Abundant explicit exact solutions to the generalized nonlinear Schrödinger equation with parabolic law and dual‐power law nonlinearities

This paper is concerned with the generalized nonlinear Schrödinger equation with parabolic law and dual‐power law. Abundant explicit and exact solutions of the generalized nonlinear Schrödinger equation with parabolic law and dual‐power law are derived uniformly by using the first integral method. These exact solutions are include that of extended hyperbolic function solutions, periodic wave solutions of triangle functions type, exponential form solution, and complex hyperbolic trigonometric function solutions and so on. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial DEs. Copyright © 2014 John Wiley & Sons, Ltd.     

Tighter uncertainty principles for periodic signals in terms of frequency

In this study, we propose some new uncertainty principles for periodic signals with sharper lower bounds than those in the existing ones. The improved lower bounds, in particular, are related to the frequency of the signal. Three examples are employed to demonstrate sharpness of the new uncertainty principles. Copyright © 2014 John Wiley & Sons, Ltd.     

Pseudo almost periodic dynamics of delay Nicholson's blowflies model with a linear harvesting term

In this paper, we investigate a class of delay Nicholson's blowflies model with a linear harvesting term, new criteria for the existence and convergence dynamics of positive pseudo almost periodic solutions are established by using the fixed point method and the properties of pseudo almost periodic function, together with constructing suitable Lyapunov functionals. The obtained results extend previously known results, and they also partially answer an open problem proposed by L. Berezansky et al. Finally, an example with simulation is presented to demonstrate the effectiveness of theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Trapped modes along a periodic array of freely floating obstacles

We consider the coupled problem describing the motion of a linear array of three‐dimensional obstacles floating freely in a homogeneous fluid layer of finite depth. The interaction of time‐harmonic waves with the floating objects is analyzed under the usual assumptions of linear water‐wave theory. Quasi‐periodic boundary conditions and a simplified reduction scheme turn the system into a linear spectral problem for a self‐adjoint operator in Hilbert space. Based upon the operator formulation, we derive a sufficient condition for the nonemptiness of its discrete spectrum. Various examples of obstacles that generate trapped modes are given. Copyright © 2014 John Wiley & Sons, Ltd.     

Periodic solutions for fourth-order nonlinear functional difference equations

By using the critical point method, some new criteria are obtained for the existence and multiplicity of periodic solutions for fourth-order nonlinear functional difference equations. The proof is based on the linking theorem in combination with variational technique. Recent results in the literature are generalized and significantly improved. Copyright © 2013 John Wiley & Sons, Ltd.     

Design of a reaction field using a linear‐combination‐based isotropic periodic sum method

In our previous study (Takahashi et al., J. Chem. Theory Comput. 2012, 8, 4503), we developed the linear‐combination‐based isotropic periodic sum (LIPS) method. The LIPS method is based on the extended isotropic periodic sum theory that produces a ubiquitous interaction potential function to estimate homogeneous and heterogeneous systems. The LIPS theory also provides the procedure to design a periodic reaction field. To demonstrate this, in the present work, a novel reaction field of the LIPS method was developed. The novel reaction field was labeled LIPS‐SW, because it provides an interaction potential function with a shape that resembles that of the switch function method. To evaluate the ability of the LIPS‐SW method to describe in homogeneous and heterogeneous systems, we carried out molecular dynamics (MD) simulations of bulk water and water–vapor interfacial systems using the LIPS‐SW method. The results of these simulations show that the LIPS‐SW method gives higher accuracy than the conventional interaction potential function of the LIPS method. The accuracy of simulating water–vapor interfacial systems was greatly improved, while that of bulk water systems was maintained using the LIPS‐SW method. We conclude that the LIPS‐SW method shows great potential for high‐accuracy, high‐performance computing to allow large scale MD simulations. © 2014 Wiley Periodicals, Inc.     

Formation of Periodic γ‐Turns in α/β‐Hybrid Peptides: DFT and NMR Experimental Evidence

Hybrid peptidic oligomers comprising natural and unnatural amino acid residues that can exhibit biomolecular folding and hydrogen‐bonding mimicry have attracted considerable interest in recent years. While a variety of hybrid peptidic helices have been reported in the literature, other secondary structural patterns such as γ‐turns and ribbons have not been well explored so far. The present work reports the design of novel periodic γ‐turns in the oligomers of 1:1 natural‐α/unnatural trans‐β‐norborenene (TNAA) amino acid residues. Through DFT, NMR, and MD studies, it is convincingly shown that, in the mixed conformational pool, the heterogeneous backbone of the hybrid peptides preferentially adopt periodic 8‐membered (pseudo γ‐turn)/7‐membered (inverse γ‐turn) hydrogen bonds in both polar and non‐polar solvent media. It is observed that the stereochemistry and local conformational preference of the β‐amino acid building blocks have a profound influence on accessing the specific secondary fold. These findings may be of significant relevance for the development of molecular scaffolds that facilitate desired positioning of functional side‐chains.     

Conformational polymorphs of 3‐cyclopropyl‐5‐(3‐methyl‐[1,2,4]triazolo[4,3‐a]pyridin‐7‐yl)‐1,2,4‐oxadiazole

The dipharmacophore compound 3‐cyclopropyl‐5‐(3‐methyl‐[1,2,4]triazolo[4,3‐a]pyridin‐7‐yl)‐1,2,4‐oxadiazole, C₁₂H₁₁N₅O, was studied on the assumption of its potential biological activity. Two polymorphic forms differ in both their molecular and crystal structures. The monoclinic polymorphic form was crystallized from more volatile solvents and contains a conformer with a higher relative energy. The basic molecule forms an abundance of interactions with relatively close energies. The orthorhombic polymorph was crystallized very slowly from isoamyl alcohol and contains a conformer with a much lower energy. The basic molecule forms two strong interactions and a large number of weak interactions. Stacking interactions of the `head‐to‐head' type in the monoclinic structure and of the `head‐to‐tail' type in the orthorhombic structure proved to be the strongest and form stacked columns in the two polymorphs. The main structural motif of the monoclinic structure is a double column where two stacked columns interact through weak C—H…N hydrogen bonds and dispersive interactions. In the orthorhombic structure, a single stacked column is the main structural motif. Periodic calculations confirmed that the orthorhombic structure obtained by slow evaporation has a lower lattice energy (0.97 kcal mol^?1) compared to the monoclinic structure.     

Polymorphism of methyl 4‐amino‐3‐phenylisothiazole‐5‐carboxylate: an experimental and theoretical study

Being a close analogue of amflutizole, methyl 4‐amino‐3‐phenylisothiazole‐5‐carboxylate (C₁₁H₁₀N₂O₂S) was assumed to be capable of forming polymorphic structures. Noncentrosymmetric and centrosymmetric polymorphs have been obtained by crystallization from a series of more volatile solvents and from denser tetrachloromethane, respectively. Identical conformations of the molecule are found in both structures. The two polymorphs differ mainly in the intermolecular interactions formed by the amino group and in the type of stacking interactions between the π‐systems. The most effective method for revealing packing motifs in structures with intermolecular interactions of different types (hydrogen bonding, stacking, dispersion, etc.) is to study the pairwise interaction energies using quantum chemical calculations. Molecules form a column as the primary basic structural motif due to stacking interactions in both polymorphic structures under study. The character of a column (straight or zigzag) is determined by the orientations of the stacked molecules (in a `head‐to‐head' or `head‐to‐tail' manner). Columns bound by intermolecular N—H…O and N—H…N hydrogen bonds form a double column as the main structural motif in the noncentrosymmetric structure. Double columns in the noncentrosymmetric structure and columns in the centrosymmetric structure interact strongly within the ab crystallographic plane, forming a layer as a secondary basic structural motif. The noncentrosymmetric structure has a lower density and a lower (by 0.59 kJ mol^?1) lattice energy, calculated using periodic calculations, compared to the centrosymmetric structure.     

A Quantitative Regularity Estimate for Nonnegative Supersolutions of Uniformly Parabolic Equations

This note establishes an interior quantitative lower bound for nonnegative supersolutions of fully nonlinear uniformly parabolic equations. The result may be interpreted as a quantitative version of a growth lemma established by Krylov and Safonov for nonnegative supersolutions of linear uniformly parabolic equations in nondivergence form. Our approach is different, and follows from an application of a reverse Holder inequality. The result is the parabolic analogue of an elliptic regularity estimate established by Caffarelli, Souganidis, and Wang in the stochastic homogenization of fully nonlinear uniformly elliptic equations.