Generalisations of Heyman's and Foulkes' theorems using dual formulation

Existing duality principles in structural optimisation are briefly reviewed and then they are extended to structures with segment-wise constant cross-sections. All theories are discussed in the particular context of optimal plastic beam design with symmetric convex specific cost functions and are confirmed by independent calculations on illustrative examples. It is shown that the optimal solution is always associated with a displacement field in which the mean absolute curvature value for each segment equals the subgradient of the specific cost function, with respect to the maximum absolute moment value for that segment. Moreover, the dual problem consists of the maximisation of the difference of two terms: the first one is the integral of the product of load and deflection (external work), and the second is the sum of products of segment lengths and the mean complementary cost values (taken with respect to the mean absolute curvature for that segment). Finally, some tentative proposals for a class of non-convex optimisation problems are presented. For special cases, the proposed general statements reduce to theorems by Heyman, Foulkes and Hemp.     

Measurement of the delayed-neutron yields in the fission of233U,236U,237Np,240Pu,and241Pu by neutrons from the spectrum of a fast reactor

Translated from Atomnaya Énergiya, Vol. 66, No. 2, pp. 100–103, February, 1989.     

Dosimetric characteristic of VVR-M reactor with respect to tritium

Translated from Atomnaya Énergiya, Vol. 67, No. 2, pp. 111–113, August, 1989.     

Some Regularities of Heat and Mass Transfer in the Case of Fire Within a Building

Results of a numerical investigation of heat and mass transfer at the initial stage of fire within a building in combustion of kerosene, carried out with the use of a three-dimensional mathematical field model, are presented. A comparison of the distribution of the averaged temperatures and velocities along the vertical axis of the convective column and of the mass rates of gas flows through an open opening with the experimental data has been made. Substantial three-dimensional inhomogeneities of the velocities and the temperatures in the near-ceiling layer have been revealed. It has been established that near the opening there is a critical separation zone which influences significantly the parameters of natural gas transfer.     

Adaptive Optimal Nonlinear Filtration and Certain Related Topics. II

The properties of the solutions of optimal parametric filtration equations and an adaptive variant of the problem with regard for time-drift of the unknown parameters of the system are studied. Along with the Kalman interpretation of the optimal adaptive nonlinear filter, the Bayes approach to applying the respective a posteriori densities is also studied.