Although quasicrystals have been studied for 25 years, there are many open questions concerning their stability: What is the role of phason fluctuations? Do quasicrystals transform into periodic crystals at low temperature? If yes, by what mechanisms? We address these questions here for a simple two-dimensional model system, a monatomic decagonal quasicrystal, which is stabilized by the Lennard...

We consider the problem of approximating a function f from an Euclidean domain to a manifold M by scattered samples [Formula: see text], where the data sites [Formula: see text] are assumed to be locally close but can otherwise be far apart points scattered throughout the domain. We introduce a natural approximant based on combining the moving least square method and the Karcher mean. We prove ...

Padé approximant is exploited for an efficient sum-over-poles decomposition of Fermi and Bose functions. The resulting poles are all pure imaginary and can therefore be used to define Padé frequencies, in analogy with the celebrated Matsubara frequencies. The proposed Padé spectrum decomposition is shown to be equivalent to a truncated continued fraction. It converges significantly faster than ...

The classical Chebyshev theory of best uniform approximation to continuous functions by polynomials of degree <n was initiated by Chebyshev in [2]. This theory has a distinct advantage over the corresponding ones for L4-norms, 1 < q < co, in that the unique best approximant is characterized by a remarkable geometric property. Let f be a realvalued function, continuous on [0, 11, and, for n = 0,...

Consider a triangulation of the xy plane, and a general surface z = f(x; y). The points of the triangle, when lifted to the surface, form a linear spline approximation to the surface. We are interested in the error between the surface and the linear approximant. In fact, we are interested in building triangulations in the plane such that the induced linear approximant is near-optimal with respe...

While the concept of Padé approximant is essentially several centuries old, its multivariate version dates only from the early seventies. In the last century many univariate convergence results were proven, describing the approximation power for several function classes. It is not our aim to give a general review of the univariate case, but to discuss only these theorems that have a multivariat...

This paper proposes a unified frame work for identification and control using time moments(TM) in which delta operator is used. Dynamic systems modelling with delta operator provides a unified framework in rapprochement between discrete-time systems and its continuous-time counterpart at fast sampling The theory of delta time moments(DTM) is utilized to develop algorithms for load frequency con...

A problem from a class of unsteady plane potential flows with free boundary is considered. The entire occupied by the liquid free, and zero pressure maintained. There are neither external nor capillary forces. motion driven inertia. parameters prescribed at initial time velocity field domain fluid. task to determine these subsequent instants. solution sought in form power series, which then sum...

Given a function f holomorphic at infinity, the n-th diagonal Padé approximant to f, denoted by [n/n]f, is a rational function of type (n,n) that has the highest order of contact with f at infinity. Nuttall’s theorem provides an asymptotic formula for the error of approximation f− [n/n]f in the case where f is the Cauchy integral of a smooth density with respect to the arcsine distribution on [...