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On a compact oriented Finsler manifold without boundary, every cohomology class has a unique harmonic representation. The dimension of the space of all harmonic forms of ...

The mathematical study of a nonlinear equation f(phi)=y, where f maps from a Hilbert space X to a Hilbert space Y and y in Y which abstracts the construction of optical ...

The Hopf invariant one theorem, sometimes also called Adams' theorem, is a deep theorem in homotopy theory which states that the only n-spheres which are H-spaces are S^0, ...

A sextic surface given by the implicit equation 4(x^2+y^2+z^2-13)^3+27(3x^2+y^2-4z^2-12)^2=0.

The metric ds^2=(dx^2+dy^2)/((1-x^2-y^2)^2) for the Poincaré hyperbolic disk, which is a model for hyperbolic geometry. The hyperbolic metric is invariant under conformal ...

Also known as the a Lorentz transformation or Procrustian stretch, a hyperbolic transformation leaves each branch of the hyperbola x^'y^'=xy invariant and transforms circles ...

The multiplicative subgroup of all elements in the product of the multiplicative groups k_nu^× whose absolute value is 1 at all but finitely many nu, where k is a number ...

The identric mean is defined by I(a,b)=1/e((b^b)/(a^a))^(1/(b-a)) for a>0, b>0, and a!=b. The identric mean has been investigated intensively and many remarkable inequalities ...

An incircle is an inscribed circle of a polygon, i.e., a circle that is tangent to each of the polygon's sides. The center I of the incircle is called the incenter, and the ...

The ratio of the independence number of a graph G to its vertex count is known as the independence ratio of G (Bollobás 1981). The product of the chromatic number and ...