We report on a method to achieve multiple microscopic particles being trapped and manipulated transversely by using a size-tunable Bessel beam generated by cross-phase modulation(XPM)based on the thermal nonlinear opt...We report on a method to achieve multiple microscopic particles being trapped and manipulated transversely by using a size-tunable Bessel beam generated by cross-phase modulation(XPM)based on the thermal nonlinear optical effect.The results demonstrate that multiple polystyrene particles can be stably trapped simultaneously,and the number of the trapped particles can be controlled by varying the trapping beam power.In addition,the trapped particles can be manipulated laterally with micron-level precision by changing the size of J_(0)Bessel beam.This work provides a simple but efficient way to trap and manipulate multiple particles simultaneously,which would have potential applications in many fields such as cell sorting and transportation.展开更多
In this paper,the notion of C-semigroup of continuous module homomorphisms on a complete random normal(RN)module is introduced and investigated.The existence and uniqueness of solution to the Cauchy problem with respe...In this paper,the notion of C-semigroup of continuous module homomorphisms on a complete random normal(RN)module is introduced and investigated.The existence and uniqueness of solution to the Cauchy problem with respect to exponentially bounded C-semigroups of continuous module homomorphisms in a complete RN module are established.展开更多
Let(B,||·||)be a Banach space,(?,F,P)a probability space,and L^0(F,B)the set of equivalence classes of strong random elements(or strongly measurable functions)from(?,F,P)to(B,||·||).It is well known that L^0...Let(B,||·||)be a Banach space,(?,F,P)a probability space,and L^0(F,B)the set of equivalence classes of strong random elements(or strongly measurable functions)from(?,F,P)to(B,||·||).It is well known that L^0(F,B)becomes a complete random normed module,which has played an important role in the process of applications of random normed modules to the theory of Lebesgue-Bochner function spaces and random operator theory.Let V be a closed convex subset of B and L^0(F,V)the set of equivalence classes of strong random elements from(?,F,P)to V.The central purpose of this article is to prove the following two results:(1)L^0(F,V)is L^0-convexly compact if and only if V is weakly compact;(2)L^0(F,V)has random normal structure if V is weakly compact and has normal structure.As an application,a general random fixed point theorem for a strong random nonexpansive operator is given,which generalizes and improves several well known results.We hope that our new method,namely skillfully combining measurable selection theorems,the theory of random normed modules,and Banach space techniques,can be applied in the other related aspects.展开更多
Let W be a classical Weyl group and ∏ be the corresponding system of simple roots. For w∈ W, let R(w)={α∈∏|l(ws_α)【l(w)}, where we denote by s_α the simple reflection in the hyperplane orthogonal to α for α...Let W be a classical Weyl group and ∏ be the corresponding system of simple roots. For w∈ W, let R(w)={α∈∏|l(ws_α)【l(w)}, where we denote by s_α the simple reflection in the hyperplane orthogonal to α for α∈∏ and by l(w)the minimal length of an expression of w as a product of simple reflections. To any Weyl group one can associate a展开更多
The effect of sucrose on nanometer Se0 in liquid phase was reported.Transmission electron microscope（TEM）,laser light scattering image and Resonance Rayleigh Scattering（RRS） were used to study the configuration an...The effect of sucrose on nanometer Se0 in liquid phase was reported.Transmission electron microscope（TEM）,laser light scattering image and Resonance Rayleigh Scattering（RRS） were used to study the configuration and stability of nanometer Se0 particles.The results show that sucrose solution modulated the assemble of nanometer Se0 particles and stabilized the Se0 particles in liquid phase.From the concentration of 1.07 to 42.8 μmol/L,the diameter of Se0 particles were 47—600 nm.However,in the presence of 1.0% sucrose solution,the major distribution range of Se0 diameter was 20—80 nm.Furthermore,the nanometer Se0 sol-gel could be preserved stably in sucrose solution at least for 2 months at 2—10 ℃.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61805200,51927804,and12104365)the Natural Science Foundation of Shaanxi Province,China(Grant No.2020JM-432)+1 种基金the Fund for Young Star in Science and Technology of Shaanxi Province,China(Grant No.2021KJXX-27)the Fund from the Education Department of Shaanxi Province,China(Grant No.21JK0915)。
文摘We report on a method to achieve multiple microscopic particles being trapped and manipulated transversely by using a size-tunable Bessel beam generated by cross-phase modulation(XPM)based on the thermal nonlinear optical effect.The results demonstrate that multiple polystyrene particles can be stably trapped simultaneously,and the number of the trapped particles can be controlled by varying the trapping beam power.In addition,the trapped particles can be manipulated laterally with micron-level precision by changing the size of J_(0)Bessel beam.This work provides a simple but efficient way to trap and manipulate multiple particles simultaneously,which would have potential applications in many fields such as cell sorting and transportation.
文摘In this paper,the notion of C-semigroup of continuous module homomorphisms on a complete random normal(RN)module is introduced and investigated.The existence and uniqueness of solution to the Cauchy problem with respect to exponentially bounded C-semigroups of continuous module homomorphisms in a complete RN module are established.
基金This work was supported by National Natural Science Foundation of China(11571369)。
文摘Let(B,||·||)be a Banach space,(?,F,P)a probability space,and L^0(F,B)the set of equivalence classes of strong random elements(or strongly measurable functions)from(?,F,P)to(B,||·||).It is well known that L^0(F,B)becomes a complete random normed module,which has played an important role in the process of applications of random normed modules to the theory of Lebesgue-Bochner function spaces and random operator theory.Let V be a closed convex subset of B and L^0(F,V)the set of equivalence classes of strong random elements from(?,F,P)to V.The central purpose of this article is to prove the following two results:(1)L^0(F,V)is L^0-convexly compact if and only if V is weakly compact;(2)L^0(F,V)has random normal structure if V is weakly compact and has normal structure.As an application,a general random fixed point theorem for a strong random nonexpansive operator is given,which generalizes and improves several well known results.We hope that our new method,namely skillfully combining measurable selection theorems,the theory of random normed modules,and Banach space techniques,can be applied in the other related aspects.
基金Project supported by the National Natural Science Foundation of China.
文摘Let W be a classical Weyl group and ∏ be the corresponding system of simple roots. For w∈ W, let R(w)={α∈∏|l(ws_α)【l(w)}, where we denote by s_α the simple reflection in the hyperplane orthogonal to α for α∈∏ and by l(w)the minimal length of an expression of w as a product of simple reflections. To any Weyl group one can associate a
文摘The effect of sucrose on nanometer Se0 in liquid phase was reported.Transmission electron microscope（TEM）,laser light scattering image and Resonance Rayleigh Scattering（RRS） were used to study the configuration and stability of nanometer Se0 particles.The results show that sucrose solution modulated the assemble of nanometer Se0 particles and stabilized the Se0 particles in liquid phase.From the concentration of 1.07 to 42.8 μmol/L,the diameter of Se0 particles were 47—600 nm.However,in the presence of 1.0% sucrose solution,the major distribution range of Se0 diameter was 20—80 nm.Furthermore,the nanometer Se0 sol-gel could be preserved stably in sucrose solution at least for 2 months at 2—10 ℃.
