The errorfunction, as well as related functions, occurs in theoretical aspects of many parts of atmospheric science. This note presents a closed-form approximation for the error, complementaryerror, and scaled compl...
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The errorfunction, as well as related functions, occurs in theoretical aspects of many parts of atmospheric science. This note presents a closed-form approximation for the error, complementaryerror, and scaled complementary error functions, with maximum relative errors within 0.8%. Unlike other approximate solutions, this single equation gives answers within the stated accuracy for real variable x is an element of [0 infinity). The approximation is very useful in solving atmospheric science problems by providing analytical solutions. Examples of the utility of the approximation are: the computation of cirrus cloud physics inside a general circulation model, the cumulative distribution functions of normal and log-normal distributions, and the recurrence period for risk assessment. Copyright (C) 2007 Royal Meteorological Society
In this work we will introduce theorems relating the Riemann-Liouville fractional integral and the Weyl fractional integral to some well-known integral transforms including Laplace transforms, Stieltjes transforms, ge...
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In this work we will introduce theorems relating the Riemann-Liouville fractional integral and the Weyl fractional integral to some well-known integral transforms including Laplace transforms, Stieltjes transforms, generalized Stieltes transforms, Hankel transforms, and K-transforms. As applications of the theorems and their results, a number of infinite integrals of elementary functions and special functions are evaluated and some illustrative examples are presented. (C) 2006 Elsevier Inc. All rights reserved.
Elementary expressions are derived for the various probabilities of false alarm considered by Meziani and Soltani [Performance analysis of some CFAR detectors in homogeneous and non-homogeneous Pearson-distributed clu...
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Elementary expressions are derived for the various probabilities of false alarm considered by Meziani and Soltani [Performance analysis of some CFAR detectors in homogeneous and non-homogeneous Pearson-distributed clutter, Signal Process. 86 (August 2006) 2115-2122] with respect to CFAR detection. (c) 2006 Elsevier B.V. All rights reserved.
In the present paper Parseval-Goldstein type theorems involving the L-2-transform and the Laplace transform are proved. The theorems are then shown to yield a number of new identities involving several well-known inte...
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In the present paper Parseval-Goldstein type theorems involving the L-2-transform and the Laplace transform are proved. The theorems are then shown to yield a number of new identities involving several well-known integral transforms and special functions. Using the theorem and its corollaries, a number of interesting infinite integrals of elementary and special functions are presented. Some illustrative examples are also given. (C) 1999 Elsevier Science Inc. All rights reserved.
In the article, many inequalities of the integrals integral(infinity)(x) e(-tp) dt, integral(x)(0) e(-tp) dt, integral(x)(0) e(tp) dt for p > 0, which are related to the incomplete gamma function, are established. ...
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In the article, many inequalities of the integrals integral(infinity)(x) e(-tp) dt, integral(x)(0) e(-tp) dt, integral(x)(0) e(tp) dt for p > 0, which are related to the incomplete gamma function, are established. The approach used in the paper could yield more particular inequalities of the above functions. Some known results are generalized, extended or refined.
We investigated the adequacy of three different functions that have been used in the literature to characterize the relationship between mean systemic arterial pressure (SAP) and mean baroreceptor pressure (BP) in ope...
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We investigated the adequacy of three different functions that have been used in the literature to characterize the relationship between mean systemic arterial pressure (SAP) and mean baroreceptor pressure (BP) in open-loop experimental preparations. These curves are the normal cumulative distribution function (CDF), the logis tic (or growth) function (LF), and the third-order polynomial (TOP). Ten sets of experimental data from isolated carotid sinus preparations were selected from the literature as being representative of all baroreflex curves. Then, the Levenberg-Marquardt method was used to obtain best least-square approximation to these data and parameter estimates for each of the three approximating curves. The first derivative of each best-fit SAP-BP curve yielded a curve for the open-loop gain (G) as a function of BP. Our analysis indicated that both the CDF and the LF were superior to the TOP in fitting the SAP-BP data and in giving a realistic description of the G-BP curve. The operative range of BP was evaluated by estimating threshold (BPth) and saturation (BPsat) BPs using arbitrary definitions reported in the literature. The TOP did not allow this evaluation, The other two curves showed some disagreement due to different definitions of BPth and BPsat. After modifying the definition of these parameters associated with the LF, we could conclude that the analytical descriptions of SAP-BP and G-BP curves as obtained from the LF and the CDF were practically equivalent. Approximation method using the TOP should be avoided.
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