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111.
112.
设M是二维紧致、曲率K(M)≤0的Riemann流形.对任一x M,在M上类数≥3的点集非空且只有有限个点{α1,α2,…;αd}.用Kj表示αj的类数,即αj到x的最短测地线的条数.那么,M的Euler数X(M)可以表示为:X(M)=(d+1)=Kj.如果M上类数23的点只有一个,那么这个点是M上距离x最远的点. 相似文献
113.
Saburo Higuchi 《Nuclear Physics B》1999,540(3):5677-741
A Hamiltonian cycle of a graph is a closed path that visits every vertex once and only once. It has been difficult to count the number of Hamiltonian cycles on regular lattices with periodic boundary conditions, e.g. lattices on a torus, due to the presence of winding modes. In this paper, the exact number of Hamiltonian cycles on a random trivalent fat graph drawn faithfully on a torus is obtained. This result is further extended to the case of random graphs drawn on surfaces of an arbitrary genus. The conformational exponent y is found to depend on the genus linearly. 相似文献
114.
A multi-wavelength microsphere laser system, using a chirped fibre Bragg grating and a microsphere resonator as wavelength-selective elements and a high dopant erbium doped fibre as the gain material, has been successfully demonstrated. The multi-wavelength generation of the laser system arises from both the microsphere whispering gallery mode selection and from the additional Raman scattering inside the microsphere cavity when the erbium laser is operating at resonance with the whispering gallery modes. Through an appropriate design and fabrication of a microsphere and of a fibre taper, a selective multi-wavelength fibre laser has been realized when the pump power is above threshold required. The laser output lines created have shown much narrower linewidths than those from conventional fibre lasers and these characteristics are particularly suitable for the range of sensor applications envisaged in the work. 相似文献
115.
A high-order numerical method for the nonlinear Helmholtz equation in multidimensional layered media
We present a novel computational methodology for solving the scalar nonlinear Helmholtz equation (NLH) that governs the propagation of laser light in Kerr dielectrics. 相似文献
116.
Luiz C. L. Botelho 《International Journal of Theoretical Physics》2009,48(6):1695-1700
We present a Wilson Loop evaluation of the binding energy of electric static charges in A.M. Polyakov’s Compact QED in R
4 through path integrals. 相似文献
117.
M.H.M. Rashid Yahya El-Qaderi 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):6276-6282
In this paper, we study the local and global existence of mild solutions to a class of fractional integro-differential equations in an arbitrary Banach space associated with operators generating compact semigroup on the Banach space. 相似文献
118.
119.
Ondej F.K. Kalenda 《Journal of Mathematical Analysis and Applications》2009,350(2):464-484
We collect examples of Valdivia compact spaces, their continuous images and associated classes of Banach spaces which appear naturally in various branches of mathematics. We focus on topological constructions generating Valdivia compact spaces, linearly ordered compact spaces, compact groups, L1 spaces, Banach lattices and noncommutative L1 spaces. 相似文献
120.
We prove that the G-invariant orbital measures supported on adjoint orbits in the Lie algebra of a classical, compact, connected, simple Lie
group satisfy a smoothness dichotomy: Either μ
k
is singular to Lebesgue measure or μ
k
∈ L
2. The minimum k for which μ
k
∈ L
2 is specified and is also the minimum k such that the k-fold sum of the orbit has positive measure.
S. K. Gupta appreciates the hospitality of the Department of Pure Mathematics at the University of Waterloo where some of
this research was done. K. E. Hare was supported in part by NSERC. 相似文献