Answers and hints to selected exercises

  title={Answers and hints to selected exercises},
  author={Gangsong Leng and Yongming Liu},


A novel method for the construction of orthogonal p -wavelet packets on a positive half-line R + was given by the author in [ Construction of wavelet packets on p -adic field, Int. J. Wavelets
Harmonic and musical wavelets
  • D. Newland
  • Computer Science
    Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
  • 1994
It is shown that this family of mixed wavelets with the structure wm, n(x) provides a complete set of orthogonal basis functions for signal analysis and provides greater frequency discrimination than is possible with harmonic wavelets whose frequency interval is always an octave.
A Mathematical Introduction to Wavelets
This book presents a mathematical introduction to the theory of orthogonal wavelets and their uses in analysing functions and function spaces, both in one and in several variables. Starting with a
An identification of Energy Cascade in Turbulence by Orthonormal Wavelet Analysis
Orthonormal wavelet expansion method is applied to an analysis of atmospheric turbulence data which shows more than two decades of the inertial subrange spectrum. The result of the orthonor­ mal
On the fine-scale structure of turbulence
  • A. Townsend
  • Physics, Engineering
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1951
Recent experimental measurements of the energy spectrum of turbulence at very large wave-numbers have shown that the motion represented by these wave-number components is determined by the kinematic
Mathematical Foundations of Quantum Mechanics
Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth
Spectral large-eddy simulation of isotropic and stably stratified turbulence
We first recall the concepts of spectral eddy viscosity and diffusivity, derived from the two-point closures of turbulence, in the framework of large-eddy simulations in Fourier space. The case of a
The spatial structure and statistical properties of homogeneous turbulence
A direct numerical simulation at resolution 2403 is used to obtain a statistically stationary three-dimensional homogeneous and isotropic turbulent field at a Reynolds number around 1000 (Rλ ≈ 150).