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We prove several improved versions of Bohr’s inequality for the harmonic mappings of the form , where is bounded by 1 and . 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 under the mapping 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
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Jose-Maria Lopez-Pedrosa Stanley M. Roberts Shanthini Saminathan 《Tetrahedron letters》2004,45(26):5073-5075
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
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Saminathan IS Zhao J Siu KW Hopkinson AC 《Physical chemistry chemical physics : PCCP》2011,13(41):18307-18314
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
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Kayumov Ilgiz R. Ponnusamy Saminathan Kaliraj Anbareeswaran Sairam 《Potential Analysis》2020,52(1):105-113
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
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Bappaditya Bhowmik Saminathan Ponnusamy Karl-Joachim Wirths 《Monatshefte für Mathematik》2010,161(1):59-75
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
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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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Zayid?Abdulhadi Yusuf?Abu?Muhanna Saminathan?PonnusamyEmail authorView authors OrcID profile 《Mediterranean Journal of Mathematics》2018,15(4):187
In this paper, we shall discuss the family of biharmonic mappings for which the maximum principle holds. As a consequence of our study, we present Schwarz Lemma for certain class of biharmonic mappings. Also we discuss the univalency of certain class of biharmonic mappings. 相似文献
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