Szasz-type operators can be constructed by a Poisson process. The purpose of this paper is to derive the converse result in connection with Szasz-type operators by Steckin-Marchaud-type inequalities and new Ditzian mo...Szasz-type operators can be constructed by a Poisson process. The purpose of this paper is to derive the converse result in connection with Szasz-type operators by Steckin-Marchaud-type inequalities and new Ditzian modulus of continuity. The degree of approximation on deterministic signals is also given.展开更多
Locality preserving projection (LPP) is a newly emerging fault detection method which can discover local manifold structure of a data set to be analyzed, but its linear assumption may lead to monitoring performance de...Locality preserving projection (LPP) is a newly emerging fault detection method which can discover local manifold structure of a data set to be analyzed, but its linear assumption may lead to monitoring performance degradation for complicated nonlinear industrial processes. In this paper, an improved LPP method, referred to as sparse kernel locality preserving projection (SKLPP) is proposed for nonlinear process fault detection. Based on the LPP model, kernel trick is applied to construct nonlinear kernel model. Furthermore, for reducing the computational complexity of kernel model, feature samples selection technique is adopted to make the kernel LPP model sparse. Lastly, two monitoring statistics of SKLPP model are built to detect process faults. Simulations on a continuous stirred tank reactor (CSTR) system show that SKLPP is more effective than LPP in terms of fault detection performance.展开更多
The continuous affinity- recycle extraction (CARE) process is extended ic a system with ultrafiltration membranes. The mathematical model of the process is established by taking into account membrane rejections to th...The continuous affinity- recycle extraction (CARE) process is extended ic a system with ultrafiltration membranes. The mathematical model of the process is established by taking into account membrane rejections to the components in a crude mixture. The process performance, defined as concentration factor (CF ), purification factor (PF ) and recovery yield (REC), is analyzed by computer simulations. The results show that CF and REC increase, but PF decreases with the membrane rejection. It is likely that optimum operating conditions exist to give the best process performance because the increases in eluant and affinity-recycle flow rate improve REC but decrease PF.展开更多
The increased production efficiency of heat treatable A1 alloys, as the result of applied electromagnetic field during continuous casting process was investigated. The applied frequency of the electromagnetic field （...The increased production efficiency of heat treatable A1 alloys, as the result of applied electromagnetic field during continuous casting process was investigated. The applied frequency of the electromagnetic field （EMF） during the AI alloys continuous casting was changing from 30 Hz to 50 Hz, while some castings were obtained without the EMF influence. The mechanical characterization of continuous casted AI alloys EN AW 2007 and En AW 2024 was done on testing machine Zwick/Roell Z 100. The microstructure of as-cast samples was examined, as well. When the frequency decreases （from 50 Hz to 30 Hz）, the grain size decreases as well, what is noticeable through the finer microstructure and its uniformity throughout the cross-section. These results have shown that low frequency electromagnetic field significantly influenced the microstructure and therefore the mechanical properties of as cast ingots. Thus, through improved castings quality, operation time and energy savings, the production efficiency was increased.展开更多
Let X and Y be metrizable topological linear spaces. In this paper, the following results are proved. (1) If X and Y are complete, g: X→Y is a point closed u. s. c.,and symmetric process with F(X)=Y,then either F(X) ...Let X and Y be metrizable topological linear spaces. In this paper, the following results are proved. (1) If X and Y are complete, g: X→Y is a point closed u. s. c.,and symmetric process with F(X)=Y,then either F(X) is meager in Y,or else F is an open muRifunction with F(X)=Y. (2) If X is complete, and F: X→Y is a process with a subclosed graph, then F is I s. c.. We also discuss topological multi-homomorphisms between topological linear spaces.展开更多
This paper obtains functional modulus of continuity and Strassen's functional LIL of theinfinite series of independent Ornstein-Uhlenbeck processes, which also imply the Levy's exactmodulus of continuity and L...This paper obtains functional modulus of continuity and Strassen's functional LIL of theinfinite series of independent Ornstein-Uhlenbeck processes, which also imply the Levy's exactmodulus of continuity and LIL of this process respectively.展开更多
Let L be a L′evy process with characteristic measureν,which has an absolutely continuous lower bound w.r.t.the Lebesgue measure on Rn.By using Malliavin calculus for jump processes,we investigate Bismut formula,grad...Let L be a L′evy process with characteristic measureν,which has an absolutely continuous lower bound w.r.t.the Lebesgue measure on Rn.By using Malliavin calculus for jump processes,we investigate Bismut formula,gradient estimates and coupling property for the semigroups associated to semilinear SDEs forced by L′evy process L.展开更多
Suppose that Xt is the Fleming-Viot process associated with fractional power Laplacian operator -(-△)α/2 0 < α≥ 2, and Yt= f_0￣t Xs.ds is the so-called occupation time process.In this paper) the asymptotic be...Suppose that Xt is the Fleming-Viot process associated with fractional power Laplacian operator -(-△)α/2 0 < α≥ 2, and Yt= f_0￣t Xs.ds is the so-called occupation time process.In this paper) the asymptotic behavior at a large time and the absolute continuity of Yt are investigated.展开更多
This paper considers the fed-batch culture in microbial fermentation process, which consists of batch and continuous culture. The goal is to explore the properties of a novel model which can describe the characteristi...This paper considers the fed-batch culture in microbial fermentation process, which consists of batch and continuous culture. The goal is to explore the properties of a novel model which can describe the characteristics of multistage for the population growth of microorganisms in nonlinear switch dynamic system. The improved model is developed based on the experimental data to describe the delayed, developmental and stationary stages well for the phases of batch culture. Then the existence, uniqueness and boundedness of solutions to the nonlinear multistage switch system and the Lipschitz continuity and differentiability of solutions with respect to the initial state is discussed as well. Finally, a numerical simulation is employed for the nonlinear multistage switch system.展开更多
基金Supported by National Natural Science Foundation of China (No.60872161)Natural Science Foundation of Tianjin (No. 08JCYBJC09600)
文摘Szasz-type operators can be constructed by a Poisson process. The purpose of this paper is to derive the converse result in connection with Szasz-type operators by Steckin-Marchaud-type inequalities and new Ditzian modulus of continuity. The degree of approximation on deterministic signals is also given.
基金Supported by the National Natural Science Foundation of China （61273160）, the Natural Science Foundation of Shandong Province of China （ZR2011FM014） and the Fundamental Research Funds for the Central Universities （10CX04046A）.
文摘Locality preserving projection (LPP) is a newly emerging fault detection method which can discover local manifold structure of a data set to be analyzed, but its linear assumption may lead to monitoring performance degradation for complicated nonlinear industrial processes. In this paper, an improved LPP method, referred to as sparse kernel locality preserving projection (SKLPP) is proposed for nonlinear process fault detection. Based on the LPP model, kernel trick is applied to construct nonlinear kernel model. Furthermore, for reducing the computational complexity of kernel model, feature samples selection technique is adopted to make the kernel LPP model sparse. Lastly, two monitoring statistics of SKLPP model are built to detect process faults. Simulations on a continuous stirred tank reactor (CSTR) system show that SKLPP is more effective than LPP in terms of fault detection performance.
文摘The continuous affinity- recycle extraction (CARE) process is extended ic a system with ultrafiltration membranes. The mathematical model of the process is established by taking into account membrane rejections to the components in a crude mixture. The process performance, defined as concentration factor (CF ), purification factor (PF ) and recovery yield (REC), is analyzed by computer simulations. The results show that CF and REC increase, but PF decreases with the membrane rejection. It is likely that optimum operating conditions exist to give the best process performance because the increases in eluant and affinity-recycle flow rate improve REC but decrease PF.
文摘The increased production efficiency of heat treatable A1 alloys, as the result of applied electromagnetic field during continuous casting process was investigated. The applied frequency of the electromagnetic field （EMF） during the AI alloys continuous casting was changing from 30 Hz to 50 Hz, while some castings were obtained without the EMF influence. The mechanical characterization of continuous casted AI alloys EN AW 2007 and En AW 2024 was done on testing machine Zwick/Roell Z 100. The microstructure of as-cast samples was examined, as well. When the frequency decreases （from 50 Hz to 30 Hz）, the grain size decreases as well, what is noticeable through the finer microstructure and its uniformity throughout the cross-section. These results have shown that low frequency electromagnetic field significantly influenced the microstructure and therefore the mechanical properties of as cast ingots. Thus, through improved castings quality, operation time and energy savings, the production efficiency was increased.
基金This paper was reported at the 5th National Functional Analysis Conference held at Nanjing in Nov.,1990.
文摘Let X and Y be metrizable topological linear spaces. In this paper, the following results are proved. (1) If X and Y are complete, g: X→Y is a point closed u. s. c.,and symmetric process with F(X)=Y,then either F(X) is meager in Y,or else F is an open muRifunction with F(X)=Y. (2) If X is complete, and F: X→Y is a process with a subclosed graph, then F is I s. c.. We also discuss topological multi-homomorphisms between topological linear spaces.
文摘This paper obtains functional modulus of continuity and Strassen's functional LIL of theinfinite series of independent Ornstein-Uhlenbeck processes, which also imply the Levy's exactmodulus of continuity and LIL of this process respectively.
文摘Let L be a L′evy process with characteristic measureν,which has an absolutely continuous lower bound w.r.t.the Lebesgue measure on Rn.By using Malliavin calculus for jump processes,we investigate Bismut formula,gradient estimates and coupling property for the semigroups associated to semilinear SDEs forced by L′evy process L.
文摘Suppose that Xt is the Fleming-Viot process associated with fractional power Laplacian operator -(-△)α/2 0 < α≥ 2, and Yt= f_0￣t Xs.ds is the so-called occupation time process.In this paper) the asymptotic behavior at a large time and the absolute continuity of Yt are investigated.
基金supported by the National Natural Science Foundation of China under Grant Nos.11171050,11101262 and 11371164the National Natural Science Foundation for the Youth of China under Grant Nos.11301081,11401073
文摘This paper considers the fed-batch culture in microbial fermentation process, which consists of batch and continuous culture. The goal is to explore the properties of a novel model which can describe the characteristics of multistage for the population growth of microorganisms in nonlinear switch dynamic system. The improved model is developed based on the experimental data to describe the delayed, developmental and stationary stages well for the phases of batch culture. Then the existence, uniqueness and boundedness of solutions to the nonlinear multistage switch system and the Lipschitz continuity and differentiability of solutions with respect to the initial state is discussed as well. Finally, a numerical simulation is employed for the nonlinear multistage switch system.
