Sufficient conditions of non‐uniqueness for the Coulomb friction problem

We consider the Signorini problem with Coulomb friction in elasticity. Sufficient conditions of non‐uniqueness are obtained for the continuous model. These conditions are linked to the existence of real eigenvalues of an operator in a Hilbert space. We prove that, under appropriate conditions, real eigenvalues exist for a non‐local Coulomb friction model. Finite element approximation of the eigenvalue problem is considered and numerical experiments are performed. Copyright © 2003 John Wiley & Sons, Ltd.     

Acute Triangulations of the Regular Icosahedral Surface

We prove here that the surface of the regular icosahedron can be triangulated with 8 non-obtuse and with 12 acute triangles. We also show these numbers to be smallest possible.     

A virtual instrumentation based protocol for the automated implementation of the inner field compensation method

One influential parameter which mediates interactions between many types of molecules and biological membranes stems from the lumped contributions of the transmembrane potential, dipole potential and the difference in the surface potentials on both sides of a membrane. With relevance to cell physiology, such electrical features of a biomembrane are prone to undergoing changes as a result of interactions with the aqueous surrounding. Among the most useful tools devoted to exploring changes of electrical parameters of a lipid membrane induced by certain extracellular ions, lipid composition, and embedded membrane peptides and proteins, are spectroscopic imaging and the inner field compensation (IFC) method. In this work we layout the principles of a fully computerized version of the IFC method, which makes it more readily available to users. As a direct application, we deployed this improved version of the IFC method to time-resolve changes induced by alamethicin monomers upon membrane dipole potential, following their aggregation within an artificial lipid membrane. Intriguingly, even prior crossing the membrane core, the membrane-bound alamethicin monomers are shown to significantly increase the dipole potential of the monolayer they reside in. Such data further emphasize the yet less-explored interplay between membrane-based protein and peptides, and the membrane dipole potential.     

Acute Triangulations of Flat Mobius Strips

In this paper we investigate the acute triangulations of flat Mobius strips. We find out that we can always triangulate a flat Mobius strip with at most nine acute triangles, and sometimes (but not always) that many triangles are really needed.     

On the Equivalence of Multiparameter Gaussian Processes

Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law to the Brownian sheet and to the fractional Brownian sheet. We survey multiparameter analogues of the Hitsuda, Girsanov and Shepp representations. As an application, we study a special type of stochastic equation with linear noise.      

Optimal control for semilinear stochastic evolution equations

Existence, uniqueness, continuous dependence with respect to controls and convergence in the probability of finite differences for controlled semilinear stochastic evolution equations, driven by continuous semimartingales, are considered under Lipschitz and monotone coefficients. The existence of discrete-optimal feedback controls for an associated optimization problem is proved.     

The interaction between TEOS and some polyols

Hybrid organic-inorganic materials, silica – polyols (ethylene-glycol – EG; 1,2 propane diol – 1,2PG; 1,3 propane diol – 1,3PG and glycerol – GL), were prepared by a sol-gel process starting from tetraethylorthosilicate (TEOS) and polyols, in acid catalysis. The resulting materials were studied by thermal analysis (in air and nitrogen), FTIR and solid state ²⁹Si-NMR spectroscopy. These techniques evidenced the presence of polyols in the silica matrix both hydrogen bounded and chemically bounded in the silica network. The thermal analysis proves to be the most appropriate technique to evidence the organic chains linked in the matrix network and to follow the thermal evolution of the gels to the SiO₂ matrix.     

Synthese und Kristallstruktur von Bis(1,2-dimethyl-5-nitro-imidazol)dichlorocobalt(II)

Synthesis and Crystal Structure of Bis(1,2-dimetyl-5-nitro-imidazole)dichlorocobalt(II) Bis(1,2-dimethyl-5-nitro-imidazol)dichlorocobalt(II) was obtained by reaction of CoCl₂ · 6 H₂O with 1,2-dimethyl-5-nitro-imidazole in methanol. The compound forms blue crystals which were characterized by IR and UV-vis spectroscopy and by an X-ray crystal structure determination. Co(C₅H₇N₃O₂)₂Cl₂: tetragonal, space group I4 2d, Z = 8, a = 1142.1(1) pm, c = 2577.3(2) pm. R = 0.036 for 670 independent reflexions. The Co atom is tetrahedrally surrounded by two chlorine and two N atoms at distances of 222.8(2) and 203.5(4) pm.     

Parametric analysis of oscillatory oxidation reactions

A complete parametric analysis, concerning an overall kinetic model for oscillating catalytic deep oxidation of alcohols, carbon monoxide or hydrogen, is presented. The model contains four parameters.