Coloring complete bipartite graphs from random lists

Let K_n,n be the complete bipartite graph with n vertices in each side. For each vertex draw uniformly at random a list of size k from a base set S of size s = s(n). In this paper we estimate the asymptotic probability of the existence of a proper coloring from the random lists for all fixed values of k and growing n. We show that this property exhibits a sharp threshold for k ≥ 2 and the location of the threshold is precisely s(n) = 2n for k = 2 and approximately for k ≥ 3. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

Experimental and theoretical studies of lambda doublings and permanent electric dipoles in the low-lying 1pi states of NaCs

We present experimental data on the electric permanent dipole moments d(v',J') and lambda splittings (q factors) in the quasidegenerate (3) 1pi(e/f) state of the NaCs molecule over a wide range of the vibrational (v') and rotational (J') quantum numbers by using the combination of dc Stark mixing and electric radio frequency-optical double resonance methods. Within the experimental (3) 1pi state v' ranged from v' = 0 to 34, q values exhibited a pronounced decrease from 7.91x10(-6) to 0.47x10(-6) cm(-1), while absolute value(d) values varied between 8.0 and 5.0 D. Experimental evaluation yielded small d values about 1 D for D2 1pi state v' < 3 levels. The experiment is supported by ab initio electronic structure calculations performed for the (1-3) 1pi states of NaCs by means of the many-body multipartitioning perturbation theory of potential energy curves, permanent dipole, and angular coupling matrix elements for the lowest singlet states. The predicted d values reproduce their experimental counterparts within the measurement errors while theoretical q factors reproduce the measured v' dependence being, however, systematically overestimated by ca. 1x10(-6) cm(-1). The present NaCs data are compared with those of the NaK and NaRb molecules.     

Triplet interactions in star polymer solutions

We analyze the effective triplet interactions between the centers of star polymers in a good solvent. Using an analytical short-distance expansion inspired by scaling theory, we deduce that the triplet part of the three-star force is attractive but only 11% of the pairwise part even for a close approach of three star polymers. We have also performed extensive computer simulations for different arm numbers f to extract the effective triplet force. The simulation data show good correspondence with the theoretical predictions. Our results justify the effective pair potential picture even beyond the star polymer overlap concentration. Received 1 September 1999 and Received in final form 18 January 2000     

High-multiplicity N-fold IP via configuration LP

Mathematical Programming - N-fold integer programs (IPs) form an important class of block-structured IPs for which increasingly fast algorithms have recently been developed and successfully...