Abdelmoula, Lobna Baklouti, Ali Bouaziz, Yasmine
Published in
Advances in Pure and Applied Mathematics

Let G be a type 1 connected and simply connected solvable Lie group. The generalized moment map for π in G ^ {\widehat{G}} , the unitary dual of G, sends smooth vectors of the representation space of π to 𝒰 ( 𝔤 ) * {{\mathcal{U}(\mathfrak{g})}^{*}} , the dual vector space of 𝒰 ( 𝔤 ) {\mathcal{U}(\mathfrak{g})} . The convex hull of the image of ...

Deleaval, Luc
Published in
Advances in Pure and Applied Mathematics

This note is a contribution to the Proceedings of the Conference of the Tunisian Mathematical Society CSMT 2017. After briefly revisiting the case of the standard Hardy–Littlewood maximal operator, we will discuss the behavior of the Dunkl maximal operator in both the scalar and vector-valued cases.

Rao, Sabbavarapu Nageswara
Published in
Advances in Pure and Applied Mathematics

Values of the parameters λ and μ are determined for which there exist positive solutions for the system of fractional order with p-Laplacian two-point boundary value problems. The well-known Guo–Krasnosel’skii fixed point theorem is applied.

Roukbi, Ahmed Lehlou, Fouad Moussa, Mohammed
Published in
Advances in Pure and Applied Mathematics

Let ( X , * ) {(X,*)} be a hypergroup and let w 0 {w_{0}} be a fixed measure on X. In this paper we study the two functional equations 〈 δ x * δ y * ω 0 , g 〉 + 〈 δ x * δ y ˇ * ω 0 , g 〉 = 2 g ( x ) g ( y ) , x , y ∈ X , \langle\delta_{x}*\delta_{y}*\omega_{0},g\rangle+\langle\delta_{x}*\delta_{% \check{y}}*\omega_{0},g\rangle=2g(x)g(y),\qu...

Okposo, Newton Willie, Robert
Published in
Advances in Pure and Applied Mathematics

In this paper, we study well-posedness, existence of a lower finite time blow-up bound and variants of controllability of the classical chemotaxis model in Ω × ( 0 , T ) {\Omega\times(0,T)} , where Ω ⊂ ℝ N {\Omega\subset\mathbb{R}^{N}} , N = 1 , 2 , 3 {N=1,2,3} . The spatial domain restrictions allow the system with initial data in L 2 ( Ω ) {L^{...

Oliveira, Daniela S. Capelas de Oliveira, Edmundo
Published in
Advances in Pure and Applied Mathematics

In this paper, we present a new differential operator of arbitrary order defined by means of a Caputo-type modification of the generalized fractional derivative recently proposed by Katugampola. The generalized fractional derivative, when convenient limits are considered, recovers the Riemann–Liouville and the Hadamard derivatives of arbitrary orde...

C, Sivaramakrishnan D, Sukumar Dogga, Venku Naidu
Published in
Advances in Pure and Applied Mathematics

In this article, we consider the Schrödinger semigroup for the Laplacian Δ on ℝ n {\mathbb{R}^{n}} , and characterize the image of a Sobolev space in L 2 ( ℝ n , e u 2 d u ) {L^{2}(\mathbb{R}^{n},e^{u^{2}}du)} under this semigroup as weighted Bergman space (up to equivalence of norms). Also we have a similar characterization for Hermite Sobol...

Boulaaras, Salah Guefaifia, Rafik Zennir, Khaled
Published in
Advances in Pure and Applied Mathematics

In this article, we discuss the existence of positive solutions by using sub-super solutions concepts of the following p ( x ) {p(x)} -Kirchhoff system: { - M ( I 0 ( u ) ) △ p ( x ) u = λ p ( x ) [ λ 1 f ( v ) + μ 1 h ( u ) ] in Ω , - M ( I 0 ( v ) ) △ p ( x ) v = λ p ( x ) [ λ 2 g ( u ) + μ 2 τ ( v ...

Foissy, Loïc
Published in
Advances in Pure and Applied Mathematics

To any poset or quasi-poset is attached a lattice polytope, whose Ehrhart polynomial we study from a Hopf-algebraic point of view. We use for this two interacting bialgebras on quasi-posets. The Ehrhart polynomial defines a Hopf algebra morphism with values in ℚ [ X ] \mathbb{Q}[X] . We deduce from the interacting bialgebras an algebraic proof of...

Shokooh, Saeid Afrouzi, Ghasem A.
Published in
Advances in Pure and Applied Mathematics

In this paper, by employing a critical point theorem, we establish the existence of infinitely many solutions for fourth-order impulsive differential equations depending on two real parameters.