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A cusp catastrophe is a catastrophe which can occur for two control factors and one behavior axis. The cusp catastrophe is the universal unfolding of the singularity f(x)=x^4 ...

Consider two cylinders as illustrated above (Hubbell 1965) where the cylinders have radii r_1 and r_2 with r_1<=r_2, the larger cylinder is oriented along the z-axis, and ...

The group D_5 is one of the two groups of order 10. Unlike the cyclic group C_(10), D_5 is non-Abelian. The molecule ruthenocene (C_5H_5)_2Ru belongs to the group D_(5h), ...

The v coordinates are the asymptotic angle of confocal hyperbolic cylinders symmetrical about the x-axis. The u coordinates are confocal elliptic cylinders centered on the ...

The equilateral elongated square dipyramid, illustrated above together with its net, is Johnson solid J_(15). A version of the elongated square dipyramid that is "squashed" ...

Engineering notation is a version of scientific notation in which the exponent p in expressions of the form a×10^p is chosen to always be divisible by 3. Numbers of forms ...

A univariate function f(x) is said to be even provided that f(x)=f(-x). Geometrically, such functions are symmetric about the y-axis. Examples of even functions include 1 ...

A module M over a unit ring R is called faithful if for all distinct elements a, b of R, there exists x in M such that ax!=bx. In other words, the multiplications by a and by ...

A fractional ideal is a generalization of an ideal in a ring R. Instead, a fractional ideal is contained in the number field F, but has the property that there is an element ...

Gabriel's horn, also called Torricelli's trumpet, is the surface of revolution of the function y=1/x about the x-axis for x>=1. It is therefore given by parametric equations ...