BiVO<Subscript>4</Subscript>-NPs: an efficient nano-catalyst for the synthesis of biscoumarins,bis(indolyl)methanes and 3,4-dihydropyrimidin-2(1<Emphasis Type="Italic">H</Emphasis>)-ones (thiones) derivatives

BiVO₄-NPs can be used as an efficient and reusable nano-catalyst for the promotion of the synthesis of biscoumarins, bis(indolyl)methanes and 3,4-dihydropyrimidin-2(1H)-ones (thiones) derivatives. The structures of the products were characterized by IR, ¹H NMR and ¹³C NMR spectroscopy and comparison with the authentic samples. Easy work-up procedure, excellent yields, short reaction times and reusability of the catalyst are some advantages of this work. In addition, in this article and for the first time, the preparation of 3,4-dihydropyrimidin-2(1H)-ones and -thiones from the protected derivatives of aldehydes including oximes, semicarbazones and 1,1-diacetates is reported.     

Synthesis of new dyes containing double tetrazole groups for sensitization of TiO<Subscript>2</Subscript> nanoparticles in dye-sensitized solar cells

Di(1H-tetrazol-5-yl)methane is employed as a new electron acceptor group in the synthesis of two metal-free organic dyes containing triphenylamine donor group. Dye-sensitized nanocrystalline TiO₂ solar cell (DSSC) applying these novel dyes is constructed for consideration of their photovoltaic properties. The electronic properties of the dyes are also considered with the aid of theoretical calculations. The DSSC constructed from 4-(2,2-di(1H-tetrazol-5-yl)vinyl)-N,N-diphenylaniline (T1) shows a short-circuit photocurrent density of 13.38 mA cm^?2, an open circuit voltage of 578 mV, and a fill factor of 0.54, with a resulted solar energy-to-electricity conversion efficiency of 4.18% under simulated 1 sun irradiation (100 mW cm^?2). This result reveals that the dye with the di(1H-tetrazol-5-yl)methane anchoring group injects more electrons to the conduction band of TiO₂ in comparison with its analogs with single tetrazole ring in their anchoring group. It is found that in spite of a red-shift of the absorption spectrum resulted from the lengthening of the molecule, the dye with two di(1H-tetrazol-5-yl)methane groups gives lower performance than the dye with a single electron acceptor.     

Multiple solutions for non-homogeneous degenerate Schrödinger equations in cone Sobolev spaces

The present paper deals with the study of semilinear and non-homogeneous Schrödinger equations on a manifold with conical singularity. We provide a suitable constant by Sobolev embedding constant and for p ∈ (2, 2?) with respect to non-homogeneous term g(x) ∈ L ₂ ^n/2 (B), which helps to find multiple solutions of our problem. More precisely, we prove the existence of two solutions to the problem 1.1 with negative and positive energy in cone Sobolev space H _2,0 ^1,n/2 (B). Finally, we consider p = 2 and we prove the existence and uniqueness of Fuchsian-Poisson problem.     

A spectral element method using the modal basis and its application in solving second‐order nonlinear partial differential equations

We present a high‐order spectral element method (SEM) using modal (or hierarchical) basis for modeling of some nonlinear second‐order partial differential equations in two‐dimensional spatial space. The discretization is based on the conforming spectral element technique in space and the semi‐implicit or the explicit finite difference formula in time. Unlike the nodal SEM, which is based on the Lagrange polynomials associated with the Gauss–Lobatto–Legendre or Chebyshev quadrature nodes, the Lobatto polynomials are used in this paper as modal basis. Using modal bases due to their orthogonal properties enables us to exactly obtain the elemental matrices provided that the element‐wise mapping has the constant Jacobian. The difficulty of implementation of modal approximations for nonlinear problems is treated in this paper by expanding the nonlinear terms in the weak form of differential equations in terms of the Lobatto polynomials on each element using the fast Fourier transform (FFT). Utilization of the Fourier interpolation on equidistant points in the FFT algorithm and the enough polynomial order of approximation of the nonlinear terms can lead to minimize the aliasing error. Also, this approach leads to finding numerical solution of a nonlinear differential equation through solving a system of linear algebraic equations. Numerical results for some famous nonlinear equations illustrate efficiency, stability and convergence properties of the approximation scheme, which is exponential in space and up to third‐order in time. Copyright © 2014 John Wiley & Sons, Ltd.     

Selecting symmetric weights as a secondary goal in DEA cross-efficiency evaluation

In data envelopment analysis (DEA), the cross-efficiency evaluation method introduces a cross-efficiency matrix, in which the units are self and peer evaluated. A problem that possibly reduces the usefulness of the cross-efficiency evaluation method is that the cross-efficiency scores may not be unique due to the presence of alternate optima. So, it is recommended that secondary goals be introduced in cross-efficiency evaluation. In this paper we propose the symmetric weight assignment technique (SWAT) that does not affect feasibility and rewards decision making units (DMUs) that make a symmetric selection of weights. A numerical example is solved by our proposed method and its solution is compared with those of alternative approaches.     

On the Roman Bondage Number of Planar Graphs

A Roman dominating function on a graph G is a function f : V(G) → {0, 1, 2} satisfying the condition that every vertex u for which f (u) = 0 is adjacent to at least one vertex v for which f (v) = 2. The weight of a Roman dominating function is the value f (V(G)) = ?_{u ? V(G)} f (u){f (V(G)) = \sum_{u\in V(G)} f (u)}. The Roman domination number, γ _R (G), of G is the minimum weight of a Roman dominating function on G. The Roman bondage number b _R (G) of a graph G with maximum degree at least two is the minimum cardinality of all sets E^￠ í E(G){E^{\prime} \subseteq E(G)} for which γ _R (G − E′) > γ _R (G). In this paper we present different bounds on the Roman bondage number of planar graphs.     

Diversity of phage-displayed libraries of peptides during panning and amplification

The amplification of phage-displayed libraries is an essential step in the selection of ligands from these libraries. The amplification of libraries, however, decreases their diversity and limits the number of binding clones that a screen can identify. While this decrease might not be a problem for screens against targets with a single binding site (e.g., proteins), it can severely hinder the identification of useful ligands for targets with multiple binding sites (e.g., cells). This review aims to characterize the loss in the diversity of libraries during amplification. Analysis of the peptide sequences obtained in several hundred screens of peptide libraries shows explicitly that there is a significant decrease in library diversity that occurs during the amplification of phage in bacteria. This loss during amplification is not unique to specific libraries: it is observed in many of the phage display systems we have surveyed. The loss in library diversity originates from competition among phage clones in a common pool of bacteria. Based on growth data from the literature and models of phage growth, we show that this competition originates from growth rate differences of only a few percent for different phage clones. We summarize the findings using a simple two-dimensional "phage phase diagram", which describes how the collapse of libraries, due to panning and amplification, leads to the identification of only a subset of the available ligands. This review also highlights techniques that allow elimination of amplification-induced losses of diversity, and how these techniques can be used to improve phage-display selection and enable the identification of novel ligands.     

Bis(methyltri‐o‐tolylphosphonium) octaiodide

In the crystal structure of the title compound, 2C₂₂H₂₄P⁺·I₈²⁻, the I₈²⁻ anion is located on a crystallographic inversion centre and consists of two tri‐iodide anions linked by di‐iodine at angles of 89.92 (4)° to form a planar `Z'‐shaped dianion. The octaiodides are linked via long‐range interactions [3.877 (11) Å] into infinite polyiodide ribbons. This is the first example of a structure containing an [(o‐tolyl)₃PMe]⁺ cation, and the C_Me—P—C—C_Me torsion angles of −54.0 (11), −51.3 (11) and −48.2 (11)° indicate that the configuration is exo₃.     

Buckling analysis of stringer-stiffened laminated cylindrical shells with nonuniform eccentricity

In this study, the influence of nonuniformity of eccentricity of stringers on the general axial buckling load of stiffened laminated cylindrical shells with simply supported end conditions is investigated. The critical loads are calculated using Love’s First-order Shear Deformation Theory and solved using the Rayleigh-Ritz procedure. The effects of the shell length-to-radius ratio, shell thickness-to-radius ratio, number of stringers, and stringers depth-to-width ratio on the buckling load of nonuniformly eccentric shells, are examined. The research demonstrates that an appropriate nonuniform distribution of eccentricity of stringers leads the buckling load to increase significantly.     

A Langevin equation for the rates of currency exchange based on the Markov analysis

We propose a method for analyzing the data for the rates of exchange of various currencies versus the U.S. dollar. The method analyzes the return time series of the data as a Markov process, and develops an effective equation which reconstructs it. We find that the Markov time scale, i.e., the time scale over which the data are Markov-correlated, is one day for the majority of the daily exchange rates that we analyze. We derive an effective Langevin equation to describe the fluctuations in the rates. The equation contains two quantities, D⁽¹⁾ and D⁽²⁾, representing the drift and diffusion coefficients, respectively. We demonstrate how the two coefficients are estimated directly from the data, without using any assumptions or models for the underlying stochastic time series that represent the daily rates of exchange of various currencies versus the U.S. dollar.