Related papers: Subderivative-subdifferential duality formula
In this paper we generalize the DP framework to a relative DP framework, where a so called split is possible.
In the present paper, we define a new general subclass of bi-univalent functions involving a differential operator in the open unit disk U. For this purpose, we use the Faber polynomial expansions. Several connections to some of the earlier…
The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…
In this note, we describe some desingularizations of some subvarieties of the cartesian powers of a semisimple Lie algebra of finite dimension.
This paper is concerned with the directional derivative of the value function for a very general set-constrained optimization problem under perturbation. Under reasonable assumptions, we obtain upper and lower estimates for the upper and…
The simplicial extension of any functor from Sets to Sets which commutes with directed colimits takes weak equivalences to weak equivalences. The goal of the present paper is construct a framework which can be used to proof results of this…
Given a two-variable function $f$ without critical points and a compact region $R$ bounded by two level curves of $f$, this note proves that the integral over $R$ of the second-order directional derivative of $f$ in the tangential…
In this brief note we critically examine the process of partial and of total differentiation, showing some of the problems that arise when we relate both concepts. A way to solve all the problems is proposed.
We give a formula for matrix exponentials and partial fraction decompositions.
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
A new method for approximating fractional derivatives of the Gaussian function and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann-Liouville integral using polynomial…
We equip a family of algebras whose noncommutativity is of Lie type with a derivation based differential calculus obtained, upon suitably using both inner and outer derivations, as a reduction of a redundant calculus over the Moyal four…
The purpose of this note is to show how some results from the theory of partial differential equations apply to the study of pseudo-spectra of non-self-adjoint operators, which is a topic of current interest in applied mathematics.
A generalization of the classical Leibniz rule for the covariant derivative on a vector bundle is obtained.
Fractional derivatives are generalization to classical integer-order derivatives. The rules which are true for classical derivative need not hold for the fractional derivatives, for example, we cannot simply add the fractional orders…
In this paper we generalize the result valid for associative rings due \cite[Martindale III]{Mart} and \cite[Bre$\check{s}$ar]{bresar} to alternative rings. Let $\mathfrak{R}$ be an unital alternative ring, and $\mathfrak{D}: \mathfrak{R}…
We discuss how countable subadditivity of operators can be derived from subadditivity under mild forms of continuity, and provide examples manifesting such circumstances.
In this review we discuss what is known about semiorthogonal decompositions of derived categories of algebraic varieties. We review existing constructions, especially the homological projective duality approach, and discuss some related…
In this paper, we introduce a new generalized derivative, which we term the specular derivative. We establish the Quasi-Rolles' Theorem, the Quasi-Mean Value Theorem, and the Fundamental Theorem of Calculus in light of the specular…
In this paper we first provide a general formula of inclusion for the Dini-Hadamard epsilon-subdifferential of the difference of two functions and show that it becomes equality in case the functions are directionally approximately…