Fuzzy Weirstrass theorem and convex fuzzy mappings

The convexity and continuity of fuzzy mappings are defined through a linear ordering and a metric on the set of fuzzy numbers. The local-global minimum property of real-valued convex functions is extended to convex fuzzy mappings. It is proved that a strict local minimizer of a quasiconvex fuzzy mapping is also a strict global minimizer. Characterizations for convex fuzzy mappings and quasiconvex fuzzy mappings are given. In addition, the Weirstrass theorem is extended from real-valued functions to fuzzy mappings.     

Processes of the Collision Interaction between Ceramic Particles Being Crushed in a Circulation Pneumatic Crusher

A new circulation pneumatic crusher capable of producing submicron powders of refractory materials is presented. A mathematical model is constructed for the dynamic breaking of ceramic macroparticles. This model allows the basic laws of shock-wave crushing in the circulation pneumatic apparatus to be analyzed.__________Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 3, 2005, pp. 327–333.Original Russian Text Copyright © 2005 by Belov, Biryukov, Roslyak, Yugov, Afanas’ev.     

The focusing magnetic resonance system with a new type of supersonic atomic beam source

A focusing magnetic resonance system (MRS) with a new type of supersonic atomic - and molecular - beam source is suggested. The beam sources used in the MRS are discussed and the main operation principles of the suggested supersonic beam source as well as the advantages of this type of source over the rest are shown. An optimization procedure for the magnetic resonance system with the effect of the finite source size taken into account is considered. Numerical results are given and analyzed. The MRS with the new type of beam source possesses higher transmission with low background and is simpler and cheeper in construction as compared to the conventional systems.     

Effects of alloy additions on the microstructures and tensile properties of cast Co-Cr-Mo alloy used for surgical implants

The composition of the Co-Cr-Mo alloy has been modified by additions of nickel and some trace elements aluminium, titanium and boron. In this paper, the first part of the present study, the effects of alloy additions on the microstructures and tensile properties of the as-cast Co-Cr-Mo alloy are discussed. The effects of alloy additions on the fatigue behaviour of the alloy will be discussed in the second part of the present study. It is found that alloy additions do not seem to result in changes in the nature of the casting structure. A directional, coarse dendritic cast structure is produced in the modified alloys as in the base alloY. However, the alloy additions affect the carbide precipitations and the formation of some fine details of the microstructure such as dislocations, stacking faults and twins produced during the solidification. A considerable improvement in the transient mechanical properties, especially in the tensile ductility, is achieved by modifying the base alloy with alloy additions.     

Calibrating high-vacuum gauges

Translated from Izmeritel'naya Tekhnika, No. 6, pp. 19–20, June, 1989.     

Plastic flow and fracture of Pd40Ni40P20 metallic glass under an indentor

The geometry of plastic flow under spherical and Vickers indentors in Pd₄₀Ni₄₀P₂₀ metallic glass has been investigated by sectioning and etching. The surface pile-ups and slip lines around the indentations are found to be only a small part of the total deformation. Beneath the surface extensive plastic zones are formed in which material is moved radially away from the indentor, but this movement is produced by slip on surfaces of high shear stress rather than by direct radial flow or compaction. Networks of cracks or incipient cracks also form around an indentation but are not normally visible until the material is etched.