A note on the necessary conditions for the algebraic Riccati equation

We derive some useful and easily computable necessary conditionsfor the existence of a positive semi-definite solution to thealgebraic Ricatti equation (ARE). A motivating example is givento highlight the usefulness of the conditions for controllerand observer designs for nonlinear systems. Further, an upperbound on the trace of the solution to the ARE is also derived.     

Cooperative Strategies for Solving the Bicriteria Sparse Multiple Knapsack Problem

For hard optimization problems, it is difficult to design heuristic algorithms which exhibit uniformly superior performance for all problem instances. As a result it becomes necessary to tailor the algorithms based on the problem instance. In this paper, we introduce the use of a cooperative problem solving team of heuristics that evolves algorithms for a given problem instance. The efficacy of this method is examined by solving six difficult instances of a bicriteria sparse multiple knapsack problem. Results indicate that such tailored algorithms uniformly improve solutions as compared to using predesigned heuristic algorithms.     

First example of the C-alkylation of indoles with Baylis-Hillman acetates

Baylis-Hillman acetates undergo S_N2′ allylic substitution with indoles in the presence of 20 mol % of indium tribromide under mild conditions to afford a new class of substituted indoles in high yields with (E)-stereoselectivity. The stereochemistry of the products was assigned by various NMR experiments.     

Organoboranes—34 : General synthesis of chiral boronic and borinic esters via asymmetric hydroboration-displacement. carbenoidation of chiral borinic esters to acyclic ketones of high enantiomeric purities

Asymmetric hydroboration of appropriate alkenes with diisopinocampheylborane (Ipc₂BH) or monoisopinocampheylborane (IpcBH₂) produces intermediates that readily eliminate α-pinene on treat- ment with acetaldehyde, providing a direct, convenient route to chiral boronic esters of high enantiomeric purities. Mixed chiral trialkylboranes, readily prepared by stepwise hydroboration of appropriate alkenes with IpcBH₂, eliminate α-pinene on treatment with acetaldehyde under very mild conditions. The procedure makes readily available chiral borinic esters of high enantiomeric purities. The synthetic utility of chiral borinic esters is demonstrated by converting them into acyclic ketones including an alarm pheromone of the ant Monica mutica.     

A comparative study of various computational approaches in calculating the structure of pyridoxal 5'-phosphate (PLP)-dependent beta-lyase protein. The importance of protein environment

Various computational approaches, using molecular mechanics (Amber), semiempirical (AM1), density functional (B3LYP), and various ONIOM methods, have been comparatively investigated for the structure of Escherichia coli NifS CsdB protein. The structure of the entire monomer containing 407 amino acid residues and 579 surrounding water molecules has been optimized. The full geometry optimization in the "active site-only" approach (including only active site atoms) has been found to give the largest root-mean-square (RMS) deviation from the X-ray structure; a much better agreement has been achieved by keeping the atoms leading to the backbones of some amino acids frozen in their positions in the X-ray structure. The best agreement has been attained by including the surrounding protein in the calculations using the two-layer ONIOM (B3LYP:Amber) approach. The results presented in this study conclusively demonstrate the importance of the protein/active-site interaction on the active-site structure of the enzyme. The present theoretical study represents the largest system studied at the ONIOM level to date, containing 7992 atoms, including 84 atoms in the QM region and rest in the MM region.     

A comparison of the mechanism for the reductive half-reaction between pea seedling and other copper amine oxidases (CAOs)

In a previous DFT study a mechanism for the reductive half-reaction of pea seedling amine oxidase (PSAO) was suggested. In many of the suggested steps a lysine at the active site plays an important role. However, this lysine is not found in other amine oxidases. The primary aim of the present DFT study is therefore to investigate alternative mechanisms for those amine oxidases (CAO) where the lysine residue is not present. One of the most important roles suggested for the lysine in PSAO was to protonate the O2-site of TPQ before the critical Cbond;H bond cleavage of the substrate. In the absence of lysine the O2-site of TPQ is now suggested to be protonated by a water ligand on the copper metal complex, in line with experimental suggestions. In other steps the role of lysine is taken over by an asparagine. All results are compared with experimental observations and good agreement is generally found.     

Polyhydroxamic Acid Sorbents for Uranium Recovery

Crosslinked polyacrylamides were synthesized by solution polymerization using benzoyl peroxide as the radical initiator. The water–insoluble polymer obtained was functionalized by reacting with hydroxylamine to convert the amide group into hydroxamic acid group. The resultant functionalized polymer was characterized in terms of moisture uptake, elemental composition, IR spectra, thermal stability, exchange capacity and heavy metal sorption. The sorbent, obtained in particulate form, was investigated for its sorption properties with respect to uranium from uranyl nitrate solutions under unstirred batch conditions. This paper will concentrate on preparation, characterization and performance evaluation with respect to uranium sorption as a function of concentration, time, solution pH and temperature. The potential of this sorbent for uranium and other heavy metal ion recovery from sea water is ascertained.