# Ai Sentence Examples

- - The
**AI**Harpoon Ship Log. **Ai**, emph.**AI**was for animals, not humans.- By similarly transforming the binary n ic form ay we find Ao = (
**aI**A 1 +a2 A2) n = aAn A l = (alAi - I -a 2 A 2) n1 (a1ï¿½1 +a2m2) = aa a ï¿½ - A i n-1 A2, n-k k n-k k n-k k A = (al l+a2A2) (alï¿½1+a2ï¿½2) = a A ï¿½ =A 1 A2, so that the umbrae A1, A 2 are a A, a ï¿½ respectively. - Such a filament is called a simple magnetic solenoid, and the product
**aI**is called the strength of the solenoid. - The name (originally
**Ai**i rr t) is generally derived from the nurse of Aeneas. - If al, a2, ...a, n be the roots of f=o, (1, R2, -
**Ai**the roots of 0=o, the condition that some root of 0 =o may qq cause f to vanish is clearly R s, 5 =f (01)f (N2) ï¿½ ï¿½;f (Nn) = 0; so that Rf,q5 is the resultant of f and and expressed as a function of the roots, it is of degree m in each root 13, and of degree n in each root a, and also a symmetric function alike of the roots a and of the roots 1 3; hence, expressed in terms of the coefficients, it is homogeneous and of degree n in the coefficients of f, and homogeneous and of degree m in the coefficients of 4.. - Hence, if f(
**ai**, a 2, ...a n) _ (?i?2%?3ï¿½ï¿½ï¿½), 1 2 3 +,01(X2A3...) +02(X1X3.ï¿½.) +IlA'(XlX2.ï¿½.) +... - To express the function aoa2 - _ which is the discriminant of the binary quadratic aoxi -+-2a1x2x2-+a2x2 =
**ai**=1, 1, in a symbolic form we have 2(aoa 2 -**ai**) =aoa2 +aGa2 -2 a1 ï¿½ al = a;b4 -}-alb? - A 1, A2 ï¿½
**Ai**, A 1 A 2, A2 and then Ao = al**Ai**+2a1a2AIA2+a2 A2 - (a1A1+a2A2) 2 = a?, A l = (a 1 A 1 +a2A2) (alï¿½l +a2ï¿½2) = aAaï¿½, A 2 = (alï¿½l +a2/-12) 2 = aM; so that A = aa l +2a A a u 152+aM5 2 = (aA6+a,e2)2; whence A1, A 2 become a A, a m, respectively and ?(S) = (a21+a,E2) 2; The practical result of the transformation is to change the umbrae a l, a 2 into the umbrae a s = a1A1 +a2A2, a ï¿½ = a1/ï¿½1 + a21=2 respectively. - -2 _ ab 2an-2bn-2Crz z x () x x x, Each term on the right-hand side may be shown by permutation of a, b, c to be the symbolical representation of the same covariant; they are equivalent symbolic products, and we may accordingly write 2(ac) (bc)
**ai**-1 bi -1 cx 2 =(ab)2a:-2b:-2c:, a relation which shows that the form on the left is the product of the two covariants n (ab) ay 2 by 2 and cZ. **Ai**by substituting for y 1, y 2 the cogredient quantities b2,-b1, and multiplying by by-k.- The simultaneous system of two quadratic forms
**ai**, ay, say f and 0, consists of six forms, viz. - Take and Uk = (af) k
**ai**k the linear factor which occurs to the second power in f. - F=
**ai**; the Hessian H = (ab) 2 azbx; the quartic i= (ab) 4 axb 2 x; the covariants 1= (**ai**) 4 ay; T = (ab)2(cb)aybyci; and the invariants A = (ab) 6; B = (ii') 4 . - If
**ai**, bx, cx be different forms we obtain, after development of the squared determinant and conversion to the real form (employing single and double dashes to distinguish the real coefficients of bx and cz), a(b'c"+b"c'-2 f'f") +b(c'a"+c"a'-2g'g") +c(a' +a"b'-2h'h")+2f(g'h"+g"h'-a' + 2g (h ' f"+h"f'-b'g"-b"g')+2h(f'g"+f"g'-c'h"-c"h'); a simultaneous invariant of the three forms, and now suppressing the dashes we obtain 6 (abc+2fgh -af t - bg 2 -ch2), the expression in brackets being the S well-known invariant of az, the vanishing of which expresses the condition that the form may break up into two linear factors, or, geometrically, that the conic may represent two right lines. - If we expand the symbolic expression by the multinomial theorem, and remember that any symbolic product
**ai**1 a2 2 a3 3 ... - Taking the variables to be x, y and effecting the linear transformation x = X1X+1.11Y, y = X2X+It2Y, X 2 +Y2X Y Xl - X2 y = _ x X I +
**AI**R X 122 so that - ï¿½l b it is seen that the two lines, on which lie (x, y), (X, Y), have a definite projective correspondence. - Then of course (AB) = (ab) the fundamental fact which appertains to the theory of the general linear substitution; now here we have additional and equally fundamental facts; for since A i = Xa i +,ia2, A2= - ï¿½ay + X a2, AA =A?-}-A2= (X2 +M 2)(a i+ a z) =aa; A B =AjBi+A2B2= (X2 +, U2)(albi+a2b2) =ab; (XA) = X i A2 - X2
**Ai**= (Ax i + /-Lx2) (- /-jai + Xa2) - (- / J.x i '+' Axe) (X a i +%Ga^2) = (X2 +, u 2) (x a - = showing that, in the present theory, a a, a b, and (xa) possess the invariant property. - If A=ZaE, then, by definition, IA=EajE, and hence
**AI**(B+C) =**AIB**+**AIC**. - (b-a.0-a) (6) (Q)
**AI**(a-a .0b) ch n2= ch log (Q) n cos 114+i sh log (9) re sin n9 = 2(r+ fi n) = b - a ' ju -a (7) a-a' l u-b nf2 = sh log (cos nO +1 ch log (" sin 110 =2(?" - Expressed as a differential relation, with the value of c-TKL
**ai**,G+2 (a 2 +A) a d ? - There arc four narrow avenues connecting this remarkable body of water with the Pacific and the Japan Sea; that on the west, called Shirnonoseki Strait, has a width of 3000 yds., that on the south, known
**ai**Hayarnoto Strait, is 8 m. - The principal elevations in this range are Shiranesanwith three summits, NOdori (9970 ft.),
**Ai-no-take**(10,200 ft.) and Kaigane (10,330 ft.)and HOOzan (9550 ft.). **Ai**a, blood), or native peroxide of iron, is also sometimes called "bloodstone."- She didn't come here to discuss adoption with Mums and
**AI**wasn't something she would ever agree to. - She had protested the morality of
**AI**until she lost her uterus, finally giving in to surrogacy a few years ago. - (7) The decay of all diphthongs;
**ai**, oi, ei all become a monophthong variously written e and i (rarely ei), as in the dat. - ~any Algae, lichens, and mosses are included among lithophytes,
**ai**id also Saxifraga**Aizoon**, S. - Oppositifolia, Silene acauhs, and
**ai**naphalium tuteo-al bum. - The resemblances consist, in fact, not so much in the existence of one general facies running through the regions, as is the case with the northern flora, but in the presence of peculiar types, such
**ai**those belonging to the families Restiaceae, Proteaceae, Ericaceae Mutisiaceac and Rutaceae. - This fact is overshadowed in England, partly by the habitual use of the word "gentleman" (q.v.) in various secondary uses, partly by the prevalent confusion between
**ai**dg retry. **AI**[Sept.- Abraham pitched his tent between
**Ai**and Bethel (Gen. - This may possibly be the site of
**Ai**; it agrees with all the intimations as to its position. - In final syllables the diphthongs
**ai**, ei, oi, all appear as e. - Maintains the diphthongs
**ai**and au, which in Hebrew have usually passed into e and o. - The diphthong
**ai**is 1 K. **Ai**-, t Yen? ?- Also Angelopoulos, Hepi IIecpauas Hai rcov Xtgivcov
**ai**)rou (Athens, 1898). - 2 The identification of the Israelite king with Me-ni-hi-(im)-mi of Sa-me-ri-na-
**ai**on the Ass. - From the invariant a2 -2a 1 a 3 -2aoa4 of the quartic the diminishing process yields
**ai-**2a 0 a 21 the leading coefficient of the Hessian of the cubic, and the increasing process leads to a3 -2a 2 a 4 +2a i a 5 which only requires the additional term-2aoa 6 to become a seminvariant of the sextic. A more important advantage, springing from the new form of S2, arises from the fact that if x"-**aix**n- +a2x n-2. - The sum and product of two quantities are defined in the first instance by the formulae zae -IE(3e = E (a +0) e, Za,ei X E
**ai**e j = (a iai) eie9, so that the laws A, C, D of ï¿½ 3 are satisfied. - Lombroso, Antropometria di 400 delinquenti (1872); Roberts, Manual of Anthropometry (1878); Ferri, Studi comparati di antropometria (2 vols., 1881-1882); Lombroso, Rughe anomale speciali
**ai**criminali (1890); Bertillon, Instructions signaletiques pour l'identification anthropometrique (1893); Livi, Anthropometria (Milan, D900); Furst, Indextabellen zum anthropometrischen Gebrauch (Jena, 1902); Report of Home Office Committee on the Best Means of Identifying Habitual Criminals (1893-1894). - 28 sqq., led southwards from
**Ai**over an undulating plateau to Michmash. - This little plateau, about a mile east of the present village of Mukhmas, seems to have been the post of the Philistines, lying close to the centre of the insurrection, yet possessing unusually good communication with their establishments on Mount Ephraim by way of
**Ai**and Bethel, and at the same time commanding the routes leading down to the Jordan from**Ai**and from Michmash itself. - Another variety of carving much affected by artists of the 17th century, and now largely used, is called shishi-
**ai-bori**or niku-**ai-bori**.