Solving the multi-commodity capacitated multi-facility Weber problem using Lagrangean relaxation and a subgradient-like algorithm

The Multi-commodity Capacitated Multi-facility Weber Problem (MCMWP) is concerned with locating I-capacitated facilities in the plane in order to satisfy the demands of J customers for K commodities so that the total transportation cost is minimized. We propose a Lagrangean relaxation scheme and a subgradient-like algorithm based on the relaxation of the capacity and commodity bundle constraints. The resulting subproblem is a variant of the well-known Multi-facility Weber Problem and it can be solved by using column generation and branch-and-price on an equivalent set covering formulation, which is accurate but extremely inefficient. Therefore, we devise different strategies to increase the efficiency. They mainly benefit from the effective usage of the lower and upper bounds on the optimal value of the Lagrangean subproblem. On the basis of extensive computational tests, we can say that they increase the efficiency considerably and result in accurate Lagrangean heuristics.     

On co-ordinated quasi-convex functions

A function f: I → ?, where I ? ? is an interval, is said to be a convex function on I if $$f(tx + (1 - t)y) \le tf(x) + (1 - t)f(y)$$ holds for all x, y ∈ I and t ∈ [0, 1]. There are several papers in the literature which discuss properties of convexity and contain integral inequalities. Furthermore, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations. We define some new classes of convex functions that we name quasi-convex, Jensenconvex, Wright-convex, Jensen-quasi-convex and Wright-quasi-convex functions on the coordinates. We also prove some inequalities of Hadamard-type as Dragomir’s results in Theorem 5, but now for Jensen-quasi-convex and Wright-quasi-convex functions. Finally, we give some inclusions which clarify the relationship between these new classes of functions.     

The synthesis,characterization and antibacterial activities of dinuclear Ni(II), Cu(II) and Fe(III) Schiff base complexes

Schiff base; N,N′-bis-(2-hydroxy-1-naphthaldimine)-1,3-diaminopropanol (napdapOH) reacts with metal chlorides to form dinuclear complexes of the type [M₂L₂] · nCl₂ where M = Ni, Cu, Fe and n = 0, 1. Schiff base complexes were characterized by using FT-IR, LC-MS, magnetic moments and conductance measurements. Coordination was found to be through the phenolic oxygen atoms and azomethine nitrogen atoms. The electronic properties of the compounds were investigated theoretically by performing semiempirical molecular orbital theory PM3 method in Hyperchem 7 (Release). The antibacterial activities of the compounds were investigated against Escherichia coli ATCC 11230, Bacillus subtilis RSKK 244, Bacillus megaterium RSKK 5117, Salmonella enteritidis ATCC 13076, Staphylococcus aureus ATCC 25923 by using microdilution method.     

Fractional optimal control of a 2-dimensional distributed system using eigenfunctions

This paper presents an eigenfunctions expansion based scheme for Fractional Optimal Control (FOC) of a 2-dimensional distributed system. The fractional derivative is defined in the Riemann–Liouville sense. The performance index of a FOC problem is considered as a function of both state and control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equation (PFDE) containing two space parameters and one time parameter. Eigenfunctions are used to eliminate the terms containing space parameters and to define the problem in terms of a set of generalized state and control variables. For numerical computation Grünwald–Letnikov approximation is used. A direct numerical technique is proposed to obtain the state and the control variables. For a linear case, the numerical technique results into a set of algebraic equations which can be solved using a direct or an iterative scheme. The problem is solved for different number of eigenfunctions and time discretization. Numerical results show that only a few eigenfunctions are sufficient to obtain good results, and the solutions converge as the size of the time step is reduced.     

Suzuki reaction of aryl chlorides using saturated N‐heterocarbene ligands

From readily available starting materials, six 1,3‐dialkyl‐imidazolinium bromides ( 2a–f ) have been prepared and characterized by conventional spectroscopic methods and elemental analyses. The incorporation of saturated N‐heterocyclic carbenes into palladium precatalysts gives high catalyst activity in the Suzuki coupling of deactivated aryl chloride substrates in aqueous media. The complexes were generated in the presence of Pd(OAc)₂ by in situ deprotonation of 2a–f . © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:557–561, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20140     

Energy elastic effects and the concept of temperature in flowing polymeric liquids

The incorporation of energy elastic effects in the modeling of flowing polymeric liquids is discussed. Since conformational energetic effects are determined by structural features much smaller than the end-to-end vector of the polymer chains, commonly employed single conformation tensor models are insufficient to describe energy elastic effects. The need for a local structural variable is substantiated by studying a microscopic toy model with energetic effects in the setting of a generalized canonical ensemble. In order to examine the dynamics of flowing polymeric liquids with energy elastic effects, a thermodynamically admissible set of evolution equations is presented that accounts for the evolution of the microstructure in terms of a slow tensor, as well as a fast, local scalar variable. It is demonstrated that the temperature used in the definition of the heat flux is directly related to the Lagrange multiplier of the microscopic energy in the generalized canonical partition function. The temperature equation is discussed with respect to, first, the dependence of the heat capacity on the polymer conformation and, second, the possibility to measure experimentally the effects of the conformational energy.

N-Heterocyclic carbene-Pd(II)-PPh3 complexes as a new highly efficient catalyst system for the Sonogashira cross-coupling reaction: Synthesis,characterization and biological activities

A novel series of N-heterocyclic carbene-phosphine palladium(II) complexes has been synthesized and fully characterized by IR, ¹H NMR, ¹³C NMR, and ³¹P NMR spectroscopies, and elemental analysis. The new N-heterocyclic carbene (NHC)-phosphine palladium(II) complexes 3a–h have been easily prepared by the reaction of the corresponding PEPPSI (pyridine-enhanced precatalyst preparation stabilization and initiation) complexes 2a–h and triphenylphosphine in dichloromethane in high yields. These complexes were applied as catalyst precursors which efficiently catalyzed Sonogashira reactions between aryl bromides and phenylacetylene to afford the corresponding products in good yields. The bulky NHC-Pd-PPh₃ complexes 3 were tested against Gram-positive and Gram-negative bacteria to study their biological activity. All the complexes exhibit antibacterial against these organisms. Investigation of the anti-acetylcholinesterase activity of the studied complexes showed that compounds 3a and 3b exhibited moderate activity at 100 μg mL^?1 and product 3b is the most active.     

Direct C—H Bond Activation of Benzoxazole and Benzothiazole with Aryl Bromides Catalyzed by Palladium(II)‐N‐heterocyclic Carbene Complexes

Herein, we report that a series of novel palladium(II)‐NHC complexes (NHC=N‐heterocyclic carbene) were synthesized. The structures of all novel complexes were characterized by ¹H NMR, ¹³C NMR, FT‐IR spectroscopy and elemental analysis techniques. These palladium(II)‐NHC complexes were tested as efficient catalysts in the direct C—H bond activation of benzoxazole and benzothiazole with aryl bromides in the presence of 1 mol% catalyst loading at 150 °C for 4 h. Under the given conditions, various aryl bromides were successfully applied as the arylating reagents to achieve the 2‐arylbenzoxazoles and 2‐arylbenzothiazoles in acceptable to high yields.     

Evaluation of infection imaging potential of <Superscript>131</Superscript>I-labeled imidazolium salt

Effective antimicrobial compounds are necessary due to increased resistance of antibiotics against microorganisms causing infectious diseases. In this study, imidazolium-TFSI salt [ITFSI: octyl-bis(3-methylimidazolium)-di(bis(trifluoromethane)sulfonimide)] was labeled with ¹³¹I with high efficiency. In vitro uptake experiments of ¹³¹I-ITFSI showed high uptake in gram-positive Staphylococcus aureus bacteria. ¹³¹I-ITFSI was also evaluated for comparison between bacterial infection and sterile inflammation by in vivo studies. The biodistribution results revealed that ¹³¹I-ITFSI might be used as a nuclear imaging agent for detection of bacterial infection.     

A kinetic study on methylation of naphthalene over Fe/ZSM-5 zeolite catalysts

2,6-Dimethylnaphthalene is an important dimethylnaphthalene isomer which can be used in the production of polyethylene naphthalate. The novelty of this study is to reveal Langmuir–Hinshelwood and Eley–Rideal reaction rate equations for the methylation of naphthalene over Fe/ZSM-5 zeolite catalysts besides the proposed reaction rate equation. To investigate the kinetics and mechanisms of naphthalene methylation, the methylation experiments were carried out in a gas–solid catalytic fixed-bed reactor in the presence of Fe/ZSM-5 zeolite catalysts at two different temperatures (450 and 500 °C) and five different weight hourly space velocities (0.5, 1.0, 1.5, 2.0, 2.5, 3.0 h^?1). A naphthalene:methanol:1,2,4-trimethyl benzene mixture having a 1:3:10 molar ratio was used as a feed stream. The methylation products were identified by using GC–MS. For the methylation kinetics of naphthalene, the reaction rates depending on the naphthalene and methanol concentration were determined. Furthermore, the effects of temperature and weight hourly space velocity on the conversion of naphthalene, the selectivity of 2,6-dimethylnaphthalene, and the ratio of 2-methylnaphthalene/1-methylnaphthalene were determined. The results of this study demonstrate that the Langmuir–Hinshelwood reaction mechanism for naphthalene methylation is more compatible at 450 °C and the Eley–Rideal reaction mechanism at 500 °C. Moreover, in addition to 2,6-dimethylnaphthalene, other dimethylnaphthalene and tri-methylnaphthalene isomers were formed in the methylation of naphthalene. The conversion of naphthalene reached approximately 70%. Moreover, the highest selectivity of 2,6-dimethylnaphthalene was almost 40%. The ratios of 2-methylnaphthalene/1-methylnaphalene demonstrate that the methylation of naphthalene to 2-methynaphthalene is much higher than to 1-methynaphthalene.