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A fibered category F over a topological space X consists of 1. a category F(U) for each open subset U subset= X, 2. a functor i^*:F(U)->F(V) for each inclusion i:V↪U, and 3. ...

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 ...

Consider h_+(d) proper equivalence classes of forms with discriminant d equal to the field discriminant, then they can be subdivided equally into 2^(r-1) genera of ...

Given a linear code C, a generator matrix G of C is a matrix whose rows generate all the elements of C, i.e., if G=(g_1 g_2 ... g_k)^(T), then every codeword w of C can be ...

The upper central series of a group G is the sequence of groups (each term normal in the term following it) 1=Z_0<=Z_1<=Z_2<=...<=Z_n<=... that is constructed in the ...

A purple cow is a confirming instance of the hypothesis that all crows are black.

Refer to the above figures. Let X be the point of intersection, with X^' ahead of X on one manifold and X^('') ahead of X of the other. The mapping of each of these points ...

The incentral triangle DeltaI_AI_BI_C is the Cevian triangle of a triangle DeltaABC with respect to its incenter I. It is therefore also the triangle whose vertices are ...

A generalization of the complete beta function defined by B(z;a,b)=int_0^zu^(a-1)(1-u)^(b-1)du, (1) sometimes also denoted B_z(a,b). The so-called Chebyshev integral is given ...

Let sumu_k be a series with positive terms and let f(x) be the function that results when k is replaced by x in the formula for u_k. If f is decreasing and continuous for ...