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1.
2.
M. N. Sheremeta 《Ukrainian Mathematical Journal》1990,42(5):591-595
For a function f analytic in a disk {z ¦ z ¦ <R }, 0 <R + , a criterion is obtained, in terms of the Taylor coefficients of the function, for the validity of the relation
(r) ln+
M (r)dr < + , whereM (r)= max {¦ (f (z) ¦ ¦z ¦=r < R}, and is a function positive on [0, R) and satisfying certain conditions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 5, pp. 668–673, May, 1990. 相似文献
3.
Rudzevich Y Vysotsky MO Bohmer V Brody MS Rebek Jr J Broda F Thondorf I 《Organic & biomolecular chemistry》2004,2(21):3080-3084
The dimerization of tetratolyl- and tetratosyl-urea derivatives 1 and 2, derived from a tetrapentoxy calix[4]arene in the cone conformation and of the corresponding tetra-urea derivatives 3 and 4, in which the cone conformation is rigidified by the two crown-3 tethers, have been studied. All six possible equimolar mixtures were examined by 1H NMR using CDCl3 and CD2Cl2 as solvents. While no heterodimers are found for the combinations 1/3 and 2/4 in either solvent, all remaining combinations lead to the (exclusive) formation of heterodimers in CD2Cl2. In CDCl3 heterodimers are only observed for the combinations of 3 with 2 or 4. These results are discussed in terms of entropic and enthalpic contributions and compared with MD-simulations in a box of chloroform solvent molecules. 相似文献
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The affinities of ferrocene (2) and the cobaltocenium cation (3+), which have roughly the same size and differ in their charge, towards the inner cavity of the dimeric capsule formed by tetraurea calix[4]arene (1) were studied in C2D4Cl2 solutions. While 3+, which occupies more than 75% of the internal volume of the dimer, is readily encapsulated this is not the case for 2. This is probably due to cation-pi interactions, which operate only between 3+ and the aromatic rings of the calix[4]arene dimer. We found that the affinity of the cobaltocenium cation is higher than that of the tropylium cation (4+) and is only 2-3 times less than that of the tetraethylammoniun cation (5+). From the variable temperature 1H NMR spectra of this capsule, the free energy of activation at 298 K (deltaGdouble dagger(298K)) for the reorientation of the hydrogen bonded belt between the two parts of the dimer could be determined by total line shape analysis for the aromatic protons of the calixarene. The value of 14.3 +/- 0.2 kcal mol(-1) for the dimeric capsules of 3+ PF6- is very similar to the free activation energy found for dimeric capsules of 1 with 4+ PF6- and 5+ PF6- in C2D4Cl2. It becomes significantly lower, if PF6- is replaced by BF4-. We also found that ten times more DMSO is needed to disrupt the capsule 1 x 3+ x 1 than the corresponding 1 x 1 dimer containing benzene as guest. This demonstrates again the importance of the cation-pi interactions for the stability of such hydrogen-bonded dimeric capsules. 相似文献
6.
Anna Kryshchyshyn-Dylevych Myroslav Garazd Andrew Karkhut Sviatoslav Polovkovych 《合成通讯》2020,50(18):2830-2838
AbstractA mild and efficient method for the synthesis of 1-oxo-9H-thiopyrano[3,4-b]indole-3-carboxylic acids and dimerized 3-(4-carboxy-1H-3-indolyl)-2-propenoic acids via alkaline hydrolysis of 3-(rhodanin-5-yl)-1H-indole-2-carboxylic acids derivatives was elaborated. Anticancer activity screening in NCI60-cell lines assay allowed identification of 5-fluoro-3-(4-oxo-2-thioxothiazolidin-5-ylidenemethyl)-1H-indole-2-carboxylic acid methyl ester 2a with significant antimitotic activity at micromolar and submicromolar concentrations. 相似文献
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We establish a necessary and sufficient condition for the coefficients a
n of an entire function
under which its central index and the logarithms of the maximum of the modulus and the maximum term are regularly varying functions. We construct an entire function the logarithm of the maximum of whose modulus is a regularly varying function, whereas the Nevanlinna characteristic function is not a regularly varying function. 相似文献
10.
Let M() be the maximum modulus and let () be the maximum term of an entire Dirichlet series with nonnegative exponents
n
increasing to . We establish a condition for
n
under which the relations
and
are equivalent under certain conditions on the functions 1 and 2. 相似文献