Hilbert modular forms of weight 1/2 and theta functions

Serre and Stark found a basis for the space of modular forms of weight 1/2 in terms of theta series. In this paper, we generalize their result—under certain mild restrictions on the level and character—to the case of weight 1/2 Hilbert modular forms over a totally real field of narrow class number 1. The methods broadly follow those of Serre-Stark; however we are forced to overcome technical difficulties which arise when we move out of Q.     

Exact solution of the Klein‐Gordon equation for the PT‐symmetric generalized Woods‐Saxon potential by the Nikiforov‐Uvarov method

The exact solution of the one‐dimensional Klein‐Gordon equation of the ????‐symmetric generalized Woods‐Saxon potential is obtained. The exact energy eigenvalues and wavefunctions are derived analytically by using the Nikiforov and Uvarov method. In addition, the positive and negative exact bound states of the s‐states are also investigated for different types of complex generalized Woods‐Saxon potentials.     

Some generalizations of the Cauchy–Schwarz and the Cauchy–Bunyakovsky inequalities involving four free parameters and their applications

Some generalizations of the well-known Cauchy–Schwarz inequality and the analogous Cauchy–Bunyakovsky inequality involving four free parameters are given for both discrete and continuous cases. Several particular cases of interest are also analyzed. Some of the applications of our main results include (for example) the Wagner inequality.     

Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential

The Klein-Gordon equation in D-dimensions for a recently proposed ring-shaped Kratzer potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound states and the corresponding wave functions of the Klein-Gordon are obtained in the presence of the non-central equal scalar and vector potentials. The results obtained in this work are more general and can be reduced to the standard forms in three dimensions given by other works.      

Interpenetrating Networks Obtained by Crosslinking in the Vinylacetate (VAc)-Triethoxyvinylsilane (VTES)-Tetraethoxysilane (TEOS) System

In the present work the sol-gel process in the ternary system VAc-VTES-TEOS was approached. The monomer that ensures the crosslinking of the obtained networks is VTES, which could react with VAc by free-radical polymerisation and with TEOS by hydrolysis-polycondensation. The early stage evolution of the process was monitored by gas chromatography coupled with mass spectrometry (GC-MS). The gels obtained were characterised by IR spectroscopy, DTA/TG analysis and DSC measurements. Important differences in the gelling process and in the properties of the obtained gels could be noticed, related to the presence of VAc and VTES in the reaction mixtures. The investigation allowed to establish the compositions and the experimental conditions in which gels with high degree of crosslinking could be obtained.     

A Model of Discontinuous, Incompressible Two-Phase Flow

Lack of hyperbolicity is a recurring problem for models of two-phase flow assuming the form of systems of balance laws. In particular, smooth solutions occur only for very special initial data, and the standard results on the local structure of discontinuous weak solutions do not apply to such nonhyperbolic systems. A simple example is inviscid, incompressible two-fluid flow with a single pressure. We suggest that such an unattractive mathematical feature may result from the mathematical derivation of the model, rather than from the underlying physical assumptions. In particular, for the case described above we present an alternative treatment which leads to a consistent model for piecewise smooth, discontinuous solutions. We obtain admissibility conditions for the anticipated discontinuities by considering the limit of vanishing viscosity with a convenient dissipation term.      

Exchange of conserved quantities in nonhyperbolic systems--An example

The velocity function associated with a smooth solution of ``zero pressure gas dynamics' satisfies Burgers equation. Indeed an elementary generalization holds for scalar conservation laws. Weak solutions, however, are compatible in this respect only under special conditions on the initial density function. Our result depends on the uniform convexity of the flux function associated with the scalar equation, and on the entropy condition applied to both systems.

     

Synthesis of Polyvinylacetate‐Sodium Montmorillonite Hybrids by Emulsion Polymerization in the Presence of Anionic Surfactants

The emulsion polymerisation of vinyl acetate (VAc) in presence of sodium dodecylsulphate (SDS) and sodium montmorillonite (NaMMT) is used in order to achieve polymer‐clay hybrids. The influence of the polyvinylacetate (PVAc), SDS, and PVAc‐SDS complex on the NaMMT structure also was investigated. The VAc emulsion polymerization rate exhibits a maximum as the NaMMT concentration increases. The XRD patterns correspond to hybrids with intercalated structure. If a water soluble comonomer, ammonium sulphato ethylmethacrylate (ASEMA) is used for copolymerization with VAc, a exfoliated hybrid structure (from XRD spectra) is obtained. The solid materials were analysed by TGA, FTIR, XRD, SEM, and TEM.     

Notes: Polymer-Water Interaction in Emulsion Copolymerization of Vinyl Acetate

Abstract

In the case of copolymer latexes of vinyl acetate with maleic diesters, the amount of water bound to particles decreases with the increase of comonomer hydrophobicity. Increasing the concentration of bound water for more polar polymers determines a decrease of free water concentration. Therefore, the concentration of free surfactant and initiator in free water is higher and results in an increase of decomposition rate of potassium persulfate initiator. The increase of more polar copolymers hydration results in the increase of latex particle size.