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141.
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
142.
143.
This paper studies the tail behavior of the fundamental period in the MAP/G/1 queue. We prove that if the service time distribution
has a regularly varying tail, then the fundamental period distribution in the MAP/G/1 queue has also regularly varying tail,
and vice versa, by finding an explicit expression for the asymptotics of the tail of the fundamental period in terms of the
tail of the service time distribution. Our main result with the matrix analytic proof is a natural extension of the result
in (de Meyer and Teugels, J. Appl. Probab. 17: 802–813, 1980) on the M/G/1 queue where techniques rely heavily on analytic expressions of relevant functions.
I.-S. Wee’s research was supported by the Korea Research Foundation Grant KRF 2003-070-00008. 相似文献
144.
We consider the 3D Navier–Stokes equation with generalized impermeability boundary conditions. As auxiliary results, we prove the local in time existence of a strong solution (‘strong’ in a limited sense) and a theorem on structure. Then, taking advantage of the boundary conditions, we formulate sufficient conditions for regularity up to the boundary of a weak solution by means of requirements on one of the eigenvalues of the rate of deformation tensor. Finally, we apply these general results to the case of an axially symmetric flow with zero angular velocity. 相似文献
145.
146.
S. H. Faller R. W. Holloway S. C. Lee 《Journal of Radioanalytical and Nuclear Chemistry》1989,137(1):9-16
An investigation of cold fusion of deuterium was performed by electrolyzing heavy water in a cell containing a palladium cathode while monitoring levels of tritium and neutron-capture gamma rays. No activity was detected that would indicate a sustained fusion reaction had taken place. Activities that were observed can be attributed to electrolytic enrichment and a normal cosmic-ray induced background. 相似文献
147.
We investigated that the effect of the number of segregated Li atoms on the rate of oxidation on a LiAl alloy surface. Oxygen molecules adsorbed on the LiAl alloy react with the surface atoms to form stable oxides. The segregated Li atoms at reconstructed surfaces (c(2×2) and (2×1)) enhance the oxidation rate and form stable LiAlOx and Li2O. The degree of enhancement of oxidation by segregated Li atoms varies as a function of O2 exposure and annealing temperature, where the latter is directly related to the mode of surface reconstruction by Li segregation. 相似文献
148.
S.-Y. Lee T.-H. Kim D.-I. Suh E.-K. Suh N.-K. Cho W.-K. Seong S.-K. Lee 《Applied Physics A: Materials Science & Processing》2007,87(4):739-742
We demonstrate GaN nanowire (NW) current rectifiers which were formed by assembling n-GaN nanowires on a patterned p-Si substrate
by means of alternating current (ac) dielectrophoresis. The dielectrophoresis was accomplished at a frequency of 10 kHz with
three different ac bias voltages (5, 10, and 15 Vp–p), indicating that the number of aligned GaN nanowires increased with increasing ac bias voltage. The n-GaN NW/p-Si diodes
showed well-defined current rectifying behavior with a forward voltage drop of 1.2–1.5 V at a current density of 200 A/cm2. We observed that the GaN NW diode functioned well as a half-wave rectifier.
PACS 71.20.Nr; 73.40.Cg; 73.40.Ei; 73.40.Kp 相似文献
149.
Hong Ming ZHANG Xian Hong WANG Xiao Jiang ZHAO Ji LI Fo Song WANG 《中国化学快报》2006,17(4):437-440
A novel method for the preparation of oligothiophene molecular wires is described via a bi-directional solid-phase synthesis. Using an alternating sequence of bromination and Stille coupling reactions, oligomers were obtained up to the heptamer in excellent yield and purity. 相似文献
150.