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A common mechanism which generates singularities from smooth initial conditions.

For a smooth harmonic map u:M->N, where del is the gradient, Ric is the Ricci curvature tensor, and Riem is the Riemann tensor.

A two-dimensional map which is conjugate to the Hénon map in its nondissipative limit. It is given by x^' = x+y^' (1) y^' = y+epsilony+kx(x-1)+muxy. (2)

If a function phi:(0,infty)->(0,infty) satisfies 1. ln[phi(x)] is convex, 2. phi(x+1)=xphi(x) for all x>0, and 3. phi(1)=1, then phi(x) is the gamma function Gamma(x). ...

Given the functional (1) find in a class of arcs satisfying p differential and q finite equations phi_alpha(y_1,...,y_n;y_1^',...,y_n^')=0 for alpha=1,...,p ...

For homogeneous polynomials P and Q of degree m and n, then sqrt((m!n!)/((m+n)!))[P]_2[Q]_2<=[P·Q]_2<=[P]_2[Q]_2, where [P·Q]_2 is the Bombieri norm.

The domain of Booleans, sometimes denoted B, consisting of the elements True and False, implemented in the Wolfram Language as Booleans. In the Wolfram Language, a quantity ...

The system of partial differential equations u_t = b·v_x (1) b_(xt) = u_(xx)b+axv_x-2vx(vxb). (2)

A relation between compact boundaryless manifolds (also called closed manifolds). Two closed manifolds are bordant iff their disjoint union is the boundary of a compact ...

Let {A_n}_(n=0)^infty be a sequence of events occurring with a certain probability distribution, and let A be the event consisting of the occurrence of a finite number of ...