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... 0), we can write m 2 a (AP +PA 1 ) 2 3 2 AP 2 + 3PA 2 1 = 3 2 (AP 2 +BP 2 +CP 2 ) 3 4 a 2 ; if we use the formula for medians in triangle PBC. ... ... + = 360 . Now, writing that T = X T(ABC) = 1 2 X xy sin withx =AP ,y =BP ,z =CP and applying the classical Cauchy-Buniakovski inequality, we have... ...AB,A2B 1 C 1 . It is immediate that this new triangle is regular, too, and BP 1 = PB 0 , CP 1 = PC 0 , AP 1 = PA 0 (where A 0 ;B 0 ;C 0 are the projec... ...s new triangle A 1 B 1 C 1 one gets PA 0 +PB 0 +PC 0 = constant, implying: BP 1 +CP 2 +AP 3 = constant (2) This surprising constant is similar to (1),... ...d Pythagorean theorem in triangle BPC and its analogues. One obtains PC 2 =BP 2 +a 2 2aBP 1 ; PA 2 =CP 2 +a 2 2aCP 2 ; PB 2 =AP 2 +a 2 2aAP 3 : ... ... (as in 1.), but suppose that P is on the inscribed circle (as in 2.). Let BP 1 = x, CP 2 = y, AP 3 = z. From the obtained right triangles one obtains... ...t in the course of solution, many "hidden" constants were discovered, e.g. BP 2 1 +CP 2 2 +AP 2 3 = constant (14) P 1 P 2 2 +P 1 P 2 3 +P 2 P 2 3 = co... ... 2 +AP 2 3 = constant (14) P 1 P 2 2 +P 1 P 2 3 +P 2 P 2 3 = constant (15) BP 1 CP 2 +BP 1 AP 2 +CP 2 AP 3 = constant (16) PP 1 PP 2 +PP 2 P... ... ! 0 as r!1: This gives the rst part. Let now p be a prime of the form p =bp 1 :::p r + 1. Then S(p 1) =S(bp 1 :::p r ) bS(p 1 :::p r ) =bp r and S...

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...a B x;; reEram quamvis A F per d tran%euntem,.per- petuo fecans in F; hw BP ultimo @i arcum evanefcentcti A’CB ra.tSo- nem h+ebit a;quaIitatis, eo... ...vadet paulo fimplicior jungendo B T, & in WI fi opus ei1, produh capiendo Bp ad B T ut etik T R ad T fiT; & per p agendo reAam infinitam p e ipfi S ... ...rare poiret ve- loziratem AB. Nam ii ducatur B T quz tangat hyperbolam in BP & occurrat afymptoto .in T ; w&a AT zqualis erit ipfi R C, 8r tern- pu... ...&nalis, efi+ui 5!Xp quad. & area B.TY, quaz efi ad aream 2)T$?~f !Zi.Q ad’Bp#; efi ut datum D.7+. Qecrefcit igitur area EfDFunifOrm&r ;ad :h:04 dum... ...endicul+ter incumbit, ut circub AB ,acig d,i$&renti.a.m : cjrcalorwm AB & BP. baque ex =qgo perturbate, ponderis pars, qpa ibla.fundum urgetwr, eft ... ...circuitu circuli AE, ut 1X2-2 CXg ad ACq. Jati .veyo ‘Ii fphzrz diame’ter Bp ditidatur in partes innumeras xqutiles, q&bus infifiant circuli tutidem... ... ad ufque perpendiculum penultimum ME, & erit ordinatim applicata R&Z dc+bp+c$+dr+es+ft, 8x. CwoC. FIinc area3 curvarum omnium inveniri poffunt. qu...

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...cial issue on sex tourism on 8.3. 1984 (Sanisuda Ekachai), new debate e.g. BP 5.4.1999; 6.4.1999; 3.7.1999. 49. Female students Bangkok Post 30.7.19... ...ok Post 30.7.1999; 5.9.1999; 11.4.2001. Pornography and the Internet, e.g. BP 1.10.2002; 11.11.2002. 50. National Statistical Office: Education a... ...otus.com; www.buddhanet.net/sangha-metta/project.html ). On families e.g. BP 29.3.1999; 23.4.1999; 24.8.1999. The fight against Aids has continued ... ...cial issue on sex tourism on 8.3. 1984 (Sanisuda Ekachai), new debate e.g. BP 5.4.1999; 6.4.1999; 3.7.1999. 49. Female students Bangkok Post 30.7.19... ...ok Post 30.7.1999; 5.9.1999; 11.4.2001. Pornography and the Internet, e.g. BP 1.10.2002; 11.11.2002. 50. National Statistical Office: Education a... ...otus.com; www.buddhanet.net/sangha-metta/project.html ). On families e.g. BP 29.3.1999; 23.4.1999; 24.8.1999. The fight against Aids has continued ...

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...bset in a S-bigroupoid (G = G 1 ∪ G 2 , +, ) with penultimate bisubset BP(η) and BP (µ) respectively. Then for g 1 ∈ G 1 , g 2 ∈ G 2 we define... ...y i ∈ P i (µ i )} 279 () r 2 r 1 r 2 2 1 1 l 2 l 1 l ), ( P ) ( P ) ( BP , η η η η η η η η η ∪ = ∪ = ∪ = (η = η 1 ∪ η 2 , µ = µ 1 ∪ µ 2 µ i ... ... o µ 1 in G defined by η i o µ i (g i ) =      ∉ ∈ ∈ ∈ ) µ ( BP ) ( BP g if )) g ( µ ), g ( ( min ) µ ( BP ) ( BP g if ) y ( ) x ( min s...

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...lied learning algorithm of neural networks is the error-based back propagation (BP). A BP algorithm to a two-layered network as shown in Fig.1.15.1 ...

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...lied learning algorithm of neural networks is the error-based back propagation (BP). A BP algorithm to a two-layered network as shown in Fig.1.15.1 ...

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...an Dezert, ONERA (French National Establishment for Aerospace Research), BP 72 F-92322 Chatillon Cedex – France; Dr. M. Khoshnevisan, School of Acc...

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...ean Dezert, ONERA (French National Establishment for Aerospace Research), BP 72 F-92322 Chatillon Cedex, France. Dr.M.Khoshnevisan, School of Accoun...

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...e grace, Which axe and hammer ruin In the fair and holy place.” —Bp. Cleveland Coxe. WHEN next John Kenton went into Bristol to market he tr... ...e hearts that love you tremble, And your enemies have cheer.” —Bp. Cleveland Coxe. “WHAT WOULD JEPH SAY?” was the thought of both Steadfas...

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...ives now may say, For now foul sluts in dairies May fare as well as they. —BP . Corbet. AN ANCIENT LEAFLESS STUMP of a horse-chesnut stood in the midd...