A Characterization of the Optimal p-sum Labellingsof Unit Interval Graphs

1.IntroductionGraphsconsideredinthispaperarefiniteandsimple.FOragraphG,V(G)andE(G)denoteitssetofvenicesandedges,respectively.AbijectionwillbecalledalabellingofG.Letpbeapositiverealnumber.ForagivenlabellingTofagraphG,definethegndiscrepencya.(G,ac)ofTasTheobjectiveoftheminimum-p--sumproblemistofindalabelling7ofagraphGsuchthatac(G,T)isassmallaspossible.ThelabellingTminimizinga.(G,7)iscalledanoptimalHsumlabellingofG.Theminimumvalueiscalledtheminimum-psumofG.ItisshowninI31thattheminimum-…     

Invariants for normal completely positive maps on the hyperfinite II1 factor

We investigate certain classes of normal completely positive (CP) maps on the hyperfinite II₁ factorA. Using the representation theory of a suitable irrational rotation algebra, we propose some computable invariants for such CP maps. Dedicated to Professor K B Sinha     

Noise-induced asymptotic periodicity in a piecewise linear map

We examine asymptotically periodic density evolution in one-dimensional maps perturbed by noise, associating the macroscopic state of these dynamical systems with a phase space density. For asymptotically periodic systems density evolution becomes periodic in time, as do some macroscopic properties calculated from them. The general formalism of asymptotic periodicity is examined and used to calculate time correlations along trajectories of these maps as well as their limiting conditional entropy. The time correlation is shown to naturally decouple into periodic and stochastic components. Finally, asymptotic periodicity is studied in a noise-perturbed piecewise linear map, focusing on how the variation of noise amplitude can cause a transition from asymptotic periodicity to asymptotic stability in the density evolution of this system.     

基于零点的函数K图和dj图的转换

介绍了函数的最大项展开式和CRM展开式及其图形表示，提出函数K图和dj图的零点的概念，并以此为基础讨论了基于零点的函数K图和dj图之间的转换方法。     

Convergence of Riemannian Manifolds and Laplace Operators, II

We study spectral convergence of compact Riemannian manifolds or more generally certain Dirichlet spaces, obtaining some compactness results on harmonic functions and harmonic maps. Mathematics Subject Classifications (2000) 53C21, 58D17, 58J50. Atsushi Kasue: Partly supported by the Grant-in-Aid for Scientific Research (B) No. 15340053 of the Japan Society for the Promotion of Science.     

Lemniscates and inequalities for the logarithmic capacities of continua

It is shown that if P(z) = z ⁿ + ? is a polynomial with connected lemniscate E(P) = {z: ¦P(z)¦ ≤ 1} and m critical points, then, for any n? m+1 points on the lemniscate E(P), there exists a continuum γ ? E(P) of logarithmic capacity cap γ ≤ 2^?1/n which contains these points and all zeros and critical points of the polynomial. As corollaries, estimates for continua of minimum capacity containing given points are obtained.     

Random walks generated by affine mappings

This article is concerned with Markov chains on ^m constructed by randomly choosing an affine map at each stage, and then making the transition from the current point to its image under this map. The distribution of the random affine map can depend on the current point (i.e., state of the chain). Sufficient conditions are given under which this chain is ergodic.     

Mixed micellization of an anionic gemini surfactant (GA) with conventional polyethoxylated nonionic surfactants in brine solution at pH 5 and 298 K

The micellization behavior of an anionic gemini surfactant, GA with nonionic surfactants C₁₂E₈ and C₁₂E₅ in presence of 0.1 M NaCl at 298 K temperature, has been studied tensiometrically in pure and mixed states, and the related physicochemical parameters (cmc, γ _cmc, pC ₂₀, Γ _max, and A _min) have been evaluated. Tensiometric profile (γ vs log [surfactant]), for conventional surfactants, generally consists of a single point of intersection; a gradually decreasing line (normally linear, or with slight curvature) ultimately saturates in γ at a particular [surfactant], corresponding to complete monolayer saturation. The gemini, in this report, led to two unequivocal breaks in the tensiometric isotherm. An attempt to the interpretation of the two breaks from molecular point of view is provided, depending solely on the chemical structure of the surfactant. The gemini, even in mixed state with the conventional nonionic surfactants C₁₂E₅ and C₁₂E₈, manifested the dual breaks; of course, the dominance of the feature decreases with increasing mole fraction of the nonionics in the mixture. Theories of Clint, Rosen, Rubingh, Motomura, Georgiev, Maeda, and Nagarajan have been used to determine the interaction between surfactants at the interface and micellar state of aggregation, the composition of the aggregates, the theoretical cmc in pure and mixed states, and the structural parameters according to Tanford and Israelachvili. Several thermodynamic parameters have also been predicted from those theories.     

Structural determinants of steroids for cytochrome P450 3A4-mediated metabolism

Cytochrome P450 3A4 (CYP3A4), a major member of cytochrome P450 isoenzymes, metabolizes the majority of steroids in 6β-position. For the purpose of determining requisite structural features of a series of structurally related steroids for CYP3A4-mediated metabolism, three-dimensional pharmacophore modeling as well as electrotopological state map were conducted for 15 steroids. Though prior studies speculated that the chemical reactivity of the allylic 6β-position might have a greater influence on CYP3A4 selective 6-hydroxylation than steric constraints in the enzyme, our results reveal that for CYP3A4 steroidal substrates, it is not the chemical reactivity of atoms at 6β-site, but the pharmacophoric features, i.e. the two hydrophobic rings together with two H-bond donors, that act as the key factors responsible for determining the CYP3A4 selective 6-hydroxylation of steroids.