关于一类单叶函数

A sharp coefficient estimate,distortion theorem and the radius of convexityare determined for the class R(α,β,A,B) of function f(z)=z+(?)a_nzⁿ satisfyingthe condition |(f′(z)-1)/(Bf′(z)-[B+(A-B)(1-α)])|<β for some α,β(0≤α<1,0<β≤1) and -1≤A相似文献   

Ruthenium(II)-catalyzed hydrogenation of carbon dioxide to formic acid. Theoretical study of real catalyst, ligand effects, and solvation effects

Ruthenium-catalyzed hydrogenation of carbon dioxide to formic acid was theoretically investigated with DFT and MP4(SDQ) methods, where a real catalyst, cis-Ru(H)2(PMe3)3, was employed in calculations and compared with a model catalyst, cis-Ru(H)2(PH3)3. Significant differences between the real and model systems are observed in CO2 insertion into the Ru(II)-H bond, isomerization of a ruthenium(II) eta1-formate intermediate, and metathesis of the eta1-formate intermediate with a dihydrogen molecule. All these reactions more easily occur in the real system than in the model system. The differences are interpreted in terms that PMe3 is more donating than PH3 and the trans-influence of PMe3 is stronger than that of PH3. The rate-determining step is the CO2 insertion into the Ru(II)-H bond. Its deltaG(o++) value is 16.8 (6.8) kcal/mol, where the value without parentheses is calculated with the MP4(SDQ) method and that in parentheses is calculated with the DFT method. Because this insertion is considerably endothermic, the coordination of the dihydrogen molecule with the ruthenium(II)-eta1-formate intermediate must necessarily occur to suppress the deinsertion. This means that the reaction rate increases with increase in the pressure of dihydrogen molecule, which is consistent with the experimental results. Solvent effects were investigated with the DPCM method. The activation barrier and reaction energy of the CO2 insertion reaction moderately decrease in the order gas phase > n-heptane > THF, while the activation barrier of the metathesis considerably increases in the order gas phase < n-heptane < THF. Thus, a polar solvent should be used because the insertion reaction is the rate-determining step.     

Recent advances of group 14 dimetallenes and dimetallynes in bond activation and catalysis

Since the first heavy alkene analogues of germanium and tin were isolated in 1976, followed by West''s disilene in 1981, the chemistry of stable group 14 dimetallenes and dimetallynes has advanced immensely. Recent developments in this field veered the focus from the isolation of novel bonding motifs to mimicking transition metals in their ability to activate small molecules and perform catalysis. The potential of these homonuclear multiply bonded compounds has been demonstrated numerous times in the activation of H₂, NH₃, CO₂ and other small molecules. Hereby, the strong relationship between structure and reactivity warrants close attention towards rational ligand design. This minireview provides an overview on recent developments in regard to bond activation with group 14 dimetallenes and dimetallynes with the perspective of potential catalytic applications of these compounds.

This minireview highlights the recent advances in small molecule activation and catalytic applications of homonuclear dimetallenes, dimetallynes and interconnected bismetallylenes of heavier group 14 elements.     

Enantioselective reduction of ketones with optically active 2,2′-diamino-6,6′-dimethylbiphenyl-lithium aluminum hydride complex

Enantioselective reductions of prociral ketones with chiral hydride reagent prepared from optically active 2,2′-diamino-6,6′-dimethylbiphenyl and lithium aluminum hydride were accomplished in O.Y. more than 50%.     

Dialumenes – aryl vs. silyl stabilisation for small molecule activation and catalysis

Main group multiple bonds have proven their ability to act as transition metal mimics in the last few decades. However, catalytic application of these species is still in its infancy. Herein we report the second neutral NHC-stabilised dialumene species by use of a supporting aryl ligand (3). Different to the trans-planar silyl-substituted dialumene (3Si), compound 3 features a trans-bent and twisted geometry. The differences between the two dialumenes are explored computationally (using B3LYP-D3/6-311G(d)) as well as experimentally. A high influence of the ligand''s steric demand on the structural motif is revealed, giving rise to enhanced reactivity of 3 enabled by a higher flexibility in addition to different polarisation of the aluminium centres. As such, facile activation of dihydrogen is now achievable. The influence of ligand choice is further implicated in two different catalytic reactions; not only is the aryl-stabilised dialumene more catalytically active but the resulting product distributions also differ, thus indicating the likelihood of alternate mechanisms simply through a change of supporting ligand.

Ligand controlled reactivity: a trans-bent and twisted geometry enables dihydrogen activation and enhanced catalytic activity for NHC-stabilised dialumenes.     

Theoretical study of the Cp2Zr-catalyzed hydrosilylation of ethylene. Reaction mechanism including new sigma-bond activation

The Cp(2)Zr-catalyzed hydrosilylation of ethylene was theoretically investigated with DFT and MP2-MP4(SDQ) methods, to clarify the reaction mechanism and the characteristic features of this reaction. Although ethylene insertion into the Zr-SiH(3) bond of Cp(2)Zr(H)(SiH(3)) needs a very large activation barrier of 41.0 (42.3) kcal/mol, ethylene is easily inserted into the Zr-H bond with a very small activation barrier of 2.1 (2.8) kcal/mol, where the activation barrier and the energy of reaction calculated with the DFT(B3LYP) method are given and in parentheses are those values which have been corrected for the zero-point energy, hereafter. Not only this ethylene insertion reaction but also the coupling reaction between Cp(2)Zr(C(2)H(4)) and SiH(4) easily takes place to afford Cp(2)Zr(H)(CH(2)CH(2)SiH(3)) and Cp(2)Zr(CH(2)CH(3))(SiH(3)) with activation barriers of 0.3 (0.7) and 5.0 (5.4) kcal/mol, respectively. This coupling reaction involves a new type of Si-H sigma-bond activation which is similar to metathesis. The important interaction in the coupling reaction is the bonding overlap between the d(pi)-pi bonding orbital of Cp(2)Zr(C(2)H(4)) and the Si-H sigma orbital. The final step is neither direct C-H nor Si-C reductive elimination, because both reductive eliminations occur with a very large activation barrier and significantly large endothermicity. This is because the d orbital of Cp(2)Zr is at a high energy. On the other hand, ethylene-assisted C-H reductive elimination easily occurs with a small activation barrier, 5.0 (7.5) kcal/mol, and considerably large exothermicity, -10.6 (-7.1) kcal/mol. Also, ethylene-assisted Si-C reductive elimination and metatheses of Cp(2)Zr(H)(CH(2)CH(2)SiH(3)) and Cp(2)Zr(CH(2)CH(3))(SiH(3)) with SiH(4) take place with moderate activation barriers, 26.5 (30.7), 18.4 (20.5), and 28.3 (31.5) kcal/mol, respectively. From these results, it is clearly concluded that the most favorable catalytic cycle of the Cp(2)Zr-catalyzed hydrosilylation of ethylene consists of the coupling reaction of Cp(2)Zr(C(2)H(4)) with SiH(4) followed by the ethylene-assisted C-H reductive elimination.     

Properties of certain integral operators

Two integral operatorsP andQ for analytic functions in the open unit disk are introduced. The object of the present paper is to derive some properties of integral operatorsP andQ .     

Supramolecular hydrogels and organogels based on novel l-valine and l-isoleucine amphiphiles

New low-molecular-weight gelators based on l-valine and l-isoleucine gelators, which have a positively charged terminal group, can gel not only pure water and aqueous solutions containing inorganic acids and salts but also some organic solvents and oils.     

A general method for acylation of indoles at the 3-position with acyl chlorides in the presence of dialkylaluminum chloride

[reaction--see text] Indoles are selectively acylated at the 3-position in high yields on treatment with a wide variety of acyl chlorides in CH(2)Cl(2) in the presence of diethylaluminum chloride or dimethylaluminum chloride. The reaction proceeds under mild conditions and is applicable to indoles bearing various functional groups without NH protection.     

Polyhydrazides. III. N-methylated polyhydrazides by ring-opening of poly-p-phenylene-1,3,4-oxadiazole

A new ring-opening reaction of 1,3,4-oxadiazole by methylating reagents was developed in fuming sulfuric acid or polyphosphoric acid and then, by applying this reaction to poly-p-phenylene-1,3,4-oxadiazole, a high molecular weight poly-N-methylterephthalylhydrazide was obtained. Various methylating reagents were investigated as ring-opening reagents. The degrees of ring-opening in polymers were estimated and related to the properties of the polymers.