An efficient linearization technique for mixed 0-1 polynomial problem

This paper addresses a new and efficient linearization technique to solve mixed 0-1 polynomial problems to achieve a global optimal solution. Given a mixed 0-1 polynomial term z=c_tx₁x₂…x_ny, where x₁,x₂,…,x_n are binary (0-1) variables and y is a continuous variable. Also, c_t can be either a positive or a negative parameter. We transform z into a set of auxiliary constraints which are linear and can be solved by exact methods such as branch and bound algorithms. For this purpose, we will introduce a method in which the number of additional constraints is decreased significantly rather than the previous methods proposed in the literature. As is known in any operations research problem decreasing the number of constraints leads to decreasing the mathematical computations, extensively. Thus, research on the reducing number of constraints in mathematical problems in complicated situations have high priority for decision makers. In this method, each n-auxiliary constraints proposed in the last method in the literature for the linearization problem will be replaced by only 3 novel constraints. In other words, previous methods were dependent on the number of 0-1 variables and therefore, one auxiliary constraint was considered per 0-1 variable, but this method is completely independent of the number of 0-1 variables and this illustrates the high performance of this method in computation considerations. The analysis of this method illustrates the efficiency of the proposed algorithm.     

A piecewise-linearized algorithm based on the Krylov subspace for solving stiff ODEs

Numerical methods for solving Ordinary Differential Equations (ODEs) have received considerable attention in recent years. In this paper a piecewise-linearized algorithm based on Krylov subspaces for solving Initial Value Problems (IVPs) is proposed. MATLAB versions for autonomous and non-autonomous ODEs of this algorithm have been implemented. These implementations have been compared with other piecewise-linearized algorithms based on Padé approximants, recently developed by the authors of this paper, comparing both precisions and computational costs in equal conditions. Four case studies have been used in the tests that come from stiff biology and chemical kinetics problems. Experimental results show the advantages of the proposed algorithms, especially when the dimension is increased in stiff problems.     

Discrete-time orthogonal spline collocation methods for the nonlinear Schrödinger equation with wave operator

In this paper, discrete-time orthogonal spline collocation schemes are proposed for the nonlinear Schrödinger equation with wave operator. These schemes are constructed by using orthogonal spline collocation approaches combined with finite difference methods. The conservative property, the convergence, and the stability of these methods are theoretically analyzed and also verified by extensive numerical experiments. In addition, some interesting phenomena which require further theoretical analysis are discussed numerically.     

Pressure projection stabilized finite element method for Stokes problem with nonlinear slip boundary conditions

In this paper, we consider the pressure projection stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions whose variational formulation is the variational inequality problem of the second kind with the Stokes operator. The H¹ and L² error estimates for the velocity and the L² error estimate for the pressure are obtained. Finally, the numerical results are displayed to verify the theoretical analysis.     

Comment on “New types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity”

In this comment we analyze the paper [Abdelhalim Ebaid, S.M. Khaled, New types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity, J. Comput. Appl. Math. 235 (2011) 1984-1992]. Using the traveling wave, Ebaid and Khaled have found “new types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity”. We demonstrate that the authors studied the well-known nonlinear ordinary differential equation with the well-known general solution. We illustrate that Ebaid and Khaled have looked for some exact solution for the reduction of the nonlinear Schrodinger equation taking the general solution of the same equation into account.     

Short sales in Log-robust portfolio management

This paper extends the Log-robust portfolio management approach to the case with short sales, i.e., the case where the manager can sell shares he does not yet own. We model the continuously compounded rates of return, which have been established in the literature as the true drivers of uncertainty, as uncertain parameters belonging to polyhedral uncertainty sets, and maximize the worst-case portfolio wealth over that set in a one-period setting. The degree of the manager’s aversion to ambiguity is incorporated through a single, intuitive parameter, which determines the size of the uncertainty set. The presence of short-selling requires the development of problem-specific techniques, because the optimization problem is not convex. In the case where assets are independent, we show that the robust optimization problem can be solved exactly as a series of linear programming problems; as a result, the approach remains tractable for large numbers of assets. We also provide insights into the structure of the optimal solution. In the case of correlated assets, we develop and test a heuristic where correlation is maintained only between assets invested in. In computational experiments, the proposed approach exhibits superior performance to that of the traditional robust approach.     

Decay of Solutions to a 2D Schroedinger Equation

Let u ∈ C（1R, H1） be the solution to the initial value problem for a 2D semilinear Schr6dinger equation with exponential type nonlinearity, given in [1]. We prove that the Lr norms of u decay as t→±∞, provided that r〉2.     

Determination of Imidacloprid in Tomato Grown in Greenhouse Based on Copper(II) Phthalocyanine Modified Carbon Ceramic Electrode by Differential Pulse Voltammetry

A new sol‐gel derived electrocatalytic carbon ceramic electrode was prepared by incorporating copper(II) phthalocyanine (CuPc) in a carbon ceramic network. This electrode was used as a sensitive electrochemical sensor for determination of the insecticide Imidacloprid (1‐(6‐chloro‐3‐pyridylmethyl)‐N‐nitro‐imidazolidin‐2‐ylideneamine) by differential pulse voltammetry (DPV). The resulting modified electrode exhibits a cathodic peak potential shifted positively and an increasing in cathodic peak current in comparison with unmodified electrode. The redox properties of this modified electrode at various pH values and CuPc percentage were investigated. The catalytic current obtained from differential pulse voltammetry is linearly dependent on Imidacloprid concentration over the two linear ranges of 0.67‐17 μM and 17‐93 μM with correlation coefficient of R² = 0.9999 and R² = 0.990, respectively. The detection limit for Imidacloprid was found to be 0.28 μM according to lower linear range. Possible interferences from several common pesticides were also evaluated. The inherent stability, high sensitivity, low detection limit and low cost for each preparation are advantages of this sensor. Determination of Imidacloprid in commercial formulation and residual Imidacloprid in tomato grown in greenhouse (protected cultivation) was also conducted. The results obtained from commercial formulation were completely consistent with those obtained through the standard high‐performance liquid chromatography (HPLC) method.     

Micellar nucleation differential microemulsion polymerization

Polymer nanoparticles within the range of 2–5 nm with a solid content of more than 13 wt.% and a narrow molecular weight polydispersity (Mw/Mn ∼ 1.1) were for the first time prepared using a micellar nucleation differential microemulsion polymerization system emulsified by sodium dodecyl sulfate (SDS), with SDS/monomer (methyl methacrylate) and SDS/H₂O weight ratios of up to 1:16 and 1:100, respectively. It was found that for benzoyl peroxide (BPO), micellar nucleation is more favorable for the synthesis of smaller polymer nanoparticles than ammonium persulfate (APS) which gives rise to homogeneous nucleation and 2,2′-azobisisobutyronitrile (AIBN) which involves partially heterogeneous nucleation. In the polymerization process, there exists a critical stability concentration (CSC) of SDS, above which the size of the nanoparticles is to be minimized and stabilized. With an increase in the monomer addition rate, the polymerization system changes from a microemulsion system to an emulsion system. A mechanism was proposed to describe the micellar nucleation process of differential microemulsion polymerization. This study may contribute to the development of fine polymer nanoparticles for drug delivery systems.     

MassUntangler: a novel alignment tool for label-free liquid chromatography-mass spectrometry proteomic data

Liquid chromatography-mass spectrometry (LC-MS) has become an important analytical tool for quantitative proteomics and biomarker discovery. In the label-free differential LC-MS approach computational methods are required for an accurate alignment of peaks extrapolated from the experimental raw data accounting for retention time and m/z signals intensity, which are strongly affected by sample matrix and instrumental performance. A novel procedure "MassUntangler" for pairwise alignment has been developed, relying on a pattern-based matching algorithm integrated with filtering algorithms in a multi-step approach. The procedure has been optimized employing a two-step approach. Firstly, low-complexity LC-MS data derived from the enzymatic digestion of two standard proteins have been analyzed. Then, the algorithm's performance has been evaluated by comparing the results with other achieved using state-of-the-art alignment tools. In the second step, our algorithm has been used for the alignment of high-complexity LC-MS data consisting of peptides obtained by an Escherichia coli lysate available from a public repository previously used for the comparison of other alignment tools. MassUntangler gave excellent results in terms of precision scores (from 80% to 93%) and recall scores (from 68% to 89%), showing performances similar and even better than the previous developed tools. Considering the mass spectrometry sensitivity and accuracy, this approach allows the identification and quantification of peptides present in a biological sample at femtomole level with high confidence. The procedure's capability of aligning LC-MS data previously corrected for distortion in retention time has been studied through a hybrid approach, in which MassUntangler was interfaced with the OpenMS TOPP tool MapAligner. The hybrid aligner yielded better results, showing that an integration of different bioinformatic approaches for accurate label-free LC-MS data alignment should be used.