In this work, we propose an approach for computing the compromised solution of an LR fuzzy linear system by using of a ranking function when the coefficient matrix is a crisp mn matrix. To do this, we use expected interval to find an LR fuzzy vector, X , such that the vector (AX ) has the least distance from (b) in 1 norm and the 1 cut of X satisfies the crisp linear system AX = b ...

1 This paper studies nonparametric estimation of conditional moment restrictions in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum distance (PSMD) estima-tors, which are minimizers of a penalized empirical minimum dista...

People often evaluate story or situation outcomes by mentally altering preceding events and simulating what impact this would have had on the outcome. This mental simdation process plays an important role in cognition and emotion. Kahneman and Tversky (1982) and Kahneman and Miller (1986) have proposed that a fundamental rule governing mental simulation is that people tend to change exceptional...

We consider the problem of fitting an n × n distance matrix M by a tree metric T . We give a factor O(min{n, (k log n)}) approximation algorithm for finding the closest ultrametric T under the Lp norm, i.e. T minimizes ‖T, M‖p. Here, k is the number of distinct distances in M . Combined with the results of [1], our algorithms imply the same factor approximation for finding the closest tree metr...

This paper studies nonparametric estimation of conditional moment models in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum distance (PSMD) estimators which are minimizers of a penalized empirical minimum distance criter...

We consider the problem of approximation of matrix functions of class L on the unit circle by matrix functions analytic in the unit disk in the norm of L, 2 ≤ p < ∞. For an m × n matrix function Φ in L, we consider the Hankel operator HΦ : H(C) → H −(C), 1/p + 1/q = 1/2. It turns out that the space of m × n matrix functions in L splits into two subclasses: the set of respectable matrix function...

Let e(x, y, λ) be the spectral function and χλ the unit band spectral projection operator, with respect to the LaplaceBeltrami operator ∆M on a closed Riemannian manifold M . We firstly review the one-term asymptotic formula of e(x, x, λ) as λ → ∞ by Hörmander (1968) and the one of ∂ x ∂ β y e(x, y, λ)|x=y as λ → ∞ in a geodesic normal coordinate chart by the author (2004) and the sharp asympto...

Minimum residual norm iterative methods for solving linear systems Ax = b can be viewed as, and are often implemented as, sequences of least squares problems involving Krylov subspaces of increasing dimensions. The minimum residual method (MINRES) [C. Paige and M. Saunders, SIAM J. Numer. Anal., 12 (1975), pp. 617–629] and generalized minimum residual method (GMRES) [Y. Saad and M. Schultz, SIA...

In the recent past Kernelized Fuzzy C-Means clustering technique has earned popularity especially in the machine learning community. This technique has been derived from the conventional Fuzzy C-Means clustering technique of Bezdek by defining the vector norm with the Gaussian Radial Basic Function instead of a Euclidean distance. Subsequently the fuzzy cluster centroids and the partition matri...

Given a compact connected n-dimensional Riemannian manifold, we investigate the smoothness of optimal transport map between smooth densities with respect to squared distance cost. The is characterized by exp(gradu), where potential function u satisfies Monge–Ampère type equation. Delanoë [7] showed on surfaces when scalar curvature close 1 in C 2 norm. In this work, study regularity issue manif...