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.     

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.     

Thermo‐oxidative degradation of HDPE as a function of its crystalline content

The composition, the thermal properties, and the kinetics of the thermo‐oxidative degradation of high‐density polyethylene (HDPE) were studied as a function of the increasing crystalline fraction, which resulted from the selective extraction of the amorphous part, through digestion by immersion in fuming nitric acid (HNO₃) for different periods of time. The chemical and thermodynamic changes in HDPE, brought about by digestion in nitric acid for different periods of time, are discussed. Changes in the chemistry and microstructure of the HDPE, as a function of acid treatment for different periods of time, were studied using infra‐red spectroscopy (FTIR), gel permeation chromatography (GPC), and thermal analysis (DSC and TGA), as well as scanning electron microscopy (SEM). These studies were carried out as a function of the extracted amorphous fraction of HDPE samples via digestion in HNO₃. These studies showed that in the first stages of the acid chemical attack, the amorphous part first undergoes a chemical modification and then dissolves into the strong acid medium. The total crystalline fraction apparently decreases during the first stages of the chemical attack and then increases as the amorphous part is extracted. TGA results show that as the selective extraction of the amorphous part occurs, there is a displacement of the thermo‐oxidative degradation toward higher temperatures. The kinetics of the thermo‐oxidative degradation as a function of the extraction of the amorphous part was followed according to the Horowitz‐Metzger method, and it was found that as the concentration of the crystalline fraction increases, the activation energy for the thermo‐oxidative degradation increases. SEM studies show that the extraction of the amorphous part does not affect the size of the crystalline lamellar thickness of HDPE. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1906–1915, 2009     

Quantum electronic transport: Linear and nonlinear conductance from the Keldysh approach

This is a review of the derivation of the Landauer conductance using the Keldysh non-equilibrium Green's function (NEGF) formalism and the equations-of-motion (EOM) method. We consider the elastic quantum electronic transport through a multi-lead device and treat the conductor in the mean-field approximation. This is suitable for open quantum dots as well as for several molecular systems where charging effects are negligible. The focus of the presentation is to unveil the technical issues involved in the formalism. We show how the Landauer conductance emerges as a linear term in the current-voltage I-V characteristics and indicate how to go beyond this regime. We address the connection of the NEGF approach to recent developments in molecular transport and discuss the problems that arise when one tries to include interaction effects beyond the mean field.     

4-Trichloroacetyl-1,2,3-triazoles: A versatile building block for rapid assessment of carbohydrazides and rufinamide derivatives

This work reports the synthesis of a series of (1H-1,2,3-triazol-4-yl)carbohydrazides (2), which were obtained from 4-trichloroacetyl-1H-1,2,3-triazoles (1). Triazoles 1 were synthesized by 1,3-dipolar cycloaddition reaction, starting from 4-alkoxy-1,1,1-trichloroalk-3-en-2-ones and benzyl azides and easily (15 min) converted to 2 by reaction with hydrazine hydrate (73–82% yield). Carbohydrazides 2 proved to be a versatile building block for constructing a series of fluorinated heterocycles analogous to rufinamide, i.e., 1H-1,2,3-triazol-4-yl-1,3,4-oxadiazoles, a pyrrole derivative, and a 2-pyrazoline, through [4+1]–, [1+4]–, and [3+2]–cyclocondensation reactions, respectively. Finally, and according to the Lipinski’s rule of five, 2,6-difluorobenzylated 1,2,3-triazoles can be considered as potential candidates for further biological activity assays.     

Addition of Surfactants and Non-Hydrolytic Proteins and Their Influence on Enzymatic Hydrolysis of Pretreated Sugarcane Bagasse

Poly(ethylene glycol) (PEG 4000) and bovine serum albumin (BSA) were investigated with the purpose of evaluating their influence on enzymatic hydrolysis of sugarcane bagasse. Effects of these supplements were assayed for different enzymatic cocktails (Trichoderma harzianum and Penicillium funiculosum) that acted on lignocellulosic material submitted to different pretreatment methods with varying solid (25 and 100 g/L) and protein (7.5 and 20 mg/g cellulose) loadings. The highest levels of glucose release were achieved using partially delignified cellulignin as substrate, along with the T. harzianum cocktail: increases of 14 and 18 % for 25 g/L solid loadings and of 33 and 43 % for 100 g/L solid loadings were reached for BSA and PEG supplementation, respectively. Addition of these supplements could maintain hydrolysis yield even for higher solid loadings, but for higher enzymatic cocktail protein loadings, increases in glucose release were not observed. Results indicate that synergism might occur among these additives and cellulase and xylanases. The use of these supplements, besides depending on factors such as pretreatment method of sugarcane bagasse, enzymatic cocktails composition, and solid and protein loadings, may not always lead to positive effects on the hydrolysis of lignocellulosic material, making it necessary further statistical studies, according to process conditions.     

Ethanol Production from Sugarcane Bagasse Hydrolysate Using Pichia stipitis

The objective of this study was to evaluate the ethanol production from the sugars contained in the sugarcane bagasse hemicellulosic hydrolysate with the yeast Pichia stipitis DSM 3651. The fermentations were carried out in 250-mL Erlenmeyers with 100 mL of medium incubated at 200 rpm and 30 °C for 120 h. The medium was composed by raw (non-detoxified) hydrolysate or by hydrolysates detoxified by pH alteration followed by active charcoal adsorption or by adsorption into ion-exchange resins, all of them supplemented with yeast extract (3 g/L), malt extract (3 g/L), and peptone (5 g/L). The initial concentration of cells was 3 g/L. According to the results, the detoxification procedures removed inhibitory compounds from the hemicellulosic hydrolysate and, thus, improved the bioconversion of the sugars into ethanol. The fermentation using the non-detoxified hydrolysate led to 4.9 g/L ethanol in 120 h, with a yield of 0.20 g/g and a productivity of 0.04 g L^?1 h^?1. The detoxification by pH alteration and active charcoal adsorption led to 6.1 g/L ethanol in 48 h, with a yield of 0.30 g/g and a productivity of 0.13 g L^?1 h^?1. The detoxification by adsorption into ion-exchange resins, in turn, provided 7.5 g/L ethanol in 48 h, with a yield of 0.30 g/g and a productivity of 0.16 g L^?1 h^?1.     

Vortical dynamics of spinning quantum plasmas: helicity conservation

It is shown that a vorticity, constructed from the spin field of a quantum spinning plasma, combines with the classical generalized vorticity (representing the magnetic and the velocity fields) to yield a new grand generalized vorticity that obeys the standard vortex dynamics. Expressions for the quantum or spin vorticity and for the resulting generalized helicity invariant are derived. Reduction of the rather complex spinning quantum system to a well known and highly investigated classical form opens familiar channels for the delineation of physics peculiar to dense plasmas spanning solid state to astrophysical objects. A simple example is worked out to show that the magnetics of a spinning plasma can be much richer than that of the corresponding classical system.