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A quasi-cubic graph is a quasi-regular graph, i.e., a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 ...

Let {a_n} be a nonnegative sequence and f(x) a nonnegative integrable function. Define A_n=sum_(k=1)^na_k (1) and F(x)=int_0^xf(t)dt (2) and take p>1. For sums, ...

A square with side lengths 1. The unit square usually means the one with coordinates (0, 0), (1, 0), (1, 1), (0, 1) in the real plane, or 0, 1, 1+i, and i in the complex ...

Let f be a family of meromorphic functions on the unit disk D which are not normal at 0. Then there exist sequences f_n in F, z_n, rho_n, and a nonconstant function f ...

An equichordal point is a point p for which all the chords of a curve C passing through p are of the same length. In other words, p is an equichordal point if, for every ...

If 0<=a,b,c,d<=1, then (1-a)(1-b)(1-c)(1-d)+a+b+c+d>=1. This is a special case of the general inequality product_(i=1)^n(1-a_i)+sum_(i=1)^na_i>=1 for 0<=a_1,a_2,...,a_n<=1. ...

The Motzkin numbers enumerate various combinatorial objects. Donaghey and Shapiro (1977) give 14 different manifestations of these numbers. In particular, they give the ...

The center of a graph G is the set of vertices of graph eccentricity equal to the graph radius (i.e., the set of central points). In the above illustration, center nodes are ...

Guy's conjecture, which has not yet been proven or disproven, states that the graph crossing number for a complete graph K_n is ...

If the matrices A, X, B, and C satisfy AX-XB=C, then [I X; 0 I][A C; 0 B][I -X; 0 I]=[A 0; 0 B], where I is the identity matrix.