The set of toric minimal log discrepancies

We describe the set of minimal log discrepancies of toric log varieties, and study its accumulation points. This work is supported by a 21st Century COE Kyoto Mathematics Fellowship, and a JSPS Grant-in-Aid No 17740011.     

A common generalization for MV-algebras and Łukasiewicz–Moisil algebras

We introduce the notion of n-nuanced MV-algebra by performing a Łukasiewicz–Moisil nuancing construction on top of MV-algebras. These structures extend both MV-algebras and Łukasiewicz–Moisil algebras, thus unifying two important types of structures in the algebra of logic. On a logical level, n-nuanced MV-algebras amalgamate two distinct approaches to many valuedness: that of the infinitely valued Łukasiewicz logic, more related in spirit to the fuzzy approach, and that of Moisil n-nuanced logic, which is more concerned with nuances of truth rather than truth degree. We study n-nuanced MV-algebras mainly from the algebraic and categorical points of view, and also consider some basic model-theoretic aspects. The relationship with a suitable notion of n-nuanced ordered group via an extension of the Γ construction is also analyzed.     

Soft X-ray resonant magnetic scattering studies on Fe/CoO exchange bias system

We have used soft X-ray resonant magnetic scattering (XRMS) to search for the presence of an effective ferromagnetic moment belonging to the antiferromagnetic (AF) layer which is in close contact with a ferromagnetic (F) layer. Taking advantage of the element specificity of the XRMS technique, we have measured hysteresis loops of both Fe and CoO layers of a CoO(40 Å)/Fe (150 Å) exchange bias bilayer. From these measurements we have concluded that the proximity of the F layer induces a magnetic moment in the AF layer. The F moment of the AF layer has two components: one is frozen and does not follow the applied magnetic field and the other one follows in phase the ferromagnetic magnetization of the F layer. The temperature dependence of the F components belonging to the AF layer is shown and discussed.     

Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier

Based on the matrix-analytic approach to fluid flows initiated by Ramaswami, we develop an efficient time dependent analysis for a general Markov modulated fluid flow model with a finite buffer and an arbitrary initial fluid level at time 0. We also apply this to an insurance risk model with a dividend barrier and a general Markovian arrival process of claims with possible dependencies in successive inter-claim intervals and in claim sizes. We demonstrate the implementability and accuracy of our algorithms through a set of numerical examples that could also serve as test cases for comparing other solution approaches.      

Sur quelques problèmes de probabilités géométriques pour des réseaux irréguliers dans l'espace euclidienE 2 etE n

Dans ce travail on détermine quelques probabilités géométriques concernant des réseaux irréguliers dans le plan euclidienE ₂ et dans l'espace euclidienE _n . Les propriétés généralisent certains résultats de Buffon, Deltheil et Stoka. Travail effectué avec l'aide du MURST (40%, 60%).     

DTA and X-ray diffraction investigations of laser-irradiated CeO2 powders

The TG and DTA curves and diffractograms of powdered CeO₂ samples irradiated with a CO₂ laser beam with powers of 0.41–1.39 kW/cm² are presented. The laser treatment induced structural changes and probably generation of a metastable phase. X-ray diffraction coupled with thermal analysis was used to establish the structural modifications in the irradiated samples after heating.     

Continuous-time Markov model for geriatric patients behavior. Optimization of the bed occupancy and computer simulation

Previous research has shown that the flow of patients around departments of geriatric medicine and ex-patients in the community may be modelled by the application of a mixed-exponential distribution. In this paper we considered a five-compartment model using a continuous-time Markov process to describe the flow of patients. Using a M/Ph/c queuing model, we present a way of optimizing the number of beds in order to maintain an acceptable delay probability at a sufficiently low level. Finally, we constructed a Java computer simulation, using data from St George’s Hospital, London.     

A bicontinuous structure in some systems with cubic mesophases

A cubic structure of polymer colloid complexes is studied. The technique of the research includes i) an analysis of well-known literature SAXS data; on this basis, ii) constructing a simple model to estimate geometric structure parameters and to obtain a simulated scattering curve; and iii) comparing the model with the real structure obtained from the SAXS data, using the reconstruction of electron density distribution. A bicontinuous structure in cubic mesophases is formed. Dedicated to the memory of Alexander T. Dembo     

Simple vertices of maximal minor polytopes

Themaximal minor polytope Π _{m, n} is the Newton polytope of the product of all maximal minors of anm×n matrix of indeterminates. The family of polytopes {Π _{m, n} } interpolates between the symmetric transportation polytope (form=n−1) and the permutohedron (form=2). Both transportation polytope and the permutohedron aresimple polytopes but in general Π _{m, n} is not simple. The main result of this paper is an explicit construction of a class of simple vertices of Π _{m, n} for generalm andn. We call themvertices of diagonal type. For every such vertexv we explicitly describe all the edges and facets of Π _{m, n} which containv. Simple vertices of Π _{m, n} have an interesting algebro-geometric application: they correspond tononsingular extreme toric degenerations of the determinantal variety ofm×n matrices not of full rank. Andrei Zelevinsky was partially supported by the NSF under Grant DMS-9104867.     

The high‐pressure form of cadmium vanadate,CdV2O6

The crystal structure of a new high‐pressure modification of cadmium divanadium hexaoxide, CdV₂O₆, was refined from X‐ray single‐crystal data. It contains zigzag chains of edge‐sharing VO₆ octahedra. Octahedra in adjacent chains share corners and form corrugated layers. Octahedrally coordinated Cd atoms, which lie on twofold axes, are situated between the layers. The columbite‐like structure results in a strong distortion of the CdO₆ octahedra which may be stabilized only at high pressure.