Received: from 173-13-139-235-sfba.hfc.comcastbusiness.net ([173.13.139.235]:55660 helo=jukni.digitalkingdom.org) by stodi.digitalkingdom.org with smtp (Exim 4.80.1) (envelope-from ) id 1Xwj09-0006YY-Ic; Thu, 04 Dec 2014 18:52:15 -0800 Received: by jukni.digitalkingdom.org (sSMTP sendmail emulation); Thu, 04 Dec 2014 18:52:13 -0800 From: "Apache" Date: Thu, 04 Dec 2014 18:52:13 -0800 To: webmaster@lojban.org, curtis289@att.net Subject: [jvsw] Definition Edited At Word te'i'ai -- By krtisfranks Bcc: jbovlaste-admin@lojban.org Message-ID: <54811ddd./pN5ybASjy0fRLul%webmaster@lojban.org> User-Agent: Heirloom mailx 12.5 7/5/10 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Spam-Score: 0.5 (/) X-Spam_score: 0.5 X-Spam_score_int: 5 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 @@CONTACT_ADDRESS@@ for details. Content preview: In jbovlaste, the user krtisfranks has edited a definition of "te'i'ai" in the language "English". Differences: 2,2c2,2 < 6-ary mekso/mathematical operator: Heaviside function/step/Theta function of a, of order b, in structure c, using distribution d, within approximated limit e, with value f at 0 --- > 6-ary mekso/mathematical operator: Heaviside function/step/Theta function of a, of order b, in structure c, using distribution d, within approximated limit e, with value f_b at 0 5,5c5,5 < Explanation: A sequence/family of (strictly monotonically increasingly, ordered) indexed function distributions (d), each of which is of/with respect to/in variable/indeterminant a, is considered; they must have the property that, as the index increases, they converge to some value (described later and determined by b) for all a. This happens on structure c, which defines what various values and limits mean. b is the 'order' of the result of this convergence (so that it is the bth-order integral (equivalently, -bth-order derivative) of the Heaviside step/Theta function with respect to a so that b = -1 yields the Dirac delta 'function' centered/with interesting point at 0, b = 0 yields the Heaviside step/Theta function with respect to a centered at/with interesting point 0, etc.). Natural numbers (or 0) for b yield yield a 'special' polynomial (let us call it p) of that order in indeterminant a to the right and 0 to the left so that p(a) = a^b Theta(a). Input e is for when the particular functions in d are of interest and only e of them have been computed (so that, for finite e, the output is not exactly the bth order Heaviside function); in other words, the limit of the family indices is being taken to e; this is of particular importance for negative values of b: |b| > 1, since they will not be identically 0 in some sense (else, all information is lost about the special structure/nature of this function). The contextless defaults are: b = 0, c is the field of real numbers, d is bth-order integral of ((1 + y + z erf(k a/(2^(1/2))))/2)-like functions that are properly normalized and are of proper height, e is infinity (countable). [...] Content analysis details: (0.5 points, 5.0 required) pts rule name description ---- ---------------------- -------------------------------------------------- 0.0 URIBL_BLOCKED ADMINISTRATOR NOTICE: The query to URIBL was blocked. See http://wiki.apache.org/spamassassin/DnsBlocklists#dnsbl-block for more information. [URIs: lojban.org] 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 In jbovlaste, the user krtisfranks has edited a definition of "te'i'ai" in the language "English". Differences: 2,2c2,2 < =09=096-ary mekso/mathematical operator: Heaviside function/step/Thet= a function of a, of order b, in structure c, using distribution d, with= in approximated limit e, with value f at 0 --- > =09=096-ary mekso/mathematical operator: Heaviside function/step/Thet= a function of a, of order b, in structure c, using distribution d, with= in approximated limit e, with value f_b at 0 5,5c5,5 < =09=09Explanation: A sequence/family of (strictly monotonically incre= asingly, ordered) indexed function distributions (d), each of which is = of/with respect to/in variable/indeterminant a, is considered; they mus= t have the property that, as the index increases, they converge to some= value (described later and determined by b) for all a. This happens on= structure c, which defines what various values and limits mean. b is t= he 'order' of the result of this convergence (so that it is the bth-ord= er integral (equivalently, -bth-order derivative) of the Heaviside step= /Theta function with respect to a so that b =3D -1 yields the Dirac del= ta 'function' centered/with interesting point at 0, b =3D 0 yields the = Heaviside step/Theta function with respect to a centered at/with intere= sting point 0, etc.). Natural numbers (or 0) for b yield yield a 'spec= ial' polynomial (let us call it p) of that order in indeterminant a to = the right and 0 to the left so that p(a) =3D a^b Theta(a). Input e is f= or when the particular functions in d are of interest and only e of the= m have been computed (so that, for finite e, the output is not exactly = the bth order Heaviside function); in other words, the limit of the fam= ily indices is being taken to e; this is of particular importance for n= egative values of b: |b| > 1, since they will not be identically 0 in s= ome sense (else, all information is lost about the special structure/na= ture of this function). The contextless defaults are: b =3D 0, c is the= field of real numbers, d is bth-order integral of ((1 + y + z erf(k a/= (2^(1/2))))/2)-like functions that are properly normalized and are of p= roper height, e is infinity (countable). Heaviside(0,0) =3D 1/2 =3D f_0= is typical and is a contextless default; for values of b other than 0,= f_b =3D 0 is the contextless default. --- > =09=09Explanation: A sequence/family of (strictly monotonically incre= asingly, ordered) indexed function distributions (d), each of which is = of/with respect to/in variable/indeterminant a, is considered; they mus= t have the property that, as the index increases, they converge to some= value (described later and determined by b, e, and f_b) for all a. Thi= s happens on structure c, which defines what various values and limits = mean. b is the 'order' of the result of this convergence (so that it is= the bth-order integral (equivalently, -bth-order derivative) of the He= aviside step/Theta function with respect to a so that b =3D -1 yields t= he Dirac delta 'function' centered/with interesting point at 0, b =3D 0= yields the Heaviside step/Theta function with respect to a centered at= /with interesting point 0, etc.). Natural numbers (or 0) for b yield a= 'special' polynomial (let us call it p) of that order in indeterminant= a for all values of a greater than 0 and 0 for all values of a less th= an 0 so that p(a) =3D a^b Theta(a). Input e is for when the particular = functions in d are of interest and only e of them have been computed (s= o that, for finite e, the output is not exactly the bth order Heaviside= function); in other words, the limit of the family indices is being ta= ken to e; this is of particular importance for negative values of b: |b= | > 1, since they will not be identically 0 in some sense (else, all in= formation is lost about the special structure/nature of this function).= The contextless defaults are: b =3D 0, c is the field of real numbers,= d is bth-order integral of ((1 + y + z erf(k a/(2^(1/2))))/2)-like fun= ctions that are properly normalized and are of proper height, e is infi= nity (countable). Heaviside(0,0,...,f_0) =3D 1/2 =3D f_0 is typical and= is a contextless default; for values of b other than 0, f_b =3D 0 is t= he contextless default; note that f_(-1) must be infinity 'of the prope= r magnitude' (it cannot be specified to be otherwise). 11,11d10 < =09=09Word: Heaviside function, In Sense: mekso operator; of any orde= r \n13,13c12,12 < =09=09Word: Theta function, In Sense: mekso operator; Heaviside; step= function given by family of distributions --- > =09=09Word: Heaviside function, In Sense: mekso operator; of any orde= r 14a14,14 \n> =09=09Word: Theta function, In Sense: mekso operator; Heaviside; st= ep function given by family of distributions Old Data: =09Definition: =09=096-ary mekso/mathematical operator: Heaviside function/step/Theta = function of a, of order b, in structure c, using distribution d, within= approximated limit e, with value f at 0 =09Notes: =09=09Explanation: A sequence/family of (strictly monotonically increas= ingly, ordered) indexed function distributions (d), each of which is of= /with respect to/in variable/indeterminant a, is considered; they must = have the property that, as the index increases, they converge to some v= alue (described later and determined by b) for all a. This happens on s= tructure c, which defines what various values and limits mean. b is the= 'order' of the result of this convergence (so that it is the bth-order= integral (equivalently, -bth-order derivative) of the Heaviside step/T= heta function with respect to a so that b =3D -1 yields the Dirac delta= 'function' centered/with interesting point at 0, b =3D 0 yields the He= aviside step/Theta function with respect to a centered at/with interest= ing point 0, etc.). Natural numbers (or 0) for b yield yield a 'specia= l' polynomial (let us call it p) of that order in indeterminant a to th= e right and 0 to the left so that p(a) =3D a^b Theta(a). Input e is for= when the particular functions in d are of interest and only e of them = have been computed (so that, for finite e, the output is not exactly th= e bth order Heaviside function); in other words, the limit of the famil= y indices is being taken to e; this is of particular importance for neg= ative values of b: |b| > 1, since they will not be identically 0 in som= e sense (else, all information is lost about the special structure/natu= re of this function). The contextless defaults are: b =3D 0, c is the f= ield of real numbers, d is bth-order integral of ((1 + y + z erf(k a/(2= ^(1/2))))/2)-like functions that are properly normalized and are of pro= per height, e is infinity (countable). Heaviside(0,0) =3D 1/2 =3D f_0 i= s typical and is a contextless default; for values of b other than 0, f= _b =3D 0 is the contextless default. =09Jargon: =09=09 =09Gloss Keywords: =09=09Word: Heaviside function, In Sense: mekso operator; of any order =09=09Word: Dirac delta, In Sense: mekso operator =09=09Word: Theta function, In Sense: mekso operator; Heaviside; step f= unction given by family of distributions =09=09Word: step function, In Sense: mekso operator; Heaviside =09Place Keywords: New Data: =09Definition: =09=096-ary mekso/mathematical operator: Heaviside function/step/Theta = function of a, of order b, in structure c, using distribution d, within= approximated limit e, with value f_b at 0 =09Notes: =09=09Explanation: A sequence/family of (strictly monotonically increas= ingly, ordered) indexed function distributions (d), each of which is of= /with respect to/in variable/indeterminant a, is considered; they must = have the property that, as the index increases, they converge to some v= alue (described later and determined by b, e, and f_b) for all a. This = happens on structure c, which defines what various values and limits me= an. b is the 'order' of the result of this convergence (so that it is t= he bth-order integral (equivalently, -bth-order derivative) of the Heav= iside step/Theta function with respect to a so that b =3D -1 yields the= Dirac delta 'function' centered/with interesting point at 0, b =3D 0 y= ields the Heaviside step/Theta function with respect to a centered at/w= ith interesting point 0, etc.). Natural numbers (or 0) for b yield a '= special' polynomial (let us call it p) of that order in indeterminant a= for all values of a greater than 0 and 0 for all values of a less than= 0 so that p(a) =3D a^b Theta(a). Input e is for when the particular fu= nctions in d are of interest and only e of them have been computed (so = that, for finite e, the output is not exactly the bth order Heaviside f= unction); in other words, the limit of the family indices is being take= n to e; this is of particular importance for negative values of b: |b| = > 1, since they will not be identically 0 in some sense (else, all info= rmation is lost about the special structure/nature of this function). T= he contextless defaults are: b =3D 0, c is the field of real numbers, d= is bth-order integral of ((1 + y + z erf(k a/(2^(1/2))))/2)-like funct= ions that are properly normalized and are of proper height, e is infini= ty (countable). Heaviside(0,0,...,f_0) =3D 1/2 =3D f_0 is typical and i= s a contextless default; for values of b other than 0, f_b =3D 0 is the= contextless default; note that f_(-1) must be infinity 'of the proper = magnitude' (it cannot be specified to be otherwise). =09Jargon: =09=09 =09Gloss Keywords: =09=09Word: Dirac delta, In Sense: mekso operator =09=09Word: Heaviside function, In Sense: mekso operator; of any order =09=09Word: step function, In Sense: mekso operator; Heaviside =09=09Word: Theta function, In Sense: mekso operator; Heaviside; step f= unction given by family of distributions =09Place Keywords: You can go to to see it.