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...

Homotopy Perturbation Method is an effective method to find a solution of a nonlinear differential equation, subjected to a set of boundary condition. In this method a nonlinear and complex differential equation is transformed to series of linear and nonlinear and almost simpler differential equations. These set of equations are then solved secularly. Finally a linear combination of the solutio...

In order to investigate the effects of non-linear springs in vibrating behavior of vehicles, the independent suspension of conventional vehicles could be modeled as a non-linear single degree of freedom system. The equation of motion for the system would be a non-linear third order ordinary differential equation, when considering the elasticity of rubber bushings in joints of shock absorber. It...

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...

A new method for solving algebraic equation systems common in cryptanalysis is proposed. Our method differs from the others in that the equations are not represented as multivariate polynomials, but as a system of Multiple Right Hand Sides linear equations. The method was tested on scaled versions of the AES. The results overcome significantly what was previously achieved with Gröbner Basis rel...

T-algebra is an interactive learning environment for step-by-step solving of algebra problems in four areas of mathematics, including linear equations. To make the diagnosis of mistakes more complete and the program more intelligent we designed our own rule dialogue. Each solution step in T-algebra consists of three stages: selection of the transformation rule, marking the parts of expression, ...