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61.
Lin Zhengyan 《数学年刊B辑(英文版)》1998,19(3):281-292
§1.IntroductionandResultsLet{Xn,n1}beasequenceofrandomvariableswithacommondistributionfunctionF(x)andletXn1Xn2…Xnnbetheor... 相似文献
62.
A finite volume solver for the 2D depth‐integrated harmonic hyperbolic formulation of the mild‐slope equation for wave propagation is presented and discussed. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov‐type second‐order finite volume scheme, whereby the numerical fluxes are computed using Roe's flux function. The eigensystem of the mild‐slope equations is derived and used for the construction of Roe's matrix. A formulation that updates the unknown variables in time implicitly is presented, which produces a more accurate and reliable scheme than hitherto available. Boundary conditions for different types of boundaries are also derived. The agreement of the computed results with analytical results for a range of wave propagation/transformation problems is very good, and the model is found to be virtually paraxiality‐free. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
63.
64.
We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl’s law on
manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of
the proof include the wave equation parametrix, a pretrace formula and the Dirichlet box principle. Our results develop and
extend the unpublished thesis of A. Karnaukh [Ka].
The first author was supported by NSERC, FQRNT, Alfred P. Sloan Foundation Fellowship and Dawson Fellowship. The second author
was supported by NSERC and FQRNT.
Received: April 2006 Revision: October 2006 Accepted: October 2006 相似文献
65.
An energy-dependent partitioning scheme is explored for extracting a small number of eigenvalues of a real symmetric matrix with the help of genetic algorithm. The proposed method is tested with matrices of different sizes (30 × 30 to 1000 × 1000). Comparison is made with Löwdin’s strategy for solving the problem. The relative advantages and disadvantages of the GA-based method are analyzed 相似文献
66.
Let G(x,y) and GD(x,y) be the Green functions of rotationally invariant symmetric α-stable process in Rd and in an open set D, respectively, where 0<α<2. The inequality GD(x,y)GD(y,z)/GD(x,z)?c(G(x,y)+G(y,z)) is a very useful tool in studying (local) Schrödinger operators. When the above inequality is true with c=c(D)∈(0,∞), then we say that the 3G theorem holds in D. In this paper, we establish a generalized version of 3G theorem when D is a bounded κ-fat open set, which includes a bounded John domain. The 3G we consider is of the form GD(x,y)GD(z,w)/GD(x,w), where y may be different from z. When y=z, we recover the usual 3G. The 3G form GD(x,y)GD(z,w)/GD(x,w) appears in non-local Schrödinger operator theory. Using our generalized 3G theorem, we give a concrete class of functions belonging to the non-local Kato class, introduced by Chen and Song, on κ-fat open sets. As an application, we discuss relativistic α-stable processes (relativistic Hamiltonian when α=1) in κ-fat open sets. We identify the Martin boundary and the minimal Martin boundary with the Euclidean boundary for relativistic α-stable processes in κ-fat open sets. Furthermore, we show that relative Fatou type theorem is true for relativistic stable processes in κ-fat open sets. The main results of this paper hold for a large class of symmetric Markov processes, as are illustrated in the last section of this paper. We also discuss the generalized 3G theorem for a large class of symmetric stable Lévy processes. 相似文献
67.
Generalized KKM Type Theorems in FC-Spaces with Applications (I) 总被引:1,自引:0,他引:1
Xie Ping Ding 《Journal of Global Optimization》2006,36(4):581-596
The class KKM(X,Y) (resp., s-KKM(X,Y,Z)) of set-valued mappings with KKM (resp., s-KKM) property is introduced in FC-spaces without any convexity structure. Some generalized KKM (resp., s-KKM) type theorems are proved in FC-spaces under much weak assumptions. As applications, some new section theorems and coincidence theorems are established in FC-spaces. These theorems generalize many known results in literature. The further applications of these results will be given in a follow-up paper. 相似文献
68.
W. Kotarski 《Journal of Optimization Theory and Applications》1987,54(3):565-573
Combining the results of Walczak (Ref. 1) and Lasiecka (Refs. 2 and 3), we extend the well-known Dubovicki-Milutin theorem in two directions: (i) We allow for treatment of several equality constraints in optimization problems; and (ii) We assume less regularity of optimization problems by requiring the existence of external cones instead of tangent cones. An example of an optimization problem is also considered. 相似文献
69.
V. V. Zudilin 《Mathematical Notes》2007,81(3-4):297-301
We prove two new series of Ramanujan type for 1/π2. 相似文献
70.
I. P. Rochev 《Mathematical Notes》2007,81(1-2):247-259
We consider generalizations of Pólya’s theorem to the case of entire functions taking algebraic values at natural or integer points. 相似文献