Multiple positive solutions for functional dynamic equations on time scales

AbstractIn this paper, we study the following functional dynamic equation on time scales: {[Φ(uΔ(t))]∇+a(t)f(u(t),u(μ(t)))=0,t∈(0,T)T,u(t)=φ(t),t∈[−r,0)T,u(0)−B0(uΔ(0))=0,uΔ(T)=0, where Φ:R→R is an increasing homeomorphism and a positive homomorphism and Φ(0)=0. By using the well-known Leggett–Williams fixed point theorem, existence criteria for multiple positive solutions are established. An example is also given to illustrate the main results

(Benzoato-κO)bis­(1,10-phenanthroline-κ2 N,N′)copper(II) chloride benzoic acid disolvate

In the title complex, [Cu(C7H5O2)(C12H8N2)2]Cl·2C6H5CO­OH, the CuII ion is coordinated by one carboxyl­ate O atom from a benzoate anion and four N atoms from two phenantroline ligands in a distorted five-coordinate trigonal-bipyramidal CuON4 chromophore. The Cu2+ and the Cl− ion are imposed by a twofold rotation axiss which also bisects the equally disordered benzoate anion. In the crystal, the mol­ecules are assembled into chains along [010] by C—H⋯Cl, O—H⋯Cl and C—H⋯O hydrogen-bonding inter­actions. The resulting chains are further connected into two-dimensional supra­molecular layers parallel to [100] by inter­chain π⋯π stacking inter­actions [centroid–centroid distance = 3.823 (5) Å] between the phenanthroline ligands and the benzoic acid mol­ecules, and by C—H⋯O hydrogen-bonding inter­actions. Strong π⋯π stacking inter­actions between adjacent phenantroline ligands [3.548 (4) Å] assemble the layers into a three-dimensional supra­molecular architecture

Exposure of the Hidden Anti-Ferromagnetism in Paramagnetic CdSe:Mn Nanocrystals

We present theoretical and experimental investigations of the magnetism of paramagnetic semiconductor CdSe:Mn nanocrystals and propose an efficient approach to the exposure and analysis of the underlying anti-ferromagnetic interactions between magnetic ions therein. A key advance made here is the build-up of an analysis method with the exploitation of group theory technique that allows us to distinguish the anti-ferromagnetic interactions between aggregative Mn2+ ions from the overall pronounced paramagnetism of magnetic ion doped semiconductor nanocrystals. By using the method, we clearly reveal and identify the signatures of anti-ferromagnetism from the measured temperature dependent magnetisms, and furthermore determine the average number of Mn2+ ions and the fraction of aggregative ones in the measured CdSe:Mn nanocrystals.Comment: 26 pages, 5 figure

Study on the layered dusty plasma structures in the summer polar mesopause

Traditional hydrodynamic equations are adopted to build a one-dimensional theoretical model to study the effect of gravity wave on layered dusty plasma structures formation and evolution near the polar summer mesospause region associated with polar mesosphere summer echoes (PMSE). The proposed mechanism gives consideration to the charged ice particle motion by the gravity wave modulation, making a significant contribution to the vertical transport of heavy ice particles and convergence into thin layers. And numerical results show that the pattern of the multi-layer structure depends on the ration of the initial ice particles density distribution to the vertical wavelength of the gravity waves, the ice particle size and the wind velocity caused by gravity wave. Also, the variation of ion density distribution under the influence of gravity wave has also been examined. Finally, the electron density depletions (bite-outs) layers has been simulated according to the charge conservation laws, and the results are compared to the ECT02 rocket sounding data, which agree well with the measuring

Role of AC-cAMP-PKA Cascade in Antidepressant Action of Electroacupuncture Treatment in Rats

Adenylyl cyclase (AC)-cyclic adenosine monophosphate (cAMP)-cAMP-dependent protein kinase A (PKA) cascade is considered to be associated with the pathogenesis and treatment of depression. The present study was conducted to explore the role of the cAMP cascade in antidepressant action of electroacupuncture (EA) treatment for chronic mild stress (CMS)-induced depression model rats. The results showed that EA improved significantly behavior symptoms in depression and dysfunction of AC-cAMP-PKA signal transduction pathway induced by CMS, which was as effective as fluoxetine. Moreover, the antidepressant effects of EA rather than Fluoxetine were completely abolished by H89, a specific PKA inhibitor. Consequently, EA has a significant antidepressant treatment in CMS-induced depression model rats, and AC-cAMP-PKA signal transduction pathway is crucial for it

Silicon nitride metalenses for unpolarized high-NA visible imaging

As one of nanoscale planar structures, metasurface has shown excellent superiorities on manipulating light intensity, phase and/or polarization with specially designed nanoposts pattern. It allows to miniature a bulky optical lens into the chip-size metalens with wavelength-order thickness, playing an unprecedented role in visible imaging systems (e.g. ultrawide-angle lens and telephoto). However, a CMOS-compatible metalens has yet to be achieved in the visible region due to the limitation on material properties such as transmission and compatibility. Here, we experimentally demonstrate a divergent metalens based on silicon nitride platform with large numerical aperture (NA~0.98) and high transmission (~0.8) for unpolarized visible light, fabricated by a 695-nm-thick hexagonal silicon nitride array with a minimum space of 42 nm between adjacent nanoposts. Nearly diffraction-limit virtual focus spots are achieved within the visible region. Such metalens enables to shrink objects into a micro-scale size field of view as small as a single-mode fiber core. Furthermore, a macroscopic metalens with 1-cm-diameter is also realized including over half billion nanoposts, showing a potential application of wide viewing-angle functionality. Thanks to the high-transmission and CMOS-compatibility of silicon nitride, our findings may open a new door for the miniaturization of optical lenses in the fields of optical fibers, microendoscopes, smart phones, aerial cameras, beam shaping, and other integrated on-chip devices.Comment: 16 pages, 7 figure