The two main results in this paper are analogues of the Stone-Weierstrass theorem for real-valued functions, obtained by using different function space topologies. The first (Theorem 2.3) is a Stone-Weierstrass theorem for unbounded functions. The second (Theorem 3.6) is a theorem for bounded functions ; it is stronger than the usual theorem because the topology is larger than the uniform topol...

A new elliptic equation rational expansion method is presented by a new general ansätz, which is a direct and unified algebraic method for constructing multiple and more general travelling wave solution for nonlinear partial differential equation and implemented in a computer algebraic system. The proposed method is applied to consider the shallow long wave approximate equation and obtains rich...

this paper consists of three sections. in the first section an efficient method is used for decomposition of the canonical matrices associated with repetitive structures. to this end, cylindrical coordinate system, as well as a special numbering scheme were employed. in the second section, divide and conquer method have been used for eigensolution of these structures, where the matrices are in ...

Abstract Weierstrass semigroups are well known along the literature. We present a new family of non-Weierstrass which can be written as an intersection semigroups. In addition, we provide methods for computing with genus large desired.

The Weierstrass nowhere differentiable function, and functions constructed from similar infinite series, have been studied often as examples of functions whose graph is a fractal. Though there is a simple formula for the Hausdorff dimension of the graph which is widely accepted, it has not been rigorously proved to hold. We prove that if arbitrary phases are included in each term of the summati...

In this paper, the problem of blind deconvolution of dynamical systems is considered using a state space approach. A balanced parameterized canonical form is used as a model for the underlying dynamical system instead of the more common controller or observable canonical form. The results are compared with those obtained using a controller canonical form. It is shown experimentally that using t...