Specific cleavage of the glycosidic bond between the carbohydrate and ceramide portions in glycosphingolipids using trifluoroacetolysis

A number of glycosphingolipids have been subjected to trifluoroacetolysis. Heating the glycosphingolipid at 100 degrees C for 48 h in mixtures of trifluoroacetic acid (TFA) and trifluoroacetic anhydride (TFAA) varying from 1:1 to 1:100 (v/v) resulted in complete cleavage of the glycosidic bond between the carbohydrate and the unsaturated base of the ceramide. The fatty acid(s) linked to the amino group of sphingosine were also released by transamidation. The carbohydrate portion was stable under these conditions due to stabilization of the glycosidic bonds by the electronegative O-trifluoroacetyl groups. The 2-acetamido-2-deoxy-hexose units in the glycosphingolipids were converted into their N-trifluoroacetyl analogues. The N-trifluoroacetyl functions could be removed and the 2-acetamido-2-deoxy-hexoses could be reconstituted by N-acetylation.     

Testing methods for fatigue properties of rubber materials and vibration isolators

The main purpose of this investigation was to find out if laboratory fatigue tests in tension give results which can be useful in predicting the service life of a vibration isolator.Four natural rubber vulcanizates with different curing systems were used in the tests. The fatigue life in cyclic loading was determined in tension on standard tensile specimens (dumb-bells) and in shear on two types of vibration isolators. The results indicate that the information achieved in tension is relevant for estimating the service life of an isolator. Both relaxing and non-relaxing tests in tension were made and the relaxing tests seem to give the best correlation between dumb-bells and isolators. As the relaxing tests are also the least time-consuming they are to be preferred for material testing.     

Convergence of Discrete Snakes

The discrete snake is an arborescent structure built with the help of a conditioned Galton-Watson tree and random i.i.d. increments Y. In this paper, we show that if and , then the discrete snake converges weakly to the Brownian snake (this result was known under the hypothesis ). Moreover, if this condition fails, and the tails of Y are sufficiently regular, we show that the discrete snake converges weakly to an object that we name jumping snake. In both case, the limit of the occupation measure is shown to be the integrated super-Brownian excursion. The proofs rely on the convergence of the codings of discrete snake with the help of two processes, called tours.     

Perfect matchings in random s-uniform hypergraphs

Let E = {X₁, X₂…, X_m} where the X_i ? V for 1 ≤ i ≤ m are distinct. The hypergraph G = (V, E) is said to be s-uniform if |X₁| = s for 1 ≤ i ≤ m. A set of edges M = {X_i : i ? I } is a perfect matching if (i) i ≠ j ? I implies X_i ∩ X_i = 0, and (ii) ∪_i?I X_i = V. In this article we consider the question of whether a random s-uniform hypergraph contains a perfect matching. Let s ≥ 3 be fixed and m/n^4/3 → ∞. We show that an s-uniform hypergraph with m edges chosen uniformly from [74] contains a perfect matching with high probability. This improves an earlier result of Schmidt and Shamir who showed that m/n^3/2 → ∞ suffices. © 1995 John Wiley & Sons, Inc.     

The asymptotic distributions of incomplete U-statistics

Summary An incomplete U-statistic is obtained by sampling the terms of an U-statistic. This paper derives the asymptotic distribution (if the variance is finite). Depending on the number of sampled terms, the resulting distribution is either the same as for the U-statistic, a normal distribution, or something intermediate. Also the case of a non-random sampling of the terms is treated. As an example, a non-parametric test of the independence of two circular random variables is studied. The results are generalized to generalized U-statistics.     

The first-to-zero-sound transition in non-superfluid liquid 4He

Neutron inelastic scattering from ⁴He at T = 2.3 K shows that for Q ? 2 nm^?1 “sound-wave” excitations propagate with the characteristics of ordinary or first sound while for Q ? 3 nm^?1 they propagate with the characteristics of zero sound.     

The Cut Metric,Random Graphs,and Branching Processes

In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the sequence of matrices of edge probabilities converges to an appropriate limit object (a kernel), but only in a very weak sense, namely in the cut metric. Our results thus generalize previous results on the phase transition in the already very general inhomogeneous random graph model introduced by the present authors in Random Struct. Algorithms 31:3–122 (2007), as well as related results of Bollobás, Borgs, Chayes and Riordan (Ann. Probab. 38:150–183, 2010), all of which involve considerably stronger assumptions. We also prove corresponding results for random hypergraphs; these generalize our results on the phase transition in inhomogeneous random graphs with clustering (Random Struct. Algorithms, 2010, to appear).