Faber polynomial coefficient estimates for analytic bi-close-to-convex functions

Using the Faber polynomials, we obtain coefficient expansions for analytic bi-close-to-convex functions and determine coefficient estimates for such functions. We also demonstrate the unpredictable behavior of the early coefficients of subclasses of bi-univalent functions. A function is said to be bi-univalent in a domain if both the function and its inverse map are univalent there.     

Algebraic Polynomials with Non-identical Random Coefficients

The asymptotic estimate for the expected number of real zeros of a random algebraic polynomial is known. The identical random coefficients a_j(ω) are normally distributed defined on a probability space , ω ∈Ω. The estimate for the expected number of zeros of the derivative of the above polynomial with respect to x is also known, which gives the expected number of maxima and minima of Q_n(x, ω). In this paper we provide the asymptotic value for the expected number of zeros of the integration of Q_n(x,ω) with respect to x. We give the geometric interpretation of our results and discuss the difficulties which arise when we consider a similar problem for the case of .     

Theoretical investigation of imidazolium based ionic liquid/alcohol mixture: a molecular dynamic simulation

In this work, molecular dynamic simulation of the mixture of imidazolium based ionic liquids with alcohols is implemented in order to investigate mixing excess properties and some structural and physical properties of the mixture. Excess volumes and enthalpies are evaluated for 11 different mole fractions of ionic liquids at each 0.1, in the range of 0 to 1. Radial distribution function, cohesive energy density, potential of mean force, solvation energy, and diffusion coefficient are reported and analysed. The effects of the cationic alkyl chain length, in comparison with changes of the anions, on these properties are reported. Results reveal that the methanol molecule participates with its hydrophilic characteristics in the mixing process and tends to aggregate around anion part of the ionic liquids, especially in the case of Cl.     

Investigation of Solution p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> and Thermodynamic Values of Lamivudine and Pefloxacin Drugs by Ab initio and DFT Methods

In this work we investigate the thermodynamic properties and pK_a value of lamivudine and pefloxacin drugs, in aqueous solutions, by ab initio and density functional theory (DFT) methods at different temperatures. Molecular structures and solute–solvent effects of the anions, cations, and neutral molecules of lamivudine and pefloxacin were studied by the polarizable continuum model (PCM). The calculation was done at the DFT-B3LYP/6-31+G(d) level of theory using Tomasi’s method to analyze the formation of intermolecular hydrogen bonds (IHB) in aqueous solution. The pK_a1 values of lamivudine and pK_a2 values of pefloxacin increase with temperature increase. In contrast, the pK_a1 values of pefloxacin decrease when the temperature increases. Further, the thermodynamic properties of the ionization processes (?H, ?S and ?G) of the drugs in aqueous solution were determined and discussed. The results of this work are in good agreement with the literature data at 298.15 K.     

Study of the <Superscript>190</Superscript>Hg Nucleus: Testing the Existence of U(5) Symmetry

In this paper, we have considered the energy spectra, quadrupole transition probabilities, energy surface, charge radii, and quadrupole moment of the¹⁹⁰Hg nucleus to describe the interplay between phase transitions and configuration mixing of intruder excitations. To this aim, we have used four different formalisms: (i) interacting boson model including configuration mixing, (ii) Z(5) critical symmetry, (iii) U(6)-based transitional Hamiltonian, and (iv) a transitional interacting boson model Hamiltonian in both interacting boson model (IBM)-1 and IBM-2 versions which are based on affine \( \widehat{SU\left(1,1\right)} \) Lie algebra. Results show the advantages of configuration mixing and transitional Hamiltonians, in particular IBM-2 formalism, to reproduce the experimental counterparts when the weight of spherical symmetry increased.     

A high-order Monte Carlo algorithm for the direct simulation of Boltzmann equation

A high-order algorithm of the direct simulation Monte Carlo (DSMC) method, H-DSMC, has been developed to simulate rarefied flow regimes. The mth order Taylor series expansion has been employed to obtain a more generalized form of the time discretization for the collision part of Boltzmann equation. In the purposed algorithm, the higher order collision terms are introduced as well as higher order terms in the time step of the probabilistic coefficients. These newly implemented higher order terms improve the accuracy and efficiency of the solution and enhance the convergence rate quite significantly. Comparison between results of the classic DSMC method and the H-DSMC method shows the promising performance of the introduced technique.     

Combined methane reforming over nano LaNiO<Subscript>3</Subscript> catalyst with modified active surface

In this study, nano catalyst LaNiO₃ with perovskite structure was synthesized using the citrate sol–gel method in the combined methane reforming with CO₂ and O₂ (CRM). The effects of increasing the surface area of the LaNiO₃ perovskite on the catalytic activity were investigated by changing the method of preparing and creating holes in the surface of the samples. Physical and chemical properties of the samples, before and after the reactor test, were determined through ICP, AA, XRD, TGA, TPR, BET, SEM, EDX and TEM techniques. The results of XRD, ICP, AA, SEM, EDX and TEM tests indicated that the citrate sol–gel method is a good way to prepare a homogeneous perovskite LaNiO₃ sample on a scale of nanometers. The results of the TPR test showed using etching in the citrate sol–gel method can produce samples with high stability. The BET results indicated that the surface area of the LaNiO₃ sample tripled with the method suggested in this paper. Changes in preparation method lead to induction time decreasing and temperature increasing. Use of etching in the citrate sol gel method had no significant effect in the results of activity tests versus time reaction at a temperature of 800 °C. TGA curves revealed no production of coke over the process for the produced samples.     

Coefficient estimates for certain classes of meromorphic bi-univalent functions

We define a new class of meromorphic bi-univalent functions and use the Faber polynomial expansions to determine the coefficient bounds for such functions. Our results generalize and/or improve some of the previously known results. A meromorphic function is said to be bi-univalent in a given domain Δ if both the function and its inverse map are univalent there.     

Performance of density‐functional tight‐binding models in describing hydrogen‐bonded anionic‐water clusters

Density‐functional tight‐binding (DFTB) models are computationally efficient approximations to density‐functional theory that have been shown to predict reliable structural and energetic properties for various systems. In this work, the reliability and accuracy of the self‐consistent‐charge DFTB model and its recent extension(s) in predicting the structures, binding energies, charge distributions, and vibrational frequencies of small water clusters containing polyatomic anions of the Hofmeister series (carbonate, sulfate, hydrogen phosphate, acetate, nitrate, perchlorate, and thiocyanate) have been carefully and systematically evaluated on the basis of high‐level ab initio quantum‐chemistry [MP2/aug‐cc‐pVTZ and CCSD(T)/aug‐cc‐pVQZ] reference data. Comparison with available experimental data has also been made for further validation. The self‐consistent‐charge DFTB model, and even more so its recent extensions, are shown to properly account for the structural properties, energetics, intermolecular polarization, and spectral signature of hydrogen‐bonding in anionic water clusters at a fraction of the computational cost of ab initio quantum‐chemistry methods. This makes DFTB models candidates of choice for investigating much larger systems such as seeded water droplets, their structural properties, formation thermodynamics, and infrared spectra. © 2014 Wiley Periodicals, Inc.     

On a modified Monte-Carlo method and variable soft sphere model for rarefied binary gas mixture flow simulation

The effect of new terms in the improved algorithm, the modified direct simulation Monte-Carlo (MDSMC) method, is investigated by simulating a rarefied binary gas mixture flow inside a rotating cylinder. Dalton law for the partial pressures contributed by each species of the binary gas mixture is incorporated into our simulation using the MDSMC method and the direct simulation Monte-Carlo (DSMC) method. Moreover, the effect of the exponent of the cosine of deflection angle (α) in the inter-molecular collision models, the variable soft sphere (VSS) and the variable hard sphere (VHS), is investigated in our simulation. The improvement of the results of simulation is pronounced using the MDSMC method when compared with the results of the DSMC method. The results of simulation using the VSS model show some improvements on the result of simulation for the mixture temperature at radial distances close to the cylinder wall where the temperature reaches the maximum value when compared with the results using the VHS model.