An existence result for linear partial differential equations with coefficients in an algebra of generalized functions

We prove the existence of solutions for essentially all linear partial differential equations with -coefficients in an algebra of generalized functions, defined in the paper. In particular, we show that H. Lewy's equation has solutions whenever its right-hand side is a classical -function.

     

Mössbauer study of carbide phases in catalysts for ammonia synthesis

Samples of a catalyst CA-1 for ammonia synthesis were studied. After reduction the samples were treated with CO₂ or with a mixture of 1% O₂+2.4% H₂O+CO₂ at temperatures between 600 and 783 K. Mössbauer spectroscopy data indicate that above 600 K carbide phases and magnetite are formed. A probable mechanism for carbide formation is suggested.     

Semilinear hyperbolic systems and equations with singular initial data

We study the weak limits (t, .)of solutions to semilinear strictly hyperbolic systems and wave equations with initial datau (0, .) approximating a distribution, 0 < 1. We propose an optimal link between the singularity of and the growth of the nonlinear term in order that exists. In this way we extend some of the results in [3], [10], [13].     

Manganese-enhanced magnetic resonance microscopy of mineralization

Paramagnetic manganese (II) can be employed as a calcium surrogate to sensitize magnetic resonance microscopy (MRM) to the processing of calcium during bone formation. At high doses, osteoblasts can take up sufficient quantities of manganese, resulting in marked changes in water proton T(1), T(2) and magnetization transfer ratio values compared to those for untreated cells. Accordingly, inductively coupled plasma mass spectrometry (ICP-MS) results confirm that the manganese content of treated cell pellets was 10-fold higher than that for untreated cell pellets. To establish that manganese is processed like calcium and deposited as bone, calvaria from the skull of embryonic chicks were grown in culture medium supplemented with 1 mM MnCl(2) and 3 mM CaCl(2). A banding pattern of high and low T(2) values, consistent with mineral deposits with high and low levels of manganese, was observed radiating from the calvarial ridge. The results of ICP-MS studies confirm that manganese-treated calvaria take up increasing amounts of manganese with time in culture. Finally, elemental mapping studies with electron probe microanalysis confirmed local variations in the manganese content of bone newly deposited on the calvarial surface. This is the first reported use of manganese-enhanced MRM to study the process whereby calcium is taken up by osteoblasts cells and deposited as bone.     

Crystallisation Mechanism in Gradient Temperature Zone Melting

Theory of zone recrystallization in the framwork of already known models of normal crystal growth, growth by screw dislocations and by two-dimensional nucleation is discussed. By mathematical treatment, different from Tillers approach, analytical expressions for supersaturation at the crystallisation interface, for superheating at the dissolution interface, growth rate and some other parameters have been obtained for both cases of normal and screw dislocations growth. It is possible to determine the growth mechanism.     

Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients

^** Email: todor{at}math.ethz.ch^*** Corresponding author. Email: schwab{at}math.ethz.ch A scalar, elliptic boundary-value problem in divergence formwith stochastic diffusion coefficient a(x, ) in a bounded domainD ^d is reformulated as a deterministic, infinite-dimensional,parametric problem by separation of deterministic (x D) andstochastic ( ) variables in a(x, ) via Karhúnen–Loèveor Legendre expansions of the diffusion coefficient. Deterministic,approximate solvers are obtained by projection of this probleminto a product probability space of finite dimension M and sparsediscretizations of the resulting M-dimensional parametric problem.Both Galerkin and collocation approximations are considered.Under regularity assumptions on the fluctuation of a(x, ) inthe deterministic variable x, the convergence rate of the deterministicsolution algorithm is analysed in terms of the number N of deterministicproblems to be solved as both the chaos dimension M and themultiresolution level of the sparse discretization resp. thepolynomial degree of the chaos expansion increase simultaneously.     

Controlled Annealing in Adaptive Multicomponent Gels

We use a pH-driven annealing process to convert between co-assembled and self-sorted networks in multicomponent gels. The initially formed gels at low pH are co-assembled, with the two components coexisting within the same self-assembled structures. We use an enzymatic approach to increase the pH, resulting in a gel-to-sol transition, followed by a hydrolysis to lower the pH once again. As the pH decreases, a self-sorted network is formed by a two-stage gelation process determined by the pK_a of each component. This approach can be expanded to layered systems to generate many varied systems by changing composition and rates of pH change, adapting their microstructure and so allowing access to a far greater range of morphologies and complexity than can be achieved in single component systems.     

First-second shell interactions in metal binding sites in proteins: a PDB survey and DFT/CDM calculations

The role of the second shell in the process of metal binding and selectivity in metalloproteins has been elucidated by combining Protein Data Bank (PDB) surveys of Mg, Mn, Ca, and Zn binding sites with density functional theory/continuum dielectric methods (DFT/CDM). Peptide backbone groups were found to be the most common second-shell ligand in Mg, Mn, Ca, and Zn binding sites, followed (in decreasing order) by Asp/Glu, Lys/Arg, Asn/Gln, and Ser/Thr side chains. Aromatic oxygen- or nitrogen-containing side chains (Tyr, His, and Trp) and sulfur-containing side chains (Cys and Met) are seldom found in the second coordination layer. The backbone and Asn/Gln side chain are ubiquitous in the metal second coordination layer as their carbonyl oxygen and amide hydrogen can act as a hydrogen-bond acceptor and donor, respectively, and can therefore partner practically every first-shell ligand. The second most common outer-shell ligand, Asp/Glu, predominantly hydrogen bonds to a metal-bound water or Zn-bound histidine and polarizes the H-O or H-N bond. In certain cases, a second-shell Asp/Glu could affect the protonation state of the metal ligand. It could also energetically stabilize a positively charged metal complex more than a neutral ligand such as the backbone and Asn/Gln side chain. As for the first shell, the second shell is predicted to contribute to the metal selectivity of the binding site by discriminating between metal cations of different ionic radii and coordination geometries. The first-shell-second-shell interaction energies decay rapidly with increasing solvent exposure of the metal binding site. They are less favorable but are of the same order of magnitude as compared to the respective metal-first-shell interaction energies. Altogether, the results indicate that the structure and properties of the second shell are dictated by those of the first layer. The outer shell is apparently designed to stabilize/protect the inner-shell and complement/enhance its properties.