One of the efficient and powerful schemes to solve linear and nonlinear equations is homotopy analysis method (HAM). In this work, we obtain the approximate solution of a system of partial differential equations (PDEs) by means of HAM. For this purpose, we develop the concept of HAM for a system of PDEs as a matrix form. Then, we prove the convergence theorem and apply the proposed method to fi...

An adaptive perceptron with multilinear couplings is introduced. While an adap-tive perceptron exhibits severe shortcomings if it is applied to complex tasks, this is not so for the adaptive multilinear perceptron.

When approximating a space curve, it is natural to consider whether the knot type of the original curve is preserved in the approximant. This preservation is of strong contemporary interest in computer graphics and visualization. We establish a criterion to preserve knot type under approximation that relies upon convergence in both distance and total curvature.

Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of T0 spaces instead of restricting to posets. In this paper, we respond to this calling with an attempt to formulate a topological version of the Scott Convergence Theorem, i.e., order-theoretic characterisation of those posets for which the Scott-co...

Three examples are provided which demonstrate that “convergence in probability” versions of the Toeplitz lemma, the Cesàro mean convergence theorem, and the Kronecker lemma can fail. “Mean convergence” versions of the Toeplitz lemma, Cesàro mean convergence theorem, and the Kronecker lemma are presented and a general mean convergence theorem for a normed sum of independent random variables is e...