Approximate controllability of impulsive integrodifferential equations with state-dependent delay

This paper considers the approximate controllability of mild solutions for impulsive semilinear integrodifferential equations with statedependent delay in Hilbert spaces. We obtain our significant findings using Grimmer’s resolvent operator theory and Schauder’s fixed point theorem. We give an example at the end to ensure the compatibility of the results

Some properties for ν-zeros of parabolic cylinder functions

Let Dν(z) be the Parabolic Cylinder function. We study the ν-zeros of the function ν → Dν(z) with respect to the real variable z. We establish a formula for the derivative of a zero and deduce some monotonicity results. Then we also give an asymptotic expansion for ν-zeros for large positive z

Littlewood-Paley characterization of discrete Morrey spaces and its application to the discrete martingale transform

The goal of this paper is to develop the Littlewood–Paley theory of discrete Morrey spaces. As an application, we establish the boundedness of martingale transforms. We carefully justify the definition of martingale transforms, since discrete Morrey spaces do not contain discrete Lebesgue spaces as dense subspaces. We also obtain the boundedness of Riesz potentials

A study on k-coalescence of two graphs

The k-coalescence of two graphs is obtained by merging a k-clique of each graph. The Aα-matrix of a graph is the convex combination of its degree matrix and adjacency matrix. In this paper, we present some structural properties of a non-regular graph which is obtained from the k-coalescence of two graphs. Also, we derive the Aα-characteristic poly- nomial of k-coalescence of two graphs and then compute the Aα-spectra of k-coalescence of two complete graphs. In addition, we estimate the Aα-energy of k-coalescence of two complete graphs. Furthermore, we obtain some topological indices of vertex coalescence of two graphs, and as an application, we determine the Wiener, hyper-Wiener and Zagreb indices of Lollipop and Dumbbell graphs. &nbsp

Algebraic surfaces with nonhyperelliptic linear pencil of genus 4 and irregularity one

We construct algebraic surfaces with nonhyperelliptic linear pencil of genus 4 and of rank 3 whose slope is equal to 4 and with irregularity one. Furthermore, we consider the converse. Namely, we obtain the structure of the surfaces with the above properties. &nbsp

Structure of unital Q-Fréchet algebras A satisfying: Ax^2 = Ax, for every x ∈ A

We show that a unital Q-Fréchet  algebra A satisfying Ax2  = Ax, for every x ∈ A, is isomorphic to  Cn, n ∈ N*

On a system involving an integro-differential inclusion with subdifferential and caputo fractional derivative

The current work is concerned with a new system involving an integro-differential inclusion of subdifferential type and Caputo fractional derivative, in Hilbert spaces. We use a discretization approach to deal with the integro-differential inclusion. Then, we proceed by a fixed point theorem to handle the considered system

Hahn multiplicative calculus

In this study, Hahn multiplicative calculus was introduced and as an application of this subject, the classical Sturm--Liouville problem was examined under this structure

Stability of constant equilibria in a Keller--Segel system with gradient dependent chemotactic sensitivity

This paper deals with the Keller–Segel system with gradient depen- dent chemotactic sensitivity, where Ω ⊂ Rn (n ∈ N) is a bounded domain with smooth boundary, and χ > 0, p ∈ (1, ∞) are constants. The purpose of this paper is to establish stability of constant equilibria under some smallness conditions for the initial data