Mean Value Estimation of Ideal Counting Function in Short Interval over Quadratic Algebraic Extension Field

The mean value is perhaps the most fundamental statistic and the chapter describes its properties and features that make it an important and necessary analytic tool.

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Mean Value Estimation Using Two-Phase Samples with Missing Data in Both Phases

Acta Applicandae Mathematicae ◽

10.1007/s10440-007-9110-5 ◽

2007 ◽

Vol 96 (1-3) ◽

pp. 215-220 ◽

Cited By ~ 4

Author(s):

Wojciech Gamrot

Keyword(s):

Missing Data ◽

Mean Value ◽

Two Phase ◽

Value Estimation

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On Exponential Sums Involving the Ideal Counting Function in Quadratic Number Fields

Monatshefte für Mathematik ◽

10.1007/s00605-002-0495-y ◽

2002 ◽

Vol 137 (2) ◽

pp. 129-156 ◽

Cited By ~ 1

Author(s):

Jun Furuya

Keyword(s):

Exponential Sums ◽

Counting Function ◽

Number Fields ◽

Quadratic Number ◽

Quadratic Number Fields ◽

Ideal Counting Function ◽

The Ideal

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Design of Chaotic Bifurcation Parameter Modulation Scheme using Mean Value Estimation

Iraqi Journal of Information & Communications Technology ◽

10.31987/ijict.1.1.13 ◽

2018 ◽

Vol 1 (1) ◽

pp. 52-61

Author(s):

Hikmat Najem Abdullah ◽

Ibrahim Fahmi Ali

Keyword(s):

Spread Spectrum ◽

Chaotic Map ◽

Mean Value ◽

Direct Sequence Spread Spectrum ◽

Modulation Scheme ◽

Manufacturing Cost ◽

Bifurcation Parameter ◽

Parameter Modulation ◽

Value Estimation ◽

Chaotic Parameter

In this paper, the bifurcation parameter of the chaotic map is estimated accurately by utilizing the ergodic properties of a chaotic dynamical signal. Binary Phase Shift Keying Ergodic Chaotic Parameter Modulation (BPSK-ECPM) scheme is used to modulate the information signal in the bifurcating parameter of the chaotic map. A mean value estimation technique is used at the receiver to retrieve the original information accurately. This method minimizes the computational complexity of the receiver; thereby, reduces the total manufacturing cost. Simulation results confirm that, in AWGN channel and at bit error rate (BER) of 10-3, BPSK-ECPM achieves gains in Eb/N0 of about 0.7dB and 5dB in comparison with conventional direct sequence spread spectrum with BPSK modulation (DS-SS BPSK) and conventional ergodic chaotic parameter modulation spread spectrum (ECPM-SS) systems respectively. The results also confirm that in Rayleigh fading channel and at BER of 10-3, BPSK-ECPM achieves gains in Eb/N0 of about 6.3dB and 1.6dB in comparison with DS-SS BPSK and ECPM-SS systems respectively, which make BPSK-ECPM an ideal candidate for the intelligent transportation system (ITS).

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The mean-square value of the divisor function

The Mathematical Gazette ◽

10.1017/mag.2016.56 ◽

2016 ◽

Vol 100 (548) ◽

pp. 203-212

Author(s):

Peter Shiu

Keyword(s):

Counting Function ◽

Mean Value ◽

Mean Square ◽

Divisor Function ◽

Dirichlet’S Theorem ◽

Fixed Power ◽

The Mean ◽

Dirichlet's Theorem ◽

Image Position ◽

Prime Counting Function

The behaviour of the divisor function d (n) is rather tricky. For a prime p, we have d(p) = 2, but if n is the product of the first k primes then, by Chebyshev's estimate for the prime counting function [1, Theorem 414], we have so thatfor such n then, d (n) is ‘unusually large’ — it can exceed any fixed power of log n, for example.In [2] Jameson gives, amongst other things, a derivation of Dirichlet's theorem, which shows that the mean-value of the divisor function in an interval containing n is log n. However, the result is somewhat deceptive because, for most n, the value of d (n) is substantially smaller than log n.

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