Matchings in 3-vertex-critical graphs: The odd case

A subset of vertices D of a graph G is a dominating set for G if every vertex of G not in D is adjacent to one in D. The cardinality of any smallest dominating set in G is denoted by γ(G) and called the domination number of G. Graph G is said to be γ-vertex-critical if γ(G-v)<γ(G), for every vertex v in G. A graph G is said to be factor-critical if G-v has a perfect matching for every choice of v∈V(G).In this paper, we present two main results about 3-vertex-critical graphs of odd order. First we show that any such graph with positive minimum degree and at least 11 vertices which has no induced subgraph isomorphic to the bipartite graph K_1,5 must contain a near-perfect matching. Secondly, we show that any such graph with minimum degree at least three which has no induced subgraph isomorphic to the bipartite graph K_1,4 must be factor-critical. We then show that these results are best possible in several senses and close with a conjecture.     

A Note on Cyclic Connectivity and Matching Properties of Regular Graphs

In this paper info cyclic connectivity is studied in relation to certain matching properties in regular graphs. Results giving sufficient conditions in terms of cyclic connectivity for regular graphs to be factor-critical, to be 3-factor-critical, to have the restricted matching properties E(m, n) and to have defect-d matchings are obtained.     

Power-Flow-Based Stabilization for Adaptive Feedforward Filters in Hybrid Testing

Experimental Techniques - Real-time hybrid testing is a technology which allows the coupling of simulations and component tests in order to simulate complex system dynamics. Delays and time lags...     

Solving a large nonlinear programming problem on a vector processing computer

In an earlier paper, the authors formulated an acoustic antenna array design problem as a nonlinear program. Computation times for large problems (about 400 sensors) were in the range of 8 to 10 hours on a Vax 11/780. Most of this time was spent in computing the objective function and its gradient. This paper describes how these computations (and these only) were recoded to exploit the vector processing capabilities of a Cray 1-M computer. Run times are reduced to less than one minute. The results have implications for many nonlinear programs whose function evaluations are very time consuming.     

Angle-of-incidence dependence in angle-resolved photoemission from chemisorbed molecules: c(2 × 2)O,c(2 × 2)5, and CO on Ni(100)

We have measured the angular distribution of photoemitted electrons from c(2 × 2)O, c(2 × 2)S, and CO adsorbed on a Ni(100) substrate for various independently set angles of incidence of unpolarized light at 21.2 eV. We have found that these systems have very different dependence on angle of incidence, depending upon which components of the vector potential of the light ($\text{A}$) are responsible for emission. Because the incident and reflected light combine to form a standing wave at a metal surface, the phase relationships between components of $\text{A}$ parallel and perpendicular to the surface play an important role in determining the effective orientation and magnitude of A at the emission site. We compare our measurements with macroscopic $\text{A}$ fields, calculated via the Fresnel relations, which lead to a general understanding of the effects. We further propose a method for expediting photoemission calculations by projecting out components of $\text{A}$ which preserve their phase relationships.     

A pair of forbidden subgraphs and perfect matchings in graphs of high connectivity

Sumner [7] proved that every connected K _1,3-free graph of even order has a perfect matching. He also considered graphs of higher connectivity and proved that if m ≥ 2, every m-connected K _1,m+1-free graph of even order has a perfect matching. In [6], two of the present authors obtained a converse of sorts to Sumner’s result by asking what single graph one can forbid to force the existence of a perfect matching in an m-connected graph of even order and proved that a star is the only possibility. In [2], Fujita et al. extended this work by considering pairs of forbidden subgraphs which force the existence of a perfect matching in a connected graph of even order. But they did not settle the same problem for graphs of higher connectivity. In this paper, we give an answer to this problem. Together with the result in [2], a complete characterization of the pairs is given.     

Isomechanical groups in bulk metallic glasses

Isomechanical groups are, as defined by Frost and Ashby [H.J. Frost and M.F. Ashby, Deformation–Mechanism Maps, Pergamon Press, Oxford, 1982], separate classes of materials that exhibit similar deformation and transport properties when normalised by an appropriate parameter. Fundamentally, this separation results from significant differences in material structure and bonding. Here, such an analysis is applied to 40 bulk metallic glasses (BMGs) grouped into three classes according to their Poisson's ratio, which is known to be an indicator of intrinsic toughness. Through rigorous statistical analysis, it is found that isomechanical groups are present and that they may result from (1) variation in the tendency for directional bonding, and (2) how liquid-like the structure is, which may be characterised by a quantification of local volumetric strain. These results suggest that, although experimentally observed properties from BMGs in different isomechanical groups are all typically considered within the same framework, differences in atomic packing and inter-atomic bonding mean that they should in fact be treated separately. These fundamental differences in bonding and structure may explain the known large variation in the tendency for toughness and plasticity in BMGs.     

Deformation and entanglement in semicrystalline polymers

Transmission electron microscopy (TEM) of amorphous and semicrystalline isotactic polystyrene (iPS) thin films deformed well below T _g, suggests the same crazing mechanism to operate in both cases. Therefore, by analogy with the amorphous case, highly entangled semicrystalline polymers, such as poly(ether ether ketone) (PEEK) should craze less readily in the glassy-semicrystalline state than iPS, which has a low degree of entanglement. Since this is confirmed by observation, it is reasonable to extend this analogy, and invoke entanglement in order to account for the high fracture resistance of highly entangled semicrystalline polymers, such as polyoxymethylene, using models previously applied to glassy amorphous polymers. There are nevertheless often significant decreases in fracture toughness in polyoxymethylene as the crystallization temperature is raised and/or the molecular weight is reduced, which we attribute to entanglement loss during lamellar folding.     

Modeling the folding and hydrogen production of Clostridium acetobutylicum and Clostridium saccharobutylium mutants using electrostatic potential surfaces and molecular dynamics

Electrostatic potential surfaces (EPS) were used with molecular dynamics to model the folding mechanisms and kinetics of hydrogenase mutants from wild types Clostridium acetobutylicum and Clostridium saccharobutylium. The purpose of the EPS approach was to incorporate long range electrostatic forces between widely separated regions of the mutants which contain 575 amino acids. Also, it was demonstrated that the ratio of positive to negative EPS of unfolded mutants could be used to predict the production of molecular hydrogen from the folded mutants. Using the prediction model, mutant compositions were determined that should yield hydrogen of up to 40 times that obtainable from the wild type C. acetobutylicum. It is expected that the developed EPS techniques can be used to study the folding of other proteins and to predict the reactivity of the folded protein structures.     

Vibrational modes of oxygen on W(110)

Electron energy loss measurements of the vibrational modes of oxygen on W(110) as a function of coverage up to 0.5 monolayer are presented and analyzed. A single loss at 67 meV is observed initially; with increasing exposure this loss shifts to 72 meV and another loss appears at 47 meV. These data indicate coexistence of two species on the surface with a coverage-dependent conversion. Angular profiles of the specular elastic beam show a dramatic increase in width with initial oxygen coverage; this is possibly due to an oxygen-induced static disordering of the W surface layer.