Let N be a connected and simply connected 2-step nilpotent Lie group and K be a compact subgroup of Aut(N). We say that (K,N) is a Gelfand pair when the set of integrable K-invariant functions on N forms an abelian algebra under convolution. In this paper, we construct a one-to-one correspondence between the set ∆(K, N) of bounded spherical functions for such a Gelfand pair and a set A(K, N) of...

The problem of finding periodic orbits of dynamical systems numerically is considered. It is shown that if a convergent, strongly stable, multi-step method is employed then under some suitable conditions, there exist invariant curves. The result also shows that the rates of convergence toward the invariant curves are roughly the same for different methods and different step sizes. Introduction....

This paper represents another step in overcoming a drawback of K-Means, its lack of defense against noisy features, using feature weights in the criterion. The Weighted K-Means method by Huang et al. (2008, 2004, 2005) [5–7] is extended to the corresponding Minkowski metric for measuring distances. Under Minkowski metric the feature weights become intuitively appealing feature rescaling factors...

This paper introduces a new method for accelerating current sluggish FEM and improving memory demand in FEM problems with high node resolution or bulky structures. Like most of the numerical methods, FEM results to a matrix equation which normally has huge dimension. Breaking the main matrix equation into several smaller size matrices, the solving procedure can be accelerated. For implementing ...

Spherical granules of the superionic conductor β/β́ LiZr2(PO4)3 in the range of sub 100 nm sizewere synthesizedvia freeze drying methodand fully reviewed in all aspects. Samples were characterized by the X-ray diffractometry (XRD), the Thermal analysis (TG, DSC), theFourier Transform Infra-Red Spectroscopy (FTIR) and the Scanning Electron Microscopy (SEM).Their structuredepends largely on the me...

We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates using the numerical solution of the Gross-Pitaevskii equation with both spherical and axial symmetries. We consider time-evolution problems initiated by changing the interatomic scattering length or harmonic trapping potential suddenly in a stationary condensate. These changes introduce oscillations in ...

Holm’s method and Hochberg’s method for multiple testing can be viewed as step-down and step-up versions of the Bonferroni test. We show that both are special cases of partition testing. The difference is that, while Holm’s method tests each partition hypothesis using the largest order statistic, setting a critical value based on the Bonferroni inequality, Hochberg’s method tests each partition...

An approximate query processing approach for a content-based image retrieval method based on probabilistic relaxation labeling is proposed. The novelty lies in the inclusion of a filtering mechanism based on a quasi lower bound on distance in the vector space that effectively spares the matching between the query and a number of database images from going through the expensive step of iterative...

The split-step Fourier method for solving numerically nonlinear Schrödinger equations (NLS) is considered as NLS with rapidly varying coefficients. This connection is exploited to justify the split-step approximation using an averaging technique. The averaging is done up to the second order and it is explained why (in this context) symmetric split-step produces a higher order scheme. The same a...