Let X（1） = {X（1）（s）, s ∈ R＋} and X（2） = {X（2）（t）, t ∈ R＋} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample pat...Let X（1） = {X（1）（s）, s ∈ R＋} and X（2） = {X（2）（t）, t ∈ R＋} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X （1） and X （2） are studied. More gener-ally, let E1, E2？（0,∞） and F ？Rd be Borel sets. A necessary condition and a suffcient condition for P{X（1）（E1）∩X（2）（E2）∩F 6=？}〉0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 × E2 × F in the metric space （R＋× R＋× Rd,ρb）, whereρb is an unsymmetric metric defined in R＋× R＋× Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.展开更多
A class of multi dimensional degenerate diffusion processes X ε(t) in R r(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here X ε(t) saitisfies the stochastic differen...A class of multi dimensional degenerate diffusion processes X ε(t) in R r(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here X ε(t) saitisfies the stochastic differential equation dX ε(t)=σ(X ε(t)) d W(t)+B(X ε(t)) d t+ εσ～(X ε(t)) d W(t),ε>0. X ε(t) are small random perturbations of the degenerate diffusion process X(t), which satisfies the stochastic differential equation dX(t)=σ(X(t)) d W(t)+B(X(t)) d t. A large deviation theorem for projection measures ν on R r-n (n<r) of empirical measures μ are proved展开更多
Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum represent...Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.展开更多
The entropy production rate of stationary minimal diffusion processes with smooth coefficients is calculated. As a byproduct, the continuity of paths of the minimal diffusion processes is discussed, and that the point...The entropy production rate of stationary minimal diffusion processes with smooth coefficients is calculated. As a byproduct, the continuity of paths of the minimal diffusion processes is discussed, and that the point at infinity is absorbing is proved.展开更多
Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x（L^κB） 〈∞ is pr...Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x（L^κB） 〈∞ is proved.展开更多
In this paper, we use a kind of univariate multiquadric quasi-interpolation to solve a parabolic equation with overspecified data, which has arisen in many physical phenomena. We obtain the numerical scheme by using t...In this paper, we use a kind of univariate multiquadric quasi-interpolation to solve a parabolic equation with overspecified data, which has arisen in many physical phenomena. We obtain the numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a simple forward difference to approximate the temporal derivative of the dependent variable. The advantage of the presented scheme is that the algorithm is very simple so it is very easy to implement. The results of the numerical experiment are presented and are compared with the exact solution to confirm the good accuracy of the presented scheme.展开更多
The purpose of tall Paper is to geueralize the Girsanov theorem to the case of a local martingale. The author uses the generalized Girsanov theorem to prove the existence ed uniqueness of diffusion processes with sigu...The purpose of tall Paper is to geueralize the Girsanov theorem to the case of a local martingale. The author uses the generalized Girsanov theorem to prove the existence ed uniqueness of diffusion processes with sigular drift terms.This result is much more general than the corresponding results in [4] and [8].展开更多
In this article, we consider a stochastic SIR model and show that the distributions of the solutions of the system are absolutely continuous. Furthermore, we analyze long-time behaviour of densities of the distributio...In this article, we consider a stochastic SIR model and show that the distributions of the solutions of the system are absolutely continuous. Furthermore, we analyze long-time behaviour of densities of the distributions of the solution. We prove that the densities can converge in L1 to an invariant density.展开更多
In terms of the diffusive process of the gases injected from rocket exhaust into the ionosphere and the relevant chemical reactions between the gases and the composition of ionosphere, the modifications in ionosphere ...In terms of the diffusive process of the gases injected from rocket exhaust into the ionosphere and the relevant chemical reactions between the gases and the composition of ionosphere, the modifications in ionosphere caused by the injected hydrogen and carbon dioxide gas from the rocket exhaust are investigated. The results show that the diffusive process of the injected gases at the ionospheric height is very fast, and the injected gases can lead to a local depletion of electron concentration in the F-region. Furthermore, the plasma ＇hole＇ caused by carbon dioxide is larger, deeper and more durable than that by the hydrogen.展开更多
TiN/Ti multi-permeating alloying layer has been formed on the low carbon steel by means of the double glow-discharge plasma surface alloying technique and hollow-cathode effect. The alloying layer was detected by axio...TiN/Ti multi-permeating alloying layer has been formed on the low carbon steel by means of the double glow-discharge plasma surface alloying technique and hollow-cathode effect. The alloying layer was detected by axiovert 25 CA optical microscope with computer analyzing software （LEC）, GDA-2 glow discharge spectroscopy （GDS）, X-ray diffraction （XRD） and galvanochemical method. The results showed that the thickness of TiN/Ti multi-permeating alloying layer was about 10μm, the content of Ti on the surface was up to 63.48 wt% and the content of N was up to 12.46 wt%. The atom Ti and N concentrations changed gradually across the depth of the alloying layer and the preferred orientation of TiN/Ti alloying layer was crystal surface （200）. The multi-permeating alloying layer and substrate were combined through metallurgy. The surface appearances of the multi-permeating alloying layer were uniform and of a compact cellular structure. The hardness of the surface was about 1600-3000 HV0.1. The corrosion resistance of the permeating TiN/Ti alloying layer in 0.5 mol/L H2SO4 solution was greatly increased and the corrosion rate was only 0.3082 g/m^2. h.展开更多
基金supported by National Natural Science Foundation of China(11371321)Zhejiang Provincial Natural Science Foundation of China(Y6100663)the Key Research Base of Humanities and Social Sciences of Zhejiang Provincial High Education Talents(Statis-tics of Zhejiang Gongshang University)
文摘Let X（1） = {X（1）（s）, s ∈ R＋} and X（2） = {X（2）（t）, t ∈ R＋} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X （1） and X （2） are studied. More gener-ally, let E1, E2？（0,∞） and F ？Rd be Borel sets. A necessary condition and a suffcient condition for P{X（1）（E1）∩X（2）（E2）∩F 6=？}〉0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 × E2 × F in the metric space （R＋× R＋× Rd,ρb）, whereρb is an unsymmetric metric defined in R＋× R＋× Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.
文摘A class of multi dimensional degenerate diffusion processes X ε(t) in R r(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here X ε(t) saitisfies the stochastic differential equation dX ε(t)=σ(X ε(t)) d W(t)+B(X ε(t)) d t+ εσ～(X ε(t)) d W(t),ε>0. X ε(t) are small random perturbations of the degenerate diffusion process X(t), which satisfies the stochastic differential equation dX(t)=σ(X(t)) d W(t)+B(X(t)) d t. A large deviation theorem for projection measures ν on R r-n (n<r) of empirical measures μ are proved
基金supported by the National Natural Science Foundation of China(Grant Nos.11347026,11147009,and 11244005)the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2013AM012 and ZR2012AM004)the Scientific Research Project of Liaocheng,China
文摘Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.
基金This work is supported by NSFC (10271008 and 10531070)
文摘The entropy production rate of stationary minimal diffusion processes with smooth coefficients is calculated. As a byproduct, the continuity of paths of the minimal diffusion processes is discussed, and that the point at infinity is absorbing is proved.
基金Research supported in part by Tianyuan Fund ofr Mathematics of NSFC (10526021)A Grant from Ministry of Education
文摘Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x（L^κB） 〈∞ is proved.
基金Project supported by the National Key Basic Research Program of China (Grant No. 2006CB303102)Science and Technology Commission of Shanghai Municipality, China (Grant No. 09DZ2272900)
文摘In this paper, we use a kind of univariate multiquadric quasi-interpolation to solve a parabolic equation with overspecified data, which has arisen in many physical phenomena. We obtain the numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a simple forward difference to approximate the temporal derivative of the dependent variable. The advantage of the presented scheme is that the algorithm is very simple so it is very easy to implement. The results of the numerical experiment are presented and are compared with the exact solution to confirm the good accuracy of the presented scheme.
文摘The purpose of tall Paper is to geueralize the Girsanov theorem to the case of a local martingale. The author uses the generalized Girsanov theorem to prove the existence ed uniqueness of diffusion processes with sigular drift terms.This result is much more general than the corresponding results in [4] and [8].
基金supported by Program for Changjiang Scholars and Innovative Research Team in University,NSFC of China(11371085 and 11201008)the Ph.D.Programs Foundation of Ministry of China(200918)
文摘In this article, we consider a stochastic SIR model and show that the distributions of the solutions of the system are absolutely continuous. Furthermore, we analyze long-time behaviour of densities of the distributions of the solution. We prove that the densities can converge in L1 to an invariant density.
基金supported by Pre-research Fund of Weapon and Equipment of China(No.9140A31030310JB39)
文摘In terms of the diffusive process of the gases injected from rocket exhaust into the ionosphere and the relevant chemical reactions between the gases and the composition of ionosphere, the modifications in ionosphere caused by the injected hydrogen and carbon dioxide gas from the rocket exhaust are investigated. The results show that the diffusive process of the injected gases at the ionospheric height is very fast, and the injected gases can lead to a local depletion of electron concentration in the F-region. Furthermore, the plasma ＇hole＇ caused by carbon dioxide is larger, deeper and more durable than that by the hydrogen.
基金supported by National Natural Science Foundation of China (No. 50374054)the Natural Science Foundation of Shanxi Province (No. 20031050)
文摘TiN/Ti multi-permeating alloying layer has been formed on the low carbon steel by means of the double glow-discharge plasma surface alloying technique and hollow-cathode effect. The alloying layer was detected by axiovert 25 CA optical microscope with computer analyzing software （LEC）, GDA-2 glow discharge spectroscopy （GDS）, X-ray diffraction （XRD） and galvanochemical method. The results showed that the thickness of TiN/Ti multi-permeating alloying layer was about 10μm, the content of Ti on the surface was up to 63.48 wt% and the content of N was up to 12.46 wt%. The atom Ti and N concentrations changed gradually across the depth of the alloying layer and the preferred orientation of TiN/Ti alloying layer was crystal surface （200）. The multi-permeating alloying layer and substrate were combined through metallurgy. The surface appearances of the multi-permeating alloying layer were uniform and of a compact cellular structure. The hardness of the surface was about 1600-3000 HV0.1. The corrosion resistance of the permeating TiN/Ti alloying layer in 0.5 mol/L H2SO4 solution was greatly increased and the corrosion rate was only 0.3082 g/m^2. h.
