Natural spline functions,their associated eigenvalue problem

Summary We consider the problem of studying the behaviour of the eigenvalues associated with spline functions with equally spaced knots. We show that they are wherem is the order of the spline andn, the number of knots.This result is of particular interest to prove optimality properties of the Generalized Cross-Validation Method and had been conjectured by Craven and Wahba in a recent paper.     

流动注射电化学发光测定维生素B1的研究

基于发现在强碱性介质维生素 B1对电生BrO-氧化Luminol的强化学发光有很强的抑制作用, 将在线恒电流电解产生BrO-与流动注射技术结合,建立了流动注射电化学发光测定维生素B1的新方法.该方法测定维生素B1的线性范围为1.0×10-8～6.0×10-6g·ml-1,检出限为3.2×10-9g·ml-1,相对标准偏差为1.2%(n=11).该法具有灵敏度高,可控性强等优点,用于片剂中的维生素B1含量测定,结果满意.     

Synthesis, X-ray structure and properties of a new nitrite-bound copper(II) complex with 2-(3,5- dimethylpyrazol-1-ylmethyl)pyridine in a CuN4(O) coordination

Synthesis and characterization of a nitrite-bound copper(II) compound [CuL⁴)₂(ONO)]ClO₄ have been achieved (L⁴ = 2-(3,5-dimethylpyrazol-1-ylmethyl)pyridine]. The bidentate ligand L⁴ provides a pyridine and a pyrazole donor site; however, they are separated by a methylene spacer. The complex has been structurally characterized and it belongs to only a handful of complexes having nitrito-bound mononuclear copper(II) centre. The metal atom has a distorted square pyramidal geometry with the copper atom displaced from the equatorial plane by 0.25 Å. In MeCN solution the green complex exhibits a broad ligand-field transition at 655 nm with a shoulder at 675 nm and in dichloromethane-toluene glass (80 K) it exhibits an EPR spectral feature characteristic of the unpaired electron in the d_x²−y² orbital. Variable-temperature (80–300 K) magnetic susceptibility measurements in the solid state as well as room temperature measurement in MeCN solution reveal mononuclear magnetically dilute copper(II) centre. When examined by cyclic voltammetry (MeCN solution) it displays electrochemically irreversible Cu^II---Cu^I response [cathodic peak potential, E_pc (V vs saturated calomel electrode (SCE)): −0.32]. An oxidative response is observed at 1.14 V, probably due to bound-nitrite oxidation and is partially removed to generate a solvated complex at the electrode surface. The latter species gives rise to reversible Cu^II---Cu^I redox response [ ].     

An easy preparation of per- and poly-fluoroalkyl propenyl sulfones

Sodium tridecafluorohexanesulfinate (1a) and sodium 1-chloro-2,2,2-trifluoroethanesulfinate (1b) were prepared by the treatment of 1-iodo-tridecafluorohexane and 1-bromo-1-chloro-2,2,2-trifluoroethane with sodium dithionite in a water-acetonitrile solution. Prolonged reaction of 1a with allyl bromide in DMF afforded tridecafluorohexane 1-propenyl sulfone 2 as the only product in good yield. A similar treatment of 1b gave exclusively 1-chloro-2,2,2-trifluoroethane 3-propenyl sulfone 4. Bromination of 4 followed by dehydrobromination with Et₃N resulted in a mixture of 1-chloro-2,2,2-trifluoroethane 3-bromo-1-propenyl sulfone 6 and 1-chloro-2,2,2-trifluoroethane 2-bromo-3-propenyl sulfone 7, while dehydrobromination with pyridine gave sulfone 6 practically as the only product. α,β-Unsaturated sulfones 2 and 6 were shown to be active dienophiles.     

Separation of mixtures of permanent gases and light hydrocarbons on spherical carbon molecular sieves by gas-solid chromatography

Summary Experimental results are presented on the application of Carbosieve S (Supelco) and Spherocarb (Analabs) spherical carbon molecular sieves for the gas chromatographic separation of mixtures of permanent gases and C₁–C₃ hydrocarbons using a single column or two columns in series. At a programmed temperature of 35–300°C, good separation of the sample components was obtained when using helium as the carrier gas. When hydrogen was used as the carrier gas and the analysis was carried out under isothermal conditions the elution sequence of oxygen and nitrogen reversed as the temperature was increased. This behaviour was observed within a temperature range of 35–225°C for Carbosieve S, and within a temperature range of 35–300°C for Spherocarb.     

The effect of the solvents on the specific intramolecular C-H...N interactions studied by1H NMR spectroscopy

The analysis of the effect of the solvents on the proton chemical shifts in¹H NMR spectra of 2-vinyloxypyridine indicates that the C—H...N interaction of weak intramolecular hydrogen bond type hinders the formation of intermolecular hydrogen C—H...X and C-H... bonds. The protonating solvents reduce the intramolecular C—H...N interaction due to association with the N atom of the pyridine cycle.Translated fromIzvestiya Akademii Nauk. Seriya Khimieheskaya, No. S, pp. 1202–1204, May, 1996.     

Conversion of 3-benzoyl-1-methyl-4-phenyl-γ-piperidol by arylamines and arylhydrazines. Synthesis of 3-arylamino-1-oxo-1-phenylpropanes and 1,3-diarylpyrazoles and their fragmentation under electron impact

It has been established that on heating, 3-benzoyl-4-hydroxy-1-methyl-4-phenylpiperidine is ring-opened in the presence of arylamines by a type of retroaldol reaction, with subsequent transamination of the intermediate Mannich base and the formation of 3-arylamino-1-oxo-1-phenylpropanes. When using arylhydrazines this γ-piperidol is recyclized with the formation of 1,3-diarylpyrazoles and their 4,5-dihydro derivatives. The mass spectral behavior of a series of 3-arylamino-substituted 1-phenylpropanones has been studied. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1486–1495, October, 2007.     

1-Acyldeoxyvasicinone salts as effective intermediate C-and N-acylating agents for alkaloids and amino acids

The reaction of deoxyvasicinone with acid chlorides of aliphatic (acetylbromide) and aromatic (benzoyl-, o-, p-methoxy-, p-nitrobenzoylchlorides) acids was studied. It was shown that 1-deoxyvasicinone salts were formed at room temperature; α-aroyloxymethylidenedeoxyvasicinones, in the presence of triethylamine at 80–85°C. It was found that acid chlorides cause 1-acyldeoxyvasicinone salts to transform into α-hydroxy-or α-aroyloxyarylidenedeoxyvasicinones, which indirectly confirmed their acylating properties. It was found that 1-acyldeoxyvasicinone salts were effective acylating agents for alkaloids (cytisine, 1,2-dihydrodeoxyvasicinone) and amino acids (glycine, β-alanine, α-aminobutyric acid) and can be used to acylate primary and secondary aliphatic and heterocyclic amines. __________ Translated from Khimiya Prirodnykh Soedinenii, No. 6, pp. 585–589, November–December, 2006.     

Electronic structure and conformational flexibility of 1,2-dihydropyridine, 1,2- and 1,6-dihydropyrimidines,and their ylide derivatives

Molecular and electronic structures of 1,2-dihydropyridine, 1,2- and 1,6-dihydropyrimidine, and their oxo, imino, and methylene derivatives were studied by the semiempirical quantum-chemical AM1 method. In all compounds, the heterocycle exhibits a high conformational flexibility. The transition from a planar equilibrium conformation to a distorted sofa conformation with the =C-NH-C-C(N)= torsion angle of ±20° causes an increase in the energy by less than 1.7 kcal mol^–1. All molecules have similar -electronic structures, which, apparently, determines the similarity in their conformational behavior. The bending strain and the nonaromatic character of the cyclic -system are the factors that stabilize the nonplanar conformation of the ring in unsubstituted dihydroazines and ylide derivatives, respectively.Translated fromIzvestiva Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1934–1937, August, 1996.