Received: from 173-13-139-235-sfba.hfc.comcastbusiness.net ([173.13.139.235]:40268 helo=jukni.digitalkingdom.org) by stodi.digitalkingdom.org with smtp (Exim 4.89) (envelope-from ) id 1f2SQb-0000Mw-Np for jbovlaste-admin@lojban.org; Sat, 31 Mar 2018 19:09:07 -0700 Received: by jukni.digitalkingdom.org (sSMTP sendmail emulation); Sat, 31 Mar 2018 19:09:05 -0700 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word cnanlagau -- By krtisfranks Date: Sat, 31 Mar 2018 19:09:05 -0700 MIME-Version: 1.0 Content-Type: text/plain; charset="UTF-8" Message-Id: X-Spam-Score: 3.1 (+++) X-Spam_score: 3.1 X-Spam_score_int: 31 X-Spam_bar: +++ X-Spam-Report: Spam detection software, running on the system "stodi.digitalkingdom.org", has NOT identified this incoming email as spam. The original message has been attached to this so you can view it or label similar future email. If you have any questions, see the administrator of that system for details. Content preview: In jbovlaste, the user krtisfranks has edited a definition of "cnanlagau" in the language "English". Differences: 5,5c5,5 < Elements of $x_2$ must have the same units/dimensionality; the result has the same units/dimensionality as them. If $x_3=p$ for a single extended-real number $p$, then $x_3=(p,p-1)$ also. If [...] Content analysis details: (3.1 points, 5.0 required) pts rule name description ---- ---------------------- -------------------------------------------------- 1.4 RCVD_IN_BRBL_LASTEXT RBL: No description available. [173.13.139.235 listed in bb.barracudacentral.org] -1.9 BAYES_00 BODY: Bayes spam probability is 0 to 1% [score: 0.0000] 1.0 RDNS_DYNAMIC Delivered to internal network by host with dynamic-looking rDNS 2.6 TO_NO_BRKTS_DYNIP To: lacks brackets and dynamic rDNS In jbovlaste, the user krtisfranks has edited a definition of "cnanlagau" in the language "English". Differences: 5,5c5,5 < Elements of $x_2$ must have the same units/dimensionality; the result has the same units/dimensionality as them. If $x_3=p$ for a single extended-real number $p$, then $x_3=(p,p-1)$ also. If $x_3 = (p,q)$ then the algorithm uses the $p$th-power mean ({cnanfadi}) and the $q$th-power mean; thus $x_3 = (1,0)$ corresponds to the standard arithmetic-geometric mean, $x_3 = (0, -1)$ corresponds to the geometric-harmonic mean. A poor choice of $x_3$ will lead to non-convergence of the sequences produced by the algorithm and, thus, leave $x_1$ undefined (NAN error). $x_1$ is the value to which each of the sequences produced by the algorithm converge (iff these values are mutually equal). Let $M_i$ denote the unweighted $i$th-power mean for all $i$ and let $x_2 = (a_0,g_0); x_3 = (p,q)$; then the algorithm produces potentially infinite sequences $a = (a_0, a_1, ...), g = (g_0, g_1, ...)$, where $a_n = M_p(a_{(n-1)}, g_{(n-1)}), g_n = M_q(a_{(n-1)}, g_{(n-1)})$ for all positive integers $n$. Notice that this word is symmetric ($x_1$ remains constant and none of the sumti change in meaning) under an internal permutation of the elements/entries of $x_2$ and/or of $x_3$ (when taken as a pair or set), separately. --- > Elements of $x_2$ must have the same units/dimensionality; the result has the same units/dimensionality as them. If $x_3=p$ for a single extended-real number $p$, then $x_3=(p,p-1)$ also. If $x_3 = (p,q)$ then the algorithm uses the $p$th-power mean ({cnanfadi}) and the $q$th-power mean; thus $x_3 = (1,0)$ corresponds to the standard arithmetic-geometric mean, $x_3 = (0, -1)$ corresponds to the geometric-harmonic mean. A poor choice of $x_3$ will lead to non-convergence of the sequences produced by the algorithm and, thus, leave $x_1$ undefined (NAN error). $x_1$ is the value to which each of the sequences produced by the algorithm converge (iff these values are mutually equal). Let $M_i$ denote the unweighted $i$th-power mean for all $i$ and let $x_2 = (a_0,g_0),$ $x_3 = (p,q)$; then the algorithm produces potentially infinite sequences $a = (a_0, a_1, ...), g = (g_0, g_1, ...)$, where $a_n = M_p(a_{(n-1)}, g_{(n-1)}), g_n = M_q(a_{(n-1)}, g_{(n-1)})$ for all positive integers $n$. Notice that this word is symmetric ($x_1$ remains constant and none of the sumti change in meaning) under an internal permutation of the elements/entries of $x_2$ and/or of $x_3$ (when taken as a pair or set), separately. Old Data: Definition: $x_1$ is the generalized arithmetic-geometric mean of the elements of the 2-element set $x_2$ (set; cardinality must be 2) of order $x_3$ (either single extended-real number xor an unordered pair/2-element set of extended-real numbers). Notes: Elements of $x_2$ must have the same units/dimensionality; the result has the same units/dimensionality as them. If $x_3=p$ for a single extended-real number $p$, then $x_3=(p,p-1)$ also. If $x_3 = (p,q)$ then the algorithm uses the $p$th-power mean ({cnanfadi}) and the $q$th-power mean; thus $x_3 = (1,0)$ corresponds to the standard arithmetic-geometric mean, $x_3 = (0, -1)$ corresponds to the geometric-harmonic mean. A poor choice of $x_3$ will lead to non-convergence of the sequences produced by the algorithm and, thus, leave $x_1$ undefined (NAN error). $x_1$ is the value to which each of the sequences produced by the algorithm converge (iff these values are mutually equal). Let $M_i$ denote the unweighted $i$th-power mean for all $i$ and let $x_2 = (a_0,g_0); x_3 = (p,q)$; then the algorithm produces potentially infinite sequences $a = (a_0, a_1, ...), g = (g_0, g_1, ...)$, where $a_n = M_p(a_{(n-1)}, g_{(n-1)}), g_n = M_q(a_{(n-1)}, g_{(n-1)})$ for all positive integers $n$. Notice that this word is symmetric ($x_1$ remains constant and none of the sumti change in meaning) under an internal permutation of the elements/entries of $x_2$ and/or of $x_3$ (when taken as a pair or set), separately. Jargon: Gloss Keywords: Word: AGM, In Sense: arithmetic-geometric mean Word: arithmetic-geometric mean, In Sense: Place Keywords: New Data: Definition: $x_1$ is the generalized arithmetic-geometric mean of the elements of the 2-element set $x_2$ (set; cardinality must be 2) of order $x_3$ (either single extended-real number xor an unordered pair/2-element set of extended-real numbers). Notes: Elements of $x_2$ must have the same units/dimensionality; the result has the same units/dimensionality as them. If $x_3=p$ for a single extended-real number $p$, then $x_3=(p,p-1)$ also. If $x_3 = (p,q)$ then the algorithm uses the $p$th-power mean ({cnanfadi}) and the $q$th-power mean; thus $x_3 = (1,0)$ corresponds to the standard arithmetic-geometric mean, $x_3 = (0, -1)$ corresponds to the geometric-harmonic mean. A poor choice of $x_3$ will lead to non-convergence of the sequences produced by the algorithm and, thus, leave $x_1$ undefined (NAN error). $x_1$ is the value to which each of the sequences produced by the algorithm converge (iff these values are mutually equal). Let $M_i$ denote the unweighted $i$th-power mean for all $i$ and let $x_2 = (a_0,g_0),$ $x_3 = (p,q)$; then the algorithm produces potentially infinite sequences $a = (a_0, a_1, ...), g = (g_0, g_1, ...)$, where $a_n = M_p(a_{(n-1)}, g_{(n-1)}), g_n = M_q(a_{(n-1)}, g_{(n-1)})$ for all positive integers $n$. Notice that this word is symmetric ($x_1$ remains constant and none of the sumti change in meaning) under an internal permutation of the elements/entries of $x_2$ and/or of $x_3$ (when taken as a pair or set), separately. Jargon: Gloss Keywords: Word: AGM, In Sense: arithmetic-geometric mean Word: arithmetic-geometric mean, In Sense: Place Keywords: You can go to to see it.