On-line arbitrarily vertex decomposable trees

A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by τ. An on-line version of the problem of characterizing arbitrarily vertex decomposable trees is completely solved here.     

Formation of functional groups on graphite during oxygen plasma treatment

Improved sample wettability was obtained by oxygen plasma functionalization of pyrolytic graphite. The samples were exposed to highly dissociated oxygen plasma with the density of 1 × 10¹⁶ m⁻³, the electron temperature of about 5.5 eV and the density of neutral oxygen atoms of 8 × 10²¹ m⁻³ for 20 s. The surface wettability was measured by a contact angle of water drop. The contact angle dropped from original 112° down to about 1°. The functional groups were detected by XPS analyses. The survey spectrum showed a substantial increase of oxygen concentration on the surface, while high-resolution analyses showed additional oxygen was bonded onto the graphite surface in the form of C-O polar functional group responsible for the increase of the surface energy.     

Einstein relation in chemically doped organic semiconductors

Based on the assumption of Gaussian energy distributions of the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO), analytical expressions of generalized Einstein relation in chemically doped organic semiconductor are developed, by approximation of Coulomb traps with a rectangle potential well. Numerical calculations show that traditional Einstein relations do not hold for chemically doped organic semiconductors. Similar to physical doping, the dependence of diffusion coefficient to mobility D/μ ratio on the carrier concentration has a maximum. An essential difference between chemical doping and physical doping is that, the D/μ ratio in chemically doped organic semiconductors depends not only on carrier concentration and doping concentration, but also on the applied electric field. PACS 71.20.Rv; 72.90.+y; 73.50.-h     

Students’ Reasoning About One-Object Stochastic Phenomena in an ICT-Environment

This paper focuses on the different ways in which students in lower secondary school (14–16 year olds) experience compound random events, presented to them in the form of combined junctions. A carefully designed ICT environment was developed enabling the students to interact with different representations of such structures. Data for the analysis was gathered from two interview sessions. The analysis of the interaction is based on constructivist principles on learning; i.e. we adopted a student-oriented perspective, taking into consideration the different ways students try to make sense of chance encounters. Our results show how some students give priority to geometrical and physical concerns, and we discuss how seeking causal explanations of random phenomena may have encouraged this. With respect to numerically oriented models a division strategy appears to stand out as the preferred one.     

On the genericity of chaos

Let M be a compact manifold with dimM?2. We prove that some iteration of the generic homeomorphism on M is semiconjugated to the shift map and has infinite topological entropy (Theorem 1.1).     

A benchmark-learning roadmap for regional sustainable development in China

Journal of the Operational Research Society - Serious environmental problems have accompanied China's remarkable economic growth for decades, which also have direct and indirect impacts on its...     

Optical properties of cadmium sulfide nanocrystal film prepared by electrochemical synthesis at liquid-liquid interface

Dendritic nanocrystalline CdS film was deposited at liquid-liquid interface of surfactants and an electrolyte containing 4 mmol L⁻¹ cadmium chloride (CdCl₂) and 16 mmol L⁻¹ thioacetamide (CH₃CSNH₂) with an initial pH value of 5 at 15 °C by electrochemical synthesis. The nanofilm was characterized by transmission electron microscopy (TEM), field emission scanning electron microscope (FE-SEM), atomic force microscopy (AFM), ultraviolet visible (UV-vis) absorption spectroscopy and fluorescence spectroscopy. The surface morphology and particle size of the nanofilm were investigated by AFM, SEM and TEM, and the crystalline size was 30-50 nm. The thickness of the nanofilm calculated by optical absorption spectrum was 80 nm. The microstructure and composition of the nanofilm was investigated by X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS), showing its polycrystalline structure consisting of CdS and Cd. Optical properties of the nanofilm were investigated systematically by UV-vis absorption and fluorescence spectroscopy. A λ_onset blue shift compared with bulk CdS was observed in the absorption spectra. Fluorescence spectra of the nanofilm indicated that the CdS nanofilm emitted blue and green light. The nanocomposites film electrode will bring about anodic photocurrent during illumination, showing that the transfer of cavities produces photocurrent.     

Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets

Covering numbers of precompact symmetric convex subsets of Hilbert spaces are investigated. Lower bounds are derived for sets containing orthogonal subsets with norms of their elements converging to zero sufficiently slowly. When these sets are convex hulls of sets with power-type covering numbers, the bounds are tight. The arguments exploit properties of generalized Hadamard matrices. The results are illustrated by examples from machine learning, neurocomputing, and nonlinear approximation.     

Nonvanishing cohomology and classes of Gorenstein rings

We give counterexamples to the following conjecture of Auslander: given a finitely generated module M over an Artin algebra Λ, there exists a positive integer n_M such that for all finitely generated Λ-modules N, if Ext_Λⁱ(M,N)=0 for all i?0, then Ext_Λⁱ(M,N)=0 for all i?n_M. Some of our examples moreover yield homologically defined classes of commutative local rings strictly between the class of local complete intersections and the class of local Gorenstein rings.