Geometric separation and exact solutions for the parameterized independent set problem on disk graphs

We consider the parameterized problem, whether for a given set  of n disks (of bounded radius ratio) in the Euclidean plane there exists a set of k non-intersecting disks. For this problem, we expose an algorithm running in time that is—to our knowledge—the first algorithm with running time bounded by an exponential with a sublinear exponent. For λ-precision disk graphs of bounded radius ratio, we show that the problem is fixed parameter tractable with a running time  . The results are based on problem kernelization and a new “geometric ( -separator) theorem” which holds for all disk graphs of bounded radius ratio. The presented algorithm then performs, in a first step, a “geometric problem kernelization” and, in a second step, uses divide-and-conquer based on our new “geometric separator theorem.”     

Substituent Effects on the C-C Bond Strength, 15[1] Geminal Substituent Effects, 7[2]. Thermochemistry and Thermal Decomposition of Alkyl-substituted Tricyanomethyl Compounds

The thermolysis reactions of the tricyanomethyl compounds 10a-c were studied in solution. 2,2-Dicyano-3-methyl-3-phenylbutyronitrile ( 10a ) and 2,2-dicyano-3-methyl-3-(4-nitrophenyl)butyronitrile ( 10b ) decomposed heterolytically into carbenium ions and (CN)₃C⁻ anions, while 9-methyl-9-(tricyanomethyl)fluorene ( 10c ) underwent about 11% homolytic C-C bond cleavage into 9-methyl-9-fluorenyl- and tricyanomethyl radicals. The rates of the homolysis were determined by a radical scavenger procedure under conditions of pseudozero order kinetics. From the temperature effect on the rate constants the activation parameters were determined [ΔH ( 10c ) = 155· 2 kJ mol⁻¹, ΔS ( 10c ) = 58· 5 J mol⁻¹ K⁻¹]. Standard enthalpies of formation ΔH (g) were determined for 2,2-dicyanopropionitrile ( 2 ) (422.45 kJ mol⁻¹), 2,2-dicyanohexanenitrile ( 3 ) (349.74 kJ mol⁻¹), 2,2-dicyano-3-phenylpropionitrile ( 4 ) (540.75 kJ mol⁻¹), 2-butyl-2-methylhexanentrile ( 5 ) (-133.20 kJ mol⁻¹), 2,2-dimethylpentanenitrile ( 6 ) (-45.78 kJ mol⁻¹), and 2-methylbutyronitrile ( 7 ) (2.44 kJ mol⁻¹) from the enthalpies of combustion and enthalpies of sublimation/vaporization. From these data and known Δ (g) values for alkanenitriles and -dinitriles, thermochemical increments for ΔH (g) were derived for alkyl groups with one, two, or three cyano groups attached. The comparison of these increments with those of alkanes reveals a strong geminal destabilization, which is interpreted by dipolar repulsions between the cyano groups. - From ΔH (g) of 10c and ΔH of its homolytic decomposition the radical stabilization enthalpy for the tricyanomethyl radical 1 RSE ( 1 ) = -18 kJ mol⁻¹ was determined. Thus, 1 is destabilized, in comparison with the RSEs of tertiary α-cyanalkyl (23 kJ mol⁻¹) and α,α-dicyanoalkyl (27 kJ mol⁻¹) radicals, which were recalculated from bond homolysis measurements^[4] and the new thermochemical data. This change of RSE on increasing the number of α-cyano groups is discussed as the result of the additive contributions by resonance stabilization and increasing destabilization by dipolar repulsion. The amount of the dipolar energies was estimated by molecular mechanics (MM2).     

Perturbed unstable variational inequalities with unbounded operators on approximately given sets

The stability and convergence of the solutions of perturbed and regularized variational inequality to the solutions of the primary (unstable a priori) variational inequality with proper monotone operator are investigated. All the objects of inequality: the operatorA, the right-hand partf and the set of constrains are to be perturbed. At the same time no assumptions of boundedness and smoothness of the operatorA are used. The connection between the parameters of perturbations, which guarantees strong convergence of approximate solutions, is established. It is proved that the existence of the solution to the unperturbed variational inequality is necessary and sufficient condition for convergence of the regularized perturbed inequality solutions.This research was supported in part by the Ministry of Science Grant 3481-1-91 and by the Ministry of Absorption Center for Absorption in Science.     

Coherent laser excitation of Rydberg states in a weak static magnetic field

We study one-photon excitation of atomic Rydberg- and continuum states close to a photoionization threshold in the presence of a weak static external magnetic field. A semiclassical closed orbit representation for the atomic transition amplitudes is derived, which exhibits the connection between quantum mechanics and the classical dynamics of the excited electron whose motion under the combined influence of the Coulomb field of the ionic core and the magnetic field is chaotic.     

Impedance study of Ni–Co electro-deposition on Fe powder particles in fluidised bed systems

The electrochemical impedance method was applied during the electrochemical deposition of a binary Ni–Co coating on iron powder in a fluidised bed electrode system. The influence of the suspension density on the charge transfer in the course of the electro-deposition process was studied. At a potential of −900 mV (vs. Ag/AgCl/3 M KCl), when the binary Ni–Co layer was formed, the impedance data were characterised by two semicircles with the semicircle at high frequencies being larger in magnitude. A contribution of the diffusion process to the overall current was observed. The optimal suspension density for the charge transfer in the bed was 10×10⁻³–15×10⁻³ (i.e., 4–6 g of iron powder in 50 ml of electrolyte). The most probable mechanism of the charge transfer for the studied concentrations of powder particles is the convective mechanism. The iron particles dispersed in the electrolyte were considered to act as either a depolariser or an additional working electrode depending on the applied electrode potential and on the suspension density.     

Human topoisomerase I poisoning: docking protoberberines into a structure-based binding site model

Summary Using the X-ray crystal structure of the human topoisomerase I (top1) – DNA cleavable complex and the Sybyl software package, we have developed a general model for the ternary cleavable complex formed with four protoberberine alkaloids differing in the substitution on the terminal phenyl rings and covering a broad range of the top1-poisoning activities. This model has the drug intercalated with its planar chromophore between the −1 and +1 base pairs flanking the cleavage site, with the nonplanar portion pointing into the minor groove. The ternary complexes were geometry-optimized and relative interaction energies, computed by using the Tripos force field, were found to rank in correct order the biological potency of the compounds; in addition, the model is also consistent with the top1-poisoning inactivity of berberine, a major prototype of the protoberberine alkaloids. The model might serve as a rational basis for elaboration of the most active compound as a lead structure, in order to develop more potent top1 poisons as next generation anti-cancer drugs.