Multipartite entangled states like the W-class are of growing interest since they exhibit a variety of possible applications ranging from quantum computation to genuine random number generation. Here, we present a uni...Multipartite entangled states like the W-class are of growing interest since they exhibit a variety of possible applications ranging from quantum computation to genuine random number generation. Here, we present a universal setup to generate high-order single photon W-states based on three-dimensional integrated-photonic waveguide struc- tures. Additionally, we present a novel method to charac- terize the device＇s unitary by means of classical light only.展开更多
We study the existence of positive solutions of a population model with diffusion of the form {-△pu=aup-1-f（u）-c/ua,x∈Ω,u=0,x∈Ω where △p denotes the p-Laplacian operator defined by △pz =div（｜z｜P-2z）, p 〉...We study the existence of positive solutions of a population model with diffusion of the form {-△pu=aup-1-f（u）-c/ua,x∈Ω,u=0,x∈Ω where △p denotes the p-Laplacian operator defined by △pz =div（｜z｜P-2z）, p 〉 1, Ω is a bounded domain of RN with smooth boundary, α∈ C （0, 1）, a and e are positive constants. Here f ： [0, ∞） → R is a continuous function. This model arises in the studies of population biology of one species with u representing the concentration of the species. We discuss the existence of positive solution when f satisfies certain additional conditions. We use the method of sub- and super-solutions to establish our results.展开更多
基金financial support from the German Ministry of Education and Research (Center for Innovation Competence program, Grant No. 03Z1HN31)the Thuringian Ministry for Education, Science and Culture (Research group Spacetime, Grant No. 11027-514)+1 种基金the Deutsche Forschungsgemeinschaft (Grant No. NO462/6-1)the German-Israeli Foundation for Scientific Research and Development (Grant No. 1157-127.14/ 2011)
文摘Multipartite entangled states like the W-class are of growing interest since they exhibit a variety of possible applications ranging from quantum computation to genuine random number generation. Here, we present a universal setup to generate high-order single photon W-states based on three-dimensional integrated-photonic waveguide struc- tures. Additionally, we present a novel method to charac- terize the device＇s unitary by means of classical light only.
文摘We study the existence of positive solutions of a population model with diffusion of the form {-△pu=aup-1-f（u）-c/ua,x∈Ω,u=0,x∈Ω where △p denotes the p-Laplacian operator defined by △pz =div（｜z｜P-2z）, p 〉 1, Ω is a bounded domain of RN with smooth boundary, α∈ C （0, 1）, a and e are positive constants. Here f ： [0, ∞） → R is a continuous function. This model arises in the studies of population biology of one species with u representing the concentration of the species. We discuss the existence of positive solution when f satisfies certain additional conditions. We use the method of sub- and super-solutions to establish our results.
