Exact controllability and stabilizability of the Korteweg-de Vries equation

In this paper, we consider distributed control of the system described by the Korteweg-de Vries equation

 

on the interval , with periodic boundary conditions

 

where the distributed control is restricted so that the ``volume' of the solution is conserved. Both exact controllability and stabilizibility questions are studied for the system. In the case of open loop control, if the control is allowed to act on the whole spatial domain , it is shown that the system is globally exactly controllable, i.e., for given and functions , with the same ``volume', one can alway find a control so that the system (i)--(ii) has a solution satisfying

If the control is allowed to act on only a small subset of the domain , then the same result still holds if the initial and terminal states, and , have small ``amplitude' in a certain sense. In the case of closed loop control, the distributed control is assumed to be generated by a linear feedback law conserving the ``volume' while monotonically reducing . The solutions of the resulting closed loop system are shown to have uniform exponential decay to a constant state. As in the open loop control case, a small amplitude assumption is needed if the control is allowed to act on only a small subdomain. The smoothing property of the periodic (linear) KdV equation discovered recently by Bourgain has played an important role in establishing the exact controllability and stabilizability results presented in this paper.

     

Chemistry and Biology of Cylindrols: Novel Inhibitors of Ras Farnesyl-Protein Transferase from Cylindrocarpon lucidum

Farnesyl-protein transferase (FPTase) is an enzyme responsible for the farnesylation of Ras protein. Farnesylation is required for cell-transforming activity in several tumor-types, and therefore, inhibition of FPTase activity may be a potential target for anticancer drugs. Our continued search for novel inhibitors led to the isolation of a number of bicyclic resorcinaldehyde cyclohexanone derivatives named here cylindrols A(1) to A(4), cylindrols B and B(1), and a number of known compounds, from Cylindrocarpon lucidum. The compounds were isolated by bioassay-guided separation using Sephadex LH-20, silica gel, and reverse phase HPLC. Structures were elucidated by extensive application of 2D NMR and X-ray crystallography. The determination of absolute stereochemistry was accomplished by CD measurements. Chemical transformations of the most abundant compound resulted in a number of key derivatives which were critical for the evaluation of structure activity relationship. These compounds are members of ascochlorin family and showed a wide range of inhibitory activity (0.7 &mgr;M to >140 &mgr;M) against FPTase. The FPTase activity was noncompetitive with respect to both substrates. Isolation, structures, chemical transformations, and FPTase activity are discussed in detail.     

The effect of random restrictions on formula size

We consider the formula size complexity of boolean functions over the base consisting of ∧, ∨, and ¬ gates. In 1961 Subbotovskaya proved that, for any boolean function on n variables, setting all but a randomly chosen ?n variables to randomly chosen constants, reduces the expected complexity of the induced function by at least a factor. This fact was used by Subbotovskaya to derive a lower bound of Ω(n^1.5) for the formula size of the parity function, and more recently by Andreev who exhibited at lower bound of ΩC(n^2.5/log^O(1)(n)) for a function in P. We present the first improvement of Subbotovskaya's result, showing that the expected formual complexity of a function restricted as above is at most an O(?^γ) franction of its original complexity, for This allows us to give an improved lower bound of Ω(n^2.556…) for Andreev's function. At the time of discovery, this was the best formula lower bound known for any function in NP. © 1993 John Wiley & Sons, Inc.     

Determination of trace metals in estuarine sediments by graphite-furnace atomic absorption spectrometry

A simple and rapid acid digestion method for the decomposition of estuarine sediments is described. Quantitative recovery of Cd, Pb, Cu, Ni, Co, Be and Co is demonstrated. Sensitive, precise and accurate determination of these trace metals by graphite-furnace atomic absorption spectrometry in combination with the L'vov Platform provides an interference-free technique that permits calibration with simple aqueous solutions of metal standards. The accuracy of the method has been confirmed by analysis of two marine sediment reference materials, MESS-1 and BCSS-1.     

Toward understanding the ionization of biomarkers from micrometer particles by bio-aerosol mass spectrometry

The appearance of informative signals in the mass spectra of laser-ablated bio-aerosol particles depends on the effective ionization probabilities (EIP) of individual components during the laser ionization process. This study investigates how bio-aerosol chemical composition governs the EIP values of specific components and the overall features of the spectra from the bio-aerosol mass spectrometry (BAMS). EIP values were determined for a series of amino acid, dipicolinic acid, and peptide aerosol particles to determine what chemical features aid in ionization. The spectra of individual amino acids and dipicolinic acid, as well as mixtures, were examined for extent of fragmentation and the presence of molecular ion dimers, which are indicative of ionization conditions. Standard mixtures yielded information with respect to the significance of secondary ion plume reactions on observed spectra. A greater understanding of how these parameters affect EIP and spectra characteristics of bio-aerosols will aid in the intelligent selection of viable future biomarkers for the identification of bio-terrorism agents.     

Electrochemical control of protein monolayers at indium tin oxide surfaces for the reagentless optical biosensing of nitric oxide

Cytochrome c has been immobilized onto functionalized, optically transparent indium tin oxide (ITO) electrodes by covalent and electrostatic techniques. Covalent immobilization was achieved by the formation of a disulfide bond between N-succinimidyl 3-(2-pyridyldithio)propionate-(SPDP-) modified cytochrome c and SPDP-silanized ITO. Additionally, ITO electrodes have been modified with the bifunctional reagent 1,12-dodecanedicarboxylic acid (DDCA), resulting in formation of a carboxylic acid-terminated monolayer. Covalent protein attachment to the DDCA-functionalized ITO was achieved with the cross-linker 1-[3-(dimethylamino)propyl]-3-ethylcarbodiimide hydrochloride. Electrostatic attachment of the protein involved ion-pair and hydrogen-bond interactions between the terminating carboxylic acid groups of the DDCA-functionalized ITO and the primary amine groups of the lysine residues of cytochrome c. The electrostatic interaction between the cytochrome c and the functionalized ITO resulted in greater rotational mobility of the protein at the electrode surface, leading to ca. 63% electroactivity, as compared to ca. 41% electroactivity for the covalently immobilized protein. The redox state of the electrostatically bound cytochrome c monolayers could be electrochemically switched between ferric and ferrous forms. Electrochemical control of the bound protein was used to regenerate the biosensing surface following binding of nitric oxide (NO). Ligation of NO with the cytochrome c was monitored by measurement of the change of absorbance intensity at 416 nm. Through application of a negative potential, the cytochrome c was reduced from the ferric to the ferrous form, which led to the removal of the ligated NO. Application of a positive potential regenerated the ferric cytochrome c, enabling multiple repeat measurements of NO. Such electrochemical control of proteins immobilized on transparent electrodes enables the optical biosensing of analyte targets without recourse to exogenous reagents.