A Reality Proof in PT-Symmetric Quantum Mechanics

We review the proof of a conjecture concerning the reality of the spectra of certain PT-symmetric quantum mechanical systems, obtained via a connection between the theories of ordinary differential equations and integrable models. Spectral equivalences inspired by the correspondence are also discussed.     

Quantum chemistry with an attached processor

The Floating Point Systems, Inc. Model 164 Attached Processor (FPS-164) is a high-speed, pipelined, parallel processor designed for large-scale scientific computation. Benchmark studies of operations common in quantum chemistry codes are discussed and the performance of the FPS-164 is compared with other commonly available computers. A complete system of electronic structure codes has been implemented on the FPS-164 using the Fortran-77 cross-compiler and calls to optimized vector and matrix routines. The conversion of a generalized valence bond (GVB ) code illustrates the strategy adopted to adapt Fortran codes to the FPS-164. A typical production example, a large scale (GVB ) and configuration interaction calculation on the vinyl radical, shows a net throughput equivalent to nearly nine VAX 11/780 computers.     

The electronic structure of vanadium carbide, VC

Within an energy range of 2.4 eV, we have explored 29 of the 36 states of the diatomic molecule VC that arise from the atoms in their ground state, V(4s23d3;4F)+C(2s2 2p2;3P). We use multireference methods with large atomic natural orbital basis sets. The ground state is of 2Delta symmetry with the first two excited states, 4Delta and 2Sigma+, located 4.2 and 7.0 kcal/mol above the X state. All the states examined in this work are relatively strongly bound and show significant charge transfer from V to C. The binding energy of the X 2Delta state is estimated to be 95.3 kcal/mol in good agreement with the experimental value.     

Recherches dans la série des cyclitols XXXVII Etude par spectrométrie de masse

Low resolution mass spectra of cyclohexane-triols, -tetrols, -pentols and -hexols and of some of their deuterium labelled derivatives have been measured. The results indicate that for some geometrical isomers quantitative differences between ion intensities are significant, allowing to deduce the stereochemistry of the molecule from its mass spectrum. In all these compounds the electron impact induced elimination of water occurs mainly by interaction between OH groups. There is a correlation between the relative abundance of (M – H₂O)⁺ and (M ?2 H₂O)⁺ ions and the number of axial hydroxyls in the more stable conformation of the molecule. Difficulties encountered in deducing fragmentation patterns, and determination of number and position of deuterium atoms in the molecule of ms-inositol are discussed.     

Crystal size distribution in precipitates

After a short introduction on the principles of nucleation and growth – here especially considering defect crystals – particle size distribution in precipitates is discussed. At first batch crystallization is referred to briefly. The situation in stirred continuous tank crystallizers is investigated in detail. Size distribution is considered in dependence on steady state flow rates of the reacting solutions, residence time of crystals in the tank, resulting in an exponential equation for the number of crystals per unit volume: \documentclass{article}\pagestyle{empty}\begin{document}$ n\left(r \right) = \frac{{\dot n_0 }}{{f\left(s \right)}}e^ - \frac{{vr}}{{V \cdot f\left(s \right)}} $\end{document}. With two and more tanks in series size distribution additionally becomes dependent on the difference of the supersaturations, of the occurrence of nucleation, and of the residence time of crystals in the various tanks. Equations for the size distribution are given for special conditions with two and more tanks in series.     

聚焦形貌恢复方法模型设计

采用基于拉普拉斯算符聚焦形貌恢复方法,提出了模拟目标深度测量的数值模型。数值模拟的核心是基于通过几何光学预测的理想图像的卷积与透镜广义孔径函数的多色点扩散函数,即用聚焦误差替代抛物线圆柱形貌或高斯函数。该模型可以使用基于聚焦形貌恢复方法的传感器真实组件参数、光源光谱、光学系统离差、相机的光谱灵敏度。提出了光学系统离差（消球差、消色差、色差）对确定目标表面形貌的精确度和可靠性的影响。结果表明,该模型可以有效提高实验效率,缩短时滞,降低成本。     

Global Optimization: On Pathlengths in Min-Max Graphs

Let f be a smooth nondegenerate real valued function on a finite dimensional, compact and connected Riemannian manifold. The bipartite min-max graph is defined as follows. Its nodes are formed by the set of local minima and the set of local maxima. Two nodes (a local minimum and a local maximum) are connected in by means of an edge if some trajectory of the corresponding gradient flow connects them. Given a natural number k, we construct a function f such that the length of the shortest path in between two specific local minima exceeds k. The latter construction is independent of the underlying Riemannian metric.     

Extended formulations in mixed integer conic quadratic programming

In this paper we consider the use of extended formulations in LP-based algorithms for mixed integer conic quadratic programming (MICQP). Extended formulations have been used by Vielma et al. (INFORMS J Comput 20: 438–450, 2008) and Hijazi et al. (Comput Optim Appl 52: 537–558, 2012) to construct algorithms for MICQP that can provide a significant computational advantage. The first approach is based on an extended or lifted polyhedral relaxation of the Lorentz cone by Ben-Tal and Nemirovski (Math Oper Res 26(2): 193–205 2001) that is extremely economical, but whose approximation quality cannot be iteratively improved. The second is based on a lifted polyhedral relaxation of the euclidean ball that can be constructed using techniques introduced by Tawarmalani and Sahinidis (Math Programm 103(2): 225–249, 2005). This relaxation is less economical, but its approximation quality can be iteratively improved. Unfortunately, while the approach of Vielma, Ahmed and Nemhauser is applicable for general MICQP problems, the approach of Hijazi, Bonami and Ouorou can only be used for MICQP problems with convex quadratic constraints. In this paper we show how a homogenization procedure can be combined with the technique by Tawarmalani and Sahinidis to adapt the extended formulation used by Hijazi, Bonami and Ouorou to a class of conic mixed integer programming problems that include general MICQP problems. We then compare the effectiveness of this new extended formulation against traditional and extended formulation-based algorithms for MICQP. We find that this new formulation can be used to improve various LP-based algorithms. In particular, the formulation provides an easy-to-implement procedure that, in our benchmarks, significantly improved the performance of commercial MICQP solvers.