Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computation

Set-Valued and Variational Analysis - R. Tyrell Rockafellar and his collaborators introduced, in a series of works, new regression modeling methods based on the notion of superquantile (or...     

Fractional green function for linear time-fractional inhomogeneous partial differential equations in fluid mechanics

This paper deals with the solutions of linear inhomogeneous time-fractional partial differential equations in applied mathematics and fluid mechanics. The fractional derivatives are described in the Caputo sense. The fractional Green function method is used to obtain solutions for time-fractional wave equation, linearized time-fractional Burgers equation, and linear time-fractional KdV equation. The new approach introduces a promising tool for solving fractional partial differential equations.     

On the electronic structure of transition-metal complexes II. Bonding characteristics in titanium chloride systems

The electronic structure of [TiCl₄]ⁿ systems (n = 0, ?1, ?2, ?3, and ?4) has been investigated by the INDO method. Calculations show the stability of the tetrahedral structure over the square-planar one, for any value of n, in accord with experimental observation. The occupation of the 4p orbitals of the titanium atom was found to increase regularly as the dihedral angle decreases and reaches a maximum at the square-planar conformation. Energy partitioning analysis enabled much deeper understanding of bonding characteristics of the studied systems. It has been shown that the one-atom energy component may be a very sensitive measure of the stability of the central metal atom in its various oxidation states.     

Preconcentration and separation of iron, zinc, cadmium and mercury, from waste water using Nile blue a grafted polyurethane foam

The present work describes a novel method for the incorporation of Nile blue A into polyurethane foam matrix. This foam material was found to be very suitable for the extraction of metal ions from aqueous solutions. The characterization of Nile blue A grafted foam and the effect of halide concentration, pH, shaking time, extraction isotherm and capacity have been investigated. This foam material was found to be suitable for the separation and preconcentration of iron (III), zinc (II), cadmium (II) and mercury (II) from waste water. The extraction was accomplished in (15-20) minutes. Iron was separated from acid medium (2-4 M HCl), zinc from (3-5 M HCl), cadmium from (4-6 M HCl) as thiocyanate complexes and mercury was separated from (1-2 M HCl) as chloride.     

Thermal dissociation of 1,2-dioxethane. III. Localized molecular-orbital study

The localized MO 's (LMO 's) of 1,2-dioxethane in its ground state and along the dissociation reaction path (to formaldehyde products) are generated using Boys' criteria for localization. The total charge density in each LMO is partitioned into atomic and overlap densities and the binding or antibinding character of each LMO is discussed in terms of the forces exerted on the nuclei by these densities. The driving force for the dissociation reaction is shown to arise essentially from the atomic dipole forces exerted on the oxygen nuclei by their lone-pair LMO 's. The characterization of a saddle point on the potential energy surface has been discussed in terms of the electrostatic equilibrium between forces exerted by the electron clouds “incomplete following” and “preceding.” The differences between the LMO 's obtained from the two Hartree–Fock solutions to which the SCF procedure converges have been discussed.     

DFT investigation of sites of protonation of antitumor of 2‐(4‐aminophenyl)benzazoles in the gas phase and in solution

The proton affinity on each of the possible sites in the antitumor 2‐(4‐aminophenyl)benzazoles has been calculated at the B3LYP/6‐311G** level of theory in the gas phase and in solution. The N₃‐site of protonation is found to be strongly favored over the NH₂‐site for the studied compounds both in gas phase and in solution. The stability of N₃‐protonated species is explained by the resonance interaction of the NH₂‐group with the heterocyclic ring. The potential energy surface (PES) for the protonation process was studied at the density functional theory (DFT)/B3LYP/6‐311++G** level of theory. Solvent effects on the PES were also examined using two models: Onsager self‐consistent field and polarizable continuum model (PCM). © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Estimation of the ionization pK(a) of pharmaceutical substances using the computer program Sparc

The computer program sparc was used to calculate the pK(a) values of some important pharmaceutical substances. The sparc models proved to be suitable for estimating the pK(a) values of beta-adrenergic blocking agents and benzodiazepine drugs. Ionization macroconstants, microconstants, zwitterionic equilibria, speciation curves as a function of the pH and the isoelectric points of a semi-essential amino acid, arginine, and an anti-inflammatory, niflumic acid, were calculated.     

Electronic structure of the peptide linkage. I. Equilibrium geometry and electronic properties of formhydroxamic acid

The equilibrium geometry of formhydroxamic acid has been calculated within the framework of the INDO –MO formalism. Various structural factors are analyzed and discussed in terms of the calculated force constants and charge distribution. The possibility of internal rotation around the C? N bond of formhydroxamic acid has been examined. The potential energy surface for the amide-imide tautomerism is explored by calculating the geometries and characterizing saddle points on that surface. The cyclic and open dimers of formhydroxamic acid are examined and the hydrogenbond energy and length are calculated.     

Selective separation of gold from iron ore samples using ion exchange resin

Gold in iron ore samples is separated from iron (major matrix cation), antimony and vanadium using anion exchange resin in (0.2 M) HBr, potassium peroxodisulfate and acetone:water:nitric acid media. The exchangeable anion Cl⁻ of the ion exchanger Dowex 1X 4 is replaced by Br⁻ using (6 M) HBr solution. Certified reference material DGP-M1, spiked ferric magnetic oxide, gold radioactive tracer ¹⁹⁸Au and gold standard solutions are used to study the adsorption efficiency and the yield recovery of tetrabromoaurate AuBr₄⁻ from the resin. Ten eluents have been tried to elute gold from the column, and it has been found that a 10 ml potassium peroxodisulfate and 240 ml acetone:water:nitric acid [125:5:5] solution fulfills the objective. The set up of the separation procedure allows quantitative adsorption of gold by the resin, while the major matrix cation (Fe) and others (Cd, Ag, Cu, V, Sb, Ti) have been passed through the column with the feeding solution (0.2 M) HBr. The resin selectivity coefficient (K) of separating Au from Fe has been found to be K_Fe^Au≈6.4×10¹¹. The eluted Au is treated with K₂S₂O₈ and H₂O₂ for spectrophotometric determination as rhodamine-B complex at 555.6 nm. The linearity, detection limit, precision, and accuracy of the determination method have been found to be up to 2.0 μg g⁻¹, 0.018 μg g⁻¹, 0.009 μg g⁻¹ and 3%, respectively.     

Structure and cooperativity of the hydrogen bonds in sodium dihydrogen triacetate

Geometry and energetics of low energy conformers of sodium dihydrogen triacetate (SDHTA) and its anion are studied using density functional theory (DFT) at the Becke, Lee‐Yang‐Parr hybrid functional (BLYP) and Becke, three‐parameter, Lee‐Yang‐Parr hybrid functional (B3LYP) levels. For both cases, two structures of comparable energy are found, which have different symmetry with respect to the two hydrogen bonds (HBs). DFT‐based Born–Oppenheimer molecular dynamics simulations are performed for SDHTA, which show that both structures are visited at room temperature conditions. The trajectory analysis further reveals that the two HBs behave anticooperative, that is, on average elongation of one HB is accompanied by a compression of the other one. This is in accord with nuclear magnetic resonance (NMR) experimental studies for a similar counter ion–dihydrogen triacetate complex. © 2012 Wiley Periodicals, Inc.