Ions in a binary asymmetric dipolar mixture: mole fraction dependent Born energy of solvation and partial solvent polarization structure

Mean spherical approximation (MSA) for electrolyte solution has been extended to investigate the role of partial solvent polarization densities around an ion in a completely asymmetric binary dipolar mixture. The differences in solvent diameters, dipole moments, and ionic size are incorporated systematically within the MSA framework in the present theory for the first time. In addition to the contributions due to difference in dipole moments, the solvent-solvent and ion-solvent size ratios are found to significantly affect the nonideality in binary dipolar mixtures. Subsequently, the theory is used to investigate the role of ion-solvent and solvent-solvent size ratios in determining the nonideality in Born free energy of solvation of a unipositive rigid ion in alcohol-water and dimethyl sulfoxide-acetonitrile mixtures, where the solvent components are represented only by their molecular diameters and dipole moments. Nonideality in Born free energy of solvation in such simplified mixtures is found to be stronger for smaller ions. The slope of the nonideality for smaller alkali metal ions in methanol-water mixture is found to be opposite to that for larger ion, such as quaternary tertiary butyl ammonium ion. For ethanol-water mixtures, the slopes are in the same direction for all the ions studied here. These results are in qualitative agreement with experiments, which is surprising as the present MSA approach does not include the hydrogen bonding and hydrophobic interactions present in the real mixtures. The calculated partial polarization densities around a unipositive ion also show the characteristic deviation from ideality and reveal the microscopic origin of the ion and solvent size dependent preferential solvation. Also, the excess free energy of mixing (in the absence of any ion) for these binary mixtures has been calculated and a good agreement between theory and experiment has been found.     

Estimation of atorvastatin calcium and fenofibrate in tablets by derivative spectrophotometry and liquid chromatography

Two simple and accurate methods to determine atorvastatin calcium (ATO) and fenofibrate (FEN) in combined dosage forms were developed using second-derivative spectrophotometry and reversed-phase liquid chromatography (LC). ATO and FEN in combined preparations (tablets) were quantitated using the second-derivative responses at 245.64 nm for ATO and 289.56 nm for FEN in spectra of their solution in methanol. The calibration curves were linear [correlation coefficient (r) = 0.9992 for ATO and 0.9995 for FEN] in the concentration range of 3-15 microg/mL for ATO and FEN. In the LC method, analysis was performed on a Hypersil ODS-C18 column (250 mm x 4.6 mm id, 5 microm particle size) in the isocratic mode using the mobile phase methanol-water (90 + 10, v/v), adjusted to pH 5.5 with orthophosphoric acid, at a flow rate of 1 mL/min. Measurement was made at a wavelength of 246.72 nm. Both drugs were well resolved on the stationary phase, and the retention times were 1.95 min for ATO and 5.50 min for FEN. The calibration curves were linear (r = 0.9985 for ATO and 0.9976 for FEN) in the concentration range of 3-15 microg/mL for ATO and FEN. Both methods were validated, and the results were compared statistically. They were found to be accurate, precise, and specific. The methods were successfully applied to the estimation of ATO and FEN in combined tablet formulations.     

Mesoporous Porphyrin-Silica Nanocomposite as Solid Acid Catalyst for High Yield Synthesis of HMF in Water

Solid acid catalysts occupy a special class in heterogeneous catalysis for their efficiency in eco-friendly conversion of biomass into demanding chemicals. We synthesized porphyrin containing porous organic polymers (PorPOPs) using colloidal silica as a support. Post-modification with chlorosulfonic acid enabled sulfonic acid functionalization, and the resulting material (PorPOPS) showed excellent activity and durability for the conversion of fructose to 5-hydroxymethyl furfural (HMF) in green solvent water. PorPOPS composite was characterized by N₂ sorption, FTIR, TGA, CHNS, FESEM, TEM and XPS techniques, justifying the successful synthesis of organic networks and the grafting of sulfonic acid sites (5 wt%). Furthermore, a high surface area (260 m²/g) and the presence of distinct mesopores of ~15 nm were distinctly different from the porphyrin containing sulfonated porous organic polymer (FePOP-1S). Surprisingly the hybrid PorPOPS showed an excellent yield of HMF (85%) and high selectivity (>90%) in water as compared to microporous pristine-FePOP-1S (yield of HMF = 35%). This research demonstrates the requirement of organic modification on silica surfaces to tailor the activity and selectivity of the catalysts. We foresee that this research may inspire further applications of biomass conversion in water in future environmental research.     

In water organic synthesis: Introducing itaconic acid as a recyclable acidic promoter for efficient and scalable synthesis of quinoxaline derivatives at room temperature

Substituted quinoxaline derivatives are traditionally synthesized by co-condensation of various starting materials. Herein, we describe a novel environmentally benign in water synthetic route for the synthesis of structurally and electronically diverse ninety quinoxalines with readily available substituted o-phenylenediamine and 1,2-diketones using cheap and biodegradable itaconic acid as a mild acid promotor in 1 hours. The reaction is performed at room temperature, which proceeds through cyclo-condensation reaction followed by obtaining the aforesaid nitrogen-containing heterocyclic adducts without performing the column chromatography up to 96% total yields. The simplicity, high efficiency, and reusable of the catalyst merits this reaction condition as “green synthesis” which enables it to be useful in synthetic transformations upto gram scale level.     

Relaxations and discretizations for the pooling problem

The pooling problem is a folklore NP-hard global optimization problem that finds applications in industries such as petrochemical refining, wastewater treatment and mining. This paper assimilates the vast literature on this problem that is dispersed over different areas and gives new insights on prevalent techniques. We also present new ideas for computing dual bounds on the global optimum by solving high-dimensional linear programs. Finally, we propose discretization methods for inner approximating the feasible region and obtaining good primal bounds. Valid inequalities are derived for the discretized models, which are formulated as mixed integer linear programs. The strength of our relaxations and usefulness of our discretizations is empirically validated on random test instances. We report best known primal bounds on some of the large-scale instances.     

Existence and Weyl’s law for spherical cusp forms

Let G be a split adjoint semisimple group over and a maximal compact subgroup. We shall give a uniform, short and essentially elementary proof of the Weyl law for cusp forms on congruence quotients of . This proves a conjecture of Sarnak for -split groups, previously known only for the case G = PGL(n). The key idea amounts to a new type of simple trace formula. Received: April 2005 Revision: June 2006 Accepted: October 2006     

Relay placement for fault tolerance in wireless networks in higher dimensions

In this paper we consider the problem of adding the smallest number of additional (relay) nodes to a network of static nodes with limited communication range so that the induced communication graph is 2-connected (we consider both edge and vertex connectivity). The problem is NP-hard. We develop algorithms that find close to optimal solutions for both edge and vertex connectivity. We prove the algorithms have an approximation ratio of 2M for nodes distributed in a d-dimensional Euclidean space, where M is the maximum node degree of a Minimum Spanning Tree in d dimensions using Euclidean metrics. In addition, our methods extend with the same approximation guarantees to a generalization when the locations of relays are required to avoid certain polygonal regions (obstacles).     

Non-Iterative Regularized reconstruction Algorithm for Non-CartesiAn MRI: NIRVANA

We introduce a novel noniterative algorithm for the fast and accurate reconstruction of nonuniformly sampled MRI data. The proposed scheme derives the reconstructed image as the nonuniform inverse Fourier transform of a compensated dataset. We derive each sample in the compensated dataset as a weighted linear combination of a few measured k-space samples. The specific k-space samples and the weights involved in the linear combination are derived such that the reconstruction error is minimized. The computational complexity of the proposed scheme is comparable to that of gridding. At the same time, it provides significantly improved accuracy and is considerably more robust to noise and undersampling. The advantages of the proposed scheme makes it ideally suited for the fast reconstruction of large multidimensional datasets, which routinely arise in applications such as f-MRI and MR spectroscopy. The comparisons with state-of-the-art algorithms on numerical phantoms and MRI data clearly demonstrate the performance improvement.