Azidoacetone as a complexing agent of transition metals Ni2+/Co2+ promoted dissociation of the C-C bond in azidoacetone

The relevance of metal interactions with azides has led us to the study of the complexation of some transition metals, nickel and cobalt, by azidoacetone by means of electrospray ionization mass spectrometry (ESI-MS). Complexes were obtained from solutions of NiCl(2) and CoCl(2) , in methanol/water. Nickel was electrosprayed with other counter ion, bromide (Br), as well as other solvent (ethanol/water). For nickel and cobalt, the complexes detected were single positively charged, with various stoichiometries, some resulted from the fragmentation of the ligand, the loss of N(2) being quite common. The most abundant species were [Ni(II)Az(2)X](+) where X = Cl, Br and Az = azidoacetone. Some of the complexes showed solvation with the solvent components. Metal reduction was observed in complexes where a radical was lost, resulting from the homolytic cleavage of a metal coordination bond. Collision-induced dissociation (CID) experiments followed by tandem mass spectrometry (MS-MS) analysis were not absolutely conclusive about the coordination site. However, terminal ions of the fragmentation routes were explained by a gas-phase mechanism proposed where a C-C bond was activated and the metal inserted subsequently. Density functional theory calculations provided structures for some complexes. In [Ni(II)Az(2)X](+) species, one azidoacetone ligand is monodentate and the dominant binding location is the alkylated nitrogen and not the carbonyl group. The other azidoacetone ligand is bidentate showing coordination through alkylated nitrogen and the carbonyl group. These are also the preferential binding sites for the most stable isomer of [Ni(II)AzX](+) species.     

On the numerical radius of operators in Lebesgue spaces

We show that the absolute numerical index of the space Lp(μ) is (where ). In other words, we prove that

     

Moduli of convexity and smoothness of reflexive subspaces of L

We show that for any probability measure μ there exists an equivalent norm on the space L¹(μ) whose restriction to each reflexive subspace is uniformly smooth and uniformly convex, with modulus of convexity of power type 2. This renorming provides also an estimate for the corresponding modulus of smoothness of such subspaces.     

Decay estimates of functions through singular extensions of vector-valued Laplace transforms

Let X be a Banach space and let f∈L^∞(R⁺;X) whose Laplace transform extends analytically to some region containing iR?{0}, possibly having a pole at the origin. In this paper, we give estimates of the decay of certain slight suitable modification of f in terms of the growth of its Laplace transform along the imaginary axis. This technique is applied to obtain decay estimates of smooth orbits of bounded C₀-semigroups whose infinitesimal generators have an arbitrary finite boundary spectrum. These results are close to those given recently by C.J.K. Batty and T. Duyckaerts.     

Well-posedness and stability of the repairable system with N failure modes and one standby unit

The well-posedness and stability of the repairable system with N failure modes and one standby unit were discussed by applying the c₀ semigroups theory of function analysis. Firstly, the integro-differential equations described the system were transformed into some abstract Cauchy problem of Banach space. Secondly, the system operator generates positive contractive c₀ semigroups T(t) and so the well-posedness of the system was obtained. Finally, the spectral distribution of the system operator was analyzed. It was proven that 0 is strictly dominant eigenvalue of the system operator and the dynamic solution of the system converges to the steady-state solution. The steady-state solution was shown to be the eigenvector of the system operator corresponding to the eigenvalue 0. At the same time the dynamic solution exponentially converges to the steady-state solution.     

An expectation formula with applications

In this paper, we derive an expectation formula of a random variable having distribution W(x;q). As applications of the expectation formula, we give a transformation formula and an expansion of Sears? transformation formula.     

Divergence points of self-similar measures satisfying the OSC

Recently, Barreira and Schmeling (2000) [1] and Chen and Xiong (1999) [2] have shown, that for self-similar measures satisfying the SSC the set of divergence points typically has the same Hausdorff dimension as the support K. It is natural to ask whether we obtain a similar result for self-similar measures satisfying the OSC. However, with only the OSC satisfied, we cannot do most of the work on a symbolic space and then transfer the results to the subsets of Rd, which makes things more difficult. In this paper, by the box-counting principle we show that the set of divergence points has still the same Hausdorff dimension as the support K for self-similar measures satisfying the OSC.     

Riesz means associated with certain product type convex domain

In this paper we study the maximal operators and the convolution operators Tδ associated with multipliers of the form

     

Passivity-based control for Hopfield neural networks using convex representation

This paper considers the problem of passivity-based controller design for Hopfield neural networks. By making use of a convex representation of nonlinearities, a feedback control scheme based on passivity and Lyapunov theory is presented. A criterion for existence of the controller is given in terms of linear matrix inequality (LMI), which can be easily solved by a convex optimization problem. An example and its numerical simulation are given to show the effectiveness of the proposed method.