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81.
Boniface Nkemzi 《Mathematical Methods in the Applied Sciences》2006,29(9):1053-1080
This paper is concerned with the structure of the singular and regular parts of the solution of time‐harmonic Maxwell's equations in polygonal plane domains and their effective numerical treatment. The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation and it is proved that the solution of the boundary value problem does not belong locally to H2 when the boundary of the domain has non‐acute angles. A splitting of the solution into a regular part belonging to the space H2, and an explicitly described singular part is presented. For the numerical treatment of the boundary value problem, we propose a finite element discretization which combines local mesh grading and the singular field methods and derive a priori error estimates that show optimal convergence as known for the classical finite element method for problems with regular solutions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
82.
Teruhisa Tsuda 《Letters in Mathematical Physics》2006,77(1):21-30
Starting from certain point sets in the projective plane, we construct a tropical (or subtraction-free birational) representation of Weyl groups over the field of τ-functions. In particular, our construction includes E
8
(1)
, E
7
(1)
, E
6
(1)
and D
5
(1)
as affine cases; each of them gives rise to the q-difference Painlevé equation. 相似文献
83.
Fidel Casarrubias-Segura Alejandro Ramírez-Páramo 《Topology and its Applications》2007,154(7):1307-1313
In this paper we make use of the Pol-Šapirovski?'s technique to prove several cardinal inequalities, which generalize other well-known inequalities. 相似文献
84.
The q-Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q = 1, to the Catalan numbers: 1, 1, 2, 5, 14,…, a log-convex sequence. We use a combinatorial interpretation of these polynomials
to prove a q-log-convexity result. The sequence of q-Catalan numbers is not q-log-convex in the narrow sense used by other authors, so our work suggests a more flexible definition of q-log convex be adopted.
Received January 2, 2007 相似文献
85.
In this paper, the possibility of using the gradients of the temperature and of the internal parameters as additional state variables in Continuum Thermodynamics is considered. The expressions of the two principles are discussed and Clausius–Duhem inequality is derived under an appropriate statement of the internal entropy production. Several formulations are proposed and compared to existing results in the literature. To cite this article: P. Ireman, Q.S. Nguyen, C. R. Mecanique 332 (2004). 相似文献
86.
Hirofumi Tsumura 《Journal of Number Theory》2004,106(1):155-168
In this paper, we define the multiple Euler numbers and consider some multiple harmonic series of Mordell-Tornheim's type, which is a partial sum of the Mordell-Tornheim zeta series defined by Matsumoto. Indeed, we prove a certain reducibility of these series as well as the multiple zeta values. 相似文献
87.
We prove that, in Euclidean space, any nonnegatively curved, compact, smoothly immersed hypersurface lies outside the convex hull of its boundary, provided the boundary satisfies certain required conditions. This gives a convex hull property, dual to the classical one for surfaces with nonpositive curvature. A version of this result in the nonsmooth category is obtained as well. We show that our boundary conditions determine the topology of the surface up to at most two choices. The proof is based on uniform estimates for radii of convexity of these surfaces under a clipping procedure, a noncollapsing convergence theorem, and a gluing procedure. 相似文献
88.
Moira Chas 《Topology》2004,43(3):543-568
Goldman (Invent. Math. 85(2) (1986) 263) and Turaev (Ann. Sci. Ecole Norm. Sup. (4) 24 (6) (1991) 635) found a Lie bialgebra structure on the vector space generated by non-trivial free homotopy classes of curves on a surface. When the surface has non-empty boundary, this vector space has a basis of cyclic reduced words in the generators of the fundamental group and their inverses. We give a combinatorial algorithm to compute this Lie bialgebra on this vector space of cyclic words. Using this presentation, we prove a variant of Goldman's result relating the bracket to disjointness of curve representatives when one of the classes is simple. We exhibit some examples we found by programming the algorithm which answer negatively Turaev's question about the characterization of simple curves in terms of the cobracket. Further computations suggest an alternative characterization of simple curves in terms of the bracket of a curve and its inverse. Turaev's question is still open in genus zero. 相似文献
89.
N.M. Shash F.E. Salman M.G. El-Sharawy M.K. El-Mansy 《Journal of Physics and Chemistry of Solids》2004,65(5):881-889
Vitrification suppression in the (V2O5)1−x (P2O5)x glasses where x=0.10, 0.15, 0.20, and 0.25 was controlled by changing the rate of quenching glasses. The structure variations occurring in the glasses were detected by differential thermal analysis and optical microscope. The results implied the separation and growth of V2O5 orthorhombic microcrystal in the samples with x=0.10 and 0.15 whereas other samples did not illustrate remarkable changes in their microstructure. However, in temperature range between 300 and 473 K a semiconducting behavior for all samples appears during the study of electrical conductivity-temperature dependence. A decrease in conductivity values accompanied with some variations in activation energies by reducing quenching rate was observed. The conductivity results suggested that the conduction occurs by the phonon assisted hopping of a small polaron between V4+ and V5+ states at relatively higher temperature range above θD/2. Whereas at relatively low temperatures the conduction may occur by electron jumping between filled and empty states at Fermi level in the disordered matrix besides polaronic conduction. Reasonable values for the density of localized states, carrier concentration and carrier mobility were estimated and discussed. Also, dielectric constant and dielectric loss were studied as a function of frequency at different temperatures confirming the structure variations in the glass system. 相似文献
90.
V.B. Nalbandyan 《Journal of Physics and Chemistry of Solids》2004,65(6):1201
The irreproducibility of electrical properties of Na0.88Li0.12NbO3 solid solution on thermal cycling reported by M.A.L. Nobre and S. Lanfredi is explained by gradual decomposition of the supersaturated solid solution below ca. 800 °C. 相似文献