A set of parametric equations of an algebraic curve or surface is called normal, if all the points of the curve or the surface can be given by the parametric equations. In this paper, we present a method to decide whether a set of parametric equations is normal. In addition, we give some simple criteria for a set of parametric equations to be normal. As an application, we present a method to fi...

Since the inception of intuitionistic fuzzy sets in 1986, many authors have proposed different methods for ranking intuitionistic fuzzy numbers (IFNs). How ever, due to the complexity of the problem, a method which gives a satisfactory result to all situations is a challenging task. Most of them contained some shortcomings, such as requirement of complicated calculations, inconsistency with hum...

Accurate estimation of an underlying function and its derivatives is one of the central problems in statistics. Parametric forms are often proposed based on the expert opinion or prior knowledge of the underlying function. However, these strict parametric assumptions may result in biased estimates when they are not completely accurate. Meanwhile, nonparametric smoothing methods, which do not im...

Since the seminal work of Gilboa and Schmeidler [28, p. 142] a relation between decision making under ambiguity and robust Bayesian statistics has been hinted at, and indeed immediate similarities are quite evident. At the same time, a formal treatment of this topic and a complete characterization of the relation between the two approaches is still missing. The object of this paper is to …ll th...

Non-parametric graphical models, embedded in reproducing kernel Hilbert spaces, provide a framework to model multi-modal and arbitrary multi-variate distributions, which are essential when modeling complex protein structures. Non-parametric belief propagation requires the structure of the graphical model to be known a priori. Currently there are nonparametric structure learning algorithms avail...

This paper characterizes completely the behavior of the logarithmic barrier method under a standard second order condition, strict (multivalued) complementarity and MFCQ at a local minimizer. We present direct proofs, based on certain key estimates and few well-known facts on linear and parametric programming, in order to verify existence and Lipschitzian convergence of local primal-dual soluti...

Euler deconvolution has come into wide use as an aid to interpreting profile or gridded magnetic survey data. It provides automatic estimates of source location and depth. In doing this, it uses a Structural Index (SI) to characterise families of source types. Euler deconvolution can be usefully applied to gravity data. For simple bodies, the gravity SI is one less than the magnetic SI. For mor...

in this paper, we propose a parametric uniform approximation method to solve np-hard absolute value equations. for this, we uniformly approximate absolute value in such a way that the nonsmooth absolute value equation can be formulated as a smooth nonlinear equation. by solving the parametric smooth nonlinear equation using newton method, for a decreasing sequence of parameters, we can get the ...

Consider two random variables contaminated by two unknown transformations. The aim of this paper is to test the equality of those transformations. Two cases are distinguished: first, the two random variables have known distributions. Second, they are unknown but observed before contaminations. We propose a nonparametric test statistic based on empirical cumulative distribution functions. Monte ...

In this paper, a parametric model order reduction (pMOR) technique is proposed to find a simplified system representation of a large-scale and complex thermal system. The main principle behind this technique is that any change of the physical parameters in the high-fidelity model can be updated directly in the simplified model. For deriving the parametric reduced model, a Krylov subspace method...