Structure of <Emphasis Type="Italic">H</Emphasis>-Semiprime Artinian Algebras

Let H be a Hopf algebra over a field. It is proved that every H-semiprime right artinian left H-module algebra A is quasi-Frobenius and H-semisimple. If H grows slower than exponentially, then all H-equivariant A-modules are shown to be A-projective. With the additional assumption that H is cosemisimple it is proved that the Jacobson radical of any right artinian left H-module algebra is stable under the action of H.     

Polyhedral Suspensions of Arbitrary Genus

A new class of polyhedra is discovered—bipyramids of arbitrarily prescribed genus. A two-dimensional generalization of Fáry’s Theorem is established. A purely combinatorial definition of a polyhedral suspension is given. A new regular two-dimensional polyhedron is constructed in four dimensions.     

Gradient‐based solvent suppression methods on a benchtop spectrometer

Benchtop NMR emerges as an appealing alternative to widely extend the scope of NMR spectroscopy in harsh environments and for on‐line monitoring. Obviously, the use of low‐field magnets induces a dramatic reduction of the spectral resolution leading to frequent peak overlaps. This issue is even more serious because applications such as chemical process monitoring involve the use of non‐deuterated solvents, leading to intense and broad peaks overlapping with the signals of interest. In this article, we highlight the need for efficient suppression methods compatible with flowing samples, which is not the case of the common pre‐saturation approaches. Thanks to a gradient coil included in our benchtop spectrometer, we were able to implement modern and efficient solvent suppression blocks such as WET or excitation sculpting to deliver quantitative spectra in the conditions of the on‐line monitoring. While these methods are commonly used at high field, this is the first time that they are investigated on a benchtop setting. Their analytical performance is evaluated and compared under static and on‐flow conditions. The results demonstrate the superiority of gradient‐based methods, thus highlighting the relevance of implementing this device on benchtop spectrometers. The comparison of major solvent suppression methods reveals an optimum performance for the WET‐180‐NOESY experiment, both under static and on‐flow conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

Isoperimetric Constants of Infinite Plane Graphs

   Abstract. Let G be an infinite locally finite plane graph with one end and let H be a finite plane subgraph of G . Denote by a(H) the number of finite faces of H and by l(H) the number of the edges of H that are on the boundary of the infinite face or a finite face not in H . Define the isoperimetric constant h (G) to be inf _H l(H) / a(H) and define the isoperimetric constant h (δ) to be inf _G h (G) where the infimum is taken over all infinite locally finite plane graphs G having minimum degree δ and exactly one end. We establish the following bounds on h (δ) for δ ≥ 7 :

The Probability Content of Cones in Isotropic Random Fields

This paper provides computable representations for the evaluation of the probability content of cones in isotropic random fields. A decomposition of quadratic forms in spherically symmetric random vectors is obtained and a representation of their moments is derived in terms of finite sums. These results are combined to obtain the distribution function of quadratic forms in spherically symmetric or central elliptically contoured random vectors. Some numerical examples involving the sample serial covariance are provided. Ratios of quadratic forms are also discussed.     

Approximation Algorithms for Steiner and Directed Multicuts

In this paper we consider theSteiner multicutproblem. This is a generalization of the minimum multicut problem where instead of separating nodepairs, the goal is to find a minimum weight set of edges that separates all givensetsof nodes. A set is considered separated if it is not contained in a single connected component. We show anO(log³(kt)) approximation algorithm for the Steiner multicut problem, wherekis the number of sets andtis the maximum cardinality of a set. This improves theO(t log k) bound that easily follows from the previously known multicut results. We also consider an extension of multicuts to directed case, namely the problem of finding a minimum-weight set of edges whose removal ensures that none of the strongly connected components includes one of the prespecifiedknode pairs. In this paper we describe anO(log² k) approximation algorithm for this directed multicut problem. Ifk ? n, this represents an improvement over theO(log n log log n) approximation algorithm that is implied by the technique of Seymour.     

La densité de la loi-limite d'un processus en cascade expansif

Sans résumé     

Non-quasi-stationary state pyrolysis of ethane

An induction period has been observed in the pyrolysis of ethane in a continuous-flow stirred tank reactor at 530°C. The rate constants of the initiation, determining propagation and termination steps, have been determined.