To give a more definite criterion using electroencephalograph (EEG) approach on brain death determination is vital for both reducing the risks and preventing medical misdiagnosis. This paper presents several novel adaptive computable entropy methods based on approximate entropy (ApEn) and sample entropy (SampEn) to monitor the varying symptoms of patients and to determine the brain death. The p...

It is well known that n bits of entropy are necessary and sufficient to perfectly encrypt n bits (one-time pad). Even if we allow the encryption to be approximate, the amount of entropy needed doesn’t asymptotically change. However, this is not the case when we are encrypting quantum bits. For the perfect encryption of n quantum bits, 2n bits of entropy are necessary and sufficient (quantum one...

A two-dimensional model of Al, Si ordering in alkali feldspar is formulated and used to calcul~tea ccurately the configurational entropy for the model. For this purpose, a new method called Independent Basic Unit or IBU is introduced. To compare the results with the exact values, this method is applied to the onedimensional model of albite. The results given by IBU are found to be accurate ...

Given a collection of probability distributions p 1 , xmlns:xlink="http://www.w3.org/1999/xlink">⋯ ,p xmlns:xlink="http://www.w3.org/1999/xlink">m the minimum entropy coupling is X ,X ( xmlns:xlink="http://www.w3.org/1999/xlink">i ~ ) with smallest H(X ). While this problem kno...

We present a streamline diffusion shock capturing spacetime discontinuous Galerkin (DG) method to approximate nonlinear systems of conservation laws in several space dimensions. The degrees of freedom are in terms of the entropy variables and the numerical flux functions are the entropy stable finite volume fluxes. We show entropy stability of the (formally) arbitrarily high order accurate meth...

We propose a numerical scheme to approximate the weak solutions of the 10-moment Gaussian closure. The moment Gaussian closure for gas dynamics is governed by a conservative hyperbolic system supplemented by entropy inequalities whose solutions satisfy positiveness of density and tensorial pressure. We consider a Suliciu-type relaxation numerical scheme to approximate the solutions. These metho...

In this paper we study an integro-differential equation describing slow erosion, in a model of granular flow. In this equation the flux is non local and depends on x, t. We define approximate solutions by using a front tracking technique, adapted to this special equation. Convergence of the approximate solutions is established by means of suitable a priori estimates. In turn, these yield the gl...

Weconsider ahyperbolic conservation lawposedonan (N+1)-dimensional spacetime, whose flux is a field of differential forms of degree N. Generalizing the classical Kuznetsov’s method, we derive an L1 error estimate which applies to a large class of approximate solutions. In particular, we apply our main theorem and deal with two entropy solutions associated with distinct flux fields, as well as w...

The Kolmogorov-Sinai entropy in the sense of Tsallis under Bernoulli shifts was obtained by Mesón and Vericat [J. Math. Phys. 37, 4480(1996)]. In this paper, we propose a revised generalized Kolmogorov-Sinai-q entropy under Markov shifts. The form of this generalized entropy with factor q is nonextensive. The new generalized entropy contains the classical Kolmogorov-Sinai entropy and Renýı entr...