| 词汇 | example_english_entropy |
| 释义 | Examples of entropyThese examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. The difference between the two entropies is a measure of the structure imposed upon the spike train by the original stimulus. We also recall how these entropies are related. Recently, the pre-image structure of maps has become deeply characterized via entropies (see [4-9]). In particular, it is easy to see that for locally symmetric metrics both entropies coincide. The entropies of the two sets of spike trains, which we term "repeated" and "rerandomized," were calculated as a function of time as follows. The relations between these entropies are explained. The following statement will allow us to estimate the topological entropies of the sets from below, without constructing probability measures, which are invariant and concentrated on a given set. Multifractal analysis of local entropies for expansive homeomorphisms with specification. Calculations of activation entropies of chemical reactions in solution. The topological entropy (see [1]) is a well-known quantitative measure of the dynamical complexity of a model. The entropy of a skew product of measure preserving transformations. Right-closing factor maps are bounded-to-one and hence preserve topological entropy. The volume entropy can be normalized by the volume. Other similar bounds on the entropy have been established in [10] for systolically extremal surfaces (see [16] for a generalization in higher dimension). Since the system has finite entropy log h, the number of cylinders of length n is bounded above by hn (see [6, p. 213]). However, there is an explicit bound on the number of such maximal entropy preimages. We turn to the sufficiency of the entropy condition. Most quasicrystalline materials are less ordered and are thought to have positive entropy and be entropically stabilized. Finally, in this paper we investigate the existence of strictly local maxima for the entropy function of subshifts. Here we construct an example of a one-dimensional subshift with the property that its entropy function has a strictly local maximum. A measure-preserving transformation (respectively a topological system) is null if the metric (respectively topological) sequence entropy is zero for any sequence. Localizing the notion of sequence entropy, we define sequence entropy pairs and show that there is a maximal null factor for any system. Related to the topological entropy is the measure theoretic entropy. In other words, the entropy of f is lower semi-continuous. Furthermore, is ergodic [32] and it is the unique measure of maximal entropy [22]. Next, we consider the analogous notion of metric pre-image entropy. Finally, we relate, in higher dimension, the isoembolic ratio to the minimal entropy. A variation on the variational principle and applications to entropy pairs. No other relations between the above approaches to operator entropy have been established. Moreover, both flows have the same topological entropy. Finally, by induction assumptions, the entropy of is zero. We give a different argument for the completely positive entropy step. We shall now exhibit examples when the entropy is positive, but the system does not have completely positive entropy. In our setting, the entropy function h() is upper semicontinuous. Another variation of entropy convergence rates is related to an existing concept in the theory of entropy. Vanishing of metric entropy for a measure does not imply that there is no topological entropy carried on its support. The final temperature (after expansion of the gas to a given pressure) was calculated by summing the entropy changes. Finiteness of the transition entropy characterizes the existence of a generator with bounded degree. We introduce transition entropy and periodic entropy for locally compact subshifts. The statement about entropy in (2) is analogous to the situation in the measure-preserving category. However, these processes frequently have infinite entropy, particularly when the random variables take their values in a non-discrete space. The variational principle states that the topological entropy of a topological dynamical system is equal to the sup of the entropies of invariant measures. The main application we had in mind was to the study of entropy pairs. Since the action is rotation on a compact abelian group it has discrete spectrum and entropy zero. If it turns out to be true in general it will present a striking resemblance with the variational principle for the topological entropy. The random entropy defined above can be related to the fibre entropy of a skew product as follows. In this paper we are concerned with the entropy of random transformations. The first term in the right-hand side is the entropy obtained by observing which transformations are chosen. In 3, we develop a notion of random entropy which is based on this idea, and which gives satisfactory results in any dimension. If the flow is not homentropic but diffusion is neglected, the entropy along a path line is constant. To study the relationship between the two kinds of entropy pairs or tuples, one needs a local version of the variational principle. The partition constructed on the first step carries already most of the entropy. The definition and some fundamental facts about the topological entropy of non-compact sets are collected in the following section. Measures that maximize weighted entropy for factor maps between subshifts of finite type. However, the various notions of entropy in this setting are still not well understood. They ask whether such a system may have positive entropy. The reader should be reminded of the definition of entropy pairs for an invariant measure [4]. Measure-preserving homeomorphisms of the torus represent all finite entropy ergodic transformations. Entropy of semipatterns or how to connect the dots to minimize entropy. In the rest of this section we will consider the problem of obtaining a finite algorithm to compute the entropy of an action. The extension of the notion of entropy onto quantum systems was treated as a difficult mathematical problem. In [4], axiom v is needed mainly for the construction of m-entropy and its use in the m-equivalence theorem. In this paper we prove that permutations of even length with maximal entropy are not unique. Since any subshift is expansive, it follows that the set of measures of maximal entropy is a non-empty compact convex set. However, in higher dimensions there may be more than one measure of maximal entropy [1]. The entropy of a skew product of measure preserving transformation. The geodesic flows constructed here do have positive topological entropy because they contain horseshoes. An interesting problem is the influence of the entropy change on the flow behind the shock wave. His formal definition of residual entropy is as follows. The topological entropy for the maps near gt fails to be a constant. As in the one-dimensional case this entropy is either the classical entropy or is zero. Associated to each size is an entropy which is an equivalence invariant. We now want to see that our two definitions of m-entropy agree. The size m1 corresponding to isomorphisms, however, will be seen directly to be entropy preserving. The entropy is in general not continuous (see [3] and (4.17) in [7]). Covering dimension and topological entropy in dynamical systems. The emphasis of our work is on the geometric bounds for the entropy. We will now introduce the different types of entropy convergence rates. Lectures on the entropy theory of measure preserving transformations. More precisely, this dynamical invariant agrees with the volume entropy when the metric has no conjugate points (see [4] and [13]). Thus, it is possible to make the topological entropy arbitrarily large (see [14]) while keeping the systole fixed. Corollary 4.1 enables us to verify the entropy stability of secondorder accurate schemes as well. We generalize the construction of second-order entropy-conservative schemes to higher orders. We refer to the last statement as a quasi-cel l entropy inequality since the last expression on the right is not conservative. The use of different subpaths allows us to stabilize rarefactions while avoiding spurious entropy dissipation with shocks. We close this section with the following example, which shows how to enforce entropy stability a posteriori by carefully removing any viscosity production. He proved the existence of the entropy solution by using the vanishing viscosity method. A direct consequence of this result is the following characterization of the entropy solution. Then, he used a compactness argument to show that, when tends to zero, the functions u converge to a limit that satisfies the entropy inequality. We obtain analogs of many known results for topological and measure-theoretic entropies. We prove that these averages of entropies always converge. We can identify two regularities in these graphs: the relationship between the three types of link entropies and the overall trend. Here we prove directly that the entropies for two systems must be equal. We define and study new invariants called pre-image entropies which are similar to the standard notions of topological and measure-theoretic entropies. To see how to obtain all entropies, first note that to verify u. s. d. one needs only to check it on one partition. We shall use the rome method to estimate the topological entropies of the maps we construct below. The estimation of these terms, and especially of their entropies, remains a very difficult problem. Free-energy profiles are in thermodynamic terms exact so long as no approximations are made in evaluation of the energies and entropies. Of course, there is some choice in where to perform entropies. Overall, the blindfolded sessions have higher entropies and link indices in both groups. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
反思网英语在线翻译词典收录了377474条英语词汇在线翻译词条，基本涵盖了全部常用英语词汇的中英文双语翻译及用法，是英语学习的有利工具。