We consider the 2-dimensional quasi-geostrophic equation with supercritical dissipation and dispersive forcing in the whole space. When the dispersive amplitude parameter is large enough, we prove the global well-posedness of strong solution to the equation with large initial data. We also show the strong convergence result as the amplitude parameter goes to ∞. Both results rely on the Strichar...

Because of the global warming and the rising sea level, residents living in southwestern coastland, Taiwan are faced with the submerged land and may move to higher elevation area. It is desirable to discuss the key consideration factor for selecting the migration location under five dimensions of security”, “health”, “convenience”, “comfort” and “socio-economic” based on the document reviews. T...

Geometric reduction methods for differential-algebraic equations (DAEs) aim at an iterative reduction of the problem to an explicit ODE on a lower-dimensional submanifold of the so-called semistate space. This approach usually relies on certain algebraic (typically constant-rank) conditions holding at every reduction step. When these conditions are met the DAE is called regular. We discuss in t...

In the process of designing a tensegrity system, some constraints are usually introduced for geometry and/or forces to ensure uniqueness of the solution, because the tensegrity systems are underdetermined in most cases. In this paper, a new approach is presented to enable designers to specify independent sets of axial forces and nodal coordinates consecutively, under the equilibrium conditions ...

For linear di erential algebraic equations of tractability index 1 the notion of the adjoint equation is analysed in full detail. Its solvability is shown at the lowest possible smoothness. The fundamental matrices of both equations are de ned and their relationships are characterized.

In this paper we analyse the algebraic properties over the field GF(2) of the addition modulo 2. We look at implicit quadratic equations describing this operation, and at probabilistic conditional linear equations. We show that the addition modulo 2 can be partly or totally linearized when the output is fixed, and this for a large family of outputs. We apply these results to analyse the resista...

Self-assessment and study choice are two important metacognitive processes involved in Self-Regulated Learning. Yet not much empirical work has been conducted in ITSs to investigate how we can best support these two processes and improve students’ learning outcomes. The present work redesigned an Open Learner Model (OLM) with three features aimed at supporting self-assessment (self-assessment p...

This article gives sharp convergence results for stiffly accurate colloca-tion methods as applied to differential-algebraic equations (DAE's) of index 3 in Hessenberg form, proving partially a conjecture of Hairer, Lubich, and Roche.

Despite a steady supply of equipment and continuous training, teachers’ use of computers for instruction seems to be limited. Whether the problem is due to teachers’ ability or usage of computers for instruction is not well understood. In order to better understand the role of ability and usage in technology integration, teachers’ proficiency of technology integration was evaluated by separate ...

In this paper we investigate the optimal risk control and dividend distribution problem for a diffusion model with a terminal value. Usually the insurer cedes risk by means of a reinsurance contract, and pays dividends out dynamically from the surplus. Consider that the insurer is trying to balance risk control and dividend payout in terms of reinsurance and dividend distribution policies. Then...