Exact Solutions of Covariant Wave Equations with a Multipole Source Term on Curved Spacetimes

A formalism is presented for calculating exactsolutions of covariant inhomogeneous scalar and tensorwave equations whose source terms are arbitrary ordermultipoles on a curved background spacetime. The developed formalism is based on the theory ofthe higher-order fundamental solutions for wave equationwhich are the distributions that satisfy theinhomogeneous wave equation with the corresponding order covariant derivatives of the Dirac deltafunction on the right-hand side. Like the classicalGreen's function for a scalar wave equation, thehigher-order fundamental solutions contain a direct termwhich has support on the light cone as well as a tailterm which has support inside the light cone. Knowinghow to compute the fundamental solutions of arbitraryorder, one can find exact multipole solutions of wave equations on curved spacetimes. Wepresent complete recurrent algorithms for calculatingthe arbitrary-order fundamental solutions and the exactmultipole solutions in a form convenient for practical computations. As an example we apply thealgorithm to a massless scalar wave field on aparticular Robertson-Walker spacetime.     

The Effects of Morphological Properties of Henequen Fiber Irradiated by EB on the Mechanical and Thermal Properties of Henequen Fiber/PP Composites

The aim of this study was to investigate the effects of electron beam (EB) irradiation on the morphological properties, crystallinity and surface area of henequen fiber and on the mechanical and thermal properties of henequen fiber reinforced polypropylene (PP) composites. The structure of henequen fiber was characterized by X-ray diffraction, mercury porosimetry and BET surface area analysis. The EB irradiation of 10 kGy led to the increasing of crystalline and surface pore area of henequen fiber, which contributed to the number of interlocking places with PP. From the results of tensile and impact strength tests, the highest value was observed for the composite reinforced with the henequen fiber treated with EB dose of 10 kGy, decreasing overall as EB dose increased. This tendency was also shown by coefficient of thermal expansion (CTE) measurements, but the value of CTE decreased until 50 kGy, meaning that a large total surface area can provide many interlocking places and so improve adhesion between fiber and matrix. Therefore, it can be concluded that the optimum pore surface area by 10 kGy irradiation contributes to successful mechanical interlocking between fiber and matrix and consequently enhances the mechanical and thermal properties of the composites.     

Proposal of refined interface models and their application for free-edge effect

Two interface models based on physical considerations are proposed to analyze the freeedge effects in unidirectional multilayered composites. The first model is a transition behavior law describing the graded properties of the interlayer between two adjacent layers. It is defined according to the stacking direction and based on a microscopic analysis of the fiber distribution in the vicinity of the interlayer. Used in a numerical simulation, this model gives accurate stress distributions in the laminate, including the interlaminar stresses at the free-edge that are not singular. The second model utilizes an interface law, defined on the material surface, resulting from the asymptotic resolution of an elastic problem pertaining to the interlayer and simulating a very thin flexible layer. This model also gives no singular free-edge interlaminar stresses close to those obtained with the first model.     

Preparation and properties of transparent poly(methyl methacrylate) nanocomposite films

PMMA nanocomposites based on the synthetic smectite were prepared and characterized. The synthetic smectites, STN and SPN, were effectively hybridized in the PMMA matrix, as confirmed by X-ray diffraction patterns and by transmission electron microscopy, and optical and thermal properties were measured. The morphologies of PMMA nanocomposite films, containing 1–9 wt% with respect to synthetic smectite, were defined as exfoliated-immiscible and exfoliated-intercalated nanocompostites for CHT and CHP series, respectively. The optical properties, such as haze and UV transmittance, were maintained for organoclay loading of 9 wt% for CHP series. Thermal stability evaluated by TGA showed a small increase in the maximum decomposition temperature (T _d); however, the coefficient of thermal expansion (CTE) dramatically decreased with the amount of organoclay content. The storage modulus and loss modulus increased with the weight fraction of organoclay.     

On truncation error bound for multidimensional sampling expansion laplace transform

The truncation error associated with a given sampling representation is defined as the difference between the signal and an approximating sumutilizing a finite number of terms. In this paper we give uniform bound for truncation error of bandlimited functions in the n dimensional Lebesgue space Lp(R^n) associated with multidimensional Shannon sampling representation.     

Hausdorff dimension of some kind of alternating Oppenheim series expansion

For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number.     

Approaches to the Monopole-Dynamic Dipole Vacuum Solution Concerning the Structure of Its Ernst Potential on the Symmetry Axis

The FHP (Fodor, Hoenselaers, Perjés) algorithm [1] allows to obtain the relativistic multipole moments of a vacuum stationary axisymmetric solution in terms of coefficients which appear in the expansion of its Ernst potential on the symmetry axis. First of all, we will use this result in order to determine, at a certain approximation degree, the Ernst potential on the symmetry axis of the metric whose only multipole moments are mass and angular momentum. By using Sibgatullin's method [2] we then analyse a series of exact solutions with the afore mentioned multipole characteristic; besides, we present an approximate solution whose Ernst potential is introduced as a power series of a dimensionless parameter. The calculation of its multipole moments allows us to understand the existing differences between both approximations to the proposed pure multipole solution.     

Compactification, Vacuum Energy and Quintessence

We study the possibility that the vacuum energydensity of scalar and internal-space gauge fieldsarising from the process of dimensional reduction ofhigher dimensional gravity theories plays the role of quintessence. We show that, for themultidimensional Einstein-Yang-Mills system compactifiedon a R × S³ × S^dtopology, there are classically stable solutions suchthat the observed accelerated expansion of the Universe atpresent can be accounted for without upsetting structureformation scenarios or violating observational bounds onthe vacuum energy density.     

The complete asymptotic expansion for Baskakov operators

In this paper, we derive the complete asymptotic expansion of classical Baskakov operators Vn （f;x） in the form of all coefficients of n^-k, k = 0, 1... being calculated explic- itly in terms of Stirling number of the first and second kind and another number G（i, p）. As a corollary, we also get the Voronovskaja-type result for the operators.     

Note on asymptotic expansion of Riemann-Siegel integral

In this note we establish two theorems concerning asymptotic expansion of Riemann-Siegel integrals as well as formula of generating function （double series） of coefficents of that expansion （for computation aims）; we also discuss similar results for Dirichlet series （L（s, fh） and L（s, X））, with m odd integer and X （ n ） （mod（ m ） ） （even） primitive characters （ inappendix B ） .