Multiple ergodic theorems

Given measure preserving transformationsT ₁,T ₂,...,T _s of a probability space (X,B, μ) we are interested in the asymptotic behaviour of ergodic averages of the form $$\frac{1}{N}\sum\limits_{n = 0}^{N - 1} {T_1^n f_1 \cdot T_2^n f_2 } \cdot \cdots \cdot T_s^n f_s $$ wheref ₁,f ₂,...,f _s ?L ^∞(X,B,μ). In the general case we study, mainly for commuting transformations, conditions under which the limit of (1) inL ²-norm is ∫ _x f ₁ dμ·∫ _x f ₂ dμ...∫ _x f _s dμ for anyf ₁,f ₂...,f _s ?L ^∞(X,B,μ). If the transformations are commuting epimorphisms of a compact abelian group, then this limit exists almost everywhere. A few results are also obtained for some classes of non-commuting epimorphisms of compact abelian groups, and for commuting epimorphisms of arbitrary compact groups.     

Correlation length bounds for disordered Ising ferromagnets

Thed-dimensional, nearest-neighbor disordered Ising ferromagnet: $$H = - \sum {J_{ij} \sigma _i \sigma _j }$$ is studied as a function of both temperature,T, and a disorder parameter,λ, which measures the size of fluctuations of couplingsJ _ij ≧0. A finite-size scaling correlation length,ζ _f (T, λ), is defined in terms of the magnetic response of finite samples. This correlation length is shown to be equivalent, in the scaling sense, to the quenched average correlation lengthζ(T, λ), defined as the asymptotic decay rate of the quenched average two-point function. Furthermore, the magnetic response criterion which definesζ _f is shown to have a scale-invariant property at the critical point. The above results enable us to prove that the quenched correlation length satisfies: $$C\left| {\log \xi (T)} \right|\xi (T) \geqq \left| {T - T_c } \right|^{ - {2 \mathord{\left/ {\vphantom {2 d}} \right. \kern-\nulldelimiterspace} d}}$$ which implies the boundv≧2/d for the quenched correlation length exponent.     

Nouveaux thiochlorures de molybdène(II): Mo6Cl10Y (Y = S,Se, Te): Structure et propriétés magnétiques et électriques

The thiochlorides Mo₆Cl₁₀Y (Y = S, Se, Te) have been prepared; they are isostructural with Nb₆I₁₁, space group Pccn, and have four formula units per unit cell. The X-ray structure of Mo₆Cl₁₀Se has been determined from three-dimensional single-crystal counter data and refined to a final R value of 0.053 for 3350 independent reflections. The most important result concerning this structure is a statistical distribution of the Se atom on the unit (Mo₆X′₈) with $\text{X′ ?}\text{7}\text{8}\text{Cl}\text{+}\text{1}\text{8}\text{Se}$: so the compound Mo₆Cl₁₀Se must be formulated $\text{(Mo}{}_6\text{Cl}{}_7\text{Se)Cl}{}_{\mathrm{<mtext>4</mtext><mtext>2</mtext>}}\text{Cl}{}_{\mathrm{<mtext>2</mtext><mtext>2</mtext>}}$. The diamagnetic and dielectric behavior of these new thiochlorides is discussed.     

Rotational contour analysis of the electronic origin band in the emission spectrum of the orthoxylyl radical at 4683 Å

The rotational contour of the 4683 Å emission band of the o-xylyl radical was studied at high resolution. Calculations of the rotational contour of this hybrid band were made in the rigid rotor approximation for various sets of values of the excited state rotational constants and directions of the transition moment μ. Matching of computed and experimental rotational features showed that μ is oriented at +37° or ?37° with respect to the b inertial axis. The nature of the excited states of o-xylyl and the methyl-to-ring interaction are discussed with respect to these two possible assignments     

Structural and electronic comparative analysis of aminopyridazines showing anti-GABA activity. Crystal structure of 2-(carboxy-3′-propyl)-3-amino-6-cyclohexylpyridazinium bromide.Ab initio Mulliken population analysis of the 6-phenyl-substituted analog compared to GABA

The crystal structure of 2-(carboxy-3-propyl)-3-amino-6-cyclohexylpyridazinium bromide has been determined by single-crystal X-ray diffraction techniques and refined by full-matrix least squares. The compound crystallized in the tri-clinic space groupP ¯1 witha=10.275(1),b=11.215(1),c=7.082(1) Å,=91.84(1),=102.21(1), =106.77(1)°, andZ=2. FinalR-factor is 0.045. The main structural results are very similar to the ones observed for the 6-phenyl analog. These two compounds are GABA-A antagonists.Ab initio molecular orbital calculations, with STO-3G and 4-31G basis sets, suggest that the exocyclic nitrogen accurately mimics the nitrogen atom of GABA.     

The size of sums of sets,II

We prove inequalities which give lower bounds for the Lebesgue measures of setsE +K whereK is a certain kind of Cantor set. For example, ifC is the Cantor middle-thirds subset of the circle groupT, then $$m(E)^{1 - log2/log3} \leqq m(E + C)$$ for every BorelE ?T.     

The “Facilitated Transition” hypothesis as an explanation for the gemdialkyl effect

A new technique of searching the conformational space of transition states was used to explore the cause of the rate acceleration in the gem-dialkyl effect in intramolecular cyclization reactions. Several previous hypotheses were discarded and a new hypothesis was advanced based on this new data. This hypothesis, the “Facilitated Transition” hypothesis, states that increased steric hindrance reduces the overall activation energy by facilitating rotation through the transition state. The older “Reactive Rotamer” hypothesis was eliminated by generating all conformations of the starting materials using the and computer programs and demonstrating that no relationship is found between rate increase and a change in the concentration of “reactive rotamers”.     

A rapid radiochemical procedure for indium

A rapid radiochcmical procedure was developed for the separation of indium radionuclides from a mixed fission-product solution. An alcoholic pyridine solution is added to a uranium solution containing indium and tin carriers. The resulting tin precipitate is separated from the indium-containing solution by filtering through a cellulose membrane filter. The decontamination factor for tin is 2·10³. Other fission products are only partially removed. The chemical yield of indium is about 44%, and the time required for the separation is about 10 sec. After the tin-separated indium has decayed, the tin daughters of indium are removed from all the other fission products at a specified time and measured, so that the amount of indium present at the time of the tin precipitation is determined.     

cis-UROCANIC ACID FAILED TO AFFECT in vitro HUMAN LANGERHANS CELL ALLOSTIMULATORY FUNCTION

Abstract— -Urocanic acid (UCA) represents the major ultraviolet B (UVB, 290–320 nm)-absorbing component of the skin. Trans-UCA is naturally produced in the stratum corneum and converts to the cis isomer upon UVB irradiation. In this study, we examined the effect of purified cis -UCA (about 99% of cis isomer) on the human Langerhans cell (LC) allostimulatory function by using the mixed epidermal cell-lymphocyte reaction (MELR). We found that addition of increasing amounts (6.5–400 μg/mL) of purified cis-UCA or (rara-UCA did not modify the T-cell response supported by enriched LC (eLC: 8–25% LC) as well as purified LC (pLC: 70–90% LC) suspensions. Because cis-UCA had no effect on the allostimulatory function of untreated LC, we investigated whether this compound could modify T-cell proliferation induced by UVB-irradiated LC. The UVB exposure of eLC or pLC to 100 J/m² significantly inhibited the capacity of both suspensions to mount a T-cell response. However, addition of cis- UCA did not potentiate this UVB-induced immunosuppression. The eLC or pLC were then incubated with cis-UCA for 18 h at 37°C and washed before adding to allogeneic T cells. The obtained proliferative response was similar to that induced by control LC incubated in medium alone, demonstrating that pretreatment with cis -UCA did not alter human LC function. In conclusion, these results strongly suggest that cis-UCA has no direct effect on human LC antigen-presenting function.