Thermodynamic functions characterizing intermolecular interactions

It is shown that the Gibbs vaporization potential G^* is additive with respect to molecular groups at all temperatures and it most completely characterizes the intermolecular interactions. The excess entropy of vaporization is identical for all spherical molecules (30 J/mole·K and does not depend on the size of the molecule or the temperature. In long-chain molecules it is additive with respect to the number of links in the chain, varies with temperature, and is equal to the difference between the heat capacities of the gas and liquid and exceeds 30 J/mole·K.Leningrad State Scientific Institute of Industrial Chemistry. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, No. 1, pp. 66–70, January–February, 1991. Original article submitted April 27, 1988.     

Graphs Without Large Apples and the Maximum Weight Independent Set Problem

An apple A _k is the graph obtained from a chordless cycle C _k of length k ≥ 4 by adding a vertex that has exactly one neighbor on the cycle. The class of apple-free graphs is a common generalization of claw-free graphs and chordal graphs, two classes enjoying many attractive properties, including polynomial-time solvability of the maximum weight independent set problem. Recently, Brandstädt et al. showed that this property extends to the class of apple-free graphs. In the present paper, we study further generalization of this class called graphs without large apples: these are (A _k , A _k+1, . . .)-free graphs for values of k strictly greater than 4. The complexity of the maximum weight independent set problem is unknown even for k = 5. By exploring the structure of graphs without large apples, we discover a sufficient condition for claw-freeness of such graphs. We show that the condition is satisfied by bounded-degree and apex-minor-free graphs of sufficiently large tree-width. This implies an efficient solution to the maximum weight independent set problem for those graphs without large apples, which either have bounded vertex degree or exclude a fixed apex graph as a minor.     

Scattering of Josephson plasmons on random quantum jumpers in a disordered <Emphasis Type="Italic">I</Emphasis>-layer of an <Emphasis Type="Italic">S</Emphasis>–<Emphasis Type="Italic">I</Emphasis>–<Emphasis Type="Italic">S</Emphasis> junction

A formula for the relaxation time of Josephson plasmons on random quantum jumpers, i.e., quantum resonant-percolation trajectories (QRPT) in a disordered I-layer of a tunnel S–I–S junction is derived. Domain Ω_r (μ ? E₀, c), in which the strongest plasmon damping takes place, is plotted in the plane of parameters (μ ? E₀, c).     

Effect of Quantum Jumpers on the Critical Supercurrent in Dirty S–I–S Junctions

It has been shown that the presence of narrowband quantum jumpers in “dirty” (low concentrations of identical nonmagnetic impurities in the insulator (I) layer) S–I–S (S is a superconductor) junctions at the temperature T = 0 significantly reduces the critical supercurrent (Josephson current) as compared to the value given by the known the Ambegaokar–Baratoff relation. The performed estimates have shown the possibility of the experimental manifestation of this effect.     

On the Jump Number Problem in Hereditary Classes of Bipartite Graphs

We prove a necessary condition for polynomial solvability of the jump number problem in classes of bipartite graphs characterized by a finite set of forbidden induced bipartite subgraphs. For some classes satisfying this condition, we propose polynomial algorithms to solve the jump number problem.     

Effect of Random Quantum Jumpers on the Single-Particle Low-Temperature Current in Dirty SIN Junctions

JETP Letters - A formula has been obtained for a single-particle current in “dirty” (low concentrations of identical nonmagnetic impurities in the I layer) SIN junctions (S is a...     

Influence of quantum resonance-percolation trajectories in a disordered I layer on the critical current of a Josephson S-I-S junction

Formulas for a critical current and the magnitude of its mesoscopic structural fluctuations are obtained in the form of sums over quantum resonance-percolation trajectories [1] randomly formed in a disordered I layer and connecting opposite S banks of the junction at T = 0 in the energy region of tunnel S-I-S resonances (S denotes the superconductor, I, insulator) for a tunnel junction with weak structural disorders (low impurity concentrations) in the I layer.     

Boundary Properties of Factorial Classes of Graphs

For a class of graphs X, let be the number of graphs with vertex set in the class X, also known as the speed of X. It is known that in the family of hereditary classes (i.e. those that are closed under taking induced subgraphs) the speeds constitute discrete layers and the first four lower layers are constant, polynomial, exponential, and factorial. For each of these four layers a complete list of minimal classes is available, and this information allows to provide a global structural characterization for the first three of them. The minimal layer for which no such characterization is known is the factorial one. A possible approach to obtaining such a characterization could be through identifying all minimal superfactorial classes. However, no such class is known and possibly no such class exists. To overcome this difficulty, we employ the notion of boundary classes that has been recently introduced to study algorithmic graph problems and reveal the first few boundary classes for the factorial layer.     

On finding augmenting graphs

Method of augmenting graphs is a general approach to solve the maximum independent set problem. As the problem is generally NP-hard, no polynomial time algorithms are available to implement the method. However, when restricted to particular classes of graphs, the approach may lead to efficient solutions. A famous example of this type is the maximum matching algorithm: it finds a maximum matching in a graph G, which is equivalent to finding a maximum independent set in the line graph of G. In the particular case of line graphs, the method reduces to finding augmenting (alternating) chains. Recent investigations of more general classes of graphs revealed many more types of augmenting graphs. In the present paper we study the problem of finding augmenting graphs different from chains. To simplify this problem, we introduce the notion of a redundant set. This allows us to reduce the problem to finding some basic augmenting graphs. As a result, we obtain a polynomial time solution to the maximum independent set problem in a class of graphs which extends several previously studied classes including the line graphs.     

Violation of the Ambegaokar–Baratoff Relation in Dirty S–I–S Junctions

JETP Letters - It has been shown that the presence of narrow-gap quantum jumpers in “dirty” (low concentrations of identical nonmagnetic impurities in the insulator layer)...