Is the List of Incomplete Open Cubes Complete?

Variations of Incomplete Open Cubes is the major project by the twentieth-century conceptual artist Sol LeWitt. In this paper we interpret the enumerative component of the project as embeddings of graphs. This formulation permits use of an algorithm to check the completeness of the list of the structures produced by the artist. Our conclusion is that the artist found the correct number of structures (that is, 122), but that his list contains a mistake in the presentation of a pair of incomplete cubes, a discovery that appears not to have been noted before.     

Structural dependence of microwave dielectric properties of spinel structured Mg2(Ti1-xSnx)O4 solid solutions: Crystal structure refinement,Raman spectra study and complex chemical bond theory

Mg₂(Ti_1-xSn_x)O₄ (x?=?0–1) ceramics were prepared through conventional solid-state method. This paper focused on the dependence of microwave dielectric properties on crystal structural characteristics via crystal structure refinement, Raman spectra study and complex chemical bond theory. XRD spectrums delineated the phase information of a spinel structure, and structural characteristic of these compositions were achieved with the help of Rietveld refinements. Raman spectrums were used to depict the correlations between vibrational phonon modes and dielectric properties. The variation of permittivity is ascribed to the Mg₂(Ti_1-xSn_x)O₄ average bond covalency. The relationship among the B-site octahedral bond energy, tetrahedral bond energy and temperature coefficient are discussed by defining on the change rate of bond energy and the contribution rate of octahedral bond energy. The quality factor is affected by systematic total lattice energy, and the research of XPS patterns illustrated that oxygen vacancies can be effectively restrained in rich oxygen sintering process. Obviously, the microwave dielectric properties of Mg₂(Ti_1-xSn_x)O₄ compounds were obtained (${\epsilon }_r$= 12.18, $Q\times f$?=?170,130?GHz, ${\tau }_f$?=??53.1?ppm/°C, x?=?0.2).     

Volumetric out-of-furnace heat treatment of 3600-M3 decomposers

Specifications require that all the welds in 12-m-diam. decomposers with a capacity of 3600 m³ be subjected to high-temperature tempering before going into service in order to alleviate the stresses from the welding operation. Specialists at the organizations VNIIPTkhimnefteapparatury and VNIImontazhspetsstroi have proposed out-of-furnace volumetric (complete) of the assembled decomposer with the use of special heaters. The use of this heating method has shortened assembly operations while providing the welds with a highquality heat treatment and reducing the stresses overall (including welding stresses, stresses from assembly of the decomposer, etc.) The technology ensures uniform heating of the housing of the decomposer and provides for close control over the process. The experience gained in heat-treating decomposers can also be used in the construction of other containers that come into contact with corrosive media. __________ Translated from Metallurg, No. 3, pp. 61–64, March, 2006.     

Optimal control of the effects from industrial transportation on the environment

The paper discusses optimal control of ecosystem state for observation of a generalized monotonically varying random parameter. A model is proposed for the controlled vector random process, whose components are assigned acceptable ranges and the observations are performed discretely. __________ Translated from Khimicheskoe i Neftegazovoe Mashinostroenie, No. 6, pp. 40–44, June, 2006.