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Let A denote an R-algebra, so that A is a vector space over R and A×A->A (1) (x,y)|->x·y. (2) Then A is said to be alternative if, for all x,y in A, (x·y)·y=x·(y·y) (3) ...

Define O = lim_(->)O(n),F=R (1) U = lim_(->)U(n),F=C (2) Sp = lim_(->)Sp(n),F=H. (3) Then Omega^2BU = BU×Z (4) Omega^4BO = BSp×Z (5) Omega^4BSp = BO×Z. (6)

The evolute of the cardioid x = cost(1+cost) (1) y = sint(1+cost) (2) is the curve x_e = 2/3a+1/3acostheta(1-costheta) (3) y_e = 1/3asintheta(1-costheta), (4) which is a ...

For the cardioid given parametrically as x = a(1+cost)cost (1) y = a(1+cost)sint, (2) the involute is given by x_i = 2a+3acostheta(1-costheta) (3) y_i = ...

The orthotomic of the unit circle represented by x = cost (1) y = sint (2) with a source at (x,y) is x_o = xcos(2t)-ysin(2t)+2sint (3) y_o = -xsin(2t)-ycos(2t)+2cost. (4)

The four following types of groups, 1. linear groups, 2. orthogonal groups, 3. symplectic groups, and 4. unitary groups, which were studied before more exotic types of groups ...

The evolute of the cycloid x(t) = a(t-sint) (1) y(t) = a(1-cost) (2) is given by x(t) = a(t+sint) (3) y(t) = a(cost-1). (4) As can be seen in the above figure, the evolute is ...

The involute of the cycloid x = a(t-sint) (1) y = a(1-cost) (2) is given by x_i = a(t+sint) (3) y_i = a(3+cost). (4) As can be seen in the above figure, the involute is ...

The radial curve of the deltoid x = 1/3a[2cost+cos(2t)] (1) y = 1/3a[2sint-sin(2t)] (2) with radiant point (x_0,y_0) is the trifolium x_r = x_0+4/3a[cost-cos(2t)] (3) y_r = ...

The inverse of the Laplace transform F(t) = L^(-1)[f(s)] (1) = 1/(2pii)int_(gamma-iinfty)^(gamma+iinfty)e^(st)f(s)ds (2) f(s) = L[F(t)] (3) = int_0^inftyF(t)e^(-st)dt. (4)