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...

In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than sol...

This paper is concerned with solving Cauchy problem for parabolic equation by minimizing an energy-like error functional and by taking into account noisy Cauchy data. After giving some fundamental results, numerical convergence analysis of the energy-like minimization method is carried out and leads to an adapted stopping criterion depending on noise rate for the minimization process. Numerical...

This paper explores the development of students' knowledge of mathematical procedures. Students' tendency to develop rote knowledge of procedures has been widely commented on. I postulate an alternative, more "intelligent" endpoint for the development of procedural knowledge, where students choose to deviate from established solving patterns on particular problems for greater efficiency. The pu...

We study the temporal formation of quantum-mechanical bound states within a one-dimensional attractive square-well potential by first solving time-independent Schr\"odinger equation and then studying time-dependent system with an external potential. For this we introduce Gaussian potentials different spatial extensions generalize description also for subsequent pulses random noisy potentials. O...

This paper is concerned with solving the Cauchy problem for an elliptic equation by minimizing an energy-like error functional and by taking into account noisy Cauchy data. After giving some fundamental results, numerical convergence analysis of the energy-like minimization method is carried out and leads to adapted stopping criteria for the minimization process depending on the noise rate. Num...

In this paper, an iterative method is proposed for solving large general Sylvester matrix equation $AXB+CXD = E$, where $A in R^{ntimes n}$ , $C in R^{ntimes n}$ , $B in R^{stimes s}$ and  $D in R^{stimes s}$ are given matrices and $X in R^{stimes s}$  is the unknown matrix. We present a global conjugate gradient (GL-CG) algo- rithm for solving linear system of equations with multiple right-han...

This paper presents IMHOTEP-SMT, a solver for the detection and mitigation of sensor attacks in cyber-physical systems. IMHOTEP-SMT receives as inputs a description of the physical system in the form of a linear difference equation, the system input (control) signal, and a set of output (sensor) measurements that can be noisy and corrupted by a malicious attacker. The output is the solution of ...