Alternating,all-trans polyenynes: Model compounds for poly(diacetylene)s with defined conjugation length

The syntheses of polyenynes as model compounds for poly(diacetylene)s (PDAs) are described. Variation of properties (UV–VIS, Raman, NMR and bond geometries) as a function of the chain length was investigated. After extrapolation to infinite chain length these data were compared to those for PDAs. From UV–VIS spectra a value of λ = 551 nm (2.25 eV) was calculated corresponding to the electronic transition of a single polyenyne chain. This energy is located at the low energy end of a yellow PDA solution spectrum. From Raman scattering v_(C?C) = 2108–2128 cm^?1 and v_(C?C) = 1505–1532 cm^?1 were calculated after extrapolation. Similarly sp-C¹³C NMR data yielded a shift of δ = 100 ppm. These data are almost identical to data known for yellow PDA solutions. Bond geometries are almost identical to those of poly(diacetylene)s and theoretical data.     

转移法色交换

将图Ｇ的着色由一种变为中一种，通常用Ｋｅｍｐｅ法以交换。但是，对于某些情况，用此法无效。针对这个问题，本文提出了一种转移法色交换，它适用于平面图着色，方法直观，清晰且有效。     

The thermal ignition of lignocellulosics in infinite slab and cubic geometries

Wood shaving samples were heated in both cubic baskets and in a previously described system realising the conditions of the ‘infinite slab’ in thermal ignition. Results from the two sets of experiment were found to be totally consistent with each other.     

SYMMETRIC STABLE SEQUENCES WITH MISSING OBSERVATIONS

Abstract. A procedure for evaluating optimal linear estimates of missing values in the minimum dispersion sense is proposed for stationary symmetric stable processes. Analytical expressions for the estimates are obtained for the autoregressive moving-average process and it is shown that the finite variance setting results are special cases. Cases of one and more than one missing value are considered.     

Stability analysis for multi-agent systems using the incidence matrix: Quantized communication and formation control

The spectral properties of the incidence matrix of the communication graph are exploited to provide solutions to two multi-agent control problems. In particular, we consider the problem of state agreement with quantized communication and the problem of distance-based formation control. In both cases, stabilizing control laws are provided when the communication graph is a tree. It is shown how the relation between tree graphs and the null space of the corresponding incidence matrix encode fundamental properties for these two multi-agent control problems.     

Antimagic labeling and canonical decomposition of graphs

An antimagic labeling of a connected graph with m edges is an injective assignment of labels from {1,…,m} to the edges such that the sums of incident labels are distinct at distinct vertices. Hartsfield and Ringel conjectured that every connected graph other than K₂ has an antimagic labeling. We prove this for the classes of split graphs and graphs decomposable under the canonical decomposition introduced by Tyshkevich. As a consequence, we provide a sufficient condition on graph degree sequences to guarantee an antimagic labeling.     

Probability of graphs with large spectral gap by multicanonical Monte Carlo

Graphs with large spectral gap are important in various fields such as biology, sociology and computer science. In designing such graphs, an important question is how the probability of graphs with large spectral gap behaves. A method based on multicanonical Monte Carlo is introduced to quantify the behavior of this probability, which enables us to calculate extreme tails of the distribution. The proposed method is successfully applied to random 3-regular graphs and large deviation probability is estimated.     

Re-engineering of the design process for concurrent engineering

According to the requirements of concurrent engineering, three interdependency relationships (uncoupled relationship, coupled relationship and decoupled relationship) between design activities are presented in this paper. And the coupled relationship plays an important role in concurrent product design process. To represent the precedence relationships among design activities, a directed graph is used to describe the design process. And the interdependency relationship between activities is illustrated by a Design Structure Matrix which is the transpose of the accessibility matrix of the corresponding graph. Using the DSM, an algorithm of recognizing the coupled activities during the design process is presented. Moreover, an algorithm to figure out the order levels of activities during the design process is proposed. And both algorithms are illustrated with a die design example.     

A new neural network algorithm for planarization problems

To deal with the planarization problem widely used in many applications including routing very-large-scale integration （VLSI） circuits, this paper points out that only when its vertices are arranged in some specific order in a line can a planar graph be embedded on a line without any cross connections or cross edges. Energy function is proposed to meet the need of embedding a graph on a single line and route it correctly. A Hopfield network is designed according to the proposed energy function for such embedding and routing. The advantage of the proposed method is that it not only can detect if a graph is a planar one or not, but also can embed a planar graph or the maximal planar subgraph of a non-planar graph on a single line. In addition, simulated annealing is employed for helping the network to escape from local minima during the running of the Hopfield network. Experiments of the proposed method and its comparison with some existent conventional methods were performed and the results indicate that the proposed method is of great feasibility and effectiveness especially for the planarization problem of large graphs.     

Dynamics of Flexible Multibody Systems Using Virtual Work and Linear Graph Theory

By combining linear graph theory with the principle of virtualwork, a dynamic formulation is obtained that extends graph-theoreticmodelling methods to the analysis of flexible multibody systems. Thesystem is represented by a linear graph, in which nodes representreference frames on rigid and flexible bodies, and edges representcomponents that connect these frames. By selecting a spanning tree forthe graph, the analyst can choose the set of coordinates appearing inthe final system of equations. This set can include absolute, joint, orelastic coordinates, or some combination thereof. If desired, allnon-working constraint forces and torques can be automaticallyeliminated from the dynamic equations by exploiting the properties ofvirtual work. The formulation has been implemented in a computerprogram, DynaFlex, that generates the equations of motion in symbolicform. Three examples are presented to demonstrate the application of theformulation, and to validate the symbolic computer implementation.