Related papers: Second-order differential subordinations for analy…
We consider the family of all analytic and univalent functions in the unit disk of the form $f(z)=z+a_2z^2+a_3z^3+\cdots$. Our objective in this paper is to estimate the difference of the moduli of successive coefficients, that is $\big |…
For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…
We consider two types of convolutions ($\ast$ and $\star$) of functions on spaces of finite configurations (finite subsets of a phase space), and some their properties are studied. A connection of the $\ast$-convolution with the convolution…
Derivation of two-time second-order correlation function by following approaches such as stochastic differential equation, coherent-state propagator, and quasi-statistical distribution function is presented. In the process, the time…
In this work we study the solutions to some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be…
(Renegar, 2016) introduced a novel approach to transforming generic conic optimization problems into unconstrained, uniformly Lipschitz continuous minimization. We introduce {\it radial transformations} generalizing these ideas, equipped…
The purpose of this present paper is to investigate the geometric structure of regular overdetermined systems of second order with two independent and one dependent variables from the point of view of rank 2 prolongations. Utilizing this…
Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are mappings given in an integral form depending on two variables, the first a finite dimensional decision vector and the…
The aim of this work is to provide formulae for the subdifferential and the conjungate function of the supremun function over an arbitrary family of functions. The work is principally motivated by the case when data functions are lower…
The estimates for the second Hankel determinant a_2a_4-a_3^2 of analytic function f(z)=z+a_2 z^2+a_3 z^3+...b for which either zf'(z)/f(z) or 1+zf"(z)/f'(z) is subordinate to certain analytic function are investigated. The estimates for 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…
We propose first order algorithms for convex optimization problems where the feasible set is described by a large number of convex inequalities that is to be explored by subgradient projections. The first algorithm is an adaptation of a…
In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
We develop a principled approach to obtain exact computer-aided worst-case guarantees on the performance of second-order optimization methods on classes of univariate functions. We first present a generic technique to derive interpolation…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem.
We present an adaptation of two recent low-rank approximation technique proposed for first-order model reduction systems to the second-order systems. The resulting reduced order models are guaranteed to keep the second order structure which…
Optimization in Deep Learning is mainly dominated by first-order methods which are built around the central concept of backpropagation. Second-order optimization methods, which take into account the second-order derivatives are far less…