A Regularization Technique for a Class of Singular Integral Problems

We discuss here a method for the extraction of the singularparts of a variety of problems involving singular integrands.The method is based on the systematic use of a partial fractionidentity; we give here applications to numerical quadratureand to the solution of singular integral equations of variouskinds.     

Homogenization of Periodic Systems with Large Potentials

We consider the homogenization of a system of second-order equations with a large potential in a periodic medium. Denoting by the period, the potential is scaled as ^–2. Under a generic assumption on the spectral properties of the associated cell problem, we prove that the solution can be approximately factorized as the product of a fast oscillating cell eigenfunction and of a slowly varying solution of a scalar second-order equation. This result applies to various types of equations such as parabolic, hyperbolic or eigenvalue problems, as well as fourth-order plate equation. We also prove that, for well-prepared initial data concentrating at the bottom of a Bloch band, the resulting homogenized tensor depends on the chosen Bloch band. Our method is based on a combination of classical homogenization techniques (two-scale convergence and suitable oscillating test functions) and of Bloch waves decomposition.     

Homogenization of the Schrödinger Equation and Effective Mass Theorems

In this paper we discuss two different models of dependent percolation on the graph ². These models can be thought of as percolation in a random environment. They were inspired by the work of McCoy and Wu [7,8] on the Ising model in a random environment as well as other models of particle systems in a random environment [9, 5, 6, 3]. We show that both models of dependent percolation exhibit phase transitions. This proves a version of stability for percolation on ² and proves a conjecture of Jonasson, Mossel and Peres [4], who proved a similar result on ³.Research supported in part by an NSF postdoctoral fellowshipAcknowledgement I would like to thank David Levin and Yuval Peres for introducing me to the problem. I would also like to thank Yuval Peres and Eric Babson for helpful conversations.     

Some natural aqueous extracts of plants as green inhibitor for carbon steel corrosion in 0.5 M sulfuric acid

The inhibiting impact of natural aqueous extracts of some plants such as curcumin, parsley and cassia bark extracts for the corrosion of carbon steel (C-steel) in 0.5 M H₂SO₄ solution was inspected utilizing some techniques such as galvanostatic and potentiodynamic anodic polarization and weight loss measurements. Outcomes indicated that the percentage inhibition efficiency increases with increasing the concentration of the extract due to its horizontal adsorption on the C-steel surface. The process of adsorption is followed by the Temkin isotherm. These natural extracts acted as pitting corrosion inhibitors by shifting the pitting potential to more noble values. The sequence of inhibition efficiency of the natural extracts decreases in the following order: cassia bark extract > parsley extract > curcumin extract. This arrangement is related to the molecular size of the major components of the three natural extracts used.     

Spectral problem with Steklov condition on a thin perforated interface

A two-dimensional Steklov-type spectral problem for the Laplacian in a domain divided into two parts by a perforated interface with a periodic microstructure is considered. The Steklov boundary condition is set on the lateral sides of the channels, a Neumann condition is specified on the rest of the interface, and a Dirichlet and Neumann condition is set on the outer boundary of the domain. Two-term asymptotic expansions of the eigenvalues and the corresponding eigenfunctions of this spectral problem are constructed.     

Detecting electronic states at stacking faults in magnetic thin films by tunneling spectroscopy

Co islands grown on Cu(111) with a stacking fault at the interface present a conductance in the empty electronic states larger than the Co islands that follow the stacking sequence of the Cu substrate. Electrons can be more easily injected into these faulted interfaces, providing a way to enhance transmission in future spintronic devices. The electronic states associated with the stacking fault are visualized by tunneling spectroscopy, and its origin is identified by band structure calculations.     

Ultra high performance liquid chromatography with mass spectrometry method for the simultaneous determination of phenolic constituents in honey from various floral sources using multiwalled carbon nanotubes as extraction sorbents

An ultra high performance liquid chromatography with mass spectrometry method has been developed for the simultaneous separation, identification and determination of 22 phenolic constituents in honey from various floral sources from Yemen. Solid‐phase extraction was used for extraction of the target phenolic constituents from honey samples, while multiwalled carbon nanotubes were used as solid‐phase adsorbent. The chromatographic separation of all phenolic constituents was performed on a BEH C₁₈ column using a linear gradient elution with a binary mobile phase mixture of aqueous 0.1% formic acid and methanol. The quantitation was carried out in selected ion reaction monitoring acquisition mode. The total amount of phenolic acids, flavonoids and other phenols in each analyzed honey was found in the range of 338–3312, 122–5482 and 2.4–1342 μg/100 g of honey, respectively. 4‐Hydroxybenzoic acid was found to be the major phenolic acid. The main detected flavonoid was chrysin, while cinnamic acid was found to be the major other phenol compound. The regeneration of solid phase adsorbent to be reused and recovery results confirm that the proposed method could be potentially used for the routine analysis of phenolic constituents in honey extract.     

Design and chemical synthesis of [1,2,4]triazol[1,5-c]pyrimidin-5-yl amines, a novel class of VEGFR-2 kinase inhibitors

The Letter describes a facile approach to 7,8-dihydro[1,2,4]triazol[1,5-c]pyrimidin-5-yl amines, a novel class of potent inhibitors of vascular endothelial growth factor receptor II (VEGFR-2). The synthetic sequence is centered around preparation of the key 3(5)-cyanomethyl-1,2,4-triazole intermediates and their Knoevenagel condensation with aromatic aldehydes. A subsequent three-step conversion of Knoevenagel adducts involving a reduction of vinyl nitriles followed by the reaction of the resulting amines with aryl isothiocyanates and cyclization of the respective thioureas yielded targeted heterocycles as a 1:1 mixture of tautomers. A representative molecule featured sound activity against VEGFR-2 in both enzymatic and cellular assays.     

On the analysis of a kind of nonlinear Sobolev equation through locally applied pseudo‐spectral meshfree radial point interpolation

In this study, we develop an approximate formulation for two‐dimensional nonlinear Sobolev problems by focusing on pseudospectral meshless radial point interpolation (PSMRPI) which is a kind of locally applied radial basis function interpolation and truthfully a meshless approach. In the PSMRPI method, the nodal points do not need to be regularly distributed and can even be quite arbitrary. It is easy to have high order derivatives of unknowns in terms of the values at nodal points by constructing operational matrices. The convergence and stability of the technique in some sense are studied via some examples to show the validity and trustworthiness of the PSMRPI technique.