Development of measuring magnetic Compton profiles by grazing incidence geometry

A novel technique of measuring a magnetic Compton profile using the grazing angle geometry against a sample surface (Grazing Incidence Magnetic Compton Profile) has been successively developed. Measurements of a magnetic moment and a magnetic Compton profile are possible for a Fe 200 nm film on a thick glass substrate. The estimated thinnest limit for measurements is 100 nm for a Fe film.     

Surface bodies and p-affine surface area

The surface body is a generalization of the floating body. Its relation to p-affine surface area is studied.     

Approximation of a laminated microstructure for a rotationally invariant,double well energy density

Summary. We give error estimates for the approximation of a laminated microstructure which minimizes the energy for a rotationally invariant, double well energy density . We present error estimates for the convergence of the deformation in the convergence of directional derivatives of the deformation in the “twin planes,” the weak convergence of the deformation gradient, the convergence of the microstructure (or Young measure) of the deformation gradients, and the convergence of nonlinear integrals of the deformation gradient. Received July 25, 1995 / Revised version received November 20, 1995     

Proof of a conjecture on the supports of Wigner distributions

In this note we prove that the Wigner distribution of an f ∈ L₂(ℝ_n) cannot be supported by a set of finite measure in ℝ_2n unless f=0. We prove a corresponding statement for cross-ambiguity functions. As a strengthening of the conjecture we show that for an f ∈ L₂(ℝ_n) its Wigner distribution has a support of measure 0 or ∞ in any half-space of ℝ_2n.     

First countability, tightness, and other cardinal invariants in remainders of topological groups

We consider the following natural questions: when a topological group G has a first countable remainder, when G has a remainder of countable tightness? This leads to some further questions on the properties of remainders of topological groups. Let G be a topological group. The following facts are established. 1. If Gω has a first countable remainder, then either G is metrizable, or G is locally compact. 2. If G has a countable network and a first countable remainder, then either G is separable and metrizable, or G is σ-compact. 3. Under (MA+¬CH) every topological group with a countable network and a first countable remainder is separable and metrizable. Some new open problems are formulated.     

Pullback attractors for a non-autonomous incompressible non-Newtonian fluid

This paper studies the pullback asymptotic behavior of solutions for a non-autonomous incompressible non-Newtonian fluid in two-dimensional (2D) bounded domains. We first prove the existence of pullback attractors AV in space V (has H²-regularity, see notation in Section 2) and AH in space H (has L²-regularity) for the cocycle corresponding to the solutions of the fluid. Then we verify the regularity of the pullback attractors by showing AV=AH, which implies the pullback asymptotic smoothing effect of the fluid in the sense that the solutions become eventually more regular than the initial data.     

An asymmetric Ellis theorem

In 1957 Robert Ellis proved that a group with a locally compact Hausdorff topology T making all translations continuous also has jointly continuous multiplication and continuous inversion, and is thus a topological group. The theorem does not apply to locally compact asymmetric spaces such as the reals with addition and the topology of upper open rays. We first show a bitopological Ellis theorem, and then introduce a generalization of locally compact Hausdorff, called locally skew compact, and a topological dual, Tk, to obtain the following asymmetric Ellis theorem which applies to the example above:Whenever (X,⋅,T) is a group with a locally skew compact topology making all translations continuous, then multiplication is jointly continuous in both (X,⋅,T) and (X,⋅,Tk), and inversion is a homeomorphism between (X,T) and (X,Tk).This generalizes the classical Ellis theorem, because T=Tk when (X,T) is locally compact Hausdorff.     

Bounded sets in topological groups and embeddings

We show that the existence of a non-metrizable compact subspace of a topological group G often implies that G contains an uncountable supersequence (a copy of the one-point compactification of an uncountable discrete space). The existence of uncountable supersequences in a topological group has a strong impact on bounded subsets of the group. For example, if a topological group G contains an uncountable supersequence and K is a closed bounded subset of G which does not contain uncountable supersequences, then any subset A of K is bounded in G?(K?A). We also show that every precompact Abelian topological group H can be embedded as a closed subgroup into a precompact Abelian topological group G such that H is bounded in G and all bounded subsets of the quotient group G/H are finite. This complements Ursul's result on closed embeddings of precompact groups to pseudocompact groups.     

On the analysis of the Gerber-Shiu discounted penalty function for risk processes with Markovian arrivals

In this paper, we consider an insurance risk model governed by a Markovian arrival claim process and by phase-type distributed claim amounts, which also allows for claim sizes to be correlated with the inter-claim times. A defective renewal equation of matrix form is derived for the Gerber-Shiu discounted penalty function and solved using matrix analytic methods. The use of the busy period distribution for the canonical fluid flow model is a key factor in our analysis, allowing us to obtain an explicit form of the Gerber-Shiu discounted penalty function avoiding thus the use of Lundberg’s fundamental equation roots. As a special case, we derive the triple Laplace transform of the time to ruin, surplus prior to ruin, and deficit at ruin in explicit form, further obtaining the discounted joint and marginal moments of the surplus prior to ruin and the deficit at ruin.     

A local characterization of the johnson scheme

Within the Johnson schemeI(m, d) we find the graphK(m, d) ofd-subsets of anm-set, two such adjacent when disjoint. Among all connected graphs,K(m, d) is characterized by the isomorphism type of its vertex neighborhoods providedm is sufficiently large compared tod. Partial support provided by NSF (USA), SERC (UK), ZWO (NL).