Uniqueness,reciprocity theorem,and plane waves in thermoelastic diffusion with a fractional order derivative

In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.

Uniqueness Theorems for Meromorphic Functions

In this paper we studies the problem of uniqueness of meromorphic functions. We will prove a result has a relation with the result of H.Ueda.

Uniqueness theorem,theorem of reciprocity,and eigenvalue problems in linear theory of porous piezoelectricity

The uniqueness theorem and the theorem of reciprocity in the linearized porous piezoelectricity are established under the assumption of positive definiteness of elastic and electric fields. General theorems in the linear theory of porous piezoelectric materials are proved for the quasi-static electric field approximation. The uniqueness theorem is also proved without using the positive definiteness of the elastic field. An eigenvalue problem associated with free vibrations of a porous piezoelectric body is stud- ied using the abstract formulation. Some properties of operators are also proved. The problem of frequency shift due to small disturbances, based on an abstract formulation, is studied using a variational and operator approach. A perturbation analysis of a special ease is also given.

A UNIQUENESS THEOREM FOR HOLOMORPHIC MAPPINGS IN THE DISK SHARING TOTALLY GEODESIC HYPERSURFACES

In this paper,we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces(totally geodesic hypersurfaces with respect to a meromorphic connection) in the complex projective space P^(k).This is a generalization of Cartan’s Second Main Theorem.As a consequence,we establish a uniqueness theorem for holomorphic mappings which intersect O(k^(3)) many totally geodesic hypersurfaces.

A uniqueness theorem for indefinite Sturm-Liouville operators

In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spectral sets {λn（q, ha,hk）}＋∞k=1 and {λ-n（q, hb,hk）}＋∞k=1 for distinct hk are sufficient to determine the potential q（x） on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.

A NOTE ON A STRONG UNIQUENESS THEOREM OF STRAUSS

In this paper we present a correction of the proofofa strong uniqueness theorem given by H.Strauss in 1992 on approximation by reciprocals of functions of an n-dimensional space span (u_1,…,u_n) satisfying coefficient constraints.

A NOTE ON A STRONG UNIQUENESS THEOREM OF SITRAUSS

In this paper we present a correction of the proof of u strong uniqueness theorem given by H. Struuss [1] in 1992 on approximation by reciprocals of functions uf an n-dimensional space (u,…un) satisfying coefficient constraints.

Several Fundamental Theorems and Conservative Integrals in Quasicrystal Elasticity Theory

Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.

UNIQUENESS PROBLEM FOR MEROMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES INTO P^N(C) WITH TRUNCATED MULTIPLICITIES

This paper proves some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space p^N（C） with truncated multiplicities, and our results improve some earlier work.

UNIQUENESS PROBLEM WITH TRUNCATED MULTIPLICITIES OF MEROMORPHIC MAPPINGS FOR MOVING TARGETS

In this article, two uniqueness theorems of meromorphic mappings on moving targets with truncated multiplicities are proved.

Uniqueness of the Reissner-Nordstrom metric near the null infinity

In the Newman-Penrose formalism,we prove that the Reissner-Nordstrom metric is the only asymptotically fat,static,axially symmetric,Petrov type-D analytic solution of the electro-vacuum Einstein-Maxwell equations near the null infinity.

ON THE OPERATIONS OF ALGEBROID FUNCTIONS

In this article, we first investigate the operational properties of algebroid functions. Then we prove two uniqueness theorems for algebroid functions.

A Comparison Theorem and Uniqueness Theorem of Backward Doubly Stochastic Differential Equations

In this paper, we deal with one dimensional backward doubly stochastic differential equations （BDSDEs）. We obtain a comparison theorem and a uniqueness theorem for BDSDEs with continuous coefficients.

Uniqueness Theorem of Meromorphic Mappings with Moving Targets

Some uniqueness theorems of meromorphic mappings with moving targets are given under the inclusion relations between the zeros sets of meromorphic mappings.

INVERSE SCATTERING BY AN INHOMOGENEOUS PENETRABLE OBSTACLE IN A PIECEWISE HOMOGENEOUS MEDIUM

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the integral equation method. We then proceed to establish two tools that play important roles for the inverse problem： one is a mixed reciprocity relation and the other is a priori estimates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.

The Tychonoff uniqueness theorem for the G-heat equation

In this paper we shall investigate a uniqueness result for solutions of the G-heat equation. We obtain the Tychonoff uniqueness theorem for the G-heat equation.

MEROMORPHIC FUNCTIONS THAT SHARE TWO SETS, Ⅱ

This paper deals with the problem of uniqueness of meromorphic functions, and gets the following result: There exists a set S with 13 elements such that any two non-constant meromorphic functions / and g satisfying E(S,f) = E(S,g) and E({∞},f) = E({∞},g) must be identical. This is the best result on this question until now.

SOLUTIONS TO A CLASS OF PARABOLIC INHOMOGENEOUS NORMALIZED p-LAPLACE EQUATIONS

In this article, we prove that viscosity solutions of the parabolic inhomogeneous equationsn＋p/put-△p^Nu=f（x,t）can be characterized using asymptotic mean value properties for all p ≥ 1, including p = 1 and p = ∞. We also obtain a comparison principle for the non-negative or non-positive inhomogeneous term f for the corresponding initial-boundary value problem and this in turn implies the uniqueness of solutions to such a problem.

A Uniqueness Theorem of a System of Nonlinear Equations and Its Applications

A uniqueness theorem of a solution of a system of nonlinear equations is given. Using this result uniqueness theorems for power orthogonal polynomials, for a Gaussian quadrature formula of an extended Chebyshev system, and for a Gaussian Birkhoff quadrature formula are easily deduced.

Uniqueness Theorems for Meromorphic Mappings in Several Complex Variables into P^N(C) with Two Families of Moving Targets

The authors prove some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space PN(C)with two families of moving targets,and the results obtained improve some earlier work.