Ekeland’s variational principle for vectorial multivalued mappings in a uniform space

In this paper, we establish Ekeland’s variational principle and an equilibrium version of Ekeland’s variational principle for vectorial multivalued mappings in the setting of separated, sequentially complete uniform spaces. Our approaches and results are different from those in Chen et al. (2008), Hamel (2005), and Lin and Chuang (2010) [13], [14] and [15]. As applications of our results, we study vectorial Caristi’s fixed point theorems and Takahashi’s nonconvex minimization theorems for multivalued mappings and their equivalent forms in a separated, sequentially complete uniform space. We also apply our results to study maximal element theorems, which are unified methods of several variational inclusion problems. Our results contain many known results in the literature Fang (1996) [21], and will have many applications in nonlinear analysis.     

A hybrid legendre tau method for the solution of a class of nonlinear wave equations with nonlinear dissipative terms

This article presents a technique based on the hybrid Legendre tau‐finite difference method to solve the fourth order wave equation which arises in the elasto‐plastic‐microstructure models for longitudinal motion of an elasto‐plastic bar. Illustrative examples and numerical results obtained using new technique demonstrate that the proposed approach is efficient in treating longitudinal equation of ealsto‐plastic bar. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1055–1071, 2011     

Novel molecularly imprinted microsphere using a single chiral monomer and chirality-matching (S)-ketoprofen template

We designed and synthesized a cinchonine derivative to be used as a novel chiral monomer. It was employed in a dual role of functional monomer and cross-linking monomer, displaying multi-binding sites for the template (S)-ketoprofen. Monodisperse molecularly imprinted core-shell microspheres were prepared using surface imprinting method on silica gel. The results show a substantial synergistic effect in the enantioselective recognition, confirming our initial hypothesis. Computational simulation of the monomer and template pre-arrangement strongly supports our proposed chiral recognition mechanism for the imprinted microspheres.     

Computational study of FOX‐7 synthesis in a solvated reaction system

Ethene and two kinds of nitrating reagents (HNO₃ and N₂O₅) in a variety of solvents were included in respective molecular systems, and each underwent a two‐stage electrophilic and free radical nitro‐substitution reaction to obtain the corresponding nitroethene compounds. Subsequent halogenation (using Cl₂ and Br₂) and amination (using NH₃) were then performed in solvents, also by electrophilic and radical substitution, to produce the desired 1,1‐diamino‐2,2‐dinitroethene (FOX‐7) derivatives. The reaction energy barrier in the nitration stage for obtaining each kind of mononitro ethene exhibited a stepwise decreasing trend when the reaction was carried out in H₂O‐solvated and CH₃OH‐solvated systems, no matter what nitrating agent was used. Related energy barrier data showed that the nitration reaction is more feasible in an H₂O‐solvated than a CH₃OH‐solvated system. The modeling results suggested that N₂O₅ is the better agent for nitration to proceed in water, bromine is suitable for halogenation, and the bromine derivatives are convenient for further amination in an H₂O‐solvated system. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Influence of substitution on the strength and nature of CH···N hydrogen bond in XCCH···NH3 complexes

The effect of substitution on the strength and nature of CH···N hydrogen bond in XCCH···NH₃ (X = F, Cl, Br, OH, H, Me) and NCH···NH₃ complexes were investigated by quantum chemical calculations. Ab initio calculations were performed using MP2 method with a wide range of basis sets. With tacking into account the BSSE and ZPVE, the values of BEs decrease. Replacement of the nonparticipatory hydrogen atom of HCCH by the electronegative atoms (F, Cl, and Br), lead to the BEs increases. The BE corresponding to the replacement of the nonparticipatory hydrogen atom of HCCH by the OH and CH₃ groups decreases. A far greater enhancement of the interaction energy arises from replacement of HCCH by the more acidic HCN. The natural bond orbital analysis and the Bader's quantum theory of atoms in molecules were also used to elucidate the interaction characteristics of these complexes. The electrostatic nature of H‐bond interactions is predicted from QTAIM analysis. In addition, the relationship between the isotropic and anisotropic chemical shifts of the bridging hydrogen and binding energy of complexes as well as electron density at N···H BCPs were investigated. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

miR-9 and let-7g enhance the sensitivity to ionizing radiation by suppression of NFκB1

The activation of nuclear factor-kappa B1 (NFkB1) in cancer cells may confer resistance to ionizing radiation (IR). To enhance the therapeutic efficiency of IR in lung cancer, we screened for microRNAs (miRNAs) that suppress NFkB1 and observed their effects on radiosensitivity in a human lung cancer cell line. From time series data of miRNA expression in γ-irradiated H1299 human lung cancer cells, we found that the expression of miR-9 was inversely correlated with that of NFκB1. Overexpression of miR-9 down-regulated the level of NFκB1 in H1299 cells, and the surviving fraction of γ-irradiated cells was decreased. Interestingly, let-7g also suppressed the expression of NFκB1, although there was no canonical target site for let-7g in the NFκB1 3' untranslated region. From these results, we conclude that the expression of miR-9 and let-7g could enhance the efficiency of radiotherapy for lung cancer treatment through the inhibition of NFκB1.     

Evidence for water structuring forces between surfaces

Structured water on apposing surfaces can generate significant energies due to reorganization and displacement of water as the surfaces encounter each other. Force measurements on a multitude of biological structures using the osmotic stress technique have elucidated commonalities that point toward an underlying hydration force. In this review, the forces of two contrasting systems are considered in detail: highly charged DNA and nonpolar, uncharged hydroxypropyl cellulose. Conditions for both net repulsion and attraction, along with the measured exclusion of chemically different solutes from these macromolecular surfaces, are explored and demonstrate common features consistent with a hydration force origin. Specifically, the observed interaction forces can be reduced to the effects of perturbing structured surface water.     

Non-linear study of electrohydrodynamic Rayleigh-Taylor instability in a composite fluid-porous layer

The non-linear electrohydrodynamic RTI in presence of electric field bounded above by porous layer and below by a rigid surface, have been studied based on electrohydrodynamic approximations in the effect similar to the Stokes and lubrication approximations. The non-linear problem is studied numerically in the present paper using the Adams-Bashforth predictor and Adams-Moulton corrector numerical techniques. In the conclusion, the non-linear problem discussed here is quite different from that of Babchin et al. (1983) [10] considering the plane Couette flow. The present problem is greatly influenced by the slip velocity at the interface between porous layer and thin film. It is not amenable to analytical treatment as that of Babchin et al. [10]. Therefore, numerical solutions have to be found. Fourth-order accurate central differences are used for spatial discretization using predictor and corrector numerical technique.     

ANALYTICAL SOLUTIONS FOR THE LAYERED GEO-MATERIALS SUBJECTED TO AN ARBITRARY POINT LOAD IN THE CARTESIAN COORDINATE

This paper presents analytical solutions for the stress and displacement field in elastic layered geo-materials induced by an arbitrary point load in the Cartesian coordinate system. The point load solutions can be obtained by referring to the integral transform and the transfer matrix technique. However, former solutions usually exist in the cylindrical coordinate system subjected to axisymmetric loading. Based on the proposed solutions in the Cartesian coordinate, it is very easy to solve asymmetric problems and consider the condition with internal loads in multi-layered geo-materials. Moreover, point load solutions can be used to construct solutions for analytical examination of elastic problems and incorporated into numerical schemes such as boundary element methods. The results discussed in this paper indicate that there is no problem in the evaluation of the point load solutions with high accuracy and efficiency, and that the material non-homogeneity has a significant effect on the elastic field due to adjacent loading.