Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the possibility of approximation. Is the given family of functions from which we plan to approximate dense in the set of functions we wish to approximate? In this work we survey some of the main density results an...

The railway transportation planning under the fuzzy environment is investigated in this paper. As a main result, a new modeling method, called minimum risk chance-constrained model, is presented based on the credibility measure. For the convenience ofs olving the mathematical model, the crisp equivalents ofc hance functions are analyzed under the condition that the involved fuzzy parameter...

Many of the physical phenomena, like friction, backlash, drag, and etc., which appear in mechanical systems are inherently nonlinear and have destructive effects on the control systems behavior. Generally, they are modeled by hard nonlinearities. In this paper, two different methods are proposed to cope with the effects of hard nonlinearities which exist in friction various models. Simple inver...

This article proposes a fast and accurate expansion-iterative method for solving second kind linear Volterra integral equations. The method is based on a special representation of vector forms of triangular functions (TFs) and their operational matrix of integration. By using this approach, solving the integral equation reduces to solve a recurrence relation. The approximate solution of integra...

In this paper Legendre wavelet bases have been used for finding approximate solutions to singular boundary value problems arising in physiology. When the number of basis functions are increased the algebraic system of equations would be ill-conditioned (because of the singularity), to overcome this for large $M$, we use some kind of Tikhonov regularization. Examples from applied sciences are pr...

– Briefly we’ll show in Theorem 1.2 (sketched last time) that the representation question is essential — sometimes, by choosing the wrong function class, you can get a bad error, even though there are simple predictors that get 0 error. – Continuous fit I: box approximations; namely, we’ll show that a variety of functions can approximate continuous functions by showing they approximate piecewis...