Treated Rice Bran for Scavenging Cr(III) and Hg(II) from Acidic Solution

The purpose of this study was to examine the efficiency with which rice bran (treated or untreated) removes heavy metals, especially Cr(III) and Hg(II), from acidic solution. Sorption assays were done in shaken flasks in the presence of rice bran. Different experimental conditions such as pH, volume of solution, bran weight, particle size, exchange time and stirring time were improved. The efficiency of bran was studied before and after treatments. For treatment, solutions of acid, alkali and salt were used. The results show that after treating with 4 M sodium chloride solution, its efficiency in removal of Cr(III) and Hg(II) was improved. Kinetic measurements of chromium and mercury removal by bran have revealed that sorption equilibrium was obtained after 10 min of contact. Sorption experiments done with various granulometric fractions of rice bran have shown that this sorbent has the same efficiencies in meshes higher than 20. Further research is necessary in order to determine a mechanism for cations removal by the bran. It is mentioned that the process of making polished rice from brown rice discharges rice bran; therefore, it is very inexpensive, with a cost of 1/50 ? 1/40 of that of synthetic sorbent, and thus its use would significantly lower the cost of wastewater treatment.     

Thermotropic polyesters. 1: Synthesis, characterization and thermal transition of poly[4,4-bis(ω-alkoxy)biphenyl isophthalate]

A new homologous series of thermotropic polyesters has been synthesized by polycondensation reaction between isophthaloyl chloride and mesogenic diols 4,4^′-bis(ω-hydroxyalkoxy)biphenyl in which the spacer length is varied from 3 to 6 methylene units. The thermal behavior of the polymers has been characterized using polarized light microscopy and differential scanning calorimetry (DSC). The odd members exhibit a smectic C (S_C) phase in a narrow temperature interval, while the even members form a smectic A (S_A) phase in a broader temperature range. All of the obtained compounds were characterized by conventional spectroscopic methods.     

Estimation of thermal conductivity of ethylene glycol-based nanofluid with hybrid suspensions of SWCNT–Al<Subscript>2</Subscript>O<Subscript>3</Subscript> nanoparticles by correlation and ANN methods using experimental data

In the present paper, the effects of temperature and volume fraction on thermal conductivity of SWCNT–Al₂O₃/EG hybrid nanofluid are investigated. Single-walled carbon nanotube with outer diameter of 1–2 nm and aluminum oxide nanoparticles with mean diameter of 20 nm with the ratio of 30 and 70%, respectively, were dispersed in the base fluid. The measurements were conducted on samples with volume fractions of 0.04, 0.08, 0.15, 0.3, 0.5, 0.8, 1.5 and 2.5. In order to investigate the effects of temperature on thermal conductivity of the nanofluid, this characteristic was measured in five different temperatures of 30, 35, 40, 45 and 50 °C. The results indicate that enhancement of nanoparticles’ thickness in low volume fractions and at any temperature causes a considerable increment in thermal conductivity of the nanofluid. In this study, the highest enhancement of thermal conductivity was 41.2% which was achieved at the temperature of 50 °C and volume fraction of 2.5%. Based on the experimental data, an experimental correlation and a neural network are presented and for thermal conductivity of the nanofluid in terms of volume fraction and temperature. Comparing outputs of the experimental correlation and the designed artificial neural network with experimental data, the maximum error values for the experimental correlation and the artificial neural network were, respectively, 2.6 and 1.94% which indicate the excellent accuracy of both methods in prediction of thermal conductivity.     

Determination of migrated phthalic acid residues into edible oils using a green mode of air-assisted liquid–liquid microextraction followed by high-performance liquid chromatography–diode array detector

In this study, for the first time, an organic solvent-free air-assisted liquid–liquid microextraction method has been reported for the extraction and preconcentration of phthalic acids (o-phthalic acid, m-phthalic acid, and p-phthalic acid) from edible oil samples. The method is based on the repeated aspirating/injection of an alkaline aqueous solution and the oil sample mixture in a conical bottom centrifuge tube to form a cloudy solution. After phase separation by centrifuging, the sedimented phase is directly analyzed by high-performance liquid chromatography–diode array detection. Under the optimum extraction conditions, the method showed low limits of detection and quantification between 0.11–0.29 and 0.28–0.91 ng mL^?1, respectively. Extraction recoveries and enrichment factors were from 81 to 97% and 406 to 489, respectively. The relative standard deviations for the analysis of 5 ng mL^?1 of each analyte were less than 5.9% for intraday (n = 6) and interday (n = 5) precisions. Finally, different oil samples were successfully analyzed using the proposed method and m-phthalic acid, and p-phthalic acid were determined in some of them at ng mL^?1 level.     

An adaptive nonmonotone global Barzilai–Borwein gradient method for unconstrained optimization

The Barzilai–Borwein (BB) gradient method has received many studies due to its simplicity and numerical efficiency. By incorporating a nonmonotone line search, Raydan (SIAM J Optim. 1997;7:26–33) has successfully extended the BB gradient method for solving general unconstrained optimization problems so that it is competitive with conjugate gradient methods. However, the numerical results reported by Raydan are poor for very ill-conditioned problems because the effect of the degree of nonmonotonicity may be noticeable. In this paper, we focus more on the nonmonotone line search technique used in the global Barzilai–Borwein (GBB) gradient method. We improve the performance of the GBB gradient method by proposing an adaptive nonmonotone line search based on the morphology of the objective function. We also prove the global convergence and the R-linear convergence rate of the proposed method under reasonable assumptions. Finally, we give some numerical experiments made on a set of unconstrained optimization test problems of the CUTEr collection. The results show the efficiency of the proposed method in the sense of the performance profile introduced (Math Program. 2002;91:201–213) by Dolan and Moré.     

Candidates for nonzero Betti numbers of monomial ideals

Let I be a monomial ideal in the polynomial ring S generated by elements of degree at most d. In this paper, it is shown that, if the i-th syzygy of I has no elements of degrees j,…,j+(d?1) (where j≥i+d), then (i+1)-th syzygy of I does not have any element of degree j+d. Then we give several applications of this result, including an alternative proof for Green–Lazarsfeld index of the edge ideals of graphs as well as an alternative proof for Fröberg’s theorem on classification of square-free monomial ideals generated in degree 2 with linear resolution. Among all, we deduce a partial result on subadditivity of the syzygies for monomial ideals.     

Well‐posedness of initial boundary value problems on longitudinal impact on a composite linear viscoelastic bar

We investigate the correctness of the initial boundary value problem of longitudinal impact on a piecewise‐homogeneous semi‐infinite bar consisting of a semi‐infinite elastic part and finite length visco‐elastic part whose hereditary properties are described by linear integral relations with an arbitrary difference kernel. Introducing nonstationary regularization in boundary conditions and in the contact conditions, the well‐posedness of the considered problem is proved. Copyright © 2017 John Wiley & Sons, Ltd.