Sturm-liouville operators with singular potentials

This paper deals with Sturm-Liouville operators generated on a finite interval and on the whole axis by the differential expressionl(y)=−y ^" +q(x)y, whereq(x) is a distribution of first order, such that . The minimal and maximal operators corresponding to potentials of this type on a finite interval are constructed. All self-adjoint extensions of the minimal operator are described and the asymptotics of the eigenvalues of these extensions is found. It is proved that the constructed operator coincides with the norm resolvent limit of the Sturm-Liouville operators generated by smooth potentialsq _n , provided that the condition holds. The convergence of the spectra of these operators to the spectrum of the limit operator is also proved. Similar results are obtained in the case of the whole axis. Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 897–912, December, 1999.     

Preparation of 20-hydroxyecdysone-22-benzoate

20-Hydroxyecdysone-22-benzoate was for the first time synthesized from 20-hydroxyecdysone.Translated from Khimiya Prirodnykh Soedinenii, No. 5, pp. 401–403, September–October, 2004.     

Thiol–ene coupling reaction of fatty acid monomers

The reactivities and reaction rates of the thiol–ene coupling reaction of 2‐ethyl‐(hydroxymethyl)‐1,3‐propanediol trimercapto acetate and 2‐ethyl‐(hydroxymethyl)‐1,3‐propanediol trimercapto propionate with two common unsaturated fatty acid methyl esters (methyl oleate and methyl linoleate) were evaluated. The reactions were monitored with real‐time IR and ¹H NMR, which both showed that the mercapto acetate was more reactive than the mercapto propionate. Both thiols were more prone to add to the monounsaturated methyl oleate than to methyl linoleate, which contained two unconjugated double bonds. According to bond energy calculations, the thiol hydrogen of mercapto acetate was somewhat more difficult to abstract than the hydrogen of mercapto propionate. Consequently, the formed S? C bond in the acetate case was stronger than in the propionate case, and so the equilibrium was more shifted toward the addition products. The real‐time IR measurements also showed that the cis unsaturation in methyl oleate isomerized much more quickly than that in methyl linoleate, and this also had an impact on the overall addition rate of the thiols because a trans unsaturation was more reactive than a cis unsaturation. The higher isomerization rates in the oleate systems, compared with those of the linoleate systems, was suggested to be due to a more restricted rotation along the C? C bond of the reacted unsaturation in linoleate. This study showed the importance of trans unsaturations in obtaining reasonable reaction rates in thiol–ene reactions with fatty acid derivatives. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 6346–6352, 2004     

Anomalous non-coincidence effects in liquids: separation of attraction and repulsion contributions

A method enabling one to separate the contributions of repulsion and attraction forces resulting in frequency non-coincidences in liquids is presented.     

Interaction of multi-raman-processes in miniature optically pumped NH3 fir laser

The principle of Raman gain superposition was introduced to the theory of multi-Raman- processes interaction. Spectral characteristics of Raman lines from miniature NH₃-optically pumped FiR lasers were studied and measured.supported by the National Nature Science Foundation of P.R.C. and the Special Research Foundation of Doctorate Stations of P.R.C.     

Possible reaction coordinates in the metastable states of sodiumnitroprusside Na2[Fe(CN)5NO]2H2O: a discussion based on neutron diffraction- and spectroscopic measurements

The metastable states of sodiumnitroprusside are extremely stable at temperatures below 200 K. It is possible to allocate structural changes measured by neutron diffraction to measured spectroscopic parameters, but the amount of the structural change is relatively small for a reaction co-ordinate as the metastable states have an extremely long lifetime. New hypotheses for related systems try to explain such a phenomena in two ways: The first way is a bending of the NO-bond in the metastable state, the second one an exchange of the oxygen and nitrogen atoms in the NO-bond (which can be regarded as an bending). As such changes would be possible also from our density functional calculations, we re-investigated our neutron diffraction data using the new models. However, our results are not compatible with one of these models. On the contrary, the neutron diffraction data show partially opposite tendencies. We compare both models with EXAFS measurements, with vibrational spectroscopic results and the data found by M?ssbauer spectroscopy. We propose a potential scheme for all three states (GS, and ) extracted from absorption and thermodynamic data to explain the electronic and energetic rearrangement, and the population dynamics. Received: 23 June 1997 / Accepted: 13 October 1997     

Infrared spectroscopy studies of the cyclic anhydride as the intermediate for the ester crosslinking of cotton cellulose by polycarboxylic acids. I. Identification of the cyclic anhydride intermediate

The mechanism of esterification of cotton cellulose by a polycarboxylic acid was investigated using Fourier transform infrared spectroscopy (FT-IR). The infrared spectroscopic data indicate that a polycarboxylic acid esterifies with cotton cellulose through the formation of an acid anhydride intermediate. A five-member cyclic anhydride intermediate was identified in the cotton fabric treated with poly(maleic acid). The five-member cyclic anhydride is a reactive intermediate and readily esterifies when reaction sites are available. We also found that those polycarboxylic acids, which form five-member cyclic anhydride intermediates, crosslink cotton cellulose more effectively than those polycarboxylic acids which form six-member cyclic anhydride intermediates. © 1993 John Wiley & Sons, Inc.     

香兰素对甲苯胺希夫碱稀土配合物的红外光声光谱

研究了香兰素对甲苯胺希夫碱及其金属配合物在３８００－２００ ｃｍ＾－１范围的傅里叶变换红外光谱光谱，对主要谱带进行了经验归属。     

Comparison of CEPA and CP-MET methods

The known CEPA variants CEPA (v) withv = 0,1,2,3 and two new ones withv = 4, 5 are compared both formally and for various numerical examples with CP-MET. The main conclusions are: 1. In those situations where both CP-MET and the CEPA variants are justified (i.e. for “good” closed shell states) the correlation energies obtained with the 7 different schemes differ very little (by something like ±2%), with CEPA (1) closest to CP-MET (difference usually a fraction of 1%) and CEPA (4) nearly as close; this is rather insensitive to whether one uses canonical or localized orbitals. Even CEPA (3) is not too far from CP-MET, which confirms an earlier suggestion of Kelly. 2. In those cases where one of the 7 schemes fails (e.g. due to near degeneracy as in covalent molecules at large internuclear distances) the other 6 usually fail as well, though CEPA (0) is then somewhat poorer than the other schemes. Then no longer CEPA (1) but rather CEPA (3) is closest to CP-MET and then all schemes converge much better in a localized representation. 3. CEPA (2) usually leads to best agreement with experiment since it simulates to some extent triple substitutions. In none of the studied examples does CP-MET show a significant superiority as compared to the other schemes. Possible improvements to extend the domain of applicability of these methods are discussed.