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Let gamma(t) be a smooth curve in a manifold M from x to y with gamma(0)=x and gamma(1)=y. Then gamma^'(t) in T_(gamma(t)), where T_x is the tangent space of M at x. The ...

A statement which is rigorously not true. Regular two-valued logic allows statements to be only true or false, but fuzzy logic treats "truth" as a continuum which can have a ...

A collection of faces of an n-dimensional polytope or simplicial complex, one of each dimension 0, 1, ..., n-1, which all have a common nonempty intersection. In normal three ...

Given two univariate polynomials of the same order whose first p coefficients (but not the first p-1) are 0 where the coefficients of the second approach the corresponding ...

A G-space provides local notions of harmonic, hyperharmonic, and superharmonic functions. When there exists a nonconstant superharmonic function greater than 0, it is a ...

The statistical index P_H=(sumv_0)/(sum(v_0p_0)/(p_n))=(sump_0q_0)/(sum(p_0^2q_0)/(p_n)), where p_n is the price per unit in period n, q_n is the quantity produced in period ...

The integral transform (Kf)(x)=int_0^inftysqrt(xt)K_nu(xt)f(t)dt, where K_nu(x) is a modified Bessel function of the second kind. Note the lower limit of 0, not -infty as ...

A multiple root is a root with multiplicity n>=2, also called a multiple point or repeated root. For example, in the equation (x-1)^2=0, 1 is multiple (double) root. If a ...

The integral transform defined by (Kphi)(x)=int_0^inftyG_(pq)^(mn)(xt|(a_p); (b_q))phi(t)dt, where G_(pq)^(mn) is a Meijer G-function. Note the lower limit of 0, not -infty ...

For some range of r, the Mandelbrot set lemniscate L_3 in the iteration towards the Mandelbrot set is a pear-shaped curve. In Cartesian coordinates with a constant r, the ...