The Study of Translational Tiling with Fourier Analysis

A pr 2 00 3 The study of translational tiling with Fourier Analysis Lectures

Rhombellanic Crystals and Quasicrystals

Design of some crystal and quasicrystal networks, based on rhombellane tiling,is presented. [1,1,1]Propellane,is a synthesized organic molecule; its hydrogenated form, the bicyclo[1.1.1]pentane,may be represented by the complete bipartite graph K2,3 which is the smallest rhombellane. Topology of translational and radial structures involving rhombellanes is described in terms of vertex symbol, c...

1 4 A pr 1 99 9 On the structure of multi PREPRINT ple translational tilings by polygonal regions

We consider polygons with the following “pairing property”: for each edge of the polygon there is precisely one other edge parallel to it. We study the problem of when such a polygon K tiles the plane multiply when translated at the locations Λ, where Λ is a multiset in the plane. The pairing property of K makes this question particularly amenable to Fourier Analysis. After establishing a neces...

A Discrete Fractional Gabor Expansion for Time–Frequency Signal Analysis

In this work, we present a discrete fractional Gabor representation on a general, non-rectangular timefrequency lattice. The traditional Gabor expansion represents a signal in terms of time and frequency shifted basis functions, called Gabor logons. This constant-bandwidth analysis uses a fixed, and rectangular time-frequency plane tiling. Many of the practical signals require a more flexible, ...

Kinematic and Dynamic Analysis of Tripteron, an Over-constrained 3-DOF Translational Parallel Manipulator, Through Newton-Euler Approach

In this research, as the main contribution, a comprehensive study is carried out on the mathematical modeling and analysis of the inverse kinematics and dynamics of an over-constraint three translational degree-of-freedom parallel manipulator. Due to the inconsistency between the number of equations and unknowns, the problem of obtaining the constraint forces and torques of an over-constraint m...