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The fundamental group of an arcwise-connected set X is the group formed by the sets of equivalence classes of the set of all loops, i.e., paths with initial and final points ...

The curvature and torsion functions along a space curve determine it up to an orientation-preserving isometry.

Numbered rods which can be used to perform multiplication.

A decomposition of a module into a direct sum of submodules. The index set for the collection of submodules is then called the grading set. Graded modules arise naturally in ...

The center of a group is the set of elements which commute with every element of the group. It is equal to the intersection of the centralizers of the group elements.

For n>=3, there exist no additive finite and invariant measures for the group of displacements in R^n.

Given a positive sequence {a_n}, sqrt(sum_(j=-infty)^infty|sum_(n=-infty; n!=j)^infty(a_n)/(j-n)|^2)<=pisqrt(sum_(n=-infty)^infty|a_n|^2), (1) where the a_ns are real and ...

Every modular system has a modular system basis consisting of a finite number of polynomials. Stated another way, for every order n there exists a nonsingular curve with the ...

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 ...

A solution of a linear homogeneous ordinary differential equation with polynomial coefficients.