Reactions of Magnesium and Titanium Alkoxides. Preparation and Characterization of Alkoxy-Derived Magnesium Titanate Powders and Ceramics

The interaction between magnesium and titanium alkoxides is studied in order to chose the best precursors for synthesis of MgTiO₃. No reaction between magnesium and titanium methoxides and isopropoxides occurs. The solubility diagrams for Mg(OR)₂-Ti(OR)₄-ROH, R = Et,-Bu at 20°C are studied. Magnesium ethoxotitanates of variable composition Mg_nTi_4-n (OEt)_16-2n2nEtOH (n=2.0-0) which are structural analogs of Ti₄(OR)₁₆ (R = Me, Et) are isolated. This is a quite unusual example of statistical distribution of heteroatoms in molecular structures of metal alkoxides. Among the systems of metal alkoxides with simple aliphatic radicals only Mg(OBu)₂-Ti(OBu)₄-BuOH gives a convenient precursor for the synthesis of MgTiO₃. A simple scheme of preparation of magnesium titanate from the alkoxide solutions is suggested. The phase purity of MgTiO₃ is to a considerable extent dependent on the hydrolysis conditions. The alkoxy-derived magnesium titanate is obtained in the form of a uniform fine powder, it can be sintered into dense ceramics in the temperature range of 1140–1220°C which is 150–200°C lower in comparison with the conventional powders.     

On linear vertex-arboricity of complementary graphs

The linear vertex-arboricity ρ(G) of a graph G is defined to be the minimum number of subsets into which the vertex set of G can be partitioned such that each subset induces a linear forest. In this paper, we give the sharp upper and lower bounds for the sum and product of linear vertex-arboricities of a graph and its complement. Specifically, we prove that for any graph G of order p. and for any graph G of order p = (2n + 1)², where n ? Z⁺, 2n + 2 ≦ ρ(G) + ρ(G ).     

Selective rearrangements of 4a,5-epoxides of 4,4-dimethyl-1,2,3,4,6,8a-hexahydronaphthalenes.

Epoxidation selectivity of a number of 4,4-dimethyl-1,2,3,4,6,8a-hexahydronaphthalenes 4 were examined. Exposure of the isolated α-epoxides 7provided excellent yields (79–92%) or rearranged fused indene-oxetanes 8. Treatment of β-epoxides 5 with BF3·OEt₂ also yields oxetanes 8 and related alcohols 9 and 10.     

酚醛型吸附树脂在非水体系中对吡啶和N,N-二甲基苯胺的吸附性能研究

研究了酚醛型吸附树脂JDW 2在非水体系中对吡啶和N ,N 二甲基苯胺的静态吸附 .由实验结果推论正己烷中树脂对吡啶和N ,N 二甲基苯胺的吸附是以氢键吸附机理为主进行的 ,JDW 2酚醛型吸附树脂在正己烷中 ,等温吸附吡啶和N ,N 二甲基苯胺的平衡吸附数据符合Langmuir方程 ,相关系数在 0 99以上 ,因此 ,酚醛型吸附树脂在正己烷中吸附吡啶和N ,N 二甲基苯胺属单分子层吸附 ;同时对非水体系中乙醇或乙酸乙酯的含量对树脂吸附吡啶和N ,N 二甲基苯胺的影响进行了研究     

Mach's Principle and Model for a Broken Symmetric Theory of Gravity

We investigate spontaneous symmetry breaking in a conformally invariant gravitational model. In particular, we use a conformally invariant scalar tensor theory as the vacuum sector of a gravitational model to examine the idea that gravitational coupling may be the result of a spontaneous symmetry breaking. In this model matter is taken to be coupled with a metric which is different but conformally related to the metric appearing explicitly in the vacuum sector. We show that after the spontaneous symmetry breaking the resulting theory is consistent with Mach's principle in the sense that inertial masses of particles have variable configurations in a cosmological context. Moreover, our analysis allows to construct a mechanism in which the resulting large vacuum energy density relaxes during evolution of the universe.     

Nonrelativistic Strong-Field Photoionization without Making the Dipole Approximation

Within the context of the time-reversed S-matrix approach to photoionization, and employing a recently proposed strong-field solution to the Schrödinger equation, analytic expressions for the atomic photoionization rates are obtained here without using the dipole approximation. We show that the absorbed photon momentum shows up as a forward-directed momentum component for the photoelectron. All the expressions reported in this work have the correct limits when the dipole approximation is used.     

Weak Mixing in Interval Exchange Transformations of Periodic Type

Interval exchange transformations (IETs) are piecewise isometries of the interval, obtained permuting a certain number of subintervals. We give a condition on IETs in the special subclass of IETs with periodic Rauzy-Veech cocycle which guarantees weak mixing, i.e. the continuity of the spectrum. The proof involves the study of the associated spectral measures. The condition can be checked explicitly by computing a certain Galois group of a field related to the Ravzy-Veech cocycle. Explicit examples of weakly mixing IETs are constructed in the Appendix. *Dedicated to the memory of F.A. Berezin     

Polymer-bound oxathiaphospholane: a solid-phase reagent for regioselective monothiophosphorylation and monophosphorylation of unprotected nucleosides and carbohydrates

Two polymers bound to N,N-diisopropylamino-1,3,2-oxathiaphospholane were reacted with unprotected carbohydrates and nucleosides in the presence of 1H-tetrazole, followed by oxidation with tert-butyl hydroperoxide or sulfurization with Beaucage's reagent. The 1,3,2-oxathiaphospholane ring-opening with 3-hydroxypropionitrile, followed by treatment with DBU, afforded the corresponding monophosphate and monothiophosphate derivatives, respectively, through the elimination of polymer-bound ethylene episulfide. Reactions using this strategy offer the advantages of high regioselectivity, monosubstitution, and facile isolation and recovery of products.     

Selective diphosphorylation, dithiodiphosphorylation, triphosphorylation, and trithiotriphosphorylation of unprotected carbohydrates and nucleosides

[chemical reaction: see text]. Aminomethyl polystyrene resin-bound linkers of p-acetoxybenzyl alcohol were subjected to reactions with diphosphitylating and triphosphitylating reagents to yield the corresponding polymer-bound diphosphitylating and triphosphitylating reagents, respectively. A number of unprotected carbohydrates and nucleosides were reacted with the polymer-bound reagents. Oxidation with tert-butyl hydroperoxide or sulfurization with Beaucage's reagent, followed by removal of cyanoethoxy group with DBU and the acidic cleavage, respectively, afforded only one type of monosubstituted nucleoside and carbohydrate diphosphates, dithiodiphosphates, triphosphates, and trithiotriphosphates with high regioselectivity.