Three-dimensional Schwarzschild spacetimes

In the following we find all of the three-dimensional flat spacetimes which are static and rotationally symmetric.     

Aliasing Effects and Sampling Theorems of Spherical Random Fields when Sampled on a Finite Grid

Aliasing effects are investigated for spherical random fields sampled on a finite grid. Using the spherical harmonics expansion, it is shown that for a band-limited spherical random field its trend and spectrum can be uniquely reconstructed from the sampled field if the sampling points are judiciously designed. Analytical expressions are also obtained for aliasing errors in the trend and the spectrum when the field is not band-limited.     

2,4,6‐Trifluoropyrimidine. Reactions with nitrogen nucleophiles

In a continuation of our studies involving the nucleophilic displacement of one of the chlorines from 2,4,6‐trichloropyrimidine, we now report the initial displacement of one of the fluorine atoms from 2,4,6‐trifluoropyrimidine using both aliphatic and aromatic amines. The monosubstitution products favor 2‐substitution with ammonia and ethanolamine while aniline gave the 4‐substituted derivative as the preferred product.     

聚合物分散液晶光栅的衍射特性的研究

报道了一种由聚合物分散液晶膜与具有周期性条状电极结构板结合的新型光栅器件，借助于聚合物分散液晶膜的电光特性，这种栅对入射光的散射或衍射取决于对其施加的电压，即它是电场可调的，实验结果显示出当驱动电压超过器件器件阈值电压时，衍射光的强度和衍射斑的可见级次被电场调制，而且它能入射光的线性偏振态变为椭圆偏振态。     

A novel stereospecific synthesis of (±)-leukotriene A4(LTA4), methyl ester

The reaction of the phosphate $\text{1}$ with the expoxyaldehyde $\text{2}$ is reported as the key step in a novel stereospecific synthesis of (±)-LTA₄, methyl ester $\text{3}$.     

Pyrimidine N-oxides. Preparation of 6-chloro-2,4-diaminopyrimidine 3-N-oxide and its reactions

The peroxyacid oxidation of 6-chloro-2,4-diaminopyrimidine ( 1 ) led to two products, 6-chloro-2,4-diaminopyrimidine 3-N-oxide ( 2 ) and 2,4-diamino-5,6-dichloropyrimidine 3-N-oxide ( 3 ). The assignment of structure of both of these compounds was made on the basis of ir, uv, nmr, and mass spectral data. A discussion of the pathways involved in the formation of 3 is presented.     

Catalytic, asymmetric synthesis of α,α-disubstituted amino acids

Copper(salen) complex 1 has been found to catalyse the asymmetric alkylation of enolates derived from a variety of amino acids. There is a clear relationship between the size of the side chain in the substrate and the enantioselectivity of the process, so that the enantioselectivity decreases in the order alanine>aminobutyric acid>allylglycine>leucine>phenylalanine>valine. A transition state model which accounts for the influence of the size of the side chain on the enantioselectivity of the reactions is presented.     

Mechanistic studies on the asymmetric alkylation of amino ester enolates using a copper(II)salen catalyst

Hammett data indicate that the asymmetric alkylation of enolates catalysed by copper(II)salen complex 1, proceeds by an asynchronous S(N)2 reaction and that the role of the catalyst is to enhance the nucleophilicity of the enolate.     

Energy migration and transfer in poly(phenylacetylene)

Studies have been made of energy migration and transfer in dilute solutions of poly(phenylacetylene). In fluid media, “down-chain” energy migration is very efficient (being limited only by chain length in the system studied); however, in a rigid matrix, the energy migration rate is significantly lower. It is suggested that segmental rotation in a fluid environment brings neighbouring chain units into conformations suitable for resonance energy transfer and also breaks conjugated sequences functioning as exciton “traps”. The broad absorption spectrum (and relatively high extinction coefficients) coupled with the efficient transfer of the energy make these substances very efficient energy transfer additives in polymer systems.