Influence of transition metal doping on tris(thiourea)zinc(II) sulphate crystals

Optical, thermal and dielectric properties of Ni(II)-doped tris(thiourea)zinc(II) sulphate single crystals grown by slow evaporation solution growth technique has been investigated. The lattice parameters of the as-grown crystals were obtained by single crystal X-ray diffraction analysis. The modes of vibrations of different functional groups present were identified by FT-IR studies. The surface morphological changes are observed in the doped specimen. The structure and the crystallinity of the material were confirmed by powder X-ray diffraction analysis. The UV–vis optical absorption spectrum shows the lower optical cut-off at ∼284 nm and the crystals are transparent in the entire visible region. The relative second harmonic generation efficiency measurements reveal the enhancement of efficiency by doping with small quantities of Ni(II).     

On free stochastic processes and their derivatives

We study a family of free stochastic processes whose covariance kernels K$K$ may be derived as a transform of a tempered measure σ$\sigma$. These processes arise, for example, in consideration of non-commutative analysis involving free probability. Hence our use of semi-circle distributions, as opposed to Gaussians. In this setting we find an orthonormal basis in the corresponding non-commutative L²$L^2$ of sample-space. We define a stochastic integral for our family of free processes.     

On some notions of convergence for n‐tuples of operators

The aim of this paper is to show that we can extend the notion of convergence in the norm‐resolvent sense to the case of several unbounded noncommuting operators (and to quaternionic operators as a particular case) using the notion of S‐resolvent operator. With this notion, we can define bounded functions of unbounded operators using the S‐functional calculus for n‐tuples of noncommuting operators. The same notion can be extended to the case of the F‐resolvent operator, which is the basis of the F‐functional calculus, a monogenic functional calculus for n‐tuples of commuting operators. We also prove some properties of the F‐functional calculus, which are of independent interest. Copyright © 2013 John Wiley & Sons, Ltd.     

Évaluation ponctuelle et espace de Hardy : le cas multi-échelle

We define a point evaluation for transfer operators of multiscale causal dissipative systems. We associate to such a system a de Branges Rovnyak space, which serves as the state space of a coisometric realization. To cite this article: D. Alpay et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

A class of convolution integral equations involving a generalized polynomial set

The aim of this paper is to derive a solution of a certain class of convolution integral equation of Fredholm type whose kernel involves a generalized polynomial set. Our main result is believed to be general and unified in nature. A number of (known or new) results follow as special cases, simply by specializing the coefficients and parameters involved in the generalized polynomial set. For the sake of illustration, some special cases are mentioned briefly.     

A relationship between the Nehari and the Carathéodory-Toeplitz extension problems

The solutions of the two extension problems mentioned in the title are described via linear fractional transformations. In this paper, we relate the coefficient matrix functions of these transformations.     

Ecofriendly Solventless Synthesis and Reduction Reaction of Some Triazole Compounds and Evaluation of Their Antimicrobial Activity

A number of triazole-3-one compounds have been synthesized, and reduction of the carbonyl group in the molecule has been carried out to give a corresponding hydroxyl group that possesses asymmetric carbon atom in good yields and short reaction times. It is ecofriendly because it is produced by straightforward microwave irradiation in the absence of solvent. All newly synthesized compounds were also screened for their antimicrobial activities. The antimicrobial activity study revealed that 2d, 2i, 3c, and 3g–j showed good activity against a variety of microorganisms.

Supplemental materials are available for this article. Go to the publisher's online edition of Synthetic Communications® to view the free supplemental file.     

Generalized Q-functions and Dirichlet-to-Neumann maps for elliptic differential operators

The classical concept of Q-functions associated to symmetric and selfadjoint operators due to M.G. Krein and H. Langer is extended in such a way that the Dirichlet-to-Neumann map in the theory of elliptic differential equations can be interpreted as a generalized Q-function. For couplings of uniformly elliptic second order differential expression on bounded and unbounded domains explicit Krein type formulas for the difference of the resolvents and trace formulas in an H²-framework are obtained.     

Connections between the Carathéodory-Toepliz and the Nehari extension problems: The discrete scalar case

We study the connections between the Carathéodory-Toeplitz extension problem and the Nehari extension problem in the discrete scalar case. This is the discrete counterpart of our previous paper [4].