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1

On the derivative of a polynomial with prescribed zeros

Jain V. K.

Journal of Mathematics and Applications

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2017

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Vol. 40

97--120

EN

For a polynomial [wzór] of degree n having all its zeros in │z│ ≤ K, K ≥1 it is known that max [wzór]. By assuming a possible zero of order m, 0 ≤ m ≤ n - 4, at z = 0, of p(z) for n ≥ k + m + 1 with integer k ≥ 3 we have obtained a new refinement of the known result.

2

A refinement of Schwarz's lemma and its applications

Jain V. K.

Journal of Mathematics and Applications

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2016

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Vol. 39

69--80

EN

By using the value of the second derivative of the function at 0, along with the values of the function and its first derivative at 0, we have obtained a refinement of well known Schwarz’s lemma and have used this refinement to obtain refinements, of Aziz and Rather’s inequalities [2004] for a polynomial of degree n having no zeros in |z| < k, (k ≥ 1).

3

Road Traffic Noise Attenuation by Vegetation Belts at Some Sites in the Tarai Region of India

Tyagi V., Kumar K., Jain V. K.

Archives of Acoustics

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2013

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Vol. 38, No. 3

389--395

EN

Noise measurements have been carried out at eleven different sites located in three prominent cities of the Tarai region of India to evaluate the effectiveness of vegetation belts in reducing traffic noise along the roadsides. Attenuation per doubling of distance has been computed for each site and excess attenuation at different 1/3 octave frequencies has been estimated. The average excess attenuation is found to be approximately 15 dB over the low frequencies (200 Hz to 500 Hz) and between 15 dB to 20 dB over the high frequencies (8 kHz to 12.5 kHz). Over the critical middle frequencies (1-4 kHz), the average excess attenuation (between 10-15 dB) though not as high, is still significant, with a number of sites showing an excess attenuation of 15 dB or more at 1 kHz. The results indicate that sufficiently dense vegetation belts along the roadsides may prove as effective noise barriers and significant attenuation may be achieved over the critical middle frequencies (1-4 kHz).

4

Community annoyance from aircraft induced noise in Delhi

Sanyogita, Kumar K., Jain V. K.

Archives of Acoustics

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2007

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Vol. 32, No. 2

367-375

EN

Air traffic noise is a major cause of community annoyance in the residential areas near airports. The present study has been prompted by the need to examine the noise levels induced by the increased air traffic in Delhi in recent years. Noise levels have been measured in the indoor environment of two prominent residential areas of Delhi, namely, University Campus (UC) and Vasant Vihar (VV) which lie underneath the landing flight path of aircraft in Delhi. Spectral distributions show higher noise levels at lower frequencies and exhibit a declining trend with increase in frequency. With the help of spectral information, an index of aircraft noise, PNdB (perceived noise levels in decibels) is determined to assess relative annoyance or noisiness felt by the community of residential areas. PNdB values in the case of UC vary from a minimum of 66.7 to a maximum of 85.2. Further down the landing path, PNdB levels at VV are found to be appreciably higher in the range of 76.18-91.37. Results of social survey conducted to assess the community response to aircraft noise reveal that a majority (73%) of the respondents experience moderate to extreme annoyance. This is in conformity with the rather high PNdB values obtained for both the residential areas.