hilbert-space-valued responses allows to cover…
In this article, we studied the inverse Erd\H{o}s-Heilbronn problem with the restricted sumset from two components $A$ and $B$ that are not necessarily the same. We give a completely elementary proof for the problem in $\mathbb{Z}$ and some…
The leading asymptotic behaviour of the Humbert functions $\Phi_2$, $\Phi_3$, $\Xi_2$ of two variables is found, when the absolute values of the two independent variables become simultaneosly large. New integral representations of these…
We study the bi-graded Hilbert function of ideals of general fat points with same multiplicity in $\mathbb{P}^1\times\mathbb{P}^1$. Our first tool is the multiprojective-affine-projective method introduced by the second author in previous…
In these lectures we present five interpretations of the Fa' di Bruno formula which computes the n-th derivative of the composition of two functions of one variable: in terms of groups, Lie algebras and Hopf algebras, in combinatorics and…
We present two theorems concerned with algorithmic randomness and differentiability of functions of several variables. Firstly, we prove an effective form of the Rademacher's Theorem: we show that computable randomness implies…
It is developed the theory of the Dirichlet problem for harmonic functions. On this basis, for the nondegenerate Beltrami equations in the quasidisks and, in particular, in the smooth domains, it is proved the existence of regular solutions…
An approximate formula for the partitions of Goldbach's Conjecture is derived using Prime Number Theorem and a heuristic probabilistic approach. A strong form of Goldbach's conjecture follows in the form of a lower bounding function for the…
We generalize the notion of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These conjugate functions are in general far from being…
The addition relation for the Riemann theta functions and for its limits, which lead to the appearance of exponential functions in soliton type equations is discussed. The presented form of addition property resolves itself to the…
We study two extremal problems of geometric function theory introduced by A. A. Goldberg in 1973. For one problem we find the exact solution, and for the second one we obtain partial results. In the process we study the lengths of…
The famous strongly binary Goldbach's conjecture asserts that every even number $2n \geq 8$ can always be expressible as the sum of two distinct odd prime numbers. We use a new approach to dealing with this conjecture. Specifically, we…
We investigate semiconjugate rational functions, that is rational functions $A,$ $B$ related by the functional equation $A\circ X=X\circ B$, where $X$ is a rational function of degree at least two. We show that if $A$ and $B$ is a pair of…
In the article the necessary and sufficient conditions for a representation of Lipschitz function of more than two variables as a difference of two convex functions are formulated. An algorithm of this representation is given. The outcome…
We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…
We consider the nonlinear Cauchy problem for $ \Psi $- Hilfer fractional differential equations and investigate the existence, interval of existence and uniqueness of solution in the weighted space of functions. The continuous dependence of…