Marcus contextual languages consisting of primitive words

In this paper we prove that the language of all primitive (strongly primitive) words over a nontrivial alphabet can be generated by certain types of Marcus contextual grammars.     

Characterization of complex networks by higher order neighborhood properties

A concept of higher order neighborhood in complex networks, introduced previously [Phys. Rev. E 73, 046101 (2006)], is systematically explored to investigate larger scale structures in complex networks. The basic idea is to consider each higher order neighborhood as a network in itself, represented by a corresponding adjacency matrix, and to settle a plenty of new parameters in order to obtain a best characterization of the whole network. Usual network indices are then used to evaluate the properties of each neighborhood. The identification of high order neighborhoods is also regarded as intermediary step towards the evaluation of global network properties, like the diameter, average shortest path between node, and network fractal dimension. Results for a large number of typical networks are presented and discussed.     

Synthesis of polyhedral particles by dispersion polymerization in supercritical carbon dioxide

The novel synthesis of polyhedral particles was attained by the dispersion polymerization of styrene in supercritical carbon dioxide using a polydimethylsiloxane-based macroazoinitiator as a precursor of the surfactant. The macroazoinitiator, VPS-1001, composed of poly(dimethylsiloxane) and 6-8 molecules of the azo groups served as a precursor of the surfactant for the dispersion polymerization by azobisisobutylonitrile as an initiator to produce 0.8-4 μm polyhedral particles. The size of the particles decreased as a result of increasing the VPS-1001 concentration. Too high a concentration of VPS-1001 caused coagulation of the particles. A decrease in the temperature increased the particle size and size distribution, while a decrease in the pressure produced particles with nonspecific shapes. An increase in the stirring rotation speed tended to increase the size and size distribution. However, too high a speed of rotation also caused coagulation of the particles.     

Sequence Independent Lifting for Mixed Integer Programs with Variable Upper Bounds

We investigate the convex hull of the set defined by a single inequality with continuous and binary variables with variable upper bound constraints. We extend the traditional flow cover inequality, and show that it is valid for a restriction of the set in which some variables are fixed. We also give conditions under which this inequality is facet-defining and, when it is not, we show how it can be lifted to obtain valid inequalities for the entire set using sequence independent lifting. In general, computing the lifting function is NP-hard, but under an additional restriction on the cover we obtain a closed form. Finally, we show how these results imply and extend known results about the single node fixed charge flow polyhedron. This material is based upon work supported by the National Science Foundation under Grant No. 0084826. Received: April 2004     

A method for classifying orbits near asteroids

A method for classifying orbits near asteroids under a polyhedral gravitational field is presented, and may serve as a valuable reference for spacecraft orbit design for asteroid exploration. The orbital dynamics near aster- oids are very complex. According to the variation in orbit characteristics after being affected by gravitational perturbation during the periapsis passage, orbits near an as- teroid can be classified into 9 categories： （1） surrounding- to-surrounding, （2） surrounding-to-surface, （3） surrounding- to-infinity, （4） infinity-to-infinity, （5） infinity-to-surface, （6） infinity-to-surrounding, （7） surface-to-surface, （8） surface- to-surrounding, and （9） surface-to- infinity. Assume that the orbital elements are constant near the periapsis, the gravitation potential is expanded into a harmonic series. Then, the influence of the gravitational perturbation on the orbit is studied analytically. The styles of orbits are dependent on the argument of periapsis, the periapsis radius, and the periapsis velocity. Given the argument of periapsis, the orbital energy before and after perturbation can be derived according to the periapsis radius and the periapsis velocity. Simulations have been performed for orbits in the gravitational field of 216 Kleopatra. The numerical results are well consistent with analytic predictions.     

Another class of balanced graph designs: balanced circuit designs

A block considered as a set of elements together with its adjacency matrix A is called a C-block if A is the adjacency matrix of a circuit. A balanced circuit design with parameters v, b, r, k, λ (briefly, BCD(v, k, λ)) is an arrangement of v elements into bC-blocks such that each C-block contains k elements, each element occurs in exactly rC-blocks and any two distinct elements are linked in exactly λ C-blocks.We investigate conditions for the existence of BCD and show, in particular, that if the block-size k ? 6 and the trivial necessary conditions are satisfied, then the corresponding BCD exists.     

A polyhedron with alls—t cuts as vertices,and adjacency of cuts

Consider the polyhedron represented by the dual of the LP formulation of the maximums–t flow problem. It is well known that the vertices of this polyhedron are integral, and can be viewed ass–t cuts in the given graph. In this paper we show that not alls–t cuts appear as vertices, and we give a characterization. We also characterize pairs of cuts that form edges of this polyhedron. Finally, we show a set of inequalities such that the corresponding polyhedron has as its vertices alls–t cuts.Work done at the Department of Computer Science and Engineering, Indian Institute of Technology, Delhi, India.     

Unification of basic and composite nondifferentiable optimization

There are two main classes of iterative methods in nondifferentiable optimization (NDO). In thebasic NDO, the information is limited to the objective function and at least one element of its subdifferential, while in thecomposite NDO, the objective function is split into a sum of a smooth and a nonsmooth function. Our work unifies these two approaches for benefiting of their respective advantages.     

立体角在结构化学中的应用

使用立体角概念,说明由一种或几种多面体组合,达到三维无隙结构充分必要条件。本文给出常见正多面体、常见阿基米德半正多面体顶角的立体角以及二面角,并结合结构化学实例分析阐述。在空间中须满足各立体角之和等于4π(sr),故通过简单的加和,即可判断无隙堆积的可能性,得知每个点的共用情况,进而推导出空间结构。运用这种方法,可以对一些尚不存在的结构进行大胆的预测。