Semi-Balanced Colorings of Graphs: Generalized 2-Colorings Based on a Relaxed Discrepancy Condition

We generalize the concept of a 2-coloring of a graph to what we call a semi-balanced coloring by relaxing a certain discrepancy condition on the shortest-paths hypergraph of the graph. Let G be an undirected, unweighted, connected graph with n vertices and m edges. We prove that the number of different semi-balanced colorings of G is: (1) at most n+1 if G is bipartite; (2) at most m if G is non-bipartite and triangle-free; and (3) at most m+1 if G is non-bipartite. Based on the above combinatorial investigation, we design an algorithm to enumerate all semi-balanced colorings of G in O(nm²) time.Acknowledgments The authors thank Tetsuo Asano, Naoki Katoh, Kunihiko Sadakane, and Hisao Tamaki for helpful discussions and comments.Supported in part by Sweden-Japan FoundationFinal version received: November 17, 2003     

Real double flag varieties for the symplectic group

In this paper we study a key example of a Hermitian symmetric space and a natural associated double flag variety, namely for the real symplectic group G and the symmetric subgroup L, the Levi part of the Siegel parabolic $P_S$. We give a detailed treatment of the case of the maximal parabolic subgroups Q of L corresponding to Grassmannians and the product variety of $G/P_S$ and $L/Q$; in particular we classify the L-orbits here, and find natural explicit integral transforms between degenerate principal series of L and G.     

Rapidity dependence of charged antihadron to hadron ratios in Au+Au collisions at sqrt[s(NN)]=200 GeV

We present ratios of the numbers of charged antihadrons to hadrons (pions, kaons, and protons) in Au+Au collisions at sqrt[s(NN)]=200 GeV as a function of rapidity in the range y=0-3. While the ratios at midrapidity are approaching unity, the K(-)/K(+) and p;/p ratios decrease significantly at forward rapidities. An interpretation of the results within the statistical model indicates a reduction of the baryon chemical potential from mu(B) approximately 130 MeV at y=3 to mu(B) approximately 25 MeV at y=0.     

A staggered six-vertex model with non-compact continuum limit

The antiferromagnetic critical point of the Potts model on the square lattice was identified by Baxter [R.J. Baxter, Proc. R. Soc. London A 383 (1982) 43] as a staggered integrable six-vertex model. In this work, we investigate the integrable structure of this model. It enables us to derive some new properties, such as the Hamiltonian limit of the model, an equivalent vertex model, and the structure resulting from the Z₂$Z_2$ symmetry. Using this material, we discuss the low-energy spectrum, and relate it to geometrical excitations. We also compute the critical exponents by solving the Bethe equations for a large lattice width N  . The results confirm that the low-energy spectrum is a collection of continua with typical exponent gaps of order (logN)⁻²${(\log N)}^{\mathrm{-2}}$.     

Visualization and characterization of small-scale spanwise vortices in turbulent channel flow

High-resolution particle-image velocimetry (PIV) measurements are made in the streamwise-wall-normal plane of turbulent channel flow at Re_τ=566, 1184 and 1759, facilitating documentation of the population trends and core diameters of small-scale spanwise vortices. Swirling strength, an unambiguous vortex-identification criterion and hence a local marker of rotation, is used to extract small-scale spanwise vortex cores from the instantaneous velocity fields. Once the small-scale vortices are properly extracted from the PIV realizations, their characteristics are studied in detail. The present results indicate that the very-near-wall region (y < 0.1h) is densely populated by spanwise vortices with clockwise (negative) rotation. This behavior supports the notion that hairpin-like vortices are generated very close to the wall and grow into the outer layer as they advect downstream. In contrast, counterclockwise (positive) spanwise vortices are scarce in the very-near-wall region, but their presence steadily increases within the logarithmic layer presumably due to a localized generation mechanism. The average core diameter of negative spanwise vortices is found to be larger than the average diameter of positive vortices, with few positive vortices having core diameters exceeding 80y.     

Fundamental limitations to gain enhancement in periodic media and waveguides

A common strategy to compensate for losses in optical nanostructures is to add gain material in the system. By exploiting slow-light effects it is expected that the gain may be enhanced beyond its bulk value. Here we show that this route cannot be followed uncritically: inclusion of gain inevitably modifies the underlying dispersion law, and thereby may degrade the slow-light properties underlying the device operation and the anticipated gain enhancement itself. This degradation is generic; we demonstrate it for three different systems of current interest (coupled-resonator optical waveguides, Bragg stacks, and photonic crystal waveguides). Nevertheless, a small amount of added gain may be beneficial.     

Spin-orbit splitting of the copper halides and its volume dependence

We have investigated theoretically and experimentally the dependence of the spin-orbit splitting of the edge excitons in CuCl, CuBr, and CuI on volume. The results indicate a large contribution of the change in p(halogen)-d(Cu) hybridization with volume, especially for CuCl.     

A Mass for ALF Manifolds

We prove a positive mass theorem on ALF manifolds, i.e. complete noncompact manifolds that are asymptotic to a circle fibration over a Euclidean base, with fibers of asymptotically constant length.     

On sets of Haar measure zero in abelian polish groups

It is shown that the concept of zero set for the Haar measure can be generalized to abelian Polish groups which are not necessarily locally compact. It turns out that these groups, in many respects, behave like locally compact groups. Suitably modified, many theorems from harmonic analysis carry over to this case. A few applications are given and some open problems are mentioned.