It is well known that Fleming-Viot superprocesses can be obtained from the Dawson-Watanabe superprocesses by conditioning the latter to have constant total mass. The same question is investigated for measure-valued br...It is well known that Fleming-Viot superprocesses can be obtained from the Dawson-Watanabe superprocesses by conditioning the latter to have constant total mass. The same question is investigated for measure-valued branching processes with interacting intensity independent of the geographical position. It is showed that a sequence of conditioned probability laws of this kind of interacting measure-valued branching processes also approximates to the probability law of Fleming-Viot superprocesses.展开更多
Let X t be the interaction measured_valued branching α_ symmetric stable process over R d(1<α≤2) constructed by Meleard_Roelly . Frist, it is shown that X t is absolutely continuous with respect to the Lebesgue ...Let X t be the interaction measured_valued branching α_ symmetric stable process over R d(1<α≤2) constructed by Meleard_Roelly . Frist, it is shown that X t is absolutely continuous with respect to the Lebesgue measure (on R ) with a continuous density function which satisfies some SPDE. Second, it is proved that if the underlying process is a Brownian motion on R d (d≤3), the corresponding occupation_time process Y t is also absolutely continuous with respect to the Lebesgue measure.展开更多
We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),...We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),their local times exist when d≤3.A Tanaka formula of the local time is also derived.展开更多
We consider a very general interacting branching process which includes most of the important interacting branching models considered so far. After obtaining some key preliminary results, we first obtain some elegant ...We consider a very general interacting branching process which includes most of the important interacting branching models considered so far. After obtaining some key preliminary results, we first obtain some elegant conditions regarding regularity and uniqueness, Then the extinction vector is obtained which is very easy to be calculated. The mean extinction time and the conditional mean extinction time are revealed.The mean explosion time and the total mean life time of th, processes are also investigated and resolved.展开更多
Exponential trichotomy theory is developed and the Fredholm Alternative Lemma is proved for the system with exponential trichotomies. An application of thesetheories is also given to obtain the persistence condition f...Exponential trichotomy theory is developed and the Fredholm Alternative Lemma is proved for the system with exponential trichotomies. An application of thesetheories is also given to obtain the persistence condition for heteroclinic orbits connecting nonhyperbolic equilibria, which extends the corresponding result of .展开更多
Suppose that E is a Lusin topological space. We let (?)(E) denote the σ-algebra on E generated by all open sets, which is referred to as the Borel σ-algebra on E. B(E) denotes the set of all bounded (?)(E)-measurabl...Suppose that E is a Lusin topological space. We let (?)(E) denote the σ-algebra on E generated by all open sets, which is referred to as the Borel σ-algebra on E. B(E) denotes the set of all bounded (?)(E)-measurable functions on E and B(E)^+ denotes the subspace of B(E) comprising non-negative elements. Let M(E) be the totality of finite measures on (E, (?)(E)). Topologize M(E) by the weak convergence topology, so it also becomes a展开更多
A conditional log-Laplace functional （CLLF） for a class of branching processes in random environments is derived. The basic idea is the decomposition of a dependent branching dynamic into a no-interacting branching ...A conditional log-Laplace functional （CLLF） for a class of branching processes in random environments is derived. The basic idea is the decomposition of a dependent branching dynamic into a no-interacting branching and an interacting dynamic generated by the random environments. CLLF will play an important role in the investigation of branching processes and superprocesses with interaction.展开更多
We use a new approach to consider the extinction properties of the Markov branching process with immigration and migration recently discussed by Li and Liu [Sci. China Math., 2011, 54： 1043-1062]. Some much better ex...We use a new approach to consider the extinction properties of the Markov branching process with immigration and migration recently discussed by Li and Liu [Sci. China Math., 2011, 54： 1043-1062]. Some much better explicit expressions are obtained for the extinction probabilities of the subtle super-interacting case.展开更多
In order to obtain a uniform and effectively toughened poly(lactic acid)film by blending with low content of poly(ethylene octene)(POE)with high elasticity,the tailored interfacial intermolecular interaction and entan...In order to obtain a uniform and effectively toughened poly(lactic acid)film by blending with low content of poly(ethylene octene)(POE)with high elasticity,the tailored interfacial intermolecular interaction and entanglement between the two phases of the PLA/POE blend was innovatively constructed via the facile reactive melt blending process through the reaction of the epoxy/anhydride groups grafted on the POE chains with the end groups of PLA chains(PLA/GPOE-MPOE).It was observed that POE domains were embedded tightly in PLA matrix with a fuzzy interface and abundant interface transition area,and the impact fractured surface of the blend showed an obvious plastic deformation with less occurrence of fibrillation of PLA matrix or interfacial de-bonding.Compared with neat PLA and directly blended PLA/POE blends,the PLA/GPOE-MPOE blend exhibited much higher complex viscosity/storage modulus,much lower tanδvalues in the terminal region,and obvious strain-hardening behavior.The deviation in viscoelastic behavior of PLA/GPOE-MPOE from linear PLA indicated the enhanced molecular entanglement between the long-branched chains,resulting in an enhancement of the stretching ability during biaxial drawing of the blend.Uniform PLA/GPOE-MPOE films with draw ratio as high as 7×7 were obtained through biaxial stretching,which showed much higher tensile strength and the elongation at break than that of neat PLA and PLA/POE film.This work provides a facile method for fabricating toughening PLA films with application potentials.展开更多
The moments and absolute continuity of measure valued branching Brownian motions with bounded interacting intensity are investigated. An estimate of higher order moments is obtained.The absolute continuity is verifie...The moments and absolute continuity of measure valued branching Brownian motions with bounded interacting intensity are investigated. An estimate of higher order moments is obtained.The absolute continuity is verified in the one dimension case. This thereby verifies the conjecture of Méléard and Roelly in .展开更多
文摘It is well known that Fleming-Viot superprocesses can be obtained from the Dawson-Watanabe superprocesses by conditioning the latter to have constant total mass. The same question is investigated for measure-valued branching processes with interacting intensity independent of the geographical position. It is showed that a sequence of conditioned probability laws of this kind of interacting measure-valued branching processes also approximates to the probability law of Fleming-Viot superprocesses.
文摘Let X t be the interaction measured_valued branching α_ symmetric stable process over R d(1<α≤2) constructed by Meleard_Roelly . Frist, it is shown that X t is absolutely continuous with respect to the Lebesgue measure (on R ) with a continuous density function which satisfies some SPDE. Second, it is proved that if the underlying process is a Brownian motion on R d (d≤3), the corresponding occupation_time process Y t is also absolutely continuous with respect to the Lebesgue measure.
基金Partial funding in support of this work was provided by the Natural Sciences and Engineering Research Council of Canada(NSERC)the Department of Mathematics at the University of Oregon。
文摘We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),their local times exist when d≤3.A Tanaka formula of the local time is also derived.
基金supported by National Natural Science Foundation of China (Grant Nos 11371374 and 11571372)Research Fund for the Doctoral Program of Higher Education of China (Grant No 20110162110060)
文摘We consider a very general interacting branching process which includes most of the important interacting branching models considered so far. After obtaining some key preliminary results, we first obtain some elegant conditions regarding regularity and uniqueness, Then the extinction vector is obtained which is very easy to be calculated. The mean extinction time and the conditional mean extinction time are revealed.The mean explosion time and the total mean life time of th, processes are also investigated and resolved.
文摘Exponential trichotomy theory is developed and the Fredholm Alternative Lemma is proved for the system with exponential trichotomies. An application of thesetheories is also given to obtain the persistence condition for heteroclinic orbits connecting nonhyperbolic equilibria, which extends the corresponding result of .
文摘Suppose that E is a Lusin topological space. We let (?)(E) denote the σ-algebra on E generated by all open sets, which is referred to as the Borel σ-algebra on E. B(E) denotes the set of all bounded (?)(E)-measurable functions on E and B(E)^+ denotes the subspace of B(E) comprising non-negative elements. Let M(E) be the totality of finite measures on (E, (?)(E)). Topologize M(E) by the weak convergence topology, so it also becomes a
文摘A conditional log-Laplace functional （CLLF） for a class of branching processes in random environments is derived. The basic idea is the decomposition of a dependent branching dynamic into a no-interacting branching and an interacting dynamic generated by the random environments. CLLF will play an important role in the investigation of branching processes and superprocesses with interaction.
文摘We use a new approach to consider the extinction properties of the Markov branching process with immigration and migration recently discussed by Li and Liu [Sci. China Math., 2011, 54： 1043-1062]. Some much better explicit expressions are obtained for the extinction probabilities of the subtle super-interacting case.
基金financially supported by the National Natural Science Foundation of China(No.51773122 and No.51933007)the International Scientific and Technological Cooperation Project of Sichuan Province(No.2020YFH0084)
文摘In order to obtain a uniform and effectively toughened poly(lactic acid)film by blending with low content of poly(ethylene octene)(POE)with high elasticity,the tailored interfacial intermolecular interaction and entanglement between the two phases of the PLA/POE blend was innovatively constructed via the facile reactive melt blending process through the reaction of the epoxy/anhydride groups grafted on the POE chains with the end groups of PLA chains(PLA/GPOE-MPOE).It was observed that POE domains were embedded tightly in PLA matrix with a fuzzy interface and abundant interface transition area,and the impact fractured surface of the blend showed an obvious plastic deformation with less occurrence of fibrillation of PLA matrix or interfacial de-bonding.Compared with neat PLA and directly blended PLA/POE blends,the PLA/GPOE-MPOE blend exhibited much higher complex viscosity/storage modulus,much lower tanδvalues in the terminal region,and obvious strain-hardening behavior.The deviation in viscoelastic behavior of PLA/GPOE-MPOE from linear PLA indicated the enhanced molecular entanglement between the long-branched chains,resulting in an enhancement of the stretching ability during biaxial drawing of the blend.Uniform PLA/GPOE-MPOE films with draw ratio as high as 7×7 were obtained through biaxial stretching,which showed much higher tensile strength and the elongation at break than that of neat PLA and PLA/POE film.This work provides a facile method for fabricating toughening PLA films with application potentials.
文摘The moments and absolute continuity of measure valued branching Brownian motions with bounded interacting intensity are investigated. An estimate of higher order moments is obtained.The absolute continuity is verified in the one dimension case. This thereby verifies the conjecture of Méléard and Roelly in .
