Stability,periodicity, and symmetries of certain second‐order fractional difference equation with quadratic terms via KAM theory

By using the Kolmogorov–Arnold–Moser theory, we investigate the stability of the equilibrium solution of the difference equation where A ,B ,D > 0,u _?1,u ₀>0. We also use the symmetries to find effectively the periodic solutions with feasible periods. Copyright © 2016 John Wiley & Sons, Ltd.     

LOCALIZED PATTERNS OF THE SWIFT-HOHENBERG EQUATION WITH A DISSIPATIVE TERM

In this paper, the normal form analysis of quadratic-cubic Swift-Hohenberg equation with a dissipative term is investigated by using the multiple-scale method. In addition, we obtain Hamiltonian-Hopf bifurcations of two equilibria and homoclinic snaking bifurcations of one-peak and two-peak homoclinic solutions by numerical simulations.     

Spirocyclic azetidines for drug discovery: Novel Boc-protected 7'H-spiro[azetidine-3,5'-furo[3,4-d ]pyrimidines]

A novel spirocyclic scaffold of 7'H-spiro[azetidine-3,5'-furo[3,4-d]pyrimidine] chemotype was synthesized in N-Boc-protected form. However, the scaffold was revealed to be unstable to storage when deprotected. The solution was found in the brief removal of the Boc protecting group and rapid acylation of the liberated NH-azetidine with a carboxylic acid imidazolide.     

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.     

A Novel Solid Nanocrystals Self-Stabilized Pickering Emulsion Prepared by Spray-Drying with Hydroxypropyl-β-cyclodextrin as Carriers

A drug nanocrystals self-stabilized Pickering emulsion (NSSPE) with a unique composition and microstructure has been proven to significantly increase the bioavailability of poorly soluble drugs. This study aimed to develop a new solid NSSPE of puerarin preserving the original microstructure of NSSPE by spray-drying. A series of water-soluble solid carriers were compared and then Box-Behnken design was used to optimize the parameters of spray-drying. The drug release and stability of the optimized solid NSSPE in vitro were also investigated. The results showed that hydroxypropyl-β-cyclodextrin (HP-β-CD), rather than solid carriers commonly used in solidification of traditional Pickering emulsions, was suitable for the solid NSSPE to retain the original appearance and size of emulsion droplets after reconstitution. The amount of HP-β-CD had more influences on the solid NSSPE than the feed rate and the inlet air temperature. Fluorescence microscopy, confocal laser scanning microscopy and scanning electron microscopy showed that the reconstituted emulsion of the solid NSSPE prepared with HP-β-CD had the same core-shell structure with a core of oil and a shell of puerarin nanocrystals as the liquid NSSPE. The particle size of puerarin nanocrystal sand interfacial adsorption rate also did not change significantly. The cumulative amount of released puerarin from the solid NSSPE had no significant difference compared with the liquid NSSPE, which were both significantly higher than that of puerarin crude material. The solid NSSPE was stable for 3 months under the accelerated condition of 75% relative humidity and 40 °C. Thus, it is possible todevelop the solid NSSPE preserving the unique microstructure and the superior properties in vitro of the liquid NSSPE for poorly soluble drugs.     

High‐temperature superconductivity and long‐range order in strongly correlated electronic systems

A selective review of the question of how repulsive electron correlations might give rise to off‐diagonal long‐range order (ODLRO) in high‐temperature superconductors is presented. The article makes detailed explanations of the relevance to superconductivity of reduced electronic density matrices and how these can be used to understand whether ODLRO might arise from Coulombic repulsions in strongly correlated electronic systems. Time‐reversed electron pairs on alternant Cuprate and the iron‐based pnictide and chalcogenide lattices may have a weak long‐range attractive tail and much stronger short‐range repulsive Coulomb interaction. The long‐range attractive tail may find its origin in one of the many suggested proposals for high‐T_c superconductivity and thus has an uncertain origin. A phenomenological Hamiltonian is invoked whose model parameters are obtained by fitting to experimental data. A detailed summary is given of the arguments that such interacting electrons can cooperate to produce a superconducting state in which time‐reversed pairs of electrons effectively avoid the repulsive hard‐core of the Coulomb interaction but reside on average in the attractive well of the long‐range potential. Thus, the pairing of electrons itself provides an enhanced screening mechanism. The alternant lattice structure is the key to achieving robust high‐temperature superconductivity with dx²‐y² or sign alternating s‐wave or s± condensate symmetries in cuprates and iron‐based compounds. Some attention is also given to the question first raised by Leggett as to where the Coulombic energy is saved in the superconducting transition in cuprates. A mean‐field‐type model in which the condensate density serves as an order parameter is discussed. Many of the observed trends in the thermal properties of cuprate superconductors are reproduced giving strong support for the proposed model for high‐temperature superconductivity in such strongly correlated electronic systems. © 2015 Wiley Periodicals, Inc.     

[DBU‐H]+ and H2o as effective catalyst form for 2,3‐dihydropyrido[2,3‐d]pyrimidin‐4(1H)‐ones: A DFT Study

DFT investigations are carried out to explore the effective catalyst forms of DBU and H₂O and the mechanism for the formation of 2,3‐dihydropyrido[2,3‐d]‐pyrimidin‐4(1H)‐ones. Three main pathways are disclosed under unassisted, water‐catalyzed, DBU and water cocatalyzed conditions, which involves concerted nucleophilic addition and H‐transfer, concerted intramolecular cyclization and H‐transfer, and Dimroth rearrangement to form the product. The results indicated that the DBU and water cocatalyzed pathway is the most favored one as compared to the rest two pathways. The water donates one H to DBU and accepts H from 2‐amino‐nicotinonitrile ( 1 ), forming [DBU‐H]⁺‐H₂O as effective catalyst form in the proton migration transition state rather than [DBU‐H]⁺‐OH^?. The hydrogen bond between [DBU‐H]⁺···H₂O··· 1 ^? decreases the activation barrier of the rate‐determining step. Our calculated results open a new insight for the green catalyst model of DBU‐H₂O. © 2015 Wiley Periodicals, Inc.     

Natural and artificial light-harvesting systems utilizing the functions of carotenoids

Carotenoids are essential pigments in natural photosynthesis. They absorb in the blue–green region of the solar spectrum and transfer the absorbed energy to (bacterio-)chlorophylls, and so expand the wavelength range of light that is able to drive photosynthesis. This process is an example of singlet–singlet energy transfer and so carotenoids serve to enhance the overall efficiency of photosynthetic light reactions. Carotenoids also act to protect photosynthetic organisms from the harmful effects of excess exposure to light. In this case, triplet–triplet energy transfer from (bacterio-)chlorophyll to carotenoid plays a key role in this photoprotective reaction. In the light-harvesting pigment–protein complexes from purple photosynthetic bacteria and chlorophytes, carotenoids have an additional role, namely the structural stabilization of those complexes. In this article we review what is currently known about how carotenoids discharge these functions. The molecular architecture of photosynthetic systems will be outlined to provide a basis from which to describe the photochemistry of carotenoids, which underlies most of their important functions in photosynthesis. Then, the possibility to utilize the functions of carotenoids in artificial photosynthetic light-harvesting systems will be discussed. Some examples of the model systems are introduced.     

张弦梁(桁架)结构的找形方法——分级卸载法

对张弦梁(桁架)结构的找形问题进行了深入研究,根据该类结构的受力特点,提出了分级卸载法。该方法无需假定结构零状态几何,而可以一次得到对应于初状态(即预应力态)几何的结构施工放样尺寸(即零状态几何),并通过分级加载对该方法的精度进行了检验。     

The Onset of Darcy–Forchheimer Convection in Inclined Porous Layers Heated from Below

It is well known that the onset of convection in an inclined porous layer heated from below takes the form of longitudinal vortices when Darcy’s law is valid. In this paper we consider briefly how the onset criterion alters when form drag, as modelled by the Forchheimer terms, is significant. In general, the critical Rayleigh number increases substantially as form drag effects strengthen, but the wavenumber rises by only a small amount. This numerical study is supplemented by a brief asymptotic analysis of the case when the Forchheimer terms dominate and it is shown that the critical Rayleigh number increases in direct proportion with the form drag parameter.