直径不超过4的树的割宽

§ 1　IntroductionThe cutwidth problem for graphs,as well as a class of optimal labeling and embed-ding problems,have significant applications in VLSI designs,network communicationsand other areas (see [2 ] ) .We shall follow the graph-theoretic terminology and notation of [1 ] .Let G=(V,E)be a simple graph with vertex set V,| V| =n,and edge set E.A labeling of G is a bijec-tion f:V→ { 1 ,2 ,...,n} ,which can by regarded as an embedding of G into a path Pn.Fora given labeling f of G,th…     

The structure of mixed fluorides Ca1?xSrxF2 and Sr1?xBaxF2 and the luminescence of Eu2+ in these crystals

The structure of the mixed fluorites Ca_1−x Sr_xF₂ and Sr_1−x Ba_xF₂, as well as the structure of the Eu²⁺ impurity center in these crystals, is calculated within the framework of the virtual-crystal method realized in the shell model and pair-potential approximation. The phenomenological dependence of the position of the lower level of the 4f ⁶5d configuration of the Eu²⁺ ion on distance to the Eu²⁺-ligand is derived. The dependences of the Stokes shift and the Huang-Rhys factor on x are calculated for the yellow luminescence in Sr_1−x Ba_xF₂:Eu²⁺. The value of x at which the lower level of the 4f ⁶5d configuration of the Eu²⁺ ion in Sr_1−x Ba_xF₂:Eu²⁺ falls within the conduction band is found. __________ Translated from Fizika Tverdogo Tela, Vol. 45, No. 5, 2003, pp. 823–826. Original Russian Text Copyright ? 2003 by Nikiforov, Zakharov, Chernyshev, Ugryumov, Kotomanov.     

Effect of maltodextrins on the surface activity of small-molecule surfactants

We report on the effect of commercially important polysaccharides (maltodextrins with variable dextrose equivalent (Paselli SA-2, MD-6 and MD-10) on the surface activity at the air–water interface of small-molecule surfactants (sms), possessing different hydrophobic–lipophilic balance ((SSL (Na⁺), the main component is a sodium salt of stearol–lactoyl lactic acid, and PGE (080), polyglycerol ester of C18 fatty acid), and widely used in food products. A marked change of the surface activity of sms was found in the presence of maltodextrins by tensiometry. The combined data of laser multiangle light scattering and mixing calorimetry have suggested that this result is governed by specific complex formation between maltodextrins and sms in aqueous medium. Measurements have been made of the molar mass, the second virial coefficient and the enthalpy of intermolecular interactions in aqueous solutions. The implication of a degree of polymerization of maltodextrins in this phenomenon was shown. The interrelation between the molecular parameters of the formed complexes and their surface activity at the air–water interface has been revealed and discussed.     

Temperature dependences of the low-frequency internal friction and shear modulus in a bulk amorphous alloy

The logarithmic decrement and shear modulus of a bulk amorphous Zr_52.5Ti₅Cu_17.9Ni_14.6Al₁₀ alloy were studied with an inverse torsion pendulum in the range from room temperature to the crystallization temperature and in the frequency range 5–40 Hz. The activation energy spectra of reversible and irreversible structural relaxation were estimated. The results obtained are discussed in the context of a two-energy-level model.     

Methodological reflections on a three-step-design combining observation,stimulated recall and interview

In this paper a tripartite qualitative design combining abservation, stimulated recall and interview is presented and discussed. This three-step-design makes it possible to get insight into the interaction of internal and external processes when solving mathematical tasks. The data analysis depends on the research question and the methodological approach. In the light of two research projects in mathematics education two different methods of data analysis are presented and methodologically reflected.     

A market-based computational approach to collaborative organizational learning

We draw upon the concepts of knowledge market, organizational tacit knowledge, credit assignment, and single-loop learning in proposing a market-based conceptual model for collaborative organizational learning. Our proposed model is characterized by the local competition among seller agents and the global collaboration among winner agents in forming a plan, through a chain of ‘upstream–downstream’ working relationship, for task accomplishment. This feature is achieved through three closely coupled processes: the expert selection process, the capital reallocation process, and the plan formation process. Our model is intended for multiple-step learning environment in which each task consists of a sequence of single-step learning tasks. Learning at the global level is the result of a sequence of nested single-loop learning at the local level.     

Generalized binomial and negative binomial distributions of order<Emphasis Type="Italic">k</Emphasis> by the<Emphasis Type="Italic">l</Emphasis>-overlapping enumeration scheme

In this paper, we investigate the exact distribution of the waiting time for ther-th ℓ-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution of orderk and an extended Poisson distribution of orderk are discussed. We provide further insights into the run-related problems from the viewpoint of the ℓ-overlapping enumeration scheme. We also study the exact distribution of the number of ℓ-overlapping occurrences of success-runs in a fixed number of trials and derive the probability generating functions. The present work extends several properties of distributions of orderk and leads us a new type of geneses of the discrete distributions.