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The arithmetic-geometric energy of a graph is defined as the graph energy of its arithmetic-geometric matrix, i.e., the sum of the absolute values of the eigenvalues of its ...

The Greek problems of antiquity were a set of geometric problems whose solution was sought using only compass and straightedge: 1. circle squaring. 2. cube duplication. 3. ...

The statistical index P_G=[product((p_n)/(p_0))^(v_0)]^(1/Sigmav_0), where p_n is the price per unit in period n, q_n is the quantity produced in period n, and v_n=p_nq_n the ...

Given a planar graph G, its geometric dual G^* is constructed by placing a vertex in each region of G (including the exterior region) and, if two regions have an edge x in ...

The arithmetic-geometric mean agm(a,b) of two numbers a and b (often also written AGM(a,b) or M(a,b)) is defined by starting with a_0=a and b_0=b, then iterating a_(n+1) = ...

Let E be a compact connected subset of d-dimensional Euclidean space. Gross (1964) and Stadje (1981) proved that there is a unique real number a(E) such that for all x_1, ...

For positive numbers a and b with a!=b, (a+b)/2>(b-a)/(lnb-lna)>sqrt(ab).

Given n mutually exclusive events A_1, ..., A_n whose probabilities sum to unity, then P(B)=P(B|A_1)P(A_1)+...+P(B|A_n)P(A_n), where B is an arbitrary event, and P(B|A_i) is ...

The arithmetic-geometric spectral radius rho_(AG) of a graph is defined as the largest eigenvalue of its arithmetic-geometric matrix.

The probability density function (PDF) P(x) of a continuous distribution is defined as the derivative of the (cumulative) distribution function D(x), D^'(x) = ...