The regularity of solutions of reaction-diffusion equations via Lagrangian coordinates

In this paper we study the regularity of nonnegative solutions and their interfaces for the nonlinear reaction-diffusion equation $$u_t = \left( {u^m } \right)_{xx} + f\left( u \right),\left( E \right)$$ wherem>1 andf(u) is aC ¹ function withf(0)=0 and is subject to some other technical conditions. This equation has the property of finite propagation which gives rise to interfaces separating regions whereu=0 andu>0. The analysis is carried out by means of Lagrangian coordinates, formally viewing the reaction-diffusion equation as the equation governing the evolution of the density of a certain continuum. Lagrangian coordinates have been successfully applied to study nonlinear diffusion equations posed in one space dimension. The usual formulation applies to equations which can be written in the form of a conservation law, which is not the case here because of the reaction term. In problems exhibiting interfaces such technique has the merit of rendering the interfaces straight lines, much simplifying the analysis. In this paper we present anon-standard Lagrangian formulation that works innon-conservation cases. Equation (E) is then translated into this framework and we find in a natural way the necessary estimates to prove theC ¹ regularity of moving interfaces and the regularity of the weak solution near such an interface, that allows us to establish the dynamic properties of the interface for the solutions. We end the paper by describing how the method can be applied to similar problems inseveral space dimensions with radial symmetry.     

HIGHLY SENSITIVE SPECTROPHOTOMETRY OF NIOBIUM

In pH2.0-3.0,niobium(V)forms molybdonlobic acid with sodiummolybdate.A spectrophotometric method has been developed for the deter-mination of niobium based on the formation of ion-associate compound ofmolybdoniobate with Butyl Rhodamine B in aqueous solution in the presenceof polyvinyl alcohol and 0.4-0.7 mol/L H_2SO_4.The maximum absorption ofion-associate compound exhioits at 85 nm and the molar absorptivity is7.5×1.0~5 L.mol~(-1).cm~(-1)for niobium.The new method has been applied tothe determination of microamounts niobium in silicate rock,when niobiumcontent is at the level of 8×10~(-3)%,with the relative standard deviationof about 3%.     

Définition théorique des paramètres en fort niveau d’un multipôle actif non linéaire

In this paper, large signal non linear P parameters are rigorously defined, allowing the characterization of non linear active n-port circuits in the frequency domain with the aim of computer aided design of power microwave devices. No a priori conditions bind the parameters to the variables describing the input signal. However the following rules apply to the parameters: they may be function of any input variables of the n-port circuit; the expression of the large-signal parameters should become identical to the expression of the linear parameters characterizing the n-port circuit under linear operating conditions when the values of the input variables tend to zero. An application of the definition to afet is demonstrated.     

Algebraic study of chiral anomalies

The algebraic structure of chiral anomalies is made globally valid on non-trivial bundles by the introduction of a fixed background connection. Some of the techniques used in the study of the anomaly are improved or generalized, including a systematic way of generating towers of descent equations.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under contract DE-AC03-76SF00098 and in part by the National Science Foundation under research grant PHY81-18547     

Numerical Study of Pore Sizes Distribution in Gels

We introduce a new numerical technique for the calculation of the pore size distribution in two-dimensional disordered systems. Our method is based on a triangulation technique which allows a closer measurement of pores surface without any morphological hypothesis.In this work, we focus our calculations in simulated gels. Such materials are modeled in two different conditions: by means of the Diffusion-Limited and Reaction-Limited Cluster-cluster Aggregation algorithms, DLCA and RLCA, respectively. In both situations, when the particles concentration decreases, the average pores size increases. The more compact cluster in RLCA, compared with DLCA, is consistent with the pore size distribution we have calculated. The simulated mean pore size is quantitatively in agreement with experimental data from literature.     

Parallel and multiplexed bead-based assays and encoding strategies

Advances in high throughput screening (HTS), together with the rapid progress in combinatorial chemistry, genomic and proteomic sciences have dramatically stimulated the development of a variety tools to enable the drug discovery process to become more efficient. Major future challenges in HTS include obtaining high density and good quality data based on assays that are rapid, reliable, inexpensive, sensitive, simple and miniaturised. This paper reviews the development and role of bead-based assays for HTS including DNA and single nucleotide polymorphism (SNP) assays, particularly from a multiplex perspective and evaluating the recent advances in bead-based arrays. The encoding strategies that are commonly used in bead-based assays are highlighted, while the importance of magnetic beads in genomic and proteomic purifications is discussed. In conclusion, bead-based assays offer a powerful promising approach for many aspects of drug discovery.     

Optical Properties of Model Compounds of Polyaniline

The UV and visible spectra of six model compounds were studied. These compounds can be considered as models of polyaniline in the reduced, cation radical, partially oxidized and oxidized forms. After treatment of a mixture of equal molar quantities of the reduced form (DPPD) and the oxidized form (QDIM) with acid, the following reaction was observed: DPPD(I)+QDIM(III)+2H⁺=2DPPD⁺(II) After similar treatment of the partially oxidized form (V) with acid, the radical cation salt formed. The UV and visible spectra of polyaniline in the reduced form, oxidized form and conductive form are similar to the spectra of DPPD, QDIM and DPPD⁺ or radical cation salt of V respectively. We propose that the polyaniline synthesized by chemical oxidation of aniline consists of oxidized and reduced repeat units. Upon protonation a redox reaction (or electron rearrangement) occurs and forms delocalized radical cations (polarons) in the polymer chain which are highly conductive.     

Selenium speciation by coupling vesicle mediated HPLC with off-line ETAAS and on-line focused microwave digestion HG-AAS detection

A novel High Performance Liquid Chromatography (HPLC) method for the separation of selenium species with specific detection by off-line Electrothermal Atomization Atomic Absorption Spectrometry (ETAAS) or on-line focused microwave digestion (MW) Hydride Generation Atomic Absorption Spectrometry (HG-AAS) is described. Vesicular mobile phases of the cationic surfactant didodecyldimethylammonium bromide (DDAB) have been evaluated for the liquid chromatographic separation of inorganic selenium (selenite and selenate) and different selenoaminoacids (selenocystine, selenomethionine and selenoethionine) on a C(18) reversed-phase column modified by DDAB molecules. The effects of different parameters (pH, buffer and vesicle concentrations) of the mobile phase on the retention times have been determined. The detection limit for selenium with the proposed off-line HPLC-ETAAS method has been found to be 5 microg/L of Se. The detection limit using HPLC-"on line" focused microwave digestion-HG-AAS has been found to be 1 microg/L of Se, with a precision (repeatability) better than +/- 5%. The latter proved to be an exceptional on-line real-time chromatographic detector for selenium speciation purposes.     

Iron(III)-catalyzed Prins-type cyclization using homopropargylic alcohol: a method for the synthesis of 2-alkyl-4-halo-5,6-dihydro-2H-pyrans

[reaction: see text] A new Prins-type cyclization between homopropargylic alcohol and aldehydes in the presence of FeX(3) to obtain 2-alkyl-4-halo-5,6-dihydro-2H-pyrans in good yield is described. Osmium-catalyzed cis dihydroxylation provided direct access to trans-2-alkyl-3-hydroxy-tetrahydro-pyran-4-ones. Anhydrous ferric halides are also shown to be excellent catalysts for the standard Prins cyclization using homoallylic alcohol. Isolation of an intermediate acetal provides substantiation of a proposed mechanism.     

Synthesis of 4-aryl-2,3,6,7-tetrahydro-1H-pyrimido[4,5-b][1,4]-diazepin-6-ones from 4,5-diamino-1H-pyrimidin-6-ones and 1-aryl-3-(dimethylamino)-1-propanones

The reaction of 1-aryl-3-(dimethylamino)-1-propanones 1 with one equivalent of 4,5-diamino-1H-pyrimidin-6-ones 2 , in acidic medium, leads to the formation of 4-aryl-2,3,6,7-tetrahydro-1H-pyrimido[4,5-b]-[1,4]diazepin-6-ones 3 . The structure elucidation of the products is based on detail nmr analysis of experiments such as ¹³C, ¹H and DEPT including selective ¹³C{¹H} decoupling experiments.