Let β > 1 be a non-integer. We consider β-expansions of the form ∑∞ i=1 di βi , where the digits (di)i≥1 are generated by means of a random map Kβ defined on {0, 1}N× [0, bβc/(β − 1)]. We show that Kβ has a unique measure νβ of maximal entropy log(1 + bβc). Under this measure, the digits (di)i≥1 form a uniform Bernoulli process, and the projection of this measure on the second coordinate is an ...

Nonequilibrium statistical mechanics helps to estimate corrections to the entropy and energy of the fluid with heat flux in terms of the nonequilibrium distribution function, f. This leads to the coefficients of wave model of heat: relaxation time, propagation speed and thermal inertia. With these data a quadratic Lagrangian and a variational principle of Hamilton’s type follows for the fluid i...

This paper describes a fast, low-complexity, entropy efficient video coder for wavelet pyramids. This coder approaches the entropy-limited coding rate of video wavelet pyramids, is fast in both hardware and software implementations, and has low complexity (no multiplies) for use in ASICs. It consists of a modified Z-coder used to code the zero/non-zero significance function and Huffman coding f...

We present a low-complexity entropy coder originally designed to work in the JPEG2000 image compression standard framework. The algorithm is meant for embedded and non-embedded coding of wavelet coefficients inside a subband, and is called Subband-Block Hierarchical Partitioning (SBHP). It was extensively tested following the standard experiment procedures, and it was shown to yield a significa...

Here, we study the internal variable approach to viscoelasticity. First, generalize classical by introducing a fractional derivative into equation for time evolution of variables. Next, derive restrictions on coefficients that follow from dissipation inequality (entropy under isothermal conditions). In example wave propagation, show entropy are sufficient guarantee existence solution. We presen...

Entropy coding is one of the most important techniques in video codec. Two main criteria to assess an entropy coder are coding efficiency and friendly realization characteristic. In the recent development of the H.264/AVC standard, a sophisticated entropy coder, named Context-based Adaptive Variable Length Coding (CAVLC), has been invented, which supplies higher coding efficiency than other VLC...

The article provides an infrared and visible image fusion algorithm based on directionlets transform. The registered original images were decomposed into the low-frequency and high-frequency coefficients by directionlets transform. Getting the mean of the low-frequency coefficients, applying the local variance maximum principle to the high-frequency coefficients, thereby the fusion coefficients...

In this paper, personalized quantization of the filter coefficients of Linear Predictive Coding (LPC) is studied. The study covers two aspects. On the one hand, a signal-adaptive algorithm which determines when to transmit a set of LPC coefficients is introduced. This algorithm allows a reduction of about 35% of the bit rate needed to code the LPC coefficients in speech storage applications – e...

A new method based on principal component analysis (PCA) and artificial neural networks (ANN) is proposed for fault diagnosis of gearboxes. Firstly the six different base wavelets are considered, in which three are from real valued and other three from complex valued. Two wavelet selection criteria Maximum Energy to Shannon Entropy ratio and Maximum Relative Wavelet Energy are used and compared...

in this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. it is shown that it generates the kolmogorov entropy as a special case. if $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.