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rho_(n+1)(x)=intrho_n(y)delta[x-M(y)]dy, where delta(x) is a delta function, M(x) is a map, and rho is the natural invariant.

The study, first developed by Boole, of shift-invariant operators which are polynomials in the differential operator D^~. Heaviside calculus can be used to solve any ordinary ...

A necessary and sufficient condition for a measure which is quasi-invariant under a transformation to be equivalent to an invariant probability measure is that the ...

Let x:p(x)->xp(x), then for any operator T, T^'=Tx-xT is called the Pincherle derivative of T. If T is a shift-invariant operator, then its Pincherle derivative is also a ...

A phase curve (i.e., an invariant manifold) which meets a hyperbolic fixed point (i.e., an intersection of a stable and an unstable invariant manifold) or connects the ...

A transformation characterized by an invariant line and a scale factor (one-way stretch) or two invariant lines and corresponding scale factors (two-way stretch).

A metric characterizing the difference between two knots K and K^' in S^3.

A braid in which strands are intertwined in the center and are free in "handles" on either side of the diagram.

Given a general quadratic curve Ax^2+Bxy+Cy^2+Dx+Ey+F=0, (1) the quantity X is known as the discriminant, where X=B^2-4AC, (2) and is invariant under rotation. Using the ...

Togliatti (1940, 1949) showed that quintic surfaces having 31 ordinary double points exist, although he did not explicitly derive equations for such surfaces. Beauville ...