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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 ...

Arithmetic is the branch of mathematics dealing with integers or, more generally, numerical computation. Arithmetical operations include addition, congruence calculation, ...

A mathematical statement that one quantity is greater than or less than another. "a is less than b" is denoted a<b, and "a is greater than b" is denoted a>b. "a is less than ...

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

The statistical index P_H=(sumv_0)/(sum(v_0p_0)/(p_n))=(sump_0q_0)/(sum(p_0^2q_0)/(p_n)), where p_n is the price per unit in period n, q_n is the quantity produced in period ...

Let f(z) be an analytic function in |z-a|<R. Then f(z)=1/(2pi)int_0^(2pi)f(z+re^(itheta))dtheta for 0<r<R.

Apply Markov's inequality with a=k^2 to obtain P[(x-mu)^2>=k^2]<=(<(x-mu)^2>)/(k^2)=(sigma^2)/(k^2). (1) Therefore, if a random variable x has a finite mean mu and finite ...

The geometric mean is smaller than the arithmetic mean, (product_(i=1)^Nn_i)^(1/N)<=(sum_(i=1)^(N)n_i)/N, with equality in the cases (1) N=1 or (2) n_i=n_j for all i,j.

The study of the probabilities involved in geometric problems, e.g., the distributions of length, area, volume, etc. for geometric objects under stated conditions. The ...

The Pythagorean means are the three "classic" means A (the arithmetic mean), G (the geometric mean), and H (the harmonic mean) are sometimes known as the Pythagorean means. ...