Physico-chemical factors governing partition behaviour of solutes and particles in aqueous polymeric biphasic systems. III. Features of solutes and biological particles detected by the partition technique

The partition behaviour of human serum albumin and oxyhaemoglobin and several amino acids and small peptides was studied in the aqueous Ficoll-dextran biphasic system as a function of the ionic composition and pH. The partition coefficients of the solutes were expressed in terms of the equivalent number of CH2 groups, nCH2, and the equivalent number of carboxyl groups, m. The physical meaning of these two parameters and of the relationships found between them and pH for the proteins examined are discussed. A correlation was established between the difference in the relative hydrophobicities of the individual phases of various water-organic solvent systems and the interfacial tension, gamma 12, of the systems. It is argued that a relation of a similar type exists for the aqueous polymeric biphasic systems. The possibility of estimating the relative intensity of Van der Waals and hydration interactions of a solute and particle surface by examination of their partitioning in a biphasic system calibrated for the hydrophobic and hydration properties of the phases is discussed.     

Long way from the FPU-problem to chaos

This paper provides some historical comments on the study of the Fermi, Pasta, and Ulam (FPU) paper and its influence on the development of the theory of chaos. We also discuss some problems raised in the FPU paper and the links of these problems to such contemporary notions in chaos theory as ergodicity, mixing, recurrences, pseudochaos, kinetics, intermittency, etc.     

Signed graph coloring

Coloring a signed graph by signed colors, one has a chromatic polynomial with the same enumerative and algebraic properties as for ordinary graphs. New phenomena are the interpretability only of odd arguments and the existence of a second chromatic polynomial counting zero-free colorings. The generalization to voltage graphs is outlined.     

Near threshold anomalous transport in the standard map

Anomalous transport is investigated near threshold in the standard map. Very long time flights, and a large anomaly in the transport, are shown to be associated with a new form of multi-island structures causing orbit sticking. The phase space structure of these traps, and the exponents of the characteristic long time tails associated with them are determined. In general these structures are very complex, but some cases, consisting of layers of islands, allow simple modeling. (c) 1998 American Institute of Physics.     

Biased graphs whose matroids are special binary matroids

Abiased graph is a graph together with a class of polygons such that no theta subgraph contains exactly two members of the class. To a biased graph are naturally associated three edge matroids:G(), L(), L ₀ (). We determine all biased graphs for which any of these matroids is isomorphic to the Fano plane, the polygon matroid ofK ₄,K ₅ orK _3,3, any of their duals, Bixby's regular matroidR ₁₀, or the polygon matroid ofK _m form > 5. In each case the bias is derived from edge signs. We conclude by finding the biased graphs for whichL ₀ () is not a graphic [or, regular matroid but every proper contraction is.Research supported by National Science Foundation grant DMS-8407102 and SGPNR grant 85Z0701Visiting Research Fellow, 1984–1985     

Quantum chaos of atoms in a resonant cavity

A system of atoms interacting with a radiation field in a resonant cavity is studied under conditions when the dynamics in the classical limit is stochastic. This situation is called quantum chaos. Equations of motion are obtained for the quantum-mechanical expectation values which take into account the quantum correlation functions. It is shown that in a situation corresponding to quantum chaos, the quantum corrections grow exponentially, making the evolution of the system essentially quantal after a certain time tau( variant Planck's over 2pi ) has elapsed. Analytical and numerical analysis show that in this regime the time tau( variant Planck's over 2pi ) obeys the logarithmic law tau( variant Planck's over 2pi ) approximately ln N (N is the number of atoms), and not the law tau( variant Planck's over 2pi ) approximately N(alpha) (alpha is a certain constant of order unity), as would be the case in the absence of chaos.     

Nonattacking Queens in a Rectangular Strip

The function that counts the number of ways to place nonattacking identical chess or fairy chess pieces in a rectangular strip of fixed height and variable width, as a function of the width, is a piecewise polynomial which is eventually a polynomial and whose behavior can be described in some detail. We deduce this by converting the problem to one of counting lattice points outside an affinographic hyperplane arrangement, which Forge and Zaslavsky solved by means of weighted integral gain graphs. We extend their work by developing both generating functions and a detailed analysis of deletion and contraction for weighted integral gain graphs. For chess pieces we find the asymptotic probability that a random configuration is nonattacking, and we obtain exact counts of nonattacking configurations of small numbers of queens, bishops, knights, and nightriders.     

High-power terahertz-range planar gyrotrons with transverse energy extraction

To increase the output power of terahertz gyrotrons to several hundred kilowatts, we suggest using a planar geometry of interaction space with a sheet electron beam and transverse energy extraction. An advantage of this scheme in comparison with conventional cylindrical geometry is the possibility to ensure effective mode selection over the open transverse coordinate in combination with radiation outcoupling that leads to a substantial reduction of Ohmic losses. Similar to unstable resonators in optics for further growth of the radiation power it is beneficial to introduce waveguide tapering.     

Six signed Petersen graphs,and their automorphisms

Up to switching isomorphism, there are six ways to put signs on the edges of the Petersen graph. We prove this by computing switching invariants, especially frustration indices and frustration numbers, switching automorphism groups, chromatic numbers, and numbers of proper 1-colorations, thereby illustrating some of the ideas and methods of signed graph theory. We also calculate automorphism groups and clusterability indices, which are not invariant under switching. In the process, we develop new properties of signed graphs, especially of their switching automorphism groups.