一类特殊二维0-1规划的广义指派模型求解

二维0-1整数规划模型应用广泛,对广义指派问题的研究,解决了一些二维0-1整数规划问题.但有些实际问题具有特殊上限约束,目前还没有对应的方法.针对该实际情形,本文建立了相应的数学模型,利用对指派模型的推广,求得问题最优解,从理论上解决了这一类特殊约束二维0-1整数规划的最优解求取问题.并通过算例说明了方法的使用.     

On Linear-Time Algorithms for the Continuous Quadratic Knapsack Problem

We give a linear time algorithm for the continuous quadratic knapsack problem which is simpler than existing methods and competitive in practice. Encouraging computational results are presented for large-scale problems. The author thanks the Associate Editor and an anonymous referee for their helpful comments.     

Monotonic solutions of a quadratic integral equation of fractional order

In the paper we indicate an error made in the proof of the main result of the paper [M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005) 112-119]. Moreover, we provide correct proof of a slightly modified version of the mentioned result. The main tool used in our proof is the technique associated with the Hausdorff measure of noncompactness.     

Electronic structure and vibrational spectra of cis-diammine(orotato)platinum(II), a potential cisplatin analogue: DFT and experimental study

Orotic acid (vitamin B₁₃) is a key intermediate in biosynthesis of the pyrimidine nucleotides in living organisms, moreover, it may serve as the biological carrier for some metal ions. cis-Diammine(orotato)platinum(II), cis-[Pt(C₅H₂N₂O₄)(NH₃)₂] can be considered as a new potential cisplatin analogue. The FT-Raman and FT-IR spectra of the title complex are reported, for the first time. The molecular structure, vibrational frequencies, and the theoretical infrared and Raman intensities have been calculated by the density functional mPW1PW91 method. The detailed vibrational assignment has been made on the basis of the calculated potential energy distribution. The theoretically predicted IR and Raman spectra show very good agreement with experiment. Natural bond orbital (NBO) analyses were performed for cisplatin, carboplatin and the title complex. The results provided new data on the nature of platinum–ligand bonding in these compounds. Strong intramolecular hydrogen bond between the orotate ligand and the coordinated ammonia group stabilizes the structure of the platinum(II) complex. Thus, it is suggested that the orotate ligand in the title complex is more inert to the substitution reactions than the chloride ligands in cisplatin.     

ICLAS of weak transitions of water between 11 300 and 12 850 cm: Comparison with FTS databases

Very weak water vapor absorption lines have been investigated by intracavity laser absorption spectroscopy (ICLAS) in the 11 335-11 947 and 12 336-12 843 cm⁻¹ spectral regions dominated by the ν₁ + 3ν₂ + ν₃ and ν₂ + 3ν₃ bands, respectively. A detectivity on the order of α_min ∼ 10⁻⁹ cm⁻¹ was achieved with an ICLAS spectrometer based on a Ti: Sapphire laser. It allowed detecting transitions with an intensity down to 5 × 10⁻²⁸ cm/molecule which is about 10 times lower than the weakest line intensities previously detected in the considered region. A line list corresponding to 1281 transitions with intensity lower than 5 × 10⁻²⁶ cm/molecule has been generated. A detailed comparison with the line lists provided by the HITRAN database and by recent investigations by Fourier transform spectroscopy associated with very long multi pass cell is presented. The rovibrational assignment performed on the basis of the ab initio calculations of Schwenke and Partridge, has allowed for determining 176 new energy levels belonging to a total of 16 vibrational states.     

A new trust region technique for the maximum weight clique problem

A new simple generalization of the Motzkin-Straus theorem for the maximum weight clique problem is formulated and directly proved. Within this framework a trust region heuristic is developed. In contrast to usual trust region methods, it regards not only the global optimum of a quadratic objective over a sphere, but also a set of other stationary points of the program. We formulate and prove a condition when a Motzkin-Straus optimum coincides with such a point. The developed method has complexity O(n³), where n is the number of vertices of the graph. It was implemented in a publicly available software package QUALEX-MS.Computational experiments indicate that the algorithm is exact on small graphs and very efficient on the DIMACS benchmark graphs and various random maximum weight clique problem instances.     

橙皮素A的NMR研究

橙皮素A是从中药北沙参(Glehnia littoralis Fr. Schmidt ex Miquel)的正丁醇萃 取物中分离得到的一种8-O-4′-型异木脂素苷类化合物. 通过化学方法和波谱分析鉴 定了该 化合物的结构. 采用2D NMR技术对其NMR信号进行了全归属. DMSO-d₆代替CD₃OD作为溶剂，并利用重水交换，能准确读出偶合常数J_7,8值.      

126Cs的高自旋态能级结构

利用融合蒸发反应¹¹⁶Cd(¹⁴N,4n)¹²⁶Cs布居了¹²⁶Cs的高自旋态.观测到了100多条新的γ跃迁和相应的能级,建立了双奇核¹²⁶Cs由9个转动带构成的能级纲图.尝试性地指定了大部分能级的自旋和宇称以及各转动带的Nilsson单粒子组态.极大地丰富了已有的实验结果.     

A necessary condition for the minimum of a quadratic form under rearrangements

A necessary condition is derived for a quadratic form p^tGp to be minimal among all permutations of the nonnegative nontrivial vector p. The quadratic form arises from the stability problem of a fixed-fixed taut string loaded with masses at equidistant points.