Let K and L be compact convex sets in Rn. The following two statements are shown to be equivalent: (i) For every polytope Q ⊆ K having at most n+ 1 vertices, L contains a translate of Q. (ii) L contains a translate of K. Let 1 ≤ d ≤ n − 1. It is also shown that the following two statements are equivalent: (i) For every polytope Q ⊆ K having at most d+ 1 vertices, L contains a translate of Q. (i...

materials exhibit significant creep behavior at temperatures above 40% of their absolute melt temperature. lead, tin and their alloys are such materials which experience significant creep behavior in room temperature. one of the most important applications of the tin-lead alloys is soldering electronic circuits in electronic industry, and for lead are isolation walls and wet batteries. room tem...

copper is an essential micronutrient for plant growth which is involved in many metabolic processes. however excessive amounts of copper may cause environmental pollution. with an increase in the contamination of urban areas with heavy metals, more attention should be paid to the role of ornamental plants in removing pollutants from the soils. the effects of heavy metals on the growth parameter...

In this study, different volume fractions of silicon-carbide-reinforced AA2024 matrix composites were successfully fabricated using stir-casting (SC) and die-casting (DC) processes. The microstructural difference physical properties the during manufacturing process investigated in detail. analysis found that composite produced by SC had some reinforcement clusters pores; however, defects signif...