On logarithmic coefficients of some close-to-convex functions

The logarithmic coefficients $\gamma_n$ of an analytic and univalent function $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ with the normalization $f(0)=0=f'(0)-1$ is defined by $\log \frac{f(z)}{z}= 2\sum_{n=1}^{\infty} \gamma_n z^n$. Recently, D.K. Thomas [On the logarithmic coefficients of close to convex functions, {\it Proc. Amer. Math. Soc.} {\bf 144} (2016), 1681--1687] proved that $|\gamma_3|\le \frac{7}{12}$ for functions in a subclass of close-to-convex functions (with argument $0$) and claimed that the estimate is sharp by providing a form of a extremal function. In the present paper, we pointed out that such extremal functions do not exist and the estimate is not sharp by providing a much more improved bound for the whole class of close-to-convex functions (with argument $0$). We also determine a sharp upper bound of $|\gamma_3|$ for close-to-convex functions (with argument $0$) with respect to the Koebe function.Comment: 13 page

The partition and its versions in Indian English Novels: A Critical Study

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Mineral Policy Issues in the Context of Export and Domestic Use of Iron Ore in India

This study examines the utilization of iron ore in India. It takes into account the significant reserves of iron ore in India and allays fears that the country's steel industry will run out of iron ore resources if exports continue at the current level. On the contrary, it says that exports are necessary to maintain a structural balance in the market between production and consumption of lumps and fines as nearly 80% of exported ores are fines which are not adequately used in India. This study also highlights the specific problems of the Goa/Radi region. It examines the bilateral agreements with countries like Japan and Korea as well. The study says that the size of mineral resources is a dynamic concept and depends on exploratory efforts, which have not been enough in India due to lack of investments. It recommends on the basis of international experience that increased investment in the mineral sector, especially in exploration, will lead to new reserves and resources.Export of Iron Ore, Mineral Policy, Domestic Consumption, Steel Industry

DESIGN, SYNTHESIS AND MOLECULAR DOCKING STUDY OF HYBRID QUINOLINE-4-YL-OXADIAZOLES/OXATHIADIAZOLES AS POTENT ANTIFUNGAL AGENTS

Objective: The aim of the present work was to design and synthesize hybrid quinoline-4-yl-oxadiazoles/oxathiadiazole derivatives and evaluate them for in vitro antifungal activity against human disease causing pathogens.Methods: The compounds 5(a-d), 6(a-d) and 7(a-d) were efficiently synthesized in good yields. The synthesized compounds were characterized using 1H NMR, 13C NMR and Mass spectra. The synthesized compounds were screened for in vitro antifungal activity and minimum inhibitory concentration (MIC) values were determined using standard agar method. Molecular docking study was performed against fungal enzyme P450 cytochrome lanosterol 14α-demethylase using VLife MDS 4.3 software.Results: The synthesized compounds had shown good to moderate in vitro antifungal activity. The compound 6a (MIC range = 15-25 µg/ml) from 1,2,3,5-oxathiadiazole-2-oxide series showed most potent activity amongst the synthesized compounds when compared with standard clotrimazole (MIC range = 12.5-25 µg/ml). The molecular docking study of synthesized compounds showed good binding interactions against active site of fungal enzyme P450 cytochrome lanosterol 14α-demethylase.Conclusion: The results of in vitro antifungal activity and molecular docking study revealed that the synthesized compounds have potential antifungal activity and can be further optimized and developed as a lead compound.Â

Mining Functional Elements in Messenger RNAs: Overview, Challenges, and Perspectives

Eukaryotic messenger RNA (mRNA) contains not only protein-coding regions but also a plethora of functional cis-elements that influence or coordinate a number of regulatory aspects of gene expression, such as mRNA stability, splicing forms, and translation rates. Understanding the rules that apply to each of these element types (e.g., whether the element is defined by primary or higher-order structure) allows for the discovery of novel mechanisms of gene expression as well as the design of transcripts with controlled expression. Bioinformatics plays a major role in creating databases and finding non-evident patterns governing each type of eukaryotic functional element. Much of what we currently know about mRNA regulatory elements in eukaryotes is derived from microorganism and animal systems, with the particularities of plant systems lagging behind. In this review, we provide a general introduction to the most well-known eukaryotic mRNA regulatory motifs (splicing regulatory elements, internal ribosome entry sites, iron-responsive elements, AU-rich elements, zipcodes, and polyadenylation signals) and describe available bioinformatics resources (databases and analysis tools) to analyze eukaryotic transcripts in search of functional elements, focusing on recent trends in bioinformatics methods and tool development. We also discuss future directions in the development of better computational tools based upon current knowledge of these functional elements. Improved computational tools would advance our understanding of the processes underlying gene regulations. We encourage plant bioinformaticians to turn their attention to this subject to help identify novel mechanisms of gene expression regulation using RNA motifs that have potentially evolved or diverged in plant species

Zero-field spin splitting in a two-dimensional electron gas with the spin-orbit interaction revisited

We consider a two-dimensional electron gas (2DEG) with the Rashba spin-orbit interaction (SOI) in presence of a perpendicular magnetic field. We derive analytical expressions of the density of states (DOS) of a 2DEG with the Rashba SOI in presence of magnetic field by using the Green's function technique. The DOS allows us to obtain the analytical expressions of the magnetoconductivities for spin-up and spin-down electrons. The conductivities for spin-up and spin-down electrons oscillate with different frequencies and gives rise to the beating patterns in the amplitude of the Shubnikov de Hass (SdH) oscillations. We find a simple equation which determines the zero-field spin splitting energy if the magnetic field corresponding to any beat node is known from the experiment. Our analytical results reproduce well the experimentally observed non-periodic beating patterns, number of oscillations between two successive nodes and the measured zero-field spin splitting energy.Comment: 5 pages, 2 figure