Existence and Multiplicity of Solutions for Fractional Elliptic Problems with Discontinuous Nonlinearities

We consider the following fractional elliptic problem:

$$\begin{aligned} (P)\left\{ \begin{array}{ll} (-\Delta )^s u = f(u) H(u-\mu )&{} \quad \text{ in } \ \Omega ,\\ u =0 &{}\quad \text{ on } \ \mathbb{{R}}^n {\setminus } \Omega , \end{array} \right. \end{aligned}$$

where \((-\Delta )^s, s\in (0,1)\) is the fractional Laplacian, \(\Omega \) is a bounded domain of \(\mathbb{{R}}^n,(n\ge 2s)\) with smooth boundary \(\partial \Omega ,\) H is the Heaviside step function, f is a given function and \(\mu \) is a positive real parameter. The problem (P) can be considered as simplified version of some models arising in different contexts. We employ variational techniques to study the existence and multiplicity of positive solutions of problem (P).

     

Exploration of the reactivity of N2O5 with two Si(OH)4 monomers using electronic structure methods

The heterogeneous uptake of N₂O₅ on mineral dust particles may play an important role in the removal of nitrogen oxides from the atmosphere. However, the reaction of N₂O₅ with the mineral particles is not well understood. The reaction of N₂O₅ with two Si(OH)₄ monomers is explored using theoretical methods. This study represents a first step towards understanding the interaction of N₂O₅ with the hydroxyl groups of silica particles. Energies are calculated using MP2 single point calculations on the B3LYP optimized geometries and including B3LYP thermodynamic corrections. Four mechanisms are considered for the formation of two HNO₃ and one H₆Si₂O₇. The rate limiting activation barrier of the most favorable path is found to be 12.5 kcal mol^?1. This reaction appears to be more favorable than the hydrolysis of N₂O₅ with one water molecule. These results are in agreement with experimental observations, which show that N₂O₅ reacts with OH groups of Saharan dust to form nitrate. © 2012 Wiley Periodicals, Inc.     

Description of Even–Even 114–134Xe Isotopes in the Transitional Region of IBM

Properties of ^114–134Xe isotopes are studied in the U(5)?SO(6) transitional region of Interacting Boson Model (IBM-1). The energy levels and B(E2) transition rates are calculated via the affine SU(1,1) Lie Algebra. The agreement with the most recent experimental is acceptable. The evaluated Hamiltonian control parameters suggest a spherical to γ-soft shape transition and propose the ¹³⁰Xe nucleus as the best candidate for the E(5) symmetry.     

Wave mode diffusion and propagation in structural wave guide under Varying Temperature

A numerical approach is presented to study the guided wave propagation through periodic specimen with thermal dependence of material properties. There is a great interest in extending the skills of the wave finite element (WFE) method to figure out the variations in the wave propagation properties due to temperature fluctuations. Thermal effects on the dispersion curves thereby on group velocity are discussed. Comparisons between numerical results and analytical developments for various temperatures are given to prove the effectiveness of the proposed approach to predict the sensitivity of guided wave propagation characteristics in presence of temperature variations.     

Familial predictors of childhood shyness: a study of the United Arab Emirates population

OBJECTIVES: Phobic anxiety disorders generally breed true. In this regard, family studies have suggested an association between childhood shyness and maternal social phobia. In this study, the relationship between childhood shyness and maternal social anxiety was examined. SUBJECTS AND METHODS: 203 5-year-old children from an Arabian Gulf community and their mothers were evaluated. The children were assessed in stage 1 using the shyness scale of Stevenson-Hinde and Glover and the Preschool Behavior Checklist (PBCL), while mothers completed the Liebowitz Social Anxiety Scale. In the second stage, blind clinical interviews were carried out to ascertain the diagnosis of psychiatric diagnoses, if any, using DSM-IV criteria. RESULTS: 27% of the children were identified as shy using the shyness scale of Stevenson-Hinde and Glover and 19% scored above the cutoff for behavioral disturbance on the PBCL. Child shyness was associated with female gender and maternal social anxiety as indicated by scores on the Liebowitz Social Anxiety Scale, while an inverse relationship was noted with behavioral disturbance. The odds of the child having a high shyness score was increased if the mother had social anxiety (odds ratio = 2.14) and the child lived in a family that was 'not socially active' (odds ratio = 1.42). CONCLUSION: Our initial findings suggest that there may be a complex interaction between maternal social anxiety and family sociability in childhood shyness. Prospective longitudinal work is indicated.     

Cálculo eficiente de las energías de formación de escalones dobles en materiales BCC

Motion of screw dislocations in BCC materials at low temperature is believed to be related to the formation of mobile kinks on the dislocation line. Therefore, the accurate prediction of kink nucleation energies is required to fully describe mobility of screw dislocations in these materials. Studies of fundamental dislocation processes at atomic length scale are numerically and computationally intensive problems. This work studies the calculation of zero-stress formation energies of kink-pair configurations for BCC crystals. Our model for stored energy associated to a dislocation line configuration is based on the theory of discrete dislocations of Ariza and Ortiz. Its value is computed efficiently using an algorithm developed on the NVIDIA Compute Unified Device Architecture (CUDA). Results confirm those obtained using atomistic potentials and first principles calculations, and those based on the continuum theory of dislocations.     

Synthesis and properties of some 2,3‐disubstituted 6‐fluoro‐7‐(4‐methyl‐1‐piperazinyl)quinoxalines

The 2,3‐disubstituted 6‐fluoro‐7‐(4‐methyl‐1‐piperazinyl)‐quinoxalines ( 3–11 ) were synthesized for bioassay via reaction of 1.2‐diamino‐4‐fluoro‐5‐(4‐methyl‐1‐piperazinyl)benzene (2) with the appropriate 1,2‐dicarbonyl compounds. However, none of the tested compounds 3–11 showed significant in vitro activ ity against E. coli ATCC11229, S. aureus ATCC6538 and C.albicans SATCC10231.     

The chemical constituents of Capparis spinosa of Jordanian origin

Investigation of Capparis spinosa of Jordanian origin lead to isolation of two new compounds beta-sitosterylglucoside-6'-octadecanoate (1) and 3-methyl-2-butenyl-beta-glucoside (2). Linked Scan MS measurements were used to propose a mass fragmentation pattern for the alkaloid Cadabicine isolated here for the second time from nature.     

Heterocycles from nitrile oxides. II . 1,2,4-oxadiazin-6-ones

Condensation of arylnitrile oxides with α-amino acid esters, other than those of glycine and analine, has been found to constitute a synthetic route to the hitherto unknown 1,2,4-oxadiazin-6-ones 7. α-Amino alcohols yield with nitrile oxides the corresponding acyclic N-(arylhydroxamoyl)amino alcohols, which are also accessible by borohydride reduction of compounds 7 . In contrast, the adducts formed from nitrile oxides and α-amino acids are unstable; they decompose readily into the aldehyde, derived from the amino acid, together with the aldoxime, derived from the nitrile oxide. Both decomposition products are also formed when compounds 7 are subjected to mild hydrolysis.