{ We develop a framework (employing scaling functions) for the construction of multi-step quasi-Newton methods (for unconstrained optimization) which utilize values of the objective function. The methods are constructed via interpolants of the m + 1 most recent iterates / gradient evaluations, and possess a free parameter which introduces an additional degree of exibility. This permits the inte...

We show that the operational transconductance amplifier (OTA), as the active element in basic bnilding blocks, can be efficiently used for programmable nonlinear continuous-time function synthesis. Two efficient nonlinear function synthesis approaches are presented. The first approach is a ratiossaf approximation and tbe second is a piecewise.linear approach. Test circuits have been fabricated ...

We consider the problem of estimating a smooth function from noisy, sampled data. We use orthonormal bases of compactly supported wavelets to constriuct nonlinear function estimates which can significantly outperform evey linear method (kernel, smoothing spline, sieve, ...). Our estimates are simple nonlinear functions of the empirical wavelet coefficients and are asymptotically minimax over ce...

We present a comprehensive investigation into the complexity of a new private key storage apparatus: a novel silicon photonic physical unclonable function (PUF) based on ultrafast nonlinear optical interactions in a chaotic silicon microcavity that is both unclonable and impossible to emulate. This device provides remarkable improvements to total information content (raw cryptographic material)...

Dealing with a question of Lahiri [6] we study the uniqueness problem of meromorphic functions concerning two nonlinear differential polynomials sharing a small function. Our results will not only improve and supplement the results of Lin-Yi [16], Lahiri Sarkar [12] but also improve and supplement a very recent result of the first author [1].

Nonlinear systems, defined by a system of ODE’s, usually contain nonlinear terms. Under some circumstances these terms can be locally approximated by linear factors and by discretization can be transformed in the sequence of (hyperbolic) Iterated Function Systems (IFS). Then, this IFS generate a unique attractor that uses as a kind of characteristic set that reflects the dynamics in the vicinit...

The focus of this paper is using nonparametric transfer function models in forecasting. Nonparametric smoothing methods are used to model the relationship between variables (the transfer function) and the noise is modeled as an Autoregressive Moving Average (ARMA) process. The transfer function is estimated jointly with the ARMA parameters. Nonparametric smoothing methods are flexible thus can ...

It is attempted to extend a two-step without memory method to it's with memory. Then, a new two-step derivative free class of without memory methods, requiring three function evaluations per step, is suggested by using a convenient weight function for solving nonlinear equations. Eventually, we obtain a new class of methods by employing a self-accelerating parameter calculated in each iterative...

In many manufacturing processes, the quality of a product is characterized by a non-linear relationship between a dependent variable and one or more independent variables. Using nonlinear regression for monitoring nonlinear profiles have been proposed in the literature of profile monitoring which is faced with two problems 1) the distribution of regression coefficients in small samples is unkno...