A systematic method is pr-esented which synthesizes suboptimal control in the regulator problem occasioned upon the deviation of a point reactor from equilibrium. The method is based on the singular perturbation theory with advantage taken of the small ratio existing between the mean life time of the prompt neutron and the total delayed-neutron fraction. The idea of time separation is applied to the boundary layers at both ends of the control period, which yields a uniformly valid solution in the form of an asymptotic series for the control and for the neutron density trajectory. The limits of error are given for the series solution thus derived. The method is shown to bring about considerable reductions in the demands on both computer time and memory through elimination of the stiffness inherent in the original system. Some numerical examples are presented to demonstrate the validity of the proposed method. A similar formulation can be applied also to the problem of control during a change of power level, when considered as a tracking problem.

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A solution of the multi-group multi-regional diffusion equation in two-dimensional cylindrical (ρ-z) geometry is obtained in the form of a regionwise double series com-posed of Bessel and trigonometrical functions.
The diffusion equation is multiplied by weighting functions, which satisfy the homogeneous part of the diffusion equation, and the products are integrated over the region for obtaining the equations to determine the fluxes and their normal derivatives at the region boundaries. Multiplying the diffusion equation by each function of the set used for the flux expansion, then integrating the products, the coefficients of the double series of the flux inside each region are calculated using the boundary values obtained above.
Since the convergence of the series thus obtained is slow especially near the region boundaries, a method for improving the convergence has been developed. The double series of the flux is separated into two parts. The normal derivative at the region boundary of the first part is zero, and that of the second part takes the value which is obtained in the first stage of this method. The second part is replaced by a continuous function, and the flux is represented by the sum of the continuous function and the double series.
A sample critical problem of a two-group two-region system is numerically studied. The results show that the present method yields very accurately the flux integrals in each region with only a small number of expansion terms.

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When a reactor noise theory is applied to reactor diagnosis or stability analysis, it is necessary to consider non-linear non-stationary reactor noise phenomena. A new approach to the reactor noise theory is developed on the basis of recent studies on the theory of non-linear non-equilibrium statistical physics. This approach brings into relief the importance of making a clear distinction between extensive and intensive variables. A basic equation is derived in a quite general form, which yields a solution of asympto-tic character for large systems. In the lowest-order approximation, the formalism yields the conventional equations. This leads to a clear description of the relation between the Langevin and the Kolmogorov methods, and substantiates the assumption of Gaussian distribution of the number of neutrons. A rigorous analysis of the newly derived equation is made with the aid of flow patterns representing the Hamilton-Jacobi equation. A sample application of the formalism is presented for a system with randomly fluctu-ating parameters.

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An analysis of the effect of flow (or pressure) tapering on the productivity of step cascades, with account taken of the relations existing between the interstage flow rates, pressure levels and stage separation factors, revealed that productivity and separative work could increase by about 4% in a typical 3-size gaseous diffusion plant. A consider-able gain could be expected by applying the tapering to sections comprising about 30 stages, into which each step would be divided. Further, an examination is made of the extent of reduction that can be expected of the mixing loss through flow tapering.

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