For a smooth bivariate function defined on a general domain with arbitrary shape, it is difficult to do Fourier approximation or wavelet approximation. In order to solve these problems, in this paper, we give an extension of the bivariate function on a general domain with arbitrary shape to a smooth, periodic function in the whole space or to a smooth, compactly supported function in the whole ...

A reproducing kernel Hilbert space restricts the space of functions to smooth functions and has structure for function approximation and some aspects in learning theory. In this paper, the solution of an integral equation of the third kind is constructed analytically using a new method. The analytical solution is represented in the form of series in the reproducing kernel space. Some numerical ...

A filled function approach is proposed for solving a non-smooth unconstrained global optimization problem. First, the definition of filled function in Zhang 2009 for smooth global optimization is extended to non-smooth case and a new one is put forwarded. Then, a novel filled function is proposed for non-smooth the global optimization and a corresponding nonsmooth algorithm based on the filled ...

We describe the fundamentals of algorithms for minimizing a smooth nonlinear function, and extensions of these methods to the sum of a smooth function and a convex nonsmooth function. Such objective functions are ubiquitous in data analysis applications, as we illustrate using several examples. We discuss methods that make use of gradient (first-order) information about the smooth part of the f...

The backing of the fuzzy ideal is normal ideal in some ring and in same time there fuzzy set whose is not fuzzy ideal and it backing set is ideal, i.e., it crisp is normal ideal. Consequently, in this paper we constructing a fuzziness function which defined on fuzzy sets and assigns membership grade for every fuzzy set whose it backing set are crisp ideal. Now, Let  be collection of all fuzzy s...

In this paper, we consider smooth convex approximations to the maximum eigenvalue function. To make it applicable to a wide class of applications, the study is conducted on the composite function of the maximum eigenvalue function and a linear operator mapping m to n, the space of n-by-n symmetric matrices. The composite function in turn is the natural objective function of minimizing the maxim...

Semi-supervised Support vector machine has become an increasingly popular tool for machine learning due to its wide applicability. Unlike SVM, their formulation leads to a non-smooth non-convex optimization problem. In 2005, Chapelle and Zien used a Gaussian approximation as a smooth function and presented ∇TSVM. In this paper, we propose a smooth piecewise function and research smooth piecewis...

background: neurotologic signs and symptoms, especially vestibular symptoms are common in migrainous patients. involvement of the visual system in migrainures has received a great deal of attention in recent years, but the oculomotor part of the visual system has been largely ignored. the goal of this study was to investigate some parts of the central vestibular system using the oculomotor part...