Effect of Oblateness of the Secondary up to J4 on L4,5 in the Photogravitaional ER3BP

In a synodic-pulsating dimensionless coordinate, with a luminous primary and an oblate secondary, we examine the effects of radiation pressure, oblateness (quadruple and octupolar i.e. ) and eccentricity of the orbits of the primaries on the triangular points in the ER3BP. have been shown to disturb the motion of an infinitesimal body and particularly has significant effects on a satellite’s secular perturbation and orbital precessions. The influence of these parameters on the triangular points of Zeta Cygni, 54 Piscium and Procyon A/B are highlighted in this study. Triangular points are stable in the range and their stability is affected by said parameters.

Quaternionic G-Monogenic Mappings in Em

We consider a class of so-called quaternionic G-monogenic mappings associatedwith m-dimensional (m 2 f2; 3; 4g) partial differential equations and propose a description of allmappings from this class by using four analytic functions of complex variable. For G-monogenicmappings we generalize some analogues of classical integral theorems of the holomorphic functiontheory of the complex variable (the surface and the curvilinear Cauchy integral theorems,the Cauchy integral formula, the Morera theorem), and Taylor’s and Laurent’s expansions.Moreover, we investigated the relation between G-monogenic and H-monogenic (differentiablein the sense of Hausdorff) quaternionic mappings.

Asymptotic Behaviors of Wronskians and Finite Asymptotic Expansionsin the Real Domain - Part II: Mixed Scales and Exceptional Cases

In this second Part of our work we study the asymptotic behaviors of Wronskians involving both regularly- and rapidly-varying functions, Wronskians of slowly-varying functions and other special cases. The results are then applied to the theory of asymptotic expansions in the real domain.

L1-Solutions of Boundary Value Problems for Implicit Fractional Order Differential Equations with Integral Conditions

The aim of this paper is to present new results on the existence of solutions for a class of boundary value problem for fractional order implicit di erential equations with integral conditions involving the Caputo fractional derivative. Our results are based on Schauder's xed point theorem and the Banach contraction principle fi xed point theorem.

On Conformal Radii of Non-Overlapping Simply Connected Domains

The paper deals with the following open problem stated by V.N. Dubinin. Let $a_{0}=0$, $|a_{1}|=\ldots=|a_{n}|=1$, $a_{k}\in B_{k}\subset \overline{\mathbb{C}}$, where $B_{0},\ldots, B_{n}$ are disjoint domains. For all values of the parameter $\gamma\in (0, n]$ find the exact upper bound for $r^\gamma(B_0,0)\prod\limits_{k=1}^n r(B_k,a_k)$, where $r(B_k,a_k)$ is the conformal radius of $B_k$ with respect to $a_k$. For $\gamma=1$ and $n\geqslant2$ the problem was solved by V.N. Dubinin. In the paper the problem is solved for $\gamma\in (0, \sqrt{n}\,]$ and $n\geqslant2$ for simply connected domains.The paper deals with the following open problem stated by V.N. Dubinin. Let a0 = 0, ιa1ι =...= ιanι = 1, ak ∈ Bk ⊂ , where B0, ..., Bn are disjoint domains. For all values of the parameter γ∈ (0; n] find the exact upper bound nfor rγ(B0; 0) ∏ r(Bk; ak), where r(Bk; ak) is the conformal radius of Bk with respect to ak. For γ = 1 k=1 and n ≥ 2 the problem was solved by V.N. Dubinin. In the paper the problem is solved for γ ∈ (0; √n ] and n ≥ 2 for simply connected domains.

Monotone Solution of Cauchy Type Weighted Nonlocal Fractional Differential Equation

In this paper we will consider a nonlinear fractional di fferential equation withweighted initial and nonlocal conditions and will obtain monotone solution by thesequence of successive approximations starting at a lower solution converges monotonicallyto the solution of the related cauchy type weighted nonlocal fractionaldi fferential equation under some suitable conditions.

On Dentability in Locally Convex Vector Spaces

The notions of V-dentability, V-s-dentability and V-f-dentability are introduced. It is shown, in particular, that if B is a bounded sequentially complete convex metrizable subset of a locally convex vector space E and V is a neighborhood of zero in E, then the following are equivalent: 1). B is subset V-dentable; 2). B is subset V-s-dentable; 3). B is subset V-f-dentable. It follows from this that for a wide class of locally convex vector spaces E, which strictly contains the class of (BM) spaces (introduced by Elias Saab in 1978), the following is true: every closed bounded subset of E is dentable if and only if every closed bounded subset of E is f-dentable. Also, we get a positive answer to the Saab's question (1978) of whether the subset dentability and the subset s-dentability are the same forthe bounded complete convex metrizable subsets of any l.c.v. space.

Integrals Involving Aleph Function and Wright’s Generalized Hypergeometric Function

The aim of this paper is to establish certain integrals involving product of the Aleph function with Srivastava’s polynomials and Fox-Wright’s Generalized Hypergeometric function. Being unified and general in nature, these integrals yield a number of known and new results as special cases. For the sake of illustration, four corollaries are also recorded here as special case of our main results.

Generalized Composition Operators on Weighted Hilbert Spaces of Analytic Functions

Letφbe an analytic self-map of the open unit disk D andgbe an analytic function on D. The generalized composition operator induced by the mapsgandφis defined by the integral operatorI(g,φ)f(z) =∫0zf′(φ(ς))g(ς)dς. Given an admissible weightω, the weighted Hilbert spaceHωconsists of all analytic functionsfsuch that ∥f∥2Hω= |f(0)|2+∫D|f′(z)|2ω(z)dA(z) is finite. In this paper, we characterize the boundedness and compactness of the generalized composition operators on the spaceHωusing theω-Carleson measures. Moreover, we give a lower bound for the essential norm of these operators.

Asymptotic Behaviors of Wronskians and Finite Asymptotic Expansions in the Real Domain - Part I: Scales of Regularly- or Rapidly-Varying Functions

In a previous series of papers we established a general theory of finite asymptotic expansions in the real domain for functions f of one real variable sufficiently-regular on a deleted neighborhood of a point x0 ∈ R, a theory based on the use of a uniquely-determined linear differential operator L associated to the given asymptotic scale and wherein various sets of asymptotic expansions are characterized by the convergence of improper integrals involving both the operator L applied to f and certain weight functions constructed by means of Wronskians of the given scale. Very special cases apart, Wronskians have quite complicated expressions and unrecognizable asymptotic behaviors; however in the present work, split in two parts, we highlight some approaches for determining the exact asymptotic behavior of a Wronskian when the involved functions are regularly- or rapidly-varying functions of higher order. This first part contains: (i) some preliminary results on the asymptotic behavior of a determinant whose entries are asymptotically equivalent to the entries of a Vandermonde determinant; (ii) the fundamental results about the asymptotic behaviors of Wronskians involving scales of functions all of which are either regularly (or, more generally, smoothly) varying or rapidly varying of a suitable higher order. A lot of examples and applications to the theory of asymptotic expansions in the real domain are given.