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.     

Uniqueness and perturbation bounds for sparse non-negative tensor equations

We discuss the uniqueness and the perturbation analysis for sparse non-negative tensor equations arriving from data sciences. By two different techniques, we may get better ranges of parameters to guarantee the uniqueness of the solution of the tensor equation. On the other hand, we present some perturbation bounds for the tensor equation. Numerical examples are given to show the efficiency of the theoretical results.     

Structure determination of homoleptic AuI, AgI, and CuI aryl/alkylethynyl coordination polymers by X-ray powder diffraction

This article describes the structure determination of five homoleptic d(10) metal-aryl/alkylacetylides [RC triple bond CM] (M=Cu, R=tBu 1, nPr 2, Ph 3; R=Ph, M=Ag 4; Au 5) by using X-ray single-crystal and powder diffraction. Complex 1.C6H6 reveals an unusual Cu20 catenane cluster structure that has various types of tBuC triple bond C-->Cu coordination modes. By using this single-crystal structure as a starting model for subsequent Rietveld refinement of X-ray powder diffraction data, the structure of the powder synthesized from CuI and tBuC triple bond CH was found to have the same structure as 1. Complex 2 has an extended sheet structure consisting of discrete zig-zag Cu4 subunits connected through bridging nPrC triple bond C groups. Complex 3 forms an infinite chain structure with extended Cu-Cu ladders (Cu-Cu=2.49(4)-2.83(2) A). The silver(I) congener 4 is iso-structural to 3 (average Ag-Ag distance 3.11 A), whereas the gold(I) analogue 5 forms a Au...Au honeycomb network with PhC triple bond C pillars (Au-Au=2.98(1)-3.26(1) A). Solid-state properties including photoluminescence, nu(C triple bond C) stretching frequencies and thermal stability of these polymeric systems are discussed in the context of the determined structures.     

Syntheses, characterization, and photochromic studies of spirooxazine-containing 2,2'-bipyridine ligands and their zinc(II) thiolate complexes

A series of photochromic spirooxazine-containing zinc(II) diimine bis-thiolate complexes were successfully synthesized, and their photophysical and photochromic properties were studied. The X-ray crystal structure of complex 1a has also been determined. Upon excitation by UV light at 330 nm, all the ligands and complexes exhibit photochromic behavior. The thermal bleaching kinetics of the ligands and the complexes were studied in dimethylformamide at various temperatures. The photochemical quantum yields for the photochromic reactions of the ligands and complexes were also determined.     

香港花岗岩风化分级化学指标体系与风化壳分带

火成岩的化学风化过程实质上就是碱、碱土金属组分水解淋失与脱硅富铁铝化的地球化学过程。不同风化程度的岩石处于整个化学风化过程的不同阶段,因而具有不同的化学成分和风化度指标。笔者在对香港九龙两个地方5个钻孔共计150件不同深度、不同风化程度的样品化学全分析结果与岩土风化程度宏观判别结果的相互对比、选择和确认的基础上,建立了香港地区花岗岩风化岩土风化程度工程分级的化学指标体系。这一研究成果的提出不仅有利于提高花岗岩风化岩土工程分类的科。学性、可靠性和实用性,而且可以为风化岩土工程特性与风化作用关系研究提供理论依据。     

Stress induced half-metallicity in surface defected germanium nanowires

Germanium nanowires (GeNWs) with single, double, quadruple and octuple surface dangling bonds (SDBs) are investigated using density-functional-theory calculations. We show that single SDB defected GeNWs remain semiconducting as their non-defected form while double or multiple SDB defects result in either semiconducting or metallic GeNWs, depending on the defect's locations on the surface. More importantly, we show that the electronic properties of surface defected GeNWs can also be fine-tuned by applying tensile and compressive strains. Upon the right loading, the surface defected GeNWs become half-metallic. In addition, we determine that the surface defected GeNWs can be classified into three classes: (1) GeNWs with zero magnetic moment, which are either metallic or semiconducting; (2) GeNWs with net magnetic moments equal to the number of SDBs, which are semiconducting with distinct spin-up and spin-down configurations; and (3) GeNWs with net magnetic moments significantly lower than the number of SDBs. We also find that only the defected GeNWs that fall under (3) are potentially half-metallic. Our results predict that half-metallic GeNWs can be obtained via engineering of the surface defects and the structures without the presence of impurity dopants.     

Strain gage evaluation with four-point bending at moderate temperatures

This paper describes the application of the traditional four-point bending technique to conduct strain gage performance tests at moderate temperatures. The tests measure the apparent strain, linearity, drift, creep and hysteresis behavior to ascertain the reliability of strain gages to be used in the testing of experimental cylindrical vessels subjected to thermal loading. The four-point bending rig was designed to take advantage of the advances in personal computer datalogging and graphical processing software. The test rig is designed to provide a thermal barrier to minimize the heat losses and thermal isolation of the test beam while maintaining structural continuity. A low wattage and lightweight electric foil heater incorporating a precise temperature controller minimizes weight and enhances temperature stability. Gage performance data on five candidate strain gages at temperatures ranging from ambient to 215°C (419°F) are presented, and the evaluation procedure is outlined. The strain gage with the most acceptable performance was identified within the validity limits from ambient to a temperature of 215°C and from zero to a maximum strain of 1000 .     

Rotationally resolved vacuum ultraviolet pulsed field ionization-photoelectron vibrational bands for HD+(X 2Sigmag+,v+=0-20)

The authors have obtained rotationally resolved vacuum ultraviolet pulsed field ionization-photoelectron (vuv-PFI-PE) spectrum of HD in the photon energy range of 15.29-18.11 eV, covering the ionization transitions HD+(X 2Sigmag+,v+=0-21,N+)<--HD(X 1Sigmag+,v"=0,J"). The assignment of rotational transitions resolved in the vuv-PFI-PE vibrational bands for HD+(X 2Sigmag+,v+=0-20) and their simulation using the Buckingham-Orr-Sichel (BOS) model are presented. Rotational branches corresponding to the DeltaN=N+-J"=0, +/-1, +/-2, +/-3, and +/-4 transitions are observed in the vuv-PFI-PE spectrum of HD. The BOS simulation shows that the perturbation of vuv-PFI-PE rotational line intensities due to near resonance autoionization is very minor at v+>or=5 and decreases as v+ is increased. Thus, the rotationally resolved PFI-PE bands for HD+(v+>or=5) presented here provide reliable estimates of state-to-state cross sections for direct photoionization of HD, while the rotationally resolved PFI-PE bands for HD+(v+<5) are useful data for fundamental understanding of the near resonance autoionizing mechanism. On the basis of the rovibrational assignment of the vuv-PFI-PE bands, the ionization energies for the formation of HD+(X 2Sigmag+,v+=0-20,N+) from HD(X 1Sigmag+,v"=0,J") and the vibrational constants (omegae, omegaechie, omegaeye, and omegaeze), the rotational constants (Be and alphae), the vibrational energy spacings, and the dissociation energy for HD+(X 2Sigmag+) are determined. As expected, these values are found to be in excellent agreement with high level theoretical predictions.