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.     

Untersuchung von Trinkwasser, Kesselspeisewasser, Abwasser

Ohne Zusammenfassung     

Fundamental solution for linear two-point boundary value problem

The quadratic functional minimization with differential restrictions represented by the command linear systems is considered. The optimal solution determination implies the solving of a linear problem with two points boundary values. The proposed method implies the construction of a fundamental solution S(t)—a n×n matrix—and of a vector h(t) defining an adjoint variable λ(t) depending of the state variable x(t). From the extremum necessary conditions it is obtained the Riccati matrix differential equation having the S(t) as unknown fundamental solution is obtained. The paper analyzes the existence of the Riccati equation solution S(t) and establishes as the optimal solution of the proposed optimum problem. Also a superior limit of the minimum for the considered quadratic functionals class are evaluated.     

Catalytic and Atom‐Economic C −C Bond Formation: Alkyl Tantalum Ureates for Hydroaminoalkylation

Atom‐economic and regioselective C ?C bond formation has been achieved by rapid C?H alkylation of unprotected secondary arylamines with unactivated alkenes. The combination of Ta(CH₂SiMe₃)₃Cl₂, and a ureate N,O‐chelating‐ligand salt gives catalytic systems prepared in situ that can realize high yields of β‐alkylated aniline derivatives from either terminal or internal alkene substrates. These new catalyst systems realize C?H alkylation in as little as one hour and for the first time a 1:1 stoichiometry of alkene and amine substrates results in high yielding syntheses of isolated amine products by simple filtration and concentration.     

Gravitational Field Equations on Fefferman Space–Times

The total space \({\mathfrak M} \approx {\mathbb H}_1 \times S^1\) of the canonical circle bundle over the 3-dimensional Heisenberg group \({\mathbb H}_1\) is a space–time with the Lorentzian metric \(F_{\theta _0}\) (Fefferman’s metric) associated to the canonical Tanaka–Webster flat contact form \(\theta _0\) on \({\mathbb H}_1\). The matter and energy content of \(\mathfrak M\) is described by the energy-momentum tensor \({T}_{\mu \nu }\) (the trace-less Ricci tensor of \(F_{\theta _0}\)) as an effect of the non flat nature of Feferman’s metric \(F_{\theta _0}\). We study the gravitational field equations \(R_{\mu \nu } - (1/2) \, R \, g_{\mu \nu } = {T}_{\mu \nu }\) on \({\mathfrak M}\). We consider the first order perturbation \(g = F_{\theta _0} + \epsilon \, h\), \(\epsilon<< 1\), and linearize the field equations about \(F_{\theta _0}\). We determine a Lorentzian metric g on \({\mathfrak M}\) which solves the linearized field equations corresponding to a diagonal perturbation h.     

10.1007/s10955-006-9040-z

We derive hydrodynamic equations describing the evolution of a binary fluid segregated into two regions, each rich in one species,which are separated (on the macroscopic scale) by a sharp interface. Our starting point is a Vlasov-Boltzmann (VB) equation describing the evolution of the one particle position and velocity distributions, f_i (x, v, t), i = 1, 2. The solution of the VB equation is developed in a Hilbert expansion appropriate for this system. This yields incompressible Navier-Stokes equations for the velocity field u and a jump boundary condition for the pressure across the interface. The interface, in turn, moves with a velocity given by the normal component of u.     

Kobalt(III)ammin-derivate einiger Reineckesalz-Analoga mit Xylidinen

Zusammenfassung Es wurden 34 neue Komplexsalze durch doppelte Umsetzung aus wäßr.-alkohol. Lösungen der folgenden Reineckeat-Analoga: [Cr(NCS)₄(m-xylidin)₂]^–, [Cr(NCS)₄(p-xyl)₂]^– und Hexammin-, Monoacido-pentammin- und Diacido-tetramminkobalt(III)-komplexsalze erhalten. Es wurden in einigen Fällen Unterschiede in physiko-chemischen Eigenschaften, wie Farbtönung, Kristallform, Löslichkeit und papierchromatographischeR _f-Werte, bei den stellungsisomeren Salzen vom Typus: Kation · [Cr(NCS)₄(xyl)₂] und auch bei den Koordinationsisomerpaaren: [Co(DH)₂(m-xyl)₂] [Cr(NCS)₄(p-xyl)₂] und [Co(DH)₂(p-xyl)₂] [Cr(NCS)₄(m-xyl)₂] usw. beobachtet.

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Cobalt(III)ammine derivatives of some reineckate analogues with xylidines

34 new complex salts were prepared by double conversion of the reineckate analogues [Cr(NCS)₄(m-xylidine)₂]^–, [Cr(NCS)₄(p-xyl)₂]^–, with the hexammine-, monoacido-pentammine- and diacidotetrammine-complexes of Co(III). In some of the position and coordination isomeres differences of the standard physico-chemical properties, i.e. color, crystal form, solubility and paper chromatographyR _f-values were observed.