A New Complexity Analysis for Full-Newton Step Infeasible Interior-Point Algorithm for Horizontal Linear Complementarity Problems

In this paper, we first present a full-Newton step feasible interior-point algorithm for solving horizontal linear complementarity problems. We prove that the full-Newton step to the central path is quadratically convergent. Then, we generalize an infeasible interior-point method for linear optimization to horizontal linear complementarity problems based on new search directions. This algorithm starts from strictly feasible iterates on the central path of a perturbed problem that is produced by a suitable perturbation in the horizontal linear complementarity problem. We use the so-called feasibility steps that find strictly feasible iterates for the next perturbed problem. By using centering steps for the new perturbed problem, we obtain a strictly feasible iterate close enough to the central path of the new perturbed problem. The complexity of the algorithm coincides with the best known iteration bound for infeasible interior-point methods.     

Copper/Graphene/Clay Nanohybrid: A Highly Efficient Heterogeneous Nanocatalyst for the Synthesis of Novel 1,2,3‐Triazolyl Carboacyclic Nucleosides via ‘Click’ Huisgen 1,3‐Dipolar Cycloaddition

A very mild and highly efficient synthesis of some novel 1H‐1,2,3‐triazolyl carboacyclic nucleosides via a ‘Click’ Huisgen cycloaddition of N‐propargyl nucleobases and azido alcohols using Cu/aminoclay/reduced graphene oxide nanohybrid (Cu/AC/r‐GO nanohybrid) as nanocatalyst is described. The preparation and characterization of Cu/AC/r‐GO nanohybrid are discussed. This catalyst was characterized by X‐ray diffraction, FT‐IR, TEM, and energy‐dispersive analysis of X‐ray techniques. Cu/AC/r‐GO nanohybrid is a stable and highly efficient heterogeneous nanocatalyst that can be easily prepared, used, and restored from the reaction mixture by simple filtration, and reused for many consecutive trials without significant decrease in activity.     

Response surface optimization of heterogeneous Fenton-like degradation of sulfasalazine using Fe-impregnated clinoptilolite nanorods prepared by Ar-plasma

Research on Chemical Intermediates - Optimization of sulfasalazine degradation using the heterogeneous Fenton-like process in batch mode was investigated by response surface methodology. The...     

Rearrangements and minimization of the principal eigenvalue of a nonlinear Steklov problem

This paper, motivated by Del Pezzo et al. (2006) [1], discusses the minimization of the principal eigenvalue of a nonlinear boundary value problem. In the literature, this type of problem is called Steklov eigenvalue problem. The minimization is implemented with respect to a weight function. The admissible set is a class of rearrangements generated by a bounded function. We merely assume the generator is non-negative in contrast to [1], where the authors consider weights which are positively away from zero, in addition to being two-valued. Under this generality, more physical situations can be modeled. Finally, using rearrangement theory developed by Geoffrey Burton, we are able to prove uniqueness of the optimal solution when the domain of interest is a ball.     

Design of a Composite Membrane with Patches

This paper is concerned with minimization and maximization problems of eigenvalues. The principal eigenvalue of a differential operator is minimized or maximized over a set which is formed by intersecting a rearrangement class with an affine subspace of finite co-dimension. A solution represents an optimal design of a 2-dimensional composite membrane Ω, fixed at the boundary, built out of two different materials, where certain prescribed regions (patches) in Ω are occupied by both materials. We prove existence results, and present some features of optimal solutions. The special case of one patch is treated in detail.     

Artinian cofinite modules over complete Noetherian local rings

Let (R, m) be a complete Noetherian local ring, I an ideal of R and M a nonzero Artinian R-module. In this paper it is shown that if p is a prime ideal of R such that dim R/p = 1 and (0:M p) is not finitely generated and for each i ? 2 the R-module Ext _R ⁱ (M,R/p) is of finite length, then the R-module Ext _R ¹ (M, R/p) is not of finite length. Using this result, it is shown that for all finitely generated R-modules N with Supp(N) ? V (I) and for all integers i ? 0, the R-modules Ext _R ⁱ (N,M) are of finite length, if and only if, for all finitely generated R-modules N with Supp(N) ? V (I) and for all integers i ? 0, the R-modules Ext _R ⁱ (M,N) are of finite length.     

A clustering ensemble framework based on elite selection of weighted clusters

Each clustering algorithm usually optimizes a qualification metric during its progress. The qualification metric in conventional clustering algorithms considers all the features equally important; in other words each feature participates in the clustering process equivalently. It is obvious that some features have more information than others in a dataset. So it is highly likely that some features should have lower importance degrees during a clustering or a classification algorithm; due to their lower information or their higher variances and etc. So it is always a desire for all artificial intelligence communities to enforce the weighting mechanism in any task that identically uses a number of features to make a decision. But there is always a certain problem of how the features can be participated in the clustering process (in any algorithm, but especially in clustering algorithm) in a weighted manner. Recently, this problem is dealt with by locally adaptive clustering (LAC). However, like its traditional competitors the LAC suffers from inefficiency in data with imbalanced clusters. This paper solves the problem by proposing a weighted locally adaptive clustering (WLAC) algorithm that is based on the LAC algorithm. However, WLAC algorithm suffers from sensitivity to its two parameters that should be tuned manually. The performance of WLAC algorithm is affected by well-tuning of its parameters. Paper proposes two solutions. The first is based on a simple clustering ensemble framework to examine the sensitivity of the WLAC algorithm to its manual well-tuning. The second is based on cluster selection method.     

Rearrangements in Real Estate Investments

In this note we consider an investment problem in real estate. We show that it can be formulated in terms of a constrained optimization problem, and this leads to a linear rearrangement optimization problem. We address existence, uniqueness, and symmetry of the optimal solution.     

Effect of operational parameters on degradation of Malachite Green by ultrasonic irradiation

The aim of the present study was to apply ultrasonic technique to remove Malachite Oxalate Green (MG) from aqueous solution. An ultrasonic bath with frequency of 35 kHz was used to investigate the effect of different operational parameters such as MG concentration, power density, temperature, mechanical agitation and addition of EtOH, 2-PrOH and iso-BuOH. Decolorization of MG follows a first order kinetics and hydroxyl radicals have an important role in degradation of MG. The apparent reaction rate constant (k(ap)) was influenced by variation of operational parameters. The activation energy was 30.95 kJ/mol in temperature range of 21-34 degrees C, suggesting a diffusion-controlled reaction. Alcohols act as hydroxyl radicals scavengers having undesirable contribution. UV-vis spectral change of MG showed hypsochromic shift occurred with increasing sonication time, proposing N-demethylation process of MG.     

Synthesis of reduced graphene oxide functionalized with methyl red dye and its role in enhancing photoactivity in TiO2–IL/WO3 composite for toluene degradation

Research on Chemical Intermediates - A nanostructured composite material was produced through sol–gel-assisted ionic liquid (IL) synthesized TiO2, WO3 and functionalized reduced graphene...