Sentence Examples


  • Thus ortho-phenylene diamine yields the following products: N H N ./`N; Xn NZ In some cases oxidation of condensed benzenoid-heterocyclic nuclei results in the rupture of the heterocyclic ring with the formation of a benzene dicarboxylic acid; but if the aromatic nucleus be weakened by the introduction of an amino group, then it is the benzenoid nucleus which is destroyed and a dicarboxylic acid of the heterocyclic ring system obtained.
  • In general in space of n dimensions we have n substitutions similar to X l = a11x1 +a12x2 + � � � + ainxn, and we have to express the n 2 coefficients in terms of Zn(n - I)i independent quantities; which must be possible, because X1+X2+..."IL Xn =xi+x2 +x3 +...+4.
  • ..yn xi, and as a particular case (y1, Y2,...yn) (x1, x2,...xn) = 1.
  • =0, are non-unitary symmetric functions of the roots of a xn-a l xn 1 a2 x n-2 -...
  • The binomial theorem may, for instance, be stated for (x+a)n alone; the formula for (x-a)" being obtained by writing it as {x+(-)a} n or Ix+(- a) } n, so that (x-a) n =x"- 1)xn-laF...+(-)rn(r)xn-rar+..., where + (-) r means - or + according as r is odd or even.
 

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