The Cauchy Problem for a Nonlinear Diffusion Equation with Absorption and Convection

In this paper we construct the large-time solution of the equation which models the effectof nonlinear absorption on thin film flow of a viscous fluidon a sloping bed. For initial data with finite support we showhow the asymptotic structure of the Cauchy problem depends onthe absorption index . An important addition motivation forthe study is to provide a basis for extending the results tothe more general equation which has applications in plasma physics.     

A remark on partial linear spaces of girth 5 with an application to strongly regular graphs

We derive a lower bound on the number of points of a partial linear space of girth 5. As an application, certain strongly regular graphs with=2 are ruled out by observing that the first subconstituents are partial linear spaces.     

Effects of speaking rate on tongue position and velocity of movement in vowel production

This study used glossometry to examine the position of the tongue and the velocity of its movements in vowels spoken normally and at a self-selected fast rate. The subject in experiment 1 showed lingual undershoot for stressed vowels in "a big again" and "a bob again." The tongue was lower for /I/ and higher for /a/ at the fast rate than at the normal rate. The stressed vowels exerted an affect on unstressed vowels: The tongue was lower in the schwas that preceded and followed /a/ than /I/. Only one of the three subjects in experiment 2 showed no lingual undershoot for fast-rate /I/. The tongue was higher at the fast rate than at the normal rate in the schwas flanking /I/ so that the displacement was less at the fast rate than at the normal rate. Another talker increased the peak velocity of tongue movements at the fast rate and showed no undershoot for /a/. Multiple regression analyses showed that the timing of movements for successive phonetic segments accounted well for undershoot in only one of the three subjects. The results suggest that in order to model the effects of speaking rate on the tongue movements used in forming stressed vowels, it will be necessary to take into account: (1) how much vowels are shortened at a fast rate: (2) how much the peak velocity of tongue movements is increased, if at all; and (3) the position of the tongue before and after the stressed vowels. All three factors are likely to be influenced by how clearly the talker wishes to speak.     

Quasi-genericity of bifurcations to high dimensional invariant tori for maps

We consider a family of maps in a Banach spaceE near the situation when the derivative at the fixed point has two pairs of complex eigenvalues lying on the unit circle, the other part of the spectrum being strictly inside the unit disc. We focus our attention on the region of the parameter space where the truncated normal form of the maps shows a bifurcation of a family of invariantT ¹-circles into a family of invariantT ²-tori. We show that this problem needs a 3 dimensional parameter unfolding and that, for the complete maps, bifurcation occurs at points _,, where is the rotation number on the non-normally hyperbolicT ¹-circle, ande ^±2i are the eigenvalues of the constant matrix conjugated to the non-contracting part of the linearization on the normal fiber bundle overT ¹. Making some non-resonance and diophantine assumptions on (, ) leading to a positive measure Cantor set inT ², we show that in paraboloïdal regions of the 3 dim. parameter space we have clean bifurcations as for the truncated normal form. The complement of these regions forms a set of bubbles such as the ones obtained by Chenciner in [Chen] for a codimension 2 problem for maps in ². The main tool here is a generalization for a matrix function onT ¹, close to a constant, of the quasi-conjugacy to a constant, modulo a minimum of additional parameters (moved quasi-conjugacy). For the infinite dimensional case we use aC decoupling result on the angular dependent linear parts into a contraction, still angular dependent, and another part quasi-conjugated to a constant matrix. This type of analysis applies for a wide range of problems, where truncated normal forms of the maps give bifurcations fromT ⁿ toT ⁿ⁺¹ tori, and this needs a (n+1)-dimensional parameter unfolding.We gratefully acknowledge the DRET (contrat 86/1445) who supported one of the authors (J.L.) during this work. This research has been also supported by the E.E.C. contract No. ST 2J-0316-C (EDB) on Mathematical problems in nonlinear Mechanics     

Ultra'soft X-ray diagnostics of short-living plasmas

Ultrasoft X-ray plasma diagnostics in IPP is realized by using X-ray diodes with Al photocathodes and submicrometer nitrocellulose filters. The X-ray detections system is suitable for measurements in a relatively broad range of radiation intensities in the spectral interval of (10–1000) eV with the time resolution of (1–10) ns under various plasma conditions. Construction, calibration and characteristic properties of the measuring apparatus are described. To illustrate its use, some results of the diagnostics of REB-heated plasma are presented.We would like to acknowledge Dr. P. unka for many helpful discussions and Dr. J. Ullschmied for cooperation in REB-heated plasma diagnostics interpretation.     

Time dependence of the luminescence excited by rectangular pulses

The theory of the time dependence of luminescence, during and after excitation by rectangular pulse, is discussed. Some phenomena, which cannot be described as direct excited luminescence, will be mentioned. In order to explain these phenomena, the model for energy transfer between two monomolecular centres has been used. On the basis of this model, the theoretical time dependence of the luminescence is obtained. The theoretical formula describe qualitatively very well the experimental observations in ZnSMn and other compounds.     

Off-shell behaviour of theN-N interaction in a six-quark resonating group model of the deuteron

Two different 6-quark resonating group models of the deuteron are investigated to study the off-shell property of theN-N interaction. In the first model the quarks interact by a central one-gluon-exchange potential plus confinement potential. The meson-exchange contribution to then-p potential is simulated by a central GaussianN-N potential. In the second model the quarks interact by one-gluon-and one-pion-exchange potentials (central and noncentral) plus confinement potential. A small additional -exchange potential between neutron and proton binds the deuteron at the correct energy.Several off-shell variants of the two resonating group models are compared with each other by analyzing their elastic electron scattering cross sections. It is found that the standard renormalized version of the resonating group model yields potentials and wave functions that may be considered physical within the limitations of the model. Unitary off-shell transformations, which modify potentials and wave functions in any sizeable way, lead to a disagreement between the charge distribution predicted by the model via analysis of electron scattering and the charge distribution following from the microscopic quark distribution.Both of the 6-quark models support a soft repulsive core of the tripletn-p potential with a core height of around 900 MeV.     

2-Amino-4,4-disubstituted-5-carboxymethyl-Δ2-1,3,4-oxadiazolin-4-ium chlorides and their recyclization in acetic anhydride

2-Methylamino-4,4-disubstituted-5-carboethoxymethyl-²-1,3,4-oxadiazolin -4-ium chlorides were obtained from the reaction of 1,1-disubstituted-4-methylsemicarbazides with ethyl propiolate in the presence of hydrochloric acid. After hydrolysis of the ester these chlorides recyclize in acetic anhydride to 1-substituted-3-acetoxy-1H-pyrazoles. The difference in the direction of ring opening with acetic anhydride in the betaines of 1,3,4-oxadiazolin-5-acetic acids and their thia-analogs has been demonstrated.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 12, pp. 1685–1688, 1992.     

Pseudo-cross-conjugated mesomeric betaines. 1. Synthesis of pseudo-cross-conjugated mesomeric betaines from quinoxaline derivatives

A new method for the synthesis of pseudo-cross-conjugated mesomeric betainic heterocyclic compounds with an angular nitrogen atom has been developed consisting in the reaction of 1,4-dielectrophile — -carbethoxy-2-(3-chloro)quinoxalylacetonitrile with azoles. Experimental regularities have been studied and a reaction mechanism has been proposed including the stage of formation of an ylide from a quaternary azolium salt. A pseudo-crossconjugated mesomeric betainic heterocyclic compound containing a thiazole ring compound has been synthesized for the first time.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1528–1533, November, 1992.     

Synthesis and investigation of the mesomorphic properties of pyran derivatives

4-[(5,6-Dihydro-2H-pyran-4-yl)methoxy]benzylidene-4-alkoxyanilines, which have the properties of smectic liquid crystals, were synthesized. The effect of the pyran ring in the benzylidene component and the length of the aliphatic radical in the aniline component on the type and thermal stability of the meso phase was ascertained.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 327–328, March, 1992.