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Abstract  

Let f be an entire function of exponential type satisfying the condition

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$f(z) \equiv e^{i\gamma } e^{i\tau z} \overline {f(\bar z)}$$ \end{document}
for some real γ. Lower and upper estimates for ∫−∞ |f′(x)|p dx in terms of ∫−∞ |f(x)|p dx, for such a function f belonging to L p(R), have been known in the case where p ∊ [1, ∞) and γ = 0. In this paper, these estimates are shown to hold for any p ∊ (0, ∞) and any real γ.

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Abstract  

Let p(z) be a polynomial of degree n and for a complex number α, let D α p(z) = np(z) + (α-z)p'(z) denote the polar derivative of the polynomial p(z) with respect to α. In this paper, we obtain inequalities for the polar derivative of a polynomial having all its zeros in |z| ≤ K. Our results generalize and sharpen a famous inequality of Turn and some other known results in this direction.

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Journal of Radioanalytical and Nuclear Chemistry
Authors: N. Khare, P. Govil, Pankaj Kumar, A. Mazumder, S. Chopra, J. Pattanaik, S. Balakrishnan, and G. Roonwal

Abstract  

The variations in the concentration of 10Be in the core (SK 200/23) from south western Indian Ocean apparently illuminate past levels of 10Be. The level in the core where lower concentration of 10Be (1.01 × 109 atoms/g) is encountered during the Late Holocene is not at tandem with the Late Holocene southern hemisphere temperature variation. The results further suggest that during last glacial maxima (LGM) the 10Be concentration is higher (2.67 × 109 atoms/g) than the Late Holocene values. The present results, though preliminary, show that local bottom topography seems to have influenced the 10Be concentration at core site. Many studies from different geographic regions need to be undertaken before we finally consider 10Be as yet another strong proxy for palaeoclimatic reconstructions.

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