Petrol delivery tanker assignment and routing: a case study in Hong Kong

In this paper, we present a case study on a tanker assignment and routing problem for petrol products in Hong Kong. A fleet of heterogeneous dangerous goods vehicles has been assigned to deliver several types of petroleum products to petrol stations with different tank capacities. Under the vendor-managed inventory system, the delivery company is responsible for controlling the station's inventory and replenishment. The operational characteristics and challenges such as geographic zoning, size of petrol stations, routing restrictions and so on are unique and have been described in this paper. A decision support system (DSS) combining heuristic clustering and optimal routing is employed to find the optimal fleet assignment and routing. Multiple objectives are considered simultaneously such that the number of tankers used could be minimized, the number of drops in trips is minimized, profit in terms of total products delivered is maximized and utilization of resources is maximized. The case illustrates the benefit and advantages of using the proposed DSS.     

On the changing structure among Chinese equity markets: Hong Kong,Shanghai, and Shenzhen

This study investigates information discovery among five Chinese equity markets measured daily over the period 1995–2014. We employ time series methods for finding structural breaks (if any) and uncovering both short-run and long-run fluctuations. We apply a new algorithm of inductive causation for use with non-Gaussian data to study the information flows in contemporaneous time. The empirical results show that there are four break dates and that the underlying causal models changed over our study period. The Shanghai A-share market dominates the other markets in the most recent period.     

How a Chinese teacher improved classroom teaching in Teaching Research Group: a case study on Pythagoras theorem teaching in Shanghai

In China, a school-based teaching research system was built since 1952 and Teaching Research Group (TRG) exists in every school. In the paper, a teacher’s three lessons and the changes in each lesson were described, which might show a track of how lessons were continuously developed in TRG. The Mathematical Tasks Framework, The Task Analysis Guide, and Factors Associated with the Maintenance and the Decline of High-level Cognitive Demands developed in the Quantitative Understanding: Amplifying Student Achievement and Reasoning project (Stein and Smith in Math Teach Middle School 3(4):268–275, 1998; Stein et al. in Implementing stardards-based mathematics instruction. Teachers College Press, NY, pp. 1–33, 2000), were employed in this study. Based on the perspective of Mathematical Task Analysis, changes of three lessons were described and the author provided a snapshot for understanding how a Chinese teacher gradually improved his/her lessons in TRG activities.     

从反正弦律的角度看上海和香港股市

我们把第一反正弦律推广到不对称游动的模型,并得到了其极限性质。利用反正弦律的思想,本文从一个新的角度,即投资一直赢利的时间占总时间的比例,来比较了上海和香港股市。     

Curriculum traditions in Berlin and Hong Kong: a comparative case study of the implemented mathematics curriculum

Many studies (such as Pepin in Learners and pedagogy, Sage Publications, London, 1999; Kaiser in ZDM 34(6):241–257, 2002; Park and Leung in Mathematics education in different cultural traditions: a comparative study of East Asia and the West. The 13th ICMI Study, pp. 227–238, Springer, New York, 2006) have revealed that there is a strong dependence on cultural traditions in mathematics teaching in different countries. Education in Germany is influenced by the Central and North European Didaktik tradition (Westbury in Teaching as a reflective practice: the German Didaktik tradition, L. Erlbaum Associates, Mahwah, pp. 15–39, 2000), while that in East Asia is influenced by Confucian heritage culture. However, there have not been studies investigating the relationships between these two cultural traditions and their influences on teaching and learning. This study aims at filling this gap in knowledge. Some commonalities in the aims and beliefs in the underlying philosophies in education in traditional China and Germany were found and are presented in this paper. Specifically, the relationship between cultural traditions and the implemented mathematics curriculum was investigated, using Berlin and Hong Kong as examples. It was found that culture affects the implemented curriculum in a complicated way and that other factors such as the intended curriculum and textbooks may also influence the implemented curriculum.     

What is effective mathematics teaching? A study of teachers from Australia, Mainland China, Hong Kong SAR, and the United States

What is effective teaching in mathematics? How do teachers in Australia, Mainland China, Hong Kong SAR and the US view effective teaching in mathematics? What are the similarities and differences in the views of teachers from the East and West on effective teaching? This paper provides theoretical and methodological bases for addressing these questions, which are dealt with in empirical studies described in the papers of this issue.     

A case study in formalizing projective geometry in Coq: Desargues theorem

Formalizing geometry theorems in a proof assistant like Coq is challenging. As emphasized in the literature, the non-degeneracy conditions lead to long technical proofs. In addition, when considering higher-dimensions, the amount of incidence relations (e.g. point–line, point–plane, line–plane) induce numerous technical lemmas. In this article, we investigate formalizing projective plane geometry as well as projective space geometry. We mainly focus on one of the fundamental properties of the projective space, namely Desargues property. We formally prove that it is independent of projective plane geometry axioms but can be derived from Pappus property in a two-dimensional setting. Regarding at least three-dimensional projective geometry, we present an original approach based on the notion of rank which allows to describe incidence and non-incidence relations such as equality, collinearity and coplanarity homogeneously. This approach allows to carry out proofs in a more systematic way and was successfully used to fairly easily formalize Desargues theorem in Coq. This illustrates the power and efficiency of our approach (using only ranks) to prove properties of the projective space.     

Content and pedagogical content knowledge in argumentation and proof of future teachers: a comparative case study in Germany and Hong Kong

The results of a comparative case study on mathematical and pedagogical content knowledge in the area of argumentation and proof of future teachers in Germany and Hong Kong are reported in this article. The study forms part of a qualitatively oriented comparative study on future teachers in Australia, Germany, and Hong Kong. Six case studies based on interviews and written questionnaires are described. These case studies show the strengths of the Hong Kong future teachers in mathematical knowledge in the area of argumentation and proof, whereas the three German future teachers perform stronger in the related pedagogical content domain. Furthermore, regarding the German future teachers, it seems that the two domains of knowledge are more strongly connected to each other. The results are interpreted in the light of related research, such as the MT21 study.     

Conception of expert mathematics teacher: a comparative study between Hong Kong and Chongqing

This paper reports the similarities and differences in how “expert mathematics teacher” is conceptualized by mathematics educators in Hong Kong and Chongqing, two cities in China which share similar but different cultural and social backgrounds. Thirty-seven mathematics education researchers, school principals with mathematics education background, and mathematics teachers were interviewed on their perceptions of expert mathematics teacher. It is found that in both cities an expert mathematics teacher should have a profound knowledge base in mathematics, teaching, and students; strong ability in teaching; and a noble personality and a spirit of life-long learning. As for differences, an expert mathematics teacher should have the ability to conduct research, mentor other teachers, and have profound knowledge of examination and educational theories in Chongqing. These attributes were not found in Hong Kong. These similarities and differences are discussed, and relevant social and cultural factors in the two contexts are examined.     

A renewal theorem in the finite-mean case

Let be a c.d.f. on such that is regularly varying with exponent . Then as , where is the renewal function associated with . Moreover similar estimates are given for distributions in the domain of attraction of the normal distribution and for the variance of The estimates improve earlier results of Teugels and Mohan.

     

Introducing technology in algebra in Hong Kong: addressing issues in learning

A review of recent studies in Hong Kong suggests that possible problems in secondary school algebra may be due to the procedural paradigm orientation in the curriculum and the conventional style of teaching in the classroom which do not provide sufficient opportunities for students to develop conceptual understanding. Based on the works of a number of projects in the West, it is hypothesized that the introduction of technology in lessons which embody a cognitive model in their design and delivery will provide a viable alternative for enhancing algebraic thinking. The key features of the cognitive model are concrete preparation, cognitive conflict, construction, metacognition and bridging, imbedded in a ‘mediation’ style of teaching. These features are exemplified by detailed accounts of classroom episodes from a Hong Kong lesson supported by the use of graphics calculators. Results indicate that while the approach places particular demands on teachers (a tension between a transmission style of teaching and mediating) there is real potential for supporting more dynamic student constructions.     

A simultaneous bus route design and frequency setting problem for Tin Shui Wai,Hong Kong

A bus network design problem for Tin Shui Wai, a suburban residential area in Hong Kong, is investigated, which considers the bus services from the origins inside this suburban area to the destinations in the urban areas. The problem aims to improve the existing bus services by reducing the number of transfers and the total travel time of the users. This has been achieved by the proposed integrated solution method which can solve the route design and frequency setting problems simultaneously. In the proposed solution method, a genetic algorithm, which tackles the route design problem, is hybridized with a neighborhood search heuristic, which tackles the frequency setting problem. A new solution representation scheme and specific genetic operators are developed so that the genetic algorithm can search all possible route structures, rather than selecting routes from the predefined set. To avoid premature convergence, a diversity control mechanism is incorporated in the solution method based on a new definition of hamming distance. To illustrate the robustness and quality of solutions obtained, computational experiments are performed based on 1000 perturbed demand matrices. The t-test results show that the design obtained by the proposed solution method is robust under demand uncertainty, and the design is better than both the current design and the design obtained by solving the route design problem and the frequency setting problem sequentially. Compared with the current bus network design, the proposed method can generate a design which can simultaneously reduce the number of transfers and total travel time at least by 20.9% and 22.7% respectively. Numerical studies are also performed to illustrate the effectiveness of the diversity control mechanism introduced and the effects of weights on the two objective values.     

Generating,scheduling and rostering of shift crew-duties: Applications at the Hong Kong International Airport

In the context of manpower planning, goal programming (GP) is extremely useful for generating shift duties of fixed length. A fixed-length duty consists of a fixed number of contiguous hours of work in a day, with a meal/rest break somewhere preferably around the middle of these working hours. It is such properties that enable the straightforward, yet flexible GP modeling. We propose GP models for an integrated problem of crew duties assignment, for baggage services section staff at the Hong Kong International Airport. The problem is solved via decomposition into its duties generating phase—a GP planner, followed by its GP scheduling and rostering phase. The results can be adopted as a good crew schedule in the sense that it is both feasible, satisfying various work conditions, and “optimal” in minimizing idle shifts.     

Impact of information technology on the performance of logistics industry: the case of Hong Kong and Pearl Delta region

Over the last decade, a number of research studies have advocated the use of information technology (IT) in different aspects of logistics and distribution operations. This study examines the current state of the use of IT and its impact on logistics service performance through a survey of 210 logistics companies in Hong Kong and the Pearl River Delta region. A hypothetical model is also proposed in which the theories of the market-based view and the resource-based view are applied to link up the implications of IT capabilities with logistic performance. The model was tested using structural equation modelling. The findings suggested that (i) IT implementation directly enhances the service quality of the logistics companies; (ii) the impact of IT implementation improves service quality thereby creating competitiveness.     

A note on Dilworth's theorem in the infinite case

If is a poset and every antichain is finite, and if the length of the well-founded poset of antichains is less than ² ₁, then is the union of countably many chains. We also compute the length of the poset of antichains in the product of two ordinals, x.     

How algebra spoiled recreational problems: A case study in the cross-cultural dissemination of mathematics

This paper deals with a sub-class of recreational problems which are solved by a simple memorized rule resulting from an elementary arithmetical or algebraic solution, called proto-algebraic rules. Their recreational aspect is derived from a surprise or trick solution which is not immediately obvious to the subjects involved. Around 1560 many such problems wane from arithmetic and algebra textbooks to reappear in the eighteenth century. Several hypotheses are investigated why popular Renaissance recreational problems lost their appeal. We arrive at the conclusion that the emergence of algebra as a general problem solving method changed the scope of what is considered recreational in mathematics.     

A substitute for the Sard-Smale theorem in theC 1 case

IfF is a Fredholm mapping of indexΝ ∃ ℤ and classC ^max(Ν,0)+1 between separable Banach spaces, the Sard—Smale theorem yields the existence of arbitrarily small perturbations ofF having 0 as a regular value. The smoothness requirement cannot be weakened in the Sard—Smale theorem itself, at least whenΝ ≥ 0, but we prove that the approximation result remains valid irrespective of the indexΝ whenF is only of classC ¹ and satisfies appropriate properness-like conditions. The separability of the spaces is not needed either. Everything carries over to the setting of Banach manifolds modeled on spaces with a norm of classC ¹ away from the origin. We also show that in Banach spaces, theC ¹ norm assumption can be dropped without major prejudice. The application to degree theory forC ¹ Fredholm mappings of index 0 is developed in a separate paper.     

A Thom-Smale-Witten theorem on manifolds with boundary: the arbitrary metric case

In this paper, we establish the canonical isomorphism between the Witten instanton complex and the Thom-Smale complex on manifolds with boundary with arbitrary Riemannian metric using Bismut-Lebeau’s analytic localization techniques.