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1.
We prove several improved versions of Bohr’s inequality for the harmonic mappings of the form f=h+g¯, where h is bounded by 1 and |g(z)||h(z)|. The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. (Kayumov and Ponnusamy, 2018) for example a term related to the area of the image of the disk D(0,r) under the mapping f is considered. Our results are sharp. In addition, further improvements of the main results for certain special classes of harmonic mappings are provided.  相似文献   
2.
A modified procedure for performing the Juliá-Colonna epoxidation reaction effects the oxidation of some vinyl sulfones to generate the corresponding epoxides 5-8 in good to excellent optical purity.  相似文献   
3.
Nonlinear aspects of developing three-dimensional perturbations in plane Poiseuille flow have been elucidated at the primary, instead of the conventional secondary, level. Three-dimensional perturbation velocities generate normal vorticity by stretching and tilting the basic-flow vorticity. The amplitude of the induced normal vorticity, and hence that of the streamwise perturbation velocity, can grow temporally to significant peak values before the exponential decay predicted by the linear theory sets in. These growths, according to the linear theory, do not influence the amplitudes of the normal perturbation velocity that are monotonically decaying with time. It is shown in this study that the normal velocity continues to be oblivious to the development of induced normal vorticity, even in the nonlinear regime, if the perturbation velocities are described by waves traveling in a single oblique direction. Also, the Reynolds number dependence of the amplitude of the normal vorticity is discussed.  相似文献   
4.
Degeneracies of the Orr-Sommerfeld eigenmodes and direct resonances between the Orr-Sommerfeld eigenmodes and vorticity eigenmodes are studied in water-table flow. The sensitivity of the characteristics of these algebraic mechanisms to flow parameters, such as the Reynolds number (R), the slope of the table (θ), and a material parameter (γ), are investigated. It is found that the mechanisms become operative at subtransitional R, and their damping rates decrease with increasing R. When the mean flow profile is slightly distorted from the ultimate parabolic profile, the characteristics of the direct resonances show remarkable variations. Also, some of the algebraic mechanisms in watertable flow are shown to have the same characteristics and modal structures as some of those in plane Poiseuille flow.  相似文献   
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6.
Protonated a(2) and a(3) (therefore doubly charged) ions in which both charges lie on the peptide backbone are formed in collision-induced dissociations of [La(III)(peptide)(CH(3)CN)(m)](3+) complexes. Abundant (a(3)+H)(2+) ions are formed from triproline (PPP) and peptides with a proline residue at the N-terminus; these peptides are the most effective in producing ions of the type (a(2)+H)(2+) and (a(3)+H)(2+). A systematic study of the effect of the location of the proline residue and other residues of aliphatic amino acids on the generation of protonated a ions is reported. Density functional theory calculations at B3LYP/6-311++G(d,p) gave the proton affinity of the a(3) ion derived from PPP to be 167.6 kcal mol(-1), 2.6 kcal mol(-1) higher than that of water. The protonated a(2) ions of diglycine and diproline and a(3) ions of triglycine have lower proton affinities and are only observed in lower abundances, possibly due to proton transfer to water in ion-molecule reactions.  相似文献   
7.
Potential Analysis - In this article, we prove the Riesz - Fejér inequality for complex-valued harmonic functions in the harmonic Hardy space hp for all p >?1. The result is sharp...  相似文献   
8.
Let Co(α) denote the class of concave univalent functions in the unit disk ${\mathbb{D}}$ . Each function ${f\in Co(\alpha)}$ maps the unit disk ${\mathbb{D}}$ onto the complement of an unbounded convex set. In this paper we find the exact disk of variability for the functional ${(1-|z|^2)\left ( f^{\prime\prime}(z)/f^{\prime}(z)\right), f\in Co(\alpha)}$ . In particular, this gives sharp upper and lower estimates for the pre-Schwarzian norm of concave univalent functions. Next we obtain the set of variability of the functional ${(1-|z|^2)\left(f^{\prime\prime}(z)/f^{\prime}(z)\right), f\in Co(\alpha)}$ whenever f′′(0) is fixed. We also give a characterization for concave functions in terms of Hadamard convolution. In addition to sharp coefficient inequalities, we prove that functions in Co(α) belong to the H p space for p < 1/α.  相似文献   
9.
10.
Isomorphous complexes [Zn(S2CN(Me)Cy)2(bipy)] (1) and [Cd(S2CN(Me)Cy)2(bipy)] (2) (where Cy(Me)NCS2 N-cyclohexyl-N-methyldithiocarbamate anion and bipy = 2,2′-bipyridine) have been synthesised. Their structures and spectroscopic properties have been studied by IR, 1H and 13C NMR spectroscopy and single crystal X-ray analysis. IR spectrum of the complexes show the contribution of thioureide form to the structures. 1H NMR spectra of the complexes showed the desheilding of methyl protons and H-1 of cyclohexyl group on complexation. The downfield shift of N13CS2, methyl carbon and C-1 of cyclohexyl group carbon signals for 2 (205.5, 36.7 and 64.4 ppm) from the chemical shift value of 1 (204.2, 35.6 and 63.1 ppm) is attributed to the movement of more electron density from dithiocarbamate towards cadmium. Single crystal X-ray structures of 1 and 2 indicate that the central metal atom is in a distorted octahedral environment for both complexes. The presence of added 2,2′-bipyridine ligand in the coordination sphere of M(S2CN(Me)Cy)2 increases Zn–S distances and decreases S–Zn–S angles in 1 and slightly increases Cd–S distances in 2. S–Cd–S angles are not affected. This is due to the relatively larger size of the cadmium ion compared to zinc ion which alleviates the strain involved in transformation from tetrahedral to octahedral.  相似文献   
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