Two-scale finite element Green’s function approximations with applications to electrostatic potential computation

<正> In this paper,a two-scale finite element approach is proposed and analyzed for approximationsof Green's function in three-dimensions.This approach is based on a two-scale finite elementspace defined,respectively,on the whole domain with size H and on some subdomain containing singularpoints with size h (h H).It is shown that this two-scale discretization approach is very efficient.In particular,the two-scale discretization approach is applied to solve Poisson-Boltzmann equationssuccessfully.     

Removable ears of 1-extendable graphs

<正> Carvalho,Lucchesi and Murty proved that any 1-extendable graph G different from K_2and C_(2n)has at least Δ(G)edge-disjoint removable ears,and any brick G distinct from K_4 and■hasat least Δ(G)-2 removable edges,where Δ(G)denotes the maximum degree of G.In this paper,weimprove the lower bounds for numbers of removable ears and removable edges of 1-extendable graphs.It is proved that any 1-extendable graph G different from K_2 and C_(2n)has at least χ′(G)edge-disjointremovable ears,and any brick G distinct from K_4 and■has at least χ′(G)-2 removable edges,whereχ′(G)denotes the edge-chromatic number of G.     

Multilevel Innovation in Remote Networked Schools

Small remote rural schools in Quebec face an ongoing challenge to provide similar quality educational services than bigger schools. Since 2002, the Remote Network Schools (RNS) initiative afforded schools the opportunity to reinvent their practice by using online tools to experience collaborative learning activities with other remote schools. Teachers and students experienced quality learning and demonstrated agency by implementing the RNS in their context. Measures include: diversity of learning activities, quality of online classroom interactions, changes in teacher beliefs, and shifts in teacher and student roles. Our results show that it is a viable operating method for such schools and that other schools could contemplate implementing such innovative practices.     

Nonlinear Langevin model with product stochasticity for biological networks: The case of the Schnakenberg model

Langevin equation is widely used to study the stochastic effects in molecular networks, as it often approximates well the underlying chemical master equation. However, frequently it is not clear when such an approximation is applicable and when it breaks down. This paper studies the simple Schnakenberg model consisting of three reversible reactions and two molecular species whose concentrations vary. To reduce the residual errors from the conventional formulation of the Langevin equation, the authors propose to explicitly model the effective coupling between macroscopic concentrations of different molecular species. The results show that this formulation is effective in correcting residual errors from the original uncoupled Langevin equation and can approximate the underlying chemical master equation very accurately.     

Optimal control of multisolution ordinary differential equations in the absence of convexity

<正> In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of convexity.To overcome the difficulty that thecorresponding approximate optimal control problem may have no solution,relaxed controls are introduced.With the help of relaxation theory,Pontryagin's maximum principle for the optimal pairs ofthe original control problem is obtained.In the end of this paper,the authors discuss the applicationof the maximum principle by an example.     

Interior penalty bilinear IFE discontinuous Galerkin methods for elliptic equations with discontinuous coefficient

<正> This paper applies bilinear immersed finite elements (IFEs) in the interior penalty discontinuousGalerkin (DG) methods for solving a second order elliptic equation with discontinuous coefficient.A discontinuous bilinear IFE space is constructed and applied to both the symmetric and nonsymmetricinterior penalty DG formulations.The new methods can solve an interface problem on a Cartesianmesh independent of the interface with local refinement at any locations needed even if the interfacehas a nontrivial geometry.Numerical examples are provided to show features of these methods.     

Stock loan valuation under a regime-switching model with mean-reverting and finite maturity

<正> Stock loans are business contracts between borrowers and lenders in which the borroweruses shares of stock as collateral for the loan.Since the value of the collateral is subject to wide andfrequent price swings,valuing such a transaction behaves more like an option pricing problem thana debt valuation problem.This paper will list,prove,and analyze formulas for stock loan valuationwith finite horizon under various stock models,including classical geometric Brownian motion,meanreverting,and two-state regime-switching with both mean-reverting and geometric Brownian motionstates.Numerical examples are reported to illustrate the results.     

Birds of a Feather Protest Together: Theorizing Self-Organizing Political Protests with Flock Theory

The current research theorizes decentralized and self-organized political protests via flock theory (Rosen 2002), a theory of emergent self-organization in communicative human interaction. Flock theory draws from a theoretical basis of emergence and self-organizing systems, and is presented as a theory of decentralized communication structures. Focusing on the optimization of decentralized networks and roadmap based coordination of organizationally homopholous foci; the current theory poses a model of human interaction that captures the potentially egalitarian effects of cooperative evolution and collective action. Case studies of two separate decentralized political protests against Korean government and FARC are offered as evidences of such phenomena.     

Convergence rates of Markov chain approximation methods for controlled diffusions with stopping

<正> This work is concerned with rates of convergence of numerical methods using Markov chainapproximation for controlled diffusions with stopping (the first exit time from a bounded region).In lieuof considering the associated finite difference schemes for Hamilton-Jacobi-Bellman (HJB) equations,a purely probabilistic approach is used.There is an added difficulty due to the boundary condition,which requires the continuity of the first exit time with respect to the discrete parameter.To prove theconvergence of the algorithm by Markov chain approximation method,a tangency problem might arise.A common approach uses certain conditions to avoid the tangency problem.Here,by modifying thevalue function,it is demonstrated that the tangency problem will not arise in the sense of convergencein probability and in L~1.In addition,controlled diffusions with a discount factor is also treated.     

Research and Reflection: Potential Impact on the Professional Development of Undergraduate Occupational Therapy Students

In occupational therapy education in South Africa, community service (CS) focuses learning opportunities during fieldwork placements. CS therefore enabled the researcher to utilise successive small scale research projects to guide learning of students during fieldwork while simultaneously developing the occupational therapy service at a residential care facility. This community setting provided a powerful environment through which research, in combination with opportunities for reflection, contributed to nurturing skills needed by these future health professionals. A technical action research (AR) approach incorporated AR cycles and opportunities for structured reflection. Therefore situations were created for the students to embrace experiential learning. Experiential learning in the form of anticipatory reflection, reflection-in-action, reflection on reflection and retrospective reflection impacted on the quality of the students’ work. Besides encouraging unique leaning opportunities for students when engaging in research during their fieldwork placement, engagement in AR cycles simultaneously improved service delivery to residents in the facility. Key benefits of this investigation were that fieldwork education utilising AR cycles within a CS situation promoted students to identify voids in their theoretical background as well as practice skills; to apply reflective practice that could contribute to their personal and professional development; and to utilize learning opportunities optimally. Despite positive gains showed by this study, the role of power relations between the researcher as fieldwork educator and the students prohibited the AR cycles from being more emancipatory in nature and should be addressed in follow-up studies.