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51.
52.
The purpose of this paper is to find optimal estimates for the Green function of a half-space of the relativistic
α
-stable process with parameter m on ℝ
d
space. This process has an infinitesimal generator of the form mI–(m
2/α
I–Δ)
α/2, where 0<α<2, m>0, and reduces to the isotropic α-stable process for m=0. Its potential theory for open bounded sets has been well developed throughout the recent years however almost nothing
was known about the behaviour of the process on unbounded sets. The present paper is intended to fill this gap and we provide
two-sided sharp estimates for the Green function for a half-space. As a byproduct we obtain some improvements of the estimates
known for bounded sets. Our approach combines the recent results obtained in Byczkowski et al. (Bessel Potentials, Hitting
Distributions and Green Functions (2006) (preprint). ), where an explicit integral formula for the m-resolvent of a half-space was found, with estimates of the transition densities for the killed process on exiting a half-space.
The main result states that the Green function is comparable with the Green function for the Brownian motion if the points
are away from the boundary of a half-space and their distance is greater than one. On the other hand for the remaining points
the Green function is somehow related the Green function for the isotropic α-stable process. For example, for d≥3, it is comparable with the Green function for the isotropic α-stable process, provided that the points are close enough.
Research supported by KBN Grants. 相似文献
53.
Thomas Lorenz 《Set-Valued Analysis》2008,16(1):1-50
The mutational equations of Aubin extend ordinary differential equations to metric spaces (with compact balls). In first-order
geometric evolutions, however, the topological boundary need not be continuous in the sense of Painlevé–Kuratowski. So this
paper suggests a generalization of Aubin’s mutational equations that extends classical notions of dynamical systems and functional
analysis beyond the traditional border of vector spaces: Distribution-like solutions are introduced in a set just supplied
with a countable family of (possibly non-symmetric) distance functions. Moreover their existence is proved by means of Euler
approximations and a form of “weak” sequential compactness (although no continuous linear forms are available beyond topological
vector spaces). This general framework is applied to a first-order geometric example, i.e. compact subsets of ℝ
N
evolving according to the nonlocal properties of both the current set and its proximal normal cones. Here neither regularity
assumptions about the boundaries nor the inclusion principle are required. In particular, we specify sufficient conditions
for the uniqueness of these solutions.
相似文献
54.
The to and fro motion of a bouncing ball on a flat surface is represented by a low-dimensional model. To describe the repeated reversals of the horizontal velocity of the ball, the elasticity of the ball has to be taken into account. We show that a simple fly-wheel model exhibits the observed hither and thither motion of elastic balls. The suggested model is capable of describing oblique impacts of spherical bodies, which can be important in many applications, including dynamical simulation of granular materials. We find that the behaviour of the bouncing fly-wheel is sensitive to the initial conditions, and the escape time plots are used to illustrate this observation. 相似文献
55.
A. V. Isaev 《Journal of Geometric Analysis》2008,18(3):919-919
We correct the formulation of the main result in our earlier paper.
相似文献
56.
Application of X-ray diffraction, micromagnetic and hole drilling methods for residual stress determination in a ball bearing steel ring 总被引:1,自引:0,他引:1
C. O. D. Martins Ph.D. T. R. Strohaecker A. S. Rocha T. K. Hirsch 《Experimental Mechanics》2005,45(4):344-350
A basic understanding of distortion problems requires the analysis of a complete manufacturing process including an almost
complete overview of residual stress states in the component during each production step. To reduce the measurement time in
the future, three measurements methods (X-ray diffraction, micromagnetic and blind hole drilling methods) have been used to
analyze residual stress states in machined AISI 52100 ball bearing rings. X-ray diffraction was used as a state-of-the-art
method for machining induced residual stresses with pronounced gradients. The ring exhibited a complex residual stress state
with high tensile residual stresses at the surface, a strong gradient in depth, and also showed some variation along the outer
circumference due to a superimposition of machining induced residual stresses and effects from the clamping device process.
Due to this surface state, micromagnetic signals depend on the analyzing frequency. A calibration of the signals was only
possible with the X-ray diffraction data. The results of the three different measurement methods correlate reasonably well. 相似文献
57.
Mohd Rafein Zakaria Hidayah Ariffin Suraini Abd-Aziz Yoshihito Shirai 《Polymer Degradation and Stability》2010,95(8):1382-1386
Poly(3-hydroxybutyrate) [P(3HB)] homopolymer and poly(3-hydroxybutyrate-co-3-hydroxyvalerate) [P(3HB-co-3HV)] copolymer was produced by Comamonas sp. EB172 using single and mixture of carbon sources. Poly(3-hydroxyvalerate) P(3HV) incorporation in the copolymer was obtained when propionic and valeric acid was used as precursors. Incorporation of 3HV fractions in the copolymer varied from 45 to 86 mol% when initial pH of the medium was regulated. In fed-batch cultivation, organic acids derived from anaerobically treated palm oil mill effluent (POME) were shown to be suitable carbon sources for polyhydroxyalkanoate (PHA) production by Comamonas sp. EB172. Number average molecular weight (Mn) produced by the strain was in the range of 153-412 kDa with polydispersity index (Mw/Mn) in the range of 2.2-2.6, respectively. Incorporation of higher 3HV units improved the thermal stability of P(3HB-co-3HV) copolymer. Thus the newly isolated bacterium Comamonas sp. EB172 is a suitable candidate for PHA production using POME as renewable and alternative cheap raw materials. 相似文献
58.
DINEW Zywomir 《中国科学 数学(英文版)》2011,(7)
We study the set where the so-called Bergman representative coordinates (or Bergman functions) form an immersion. We provide an estimate of the size of a maximal geodesic ball with respect to the Bergman metric contained in this set. By concrete examples we show that these estimates are the best possible. 相似文献
59.
60.
We give a classification of sphere quadrangulations satisfying a condition of non‐negative curvature, following Thurston's classification of sphere triangulations under the same condition. The generic family of quadrangulations is parametrized by the points of positive square‐norm of an integral Gaußian lattice in the six‐dimensional complex Lorentz space. There is a subgroup of automorphisms of acting on this lattice whose orbits parametrize sphere quadrangulations in a one‐to‐one manner. This group acts discretely on the corresponding five‐dimensional complex hyperbolic space; is of finite co‐volume; its ball quotient is the moduli space of unordered 8 points on the Riemann sphere, and also appears in Picard‐Terada‐Deligne‐Mostow list. Both Thurston's lattice and our lattice may be thought of as parametrizations of certain families of subgroups of the modular group; equivalently, of certain families of dessins. These families also parametrize points of a moduli space. 相似文献