In this paper we study a class of optimal dividend and investment problems assuming that the underlying reserve process follows the Sparre Andersen model, that is, the claim frequency is a “renewal” process, rather than a standard compound Poisson process. The main feature of such problems is that the underlying reserve dynamics, even in its simplest form, is no longer Markovian. By using the b...

A new method to decide the invertibility of a given high-dimensional function over a domain is presented. The problem arises in the field of verified solution of differential algebraic equations (DAEs) related to the need to perform projections of certain constraint manifolds over large domains. The question of invertibility is reduced to a verified linear algebra problem involving first partia...

This paper presents using a new modified homotopy perturbation method (NHPM) for solving linear and nonlinear systems of differential-algebraic equations (DAEs) of index one or higher index without index reduction. By using this scheme, explicit exact solution is calculated in the form of a convergent power series with easily computable components. Some examples are given to illustrate the simp...

This chapter presents a review of applications of structural equation modeling (SEM) published in psychological research journals in recent years. We focus first on the variety of research designs and substantive issues to which SEM can be applied productively. We then discuss a number of methodological problems and issues of concern that characterize some of this literature. Although it is cle...

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...