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.     

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.     

Compatibility and Marginality

We present a way of introducing joint distibution function and its marginal distribution functions for non-compatible observables. Each such marginal distribution function has the property of commutativity. Models based on this approach can be used to better explain some classical phenomena in stochastic processes.     

40 GHz Mode-Locked Semiconductor Lasers: Theory, Simulations and Experiment

We study both theoretically and experimentally typical operation regimes of 40 GHz monolithic mode-locked lasers. The underlying Traveling Wave Equation model reveals quantitative agreement for characteristics of the fundamental mode-locking as pulse width and repetition frequency tuning, as well as qualitative agreement with the experiments for other dynamic regimes. Especially the appearance of stable harmonic mode-locking at 80 GHz has been predicted theoretically and confirmed by measurements. Furthermore, we derive and apply a simplified Delay-Differential-Equation model which guides us to a qualitative analysis of bifurcations responsible for the appearance and the breakup of different mode-locking regimes. Higher harmonics of mode-locking are predicted by this model as well.     

Platinum metallodrug-protein binding studies by capillary electrophoresis-inductively coupled plasma-mass spectrometry: characterization of interactions between Pt(II) complexes and human serum albumin

Characterizing how platinum metallocomplexes bind to human serum albumin (HSA) is essential in evaluating anticancer drug candidates. Using cisplatin as a reference complex, the application of capillary electrophoresis (CE) to reliably assess drug/HSA interactions was validated. Since this complex is small compared to the size of the protein, the binding response could only be recognized when applying CE coupled to a (platinum) metal-specific mode of detection, namely inductively coupled plasma-mass spectrometry (ICP-MS). This coupling allowed for confirmation of a specific affinity of cisplatin and novel Pt complexes to HSA, measurement of the kinetics of binding reactions, and determination of the number of drug molecules attached to the protein. As the cisplatin/HSA molar ratio increased, the reaction rate became faster with a maximum on the kinetic curve appearing at about 50 h of incubation at 20 times excess of cisplatin. The reaction was characterized as a pseudo-first order reaction with the rate constant k = 0.003 min(-1) at 37 degrees C. When incubated with a 20-fold excess of cisplatin, HSA bound up to 10 mol of Pt per mol of the protein. This is indicative for a strong metal-protein coordination occurring at several HSA sites other than the only protein cysteine residue. Structural analogs of cisplatin, bearing aminoalcohol ligands, showed comparable protein binding reactivity and stoichiometry but a common equilibrium was not reached even after one week of incubation. Also apparent was a two-step mechanism of the binding reaction. Results demonstrated the suitability of CE-ICP-MS as a rapid assay for high-throughput studying of drug/HSA interactions.