In the case of equation (1.2) condition (1.4) coincides with the known Kruzhkov entropy condition [9]. If the function g(u) strictly increases then any weak solution of (1.1) is an entropy solution of this equation as well (cf. [2]) but for degenerate equations this may be violated and, in particular, entropy condition (1.4) is necessary for the uniqueness of solution to the Cauchy problem for ...

An approximate relation between the vibrational entropy and the mean square displacement of the particles is derived. Using observations of the short-time dynamics in liquids of various fragility, it is argued that (i) if the crystal entropy is significantly smaller than the liquid entropy at T{g}, the extrapolation of the vibrational entropy leads to the correlation T{K} approximately T{0}, wh...

This paper presents a novel approach to automatic classifying and identifying of tree leaves using image segmentation fusion. With the development of mobile devices and remote access, automatic plant identification in images taken in natural scenes has received much attention. Image segmentation plays a key role in most plant identification methods, especially in complex background images. Wher...

Let f : M → M be a C-diffeomorphism, r ≥ 1, defined on a closed manifold M . We prove that if M is a surface and K ⊂ M is a compact invariant set such that TKM = E ⊕ F is a dominated splitting then f/K is entropy expansive. Moreover C generically in any dimension, isolated homoclinic classes H(p), p hyperbolic, are entropy expansive. Conversely, if there exists a C neighborhood U of a surface d...

Remark that real flows should be non-isentropic. The constancy of the entropy is not compatible once shock waves develop. It is only expected that the amplitude of oscillations for the entropy are of cubic order with respect to those of the flow. There is one notable exception, that of a Chaplygin gas, whose pressure has the form p(ρ, s) = g(s)− f(s)/ρ ; then the entropy remains constant even b...

In this paper, the two parameter ADK entropy, as a generalized of Re'nyi entropy, is considered and some properties of it, are investigated. We will see that the ADK entropy for continuous random variables is invariant under a location and is not invariant under a scale transformation of the random variable. Furthermore, the joint ADK entropy, conditional ADK entropy, and chain rule of this ent...

We initiate the study of weak containment and weak equivalence for μ-stationary actions for a given countable group G endowed with a generating probability measure μ. We show that Furstenberg entropy is a stable weak equivalence invariant, and furthermore is a continuous affine map on the space of stable weak equivalence classes. We prove the same for the associated stationary random subgroup (...

We calculate the Shannon entropy of a time series by using the probability density functions of the characteristic sizes of the long-range correlated clusters introduced in [A. Carbone, G. Castelli, H.E. Stanley, Phys. Rev. E 69 (2004) 026105]. We define three different measures of the entropy related, respectively, to the length, the duration and the area of the clusters. For all the three cas...

The purpose of this study is to define the concepts of Tsallis entropy and conditional Tsallis entropy of fuzzy partitions and to obtain some results concerning this kind entropy. We show that the Tsallis entropy of fuzzy partitions has the subadditivity and concavity properties. We study this information measure under the refinement and zero mode subset relations. We check the chain rules for ...

The enumeration of perfect matchings of graphs is equivalent to the dimer problem which has applications in statistical physics. A graph G is said to be n-rotation symmetric if the cyclic group of order n is a subgroup of the automorphism group of G. Jockusch (Perfect matchings and perfect squares, J. Combin. Theory Ser. A, 67(1994), 100-115) and Kuperberg (An exploration of the permanent-deter...