A generalization of the Fermi-Breit equation to non-Coulombic spatial interactions

Starting from the relativistic invariance properties at classical level, we generalize the Darwin equation to the case of non-Coulombic spatial interactions. The relativistic correction terms for vector interactions are derived from a given nonrelativistic potential. We show that, for a Coulombic potential, the results coincide with those obtained in the Coulomb gauge. The results are adapted to the quantum theory obtaining a generalization of the Fermi-Breit equation. An Hermitian interaction operator is constructed. A critical comparison with other possible treatments of the retardation terms is performed also discussing the usual choice of the Coulomb gauge. Special attention is devoted to the construction of a model for quark interaction.     

Null controllability for the parabolic equation with a complex principal part

The paper is devoted to a study of the null controllability for the semilinear parabolic equation with a complex principal part. For this purpose, we establish a key weighted identity for partial differential operators (with real functions α and β), by which we develop a universal approach, based on global Carleman estimate, to deduce not only the desired explicit observability estimate for the linearized complex Ginzburg-Landau equation, but also all the known controllability/observability results for the parabolic, hyperbolic, Schrödinger and plate equations that are derived via Carleman estimates.     

On a Boundary Value Problem for Pairs of Polyanalytic Functions

The necessary and sufficient conditions of Fredholmness and the index formula for a boundary value problems for a pair of polyanalytic functions, containing differential operators as well as operators with Carleman shift and conjugations, are obtained. Submitted: May 16, 2007. Accepted: November 5, 2007.     

Dissimilar or orthogonal reversed-phase chromatographic systems: A comparison of selection techniques

Developing an analytical separation procedure for an unknown mixture is a challenging issue. An important example is the separation and quantification of a new drug and its impurities. One approach to start method development is the screening of the mixture on dissimilar chromatographic systems, i.e. systems with large selectivity differences. After screening, the most suited system is retained for further method development. In a step prior to such strategy dissimilar chromatographic systems need to be selected. In this paper the performance of different chemometric selection approaches, described in the literature, was visually evaluated and compared. Additionally, orthogonal projection approach (OPA) was tested as another potential selection method. All techniques, including the OPA method, were able to select (a set of) dissimilar chromatographic systems and many similarities between the selections were observed. However, the Kennard and Stone algorithm performed best in selecting the most dissimilar systems in the earliest steps of the selection procedure. The generalized pairwise correlation method (GPCM) and the auto-associative multivariate regression trees (AAMRT) were also performing well. OPA and weighted pair group method using arithmetic averages (WPGMA) are less preferable.     

Necessary and sufficient conditions for parameter insensitive disturbance-rejection problems with dynamic output feedback

Email: otsuka{at}j.dendai.ac.jp Received on November 11, 2005; Accepted on December 16, 2006 In this paper, necessary and sufficient conditions for the parameterinsensitive disturbance-rejection problem with dynamic outputfeedback which was studied in Otsuka (1999) to be solvable aregiven for the structured uncertain linear systems. Further,necessary and sufficient conditions for the solvability of theproblems with static output feedback and state feedback arealso studied as special cases. The obtained results containsome extensions of the previous results to the structured uncertainlinear systems.     

Theoretical modeling of photocatalytic active species on illuminated TiO2

A theoretical study of the H₂O and O₂ adsorption on an illuminated TiO₂ anatase surface is presented. The electronic structure and the spin distribution were examined by employing the DFT formalism and the BHandHLYP functional. The adsorbates geometries were fully optimized, including the cluster relaxation. Our results show the dissociative adsorption of the H₂O molecule on the photoactivated TiO₂ (0 0 1) surface. This reaction produces one hydroxyl group with radical character (OH) and an unpaired electron localized in the 5c-Ti atom. In case of the O₂ molecule, the non-dissociative chemisorption was obtained. This molecule shows one unpaired electron and a negative charge. In these sense, the adsorbed O₂ acts as a superoxide species (O₂⁻).