On concentration of solution to a Schrödinger logarithmic equation with deepening potential well

In this work, we prove the existence of positive solution for the following class of problems where λ>0 and is a potential satisfying some conditions. Using the variational method developed by Szulkin for functionals, which are the sum of a C¹ functional with a convex lower semicontinuous functional, we prove that for each large enough λ>0, there exists a positive solution for the problem, and that, as λ→+∞, such solutions converge to a positive solution of the limit problem defined on the domain Ω=int(V^?1({0})).     

Some extensions of the operator entropy type inequalities

In this paper, we define the generalised relative operator entropy and investigate some of its properties such as subadditivity and homogeneity. As application of our result, we obtain the information inequality. In continuation, we establish some reverses of the operator entropy inequalities under certain conditions by using the Mond–Pe?ari? method.     

Explosive synchronization in a mobile network in the presence of a positive feedback mechanism

Synchronization is a process that describes the coherent dynamics of a large ensemble of interacting units.The study of explosive synchronization transition attracts considerable attention.Here,I report the explosive transition within the framework of a mobile network,while each oscillator is controlled by global-order parameters of the system.Using numerical simulation,I find that the explosive synchronization(ES)transition behavior can be controlled by simply adjusting the fraction of controlled oscillators.The influences of some parameters on explosive synchronization are studied.Moreover,due to the presence of the positive feedback mechanism,I prevent the occurrence of the synchronization of continuous-phase transition and make phase transition of the system a first-order phase transition accompanied by a hysteresis loop.     

一类变号(k,n-k)共轭边值问题正解的存在性

通过构造一个特殊的锥,利用范数形式的锥拉伸锥压缩不动点定理,在允许非线性项变号无下界且没有任何单调性假设的条件下,得出了一类高阶(k,n-k)共轭两点边值问题方程组正解的存在性结论.     

Composite Mesoporous Silica Nanoparticles with Dual-color Afterglow for Cross-correlation-based Living Cell Imaging

Room temperature phosphorescence (RTP) materials are characterized with emission after removing the excitation source. Such long-lived emission feature possesses great potential in biological fluorescence imaging because it enables a way regarding temporal dimension for separating the interference of autofluorescence and common noises typically encountered in conventional fluorescence imaging. Herein, we constructed a new type of mesoporous silica nanoparticles (MSNs)-based composite nanoparticles (NPs) with dual-color long-lived emission, namely millisecond-level green phosphorescence and sub-millisecond-level delayed red fluorescence by encapsulating a typical RTP dye and Rhodamine dye in the cavities of the MSNs with the former acting as energy donor (D) while the latter as acceptor (A). Benefiting from the close D-A proximity, energy match between the donor and the acceptor and the optimized D/A ratio in the composite NPs, efficient triplet-to-singlet Förster resonance energy transfer (TS-FRET) in the NPs occurred upon exciting the donor, which enabled dual-color long-lived emission. The preliminary results of dual-color correlation imaging of live cells based on such emission feature unequivocally verified the unique ability of such NPs for distinguishing the false positive generated by common emitters with single-color emission feature.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.