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The present paper is devoted to derive a generalized Oberhettinger-type integral formula. The derived form of the integral involves a finite product of the Srivastava polynomials with the four-parameter Bessel functions. The outcomes are obtained in terms of the Srivastava and Daoust-type functions. Some of the significant particular cases are also determined. [ABSTRACT FROM AUTHOR]

The purpose of this research is to study the generalized integral operator and its connection with generalized Mittag-Leffler functions. The objective is to evaluate composition formulas for the pathway integral operator connected to the extended Mittag-Leffler functions. The images of the generalized Mittag-Leffler functions under the classical Riemann-Liouville fractional integral operator and the Laplace integral transform are emphasized as special cases of the image of functions under the pathway integral operator. [ABSTRACT FROM AUTHOR]

We study four-dimensional boundary value problems for the nonhomogenous wave equation, known as Protter problems. Here the boundary conditions are posed on a characteristic surface of the domain and on non-characteristic one. It is known that the Protter problems are ill-posed in the frame of classical solvability and they have generalized solutions with strong singularities. The behavior of these singular solutions is not typical for hyperbolic equations: their singularities are isolated at one boundary point and the order of singularity do not depend on the regularity of the right-hand side of the equation. In this paper we consider a case with a third-type condition on the non-characteristic surface and we find an explicit integral representation of the generalized solution. Further, we study the adjoint homogeneous problem. The reason for the ill-posedness of the Protter problems is that their adjoint homogeneous problems have infinitely many nontrivial classical solutions. In the case of the first-type and the second-type boundary value problems these solutions are well known. In this work we extend these results for the third-type boundary value problem: we find the exact formulas of the classical solutions of the adjoint homogeneous problem. [ABSTRACT FROM AUTHOR]

In this paper, we show several coupled fixed point theorems in partial order metric space that are equipped with rational type contraction. These results also generalized into integral type contraction. We have also included several instances to back up our major findings. [ABSTRACT FROM AUTHOR]

A β-Laplace integral transform is a new form of generalization of Laplace integral transform. This new β-Laplace integral transform has many remarkable properties over Laplace transform. The current paper presents some results involving the Generalised Mittag-Leffler function and the β-Laplace integral transform. [ABSTRACT FROM AUTHOR]

We prove common fixed point theorems for mappings satisfying a general contractive inequality of integral type for generalized metric spaces. Our results extend of the theorem of Branciari (2002) constitutionally and we provide some examples in support of our results. [ABSTRACT FROM AUTHOR]

In the present paper we study a Darboux-Goursat problem for a hyperbolic equation with a singular coefficient, where a third-type boundary condition on the non-characteristic segment is imposed. This problem is related to a four-dimensional Protter's problem for the wave equation and it has an unique generalized solution with possible singularity at a boundary point. We find an integral representation of this solution via Riemann-Hadamard function. The singularity of the generalized solution depends on orthogonality condition on the right-hand side of the equation in respect to nontrivial classical solutions of the corresponding adjoint homogeneous problem. Here we find an explicit formula for such nontrivial classical solutions. [ABSTRACT FROM AUTHOR]

A modification of the Newtonian gravity is proposed for disk galaxies. A gravitational field flux conservation and redistribution picture is formed by generalizing the Integral Gauss's law of gravity at non-relativistic limit. 1/r dependence along with a disk thickness dependence of gravitational field and the flat rotation curves are obtained by a Gaussian surface with cylindrical symmetry, where most of the gravitational fluxes are assumed to be distributed eventually along the disk plane. Gaussian disk thickness as a hidden dynamical variable is proposed with observational evidences. Subsequently, a spherical to cylindrical transition, across a critical field strength, of the Gaussian surface symmetry is shown to give directly the algebraic M α v4 baryonic Tully-Fisher relation. The transition implies that the 10-10 m/s2 acceleration scale can be alternatively interpreted as a critical field strength where gravitational flux redistribution occurs. The universal structural-dynamical relations revealed by the radial acceleration curve from Spitzer Photometry and Accurate Rotation Curves (SPARC) data are compared to the field flux distribution picture. The Newtonian dynamics above the critical field of -10−10 N/Kg near the bulge region of High Surface Brightness Galaxies (HSBGs) can be explained by the spherical distribution of the gravitational flux while the Non-Newtonian behaviors of both the Low Surface Brightness Galaxies (LSBGs) and the outskirts of the HSBGs can be attributed to the cylindrical flux distribution below the critical field. [ABSTRACT FROM AUTHOR]

The Protter’s problems are multidimensional variants of the 2-D Darboux problems for hyperbolic and weakly hyperbolic equations and they are not well-posed in the frame of classical solvability, since their adjoint homogeneous problems have infinitely many nontrivial classical solutions. The generalized solutions of the Protter’s problem may have strong singularities even for very smooth right-hand side functions of the equation. These singularities are isolated at one boundary point and do not propagate along the bicharacteristics which is unusually for the hyperbolic equations. Here we treat a generalization of the well studied Protter’s problem for the 4-D wave equation, considering a case of more general equation involving lower order terms with constant coefficients. First, we announce explicit formulas for the nontrivial classical solutions of the corresponding adjoint homogeneous problem. Further, we give an exact integral representation of the generalized solutions of the considered problem as well as an asymptotic expansion of their singularities. [ABSTRACT FROM AUTHOR]

It is known that history of mathematics is old as history of humanity. Mathematics covered a distance significantly from ancient age to now. Recently, there are many important works for modern mathematics([6],[8]). Let X be a nonempty set and f: X → X be a mapping. If f (x) = x, for some x ∈ X, then x is fixed point of f. Banach fixed point theorem was introduced in 1922 in complete metric spaces as “(X, d) be a complete metric space and f: X → X be a self-mapping. If there exists 0 ≤ k < 1 such that d (fx, fy) ≤ kd (x, y) for all x, y ∈ X. Then f has unique fixed point”([1]).Partial metric spaces were introduced by Matthews (1994) as a generalisation of usual metric spaces where the self distance for any point need not be equal to zero. In this work, we define generalized integral type F−contractions and prove common fixed point theorems for four mappings satisfying these types contractions in partial metric spaces. [ABSTRACT FROM AUTHOR]

Positive and negative features of the Copenhagen interpretation are discussed. As positive features can be mentioned its pragmatism and its awareness of the crucial role of measurement. However, the main part of the contribution is devoted to the negative features, to wit, its pragmatism (once again), its confounding of preparation and measurement, its classical account of measurement, its completeness claims, the ambiguity of its notion of correspondence, its confused notion of complementarity. It is demonstrated how confusions and paradoxes stemming from the negative features of the Copenhagen interpretation can be dealt with in an amended interpretation, to be referred to as ‘neo-Copenhagen interpretation’, in which the role of the measuring instrument is taken seriously by recognizing the quantum mechanical character of its interaction with the microscopic object. The ensuing necessity of extending the notion of a quantum mechanical observable from the Hermitian operator of the standard formalism to the positive operator-valued measure of a generalized formalism yields a sound mathematical basis for a transition from the Copenhagen contextualistic-realist interpretation to the neo-Copenhagen empiricist one. Applications to the uncertainty relations and to the Bell inequalities are briefly discussed. [ABSTRACT FROM AUTHOR]

We consider the infinite Haar measure on a current group as an invariant distribution associated to the Wiener process on the current group. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

The Q²-dependence of the generalized Gerasimov-Drell-Hearn integral for the proton has been measured in the range 1.2 GeV² ≤ Q² ≤ 12 GeV² and 1 GeV² ≤ W² ≤ 45 GeV² by the HERMES experiment. The contributions of the nucleon-resonance and deep-inelastic regions to this integral have been evaluated separately. At low Q² the contributions from the resonance and the deep-inelastic regions are about equal in size, while the latter one dominates for Q² > 3 GeV². Since the extrapolation for the unmeasured energy range is small, this measurement provides the first evaluation of the full generalized GDH integral. It shows no significant deviation from a 1/Q² behavior in the measured range and thus no sign of large effects due to either resonance excitations or non-leading twist. [ABSTRACT FROM AUTHOR]