Sentence examples for kinds are defined from inspiring English sources
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.
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 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).
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.
As is well known, the Stirling numbers S ( l, n ) of the second kind are defined by the generating function to be ( e t − 1 ) n = n !
The Daehee numbers of the first kind are defined by frac{log(1+t)}{t}=sum_{n=0}^{infty}D_{n} frac{t^{n}}{n!} (cf. [7]).
The familiar q-Stirling numbers S ( n, k ) of the second kind are defined by ( e q ( t ) − 1 ) k [ k ] q !
Stirling numbers of the first kind are defined by bigl(log(1+t bigr)^{n} = n! sum _{m=n}^{infty}S_{1} (m,n) {t^{m} over m!}, (7) and the Stirling numbers of the second kind are defined by bigl(e^{t}-1bigr)^{n}= n! sum _{l=n}^{infty}S_{2} (n,l) frac{t^{l}}{l!} quad (n ge0).
The Stirling numbers of the first kind are defined as (x)_{n} = sum_{l=0}^{n} S_{1} (n,l) x^{l}, (18) where (S_{1} (n, l), (n,l ge0)) are called the Stirling numbers of the first kind.
As is well known, the Bernoulli polynomials of the second kind are defined by the generating function to be t log ( 1 + t ) ( 1 + t ) x = ∑ n = 0 ∞ b n ( x ) t n n ! ( see [1, p.130] ).
As is well known, the Bernoulli numbers of the second kind are defined by the generating function to be begin{aligned} frac{t}{log(1+t)} = sum _{n=0}^{infty}b_{n} frac{t^{n}}{n!}quad bigl text{see} text{[24]}bigr).
