Carathéodory-Fejér interpolation in locally convex topological vector spaces

We study Carathéodory-Herglotz functions whose values are continuous operators from a locally convex topological vector space which admits the factorization property into its conjugate dual space. We show how this case can be reduced to the case of functions whose values are bounded operators from a Hilbert space into itself.     

Enhancement of second harmonic generation efficiency: Growth and characterization of magnesium(II)-doped tetrakis(thiourea)nickel(II) chloride crystals

The influence of magnesium doping on the properties of tetrakis(thiourea)nickel(II) chloride crystals has been described. The reduction in the intensity observed in powder X-ray diffraction of doped specimen and slight shifts in vibrational frequencies confirm the lattice stress as a result of doping. Surface morphological changes due to doping of the alkaline earth metal are observed by scanning electron microscopy. The incorporation of Mg(II) into the crystal lattice was confirmed by energy dispersive X-ray spectroscopy. Lattice parameters are determined by single crystal XRD analysis. The thermogravimetric and differential thermal analysis studies reveal the purity of the materials and no decomposition is observed up to the melting point. The crystal is further characterized by Kurtz powder technique and dielectric studies.     

State space theory of automorphisms of rational matrix functions

The state space theory from linear control theory is used as a tool to describe the action of automorphisms of a certain form acting on rational matrix functions. This class consists of automorphisms representable as the composition of a linear fractional change of variable together with the operations of inverse-transpose, conjugation and an inner automorphism. We also describe in state space terms minimal factorizations within the class of functions of a certain associated group.Partially supported by NSF Grant 9000839 and by USA-Israel Binational Foundation Grant 88003094/2.     

Espaces de Branges Rovnyak et fonctions de Schur : le cas hyper-analytique

We extend to the hyperholomorphic case the notion of Schur functions and the corresponding realization theory. We introduce the notion of characteristic operator function for coisometric colligations between Hilbert spaces of hyperholomorphic functions. We show that every Schur function is the characteristic operator function of a coisometric colligation and vice-versa. To cite this article: D. Alpay et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

A7DB: a relational database for mutational,physiological and pharmacological data related to the α7 nicotinic acetylcholine receptor

Background  

Nicotinic acetylcholine receptors (nAChRs) are pentameric proteins that are important drug targets for a variety of diseases including Alzheimer's, schizophrenia and various forms of epilepsy. One of the most intensively studied nAChR subunits in recent years has been α7. This subunit can form functional homomeric pentamers (α7)₅, which can make interpretation of physiological and structural data much simpler. The growing amount of structural, pharmacological and physiological data for these receptors indicates the need for a dedicated and accurate database to provide a means to access this information in a coherent manner.     

Noise and nonlinear estimation with optimal schemes in DTI

In general, the estimation of the diffusion properties for diffusion tensor experiments (DTI) is accomplished via least squares estimation (LSE). The technique requires applying the logarithm to the measurements, which causes bad propagation of errors. Moreover, the way noise is injected to the equations invalidates the least squares estimate as the best linear unbiased estimate. Nonlinear estimation (NE), despite its longer computation time, does not possess any of these problems. However, all of the conditions and optimization methods developed in the past are based on the coefficient matrix obtained in a LSE setup. In this article, NE for DTI is analyzed to demonstrate that any result obtained relatively easily in a linear algebra setup about the coefficient matrix can be applied to the more complicated NE framework. The data, obtained using non-optimal and optimized diffusion gradient schemes, are processed with NE. In comparison with LSE, the results show significant improvements, especially for the optimization criterion. However, NE does not resolve the existing conflicts and ambiguities displayed with LSE methods.     

Non-commutative stochastic distributions and applications to linear systems theory

In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. Special inequalities which hold in this space allow to characterize its invertible elements and to develop an appropriate framework of non-commutative stochastic linear systems.