| 词汇 | example_english_perturbation |
| 释义 | Examples of perturbationThese 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. Unfortunately, these perturbations can not be joined continuously to those of the interaction region. Statistical mechanical implications of these perturbations are described. Change in the self-system is explained by perturbations in the life of the individual. Our computations give some evidence that these travelling waves are stable even to large perturbations. In this case a perfect hexagonal pattern, which is stable under symmetric perturbations, is perturbed asymmetrically. If, for example, the attractor of the parabolic limit equation is chaotic, then trajectories are sensitive to perturbations. In experiments and numerical simulations, stable spatially-periodic patterns typically arise through small, localized perturbations of the underlying unstable background state. Our stability analysis, for perturbations of localized solutions, typically leads to singularly perturbed eigenvalue problems with spatially inhomogeneous coefficients that are difficult to study analytically. An attractor state is insensitive to (small) perturbations. The situation in which we apply bump perturbations will often be of the following type. We are far from understanding how these abnormalities co-operate during tumourigenesis and how such perturbations in cell cycle control could be used clinically. We now describe the sequence of perturbations that produces the desired metric. Unlike the smooth expanding maps treated just above, such maps are in general not structurally or measure-theoretically stable with respect to deterministic perturbations. Moreover, we obtain sharp spectral stability results for deterministic and random perturbations. In the third flow region, behind the stator there is uniform axial steady flow and zero swirl with downstream-propagating acoustic and vorticity perturbations. Such sensitivity to external perturbations indicates that the selectivity of the instability is weak with a large bandwidth of unstable wavelengths. We remark that these perturbations do not affect the global desired motion. Entropy waves are also pressure-balance structures in which there are no gas pressure and magnetic field perturbations, but the entropy and density perturbations are non-zero. Stability of a gait implies that the walking or running system does not fall and that it is able to recover from perturbations. In addition, very young infants have unstable posture while reaching and their own postural wobble may act as perturbations to the growing motor memory. Then the a priori estimate (2.20) holds, and the steady state (2.7) is nonlinearly stable to arbitrary finite-amplitude perturbations. Then an a priori estimate (2.20) holds, and the steady state (2.7) is nonlinearly stable to arbitrary finite-amplitude perturbations. In particular, small-scale perturbations (k0 1) show the fastest rises. We have shown that if linear perturbations have imaginary frequencies the only possible solutions are solutions of null amplitude. Without using explicitly landscape theory, the former perturbations [(i) and (ii)] may be characterized in several ways. In nonlinear theory, however, the mean values of perturbations can be non-zero owing to the interaction of the different harmonics. The reason is that, with the perturbations that we have used so far, always globally extended modes are generated. Faced with such perturbations, the workstations and the containers have to reorganize their activities without an external centralized control. In the absence of entropy perturbations, the system admits a wave action conservation integral consisting of positive and negative energy waves. We now focus on simple cycles and describe the dynamics of nice perturbations of them: the unfolding of simple cycles preserving their affine structures. In a neural system we may expect that cycling commences or continues in response to internal and external perturbations in an attempt to maintain symmetry. Second, focusing exclusively on the effects of permanent perturbations severely limits the predictions of the model. The perturbations with small wave numbers are rejected in order to exclude the boundary conditions. In a first step, there is no need for perturbations. Despite perturbations of the plant process, which do not occur in the model, a satisfactory control performance still is secured. Proteins can be rerouted through the energy landscape by mutational or topological perturbations. We do, however, need to treat positron and ion perturbations separately [4]. The ring ions and the dust charge perturbations are described kinetically. A reduction in the number of the circulating electrons and, consequently, a decrease in the destabilizing parallel-current perturbations provides an explanation for this. Also, for the high-n ballooning modes, the trapped electrons reduce the pressure perturbations. The perturbations were assumed to be of sufficiently short wavelengths to justify the slow time and radiusfrozen-in approximation for the unperturbed systems. The method involved finding the nonlinear disper sion relation for the perturbations to the plane-periodic solutions. His results showed that three-dimensional perturbations are stabilized in the cyclonic case but destabilized in the anticyclonic case. The method can be applied to control balance in response to other external perturbations as well, and is easily extendable to the general, three-dimensional case. The modelling errors and other structured uncertainty are considered as parameter perturbations. Stability is the property of a system to recover from perturbations of its state. What causes the problem is that nonlinear economic forces, possibly nonlinear forecasting rules, and nonadditive random perturbations interact simultaneously. Thus, learnability encompasses robustness with respect to perturbations of the state variable as well as the belief parameters. A system is structurally stable when small perturbations produce topologically equivalent systems. Therefore, the average consumption of an infinitely lived representative agent is independent of the prevailing history of perturbations. If the only stochastic perturbations are i. i. d. production shocks, then we obtain the following result. The perturbations we consider are always arbitrarily small. Nonlinear couplings require strong perturbations of the magnetic field component transver se to the propagation. The conclusion is that a flux rope placed in a sheared flow is unstable to small (but not infinitesimal) perturbations. Therefore, we neglect perturbations in the s motion of ions due to such a potential. We establish nonlinear stability criterion for arbitrary axisymmetric perturbations for arbitrary flow and a poloidal field. The appropriate conditions for the perturbations are that they are squareintegrable. Analytic methods are therefore developed to calculate the effects of perturbations on population size at any time, for periodic matrix models. Figure 6 depicts the response of take-up radius to the perturbations of feed-in radius (0, t) where a = 0.05, = 25. In 7, we show how this framework implies very precise stability results on the spectrum, for deterministic and random perturbations. Given a map which is (n - 1)-transverse, we obtain one which is n-transverse by making arbitrarily small local perturbations. Stochastic stability for non-local perturbations of expanding maps. We will see that there are several interesting phenomena which appear after small perturbations when a given map f has a homoclinic tangency. However, homoclinic tangencies give rise to rich and varied dynamics under small perturbations. The perturbations to both the temperature and the salinity are dominated by the z-independent terms. The preferred steady solution becomes unstable against time-periodic perturbations a t a higher value of the forcing parameter. The isolated steady-state flow is established by initially introducing specific perturbations into the walltemperature distribution. Because the basic state is independent of direction in a plane parallel to the wall, it suffices to consider two-dimensional perturbations periodic in the x-direction. Now we obtain conjugacies between a strong nonuniform exponential dichotomy and its sufficiently small nonlinear perturbations. I n addition, our results showed that prolate shapes are stable, whereas oblate shapes are unstable to axisymmetric perturbations in shape. Small perturbations will still be assumed, but non-linear terms will be included to avoid the breakdown, which is essentially due to the linearization. We might therefore conclude that expanding jet flows are stable to small perturbations whilst contracting jet flows are not. I n complicated problems such as the present one, power relationships lead to simple zeroth perturbations. The second derivation is based on the requirement that only spatially bounded solutions to the stability perturbations equations are allowed when considering unstable modes. Their structural instability suggests that they are broken by most perturbations of the steady basic flow in which they arise. I n the present paper an attempt is made to consider flows with small perturbations, dealing only with the two-dimensional steady problem. The stability of the solutions was determined by using time-dependent linear analysis of small perturbations from equilibrium. Weakly nonlinear soliton solutions are found t o be accurate even when the perturbations they cause are fairly strong. Otherwise, the perturbations of each individual wave would trigger the linear instability. In the present calculation the two- and three-dimensional vortex shedding is generated without imposing external perturbations. The growth of bottom perturbations is thus controlled by a balance between the above two effects. In the absence of any lateral perturbations this upslope translation should be uniform in the transverse direction. In addition, the present norms allow easier estimates of the size of perturbations. Unlike the subharmonic case, a steady streaming component is present in the second-order perturbations. We notice that the assumption of rotational symmetry of the perturbations has considerably reduced the amount of algebraic work involved. The velocity traces consist of low-frequency highamplitude fluctuations representing the passage of the coherent structures and highfrequency perturbations (figure 15). The flow within the duct is taken to consist of a steady mean flow with unsteady acoustic perturbations. We decompose the density and the pressure into the basic states and their perturbations and p respectively. However, after sufficient nonlinear evolution, the interfacial dynamics is dominated by long solitary waves regardless of initial perturbations. In particular, cellular models rely on the addition of random perturbations to an initially flat, tilted surface in order to start the process of channellization. In particular, when the rotation number is irrational, by arbitrarily small perturbations we can increase its value. We will show that this property still holds for perturbations of a skew product. They showed that such maps have certain transitivity properties that are preserved under perturbations. Consequently, the branch of type will persist under small perturbations. If this is done then the effect of perturbations (and discretizations) can be readily understood. Note that neither problem has a strictly feasible solution, and arbitrary small perturbations in the data can make the optimal values jump. We mentioned earlier that such a study could have the application of finding a robust solution that is least sensitive to perturbations. We must, instead, phrase such results in terms of convergence of invariant subspaces and also provide a mechanism to encompass such perturbations. Among these multiple solutions, the one that is least sensitive to perturbations of problem data is perhaps most critical from a practical point of view. We then investigate whether the perturbations d, h, g grow or decay. 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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