Optimal scalar Lyapunov functions for decentralised stabilisation of interconnected systems

The problem of stabilisation of interconnected linear systems is considered by means of scalar Lyapunov functions and aggregation. A sufficient condition is given for an interconnected system to be stabilised using only local state feedback. The aim is to provide the least restrictive condition possible, which is termed `optimal?, by properly choosing the state-variable weighting matrices for each subsystem.     

Kinetic resolution of alpha-acetoxy N-acyl oxazolidinethiones by a chiral O-nucleophilic acyl transfer catalyst

The kinetic resolution of alpha-acetoxy N-acyl oxazolidinethiones using the chiral, nonracemic O-nucleophilic acyl transfer catalyst 8 is described. The reaction proceeds on a variety of substrates in excellent yields, with s-factors ranging from 17 to 31.     

Spectral and thermal study of the ternary complexes of nickel with sulfasalazine and some amino acids

The ternary complexes of Ni(II) with sulfasalazine (H(3)SS) as a primary ligand and alanine (ala), aspartic acid (asp), histidene (hist), methionine (meth) and serine (ser) amino acids as secondary ligands have been synthesized. Characterization of the complexes was based on elemental analyses, IR, UV-vis, mass spectra, magnetic moment and thermal analysis (TG). The isolated complexes were found to have the general formula [M(HSS)(AA)]4H(2)O (AA=ala, asp, hist, meth, or ser amino acid) where nickel is tetra-coordinated. The thermal stability of the complexes was studied and the weight losses for the decomposition of the complexes were calculated and correlated with the mass fragmentation pattern. In most cases, the amino acid moiety is removed along with the Schiff base moiety leaving NiO as a metallic residue. The metallic residue was confirmed by powder XRD measurements.     

Paranormal Elements in Normed Algebra

For a normed algebra A and natural numbers k we introduce and investigate the ∥ · ∥ closed classes P _k (A). We show that P₁(A) is a subset of P _k (A) for all k. If T in P₁(A), then Tⁿ lies in P₁(A) for all natural n. If A is unital, U, V ∈ A are such that ∥U∥ = ∥V∥ = 1, VU = I and T lies in P _k (A), then UTV lies in P _k (A) for all natural k. Let A be unital, then 1) if an element T in P₁(A) is right invertible, then any right inverse element T^?1 lies in P₁(A); 2) for ßßIßß = 1 the class P₁(A) consists of normaloid elements; 3) if the spectrum of an element T, T ∈ P₁(A) lies on the unit circle, then ∥TX∥ = ∥X∥ for all X ∈ A. If A = B(H), then the class P₁(A) coincides with the set of all paranormal operators on a Hilbert space H.     

Poly(vinyl alcohol)-Graft-Poly(ethylene glycol)-Supported Hydroxyproline Catalysis of Stereoselective Aldol Reactions

Summary: The good swelling and high loading of poly(vinyl alcohol)-graft-poly(ethylene glycol) (PVA-g-PEG) resins proved to be effective for performing supported proline-catalyzed aldol reactions stereoselectively in a wide range of polar non-protic, protic and non-polar solvents as well as in neat substrate. The catalysts could be recovered by filtration and recycled, without significant loss of activity. The use of poly(vinyl alcohol)-graft-poly(ethylene glycol) matrix improved the solubility of the proline-derived catalysts and expanded the scope of permissible solvents for performing selective aldol chemistry.     

Some common fixed point theorems for a pair of tangential mappings in symmetric spaces

A metrical common fixed point theorem for a pair of self mappings due to Sastry and Murthy (K.P.R. Sastry, I.S.R. Krishna Murthy, A common fixed points of two partially commuting tangential selfmaps on a metric space, J. Math. Anal. Appl. 250 (2000) 731734.) [8] is extended to symmetric spaces which in turn generalises a fixed point theorem due to Pant (R.P. Pant, Common fixed points of Lipschitz type mapping pairs, J. Math. Anal. Appl. 248 (1999) 280283.) [11] besides deriving some related results. Some illustrative examples to highlight the realised improvements are also furnished.     

Existence of nonnegative solutions for parabolic problem on Dirichlet forms

In this work, we investigate perturbed parabolic problem on measure spaces. For strongly local Dirichlet form, we obtain some results on existence and uniqueness of nonnegative solution. We also presented some examples as an applications.     

A Diophantine duality applied to the KAM and Nekhoroshev theorems

In this paper, we use geometry of numbers to relate two dual Diophantine problems. This allows us to focus on simultaneous approximations rather than small linear forms. As a consequence, we develop a new approach to the perturbation theory for quasi-periodic solutions dealing only with periodic approximations and avoiding classical small divisors estimates. We obtain two results of stability, in the spirit of the KAM and Nekhoroshev theorems, in the model case of a perturbation of a constant vector field on the $n$ -dimensional torus. Our first result, which is a Nekhoroshev type theorem, is the construction of a “partial” normal form, that is a normal form with a small remainder whose size depends on the Diophantine properties of the vector. Then, assuming our vector satisfies the Bruno–Rüssmann condition, we construct an “inverted” normal form, recovering the classical KAM theorem of Kolmogorov, Arnold and Moser for constant vector fields on torus.