词汇 | example_english_exponential |
释义 | Examples of exponentialThese 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 main point of difficulty lies in defining the exponentials. Section 6.5) then the expansion in (4.2) is exact for a finite product of exponentials. The formulae involve only vector additions, inner products and trigonometric functions (comparing favourably with previous formulae in ref. [16] using exponentials of skew-symmetric matrices). We explicitly solve this boundary value problem, as an infinite sum of exponentials. The above construction of map generalises to any category that has exponentials. In linear logic, contraction makes its way through the exponentials. Although it is only a toy example, the next theorem is important: the same machinery could work mutatis mutandis in the case of exponentials. A similar remark holds for unary s connectives (the exponentials '!' and '?'). The number of exponentials necessary for a good fit of the data was determined by visual inspection. The exceptions are the exponentials of the eigenvalues. Then, as the cartesian closed structure is also preserved, the construction of the exponentials in the slices coincides. As a result, negation becomes involutive, whereas weakening and contraction become attributes of special connectives - exponentials. We assume that the reader is familiar with the construction of exponentials in this category. We also mention other work on models (either discrete or diffusion) that admit steady state distributions consisting of a finite or infinite sum of product form exponentials. The novelty of our work is that our partial hyperbolicity assumptions are again non-uniform, in the sense that we allow in our assumptions extra exponentials as in (3). Tying hairs for structurally stable exponentials. Unfortunately, however, for large d (even d = 5) the analytic solutions become messy from the fact that the initial conditions for later phases are rational functions of exponentials. Tying hairs for the structurally stable exponentials. Note that the methods in [5, 6, 15] cannot be used in this general setting since they make use of explicit properties of the exponentials and the approximating polynomials. However, due to the exponentials, the dimension of these spaces cannot be restricted to be finite (the finite multi-powerset of a non-empty set is always infinite). However, most concrete problems remained beyond reach because of the complexity of the decision method he proposed (a tower of exponentials with length given by the number of variables involved). In the absence of exponentials. We have shown that there is no hope of further improving the exponential running time bounds for simulated annealing. Linear and exponential equations were fitted to describe the decay in the percentage of positive detection as a function of time. To this end we investigate exponential solutions, eikx+t, of (3.6) linearized about a uniform solution (x, t) x, (x, t) l (t), ! Figure 3 visualizes the exponential like relation between approximation order and the number of summands with respect to different random dimensions. Nevertheless, this approach cannot give an exponential estimate in (2.14), only an estimate of order c for some c > 0. Another point of interest is that these maps provide examples of dynamical systems admitting sub-exponential decay of correlations, and this is our focus. We build a telescope and show the exponential shrinking of components condition. Let us now depart from questions concerning single rays and consider the escaping sets of exponential maps in their entirety. Any orientation-preserving conjugacy of two exponential maps induces an order-preserving map on their sets of escaping points. Furthermore, we show that the principle of topological renormalization is false for attracting exponential maps. Note that, unlike exponential dichotomy, dominance and integral separateness do not imply that the angle between two invariant subspaces is bounded from below. An energy principle is presented which gives necessary and sufficient conditions for exponential stability for a large class of dissipative systems. The perturbation of the exponential behaviour is most severe on the inner bend. Furthermore, these exponential growth rates were predicted to increase with increasing amplitude of the vortex. The result is independent of whether the shear flow is unstable or not to exponential growth of wave-like disturbances. We also experimented with exponential priors for genetic effects, but no further improvement in variance components estimation was found (results not shown). We found that a simple exponential cooling schedule performs well. Any finitely generated solvable group with exponential growth has uniformly exponential growth. In 4, we prove exponential decay of correlations for skew and principal extensions of hyperbolic basic sets. As we will see, this exponential has an attracting cycle of period three. As we have pointed out the finite difference method always seems to give the exponential decay solution if one exists. Another question concerns the choice of time function (linear, cubic or exponential). An alternative trajectory that is bounded with respect to time and thus does not tend towards positive or negative infinity is the exponential function. In the worst case, it requires exponential time; but in practice on graphs encountered in everyday applications, the time complexity is tractable. Exponential mapping of quantitative trait loci governing allometric relationships in organisms. The exponential distribution has considerable importance and has had widespread use in the analysis of data in which the response variable is a lifetime. Once life has been seeded within a planet or comet it will grow at an exponential rate, checked only by the availability of sufficient nutrients. In fact, direct instantiation of any non-trivial marking problem for rose trees will take exponential time. The exponential behavior of subtypeac can be seen clearly in the following example. In general, an exponential curve reaches its extreme value (98%) at the time of 4 time constant. The reduction of the search to the position space drastically reduces computation time because of the typical exponential complexity of grid search methods. The distribution of bondholdings is assumed to be a second-order exponential. The main results are stochastic turnpike theorems with exponential estimates of the convergence rate. There also has been an exponential growth in publication of economic evaluations during the past 2 decades (19). We use in vitro data to indirectly constrain the time course of conductance gsyn(t), a double exponential. The use of an iterated exponential function would be very inefficient because of its fast growing. The single exponential model used to explain the temporal dynamics of litter decay fitted the data well, explaining 59-96% of the data variation. There is no literal attempt to illustrate the frightening exponential curve of our own blind technological revolution, for example. Temporal sensitivity functions like these were described with the simple exponential function given in the text as equation 1!. The time constant of membrane recovery was derived from the single exponential fit to the capacitance decay (superimposed curves with indicated time constants). The exponential distribution of step durations suggests that the shut-off of activated rhodopsin under these conditions is rate limited by a single first-order process. The sparsity pattern of a matrix exponential of a sparse matrix after the excision of small entries is at present unknown. Certain transcendental functions can be carried over to the surreals, including logarithms and exponentials, but most, e.g., the sine function, can not. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The nature of exponentials is that you push them out and eventually disaster happens. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Usually, it is very hard to characterize the convex hull and, moreover, an exponential number of inequalities might be required to characterize the convex hull. The algorithm has linear complexity for the case of polytrees and exponential complexity for networks with loops. Also, due to the sophisticated specializer, the transformation phase may take exponential time, which is not practical. First, our algorithm does not build any tree data-structure of potentially exponential size. The central message of these disciplines is that quantum mechanics provides a great - sometimes exponential - improvement in the information processing power of a physical system. The first server has a general service time with rate m1, whereas the second server has an exponential service time with rate m2. A hyperbolic discount function often fits empirical data better than the exponential discount function. As a discount function, they used discounting with a constant discount rate (exponential discounting). We assume exponential service times, linear holding costs, and operating costs incurred by the servers at rates proportional to their speeds. The first step is to apply an exponential gain to the received signal to compensate for the radar signal attenuation characteristic through earth material. Each robot enters the common workspace with exponential distribution, parameter k for robot k. The existence of such a bottleneck leads to the exponential time dependence of folding that is observed. The solid lines represent fits to a single exponential. Time-resolved folding and unfolding experiments with zinc-substituted azurin revealed that unfolding is a single-exponential process, whereas refolding is best fitted with doubleexponential functions. We are not aware that final lengthening is exponential. Scheduling tasks with exponential service times on non-identical processors to minimize various cost functions. In this paper we study the collapse properties of a linear two-dimensional null point by perturbing it linearly and investigating the exponential time response. Second, while most trustee discount functions had an identifiable shape, even if not always exponential in character, some did not. First, it was shown that many of our pension fund trustees have shallow and often non-exponential discount functions. The order can be increased by including more exponentials in a time step. In this limited way, we recover the features of exponentials from linear logic. Regressing to models of decaying exponentials led to improved quality in the synthesis of several of the percussive tracks. The problem is to go on, and to know what to do in, say, the delicate problem of exponentials. Let us note a general 2-categorical fact, that pullback functors between slices preserve existing exponentials. Due to the exponentials, the same cannot be said of the usual coherence semantics. We therefore consider a reformulation of the typing rules that only requires single exponentials. The best fit was obtained with two exponentials. In the presence of exponentials, the problem is with entropy, dereliction and the -rule, where points move into or out of the order variety. The solution is an infinite sum of product form exponentials. At least this is the case for our present approach to exponentials. He proposed a modification, which, under certain conditions, guarantees not only the -autonomous structure, but also linear exponentials. After initially using exponentials, they subsequently realized that polynomials in several variables provided an equivalent (but more useful) formulation. Although the number of exponentials in is generally quite large for low-rank splittings, the underlying linear algebra carries a reasonable price tag. 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. |
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