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.     

Resonant neutron filters in elemental analysis and radiography

Translated from Atomnaya Énergiya, Vol. 67, No. 4, pp. 271–274, October, 1989.     

Multifunctional alkylphenol additive

Translated from Khimiya i Tekhnologiya Topliv i Masel, No. 2, pp. 14–15, February, 1989.     

Computing hysteresis points of nonlinear equations depending on two parameters

A direct method is described for computing a hysteresis point (double turning point) corresponding to a cusp point of a system ofn nonlinear equations inn variables depending on two parameters. By addition of two equations a minimally extended system ofn+2 nonlinear equations is constructed for which the hysteresis point is an isolated solution. An efficient implementation of Newton's method is presented not requiring evaluations of second derivatives of the original problem. Two numerical examples show the efficiency of theQ-quadratically convergent method.     

Mechanisms of Active Fuzzy Expertise

Consideration was given to the decision making procedures based on the fuzzy messages of experts whose preferences on the set of collective decisions can also be fuzzy.     

Phase transformations in highly disperse powders during their rapid heating and cooling

Phase transformations in particles of ultrafine powders of graphite, hexagonal boron nitride, and quartz during rapid heating and cooling by passage through a laser beam were investigated. A continuous infrared laser with a wavelength of 10.6 μm was used as a heat source through which the powders were recycled several times. Methods of concentrating the product phases are described. Particles of diamond, carbides, cubic boron nitride, koesite and stishovite were obtained in the mixed products.     

The synthesis of distillation-based separation systems

The last dozen years have produced almost 50 English language articles on the synthesis of separation systems [1]. Most work has considered separating a single relatively ideal mixture into sharply split, usually pure-component products using systems of single-feed, two-product distillation columns. Of late, the work has considered heat-integrating these columns to reduce energy consumption. Present research will very likely produce valuable results for nonsharp separations.Earlier approaches developed both algorithmic- and heuristic-based tree search algorithms for discovering the better systems of non-heat-integrated columns. New results permit the design of heat-integrated systems.The paper highlights the above developments.     

Special numbers,still proceedings,other novelties

Modifications of solid water and their transitions are described as they relate to cryo electron microscopy. In particular, the various amorphous states (amorphous polymorphs) as they exist below 100 K are extensively investigated. The “high-density” midification exhibits a lower viscosity than the “low-density” form. Differences are also observed in the mechanism of void formation due to electron irradiation: in the high-density form, voids are formed — not, however, in the low-density form. Together with the reaction to radiation damage, the physical properties of amorphous solid water are discussed with respect to embedding of organic specimens. Finally, the conditions and pitfalls associated with preparation of thin and entirely vitrified ice layers by shock-freezing are described.