Use of the Szeged index and the revised Szeged index for measuring network bipartivity

We have revisited the Szeged index (Sz) and the revised Szeged index (Sz^∗), both of which represent a generalization of the Wiener number to cyclic structures. Unexpectedly we found that the quotient of the two indices offers a novel measure for characterization of the degree of bipartivity of networks, that is, offers a measure of the departure of a network, or a graph, from bipartite networks or bipartite graphs, respectively. This is because the two indices assume the same values for bipartite graphs and different values for non-bipartite graphs. We have proposed therefore the quotient Sz/Sz^∗ as a measure of bipartivity. In this note we report on some properties of the revised Szeged index and the quotient Sz/Sz^∗ illustrated on a number of smaller graphs as models of networks.     

Dual imbeddings and wrapped quasi-coverings of graphs

This paper gives a new method for constructing imbeddings of graphs which are “nearly” coverings of given imbedded graphs. The method is based on the dual theories of current graphs and voltage graphs. Some applications are given, in particular the following theorem: Let G be any graph which has a triangular imbedding in the sphere. Then there are infinitely many integers n for which the composition G[nK₁] has a triangular (orientable surface) imbedding.     

Quantum freeze of fidelity decay for chaotic dynamics

We show that the mechanism of quantum freeze of fidelity decay for perturbations with a zero time average, recently discovered for a specific case of integrable dynamics [New J. Phys. 5, 109 (2003)], can be generalized to arbitrary quantum dynamics. We work out explicitly the case of a chaotic classical counterpart, for which we find semiclassical expressions for the value and the range of the plateau of fidelity. After the plateau ends, we find explicit expressions for the asymptotic decay, which can be exponential or Gaussian depending on the ratio of the Heisenberg time to the decay time. Arbitrary initial states can be considered; e.g., we discuss coherent states and random states.     

Lateral photovoltage measurements in hydrogenated amorphous silicon and silicon-oxygen thin films

Hydrogenated amorphous silicon (a-Si:H) and hydrogenated amorphous silicon-oxide alloy films (a-SiO_x:H) were investigated by temperature dependence of lateral photovoltage (LPV) measurements. The suboxide sample with [O] = 27 at.%, was found to exhibit larger LPV compared to the unalloyed sample. It is difficult to simply correlate LPV measurements to related diffusion length measurements, only. On the other hand, the observed magnitude of LPV in a-Si:H and its decrease with temperature, could be explained based on an internal electric field induced by diffusion electron and hole currents, and multiple trapping of the photocarriers.     

Influence of sampling to the homogeneity of Cu-Ti-Zn alloy samples for the analyses with glow discharge optical emission spectroscopy

 Using Plackett-Burman experimental design the parameters of different ways of sampling (design and materials of the sampling mold, conditions of solidification of samples) that influence on the homogeneity of copper-titanium-zinc alloy samples in the production of titanium zinc were determined. Based on these results, the homogeneity of samples taken with two different sampling molds was investigated with GD-OES technique regarding alloyed elements (Cu and Ti) and impurities (Fe, Pb, Cd, Sn, Al) and was evaluated with analysis of variance (ANOVA). For Cu, Ti and Fe an overall (combined) uncertainty for different sampling approaches were estimated and compared to the expanded uncertainty evaluated without including the uncertainty due to sampling. Received: 28 October 2002 Accepted: 2 January 2003 Presented at CERMM-3, Central European Reference Materials and Measurements Conference: The function of reference materials in the measurement process, May 30–June 1, 2002, Rogaška Slatina, Slovenia Correspondence to B. Kokliˇc     

Investigating the interaction of x-ray free electron laser radiation with grating structure

The interaction of free electron laser pulses with grating structure is investigated using 4.6±0.1 nm radiation at the FLASH facility in Hamburg. For fluences above 63.7±8.7 mJ/cm², the interaction triggers a damage process starting at the edge of the grating structure as evidenced by optical and atomic force microscopy. Simulations based on solution of the Helmholtz equation demonstrate an enhancement of the electric field intensity distribution at the edge of the grating structure. A procedure is finally deduced to evaluate damage threshold.     

Ground state periodic solutions for difference equations with discrete p-Laplacian

We use the critical point theory to establish existence results for periodic solutions of some nonlinear boundary value problems involving the discrete p-Laplacian operator. As an application we give an alternative proof to the upper and lower solutions theorem.     

Exotic n-universal graphs

An n-universal graph is a graph that contains as an induced subgraph a copy of every graph on n vertices. It is shown that for each positive integer n > 1 there exists an n-universal graph G on 4ⁿ - 1 vertices such that G is a (v, k, λ)-graph, and both G and its complement G¯ are 1-transitive in the sense of W. T. Tutte and are of diameter 2. The automorphism group of G is a transitive rank 3 permutation group, i.e., it acts transitively on (1) the vertices of G, (2) the ordered pairs uv of adjacent vertices of G, and (3) the ordered pairs xy of nonadjacent vertices of G.