随机交通均衡配流模型及其等价的变分不等式问题

本文讨论了交通网络系统的随机用户均衡原理的数学表述问题.在路段出行成本是流量的单调函数的较弱条件下,对具有固定需求和弹性需求的模式,首次证明了随机均衡配流模型可表示为一个变分不等式问题,同时也说明了该变分不等式问题与相应的互补问题以及一个凸规划问题之间的等价关系.     

4-[(E)-2-(3, 4-二甲氧基苯基)乙烯基]苯氧基乙酸乙酯的合成及其NMR研究

以对硝基甲苯、3, 4-二甲氧基苯甲醛为起始原料,经过缩合,还原,重氮化水解,亲核取代反应,最终合成了新的化合物4-[(E)-2-(3, 4-二甲氧基苯基)乙烯基]苯氧基乙酸乙酯,用¹H 和¹³C NMR及多种二维核磁共振谱确定了该化合物的结构,完成了¹H 和¹³C NMR的归属,给出了分子中各氢,碳原子的准确化学位移.     

VIBRATIONAL SPECTRA AND NORMAL COORDINATE ANALYSIS OF 1,2-BIS(2-FORMYLGLYCINEBENZENESULFENYL) ETHANE Pd(II) DICHLORIDE COMPLEX

The normal coordinate analysis of the title complex, 1,2-bis(2-formylglycinebenzenesulfenyl) ethane Pd(II) dichloride has been carried out by using the Urey-Bradley force field. According to the molecular structure determined by x-ray crystallographic analysis, 182 internal coordinates were established and 112 theoretical vibration frequencies agree well with the observed values with the average difference of 2.53 cm^?1 and the maximum deviation of 16.0 cm^?1.     

Bicriteria problems to minimize maximum tardiness and due date assignment cost in various scheduling environments

We study bicriteria problems of minimizing maximum tardiness and total due date assignment cost in various scheduling environments. We assume that each job can be assigned a different due date without any restriction, and that each due date assignment cost is a non-decreasing function of the quoted due date. We settle the complexity of most of the problems studied by either proving that they are NP-hard or finding a polynomial time solution for them. We also include approximation and non-approximability results for several parallel-machine problems.     

Double-quantum dipolar recoupling at high magic-angle spinning rates

A full investigation of the possible homonuclear double-quantum recoupling sequences, based on the RN family of sequences with N < or = 20, is given. Several new RN sequences, R16(6)(5), R18(8)(5), and R18(10)(5), were applied at high magic-angle spinning rates and compared with theory. The R18(10)(5) technique can be used to recouple dipolar couplings at spinning rates up to 39 kHz, and the application of the sequence in an INADEQUATE experiment is shown for a spinning rate of 30 kHz.     

Probabilistic analysis of the generalised assignment problem

We analyse thegeneralised assignment problem under the assumption that all coefficients are drawn uniformly and independently from [0, 1]. We show that such problems can be solved exactly with high probability, in a well-defined sense. The results are closely related to earlier work of Lueker, Goldberg and Marchetti-Spaccamela and ourselves.Supported by NATO grant RG0088/89.Supported by NSF grant CCR-8900112 and NATO grant RG0088/89.     

An approximation algorithm for the generalized assignment problem

The generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs. Each job is to be processed by exactly one machine; processing jobj on machinei requires timep _ij and incurs a cost ofc _ij ; each machinei is available forT _i time units, and the objective is to minimize the total cost incurred. Our main result is as follows. There is a polynomial-time algorithm that, given a valueC, either proves that no feasible schedule of costC exists, or else finds a schedule of cost at mostC where each machinei is used for at most 2T _i time units.We also extend this result to a variant of the problem where, instead of a fixed processing timep _ij , there is a range of possible processing times for each machine—job pair, and the cost linearly increases as the processing time decreases. We show that these results imply a polynomial-time 2-approximation algorithm to minimize a weighted sum of the cost and the makespan, i.e., the maximum job completion time. We also consider the objective of minimizing the mean job completion time. We show that there is a polynomial-time algorithm that, given valuesM andT, either proves that no schedule of mean job completion timeM and makespanT exists, or else finds a schedule of mean job completion time at mostM and makespan at most 2T. Research partially supported by an NSF PYI award CCR-89-96272 with matching support from UPS, and Sun Microsystems, and by the National Science Foundation, the Air Force Office of Scientific Research, and the Office of Naval Research, through NSF grant DMS-8920550.Research supported in part by a Packard Fellowship, a Sloan Fellowship, an NSF PYI award, and by the National Science Foundation, the Air Force Office of Scientific Research, and the Office of Naval Research, through NSF grant DMS-8920550.     

Assignments of optically pumped CD3OH laser lines

Six FIR laser lines from CD₃OH pumped by the 10R(36) and the 10R(18) CO₂ laser lines are assigned to specific rotational energy levels in the excited C–0 stretch state. It is found that their upper laser levels are shifted by a Fermi resonance between the C–0 stretch vibration and the third and forth harmonics of the torsional mode. The Fermi resonance shifts are +0.332 cm^–1 and +2.251 cm^–1 for the upper laser levels pumped by the 10R(36) and the 10R(18) CO₂ laser lines, respectively. Calculated frequencies of the pump and the laser transitions agree with those of the pump CO₂ laser lines and the observed FIR laser lines within estimated accuracy.     

Raman and infrared spectra of tere-phthalaldehyde

The laser Raman spectrum of tere-phthalaldehyde powder has been recorded on a Jobin Yvonhg 2S spectrophotometer with a~100 mW Argon-Ion laser. The infrared spectrum of the solid substance has been recorded on a Perkin-Elmer 621 spectrophotometer in the region 300–4000 cm^-1 using KBr and nujol mull techniques. The observed frequencies have been assigned in terms of the fundamentals, overtones and combinations assumingD _2h point-group symmetry.     

Integer programming formulations of vehicle routing problems

Various mathematical formulations are available for situations represented by vehicle routing problems. The assignment-based integer programming formulations of these problems are more common and easy to understand. Such formulations are discussed in this paper and a much simpler formulation for the vechicle routing problem is presented for the case, when all the vehicles have the same load capacity and maximum allowable cost per route.