A three-dimensional voting system in Hong Kong

The voting system of the Legislative Council of Hong Kong (Legco) is sometimes unicameral and sometimes bicameral, depending on whether the bill is proposed by the Hong Kong government. Therefore, although without any representative within Legco, the Hong Kong government has certain degree of legislative power – as if there is a virtual representative of the Hong Kong government within the Legco. By introducing such a virtual representative of the Hong Kong government, we show that Legco is a three-dimensional voting system. We also calculate two power indices of the Hong Kong government through this virtual representative and consider the C-dimension and the W-dimension of Legco. Finally, some implications of this Legco model to the current constitutional reform in Hong Kong will be given.     

Distribution-free vessel deployment for liner shipping

One important problem faced by the liner shipping industry is the fleet deployment problem. In this problem, the number and type of vessels to be assigned to the various shipping routes need to be determined, in such a way that profit is maximized, while at the same time ensuring that (most of the time) sufficient vessel capacity exists to meet shipping demand. Thus far, the standard assumption has been that complete probability distributions can be readily specified to model the uncertainty in shipping demand. In this paper, it is argued that such distributions are hard, if not impossible, to obtain in practice. To relax this oftentimes restrictive assumption, a new distribution-free optimization model is proposed that only requires the specification of the mean, standard deviation and an upper bound on the shipping demand. The proposed model possesses a number of attractive properties: (1) It can be seen as a generalization of an existing variation of the liner fleet deployment model. (2) It remains a mixed integer linear program and (3) The model has a very intuitive interpretation. A numerical case study is provided to illustrate the model.     

Scheduling jobs with release dates on parallel batch processing machines to minimize the makespan

Batch processing happens in many different industries, in which a number of jobs are processed simultaneously as a batch. In this paper we develop two heuristics for the problem of scheduling jobs with release dates on parallel batch processing machines to minimize the makespan and analyze their worst-case performance ratios. We also present a polynomial-time optimal algorithm for a special case of the problem where the jobs have equal processing times.     

Ferromagnetic Convection in a Heterogeneous Darcy Porous Medium Using a Local Thermal Non-equilibrium (LTNE) Model

The combined effects of vertical heterogeneity of permeability and local thermal non-equilibrium (LTNE) on the onset of ferromagnetic convection in a ferrofluid saturated Darcy porous medium in the presence of a uniform vertical magnetic field are investigated. A two-field model for temperature representing the solid and fluid phases separately is used. The eigenvalue problem is solved numerically using the Galerkin method for different forms of permeability heterogeneity function Γ(z) and their effect on the stability characteristics of the system has been analyzed in detail. It is observed that the general quadratic variation of Γ(z) with depth has more destabilizing effect on the system when compared to the homogeneous porous medium case. Besides, the influence of LTNE and magnetic parameters on the criterion for the onset of ferromagnetic convection is also assessed.     

Quantitative screening and matrix effect studies of drug discovery compounds in monkey plasma using fast-gradient liquid chromatography/tandem mass spectrometry.

A higher-throughput bioanalytical method based on fast-gradient (1 min run time) high-performance liquid chromatography (HPLC) coupled with tandem mass spectrometry (MS/MS) was developed for screen-type analyses of plasma samples from early drug discovery studies in support of exploratory pharmacodynamic studies. The HPLC system equipped with minibore column was interfaced with either atmospheric pressure chemical ionization (APCI) or electrospray (ESI) ionization techniques. The matrix ion suppression effect of both quantitative HPLC/MS/MS analyses was compared using the post-column infusion system. The use of the described methods provided advantages such as a shorter chromatographic region of ion suppression, less solvent consumption and shorter run times in comparison with standard analytical column HPLC/MS/MS methods. The analytical results obtained by both HPLC/MS/MS methods were in good agreement (within 15% of error) and displayed a good correlation with the pharmacodynamic outcome.     

catena‐Poly­[[[bis­(perchlorato‐O)­(1,10‐phenanthroline‐N,N′)­copper(II)]‐μ‐4,4′‐bi­pyridine‐N:N′] monohydrate]

The Cu atom in the title complex {[Cu(C₁₀H₈N₂)(C₁₂H₈N₂)(ClO₄)₂]·H₂O}_n, has an N₄O₂ octahedral coordination geometry, the Cu atoms being bridged by the bi­pyridine and chelated by the phenanthroline heterocycles. Adjacent mol­ecules are linked into a zigzag chain running along the c axis of the monoclinic unit cell. The chains are connected through lattice water mol­ecules to produce a layer structure.     

Clustering methods for printed circuit board insertion problems

In a previous paper, we studied printed circuit board (PCB) insertion problems when the number of different types of components are less than the number of reels in the feeder bank. In this paper, we consider a solution technique based on the clustering approach for PCB insertion problems with the limited capacity of the feeder bank. Simulation results are reported to illustrate the effectiveness of our method.     

Solution of Some Structural Analysis Problems by Orthogonal Collocation

Abstract

Application of the method of orthogonal collocation to boundary value problems in structural and applied mechanics is investigated. Typical boundary value problems, such as the torsion of rectangular bars and the bending of plates, are employed as illustrative examples. Simplicity in application and good accuracy of orthogonal collocation are demonstrated by the solution of such complex problems as the large deflection analysis of rectangular isotropic, orthotropic, and sandwich plates. Results are compared wherever possible with existing solutions based on much more laborious and lengthy methods of computation. Excellent agreements are obtained.     

Rational symplectic field theory for Legendrian knots

We construct a combinatorial invariant of Legendrian knots in standard contact three-space. This invariant, which encodes rational relative Symplectic Field Theory and extends contact homology, counts holomorphic disks with an arbitrary number of positive punctures. The construction uses ideas from string topology.