Support Varieties of Non-Restricted Modules over Lie Algebras of Reductive Groups

Let G be a connected semisimple group over an algebraicallyclosed field K of characteristic p>0, and g=Lie (G). Fixa linear function g* and let Z_g() denote the stabilizer of in g. Set N_p(g)={xg|x^[p]=0}. Let C(g) denote the category offinite-dimensional g-modules with p-character . In [7], Friedlanderand Parshall attached to each MOb(C(g)) a Zariski closed, conicalsubset V_g(M)N_p(g) called the support variety of M. Suppose thatG is simply connected and p is not special for G, that is, p2if G has a component of type B_n, C_n or F₄, and p3 if G has acomponent of type G₂. It is proved in this paper that, for anynonzero MOb(C(g)), the support variety V_g(M) is contained inN_p(g)Z_g(). This allows one to simplify the proof of the Kac–Weisfeilerconjecture given in [18].     

Solid state synthesis and structure of two novel polyoxometalates [(n-Bu)_4N]_4[M_6o_(19)][Ag_21_4](M=Mo,W)

The reaction of [NH4]2[MO2S2],AgI and (n-Bu)4NBr in solid state produced the polyoxometalates [(n-Bu)4N]4[M6O19][Ag2l4] (1,M=Mo;2,M=W) which were structurally determined.The crystals of 1 and 2 are isomorphous,monoclinic,space group P221/c.1,a=1.6624(2),6=1.6699(3),c=1.7217(2) nm,(8=98.29(1)°,V =4.729(1) nm3,Z=2,R=0.040,Rw=0.037;2,a= 1.6636(3),6=1.6733(3),c=1.7190(3) nm,β=98.25(1)°,V=4.736(1) nm3,Z=2,R=0.038,Rw=0.047.The results of the structure determination showed that the two compounds had the same structures whose skeletons are composed of [Ag2I4]2-and [M6O19]2-The difference of them and heteropolymetalate compounds synthesized in solution is that the title compounds contain cluster ion,heteropolymetalate and organic cations,while the latter is only composed of heteropolymetalate and organic cations.     

Atomic spectrometric detection of hydride forming elements following in situ trapping within a graphite furnace

The historical development of in situ techniques in the graphite furnace based on chemical generation of hydride forming elements and mercury coupled with batch and flow injection sampling formats is presented. Detection via AAS, MIP-AES, ICP-MS and FANES is considered. The current state-of-the-art, including advantages and limitations of this approach, is discussed.     

Computing Invariant Densities and Metric Entropy

We present a method for accurately computing the metric entropy (or, equivalently, the Lyapunov exponent) of the absolutely continuous invariant measure μ for a piecewise analytic expanding Markov map T of the interval. We construct atomic signed measures μ _M supported on periodic orbits up to period M, and prove that super-exponentially fast. We illustrate our method with several examples. Received: 25 July 1999 / Accepted: 7 January 2000     

Multifractal Analysis of Lyapunov Exponent for Continued Fraction and Manneville–Pomeau Transformations and Applications to Diophantine Approximation

We extend some of the theory of multifractal analysis for conformal expanding systems to two new cases: The non-uniformly hyperbolic example of the Manneville–Pomeau equation and the continued fraction transformation. A common point in the analysis is the use of thermodynamic formalism for transformations with infinitely many branches. We effect a complete multifractal analysis of the Lyapunov exponent for the continued fraction transformation and as a consequence obtain some new results on the precise exponential speed of convergence of the continued fraction algorithm. This analysis also provides new quantitative information about cuspital excursions on the modular surface. Received: 13 October 1998 / Accepted: 19 April 1999     

Influence de la structure chimique de la séquence diimide sur la relaxation γ des polyimides

Dynamic mechanical measurements in the −150 °C /+50 °C temperature range at 1, 3 and 10 Hz were carried out on a series of polyimides based on ODA diamine. A shift of 60 °C towards the lower temperatures of the γ relaxation was found on replacing N,N′-pyromellitimide (PMDA) by bicyclo [2.2.2]oct-7-ene-2,3,5,6-tetracarboxylic di-imide (BCDA). A correlation between the dianhydride monomer structure variation and γ relaxation temperature is interpreted in terms of charge transfer interactions.     

Odderon and photon exchange in electroproduction of pseudoscalar mesons

We investigate the reaction where PS denotes a pseudoscalar meson , , , or and X either a proton or resonance or continuum state into which the proton can go by diffractive excitation. At high energies photon and odderon exchange contribute to the reaction. The photon exchange contribution is evaluated exactly using data for the total virtual photon-proton absorption cross section. The odderon exchange contribution is calculated in nonperturbative QCD, using functional integral techniques and the model of the stochastic vacuum. For the proton we assume a quark-diquark structure as suggested by the small odderon amplitude in pp and forward scattering. We show that odderon exchange leads to a much larger inelastic than elastic PS production cross section. Observation of our reaction at HERA would establish the soft odderon as an exchange object on an equal footing with the soft pomeron and would give us valuable insight into both the nucleon structure and the mechanism of high energy diffractive scattering. Received: 2 February 1999 / Revised version: 22 March 1999 / Published online: 28 May 1999     

A Functional Limit Theorem for Random Walk Conditioned to Stay Non-Negative

In this paper we consider an aperiodic integer-valued randomwalk S and a process S* that is a harmonic transform of S killedwhen it first enters the negative half; informally, S* is ‘Sconditioned to stay non-negative’. If S is in the domainof attraction of the standard normal law, without centring,a suitably normed and linearly interpolated version of S convergesweakly to standard Brownian motion, and our main result is thatunder the same assumptions a corresponding statement holds forS*, the limit of course being the three-dimensional Bessel process.As this process can be thought of as Brownian motion conditionedto stay non-negative, in essence our result shows that the interchangeof the two limit operations is valid. We also establish somerelated results, including a local limit theorem for S*, anda bivariate renewal theorem for the ladder time and height process,which may be of independent interest.