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Dyson (1962abc) conjectured that the constant term in the Laurent series product_(1<=i!=j<=n)(1-(x_i)/(x_j))^(a_i) (1) is the multinomial coefficient ...

Zeno's paradoxes are a set of four paradoxes dealing with counterintuitive aspects of continuous space and time. 1. Dichotomy paradox: Before an object can travel a given ...

Topology

Let Xi be the xi-function defined by Xi(iz)=1/2(z^2-1/4)pi^(-z/2-1/4)Gamma(1/2z+1/4)zeta(z+1/2). (1) Xi(z/2)/8 can be viewed as the Fourier transform of the signal ...

The 120-cell is a finite regular four-dimensional polytope with Schläfli symbol {5,3,3}. It is also known as the hyperdodecahedron or hecatonicosachoron, and is composed of ...

A generalization of the Lebesgue integral. A measurable function f(x) is called A-integrable over the closed interval [a,b] if m{x:|f(x)|>n}=O(n^(-1)), (1) where m is the ...

Specifying three angles A, B, and C does not uniquely define a triangle, but any two triangles with the same angles are similar. Specifying two angles of a triangle ...

Specifying two angles A and B and a side a opposite A uniquely determines a triangle with area K = (a^2sinBsinC)/(2sinA) (1) = (a^2sinBsin(pi-A-B))/(2sinA). (2) The third ...

The ABC (atom-bond connectivity) energy of a graph is defined as the graph energy of its ABC matrix, i.e., the sum of the absolute values of the eigenvalues of its ABC matrix.

The ABC (atom-bond connectivity) index of a graph is defined as half the sum of the matrix elements of its ABC matrix. It was introduced by Estrada et al. (2017) to model the ...