Related papers: Oddball determinants
In this paper, we establish the sharp bounds of certain Toeplitz determinants formed over the coefficients of mappings from a class defined on the unit ball of complex Banach space and on the unit polydisc in $\mathbb{C}^n$. Derived bounds…
Full generalization of Kasner metric for the case of $n+1$ dimensions and $m\le n+1$ essential variables is obtained. Any solution is defined by the corresponding constant matrix of Kasner parameters. This parameters form in euclidian space…
Introducing a new method we give sharp estimates of the Hermitian Toepliz determinants of third order for the class $\mathcal{S}$ of functions univalent in the unit disc. The new approach is also illustrated on some subclasses of the class…
We consider a scalar-valued implicit function of many variables, and provide two closed formulae for all of its partial derivatives. One formula is based on products of partial derivatives of the defining function, the other one involves…
A new modulus of smoothness based on the Euler angles is introduced on the unit sphere and is shown to satisfy all the usual characteristic properties of moduli of smoothness, including direct and inverse theorem for the best approximation…
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills…
We give complete and exact descriptions of spaces of ultradifferentiable functions that are closed under composition with either holomorphic or ultradifferentiable functions -- which are two distinct cases. The proof works by considering…
We present a direct approach to the construction of Lagrangians for a large class of one-dimensional dynamical systems with a simple dependence (monomial or polynomial) on the velocity. We rederive and generalize some recent results and…
We study approximation properties of weighted $\mathrm{L}^2$-orthogonal projectors onto spaces of polynomials of bounded degree in the Euclidean unit ball, where the weight is of the reflection-invariant form $(1-\lVert x \rVert^2)^\alpha…
The Laplacian functional determinants for conformal scalars and coexact one-forms are evaluated in closed form on inhomogeneous lens spaces of certain orders, including all odd primes when the essential part of the expression is given,…
The paper deals with systems of ordinary differential equations containing in the right-hand side controls which are discontinuous in phase variables. These controls cause the occurrence of sliding modes. If one uses one of the well-known…
In this paper we develop a new approach to the design of direct numerical methods for multidimensional problems of the calculus of variations. The approach is based on a transformation of the problem with the use of a new class of…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
In this manuscript, we provide and discuss another approach to get derivative of odd-power such that is based on an identity in partial derivatives in terms of polynomial function $f_y$ defined as \[ f_{y} (x, z) = \sum_{k=1}^{z}…
We prove that for every indecomposable ordinal there exists a (transfinitely valued) Euclidean domain whose minimal Euclidean norm is of that order type. Conversely, any such norm must have indecomposable type, and so we completely…
In this paper, we study derivatives of powers of Euclidean norm. We prove their H\"older continuity and establish explicit expressions for the corresponding constants. We show that these constants are optimal for odd derivatives and at most…
In this paper, we establish various maximal principles and develop the direct moving planes and sliding methods for equations involving the physically interesting (nonlocal) pseudo-relativistic Schr\"{o}dinger operators…
Primal and dual algorithms are developed for solving the $n$-dimensional convex optimization problem of finding the Euclidean ball of minimum radius that covers $m$ given Euclidean balls, each with a given center and radius. Each algorithm…
We consider the space of convex functions defined in the Euclidean $n$-dimensional space, which are lower semi-continuous and tend to infinity at infinity. We study real-valued valuations defined on this space of functions, which are…
A new method is presented for obtaining indefinite integrals of common special functions. The approach is based on a Lagrangian formulation of the general homogeneous linear ordinary differential equation of second order. A general integral…