Spectral Properties of Schrödinger Operators on Domains with Varying Orders of Thinness

We consider the Schrödinger operator on two types of domains depending on a small parameter : dumbbell domains and thin domains with varying orders of thinness. In both situations we compare the eigenvalues and eigenvectors of the Schrödinger operator with the corresponding eigenvalues and eigenvectors of a limit operator defined on the limit domain.     

Sodium‐Naphthalenide‐Driven Synthesis of Base‐Metal Nanoparticles and Follow‐up Reactions

Mo⁰, W⁰, Fe⁰, Ru⁰, Re⁰, and Zn⁰ nanoparticles—essentially base metals—are prepared as a general strategy by a sodium naphthalenide ([NaNaph])‐driven reduction of simple metal chlorides in ethers (1,2‐dimethoxyethane (DME), tetrahydrofuran (THF)). All the nanoparticles have diameters ≤10 nm, and they can be obtained either as powder samples or long‐term stable suspensions. Direct follow‐up reactions (e.g., Mo⁰+S₈, FeCl₃+AsCl₃, ReCl₅+MoCl₅), moreover, allow the preparation of MoS₂, FeAs₂, or Re₄Mo nanoparticles of similar size as the pristine metals (≤10 nm).     

Deteriorated Geometrical Stiffness for Higher Order Finite Elements with Application to Panel Flutter

Higher order elements were first design for linear problems where, in certain situations, they present advantages over the lower order elements. A method to efficiently extend their use to geometrical nonlinear problems as panel flutter and postbuckling behavior is presented. The chaotic and limit-cycle oscillations of an isotropic plate are obtained based on direct integration of the discretized equation of motion. The plate is modeled using the von Karman theory and the geometrical nonlinearities are separated in a nonlinear term of the first kind which manifests especially in the prebuckling and buckling regimes, and a nonlinear term of the second kind which is responsible for the postbuckling behavior. A fifth order, fully compatible element has been used to model thin plates while the inplane loads where introduced through a membrane element. The aerodynamics was modeled using the first order 'piston theory. The method introduces the concept of a deteriorated form of the second geometric matrix which is equivalent to neglecting higher order terms in the strain energy of the plate. This allows for a drastic reduction in the computational effort with no observable loss of accuracy. Well established results in the literature are used to validate the method.     

Green light radiation effects on free radicals inhibition in cellular and chemical systems

Free radicals generation is inhibited through green light (GL) irradiation in cellular systems and in chemical reactions. Standard melanocyte cultures were UV-irradiated and the induced cellular reactive oxygen species (ROS) were quantified by the fluorescence technique. The same cell cultures, previously protected by a 24h GL exposure, displayed a significantly lower ROS production. A simple chemical reaction is subsequently chosen, in which the production of free radicals is well defined. Paraffin wax and mineral oil were GL irradiated during thermal degradation and the oxidation products checked by chemiluminescence [CL] and Fourier transform infrared spectra [FT-IR]. The same clear inhibition of the radical oxidation of alkanes is recorded. A quantum chemistry modeling of these results is performed and a mechanism involving a new type of Rydberg macromolecular systems with implications for biology and medicine is suggested.     

A new class of contractive mappings

We introduce a new class of Picard operators which includes the class of enriched contractions, enriched Kannan mappings, enriched Chatterjea mappings, and prove some fixed point theorems for these mappings. Some examples will illustrate the generality of our results.

     

Glyconectin Cell Adhesion Epitope, β-d-GlcpNAc3S-(1→3)-α-l-Fucp,Is Involved in Blastulation of Lytechinus pictus Sea Urchin Embryos

Glycans, as the most peripheral cell surface components, are the primary candidates to mediate the initial steps of cell recognition and adhesion via glycan–glycan binding. This molecular mechanism was quantitatively demonstrated by biochemical and biophysical measurements at the cellular and molecular level for the glyconectin 1 β-d-GlcpNAc3S-(1→3)-α-l-Fucp glycan structure (GN1). The use of adhesion blocking monoclonal antibody Block 2 that specifically recognize this epitope showed that, besides Porifera, human colon carcinoma also express this structure in the apical glycocalyx. Here we report that Block 2 selectively immune-precipitate a Mr 580 × 10³ (g580) acidic non-glycosaminoglycan glycan from the total protein-free glycans of Lytechinus pictus sea urchin hatched blastula embryos. Immuno-fluorescence confocal light microscopy and immunogold electron microscopy localized the GN1 structure in the apical lamina glycocalyx attachments of ectodermal cells microvilli, and in the Golgi complex. Biochemical and immune-chemical analyses showed that the g580 glycan is carrying about 200 copies of the GN1 epitope. This highly polyvalent g580 glycan is one of the major components of the glycocalyx structure, maximally expressed at hatched blastula and gastrula. The involvement of g580 GN1 epitope in hatched blastula cell adhesion was demonstrated by: (1) enhancement of cell aggregation by g580 and sponge g200 glycans, (2) inhibition of cell reaggregation by Block 2, (3) dissociation of microvilli from the apical lamina matrix by the loss of its gel-like structure resulting in a change of the blastula embryonal form and consequent inhibition of gastrulation at saturating concentration of Block 2, and (4) aggregation of beads coated with the immune-purified g580 protein-free glycan. These results, together with the previous atomic force microscopy measurements of GN1 binding strength, indicated that this highly polyvalent and calcium ion dependent glycan–glycan binding can provide the force of 40 nanonewtons per single ectodermal cell association of microvilli with the apical lamina, and conservation of glycocalyx gel-like structure. This force can hold the weight of 160,000 cells in sea water, thus it is sufficient to establish, maintain and preserve blastula form after hatching, and prior to the complete formation of further stabilizing basal lamina.     

Laboratory set-up for X-ray diffraction at high pressures

We describe here a simple set-up for X-ray diffraction under high pressure using a diamond anvil cell employing a sealed tube. The set-up works in angular dispersive geometry and is built using rather common components that are available in a research laboratory. We show that using this set-up one can routinely acquire good-quality data for the determination of structural properties under pressure and the equations of state. Technical details are presented along with examples of experimental results for sodium chloride and LiV₂O₄.     

Possible High Power Laser Construction Using a New Discharge Type-Heated Cathode Discharge in the Copper Vapours Continuously Evaporated from the Anode

The possibility to build a high power copper laser using a new type of discharge – heated cathode discharge in the copper vapours continuously evaporated from a melted spot on the anode surface is analysed. From the experimental data on this new discharge type, the equivalent pressure of the copper atoms in the discharge space has been obtained. This pressure can be as high as 1 torr. The density of the power in the discharge volume is evaluated to be more than 1 kW/cm³.     

Morse inequalities, a function space integral approach

In this paper we prove the Morse inequalities in the non-degenerate and degenerate cases. Like the approach of J.-M. Bismut, ours is based on the idea suggested by Witten. In fact, if anything, our approach is closer to Witten's original idea than Bismut's.     

E -Theoretic Duality for Higher Rank Graph Algebras

We prove that there is a Poincaré type duality in E-theory between higher rank graph algebras associated with a higher rank graph and its opposite correspondent. We obtain an r-duality, that is the fundamental classes are in E^r. The basic tools are a higher rank Fock space and higher rank Toeplitz algebra which has a more interesting ideal structure than in the rank 1 case. The K-homology fundamental class is given by an r-fold exact sequence whereas the K-theory fundamental class is given by a homomorphism. The E-theoretic products are essentially pull-backs so that the computation is done at the level of exact sequences. Mathematics Subject Classification (2000): 46L80.