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Some Integral Mean Estimates for Polynomials with Restricted Zeros

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Analysis in Theory and Applications 2015年第1期31卷 81-91页

作者： Abdullah Mir Q.M.Dawood bilal dar Department of Mathematics University of Kashmir

Let P（z） be a polynomial of degree n having all its zeros in ｜z｜≤ k. For k = 1, it is known that for each r 〉 0 and ｜a｜≥1,n（｜a｜-1）{∫0^2π｜P（e^iθ）｜^rdθ}^1/r≤{∫0^2π｜1＋e^iθ｜^rdθ}^1/rmax｜z｜=1｜DzP（z）｜.In this paper, we shall first consider the case when k≥1 and present certain generaliza- tions of this inequality. Also for k≤ 1, we shall prove an interesting result for Lacunary type of polynomials from which many results can be easily deduced.

关键词： Polynomial zeros polar derivative.

Some Inequalities Concerning the Polar Derivative of a Polynomial-II

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Analysis in Theory and Applications 2013年第4期29卷 384-389页

作者： Abdullah Mir bilal dar Department of Mathematics University of KashmirSrinagar190006 India

In this paper, we consider the class of polynomials P（z）= anz^n＋ ∑vn=μan-vz^n-v,1≤μ≤n , having all zeros in ｜z｜≤k, k ≤1 and thereby present an alternative proof, independent of Laguerre＇s theorem, of an... 详细信息

关键词： Polar derivative of a polynomial.

Some Results on the Polar Derivative of a Polynomial

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Analysis in Theory and Applications 2014年第3期30卷 306-317页

作者： Abdullah Mir bilal dar Department of Mathematics University of Kashmir

Let P（z） be a polynomial of degree n and for any complex number α, let DαP（z） = nP（z）＋（α-z）P＇（z） denote the polar derivative of P（z） with respect to α. In this paper, we obtain certain inequalities for the polar derivative of a polynomial with restricted zeros. Our results generalize and sharpen some well-known polynomial inequalities.

关键词： Polynomial zeros polar derivative Bemstein inequality.

New Inequalities on L_γ-Spaces

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Analysis in Theory and Applications 2013年第4期29卷 390-400页

作者： Abdullah Mir bilal dar Sajad Amin Baba Department of Mathematics University of KashmirSrinagar190006India Govt.Hr.Sec.Institute KurhamaGandarbal-191201India

We consider for a fixed μ, the class of polynomialsPn,μ,s：＋{P（z）=z^2（anz^n-s＋∑j=μ^n-s an-jz^n-j-s）;1≤μ≤n-s}of degree n, having all zeros in ｜ z｜ ≤ k, k≤ 1, with s-fold zeros at the origin. In this paper, we have obtained inequalities in the reverse direction for the above class of polynomials. Besides, extensions of some Turan-type inequalities for the polar derivative of polynomials have been considered.

关键词： Polynomial Zygmund inequality polar derivative.

Performance Analysis of Three Spectrum Sensing Detection Techniques with Ambient Backscatter Communication in Cognitive Radio Networks

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Computer Modeling in Engineering & Sciences 2023年第10期137卷 813-825页

作者： Shayla Islam Anil Kumar Budati Mohammad Kamrul Hasan Saoucene Mahfoudh Syed bilal Hussian Shah Institute of Computer Science&Digital Innovation ICSDIUCSI UniversityKuala Lumpur56000Malaysia Center for Cyber Security Faculty of Information Science and TechnologyUniversiti Kebangsaan Malaysia(UKM)Selangor43600Malaysia School of Engineering Computing and InformaticsDar Al-Hekma UniversityJeddah22246Saudi Arabia

In wireless communications, the Ambient Backscatter Communication (AmBC) technique is a promisingapproach, detecting user presence accurately at low power levels. At low power or a low Signal-to-Noise Ratio(SNR), there is no dedicated power for the users. Instead, they can transmit information by reflecting the ambientRadio Frequency (RF) signals in the spectrum. Therefore, it is essential to detect user presence in the spectrum forthe transmission of data without loss or without collision at a specific time. In this paper, the authors proposed anovel Spectrum Sensing (SS) detection technique in the Cognitive Radio (CR) spectrum, by developing the *** Matched Filter Detection with Inverse covariance (MFDI), Cyclostationary Feature Detection with Inversecovariance (CFDI) and Hybrid Filter Detection with Inverse covariance (HFDI) approaches are used with AmBCto detect the presence of users at low power levels. The performance of the three detection techniques is measuredusing the parameters of Probability of Detection (PD), Probability of False Alarms (Pfa), Probability of MissedDetection (Pmd), sensing time and throughput at low power or low SNR. The results show that there is a significantimprovement via the HFDI technique for all the parameters.

关键词： Ambient backscatter communication cognitive radio MFDI CFDI HFDI

Current Status of Antenatal Care Utilization in the Context of Data Conflict: The Case of Dembecha District, Northwest Ethiopia

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Open Journal of Epidemiology 2014年第4期4卷 208-216页

作者： Molla Gedefaw bilal Muche Mekonen Aychiluhem GAMBY College of Medical Sciences Bahir Dar Ethiopia Save the Children International Bahir Dar Ethiopia

Good antenatal care (ANC) is one of the most important health care aspects known to reduce maternal mortality. In Ethiopia, regional and national data at times do not concur thus data from district to district level decision making are needed. The aim of this study was, therefore, to assess the prevalence and correlates of ANC service utilization. A community based cross-sectional study was conducted among pregnant women. Multistage sampling was used. Pre-tested structured questionnaire was data collection tool. Data were analyzed using SPSS version 16.0 for windows. Logistic regression was used to assess possible association among variables. Odds ratio at 95% confidence interval was used to measure strength, and statistical significance of associations. Prevalence of ANC service utilization was 57%. Of these, more than 80% of them received ANC for ≥4 times. This finding is more similar to the regional report (68%) than that of EDHS (2011) for Amhara Region (34%). Marital status, educational status and income were important predictors for ANC service utilization. The most outstanding finding of this study was that more than 20% and 60% of mothers received antennal care, and information about antenatal care from health extension workers. Antenatal care utilization is still low. Single, divorced, or separated mothers were less likely to utilize ANC while economically better off, and literate mothers were more likely to use ANC services than their counterparts. The finding of this study is in line with the annual reports from the Regional health bureau and disagrees with Ethiopian demographic health survey—EDHS-(2011). Therefore, districts should be encouraged to make decisions based on their own locally generated data than based on EDHS data which could at times be discouraging for districts with better performance. Further strengthening of Health Extension Program is recommended.

关键词： Prevalence Antenatal Care Utilization Associated Factors