Integral mean estimates for the polar derivative of a polynomial

Let $P(z)$ be a polynomial of degree $n$ having all zeros in $|z|\leq k$ where $k\leq 1,$ then it was proved by Dewan \textit{et al} that for every real or complex number $\alpha$ with $|\alpha|\geq k$ and each $r\geq 0$ $$n(|\alpha|-k)\left\{\int\limits_{0}^{2\pi}\left|P\left(e^{i\theta}\right)\right|^r d\theta\right\}^{\frac{1}{r}}\leq\left\{\int\limits_{0}^{2\pi}\left|1+ke^{i\theta}\right|^r d\theta\right\}^{\frac{1}{r}}\underset{|z|=1}{Max}|D_\alpha P(z)|.$$ \indent In this paper, we shall present a refinement and generalization of above result and also extend it to the class of polynomials $P(z)=a_nz^n+\sum_{\nu=\mu}^{n}a_{n-\nu}z^{n-\nu},$ $1\leq\mu\leq n,$ having all its zeros in $|z|\leq k$ where $k\leq 1$ and thereby obtain certain generalizations of above and many other known results.Comment: 8 page

Studies on resistance and associated fitness costs in Lepidoptera to Bacillus thuringiensis toxins

Microbial insecticides derived from the common soil bacterium Bacillus thuringiensis (Bt) have become increasingly important for pest management, particularly in Bt (GM) crops. In addition to crystal (Cry) proteins produced during the spore stage, vegetative insecticidal proteins (VIP) produced during vegetative growth are of current interest for use with Cry toxins in GM crops. In this thesis, the effects of Bt toxins on two target lepidopteran pest species, the bollworm, Heliothis virescens, and the diamondback moth, Plutella xylostella, are described. Cross-resistance to non-Bt insecticides was not found in populations of H. virescens (Vip3A-Sel WF06) and P. xylostella (Cry1Ac-Sel Karak) resistant to Vip3A and Cry1Ac respectively. While the synergist piperonyl butoxide (PBO), an inhibitor of microsomal mono-oxygenases and esterases, did not enhance the toxicity of Vip3A in Vip3A-Sel H. virescens and PBO and the esterase inhibitor DEF did not enhance the toxicity of Cry1Ac in P. xylostella Cry1Ac-Sel Karak. Selection studies with PBO on a population of P. xylostella (SERD4) with a history of developing resistance and cross-resistance to insecticides failed to result in resistance to PBO after selection for 20 generations. Electrophoresis studies indicated the presence of an extra esterase band in Vip3A-Sel compared with unselected H. virescens but there is no evidence that it is related to resistance. Binding experiments suggested that the labelling reaction may have inactivated the binding sites of Vip3Aa and evidence of specific binding of Vip3A toxin to midgut epithelial membranes of unselected H. virescens could not be obtained. Treatment of H. virescens (WFO6, unselected) and P. xylostella (Karak, unselected) with a sub-lethal concentration of Vip3A was found to increase larval and pupal development time and pupal weight, reduce survival (neonate larvae to adult emergence) and mating pair success, increase fecundity and reduce egg viability and the intrinsic rate of population increase (rm). Various fitness costs were found to be associated with resistance in Vip3A-Sel H. virescens and some fitness costs were shown to be temperature dependent: survival (egg to adult), mating pair success, production of viable progeny, egg viability and fecundity, and rm of Vip3A resistant insects being lower at sub-optimal culture temperatures compared with unselected insects. Vip3A resistant larvae were also found to be more susceptible to entomopathogenic nematodes, and had a lower flight muscle ratio, and a greater level of fluctuating asymmetry of morphological traits compared with unselected insects. The work is discussed with particular reference to resistance management strategies for Vip toxins

Inter-city Variation in Prices

In this paper we have constructed a relative cost of living index for 32 cities/towns of Pakistan using latest available prices to understand the extent of current differences in cost of living across cities and also to compare changes in relative cost of living since 1999 [Pasha and Pasha (2002)]. The index values reveal significant differences in cost of living across Pakistan and especially across provinces with prices significantly higher in Balochistan (overall) and NWFP (for wheat). When regressed against various explanatory variables, the variation in cost of living appears to be determined by the population in cubic form (reaching a minimum for a city size of 2.1 million) and the provincial affiliation of cities. The index also reveals that relative to 1999, the economy as a whole appears to have become less integrated as the difference in prices across cities is much greater than in 1999. However, cities in Sindh due to their close proximity to the port have become less expensive because of the increased share of imports in consumption. The findings of this paper have very important implications for public policy with respect to transfer payments to relieve poverty, urban development, inter-provincial trade and transport and allocation of development funds among provinces.Regional Economics Measurement, Regional Economic Activity, Growth, Development, and Changes

Does Political Affirmative Action Work, and for Whom? Theory and Evidence on India’s Scheduled Areas

Does political affirmative action undermine or promote development, and for whom? We examine Scheduled Areas in India, which reserve political office for the historically disadvantaged Scheduled Tribes. We apply a new theoretical framework and dataset of 217,000 villages to evaluate the overall impact of affirmative action on development, as well as its distributional consequences for minorities and non-minorities. Examining effects on the world’s largest employment program, the National Rural Employment Guarantee Scheme, we find that reservations deliver no worse overall outcomes, that there are large gains for targeted minorities, and that these gains come at the cost of the relatively privileged, not other minorities. We also find broader improvements in other pro-poor policies, including a rural roads program and general public goods. Contrary to the expectations of affirmative action skeptics, our results indicate that affirmative action can redistribute both political and economic power without hindering overall development

Information, Candidate Selection, and the Quality of Representation: Evidence from Nepal

How do we improve the quality of representation in new democracies? This paper studies candidate selection by party leaders and asks whether poor information about public preferences can lead elite choices to diverge from mass opinion. Working with a political party in Nepal, we show that while elites value voter preferences, these preferences only explain one third of elite candidate selection. Next, we embed an experiment in actual candidate selection deliberations for this party and find that party leaders not only select different candidates when polling data are presented to them, but that their updated decisions also improve the party’s vote share. By opening the black-box of candidate selection, this paper demonstrates that closing the information gap between elites and voters has the power to improve the quality of representation