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The distribution of quadratic residues and nonâresidues
Mathematika, 1957The author proves the following: Theorem 1. Let \(\delta\) and \(\varepsilon\) be any fixed positive numbers. Then, for all sufficiently large \(p\) and any \(N\), we have \[ \left\vert \sum_{n=N+1}^{N+H} \left(\frac{n}{p}\right)\right\vert < \varepsilon H \] provided \(H > p^{1/4+\delta}\). \(\left(\frac{n}{p}\right)\) is the Legendre symbol and \(p\)
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A Note on the Distribution of Residues and Non-Residues
Journal of the London Mathematical Society, 1963A slight improvement is made over a previous result [Proc. Lond. Math. Soc. (3) 12, 179--192 (1962; Zbl 0106.04003), theorem 2] of the author in the theorem. If \(\chi\) is a non-principal character to the prime modulus \(p\) and \(\chi(n) = \omega\) for \(H\) consecutive values of \(n\), then \(H\ll p^{\frac14} \log p\).
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Calcutta Statistical Association Bulletin, 2002
Residuals based on case deletion has been drawn a great deal of attention in recent years. The prime objective of these residuals is the identification of outliers in linear regression. In this paper we investigate their performances as substitutes of the true randQm disturbances and compare them with the traditionally used least squares residuals ...
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Residuals based on case deletion has been drawn a great deal of attention in recent years. The prime objective of these residuals is the identification of outliers in linear regression. In this paper we investigate their performances as substitutes of the true randQm disturbances and compare them with the traditionally used least squares residuals ...
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Urology, 1985
Uncomplicated lymphoceles can cause lateral extrinsic compression of the sigmoid colon. Ultrasound is the study of choice to define these cystic collections, which may persist many months as a postoperative complication of pelvic lymph node dissection.
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Uncomplicated lymphoceles can cause lateral extrinsic compression of the sigmoid colon. Ultrasound is the study of choice to define these cystic collections, which may persist many months as a postoperative complication of pelvic lymph node dissection.
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The Journal of the Acoustical Society of America, 1962
The residue is defined as the joint perception of a number of Fourier components. Depending on circumstances outside the scope of this paper, it has a pronounced pitch. The consequences of this phenomenon for the theory of hearing are briefly reviewed in the light of past experiments.
Schouten, J.F. +2 more
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The residue is defined as the joint perception of a number of Fourier components. Depending on circumstances outside the scope of this paper, it has a pronounced pitch. The consequences of this phenomenon for the theory of hearing are briefly reviewed in the light of past experiments.
Schouten, J.F. +2 more
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Residue Theorem and Logarithmic Residue Theorem.
Science and Technology of Engineering, Chemistry and Environmental ProtectionThis passage is written for researching the application of residue theorem and Logarithmic Residue theorem. The residue theorem is a powerful tool for the analysis of complex functions. It also can be used to calculate the integral of the real functions.
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2010
The use of veterinary drugs in animal production is necessary for the prevention and treatment of disease; however, such use may result in residues. Regulatory authorities administer legislative frameworks which ensure that foods derived from animals treated with approved veterinary drugs are safe for human consumption.
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The use of veterinary drugs in animal production is necessary for the prevention and treatment of disease; however, such use may result in residues. Regulatory authorities administer legislative frameworks which ensure that foods derived from animals treated with approved veterinary drugs are safe for human consumption.
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Pesticide residues in drinking water, their potential risk to human health and removal options
Journal of Environmental Management, 2021Yasser Z El-Nahhal, Ibrahim Y El-Nahhal
exaly
2007
Following offset of an appropriate masking stimulus, tinnitus may remain suppressed for a period, typically less than a minute. This phenomenon is known as "residual inhibition" (RI). This chapter reviews the psychoacoustic properties of RI and their relation to hearing impairment, tinnitus spectra, and the spectra of masking stimuli.
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Following offset of an appropriate masking stimulus, tinnitus may remain suppressed for a period, typically less than a minute. This phenomenon is known as "residual inhibition" (RI). This chapter reviews the psychoacoustic properties of RI and their relation to hearing impairment, tinnitus spectra, and the spectra of masking stimuli.
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