Effect of test temperature on separation number

The separation number is affected by a variety of extra-column factors (e.g. the injection process, the nature of the sample, and plumbing defects in the inlet and detector) as well as factors related to column efficiency. The magnitude of the separation number, as affected by the column, varies inversely with column temperature and directly with the partition ratios of the test compounds. The interrelationships of column temperature and partition ratios are explored.     

Electronic structure of Pu monochalcogenides and monopnictides

The electronic and magnetic properties of Pu monopnictides and monochalcogenides, PuX (X = N, P, As, Sb, Bi, O, S, Se, Te, Po), are studied using the self-interaction-corrected local spin-density approximation. This approach allows for an integer number of f-states to be localized, while the remaining f-electron degrees of freedom are available for band formation. By varying the relative proportions of localized and delocalized f-states, the energetically most favourable (groundstate) configuration can be established. We show that the experimental data can be interpreted in terms of the coexistence of both localized and delocalized f-states. Received 10 August 2001     

LIF diagnostics of C2 radical behaviour in a laser CVD environment

A laser-induced fluorescence (LIF) system was developed to diagnose the reaction and transport of radicals in the ArF-laser-assisted CVD environment. The C₂(a ³ II _u) radicals were produced by the multi-photon dissociation of C₂H₂. The transport of the radical was directly measured by LIF. The disappearance rate of the radical in C₂H₂ was also determined. By using the values determined, the in-flux of the C₂ radicals onto a substrate was investigated, based on a diffusion model.     

Complete 1H and 13C NMR spectral assignment of benzo[d]isothiazole derivatives and of an isoindole isoster

The complete (1)H and (13)C NMR assignments of the novel compound methyl 2-amino-3-(benzo[d]isothiazol-3-yl)propanoate (1), of 3-amino-5-methylbenzo[d]isothiazole (2) and N-(t-butyloxycarbonyl)-2-aminobenzo[d]isothiazol-3(2H)-one (3) and of the desulfurated isostere of 3, N-(t-butyloxycarbonyl)-2-aminoisoindolin-1-one (4), using 1D and 2D NMR techniques, including COSY, INADEQUATE, HSQC, and HMBC experiments are reported.     

Strong rigidity of generalized Bernoulli actions and computations of their symmetry groups

We study equivalence relations and II₁ factors associated with (quotients of) generalized Bernoulli actions of Kazhdan groups. Specific families of these actions are entirely classified up to isomorphism of II₁ factors. This yields explicit computations of outer automorphism and fundamental groups. In particular, every finitely presented group is concretely realized as the outer automorphism group of a continuous family of non stably isomorphic II₁ factors.     

Generalized intersection bodies are not equivalent

In [A. Koldobsky, A functional analytic approach to intersection bodies, Geom. Funct. Anal. 10 (2000) 1507-1526], A. Koldobsky asked whether two types of generalizations of the notion of an intersection body are in fact equivalent. The structures of these two types of generalized intersection bodies have been studied by the author in [E. Milman, Generalized intersection bodies, J. Funct. Anal. 240 (2) (2006) 530-567], providing substantial evidence for a positive answer to this question. The purpose of this note is to construct a counter-example, which provides a surprising negative answer to this question in a strong sense. This implies the existence of non-trivial non-negative functions in the range of the spherical Radon transform, and the existence of non-trivial spaces which embed in Lp for certain negative values of p.     

On the vertices of the -additive core

The core of a game v on N, which is the set of additive games φ dominating v such that φ(N)=v(N), is a central notion in cooperative game theory, decision making and in combinatorics, where it is related to submodular functions, matroids and the greedy algorithm. In many cases however, the core is empty, and alternative solutions have to be found. We define the k-additive core by replacing additive games by k-additive games in the definition of the core, where k-additive games are those games whose Möbius transform vanishes for subsets of more than k elements. For a sufficiently high value of k, the k-additive core is nonempty, and is a convex closed polyhedron. Our aim is to establish results similar to the classical results of Shapley and Ichiishi on the core of convex games (corresponds to Edmonds’ theorem for the greedy algorithm), which characterize the vertices of the core.     

Graphic sequences with a realization containing a generalized friendship graph

Gould, Jacobson and Lehel [R.J. Gould, M.S. Jacobson, J. Lehel, Potentially G-graphical degree sequences, in: Y. Alavi, et al. (Eds.), Combinatorics, Graph Theory and Algorithms, vol. I, New Issues Press, Kalamazoo, MI, 1999, pp. 451-460] considered a variation of the classical Turán-type extremal problems as follows: for any simple graph H, determine the smallest even integer σ(H,n) such that every n-term graphic sequence π=(d₁,d₂,…,d_n) with term sum σ(π)=d₁+d₂+?+d_n≥σ(H,n) has a realization G containing H as a subgraph. Let F_t,r,k denote the generalized friendship graph on kt−kr+r vertices, that is, the graph of k copies of K_t meeting in a common r set, where K_t is the complete graph on t vertices and 0≤r≤t. In this paper, we determine σ(F_t,r,k,n) for k≥2, t≥3, 1≤r≤t−2 and n sufficiently large.     

Separable states and positive maps

Using the natural duality between linear functionals on tensor products of C^∗-algebras with the trace class operators on a Hilbert space H and linear maps of the C^∗-algebra into B(H), we study the relationship between separability, entanglement and the Peres condition of states and positivity properties of the linear maps.     

A class of essential representations of product systems

We construct a family of essential representations of an arbitrary product system by generalizing some techniques introduced by M. Skeide and W. Arveson. We then classify the resulting E₀-semigroups up to conjugacy, by identifying their tail flows as periodic W^∗-dynamical systems acting on factors of type I_∞. The conjugacy classes of these E₀-semigroups correspond to the orbits of the action of the automorphism group of the product system on unital vectors. In the sequel, this classification shows explicitly that any E₀-semigroup admits uncountably many non-conjugate cocycle perturbations.