Stationary jointly

Show that the master equation can, in principle, be solved by means of an r-variable generating function. In particular, prove that all solutions tend to a stationary joint Poisson distribution.510... 

Fig. 7.6. The stationary joint correlation functions as a function of the parameter A. Curves 1 to 4 correspond to A = 0 10-1 1 and 10, respectively, d = 3.

Alternatively an exponential form can be used as approximation for the stationary Joint probability density function fx,v(5<.y). e-... 

Precipitation Pamphlet, Western Precipitation Company C-103R-1, Los Angeles, Calif., 1952, p. 3, E. Bakke The Application of Wet Electrostatic Precipitators for Control of Fine Particulate Matter, Paper presented at Symposium on Control of Fine Particulate Emissions from Industrial Sources for the Joint U.S.-U.S.S.R. Working Group, Stationary Source Air Pollution Control Technology, San Francisco, Calif., January 15-18, 1974, pp. 6-7. 

C Filter compartment, fitted with inlet (d) and outlet (e) for filter solution (stationary or circulating), and with ground joint (/) to D Reaction flask, fitted with gas inlet (g) and outlet (h). 

Figure 8.17 depicts MD-PC performed on three different types of stationary phase (6). The three grafted chromatographic plates (Figure 8.17(a)) are clamped in lap-joint fashion with the edges of their stationary phases in close contact. The manner in which the three plates are prepared and the separation which can theoretically be achieved are also apparent from the schematic diagrams in Figures 8.17(b-d), in which the most polar stationary phase is phase A and the least polar is stationary phase C . 

In the joint presence of an electric field E and a magnetic field B in a medium, the stationary electron velocity can be written as... 

Homogeneous, linear Fokker-Planck equations are known to admit a multi-variate Gaussian PDF as a solution.33 Thus, this closure scheme ensures that a joint Gaussian velocity PDF will result for statistically stationary, homogeneous turbulent flow. 

The U.S. Department of Energy s Office of Fossil Energy has a joint program with fuel cell developers to develop the technology for stationary power applications includes central power and distributed generation. 

Fig. 2. Salt cup dispensing device Metal pin A connects rotating Teflon disc C to upper glass joint stationary Teflon disc D is anchored by pins at B...

Second Order Stationarity. With only a single realization of the random function it would be impossible to make any meaningful inferences about the random function if we did not make some assumptions about its stationarity. A random function is said to be strictly stationary if the joint probability density function for k arbitrary points is invariant under simultaneous translation of all... 

Report of the Joint Committee on the Use of Antibiotics in Animal Husbandry and Veterinary Medicine, 1969. Her Majesty s Stationary Office, London. 

Balling, L. and Hein, D. (1989) Proceedings of the Joint Symposium on Stationary NControl, San Francisco, CA, 6-9 March 1989. 

Gasket - A deformable material clamped between essentially stationary faces to prevent the escape of matter through an opening or joint. 

A procedure similar to the condensate separation in the imperfect Bose gas was employed by Lifshitz and Pitaevski [78]. The diagrammatic technique allows us to calculate the reaction rate and steady-state joint correlation functions. A separation of a condensate from terms with k = 0 cannot be done without particle production (p = 0), in which case nA, tiq —> 0 as t —> oo. In this respect the formalism presented by Lushnikov [111] for the non-stationary processes is of certain interest. 

The origin of this unusual behaviour is partly clarified from Fig. 6.34(a) where the relevant curves 2 demonstrate the same kind of the non-monotonous behaviour as the critical exponents above. Since, according to its definition, equation (4.1.19), the reaction rate is a functional of the joint correlation function, this non-monotonicity of curve 2 arises due to the spatial re-arrangements in defect structure. It is confirmed by the correlation functions shown in Fig. 6.34(a). The distribution of BB pairs is quasi-stationary, XB(r,t) X°(r) = exp[(re/r)3], which describes their dynamic aggregation. (The only curve is plotted for XB in Fig. 6.35(a) for t = 102 (the dotted line) since for other time values XB changes not more than by 10 per cent.) This quasi-steady spatial particle distribution is formed quite rapidly already at t 10° it reaches the maximum value of XB(r, t) 103. The effect of the statistical aggregation practically is not observed here, probably, due to the diffusion separation of mobile B particles. 

The solution of the first kind is stable and arises as the limit, t —> oo, of the non-stationary kinetic equations. Contrary, the solution of the second kind is unstable, i.e., the solution of non-stationary kinetic equations oscillates periodically in time. The joint density of similar particles remains monotonously increasing with coordinate r, unlike that for dissimilar particles. The autowave motion observed could be classified as the non-linear standing waves. Note however, that by nature these waves are not standing waves of concentrations in a real 3d space, but these are more the waves of the joint correlation functions, whose oscillation period does not coincide with that for concentrations. Speaking of the auto-oscillatory regime, we mean first of all the asymptotic solution, as t —> oo. For small t the transient regime holds depending on the initial conditions. 

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