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31.
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
32.
R. N. Miroshin 《Mathematical Notes》2007,82(3-4):357-365
Multiple integrals generalizing the iterated kernels of integral operators are expressed as single integrals in the case of a special representation of the kernel (this is our theorem). Besides integral equations, Markov processes involve these integrals as well. As a consequence of the theorem, we obtain transition probability densities of certain Markov processes. As an illustration, we consider nine examples. 相似文献
33.
Satya Prakash 《Pramana》1989,33(1):109-131
This article summarizes the recent radiochemical investigations on mass, charge kinetic energy and fragment angular distributions
in low energy fission of actinides. 相似文献
34.
Optimal production and rationing decisions in supply chains with information sharing 总被引:1,自引:0,他引:1
Boray Huang 《Operations Research Letters》2007,35(5):669-676
This paper considers a two-echelon capacitated supply chain with two non-identical retailers and information sharing. We characterize the optimal inventory policies. We also study the benefits of the optimal stock rationing policy over the first come first served (FCFS) and the modified echelon-stock rationing (MESR) policies. 相似文献
35.
We construct random locally compact real trees called Lévy trees that are the genealogical trees associated with continuous-state
branching processes. More precisely, we define a growing family of discrete Galton–Watson trees with i.i.d. exponential branch
lengths that is consistent under Bernoulli percolation on leaves; we define the Lévy tree as the limit of this growing family
with respect to the Gromov–Hausdorff topology on metric spaces. This elementary approach notably includes supercritical trees
and does not make use of the height process introduced by Le Gall and Le Jan to code the genealogy of (sub)critical continuous-state
branching processes. We construct the mass measure of Lévy trees and we give a decomposition along the ancestral subtree of
a Poisson sampling directed by the mass measure.
T. Duquesne is supported by NSF Grants DMS-0203066 and DMS-0405779. M. Winkel is supported by Aon and the Institute of Actuaries,
EPSRC Grant GR/T26368/01, le département de mathématique de l’Université d’Orsay and NSF Grant DMS-0405779. 相似文献
36.
This paper studied the cost allocation for the unfunded liability in a defined benefit pension scheme incorporating the stochastic phenomenon of its returns. In the recent literature represented by Cairns and Parker [Insurance: Mathematics and Economics 21 (1997) 43], Haberman [Insurance: Mathematics and Economics 11 (1992) 179; Insurance: Mathematics and Economics 13 (1993) 45; Insurance: Mathematics and Economics 14 (1994) 219; Insurance: Mathematics and Economics 14 (1997) 127], Owadally and Haberman [North American Actuarial Journal 3 (1999) 105], the fund level is modeled based on the plan dynamics and the returns are generated through several stochastic processes to reflect the current realistic economic perspective to see how the contribution changed as the cost allocation period increased. In this study, we generalize the previous constant value assumption in cost amortization by modeling the returns and valuation rates simultaneously. Taylor series expansion is employed to approximate the unconditional and conditional moments of the plan contribution and fund level. Hence the stability of the plan contribution and the fund size under different allocation periods could be estimated, which provide valuable information adding to the previous works. 相似文献
37.
Dimensional analysis is presented as a powerful tool in the study of the paste boriding process. In particular, a dimensional method is used to study the growth kinetics of the boride layers FeB and Fe2B. Experiments were performed in AISI 1045 steel and AISI M2 steel, to test the suggested model. Samples of 1045 steel were prepared and treated using boron paste thickness of 3-5 mm, at temperatures of 1193, 1223 and 1273 K, with 2, 4 and 6 h of treatment time. The M2 specimens had boron paste thickness of 3 and 4 mm and temperatures of 1223, 1253 and 1273 K for 2 and 6 h. Results indicate that the growth of boron layers obeys power laws of the form y = αxβ, where α and β constants are a function of the material and the interface of interest. Validation of the model was carried out using experimental data with an average error percentage of 7.6% for Fe2B in 1045 steel, 15.8% for FeB and 3.4% for Fe2B in M2 steel. 相似文献
38.
39.
Feng-Yu Wang 《Stochastic Processes and their Applications》2002,100(1-2):27-39
By using probabilistic approaches, Liouville theorems are proved for a class of Riemannian manifolds with Ricci curvatures bounded below by a negative function. Indeed, for these manifolds we prove that all harmonic functions (maps) with certain growth are constant. In particular, the well-known Liouville theorem due to Cheng for sublinear harmonic functions (maps) is generalized. Moreover, our results imply the Brownian coupling property for a class of negatively curved Riemannian manifolds. This leads to a negative answer to a question of Kendall concerning the Brownian coupling property. 相似文献
40.
F. D. Saccone C. E. Rodrí guez Torres F. H. S nchez O. Gutfleisch 《Physica B: Condensed Matter》2002,320(1-4):312-315
In the present work, a quantitative analysis of the phase compositions by Mössbauer effect spectroscopy of solid and conventional hydrogen disproportionated Pr13.7Fe80.3B6.0 and Pr13.7Fe63.5Co16.7Zr0.1B6.0 alloys was carried out. Significant amounts of intermediate borides t-Fe3B and Pr(Fe, Co)12B6 were detected after solid hydrogen disproportionation treatment in Pr13.7Fe80.3B6.0 and Pr13.7Fe63.5Co16.7Zr0.1B6.0 alloys, respectively. After conventional hydrogenation–disproportionation–desorption–recombination treatment these phases were not detected and in no case residual Pr2Fe14B-phase was found. It was observed that the amount of intermediate borides after disproportionation can be correlated with the degree of texture after recombination at various temperatures. 相似文献