Resolving Sphingolipid Isomers Using Cryogenic Infrared Spectroscopy

1‐Deoxysphingolipids are a recently described class of sphingolipids that have been shown to be associated with several disease states including diabetic and hereditary neuropathy. The identification and characterization of 1‐deoxysphingolipids and their metabolites is therefore highly important. However, exact structure determination requires a combination of sophisticated analytical techniques due to the presence of various isomers, such as ketone/alkenol isomers, carbon–carbon double‐bond (C=C) isomers and hydroxylation regioisomers. Here we demonstrate that cryogenic gas‐phase infrared (IR) spectroscopy of ionized 1‐deoxysphingolipids enables the identification and differentiation of isomers by their unique spectroscopic fingerprints. In particular, C=C bond positions and stereochemical configurations can be distinguished by specific interactions between the charged amine and the double bond. The results demonstrate the power of gas‐phase IR spectroscopy to overcome the challenge of isomer resolution in conventional mass spectrometry and pave the way for deeper analysis of the lipidome.     

Effect of annealing on an amorphous GexTe1−x matrix with Te cristallites

Annealing shows very different behaviour for Te crystallites in an amorphous Ge_xTe_1?x matrix as a function of x (x = 0.1 … 0.5). For x ? 0.2, annealing at increasing temperatures increases the number (size) of the Te crystallites with subsequent GeTe + Te crystallization. However for x ? 0.3 there is first a disappearance of Te crystallites, then an appearance of GeTe crystallites, and subsequently GeTe + Te crystallization. Crystallites of either Te or GeTe act as extrinsic defects which add to the intrinsic ones. Activatioon energy decreases (increases) and conductance increases (decreases) as the number of defects increases (decreases). In all cases the final metallic state is obtained only when both GeTe and Te crystallites are present.     

The effect of spherical shells of matter on the Schwarzschild black hole

Based on previous work we show how to join two Schwarzschild solutions, possibly with different masses, along null cylinders each representing a spherical shell of infalling or outgoing massless matter. One of the Schwarzschild masses can be zero, i.e. one region can be flat. The above procedure can be repeated to produce space-times with aC ⁰ metric describing several different (possibly flat) Schwarzschild regions separated by shells of matter. An exhaustive treatment of the ways of combining four such regions is given; the extension to many regions is then straightforward. Cases of special interest are: (1) the scattering of two spherical gravitational shock waves at the horizon of a Schwarzschild black hole, and (2) a configuration involving onlyone external universe, which may be relevant to quantization problems in general relativity. In the latter example, only an infinitesimal amount of matter is sufficient to remove the Wheeler wormhole to another universe.Supported in part by the Stichting voor Fundamenteel Onderzoek der Materie     

Set to set broadcasting in communication networks

Suppose G = (V,E) is a graph whose vertices represent people and edges represent telephone lines between pairs of people. Each person knows a unique message and is ignorant of the messages of other people at the beginning. These messages are then spread by telephone calls. In each call, two people exchange all information they have so far in exactly one unit of time. Suppose A and B are two nonempty subsets of V. The main purpose of this paper is to study the minimum number b(A,B,G) of telephone calls by which A broadcasts to B; and the minimum time t(A,B,G) such that A broadcasts to B. In particular, we give an exact formula for b(A,B,K_n) and linear-time algorithms for computing b(A,B,T) and t(A,B,T) of a tree T.     

Practical strategies for generating rank-1 split cuts in mixed-integer linear programming

In this paper we propose practical strategies for generating split cuts, by considering integer linear combinations of the rows of the optimal simplex tableau, and deriving the corresponding Gomory mixed-integer cuts; potentially, we can generate a huge number of cuts. A key idea is to select subsets of variables, and cut deeply in the space of these variables. We show that variables with small reduced cost are good candidates for this purpose, yielding cuts that close a larger integrality gap. An extensive computational evaluation of these cuts points to the following two conclusions. The first is that our rank-1 cuts improve significantly on existing split cut generators (Gomory cuts from single tableau rows, MIR, Reduce-and-Split, Lift-and-Project, Flow and Knapsack cover): on MIPLIB instances, these generators close 24% of the integrality gap on average; adding our cuts yields an additional 5%. The second conclusion is that, when incorporated in a Branch-and-Cut framework, these new cuts can improve computing time on difficult instances.     

On free p-superalgebras

In this article we consider several aspects of algebraic combinatorics and combinatorial algebra over fields of prime characteristics. P-super-Radford theorem gives the structure of the free associative algebra over a field of prime characteristic with the new multiplication given by the super shuffle product, we show that this algebra is isomorphic to the reduced free super commutative algebra on s-regular words. We prove the elimination theorem for free partially commutative color Lie p-superalgebras and obtain a Schreier type formula for free Lie p-superalgebras using formal power series techniques.     

On the covariance of the level sizes in random recursive trees

In this paper we study the covariance structure of the number of nodes k and l steps away from the root in random recursive trees. We give an analytic expression valid for all k, l and tree sizes N. The fraction of nodes k steps away from the root is a random probability distribution in k. The expression for the covariances allows us to show that the total variation distance between this (random) probability distribution and its mean converges in probability to zero. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 20: 519–539, 2002     

Numerical solution of the two-dimensional Poincaré equation

This paper deals with numerical approximation of the two-dimensional Poincaré equation that arises as a model for internal wave motion in enclosed containers. Inspired by the hyperbolicity of the equation we propose a discretisation particularly suited for this problem, which results in matrices whose size varies linearly with the number of grid points along the coordinate axes. Exact solutions are obtained, defined on a perturbed boundary. Furthermore, the problem is seen to be ill-posed and there is need for a regularisation scheme, which we base on a minimal-energy approach.     

Crossed products of C*-algebras by endomorphisms

The concept of a twisted crossed product associated to a non-classical C^*-dynamical system is introduced and studied. The relationship between a covariant projective representation of the system and the corresponding induced representation of the twisted crossed product is investigated, particularly from the point of view of determining when the induced representation is faithful. Conditions are given on the C^*-dynamical system that ensure nuclearity, simplicity or primeness of the twisted crossed product.