Randomized first order algorithms with applications to ℓ 1-minimization

In this paper we propose randomized first-order algorithms for solving bilinear saddle points problems. Our developments are motivated by the need for sublinear time algorithms to solve large-scale parametric bilinear saddle point problems where cheap online assessment of the solution quality is crucial. We present the theoretical efficiency estimates of our algorithms and discuss a number of applications, primarily to the problem of ? ₁ minimization arising in sparsity-oriented signal processing. We demonstrate, both theoretically and by numerical examples, that when seeking for medium-accuracy solutions of large-scale ? ₁ minimization problems, our randomized algorithms outperform significantly (and progressively as the sizes of the problem grow) the state-of-the art deterministic methods.     

Synthesis,spectroscopic and structural characterisation of two p-nitrobenzamide compounds: experimental and DFT study

The title molecules, N-(1,5-dimethyl-3-oxo-2-phenyl-1H-3-(2H)-pyrazolyl)4-nitrobenzamide (C₁₈H₁₆N₄O₄·H₂O) (I) and 2,2-dimethyl-3-(4-nitrobenzoyl)-5-(phenylamino)-2,3-dihydro-1,3,4-thiyadiazole (C₁₇H₁₆N₄O₃S) (II), were prepared and characterised by ¹H NMR, ¹³C NMR, infrared spectroscopy (IR) and structural X-ray diffraction (XRD) techniques. The molecular geometries, vibrational frequencies of the title compounds in the ground state have been calculated by using the density functional theory (DFT) method with 6-31G(d) basis set, and compared with the experimental data. The calculated results showed that the optimised geometries from the DFT method agree with the X-ray structures well for both compounds. Theoretical calculations of harmonic vibration frequencies are in good agreement with experimental results. To determine conformational flexibility, the molecular energy profiles of the title compounds were obtained. Besides, molecular electrostatic potential (MEP), frontier molecular orbitals (FMO) analysis and thermodynamic properties of the title compounds were investigated by theoretical calculations.     

Discontinuous Boundary Value Problems with Retarded Argument and Eigenparameter-Dependent Boundary Conditions

In this paper we study the asymptotic formulas for the eigenvalues and corresponding eigenfunctions of discontinuous boundary value problems with retarded argument and eigenparameter-dependent boundary conditions.     

Improved of cathode performance of LiFePO<Subscript>4</Subscript>/C composite using different carboxylic acids as carbon sources for lithium-ion batteries

Among the several materials under development for use as a cathodes in lithium-ion batteries olivine-type LiFePO₄ is one of the most promising cathode material. However, its poor conductivity and low lithium-ion diffusion limits its practical application. In this study, we report seven different carboxylic acids used to synthesize LiFePO₄/C composite, and influences of carbon sources on electrochemical performance were intensively studied. The structure and electrochemical properties of the LiFePO₄/C were characterized by X-ray diffraction, scanning electron microscopy, electrical conductivity, and galvanostatic charge–discharge measurements. Among the materials studied, the sample E with tartaric acid as carbon source exhibited the best cell performance with a maximum discharge capacity of 160 mAh g⁻¹ at a 0.1 C-rate. The improved electrochemical properties were attributed to the reduced particle size and enhanced electrical contacts by carbon.     

Synthesis,Spectral Properties and Structure of New Novel 3,3′-Dibenzoyl-1,1′-(propan-1,3-diyl)-bisthiourea

Abstract  

A new 3,3′-dibenzoyl-1,1′-propan-1,3-diyl)bisthiourea was synthesized by using benzoylisothiocyanate with 1,3-diaminopropane in aprotic solvent. The structure was determinated by means of FT-IR, ¹H-NMR, ¹³C-NMR and mass spectroscopic techniques. The crystal structure of 3,3′-dibenzoyl-1,1′-(propan-1,3-diyl)bisthiourea has also been examined by using X-ray crystallographic techniques and found to be crystallized in the monoclinic space group P2 ₁ /c with the unit cell parameters: a = 5.968(1) ?, b = 19.471(2) ?, c = 16.585(2) ?, β = 98.32(1)°, V = 1907.0(4) ?³, Dx = 1.395 g cm⁻³, and Z = 4 respectively.     

Micelle-Enhanced Spectrofluorimetric Method for Determination of Cholesterol-Reducing Drug Ezetimibe in Dosage Forms

A simple and sensitive spectrofluorimetric method was developed for the determination of ezetimibe in its pharmaceutical formulations. The proposed method is based on investigation of the fluorescence spectral behavior of ezetimibe in sodium dodecyl sulfate (SDS) micellar system. In aqueous solution of acetate buffer pH 5.0, the fluorescence intensity of ezetimibe was greatly enhanced, 200% enhancement, in the presence of SDS. The fluorescence intensity of ezetimibe was measured at 380 nm after excitation at 268 nm. The fluorescence-concentration plot was rectilinear over the range of 0.03–3.0 μg/mL with lower detection limit of 3.08 × 10⁻³ μg/mL. The method was successfully applied to the analysis of ezetimibe in its commercial tablets; the results were in good agreement with those obtained with the reported method. The application of the proposed method was extended to the stability studies of ezetimibe after exposure to different forced degradation conditions, such as acidic, alkaline, photo and oxidative conditions, according to ICH guidelines.     

Elegant Synthesis of Highly Functionalized 1,2,3-Trisubstituted Cyclopentanes

The conversion of cyclic Baylis–Hillman acetates 1 into the corresponding cyano derivatives 2 was achieved using potassium cyanide in the presence of 1,4-diazabicyclo[2.2.2]octane (DABCO) in aqueous medium. The obtained Michael acceptors 2 easily add primary amines in absolute ethanol to produce a new family of 1,2,3-trisubstituted cyclpentanes 3 in good yields.     

Determination of 1,4-benzodiazepines in drug dosage forms by difference spectrophotometry

A spectrophotometric method has been developed for the determination of seven 1,4-benzodiazepines, namely: chlordiazepoxide, diazepam, nitrazepam, oxazepam, lorazepam, temazepam and cinolazepam. The method involves reduction of the target compounds using Zn/HCl and measuring the difference in the absorbance before and after reduction. The quantities of zinc and acid required for efficient reduction were carefully studied. 1–20 g ml^–1 of the compounds could be determined with < 1% error. The method was applied successfully to the determination of these compounds in pharmaceutical dosage forms. The results were sufficiently accurate and precise and comparable to those from the official methods.     

Experimental and theoretical studies on the functionalization reactions of 4-benzoyl-1,5-diphenyl-1H-pyrazole-3-carboxylic acid and-acid chloride with various aminophenols

The 1H-pyrazole-3-carboxylic acid 1 was converted via reactions of its acid chloride 2 with various aminophenol derivatives 3a--d into the corresponding N-(hydroxyphenyl)-1H-pyrazole-3-carboxamides 4a--d, respectively, in good yields (34–53%). The reactions of 1 or 2 with 3 in benzene or toluene for 5–7 h with no catalytic amounts of base lead to the formation of the products 4. The structures of all new synthesized compounds were established by the ¹³C NMR,¹H NMR, IR, masss spectroscopic data and elemental analyses. The reaction mechanism of 2 with 3 was studied by means of the RHF/3-21G and RHF/6-31G method.     

Synthesis and spectral characterization of novel oxo-bridged, thiocarboxylato complexes of chromium(III)

A variety of novel oxo-bridged trinuclear mixed-ligand complexes of chromium(III) were synthesized by substitution reactions of acetate ions from their respective acetate complexes. The isolated products of the types [Cr₃O(OAc)₃(OOCR] ₃ ⁺ and [Cr₃O(SOCPh)₃(OOCR)₃]⁺ (R = C₁₃H₂₇, C₁₅H₃₁ or C₁₇H₃₅) are mixed-ligand chromium(III) complexes with straight-chain carboxylic and thiocarboxylic acids. These were characterized by elemental analyses, spectral (infrared, electronic, FAB mass, and powder XRD) studies, molar conductances, and magnetic susceptibility measurements. The IR spectra suggested the bridging nature of the carboxylate and thiocarboxylate anions along with v _as (Cr₃O) vibrations in the complexes. The trinuclear nature of the complexes was assessed from the FAB mass data. Electronic absorption spectra and magnetic moment data were in favor of an octahedral environment around chromium(III), which was supported by their powder X-ray diffraction data. Conductance measurements indicated that the complexes were 1: 1 electrolytes in nitrobenzene. Structures of the complexes were established on the basis of spectral and other physicochemical studies. The text was submitted by the authors in English.