Supercompactness and measurable limits of strong cardinals II: Applications to level by level equivalence

We construct models for the level by level equivalence between strong compactness and supercompactness in which for κ the least supercompact cardinal and δ ≤ κ any cardinal which is either a strong cardinal or a measurable limit of strong cardinals, 2^δ > δ ⁺ and δ is < 2^δ supercompact. In these models, the structure of the class of supercompact cardinals can be arbitrary, and the size of the power set of κ can essentially be made as large as desired. This extends and generalizes [5, Theorem 2] and [4, Theorem 4]. We also sketch how our techniques can be used to establish a weak indestructibility result. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solvothermal synthesis of TiO2: anatase nanocrystals and rutile nanofibres from TiCl4 in acetone

This work reports a new synthetic approach for single‐phase TiO₂ nanomaterials by solvothermal treatment of titanium tetrachloride in acetone at 80–110 °C. Small, uniform, and yet size‐tunable (5–10 nm) anatase titania nanocrystallites were obtained using a low concentration of TiCl₄ in acetone (i.e., at molar ratios of TiCl₄/acetone ≤ 1:15) in the temperature range of 80–110 °C, while rutile nanofibers were synthesized using a high concentration of TiCl₄ (e.g., TiCl₄/acetone = 1:10) at 110 °C. Copyright © 2007 John Wiley & Sons, Ltd.     

The large-particle method in arbitrary nets and its application to the solution of problems in the aeroelasticity of a parachute

Modifications are introduced into the large-particle method to make it possible to use the method in arbitrary nonrectangular computing nets in the study of the flow of an ideal compressible gas over mobile thin permeable membranes. A problem in the aeroelasticity of a parachute is stated. An example is given of the solution of a problem in the stationary formulation for an axially symmetric parachute in the wake of a cylindrical leading body for supersonic flow.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 16–22     

Reaction of 2-formyl-1,3-cyclohexanediones with cyanoacetamide

Chemistry of Heterocyclic Compounds -