Fifty years of the Siberian Division of the Russian Academy of Sciences

This is a write-up on the foundation of the Sobolev Institute of Mathematics in 1957.     

逻辑函数在布尔减-异或、布尔除-符合代数系统中的规范展开式

证明了布尔减、异或运算以及布尔除、符合运算的完备性,并从与-异或及或-符合代数系统中的RM、CRM展开式出发,分别推导了任意逻辑函数在布尔减-异或及布尔除-符合代数系统中的规范展开式.举例说明了与-或-非代数系统中规范展开式与布尔减-异或、布尔除-符合代数系统中的规范展开式之间的转换.     

Rearrangement during cyclisation of some 3-(2-pyrrolyl) propionic acids and related compounds

Cyclisation of the title compounds leads to mixtures of the expected 4H-cyclopental[b]pyrrol-4-ones (1), the corresponding 6-ones (3) by a single rearrangement, and the cyclopenta[c]pyrrol-4-ones (4) by a double rearrangement, the proportions depending upon the substituents.The ¹H NMR spectra of 2-methyl-4H-cyctopenta[b]thiophen-6-one (3f) shows 6J long range $\text{CH}{}_3\text{CH}{}_2$ coupling, but this is absent in the corresponding pyrroles (3c,d). The ¹³C spectra of 1 and 3 cannot be interpreted on the basis of substituent chemical shifts in pyrroles and thiophens, and are clearly -CH = CH-X (X = NMe, NPh, S) bridged derivatives of cyclopent-2-enone.     

An electron-diffraction study of the molecular structure of gaseous perbromyl fluoride and calculation of its force field and vibrational amplitudes

The molecular structure of FBrO₃ has been studied by gas-phase electron diffraction. Least-squares refinements of the molecular geometry using fixed spectroscopic amplitudes revealed two geometrical minima. Initially, the amplitudes employed were derived from diagonal force fields obtained by spectroscopic least-squares refinements to fit observed and calculated wave numbers; for each geometry there are two spectroscopic minima. In the lowest geometrical minimum the wave number agreement is poor, however, the introduction of the ∠OBrO/∠FBrO interaction force constant removed the discrepancies; the resulting force field is F(Br-O) = 6.92 ± 0.02 mdyn Å^?1F(Br-F) = 3.22 ± 0.03 mdyn Å^?1, F(∠OBrO) = 1.06 ± 0.02 mdyn Å, F(∠FBrO) = 0.81 ± 0.03 mdyn Å, F(∠OBrO/∠FBrO) = ?0.19 ± 0.02 mdyn Å. In the corresponding geometrical minimum r_g(Br-O) = 1.582 ± 0.001 Å, r_g(Br-F) = 1.708 ± 0.003 Å, r_α(∠OBrO) = 114.9 ± 0.3°, r_α(∠FBrO) = 103.3 ± 0.3°. Perpendicular amplitude correction coefficients, calculated for each force field employed, were used throughout to relate the interatomic distances through the r_α-structure. The geometries of the r_α^o- and r_e-structures are estimated.     

Relative raman line intensities for H2 and for D2. Correction factors for molecular non-rigidity

Ab initio calculations are presented for H₂ and D₂ relative Raman intensities originating from common rotational levels for both vibrational-rotational and pure rotational transitions. Factors f(J) required to correct measured intensities for molecular non-rigidity (e.g. in temperature measurements) are tabulated. The calculations are compared with literature perturbation-theory equations (significant differences at large J in vibration-rotation) and with experiment.     

Fluorescence decay of tertiary aliphatic amines

The fluorescence decay of the tertiary aliphatic animes trimethylamine (TMA), triethylamine (TEA) and tri-n-propylamine (TPA) in the vapour phase excited between 260 and 215 nm has been shown to consist of a single, wavelength-dependent, component when the first excited state is uniquely excited, but two components when the first and second excited states are simultaneously excited. This dual exponentiality persists at pressures as low as 10 mTorr, and it is argued that the two-component decay does not arise from collisional vibrational relaxation.     

Separation and gravimetric determination of cerium and lanthanum with N-m-tolyl-m-nitrobenzohydroxamic acid

Cerium and lanthanum were determined gravimetrically by selective precipitation with N-m-tolyl-m-nitrobenzohydroxamic acid and separated from several metal ions such as Ag(+), Be(2+) , Pb(2+) , Mn(2+) , Cu(2+), Zn(2+) , Cd(2+) , Hg(2+) , Pd(2+) , Ga(3+) A1(3+) , Bi(3+) , Sb(3+), Sn(4+), Ce(3+) , Pr(3+) , Nd(3+) , Ti(4+), Zr(4+), Th(4+), V(5+) , Mo(6+) and U(6+) . The precipitates were weighted directly after drying at 110 degrees . The analytical results indicated the composition of the complexes to be (C(14)H(11)N(2)O(4))(n)M.     

An even earlier (1717) usage of the expression “golden section”

In a previous article in this journal, Roger Herz-Fischler has pointed out an early usage of the expression “golden section” from 1789. In this note an even earlier usage from 1717 is discussed.     

浅谈制药工程专业有机化学实验教学的心得和体会——以三苯甲醇的制备和重结晶实验为例

有机化学实验是制药工程专业的一门必修课,旨在训练学生有机合成基本实验技能。本文以三苯甲醇的制备和重结晶实验为例,讲述了笔者在多年教学中获得的一点感悟和经验:1)将实验步骤分解成片断讲解可以使学生更好地理解和记忆实验过程和操作目的;2)重要的基本操作应反复练习,即"学习、复习、提高",通过三次重复练习来实现巩固和熟练掌握该操作的目的。     

Wedderburn's factorization theorem application to reduced -theory

This article provides a short and elementary proof of the key theorem of reduced -theory, namely Platonov's Congruence theorem. Our proof is based on Wedderburn's factorization theorem.