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IK.

00945), Arabian geographer, also known as Ibn u1-IHa`ik.

00From the value of A we may separate those members which contain a particular element a ik as a factor, and write the portion aik A ik; A k, the cofactor of ar k, is called a minor of order n - i of the determinant.

00a ll a33 ï¿½ï¿½ï¿½ a32 a33 ï¿½ï¿½ï¿½ a3n an2 an3 ï¿½ï¿½ï¿½ ann Similarly A ik, the cofactor of aik, is shown to be the product of (-) i+k and the determinant obtained by erasing from A the ith row and k th column.

00In the latter case the sign is determined by -I raised to the same power as before, with the exception that Tux., replaces Tusk; but if one of these numbers be even the other must be uneven; hence A ik = - Aisï¿½ rk Moreover aik a,, aikarsAik +aisarkAis Aik, rk aik ars rs where the determinant factor is giyen by the four points in which the deleting lines intersect.

00Similarly ali a21 a31 A =E a ik a2k a3k A li i > k > r, zï¿½k'r alr a2r air 23',!

00The Adjoint or Reciprocal Determinant arises from A = (a11a22a33 ...a nn) by substituting for each element A ik the corresponding minor Aik so as to form D = (A 11 A 22 A 33 ï¿½ï¿½ï¿½ A nn).

00We can eliminate the quantities S l, E2, ï¿½ï¿½ï¿½ In and obtain n relations AbXi = (2B 11 - Ab)'ï¿½k1 +2B21x2+2B31x3+ï¿½ï¿½ï¿½, AbX2 = 2B12x1+ (2B22 - Ab) x2 +2B32x3+..., and from these another equivalent set Abx1 = (2B11 - X1 +2B12X2+2B13X3+ï¿½ï¿½ï¿½, Abx2 = 2B21X1+(2B22 - Ab)X2+2B23X3+ï¿½ï¿½ï¿½, and now writing 2Bii - Ab 2Bik - aii, Ob = aik, Ob we have a transformation which is orthogonal, because EX 2 = Ex2 and the elements aii, a ik are functions of the 2n(n- I) independent quantities b.

00Thus - ik.

00Then dp/dz=kdp/dz = P, = Poe ik, p - po= kpo(ez Ik -1); (16) and if the liquid was incompressible, the depth at pressure p would be (p - po) 1po, so that the lowering of the surface due to compression is ke h I k -k -z= 1z 2 /k, when k is large.

00An angular velocity R, which gives components - Ry, Ix of velocity to a body, can be resolved into two shearing velocities, -R parallel to Ox, and R parallel to Oy; and then ik is resolved into 4'1+1'2, such that 4/ 1 -R-Rx 2 and 1//2+IRy2 is constant over the boundary.

00Trans., 1890); the solution is given by ch nS2=sn w, shnS2=i cn w (II) so that, round the boundary of the polygon, ik = K', sin n8 =o; and on the surface of the vortex 1P= o, q = Q, and cos n8=sn4p,nB= Zit -am sic, (12) the intrinsic equation of the curve.

00If a solution of potassium acetate be electrolysed the products are ethane, carbon dioxide, potash and hydrogen; in a similar manner, normal potassium succinate gives ethylene, carbon dioxide, potash and hydrogen; these reactions may be represented: CH 3 ï¿½CO 2;K CH 3 CO 2 K' CH 2 ï¿½CO 2 1K CH 2 CO 2 K' --> I + + I I -i iI + CH 3 ï¿½CO 21 K CH 3 CO 2 K' CH 2 ï¿½CO 2 iK CH 2 CO 2 K' By electrolysing a solution of potassium ethyl succinate, KO 2 Cï¿½(CH 2) 2 CO 2 C 2 H 5, the KO 2 Cï¿½ groups are split off and the two residues ï¿½(CH 2) 2 CO 2 C 2 H 5 combine to form the ester (CH2)4(C02C2H5)2.

00Among contemporary composers in 1921 the foremost were Foerster, Novak, Ostrcil, and Suk; and as executants Sev ik, Kubelik and Ondricek.

00Mitchell (" Ik Marvel ") was also born here; and Norwich was the home after 1825 of William Alfred Buckingham (1804-1875), war governor of Connecticut.

00He had now three distinct space-units, i, j, k; and the following conditions regulated their combination by multiplication: - I T = 12 '=' 2 = _ 1, ij= - ji=k, jk= - kj=i, ki= - ik =j.3 And now the product of two quaternions could be at once expressed as a third quaternion, thus (a+ib+jc+kd) (a'+ib'+jc'+kd') = A+iB+jC+kD, where A=aa' - bb' - cc' - dd', B = ab'+ba'+cd' - dc', C = ac'+ca'+db' - bd', D =ad' +da'+bc' - cb'.

00J, (o, {'p?'? ?1" b ve(Ik f ?

00Posted: Sun 5th Feb 06 01:34 Alleen onder Glamor versta ik wat anders maar dat moet kunnen. comment by: Very good site.

00a ll a33 Ã¯¿½Ã¯¿½Ã¯¿½ a32 a33 Ã¯¿½Ã¯¿½Ã¯¿½ a3n an2 an3 Ã¯¿½Ã¯¿½Ã¯¿½ ann Similarly A ik, the cofactor of aik, is shown to be the product of (-) i+k and the determinant obtained by erasing from A the ith row and k th column.

00In the latter case the sign is determined by -I raised to the same power as before, with the exception that Tux., replaces Tusk; but if one of these numbers be even the other must be uneven; hence A ik = - AisÃ¯¿½ rk Moreover aik a,, aikarsAik +aisarkAis Aik, rk aik ars rs where the determinant factor is giyen by the four points in which the deleting lines intersect.

00Recalling the formula A =a11A11+a12Al2+a13A13+Ã¯¿½Ã¯¿½Ã¯¿½+a1nA1n, it will be seen that a ik and Alk involve corresponding determinants.

00Similarly ali a21 a31 A =E a ik a2k a3k A li i > k > r, zÃ¯¿½k'r alr a2r air 23',!

00The Adjoint or Reciprocal Determinant arises from A = (a11a22a33 ...a nn) by substituting for each element A ik the corresponding minor Aik so as to form D = (A 11 A 22 A 33 Ã¯¿½Ã¯¿½Ã¯¿½ A nn).

00We can eliminate the quantities S l, E2, Ã¯¿½Ã¯¿½Ã¯¿½ In and obtain n relations AbXi = (2B 11 - Ab)'Ã¯¿½k1 +2B21x2+2B31x3+Ã¯¿½Ã¯¿½Ã¯¿½, AbX2 = 2B12x1+ (2B22 - Ab) x2 +2B32x3+..., and from these another equivalent set Abx1 = (2B11 - X1 +2B12X2+2B13X3+Ã¯¿½Ã¯¿½Ã¯¿½, Abx2 = 2B21X1+(2B22 - Ab)X2+2B23X3+Ã¯¿½Ã¯¿½Ã¯¿½, and now writing 2Bii - Ab 2Bik - aii, Ob = aik, Ob we have a transformation which is orthogonal, because EX 2 = Ex2 and the elements aii, a ik are functions of the 2n(n- I) independent quantities b.

00If a solution of potassium acetate be electrolysed the products are ethane, carbon dioxide, potash and hydrogen; in a similar manner, normal potassium succinate gives ethylene, carbon dioxide, potash and hydrogen; these reactions may be represented: CH 3 Ã¯¿½CO 2;K CH 3 CO 2 K' CH 2 Ã¯¿½CO 2 1K CH 2 CO 2 K' --> I + + I I -i iI + CH 3 Ã¯¿½CO 21 K CH 3 CO 2 K' CH 2 Ã¯¿½CO 2 iK CH 2 CO 2 K' By electrolysing a solution of potassium ethyl succinate, KO 2 CÃ¯¿½(CH 2) 2 CO 2 C 2 H 5, the KO 2 CÃ¯¿½ groups are split off and the two residues Ã¯¿½(CH 2) 2 CO 2 C 2 H 5 combine to form the ester (CH2)4(C02C2H5)2.

00Ik embodies the ability to communicate and share ideas and thoughts to others.

00This sign refers to spirit, and natives of Ik may need to feel grounded in some way.

00

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.