一类排列问题的计数

给出一类排列问题的计数公式．     

奇异值估计的Brauer型定理

设Ａ＝（ａｉｊ）为ｎ阶复矩阵．记ｓｉ＝ｍａｘ∑ｊ≠ｉ｜ａｉｊ｜,∑ｊ≠ｉ｜ａｊｉ｜｛｝,ａｉ＝｜ａｉ｜（ｉ＝１,２,…,ｎ）．证明了Ａ的奇异值均属于Ｂｒａｕｅｒ型并集∪ｉ≠ｊｚ≥０：｜ｚ－ａｉ｜｜ｚ－ａｊ｜≤ｓｉｓｊ｛｝,并给出了该并集的显式表达及数值例子．     

Spectroscopic Study of the Inclusion Complexes of Phenylbutazone and Oxyphenbutazone with Cyclodextrins in Polar Reaction Media

The formation of inclusion complexes of -, -, hydroxypropyl-- (HP--) and -cyclodextrins with phenylbutazone and oxyphenbutazone has been studied in aqueous buffer solution (pH 7.5 and 0.1 mol dm^-3 NaCl), dimethylsulfoxide, and 25, 50 and 75% dimethylsulfoxide/water mixtures. These complexation reactions have been followed by UV electronic absorption spectroscopy. In addition, 1D and 2D ¹H NMR spectra were recorded to obtain structural information about the inclusion complexes formed in solution; 136 binding constant values were determined at five different temperatures (288, 293, 298, 303 and 310 K) from the electronic absorption data and, from these H_binding and S_binding values were obtained. At the studied cyclodextrin and guest concentration ranges, 1 : 1 inclusion complexes were detected. Only in three cases were 1 : 2 complexes detected, those of phenylbutazone and oxyphenbutazone with -cyclodextrin in aqueous, and oxyphenbutazone with hydroxypropyl--cyclodextrin in 75% dimethylsulfoxide/water solutions.     

Composition and properties of freeze-dried products of nicotinic acid withβ-cyclodextrin and heptakis (2,6-0-dimethyl)-β-cyclodextrin

The purpose of the study was to examine the formation of inclusion compounds in the freeze-dried products obtained from aqueous solutions of nicotinic acid and -cyclodextrin (-CD), or heptakis (2,6-0-dimethyl)--cyclodextrin (DIMEB). The molar ratios used were 1:1 and 2:1. In addition two freezing temperatures (–40 and –196°C) and different secondary drying temperatures (+50 and +80°C) were used. Freeze-dried products with -CD obtained after low temperature freezing are of the same crystallographic structure as seen in a pure inclusion compound prepared by coprecipitation. Amorphous products were formed after fast freezing. The molar ratios of included nicotinic acid in the freeze-dried products vary — dependent on the preparation conditions — between 0.75:1 and 1:1. A factorial design proves that the included drug amount can be increased by enhancement of the amount of nicotinic acid used, by faster freezing, and by the combination of these two factors. The proof of inclusion formation was given by a combination of X-ray diffractography, differential scanning calorimetry, thermogravimetry and thermofractography.The freeze-dried preparations obtained with DIMEB were amorphous mixtures of the two components. No proof for inclusion of the nicotinic acid in the cyclodextrin cavity could be given. Higher (–40°C) or lower (–196°C) freezing temperatures and the running of the secondary drying process could not influence these results. The very low stability constant of the complex and steric reasons are responsible for this behavior.     

Thermogravimetric properties of inclusion complexes ofβ-cyclodextrin with benzene,acetylsalicylic acid and methyl salicylate

This paper reports TG analyses of inclusion complexes of-cyclodextrin with benzene, acetylsalicylic acid and methyl salicylate. The data were used for calculation of the compositions of the three body complexes and the apparent kinetic parameters of the thermal decompositions. Water exclusion proceeds as a reaction with ordern=1 and an activation energy about 20 kJ/mol. The expulsion of aromatic guest molecules follows ann=1 order process with the activation energy above 155 kJ/mol, except that for the methyl salicylate complex, which was found to be ca. 64 kJ/mol.     

Preparation and Characterisation of Meloxicam Hydroxy Propyl <Emphasis Type="Italic">β</Emphasis>-Cyclodextrin Inclusion Complex

Meloxicam is a non steroidal anti inflammatory drug, used in the treatment of rheumatoid and osteoarthiritis. It is practically insoluble in water and its prolonged use is associated with the incidence of side effects like gastro intestinal perforations, ulcerations and bleeding. Therefore, an attempt has been made to improve the aqueous solubility of the drug by making an inclusion complex using hydroxy propyl β cyclodextrin(HPβ-CD). The complexes were prepared by physical mixture and freeze drying method. The different methods employed for evaluation such as DSC, XRD, SEM and FT-IR studies indicated complete formation of the complex by freeze drying method in a molar ratio of 1:2. The prepared complexes showed improved in-vitro dissolution profile as compared to the pure drug.     

Inclusion complexes of the natural product gossypol. Crystal structures of gossypol complexes with benzene and chloroform as guests

The crystal structures of the lattice inclusion complexes of gossypol with benzene and chloroform have been determined by X-ray structure analysis. The crystals of (C₃₀H₃₀O₈)₂ · C₆H₆ (GPBNZ) are triclinic, space groupPI,a = 11.241(3),b = 14.986(4),c = 17.380(4) Å, = 98.89(2), = 99.86(2), = 98.91(2)°,V = 2800(2) ų,Z = 2,D _x = 1.32 g cm^–3, (CuK ) = 7.35 cm^–1. The structure has been refined to a finalR value of 0.050 for 6146 observed reflections. The crystals of C₃₀H₃₀O₈·CHCl₃ (GPCLF) are monoclinic, space groupC2/c,a = 28.464(4),b = 8.948(1),c = 26.480(4) Å, = 108.93(2)°,V = 6380(2) ų,Z = 8,D _x = 1.33 g cm^–3, (CuK) = 30.42 cm^–1. The structure has been refined to a finalR value of 0.100 for 1980 observed reflections.GPCLF forms an intercalate-type structure and GPBNZ a clathrate-type structure. There are, however, some similarities in the packing mode of the host molecules in these two structures. On a basis of comparison of the crystal packing of GPCLF and GPBNZ one can postulate that in the desorption process of the intercalate-type GPCLF complex an intermediate clathrate structure of the GPBNZ-type should be formed.     

Can the presence of chemically inert species modify the face selectivity in asymmetric induction by cyclodextrins?

Reduction of-cyclodextrin (-CD) aromatic ketone (acetophenone and acetonaphthones) inclusion compounds were carried out in the presence of a large number of chemically inert species as potential co-guests. In several cases, it was observed that stoichiometric molar ratios of these compounds to ketone significantly modify the chiral induction yielding the inverted alcohol enantiomer and increasing the face selectivity. The results were found to depend strongly on the respective structure and shape of both the ketone and the additive, and on the molar ratio of-CD:ketone:third compound. These observations suggest the formation of a three-component inclusion complex in which the geometry of binding of the substrate and its mobility are changed with respect to the binary system.     

Inclusion by a fluorenyl diol host with substituted pyridines

The structures of the inclusion compounds formed by the host 9,9’-(ethyne-1,2-diyl)bis(fluoren-9-01) with pyridine and picolines are similar and display tubular topology. The host discriminates poorly between these guests. The kinetics of desorption of the pyridine compound is governed by the Avrami-Erofe’ev equation A2, with an activation energy of 111(7) kJ mol⁻¹.