Online Automatic Marking of Diagrams

This article describes the way in which the Open University is expanding its online quiz engine to enable students to draw free-form diagrams in response to a quiz question. The new quiz engine automatically marks a student’s diagram and provides feedback either instantaneously when used in formative mode or later when used in summative mode. The new quiz engine is hosted within the Open University’s quiz module, OpenMark, which interfaces to the Moodle VLE which is responsible for rendering both the question and the feedback in the user’s browser. The article outlines the general nature of the diagrams that our system has been designed to deal with. This is followed by an example of the use of the new question type as implemented within our e-assessment system. The article also briefly summarizes the results of experiments carried out on the accuracy of the automatic marker and reports on feedback from students who have used the new diagramming question type.     

The structure of departure process and optimal control strategy <Emphasis Type="Italic">N</Emphasis>* for <Emphasis Type="Italic">Geo/G</Emphasis>/1 discrete-time queue with multiple server vacations and Min(<Emphasis Type="Italic">N,V</Emphasis>)-Policy

This paper considers the departure process and the optimal control strategy for a discretetime Geo/G/1 queueing model in which the system operates under the control of multiple server vacations and Min(N, V)-policy. Using the law of total probability decomposition, the renewal theory and the probability generating function technique, the transient and the steady-state probabilities that the server is busy at any epoch n⁺ are derived. The authors also obtain the explicit expression of the probability generating function for the expected number of departures occurring in the time interval (0⁺, n⁺] from any initial state. Meanwhile, the relationship among departure process, server’s state process and service renewal process in server busy period is found, which shows the special structure of departure process. Especially, some corresponding results of departure process for special discrete-time queues are directly gained by our results. Furthermore, the approximate expansion for calculating the expected number of departures is presented. In addition, some other important performance measures, including the expected length of server busy period, server’s actual vacation period and busy cycle period etc., are analyzed. Finally, some numerical results are provided to determine the optimum value N* for minimizing the system cost under a given cost structure.     

Linear chaos in the quantum harmonic oscillator

In this note,it is proved that for the annihilation operator B of the unforced quantum harmonic oscillator,B~n is mixing and generically 5-chaotic with any 0 δ 2 for each positive integer n.Besides,by using the result in[Wu X and Zhu P,J.Phys.A：Math.Theor.,2011,44：505101],the authors obtain that the principal measure of B~n is equal to 1 for each positive integer n.     

Reliability indices of discrete-time Geox/G/1 queueing system with unreliable service station and multiple adaptive delayed vacations

This paper considers the discrete-time Geo~x/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the perspective of reliability research.Following problems will be discussed:1) The probability that the server is in a "generalized busy period" at time n;2) The probability that the service station is in failure at time n,i.e.,the transient unavailability of the service station,and the steady state unavailability of the service station;3) The expected number of service station failures during the time interval(0,n],and the steady state failure frequency of the service station;4) The expected number of service station breakdowns in a server’s "generalized busy period".Finally,the authors demonstrate that some common discrete-time queueing models with unreliable service station are special cases of the model discussed in this paper.     

Multitask n-vehicle exploration problem: Complexity and algorithm

This paper extends the single-task n-Vehicle Exploration Problem to Multitask n-Vehicle Exploration Problem(MTNVEP),by combining n-Vehicle Exploration Problem with Job Scheduling Problem.At first,the authors prove that MTNVEP is NP-hard for fixed number of tasks,and it is strongly NP-hard for general number of tasks.Then they propose an improved accurate algorithm with computing time O(n3~n),which is better than O(n!) as n becomes sufficiently large.Moreover,four heuristic algorithms are proposed.Effectiveness of the heuristic algorithms is illustrated by experiments at last.     

H 2/H ∞ control problems of backward stochastic systems

This paper is concerned with the mixed H2/H∞ control problem for a new class of stochastic systems with exogenous disturbance signal.The most distinguishing feature,compared with the existing literatures,is that the systems are described by linear backward stochastic differential equations（BSDEs）.The solution to this problem is obtained completely and explicitly by using an approach which is based primarily on the completion-of-squares technique.Two equivalent expressions for the H2/H∞ control are presented.Contrary to forward deterministic and stochastic cases,the solution to the backward stochastic H2/H∞ control is no longer feedback of the current state;rather,it is feedback of the entire history of the state.     

A unified approach to construct generalized B-splines for isogeometric applications

Generalized B-splines have been employed as geometric modeling and numerical simulation tools for isogeometric analysis(IGA for short). However, the previous models used in IGA,such as trigonometric generalized B-splines or hyperbolic generalized B-splines, are not the unified mathematical representation of conics and polynomial parametric curves/surfaces. In this paper,a unified approach to construct the generalized non-uniform B-splines over the space spanned by{α(t), β(t), ξ(t), η(t), 1, t, ···, t~(n-4)} is proposed, and the corresponding isogeometric analysis framework for PDE solving is also studied. Compared with the NURBS-IGA method, the proposed frameworks have several advantages such as high accuracy, easy-to-compute derivatives and integrals due to the non-rational form. Furthermore, with the proposed spline models, isogeometric analysis can be performed on the computational domain bounded by transcendental curves/surfaces, such as the involute of circle, the helix/helicoid, the catenary/catenoid and the cycloid. Several numerical examples for isogeometric heat conduction problems are presented to show the effectiveness of the proposed methods.     

Queue size distribution of Geo/G/1 queue under the Min(<Emphasis Type="Italic">N,D</Emphasis>)-policy

This paper considers a discrete-time Geo/G/1 queue under the Min(N,D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first (Min(N,D)-policy). By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of the transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n ⁺. Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution. Furthermore, the important relations between the steady state queue length distributions at different time epochs n ^-, n and n ⁺ are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.     

A conversation on guidelines for the process of facilitating systemic change in education

The International Systems Institute held its sixth annual conversation at Asilomar on November 14–19, 1993. At that meeting, seven participants self-selected themselves into a conversation group that met intensively over 4 days to develop some guidelines or principles for the process of facilitating systemic change in education. This is a report on how that group functioned and what it produced. The trigger questions addressed included: What are the major stages in the systemic change process? Can you do systems design with only a part of the “system”? How important isscale (e.g., number of people, schools)? What is an educational system? Can you use the same design process in any culture? How can one best create the idealized design? What are the major goals, obstacles, guidelines? Can we design the process without knowing the product? and Are there big differences between working within the system and outside the system? A large portion of the effort focused on guidelines for facilitating the first two phases of the systemic change process: preparing for design and designing the new system.     

From Practitioner to Researcher: Designing the Dissertation Process for Part Time Coursework Masters Students

Coursework Masters degrees that are offered as block release programmes provide opportunities for access to postgraduate education for adult students while in full time employ. These students attend structured contact modules after which they return to home and work and a distance format of study. However, these courses are generally characterised by low completion rates and lengthy time to completion, particularly of the research dissertation. While various explanations for this problem have been offered, for example, students’ non-academic commitments and supervisor–student-relations, our particular concern in this paper is students’ reading and writing practices in the transition from professional work practice and Masters coursework to the research dissertation. This paper proposes a systemic design to improve student reading and writing in this transition, and the proposal is illustrated using a block release coursework Masters programme in Management at a South African university. The design draws on interpretive systems ideas to think about the different levels of institutional and disciplinary context that impact on the research dissertation. We also use an academic literacies perspective—the concepts of literacy practice, language identity and power in particular—to think about reading and writing. This design incorporates components that include system elements, relationships, purpose and feedback that facilitate interaction between the conventions of the research practice, what the student brings to the practice, and the agency of the student.     

Design for Mass Customisation in Higher Education: a Systems-Thinking Approach

The point of this research is to investigate the impact of systems-thinking principles (Seddon 2003) on operationalising the ‘mass customisation’ capability of student services in higher education institutions. The research empirically contributes to student-service mass customisation in higher education through the findings of a case study conducted at the admission and academic registry service department of one of the UK’s leading universities. A qualitative methodology was employed with the use of semi-structured interviews, focus group, observations, and documentation supplements. It was found that the principles of systems-thinking are positively related to enhancement of mass customisation capability through the realisation of three different levels of service mass customisation determinants. These three levels are: employee level (i.e. micro determinants); operational level (i.e. meso determinants); and functional level (i.e. macro determinants). A conceptual model was developed to explain the relationships among these three organisational levels, supported by empirical evidences. The value of this paper is the introduction of a conceptual model that could operationalise ‘mass customisation’ in universities by integrating human resources, operational and functional dimensions in a systematic design to deliver customised services for students as individuals.     

Collaborative Regional Innovation Initiatives: A Booster for Local Company Innovation Processes?

It is widely acknowledged that the rate of innovations can be enhanced through interaction between new constellations of actors, crossing borderlines between different mindsets, knowledge and skill bases (e.g. Brown and Duguid, Org Sci 2(1):40–57, 1991; Cooke and Morgan, The associational economy: firms, regions, and innovation, 1998; Leonard-Barton, Wellsprings of knowledge: building and sustaining the sources of innovation, 1995, p. 64; Stamm, Managing innovation, design and creativity, 2008, p. 335). Studies of economic prosperity have also pointed to cooperation and competition between neighboring actors as a driver for competitiveness and innovativeness, be it for a company, a business area or a region (e.g. Piore and Sabel, The second industrial divide: possibilities for prosperity, 1984; Porter, The competitive advantage of nations, 1990). The hypothesis behind the geographical focus is that geographical proximity between actors promotes interaction and hence innovation. In EU, and also in Norway, this has been used actively as guidance in national and regional policy, where construction of innovation systems such as clusters and interorganizational networks are promoted and funded. To get organizations and institutions in a region to collaborate more is seen as the panacea for innovation, transformation and prosperity. However, companies often treat such constructed initiatives as an add-on to their ordinary, often long-lasting, business relationships between customers and suppliers (Håkansson et al., Business in networks, 2009, p. 13). This could imply that the necessary anchoring of such new innovation system initiatives with the companies’ own innovation processes is weak or missing. The terminology system points to the importance of the different elements (actors) in the system, their interrelatedness and their impact on each other (Meadows, Thinking in systems. A primer, 2009). An innovation system, like a network, cannot deliver innovation if the elements (i.e. the companies) of the systems don’t respond with related actions to the common endeavor. However, the different actors’ intraorganizational innovation processes are hardly mentioned in the innovation systems theories, thus lacking the important system feedback link between the intraorganizational innovation processes within the single company and the interorganizational innovation processes which are taking place in the collaborative initiative. In this article it is argued, supported by a case story, that attention to both of these processes and the nexus between them is needed in order to construct sustainable interorganizational innovation system initiatives. A model for this is proposed, based on a dual organization development process, encouraging system feedback loops and thereby bridging the single participating organization and the interorganizational collaborative initiative.     

CLT of wavelet estimator in semiparametric model with correlated errors

This paper considers the semiparametric regression model j/j= Xif3+g（U）+Vi（1 < i < n）, where（x_i,t_i） are known design points,/3 is an unknown slope parameter,g（·） is an unknown function, the correlated errors Vi=∑_j=-∞^∞c_je_i-jwith∑_j=-∞^∞|c_j|<∞,and e_i negatively associated random variables.Under appropriate conditions,the authors study the asymptotic normality for wavelet estimators ofβand g（·）.A simulation study is undertaken to investigate finite sample behavior of the estimators.     

A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials

This paper presents a new algorithm for computing the extended Hensel construction(EHC) of multivariate polynomials in main variable x and sub-variables u_1, u_2, ···, u_m over a number field K. This algorithm first constructs a set by using the resultant of two initial coprime factors w.r.t. x, and then obtains the Hensel factors by comparing the coefficients of x~i on both sides of an equation. Since the Hensel factors are polynomials of the main variable with coefficients in fraction field K(u_1, u_2, ···, u_m), the computation cost of handling rational functions can be high. Therefore,the authors use a method which multiplies resultant and removes the denominators of the rational functions. Unlike previously-developed algorithms that use interpolation functions or Gr?bner basis, the algorithm relies little on polynomial division, and avoids multiplying by different factors when removing the denominators of Hensel factors. All algorithms are implemented using Magma, a computational algebra system and experiments indicate that our algorithm is more efficient.     

The determination on weight hierarchies of <Emphasis Type="Italic">q</Emphasis>-ary linear codes of dimension 5 in class IV

The weight hierarchy of a linear [n; k; q] code C over GF(q) is the sequence (d ₁, d ₂, ···, d _k ) where d _r is the smallest support of any r-dimensional subcode of C. “Determining all possible weight hierarchies of general linear codes” is a basic theoretical issue and has important scientific significance in communication system. However, it is impossible for q-ary linear codes of dimension k when q and k are slightly larger, then a reasonable formulation of the problem is modified as: “Determine almost all weight hierarchies of general q-ary linear codes of dimension k”. In this paper, based on the finite projective geometry method, the authors study q-ary linear codes of dimension 5 in class IV, and find new necessary conditions of their weight hierarchies, and classify their weight hierarchies into 6 subclasses. The authors also develop and improve the method of the subspace set, thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV. It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes (classes III and VI), and break through the difficulties. Furthermore, the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough (not most tight nor best), so, it is important to excogitate further new necessary conditions for attacking and solving the k-dimensional problem.     

On the nonexistence of nontrivial small cycles of the µ function in 3x+1 conjecture

This paper studies the property of the recursive sequences in the 3x+ 1 conjecture.The authors introduce the concept ofμfunction,with which the 3x + 1 conjecture can be transformed into two other conjectures:one is eventually periodic conjecture of theμfunction and the other is periodic point conjecture.The authors prove that the 3x + 1 conjecture is equivalent to the two conjectures above.In 2007,J.L.Simons proved the non-existence of nontrivial 2-cycle for the T function.In this paper,the authors prove that theμfunction has no l-periodic points for 2≤l≤12.In 2005, J.L.Simons and B.M.M de Weger proved that there is no nontrivial 2-cycle for the T function for l≤68,and in this paper,the authors prove that there is no nontrivial l-cycle for theμfunction for 2≤l≤102.     

Systemic Approaches to Managing Across the Gap in the Public Sector: Results of an Action Research Programme

This paper tells the story and conclusions of a 1 year research project which took place over the calendar year of 2006. It was undertaken within a local government authority (or Local Authority—LA) in the UK. The specific research question to be answered was: “Can the application of systems methods in the LA aid Authority staff in developing and enhancing their professional practice?” A supplementary question arising was: “Can such learning be of wider value to other sections of the public sector (for example in other regions of local government or the health sector)?” In the process of the year 91 separate action research interactions took place. The research comes to three systemically linked findings: Firstly, LA middle managers are often caught between two realities ... strategic initiatives and operational demands. In the gap between these two realities they experience change in many guises but most critically in terms of government directives, ICT initiatives and restructuring. Despite this complexity managers did not appear to always have adequate tools to deal with issues arising in their context. Secondly, an assessment matrix developed originally at the Open University is a valuable tool for assessing the systemisism and reflective capacities of staff and, thirdly, a new, blended hybrid training programme to develop systemic reflective practitioners able to manage across the strategy/operations gap was developed and pilot tested in 2007. This programme shows signs of providing enhanced professional practice and, at the time of writing, is being further piloted with a view to establishing its wider applicability within the public sector.     

Robust H∞ control for networked control systems

The robust H∞ control for networked control systems with both stochastic network-induced delay and data packet dropout is studied. When data are transmitted over network, the stochastic data packet dropout process can be described by a two-state Markov chain. The networked control systems with stochastic network-induced delay and data packet dropout are modeled as a discrete time Markov jump linear system with two operation modes. The sufficient condition of robust H∞ control for networked control systems stabilized by state feedback controller is presented in terms of linear matrix inequality. The state feedback controller can be constructed via the solution of a set of linear matrix inequalities. An example is given to verify the effectiveness of the method proposed.     

On nodal line of the second eigenfunction of the Laplacian over concave domains in ℝ2

In this note, the Payne’s conjecture from convex domains to concave domains is generalized. It is shown that the nodal line N of the second eigenfunction of the Laplacian over some simply connected concave domain Ω in ?² must intersect the boundary ?Ω at exactly two points.