Sentence examples for kinds is defined from inspiring English sources

The density of cells of the first and second kinds is defined by ρ1 x, t) and ρ2 x, t), respectively, as a continuous representation of the number of cells of the first kind and second per unit length of capillary at time t at the position x.

In contrast, for the functionalist (Fodor 1997) mental kinds are defined by their functional roles, rather than by the essential properties of the neurophysiological kinds that realize them.

The generalized elliptic integrals of the first and second kinds are defined as begin{aligned} &mathscr{K}_{a}(r)=frac{pi}{2}F bigl a,1-a 1;r^{2}bigl a,1-a 1athscr {K}'_{a}(r)= mathscr{K}_{a}bigl(r'bigr),qquadmathscr} (1.2) begin{K}'_{ad} &mathscr{E}_{a}(r)=frac{pi}{2}Fbigl(a-1,1-a;1;r^{2} bigr),qquadmathscr{{E}'_{a}(r)=mathscr{E}_{a} bigl(r'bigr).

Then the Legendre complete elliptic integrals (mathcal {K}(r)) and (mathcal{E}(r)) [1, 2] of the first and second kinds are defined as mathcal{K}(r)= int_{0}^{pi/2}frac{dt}{sqrt{1-r^{2}sin^{2}(t)}}, qquadmathcal{E}(r)= int_{0}^{pi/2}sqrt{1-r^{2 0}^{pi/2}sqrt{1-r^{2pectively.

The Stirling number of the first kind is defined by (2.7).

The Stirling number of the second kind is defined by the generating function to be ( e t − 1 ) m = m !

The Stirling number of the first kind is defined by ( x ) n = ∑ l = 0 n S 1 ( n, l ) x l ( n ≥ 0 ) ( see [16] ).

The Stirling number of the second kind is defined by x n = ∑ l = 0 n S 2 ( n, l ) ( x ) l ( n ≧ 0 ).

The Stirling number of the first kind is defined by ( x ) n = x ( x − 1 ) ⋯ ( x − n + 1 ) = ∑ k = 0 n S 1 ( n, k ) x k. (9).

Still by analogy with classical statistic for scalar real random variables defined in ({mathbb {R}^), the second characteristic function (CF) of the second kind is defined as the natural logarithm of the first CF of the second kind.

The Stirling number of the first kind is defined by the falling factorial to be ( x ) n = x ( x − 1 ) ⋯ ( x − n + 1 ) = ∑ l = 0 n S 1 ( n, l ) x l. (2).