Asymptotic limit law for the close approach of two trajectories in expanding maps of the circle

Summary Given two pointsx, yS ¹ randomly chosen independently by a mixing absolutely continuous invariant measure of a piecewise expanding and smooth mapf of the circle, we consider for each >0 the point process obtained by recording the timesn>0 such that |f ⁿ (x)–f ⁿ (y)|. With the further assumption that the density of is bounded away from zero, we show that when tends to zero the above point process scaled by –1 converges in law to a marked Poisson point process with constant parameter measure. This parameter measure is given explicity by an average on the rate of expansion off.Partially supported by FAPESP grant number 90/3918-5     

Tree Oriented Pullback

Given two epimorphisms of algebras A ? B and C ? B, we consider the pullback R. We introduce a particular class of algebras, the tree oriented pullback, where there is a close relationship between the category of indecomposable modules of these algebras. This leads us to prove that if A and C are hereditary algebras, then R is a tilted algebra.     

Switching and enhanced bistability in an asymmetric nonlinear directional coupler with a metamaterial channel

We numerically simulate the propagation and switching of ultra-short pulses in a metamaterial nonlinear directional asymmetric coupler where one of the guides is a conventional medium with a positive refraction index having a decreasing Kerr nonlinearity. The second guide is based in a metamaterial. A complete study of the nonlinear dynamics of ultra-short pulses propagation and switching in this new nonlinear directional coupler, including the transmission characteristics, bistability, critical power, compression factor and extinction coefficients are presented and compared to those of a conventional coupler. We conclude that the conventional coupler has higher transmission efficiency and extinction rate when compared with the metamaterial coupler. However the metamaterial coupler presents bistability which opens the possibility of such device to be used in a large variety of optical switching, storage and logical gates. We show that the input power range leading to bistability can be optimized by controlling the profile of the nonlinear refraction index of the conventional channel.     

Parkia pendula Seed Lectin: Potential Use to Treat Cutaneous Wounds in Healthy and Immunocompromised Mice

Parkia pendula seed lectin was used to treat cutaneous wounds of normal and immunocompromised mice, inducing cicatrization. Methotrexate (0.8 mg/kg/week) was used as immunosuppressive drug. Wounds were produced in the dorsal region (1 cm²) of female albino Swiss mice (Mus musculus), health and immunocompromised. Wounds were daily topically treated with 100 μL of the following solutions: (1) control (NaCl 0.15 M), (2) control Im (0.15 M NaCl), (3) P. pendula seed lectin (100 μg/mL), and (4) P. pendula seed lectin Im (100 μg/mL). Clinical evaluation was performed during 12 days. Biopsies for histopathology analysis and microbiological examinations were carried out in the second, seventh, and 12th days. The presence of edema and hyperemia was observed in all groups during inflammatory period. The first crust was detected from the second day, only in the groups treated with P. pendula seed lectin. Microbiological analysis of wounds from day 0 to day 2 did not show bacterium at P. pendula seed lectin group; however, Staphylococcus sp. was detected every day in the other groups. The lectin markedly induced a total wound closing at P. pendula seed lectin and P. pendula seed lectin Im groups on 11th day of evolution. The present study suggests that P. pendula seed lectin is a biomaterial potential to show pharmacological effect in the repair process of cutaneous wounds.     

Colour switching with photochromic vinylidene-naphthofurans

A series of novel photochromic vinylidene-naphthofurans with extended conjugation, and a free hydroxyl function, were easily prepared using the Suzuki reaction. After silanization, these dyes were embedded in ormosil matrices affording solid and transparent materials that acquire different colourations (violet, green, bluish), reversibly, when exposed to the UV (Sun) light, for 2?min, at room temperature. The presence of an extra phenyl ring in some positions affects both the λ_max of absorption of the photochromic compounds in the uncoloured closed and open coloured form. After removal of the light source the materials lose progressively their colouration returning to the initial uncoloured state in less than 15?min?at room temperature.     

Criteria for -continuity

Bernoullicity is the strongest mixing property that a measure-theoretic dynamical system can have. This is known to be intimately connected to the so-called metric on processes, introduced by Ornstein. In this paper, we consider families of measures arising in a number of contexts and give conditions under which the measures depend -continuously on the parameters. At points where there is -continuity, it is often straightforward to establish that the measures have the Bernoulli property.

     

Universal electro-osmosis formulae for porous media

Approximate analytical formulae valid for any porous media with elongated pores are derived for the electro-osmotic coefficient alpha and for the average ionic concentration n . A macroscopic Debye-Hückel length kappa (-)(-1) based on n is introduced. Simultaneously, the electro-osmotic coefficient alpha is systematically calculated for various media, zeta potentials and electrolyte concentrations by solving the local equations. Numerical results show that kappa (-)(-1) and alpha follow universal curves valid whatever the porous medium; these curves can be approximated by the analytical formulae previously derived. These formulae can be used to provide a priori estimates of the electro-osmotic coefficient.     

Synthesis and characterization of new trifluoromethyl substituted 3‐ethoxycarbonyl‐ and 3‐pyrimidin‐2‐yl)‐(1,2,3)‐oxathiazinane‐S‐oxides

This paper describes the synthesis and characterization of a new series of 4‐substituted‐3‐ethoxycarbonyl‐6‐trifluoromethyl‐(1,2,3)‐oxathiazinane‐S‐oxides and 3‐(4,6‐diphenyl‐pyrimidin‐2‐yl)‐6‐trifluoromethyl‐(1,2,3)oxathiazinane‐S‐oxides from the cyclization reaction of 4,4,4‐trifluoro‐3‐hydroxybutylcarbamates and 4‐(4,6‐diphenyl‐pyrimidin‐2‐ylamino)‐1,1,1‐trifluoro‐butan‐2‐ols with thionyl chloride. The analysis of the NMR data allowed us to define important features of the molecular structure. Significant chemical and structural differences were observed between the trifluoromethylated oxathiazinanes obtained in this work from other analogue compounds reported in the literature.     

Efficiency of the refocused 31P-29Si MAS-J-INEPT NMR experiment for the characterization of silicophosphate crystalline phases and amorphous gels

One- and two-dimensional refocused MAS-J-INEPT NMR experiments in the solid state (through-bond polarization transfer) involving the highly abundant 31P spin and the rare 29Si spin are described for the crystalline silicophosphate phase Si5O(PO4)6 and complex mixtures of SiP2O7 polymorphs. The evaluation of the 2JP-O-Si coupling constants for all 29Si sites is obtained by the careful analysis of the INEPT build-up curves under fast MAS. The results are in agreement with the crystallographic data, taking into account the various J coupling paths. The efficiency of the experiment is demonstrated by its application to more complex systems such as silicophosphate amorphous gels (obtained by the sol-gel process).     

Comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry of monoterpenoids as a powerful tool for grape origin traceability

The establishment of the monoterpenoid profile of Vitis vinifera L. cv. 'Fern?o-Pires' white grape was achieved by headspace solid-phase microextraction coupled with comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry (GCxGC-ToF-MS). The plot of the first dimension versus the second dimension retention times using the m/z 93, 121, and 136 was used. The grapes were found to contain 56 monoterpenoids identified by GCxGC-ToF-MS. From these, 20 were reported for the first time in grapes. According to their chemical structure, the compounds were organized in different groups: monoterpene hydrocarbons and monoterpene oxygen-containing compounds, this later divided in oxides, alcohols (monoterpenols and monoterpendiols), aldehydes, esters, and ketones. A database composed by the retention indices of monoterpenoids calculated in the bi-dimensional column set was created, representing a developmental step in monoterpenoid analysis using a GCxGC system. Remarkable results were also obtained in terms of compound classification based on the organized structure of the peaks of structurally related compounds in the GCxGC contour plot. This information represents a valuable approach for future studies, as the ordered-structure principle can considerably help the establishment of the composition of samples. This study proposes a methodology and provides data that can be applied to determine the monoterpenoid profile of grapes, and its extension to the analysis of musts, and wines. As monoterpenoids are secondary metabolites whose synthesis is encoded by variety-related genes, the terpenoid profile may be used as a way to trace its varietal origin.