About twenty years ago the measure of smoothness ω φ (f, t) was introduced and related to the rate of polynomial approximation. In this article we survey developments about this and related concepts since that time. MSC: 41A10, 41A17, 41A25, 41A27, 41A30, 41A36, 41A40, 41A50, 41A63, 26A15, 26B35, 26B05, 42C05, 26A51, 26A33, 46E35 keywords: Moduli of smoothness, K-functionals, realization functi...

About twenty years ago the measure of smoothness ω φ (f, t) was introduced and related to the rate of polynomial approximation. In this article we survey developments about this and related concepts since that time. MSC: 41A10, 41A17, 41A25, 41A27, 41A30, 41A36, 41A40, 41A50, 41A63, 26A15, 26B35, 26B05, 42C05, 26A51, 26A33, 46E35 keywords: Moduli of smoothness, K-functionals, realization functi...

A novel theory for cell di erentiation is proposed, based on simulations with interacting arti cial cells which have metabolic networks within, and divide into two when the nal product is accumulated. Results of simulations with coupled chemical networks and division process lead to the following scenario of the di erentiation: Up to some numbers of cells, divisions bring about almost identical...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...