| 词汇 | example_english_equation |
| 释义 | Examples of equationThese 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. In particular, for the wave kinetic equations of energies, only the interactions between nonlinear terms involving either energies or helicities will give a contribution. Since the wave interaction equations are linear the scattering matrix (5.23) gives the solution for c (t) for general initial data c (0). We have also obtained a solution of these model e equations. The characteristic equations (4.48)-(4.50) do not take into account the symmetry of the fluid frame group velocity surface about the magnetic field. All of these terms are expressed as functions of through the energ y equations (3.1a)-(3.1d). The system of the evolution equations, (2.6)-(2.8), will be the basis of the analysis that follows. The coefficients of the wave equations depend on time through the wave vector, which includes the stretch effect by the rotation shear. We conclude this introduction with a statement of the gover ning equations. From this model two coupled differential equations for the parallel ion velocity and the perturbed electrostatic potential were derived. We present the corresponding equations at the end of the appendix. In this section, however, we give the equations describing the stability of a general rotating plasma column. Using these equations, we can find the flow in the physical plane. To describe small-amplitude wave-like phenomena, the basic equations are linearized. An iterative scheme is used to solve the linearized system of difference equations. The work is suitable for a general audience, as equations have been consigned to a comprehensive mathematical appendix. The general structure of a specific population forecast can be described with three basic equations. The growth rate then follows from the normalized equations (3.1a), (3.2a) or (3.3a) whichever is appropriate. With (21) and (23), the nonlinear equations (1)-(4) are transformed into a set of linear inhomogeneous equations. Analysis of binary outcomes in longitudinal studies using weighted estimating equations and discrete-time survival methods : prevalence and incidence of smoking in an adolescent cohort. Therefore, the dynamic equations of motion of the mobile manipulator in task space satisfy the matching condition. However, this work is interested in developing an efficient algorithm for computation of parallel link robot manipulator dynamic equations. In the third case, one adds equations expressing distributivity of every operation of one theory over every operation of the other theory. The key idea is that we do not change the decision procedure to accommodate these new equations. Each of these seven equations is required to hold only when both sides are defined. A coinductive characterisation of barbed congruence is provided, though the equations holding in this setting vary considerably from ours. No confusion means that two data can be identified only if the equality can be proved by using the equations (of the presentation). The difference is that infinite systems of equations are allowed in a cia. The total combination of these physical processes are described by a system of gasdynamics and heat-transfer equations. When linearity is tested against the smooth-transition alternative, it is soundly rejected for both equations of the system. The main idea is to have the objective function being quadratic and the transition equations being linear, and to model seasonality by a periodic representation. The models had many equations, many predetermined variables, and relatively few observations. All the properties of the decohering walk can be deduced from these equations. To emphasise that these equations are evaluated in coalgebras, we call them coequations. We show how coalgebras can be presented by operations and equations. In this appendix we give a more general theorem on the unique existence of the solution of systems of behavioural differential equations. Corollary 5.7 yields a unique solution for such a system, which is an assignment of streams to the variables making the equations hold. From this perspective, systems of (differential) equations could completely describe the physical world. We use a single method to give axiomatizability results for projective and free equations, working in the following framework. Such a translation is useful for axiomatizability results in which the equations must have their quantifiers in specified classes. The homomorphism condition for the sum (and 0) are obvious, while for the scalar product we have to use equations (6) and (7). The computation rules for f are given by the different equations in its definition. Examples are the unique solution of equations and the distributivity properties of private replications. In fact, the righthand side of their equations always has to start with a fresh free variable. The well-known notion of guardedness helps us to identify useful equations. We want to use recursive equations to define processes. There are 45 countries in the trade-share matrix, and 1041 trade-share equations have been estimated. Relaxation-type algorithms applied to differential equations have two very useful properties. To apply the relaxation algorithm the researcher simply has to insert the differential equations into the program code, instead of converting the complete maximization problem. Equations (14) and (16) are the basic dynamic equations of our model. Parameter values that satisfy these equations have the property that agents do not have an incentive to revise the parameters of their models. Taking these conditions as given, equations (9) and (10) define a two-dimensional dynamic system with one predetermined variable, the capital. Thus, equations (26) and (27) must be solved for a fixed point to obtain the desired solution. All three equations show a similar effect of inflation on financial depth. We next explored the timing for solving large linear systems of equations, the second operation. Thus, we can proceed directly by analyzing the respective differential equations. We shall prove these two equations as separate lemmas. In this paper we shall use this explicit formula to get functional equations of l-adic polylogarithms. The equations for the electric field and the velocity and pressure of the fluid are not coupled. Therefore, we do not expect additional stability problems, when solving the network equations via the multidimensional approach. In accordance with the lattice model we presented the stability analysis for the evolution system of nonlinear differential equations. We have introduced special techniques to seek solutions of the determining equations. In particular, the solutions of these determining equations yield all integrating factors. In this paper we study an alternative model which incorporates a time delay explicitly, negating the need for the auxiliary equations. We first analysed a particularly simple limit in which the model equations may be integrated exactly. In this paper, we extend the modelling with transport equations to include periods of resting where the individuals do not move. The result of homogenization is the system of equations (1.3 a) and (1.3 b) coupled with a homogenized capillary relation. The equations are analysed asymptotically and numerically and the results are compared with experiments. The equations require the function (x, t), which can be numerically evaluated at each time step. Finally, we note that this phenomenon is robust, occurring in many higher-order equations [4]. In particular, global existence results transfer from the amplitude equations to the original system [42], and upper-semicontinuity of attractors holds [34]. The laser intensity pulses can be simulated numerically by using the laser rate equations. Imposing the compatibility of this differential system we obtain an algebraic system of equations for the particular solutions gi (x) and fj (x). From the vanishing of the other coefficients of the polynomial in y we get two new equations. Therefore, it would be desirable to treat the normal equations as they are. In the case of treated and reclaimed wastewater, there is a direct cost associated with treatment as equations (13), (15), (16), and (18) show. Again we obtain macroscopic models which are either nonlinear diffusion equations or phase-field systems. Homogenized equations are derived, and convergence of solutions to the solution of the homogenized problem is proved. On the center manifold, we derive amplitude equations for the travelling-wave problem. We do not see a symmetrization effect in the limit which is valid for a wide class of (eventually) uniformly parabolic equations. In this case the formal homogenization is a standard procedure and the macroscopic equations can be derived straightforwardly. Under a spherically symmetric condition and by considering the above equations we arrive at the expression which describes the dynamics of cavitations bubble motion. We per form the stability analysis in the usual manner by linearizing fluid equations. Any noun class has its inflected forms given by equations which may specify the suffix that appears, or a stem alternation, or both. Fig.1 shows the resulting equations and estimated regression lines. In the ignitor equations, the following terms were taken into account. A mathematical model using differential equations is provided to evaluate the magnitudes of some of these effects. The applicability of these equations to layered systems of immiscible liquids requires brief clarification. The focus of this chapter is on the government side of the equations. He uncapped his fountain pen, sketched a couple of crude diagrams, and surrounded them with mathematical equations. A more general method for constructing such equations and inequalities would be needed, and it should also work for the rectangle of course. In mathematics the term is most commonly used in connection with the study of problems (differential equations) with rapidly variable coefficients. We see this as a further case of kernel engineering in the direction of partial differential equations. We would like to point out to the reader the similarity of the argument below to one used for linear equations. Finally, handling times estimated by the functional response equations should not be considered as absolute calculations of the predator's time budget. However, it was unrelated to the study variables and, therefore, dropped from further consideration to increase power for the ensuing regression equations. Thus, in four of six equations, effortful control and impulsivity were unique predictors of adjustment when entered simultaneously. Unfortunately, unlike many linear equations, these nonlinear equations are generally not solvable in closed functional mathematical form. To validate the estimation process we then form a reconstructed interaction from the model equations. The equations are designed to write down the precise form of rates of change over time. Effects for interpersonal and noninterpersonal stress were entered in the same equations to examine their independent contribution. 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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