228 research outputs found
Integral mean estimates for the polar derivative of a polynomial
Let be a polynomial of degree having all zeros in
where then it was proved by Dewan \textit{et al} that for every real
or complex number with and each
\indent In this paper, we shall present a refinement and generalization of
above result and also extend it to the class of polynomials
having
all its zeros in where and thereby obtain certain
generalizations of above and many other known results.Comment: 8 page
Lp mean estimates for an operator preserving inequalities between polynomials
If be a polynomial of degree at most which does not vanish in , it was recently formulated by Shah and Liman \cite[\textit{Integral
estimates for the family of -operators, Operators and Matrices,}
\textbf{5}(2011), 79 - 87]{wl} that for every , ,
where is a -operator with parameters in the sense of Rahman \cite{qir}, and
. Unfortunately the proof of this result is
not correct. In this paper, we present a more general sharp -inequalities
for -operators which not only provide a correct proof of the
above inequality as a special case but also extend them for as
well.Comment: 16 Page
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Choosing Ungoverned Space: The Removal of Pakistan’s Frontier Crimes Regulation
Why do administratively competent states sometimes leave substantial swathes of their territory ungoverned? We explore this question in the context of the Frontier Crimes Regulation (FCR) in Pakistan, a British Colonial law only abrogated in 2018, that left legal decisions up to local customary councils. This contrasts with areas where the British and Pakistani state built modern political and bureaucratic institutions. Using primary legal documents we create a dataset of when and where FCR applied between 1901 and 2012. Exploiting spatial variation in the Green Revolution’s impact in the 1960s, we show that governance was preferentially extended to places where the state stood to benefit the most in terms of land revenue. Our results show that technological changes which shift the returns to control influence where states choose to govern
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