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The second Zagreb index for a graph with vertex count n and vertex degrees d_i for i=1, ..., n is defined by Z_2=sum_((i,j) in E(G))d_id_j, where E(G) is the edge set of G.

Given a Seifert form f(x,y), choose a basis e_1, ..., e_(2g) for H_1(M^^) as a Z-module so every element is uniquely expressible as n_1e_1+...+n_(2g)e_(2g) (1) with n_i ...

An orientable surface with one boundary component such that the boundary component of the surface is a given knot K. In 1934, Seifert proved that such a surface can be ...

Let p run over all distinct primitive ordered periodic geodesics, and let tau(p) denote the positive length of p, then every even function h(rho) analytic in ...

Let x be a positive number, and define lambda(d) = mu(d)[ln(x/d)]^2 (1) f(n) = sum_(d)lambda(d), (2) where the sum extends over the divisors d of n, and mu(n) is the Möbius ...

A sorting algorithm which makes n passes over a set of n elements, in each pass selecting the smallest element and deleting it from the set. This algorithm has running time ...

Consider a second-order differential operator L^~u(x)=p_0(d^2u)/(dx^2)+p_1(du)/(dx)+p_2u, (1) where u=u(x) and p_i=p_i(x) are real functions of x on the region of interest ...

Let A be a C^*-algebra. An element a in A is called self-adjoint if a^*=a. For example, the real functions of the C^*-algebra of C([a,b]) of continuous complex-valued ...

A lattice polygon consisting of a closed self-avoiding walk on a square lattice. The perimeter, horizontal perimeter, vertical perimeter, and area are all well-defined for ...

A partition whose conjugate partition is equivalent to itself. The Ferrers diagrams corresponding to the self-conjugate partitions for 3<=n<=10 are illustrated above. The ...