Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

Structure of 2-Amino-4-phenyl-9H-pyrimido[4,5-b]indole and Its Nitrate in Crystal and Solution

The crystal structures of 2-amino-4-phenyl-9H-pyrimido[4,5-b]indole and its nitrate were determined by XRD analysis. ¹³C NMR, XRD, and quantum-chemical data indicate that the acid proton is predominantly localized at the N(3) atom of the pyrimidine ring in both isolated nitrate molecules and in molecules in crystal and solution.     

Properties and application of aryl-substituted azines (review)

Aryl-substituted six-membered azaaromatic heterocycles have a range of properties that make it possible to use them in scientific investigations and in modern regions of technology. The possibilities of using arylazines in chemical analysis, in catalytic processes, and as optical and photochromic materials in polymer chemistry are surveyed.Novosibirsk Institute of Organic Chemistry. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1011–1029, August, 1997.     

Synthesis of functional 2-substituted 4-phenyl-9H-pyrimido[4,5-b]indoles

A method was developed for the synthesis of 2-oxo-4-phenyl-2,3-dihydro-9H-pyrimido[4,5-b]indole as well as of 2-chloro- and 2-nitramino-4-phenylpyrimido[4,5-b]indoles. The replacement of the chlorine atom in 2-chloropyrimidoindole gave rise to a number of its functional derivatives (morpholino, azido, and cyano). The reaction of 2-chloro-substituted pyrimidoindole with hydrazine hydrate and catalytic hydrogenation of 2-nitraminopyrimidoindole were studied.     

Groups of automorphisms of finite p-groups

Thompson [1] showed that if p is an odd prime number, A is a p-group of operators of the finite group P in which the Frattini subgroup (P) is elementary and central, and P/(P) is a free Z_pA-module, then Cp(A) covers C_P/(P)(A). Then he proposed the question of whether it is possible in this theorem to weaken the hypothesis that (P) be elementary and central. In the work it is shown that this hypothesis may be replaced by a much weaker one; it is sufficient that P be met-Abelian and have nilpotence class 相似文献   

Formation of the fused system 5H,7H-pyrido[2,3-b:6,5-b′]diindole from 3-arylidene-2-ethoxyindolenines and hydrazine hydrate

Three 12-aryl-5H,7H-pyrido[2,3-b:6,5-b??]diindoles (Ar = Ph, 4-BrC₆H₄, and 4-MeOC₆H₄) were obtained from appropriate 3-arylidene-2-ethoxyindolenines and hydrazine hydrate.     

Amorphous Calcium Phosphates: Solvent-Controlled Growth and Stabilization through the Epoxide Route

Calcium phosphates stand among the most promising nanobiomaterials in key biomedical applications, such as bone repairment, signalling or drug/gene delivery. Their intrinsic properties as crystalline structure, composition, particle shape and size define their successful use. Among these compounds, metastable amorphous calcium phosphate (ACP) is currently gaining particular attention due to its inherently high reactivity in solution, which is crucial in bone development mechanisms. However, the preparation of this highly desired (bio)material with control over its shape, size and phase purity remains as a synthetic challenge. In this work, the epoxide route was adapted for the synthesis of pure and stable ACP colloids. By using biocompatible solvents, such as ethylene glycol and/or glycerine, it was possible to avoid the natural tendency of ACP to maturate into more stable and crystalline apatites. Moreover, this procedure offers size control, ranging from small nanoparticles (60 nm) to micrometric spheroids (>500 nm). The eventual fractalization of the internal mesostructured can be tuned, by simply adjusting the composition of the ethylene glycol:glycerine solvent mixture. These findings introduce the use of green solvents as a new tool to control crystallinity and/or particle size in the synthesis of nanomaterials, avoiding the use of capping agents and preserving the natural chemical reactivity of the pristine surface.     

Calculating product yields in selective catalytic oxidation in flow and gradient-free reactors

Simple analytic expressions have been obtained for the more common types of selective oxidation mechanisms provided by oxide catalysts, which relate the product yield to the extent of reaction in a flow or gradient-free reactor. It is shown to be possible to increase the yield by the use of combined catalyst layers.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 23, No. 3, pp. 345–349, May–June, 1987.     

Boundaries of Coxeter Matroids

The purpose of this paper is to introduce, for a finite Coxeter groupW, the mod 2 boundary operator on the space of all Coxeter matroids (also known asWP-matroids) forWandP, wherePvaries through all the proper standard parabolic subgroups ofW(Theorem 3 of the paper). A remarkably simple interpretation of Coxeter matroids as certain sets of faces of the generalized permutahedron associated with the Coxeter groupW(Theorem 1) yields a natural definition of the boundary of a Coxeter matroid. The latter happens to be a union of Coxeter matroids for maximal standard parabolic subgroupsQ_iofP(Theorem 2). These results have very natural interpretations in the case of ordinary matroids and flag-matroids (Section 3).