带凸资源和恶化效应的单机松弛窗口排序

研究带凸资源和恶化效应的单机窗口指派排序问题,其中窗口指的是松弛窗口,凸资源和恶化效应指的是工件的实际加工时间是其开始加工时间的线性函数,是其资源消耗量的凸函数。目标是确定工件的加工顺序,资源分配量以及窗口的开始加工时间和长度使其在总资源消耗费用(与窗口有关的排序费用)有上界限制的条件下,极小化与窗口有关的排序费用(总资源消耗费用)。获得了求解上述问题的最优算法,证明了该问题是多项式时间可解的。     

Determination of the Molecular Arrangement in Liquid Crystals by Polarization of Fluorescence

Polarized luminescence intensity reading and the polarized absorbance spectra of 4-diethyl-amino-4′-nitrostilbene “impurity” in the n-butyl-p/p-hexyloxyphenyloxycarbonyl/-phenyl-carbonate liquid crystal were measured. Degrees of orientational order, S₁ and S₂, of the nematic liquid were calculated from relative values of the absorbance and luminescence intensity components. A function, which describes the angular molecular distribution with respect to a preferred direction in the liquid crystal, is plotted.     

Internal Flow Patterns on Heat Transfer Performance of a Closed-Loop Oscillating Heat Pipe with Check Valves

This article presents the experimental results of an evaluation of the influence of internal flow patterns on the heat transfer performance of a closed-loop oscillating heat pipe with check valves. It was found that the internal flow patterns could be classified according to four flow patterns: dispersed bubble flow, bubble flow, slug flow, and annular flow, respectively. The main regime of each flow pattern can be determined from a flow pattern map. The map can be used to predict the trend of the heat transfer rate in the closed-loop oscillating heat pipe with check valves.     

The development of children's understanding of mathematical patterns through mathematical activities

In this paper we report how children (aged 8) developed their mathematical understanding through number tasks based on the Fibonacci sequence (Bamboo numbers) used in the context of a Substantial Learning Environment (SLE), which is designed to be mathematically rich, have a clear purpose and give opportunities to utilise mathematical thinking. The flexible nature of the SLEs makes it possible for teachers and children to explore various mathematical patterns. To capture children's activities when working within SLEs, we make particular reference to Pegg and Tall's work in 2005, and consider a theoretical framework based on the SOLO taxonomy (Biggs and Collis 1982) and the developmental process of understanding mathematical concepts. It was found that the key progression to be made through learning using our Bamboo number-based SLEs is from Multi-structural to Relational levels. It was also suggested that it is difficult for many children to understand the structural aspects of number patterns.     

Nonlinear waves in complex oscillator network with delay

We investigate the spatio-temporal patterns of Hopf bifurcating periodic solutions in a delay complex oscillator network. Firstly, we calculate the critical values of Hopf bifurcation. Secondly, the bifurcating periodic solutions can take on two cases: one is synchronization or anti-synchronization, and another is the coexistence of two phase-locked, N mirror-reflecting and N standing waves, because the system has group symmetry. Finally, the stability of these nonlinear oscillations is determined using the center manifold theorem and normal form method with the imaginary eigenvalues being simple and double.     

Applying the cluster method to count occurrences of generalized permutation patterns

We apply ideas from the cluster method to q-count the permutations of a multiset according to the number of occurrences of certain generalized patterns, as defined by Babson and Steingrímsson. In particular, we consider those patterns with three letters and one internal dash, as well as permutation statistics composed of counting the number of occurrences of multisets of such patterns. Counting is done via recurrences which simplify in the case of permutations. A collection of Maple procedures implementing these recurrences accompanies the article.     

INVESTIGATING TAX DISTORTIONS: AN APPLIED MODEL OF PETROLEUM EXPLORATION AND EXTRACTION DECISIONS

Abstract A numerical model is proposed for the testing of distortions caused by petroleum fiscal systems on the exploration and extraction activities of a profit‐maximizing firm. Traditional models have not been capable of testing for the distortions caused by the complex tax structures most often used by governments. Two tax combinations, as well as certain other taxes, are analyzed for distortions in the model. The model is parameterized using generic data because specific jurisdictions are not considered. The distortions due to rentals and royalties are as expected by theory. Property taxes show a new distortion result where production tilting is ambiguous.     

Piezoelectric activities and domain patterns of orthorhombic Ba(Zr,Ti)O3 ceramics

Ba(Zr_xTi_1?x)O₃ (0.025 ≤ x ≤ 0.065) ceramics were prepared by conventional solid-state reaction method. Crystalline structures were analyzed by X-ray diffraction. It was shown that all the Ba(Zr_xTi_1?x)O₃ (0.025 ≤ x ≤ 0.065) ceramics were of orthorhombic phase at room temperature. Piezoelectric activities and domain patterns were investigated and compared with those of BaTiO₃ ceramic. All the Ba(Zr_xTi_1?x)O₃ ceramics showed nearly the same d₃₃ values of about 265 pC/N and the same domain width of about 220 nm. By comparing the grain sizes and domain width of the Ba(Zr_xTi_1?x)O₃ ceramics with those of BaTiO₃ ceramic, it is speculated that the variation of domain width with grain sizes in orthorhombic Ba(Zr_xTi_1?x)O₃ ceramics may be different with that in tetragonal BaTiO₃ ceramic. Besides domain width, the effective inertia mass of domain wall is also considered to be a very important factor that impacts the piezoelectric activities of the Ba(Zr_xTi_1?x)O₃ ceramics.