Rational matrix pseudodifferential operators

The skewfield $\mathcal{K }(\partial )$ of rational pseudodifferential operators over a differential field $\mathcal{K }$ is the skewfield of fractions of the algebra of differential operators $\mathcal{K }[\partial ]$ . In our previous paper, we showed that any $H\in \mathcal{K }(\partial )$ has a minimal fractional decomposition $H=AB^{-1}$ , where $A,B\in \mathcal{K }[\partial ],\,B\ne 0$ , and any common right divisor of $A$ and $B$ is a non-zero element of $\mathcal{K }$ . Moreover, any right fractional decomposition of $H$ is obtained by multiplying $A$ and $B$ on the right by the same non-zero element of $\mathcal{K }[\partial ]$ . In the present paper, we study the ring $M_n(\mathcal{K }(\partial ))$ of $n\times n$ matrices over the skewfield $\mathcal{K }(\partial )$ . We show that similarly, any $H\in M_n(\mathcal{K }(\partial ))$ has a minimal fractional decomposition $H=AB^{-1}$ , where $A,B\in M_n(\mathcal{K }[\partial ]),\,B$ is non-degenerate, and any common right divisor of $A$ and $B$ is an invertible element of the ring $M_n(\mathcal{K }[\partial ])$ . Moreover, any right fractional decomposition of $H$ is obtained by multiplying $A$ and $B$ on the right by the same non-degenerate element of $M_n(\mathcal{K } [\partial ])$ . We give several equivalent definitions of the minimal fractional decomposition. These results are applied to the study of maximal isotropicity property, used in the theory of Dirac structures.     

Coexistence of negatively and positively buckled isomers on n+-doped Si(111) − 2 × 1

A long-standing puzzle regarding the Si(111) ? 2 × 1 surface has been solved. The surface energy gap previously determined by photoemission on heavily n-doped crystals was not compatible with a strongly bound exciton known from other considerations to exist. New low-temperature angle-resolved photoemission and scanning tunneling microscopy data, together with theory, unambiguously reveal that isomers with opposite bucklings and different energy gaps coexist on such surfaces. The subtle energetics between the isomers, dependent on doping, leads to a reconciliation of all previous results.     

Action functional and quasi‐potential for the burgers equation in a bounded interval

Consider the viscous Burgers equation u_t + f(u)_x = εu_xx on the interval [0,1] with the inhomogeneous Dirichlet boundary conditions u(t,0) = ρ₀, u(t,1) = ρ₁. The flux f is the function f(u) = u(1 − u), ε > 0 is the viscosity, and the boundary data satisfy 0 < ρ₀ < ρ₁ < 1. We examine the quasi‐potential corresponding to an action functional arising from nonequilibrium statistical mechanical models associated with the above equation. We provide a static variational formula for the quasi‐potential and characterize the optimal paths for the dynamical problem. In contrast with previous cases, for small enough viscosity, the variational problem defining the quasi‐potential admits more than one minimizer. This phenomenon is interpreted as a nonequilibrium phase transition and corresponds to points where the superdifferential of the quasi‐potential is not a singleton. © 2011 Wiley Periodicals, Inc.     

A molecularly imprinted polymer for the determination of neopterin

A molecularly imprinted polymer (MIP) for the specific retention of neopterin has been developed. A set of 6 polymers was prepared by radical polymerization under different experimental condition using methacrylic acid as functional monomer and ethylene glycol dimethacrylate as crosslinker, with the aim to understand their influence on the efficiency of the MIP. The performance of each MIP was tested in batch experiments via their binding capacity. The MIP prepared in the presence of nickel ions in dimethylsulfoxide-acetonitrile mixture (P4) exhibited the highest binding capacity for neopterin (260 μmol per gram of polymer). A selectivity study with two other pteridines demonstrated the polymer P4 also to possess the best selectivity.

A molecularly imprinted polymer for the specific retention of neopterin was developed. A set of 6 polymers was prepared under different experimental condition. The performance of each MIP was tested through their binding capacity. The MIP P4 prepared in the presence of nickel ions exhibited the highest binding capacity

     

All-optical determination of initial oxidation of Si(100) and its kinetics

By comparison of measured and ab initio calculated surface optical spectra we demonstrate that two main oxidation processes initially occur after dissociation of oxygen molecules, forming in both cases Si–O–Si entities: (i) breaking of Si dimers by incorporation of oxygen atoms; (ii) incorporation into the silicon backbonds. The kinetics up to half-monolayer coverage is determined, and explained in terms of Langmuir-like adsorption mechanisms with different probabilities.