In this study, the momentum and energy equations of laminar flow of a non-Newtonian fluid are solved in an axisymmetric porous channel using the least square and Galerkin methods. The bottom plate is heated by an external hot gas, and a coolant fluid is injected into the channel from the upper plate. The arising nonlinear coupled partial differential equations are reduced to a set of coupled no...

Sauerland (1999) used such examples as the basis of an argument in favor of the traditional representation of pronouns as indexed variables, and against Jacobson’s Variable Free Semantics (VFS). In her response, Jacobson defends the VFS framework and argues that it can account for a broader range of examples than Sauerland’s proposal. In particular, Jacobson proposes that we can account for suc...

The recent discovery of boron triangular nanotubes competes with carbon in many respects. The closed form of M-polynomial of nanotubes produces closed forms of many degree-based topological indices which are numerical parameters of the structure and, in combination, determine properties of the concerned nanotubes. In this report, we give M-polynomials of boron triangular nanotubes and recover m...

In this paper, a new kind of repairable system with repairman vacation and warning device is discussed, in which the delayed vacation rate and failure rates are functions related to system working time. The system model is established by using probability analysis method, which then is translated into a initial value problem of a class of abstract semi-linear evolution equation in a suitable Ba...

In this paper, we solve higher index differential algebraic equations (DAEs) by transforming them into integral algebraic equations (IAEs). We apply collocation methods on continuous piece-wise polynomials space to solve the obtained higher index IAEs. The efficiency of the given method is improved by using a recursive formula for computing the integral part. Finally, we apply the obtained algo...

Quasi-linear differential-algebraic equations (DAEs) are essential tools for modeling dynamical processes, e.g. for mechanical systems, electrical circuits or chemical reactions. These models are in general of higher index and contain so called hidden constraints which lead to instabilities and order reductions during numerical integration of the model equations. In this article we consider dyn...

Proper reparametrization is a basic simplifying process for rational parameterized curves. There are complete results proposed for the curves with exact coefficients but few papers discuss the situations with numerical coefficients which have many practical applications. In this paper, we deal with mathematical objects that are assumed to be given approximately. The approximate improper index i...