Lifetimes and landé factors in the AOu+ and BO u+ states of 130Te2

Lifetimes and Landé factors were measured for rovibronic levels of the A O_u⁺ and B O_u⁺ states of ¹³⁰Te₂ excited by 514.5.496.5 and 488.0 nm Ar⁺-laser lines. Effective relaxation cross sections were obtained for collisions with ¹³⁰Te₂.     

Molecular orbital studies on the optical activity of chiral nitrosamines and nitramines

The chiroptical properties of the two lowest energy singlet-singlet transitions in a series of N-nitrosopiperidine derivatives are examined on a CNDO/S-CI molecular orbital (MO) model in which rotatory strengths are calculated directly from total molecular electronic wave functions. Similar calculations are carried out for the three lowest energy singlet-singlet transitions in a series of chiral N-nitropiperidine derivatives. The results obtained for the low energy n→π^* transitions in these compounds are compared to those predicted by sector rules proposed for chiral N-nitrosamine and N-nitramine systems.     

Conformational dependence of the 1Lb and n → π* rotatory strengths in α-substituted phenylacetic acids

The chiroptical properties of a series of chiral phenylacetic acid derivatives are examined on a theoretical model in which electronic rotatory strengths are calculated directly from molecular wave functions derived from semiempirical molecular orbital calculations. The CNDO/S SCF-MO model is used to calculate ground state wave functions and excited states are constructed in the virtual orbital-configuration interaction approximation. Of special interest are the rotatory strengths associated with the ¹L_b transition of the phenyl chromophore and the n → π^* transition of the carboxyl chromophore. Calculations are carried out on a large number of conformational isomers of the compounds: α-methyl phenylacetie acid (and its methyl ester), α-methylmandelic acid (and its methyl ester), and mandelic acid (and its methyl ester). The dependence of rotatory strength (¹L_b and n → π^*) on conformational variables is examined and discussed, and comparisons between available experimental data and the calculated results are made. Coupling between the phenyl and carboxyl chromophoric moieties is considered and possible spectra-structure relationships are examined.     

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     

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.     

A better approximation algorithm for the budget prize collecting tree problem

Given an undirected graph G=(V,E), an edge cost c(e)?0 for each edge e∈E, a vertex prize p(v)?0 for each vertex v∈V, and an edge budget B. The BUDGET PRIZE COLLECTING TREE PROBLEM is to find a subtree T′=(V′,E′) that maximizes , subject to . We present a (4+ε)-approximation algorithm.     

Operator product expansion on a fractal: The short chain expansion for polymer networks

We prove to all orders of renormalized perturbative polymer field theory the existence of a short chain expansion applying to polymer solutions of long and short chains. For a general polymer network with long and short chains we show factorization of its partition sum by a short chain factor and a long chain factor in the short chain limit. This corresponds to an expansion for short distance along the fractal perimeter of the polymer chains connecting the network vertices and is related to a large mass expansion of field theory.

The scaling of the second virial coefficient for bimodal solutions is explained. Our method also applies to the correlations of the multifractal measure of harmonic diffusion onto an absorbing polymer. We give a result for expanding these correlations for short distance along the fractal carrier of the measure.     

Analysis of sulphonated phthalocyanine dyes by capillary electrophoresis

Sulphonated phthalocyanine dyes may be prepared either by direct sulphonation or by mixed condensation methods. Both syntheses will produce mixtures of products. Such mixtures may be analysed by capillary electrophoresis to identify the various degrees of substitution and to indicate the approximate composition of the mixtures.     

The constrained minimum weighted sum of job completion times problem

We consider the problem of minimizing the weighted sum of job completion times on a single machine (subject to certain job weights) with an additional side constraint on the weighted sum of job completion times (with respect to different job weights). This problem is NP-hard, and we provide a polynomial time approximation scheme for this problem. Our method is based on Lagrangian relaxation mixed with carefully guessing the positions of certain jobs in the schedule. An earlier version of this paper appeared in the Proceedings of the 10th International IPCO Conference.     

Multifractality of Brownian motion near absorbing polymers

We characterize the multifractal behavior of Brownian motion in the vicinity of an absorbing star polymer. We map the problem to an O(M)-symmetric phi(4)-field theory relating higher moments of the Laplacian field of Brownian motion to corresponding composite operators. The resulting spectra of scaling dimensions of these operators display the convexity properties that are necessarily found for multifractal scaling but unusual for power of field operators in field theory. Using a field-theoretic renormalization group approach we obtain the multifractal spectrum for absorption at the core of a polymer star as an asymptotic series. We evaluate these series using resummation techniques.