Consider a branching random walk, where the underlying branching mechanism is governed by a Galton-Watson process and the moving law of particles by a discrete random variable on the integer lattice Z. Denote by Zn（z...Consider a branching random walk, where the underlying branching mechanism is governed by a Galton-Watson process and the moving law of particles by a discrete random variable on the integer lattice Z. Denote by Zn（z） the number of particles in the n-th generation in the model for each z ∈ Z. We derive the exact convergence rate in the local limit theorem for Zn（z） assuming a condition like ＂EN（logN）1＋λ 〈 ∞＂ for the offspring distribution and a finite moment condition on the motion law. This complements the known results for the strongly non-lattice branching random walk on the real line and for the simple symmetric branching random walk on the integer lattice.展开更多
We prove that, for non-uniformly hyperbolic diffeomorphisms in the sense of Young, the local central limit theorem holds, and the speed in the central limit theorem is O（1/√n）.
The isothermal local loading forming technology provides a feasible way to form Ti-alloy large-scale rib-web components in aerospace and aviation fields.However,the local loading process forming limit is restricted by...The isothermal local loading forming technology provides a feasible way to form Ti-alloy large-scale rib-web components in aerospace and aviation fields.However,the local loading process forming limit is restricted by forming defects in the transitional region.In this work,the feasibility of controlling forming defects and improving the process forming limit by adjusting die parameters is explored through finite element（FE） simulation.It is found that the common cavum and folding defects in the transitional region are significantly influenced by the fillet radii of left rib and middle rib,respectively.The cavum and folding defects can be effectively controlled by increasing the fillet radii of left rib and middle rib,respectively.The process forming limits considering forming defects in the transitional region are determined by the stepwise searching method under various die parameters.Moreover,the relationship between the process forming limit and die parameters is developed through the response surface methodology（RSM）.The developed RSM models suggest that increasing the fillet radii of left and middle ribs is effective to improve the process forming limit during local loading forming of rib-web components.The results will provide technical basis for the design of die parameters and the reduction amount,which is of great importance to control forming defects and improve the process forming limit in local loading forming of Ti-alloy large-scale rib-web components.展开更多
In this paper, we investigate the existence of local limit cycles obtained by perturbing degenerate and weak foci of two-dimensional cubic systems of differential equations. In particular, we consider a specific class...In this paper, we investigate the existence of local limit cycles obtained by perturbing degenerate and weak foci of two-dimensional cubic systems of differential equations. In particular, we consider a specific class of such systems where the origin is a degenerate focus. By utilizing a Liapunov function method and the stability results that follow, we first determine constraints on the system to maximize the number of local limit cycles that can be obtained by perturbing the degenerate focus at the origin. Once this is established, we add on the additional assumption that the system has a weak focus at , where , and determine conditions to maximize the number of additional local limit cycles that can be obtained near this fixed point. We will ultimately achieve an example of a cubic system with three local limit cycles about the degenerate focus and one local limit cycle about the weak focus.展开更多
Fluorescent dye （YOYO-I） intercalated with single DNA molecules were investigated via bindingactivated localization microscopy （BALM） at sub-diffraction limit resolutions. Various dye-to-DNA base pair （bp） ratio...Fluorescent dye （YOYO-I） intercalated with single DNA molecules were investigated via bindingactivated localization microscopy （BALM） at sub-diffraction limit resolutions. Various dye-to-DNA base pair （bp） ratios were imaged using the blinking property of YOYO-1 dye under optimum BALM switching buffer conditions. Individual DNA molecules exhibited regular/irregular intercalating phenomena with respect to dye-to-DNA bp ratio. The acquired images were reconstructed into super-resolution images by applying a Gaussian fit to the centroid of the point spread function. The YOYO-1 intercalated with λ-DNA possessed a non-homogeneous region due to the different binding modes of YOYO-1 with λ-DNA. Each binding mode was imaged at the sub-diffraction limit super-resolution. The distance between homogenously localized intercalating dyes within the DNA molecules was measured to be 34nm （n= 10; dye：DNAbp= 1：100） without photocleavage in 50mmol/L β-mercaptoethylamine buffer. The results were similar to those of the theoretical values without photocleavage in the base pairs of single DNA molecules below the diffraction limit. The results paved the way for an in-depth microscopic analysis of molecular variation with single λ-DNA molecules. With this method, it should be possible to analyze the exact base pair breakdown during various stages of cell apoptosis.展开更多
de Broglie relation is revisited,in consideration of a generalization of canonical commuting relation.Thepossible effects on particle's localization and black hole physics are also discussed,in a heuristic manner.
The nonlinear local Lyapunov exponent（NLLE） can be used as a quantification of the local predictability limit of chaotic systems. In this study, the phase-spatial structure of the local predictability limit over the...The nonlinear local Lyapunov exponent（NLLE） can be used as a quantification of the local predictability limit of chaotic systems. In this study, the phase-spatial structure of the local predictability limit over the Lorenz-63 system is investigated. It is found that the inner and outer rims of each regime of the attractor have a high probability of a longer than average local predictability limit, while the center part is the opposite. However, the distribution of the local predictability limit is nonuniformly organized, with adjacent points sometimes showing quite distinct error growth.The source of local predictability is linked to the local dynamics, which is related to the region in the phase space and the duration on the current regime.展开更多
Consider a branching random walk with a random environment in time in the d-dimensional integer lattice.The branching mechanism is governed by a supercritical branching process,and the particles perform a lazy random ...Consider a branching random walk with a random environment in time in the d-dimensional integer lattice.The branching mechanism is governed by a supercritical branching process,and the particles perform a lazy random walk with an independent,non-identical increment distribution.For A■Z^(d),let Z_(n)(A)be the number of offsprings of generation n located in A.The exact convergence rate of the local limit theorem for the counting measure Z_(n)(·)is obtained.This partially extends the previous results for a simple branching random walk derived by Gao(2017,Stoch.Process Appl.).展开更多
In this paper, we present a local Csorgo- Revesz type functional limit theorem for increments of Brownian motion and give its convergence rate. The results also extend the functional forms of Levy＇s modulus of contin...In this paper, we present a local Csorgo- Revesz type functional limit theorem for increments of Brownian motion and give its convergence rate. The results also extend the functional forms of Levy＇s modulus of continuity for Brownian motion.展开更多
This paper establishes a local limit theorem for solutions of backward stochastic differential equations with Mao＇s non-Lipschitz generator, which is similar to the limit theorem obtained by [3] under the Lipschitz a...This paper establishes a local limit theorem for solutions of backward stochastic differential equations with Mao＇s non-Lipschitz generator, which is similar to the limit theorem obtained by [3] under the Lipschitz assumption.展开更多
By using Chen,Hou and Mu’s extended Zeilberger algorithm,the authors obtain two recurrence relations for Callan’s generalization of Narayana polynomials.Based on these recurrence relations,the authors further prove ...By using Chen,Hou and Mu’s extended Zeilberger algorithm,the authors obtain two recurrence relations for Callan’s generalization of Narayana polynomials.Based on these recurrence relations,the authors further prove the real-rootedness and asymptotic normality of Callan’s Narayana polynomials.展开更多
文摘Consider a branching random walk, where the underlying branching mechanism is governed by a Galton-Watson process and the moving law of particles by a discrete random variable on the integer lattice Z. Denote by Zn（z） the number of particles in the n-th generation in the model for each z ∈ Z. We derive the exact convergence rate in the local limit theorem for Zn（z） assuming a condition like ＂EN（logN）1＋λ 〈 ∞＂ for the offspring distribution and a finite moment condition on the motion law. This complements the known results for the strongly non-lattice branching random walk on the real line and for the simple symmetric branching random walk on the integer lattice.
基金Supported by NSF of China (10571174)the Scientific Research Foundation of Ministry of Education for Returned Overseas Chinese Scholarsthe Scientific Research Foundation of Ministry of Human and Resources and Social Security of China for Returned Overseas Scholars
文摘We prove that, for non-uniformly hyperbolic diffeomorphisms in the sense of Young, the local central limit theorem holds, and the speed in the central limit theorem is O（1/√n）.
基金the support of the National Natural Science Foundation of China(Nos.51605388,51675433)111 Project(B08040)+2 种基金the Research Fund of the State Key Laboratory of Solidification Processing(NWPU)in China(Grant No.131-QP-2015)the Fundamental Research Funds for the Central Universitiesthe Open Research Fund of State Key Laboratory of Materials Processing and Die&Mold Technology at Huazhong University of Science and Technology
文摘The isothermal local loading forming technology provides a feasible way to form Ti-alloy large-scale rib-web components in aerospace and aviation fields.However,the local loading process forming limit is restricted by forming defects in the transitional region.In this work,the feasibility of controlling forming defects and improving the process forming limit by adjusting die parameters is explored through finite element（FE） simulation.It is found that the common cavum and folding defects in the transitional region are significantly influenced by the fillet radii of left rib and middle rib,respectively.The cavum and folding defects can be effectively controlled by increasing the fillet radii of left rib and middle rib,respectively.The process forming limits considering forming defects in the transitional region are determined by the stepwise searching method under various die parameters.Moreover,the relationship between the process forming limit and die parameters is developed through the response surface methodology（RSM）.The developed RSM models suggest that increasing the fillet radii of left and middle ribs is effective to improve the process forming limit during local loading forming of rib-web components.The results will provide technical basis for the design of die parameters and the reduction amount,which is of great importance to control forming defects and improve the process forming limit in local loading forming of Ti-alloy large-scale rib-web components.
文摘In this paper, we investigate the existence of local limit cycles obtained by perturbing degenerate and weak foci of two-dimensional cubic systems of differential equations. In particular, we consider a specific class of such systems where the origin is a degenerate focus. By utilizing a Liapunov function method and the stability results that follow, we first determine constraints on the system to maximize the number of local limit cycles that can be obtained by perturbing the degenerate focus at the origin. Once this is established, we add on the additional assumption that the system has a weak focus at , where , and determine conditions to maximize the number of additional local limit cycles that can be obtained near this fixed point. We will ultimately achieve an example of a cubic system with three local limit cycles about the degenerate focus and one local limit cycle about the weak focus.
基金supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology(No. 2015R1A2A2A01003839)
文摘Fluorescent dye （YOYO-I） intercalated with single DNA molecules were investigated via bindingactivated localization microscopy （BALM） at sub-diffraction limit resolutions. Various dye-to-DNA base pair （bp） ratios were imaged using the blinking property of YOYO-1 dye under optimum BALM switching buffer conditions. Individual DNA molecules exhibited regular/irregular intercalating phenomena with respect to dye-to-DNA bp ratio. The acquired images were reconstructed into super-resolution images by applying a Gaussian fit to the centroid of the point spread function. The YOYO-1 intercalated with λ-DNA possessed a non-homogeneous region due to the different binding modes of YOYO-1 with λ-DNA. Each binding mode was imaged at the sub-diffraction limit super-resolution. The distance between homogenously localized intercalating dyes within the DNA molecules was measured to be 34nm （n= 10; dye：DNAbp= 1：100） without photocleavage in 50mmol/L β-mercaptoethylamine buffer. The results were similar to those of the theoretical values without photocleavage in the base pairs of single DNA molecules below the diffraction limit. The results paved the way for an in-depth microscopic analysis of molecular variation with single λ-DNA molecules. With this method, it should be possible to analyze the exact base pair breakdown during various stages of cell apoptosis.
基金National Natural Science Foundation of China under Grant No.10663001Natural Science Foundation of Jiangxi Province under Grant No.0612038
文摘de Broglie relation is revisited,in consideration of a generalization of canonical commuting relation.Thepossible effects on particle's localization and black hole physics are also discussed,in a heuristic manner.
基金supported by the National Natural Science Foundation of China[grant number 41375110]
文摘The nonlinear local Lyapunov exponent（NLLE） can be used as a quantification of the local predictability limit of chaotic systems. In this study, the phase-spatial structure of the local predictability limit over the Lorenz-63 system is investigated. It is found that the inner and outer rims of each regime of the attractor have a high probability of a longer than average local predictability limit, while the center part is the opposite. However, the distribution of the local predictability limit is nonuniformly organized, with adjacent points sometimes showing quite distinct error growth.The source of local predictability is linked to the local dynamics, which is related to the region in the phase space and the duration on the current regime.
基金supported by the National Natural Science Foundation of China(No.11971063)。
文摘Consider a branching random walk with a random environment in time in the d-dimensional integer lattice.The branching mechanism is governed by a supercritical branching process,and the particles perform a lazy random walk with an independent,non-identical increment distribution.For A■Z^(d),let Z_(n)(A)be the number of offsprings of generation n located in A.The exact convergence rate of the local limit theorem for the counting measure Z_(n)(·)is obtained.This partially extends the previous results for a simple branching random walk derived by Gao(2017,Stoch.Process Appl.).
基金Supported by NSFC(Grant Nos.11571262 and 11661025)Science Research Foundation of Guangxi Education Department(Grant No.YB2014117)
文摘In this paper, we present a local Csorgo- Revesz type functional limit theorem for increments of Brownian motion and give its convergence rate. The results also extend the functional forms of Levy＇s modulus of continuity for Brownian motion.
基金the National Natural Science Foundation of China(No.10671205)China Postdoctoral Science Foundation(No.20060400158)973 Program of China(No.2007CB814901)
文摘This paper establishes a local limit theorem for solutions of backward stochastic differential equations with Mao＇s non-Lipschitz generator, which is similar to the limit theorem obtained by [3] under the Lipschitz assumption.
基金supported by the National Natural Science Foundation of China under Grant No.11601062the National Natural Science Foundation of China under Grant Nos.11971249+1 种基金partially supported by the National Natural Science Foundation of China under Grant Nos.11771330 and 11971203supported in part by the Fundamental Research Funds for the Central Universities under Grant Nos.11522110。
文摘By using Chen,Hou and Mu’s extended Zeilberger algorithm,the authors obtain two recurrence relations for Callan’s generalization of Narayana polynomials.Based on these recurrence relations,the authors further prove the real-rootedness and asymptotic normality of Callan’s Narayana polynomials.
