Simplifying equations in Arabic algebra

Historians have always seen jabr (restoration) and muqābala (confrontation) as technical terms for specific operations in Arabic algebra. This assumption clashes with the fact that the words were used in a variety of contexts. By examining the different uses of jabr, muqābala, ikmāl (completion), and radd (returning) in the worked-out problems of several medieval mathematics texts, we show that they are really nontechnical words used to name the immediate goals of particular steps. We also find that the phrase al-jabr wa'l-muqābala was first used within the solutions of problems to mean al-jabr and/or al-muqābala, and from there it became the name of the art of algebra.     

Fabrication of hollow silica microspheres utilizing a hydrothermal approach

Hollow silica microspheres(HSMSs) have been successfully fabricated via a facile hydrothermal route using D-glucose as the sacrificial template and sodium silicate powder as the silica precursor.The resulting silica hollow particles were characterized by scanning electron microscopy(SEM),transmission electron microscopy(TEM),X-ray diffraction(XRD),and infrared spectroscopy(IR).The surface area was determined using the BET method.SEM and TEM images exhibited micro-sized silica hollow particles with a size of ~1.5μm.     

Macrocyclization of polymers via ring‐closing metathesis and azide/alkyne‐“click”‐reactions: An approach to cyclic polyisobutylenes

The end‐to‐end cyclization of telechelic polyisobutylenes (PIB's) toward cyclic polyisobutylenes is reported, using either ring‐closing metathesis (RCM) or the azide/alkyne‐“click”‐reaction. The first approach uses bisallyl‐telchelic PIB's (M_n = 1650, 3680, 9770 g mol^?1) and Grubbs 1st‐, 2nd‐, and 3rd‐generation catalyst leading to cyclic PIB's in 60–80% yield, with narrow polydispersities (M_w/M_n = 1.25). Azide/alkyne‐“click”‐reactions of bisalkyne‐telechelic PIB's (M_n = 3840 and 9820 g mol^?1) with excess of 1,11‐diazido‐undecane leads to the formation of mixtures of linear/cyclic PIB's under formation of oligomeric cycles. Subsequent reaction of the residual azide‐moieties in the linear PIB's with excess of alkyne‐telechelic PEO enables the chromatographic removal of the resulting linear PEO‐PIB‐block copolymers by column chromatography. Thus pure cyclic PIB's can be obtained using this double‐“click”‐method, devoid of linear contaminants. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 671–680, 2010     

Supply chain optimization of petroleum organization under uncertainty in market demands and prices

A multi-period stochastic planning model has been developed and implemented for a supply chain network of a petroleum organization operating in an oil producing country under uncertain market conditions. The proposed supply chain network consists of all activities related to crude oil production, processing and distribution. Uncertainties were introduced in market demands and prices. A deterministic optimization model was first developed and tested. The impact of uncertainty on the supply chain was studied by performing a sensitivity analysis in which ±20% deviations were introduced in market demands and prices of different commodities. A stochastic formulation was then proposed, which is based on the two-stage problem with finite number of realizations. The proposed stochastic programming approach proved to be quite effective in developing resilient production plans in light of high degree of uncertainty in market conditions. The anticipated production plans have a considerably lower expected value of perfect information (EVPI). The main conclusion of this study is that for an oil producing country with oil processing capabilities, the impact of economic uncertainties may be tolerated by an appropriate balance between crude exports and processing capacities.     

New benzylpiperazine derivatives bearing mono‐ and bis‐dialkyl substituted 1,2,4‐triazoles

Cycloaddition of the 1‐aza‐2‐azoniaallenes 3 with p‐cyanobenzyl chlorides afforded, after spontaneous rearrangement, the 1,5‐dialkyl‐3‐[4‐chloromethyl)phenyl]‐1H‐[1,2,4]‐triazoles 6 . A series of 1,5‐dialkyl‐1H‐[1,2,4]‐triazol‐3‐yl)benzyl‐piperazines 7 and 8 were prepared from direct condensation of 6 with piperazine and N‐methylpiperazine, respectively. The structures of the newly synthesized products were identified by 2D NMR spectroscopy. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:28–32, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.20061     

Electrocortical and Biochemical Evaluation of Antidepressant Efficacy of Formulated Nanocurcumin

Applied Biochemistry and Biotechnology - The present study aims to evaluate the antidepressant efficacy of curcumin nanoparticles on rat model of depression induced by reserpine. Rats were divided...     

The odd log-logistic Topp–Leone G family of distributions: heteroscedastic regression models and applications

We introduce a new class of distributions and provide a comprehensive treatment of its mathematical properties. The maximum likelihood method is discussed to estimate the parameters of the new model by means of Monte-Carlo simulation study. The heteroscedastic regression models with long-term survival are introduced to model data sets with the non homogeneity of the error variances in the presence of cured individuals. The potentiality of the proposed models is illustrated by means of four real data sets.     

Cyclic alkoxyamine‐initiator tethered by azide/alkyne‐“click”‐chemistry enabling ring‐expansion vinyl polymerization providing macrocyclic polymers

A cyclic initiator for the nitroxide‐mediated controlled radical polymerization (NMP) is a powerful tool for the preparation of macrocyclic polymers via a ring‐expansion vinyl polymerization mechanism. For this purpose, we prepared a Hawker‐type NMP‐initiator that includes an azide and a terminal alkyne as an acyclic precursor, which is subsequently tethered via an intramolecular azide/alkyne‐“click”‐reaction, producing the final cyclic NMP‐initiator. The polymerization reactions of styrene with cyclic initiator were demonstrated and the resultant polymers were characterized by the gel permeation chromatography (GPC) and the matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry (MALDI‐TOF MS). These results prove that the ring‐expansion polymerization of styrene occurred together with the radical ring‐crossover reactions originating from the exchange of the inherent nitroxides generating macrocyclic polystyrenes with higher expanded rings. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3402–3416, 2010     

Optimization of module configuration in membrane gas separation

Mathematical models have been developed to optimize three configurations for membrane gas separation modules. The three systems include the single stage, the two stage, and the continuous membrane column (CMC). Analysis of the three systems is carried out for the case of enriching a binary mixture of methane and carbon dioxide, where the reject stream is the desired product. The cost optimization function includes the capital cost for compressors and membranes as well as the energy operating cost. The cost function is solved subject to a set of equality and inequality constraints. The equality constraints include the module balance equations and the permeation fluxes across the membrane. The inequality equations include constraints on mole fractions in permeate and reject streams, operating pressure, membrane area, and the amount of methane recovered in reject stream. Model equations for the three systems are solved using GINO, a program for nonlinear optimization. A quasi-Newton search method is selected and found quite efficient for solution of the equations. Over the range of parameters considered in the analysis, results show that the two stage configuration has a lower production cost than the other two systems. In addition, the operating cost for the CMC and the single stage systems are found to be comparable. Irrespective of this, the optimum amount of methane recovered is the highest for the CMC system. Although the optimum operating costs for the CMC and the single stage systems are higher than the two stage system, comparison should consider other factors including higher methane recoveries generated by the CMC system and the simplicity of design and operation for the single stage system.