Problems Equivalents

For simplicity we will consider the flow through the 2D slit O = (0,+oo) X (0,H). To have a 2D problem equivalent to the case (B) from Taylor s article, we reformulate the characteristic velocity and the radius. Obviously we have... 

Substitution of equation (7.1.19) into equation (7.1.17) leads to the problem equivalent to the calculation of statistical integrals in a system of m particles placed in volume vq and interacting by the pair-wise forces. It is clear that such a problem could be solved only approximately. The main approximation we use hereafter is the replacement of the mean value of a product of functions for a product of two mean values. Thus... 

This means that there is no potential problem equivalent to the hydrostannation in the tin hydride method. 

For the stability analysis of fluid dynamical system whose equilibrium solution is given by a parallel or quasi-parallel flow, one has to solve the Orr-Sommerfeld equation depending on whether the mean flow is two- or three-dimensional. For the two-dimensional problem equivalent boundary conditions are given by... 

The Decision Representation Language (DRL, [808, 809]) is a notation for decision rationale. Its top-level element is the Decision Problem, equivalent to the Question in QOC. Alternatives and Goals in DRL correspond to Options and Criteria, respectively. The outstanding characteristic of DRL is that Claims, i.e., statements which may be judged or evaluated, can be linked in a way that enables to represent complex argumentations in a straightforward... 

Two-body problem, equivalent, dquivalentes Zweikorper problem 459-... 

With this specialization, the perturbed eigen-problem equivalently becomes ... 

Further restriction of the interactions to nearest neighbors makes this problem equivalent to that of the Ising model with nearest neighbor interactions. Then the partition function can be mapped onto an Ising model with spin variables Si = 1 by means of the transformation... 

It represents a linear differential equation of the first order, implying the assumption that, for a system in non-equilibrium, relaxation takes place with a rate which increases linearly with the distance from the equilibrium state. This is not a specific kind of expression devised to deal exclusively with our problem. Equivalent equations are broadly used in thermodynamics to describe the kinetics of all sorts of irreversible processes. Importantly, the equation includes one time constant only, the relaxation time r. 

Several parameters come into the relation between density and equivalence ratio. Generally, the variations act in the following sense a too-dense motor fuel results in too lean a mixture causing a potential unstable operation a motor fuel that is too light causes a rich mixture that generates greater pollution from unburned material. These problems are usually minimized by the widespread use of closed loop fuel-air ratio control systems installed on new vehicles with catalytic converters. 

A problem obviously exists in trying to characterise anomalies in concrete due to the limitations of the individual techniques. Even a simple problem such as measurement of concrete thickness can result in misleading data if complementary measurements are not made In Fig. 7 and 8 the results of Impact Echo and SASW on concrete slabs are shown. The lE-result indicates a reflecting boundary at a depth corresponding to a frequency of transient stress wave reflection of 5.2 KHz. This is equivalent to a depth of 530 mm for a compression wave speed (Cp) of 3000 m/s, or 706 mm if Cp = 4000 m/s. Does the reflection come from a crack, void or back-side of a wall, and what is the true Cp ... 

Equation XVII-70 bears a strong resemblance to the Langmuir equation (see Ref. 4)—to the point that it is doubtful whether the two could always be distinguished experimentally. An equivalent form obtained by Volmer [53] worked well for data on the adsorption of various organic vapors on mercury [54] (see Problem XVII-40). 

A second recent development has been the application 46 of the initial value representation 47 to semiclassically calculate A3.8.13 (and/or the equivalent time integral of the flux-flux correlation fiinction). While this approach has to date only been applied to problems with simplified hannonic baths, it shows considerable promise for applications to realistic systems, particularly those in which the real solvent bath may be adequately treated by a fiirther classical or quasiclassical approximation. 

A fiill solution of tlie nonlinear radiation follows from the Maxwell equations. The general case of radiation from a second-order nonlinear material of finite thickness was solved by Bloembergen and Pershan in 1962 [40]. That problem reduces to the present one if we let the interfacial thickness approach zero. Other equivalent solutions involved tlie application of the boundary conditions for a polarization sheet [14] or the... 

Suppose now that the sites are not independent, but that addition of a second (and subsequent) ligand next to a previously bound one (characterized by an equilibrium constant K ) is easier than the addition of the first ligand. In the case of a linear receptor B, the problem is fonnally equivalent to the one-dimensional Ising model of ferromagnetism, and neglecting end effects, one has [M] ... 

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