The IVP for the dispersion generalized Benjamin–Ono equation in weighted Sobolev spaces

We study the initial value problem associated to the dispersion generalized Benjamin–Ono equation. Our aim is to establish persistence properties of the solution flow in weighted Sobolev spaces and to deduce from them some sharp unique continuation properties of solutions to this equation. In particular, we shall establish optimal decay rate for the solutions of this model.     

The Cayley–Dickson process for dialgebras

We adapt the algorithm of Kolesnikov and Pozhidaev, which converts a polynomial identity for algebras into the corresponding identities for dialgebras, to the Cayley–Dickson doubling process. We obtain a generalization of this process to the setting of dialgebras, establish some of its basic properties, and construct dialgebra analogues of the quaternions and octonions.     

On Transfer Operators for Continued Fractions with Restricted Digits

For any non-empty subset I of the natural numbers, let _I denotethose numbers in the unit interval whose continued fractiondigits all lie in I. Define the corresponding transfer operator for , where Re (rß) = _I is the abscissa of convergence of the series . When acting on a certain Hilbert space H_I, rß, weshow that the operator L_I, rß is conjugate to an integraloperator K_I, rß. If furthermore rß is real,then K_I, rß is selfadjoint, so that L_I, rß: H_I, rß H_I, rß has purely real spectrum.It is proved that L_I, rß also has purely real spectrumwhen acting on various Hilbert or Banach spaces of holomorphicfunctions, on the nuclear space C [0, 1], and on the Fréchetspace C [0, 1]. The analytic properties of the map rß L_I, rßare investigated. For certain alphabets I of an arithmetic nature(for example, I = primes, I = squares, I an arithmetic progression,I the set of sums of two squares it is shown that rß L_I, rß admits an analytic continuation beyond thehalf-plane Re rß > _I. 2000 Mathematics SubjectClassification 37D35, 37D20, 30B70.     

BEST MONOTONE L_■-APPROXIMATIONS IN SEVERAL VARIABLES

Given a continuous function f defined on the unit cube of R~n and a convexfunction _t,_t(0)-0,_t(x)>0,for x>0,we prove that the set ofbest L~(t)-approximations by monotone functions has exactly one elementft,which is also a continuous function.Moreover if the family of convexfunctions {_t}t>0 converges uniformly on compact sets to a function _0,then the best approximation f_t→f_0 uniformly,as t→0,where fo is thebest approximation of f within the Orlicz space L~(0) The best approxima-tions{f_t}are obtained as well as minimizing integrals or the Luxemburgnorm     

A simple protocol for the preparation of β-enamino ketones catalyzed by NbOPO4 under solvent free conditions

A novel application of the highly stable niobium oxide phosphate (NbOPO₄) as an efficient catalyst for the synthesis of β-enamino ketones under solvent-free conditions is described. This protocol, exhibits attractive yields, short reaction periods, lower loading of catalyst and high chemoselectivity.     

Intramolecular Hydroamination of Selenoalkynes to 2-Selenylindoles in the Absence of Catalyst

In this work, a series of 2-chalcogenylindoles was synthesized by an efficient methodology, starting from chalcogenoalkynes, including a previously unreported tellurium indole derivative. For the first time, these 2-substituted chalcogenylindoles were obtained in the absence of metal catalyst or base, under thermal conditions only. In addition, the results described herein represent a methodology with inverse regioselectivity for the chalcogen functionalization of indoles.     

Influence of metal ions on antioxidant behaviour in polypropylene

The effect of Cr(III), Fe(III) and Cu(II) ions, at trace levels, on the effectiveness of four commercial antioxidant systems, viz. Topanol, Santowhite, Hostanox 03 and Irganox 1425, in polypropylene (PP) films is examined using infra-red and second-order derivative uv spectroscopy. The results show that at these levels the metal ions have a minor effect on the unstabilised polymer. However, the ions can have a beneficial or adverse effect on antioxidant activity, particularly under oven ageing conditions. The observed effect depends on the metal/antioxidant system, and is attributed to an indirect interaction between the components which can delay or accelerate antioxidant decomposition in the polymer. An exception to this behaviour is the metal complex Irganox 1425, which interacts strongly with copper ions in the polymer matrix. The antioxidant is partially transformed by copper ions during the compression moulding stage. The beneficial effect present in some cases is in direct contrast with what has generally been observed in studies using unstabilised polymers.     

Operator Splitting Multiscale Finite Volume Element Method for Two-Phase Flow with Capillary Pressure

A numerical method used for solving a two-phase flow problem as found in typical oil recovery is investigated in the setting of physics-based two-level operator splitting. The governing equations involve an elliptic differential equation coupled with a parabolic convection-dominated equation which poses a severe restriction for obtaining fully implicit numerical solutions. Furthermore, strong heterogeneity of the porous medium over many length scales adds to the complications for effectively solving the system. One viable approach is to split the system into three sub-systems: the elliptic, the hyperbolic, and the parabolic equation, respectively. In doing so, we allow for the use of appropriate numerical discretization for each type of equation and the careful exchange of information between them. We propose to use the multiscale finite volume element method (MsFVEM) for the elliptic and parabolic equations, and a nonoscillatory difference scheme for the hyperbolic equation. Performance of this procedure is confirmed through several numerical experiments.     

Thermal behavior of verapamil hydrochloride and its association with excipients

The thermal properties of verapamil hydrochloride (VRP) and its physical association as binary mixtures with some common excipients were evaluated. Thermogravimetry (TG) was used to determine the thermal mass loss, as well as to study the kinetics of VRP thermal decomposition, using the Flynn-Wall-Ozawa model. Based on their frequent use in pharmacy, five different excipients (microcrystalline cellulose, magnesium stearate, hydroxypropyl methylcellulose, polyvinylpyrrolidone and talc) were blended with VRP. Samples were prepared by mixing the analyte and excipients in a proportion of 1:1 (m/m). DSC curves for pure VRP presented an endothermic event at 143 ± 2 °C (ΔH_melt = 132 ± 4 J g⁻¹), which corresponds to the melting (literature T_m = 143.7 °C, ΔH_melt = 130.6 J g⁻¹). Comparisons among the observed results for each compound and their binary physical mixtures presented no relevant changes. This suggests no interaction between the drug and excipient.