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The term energy has an important physical meaning in physics and is an extremely useful concept. There are several forms energy defined in mathematics. In measure theory, let ...
There are three types of so-called fundamental forms. The most important are the first and second (since the third can be expressed in terms of these). The fundamental forms ...
The two recursive sequences U_n = mU_(n-1)+U_(n-2) (1) V_n = mV_(n-1)+V_(n-2) (2) with U_0=0, U_1=1 and V_0=2, V_1=m, can be solved for the individual U_n and V_n. They are ...
A generalization of Poncelet's continuity principle made by H. Schubert in 1874-1879. The conservation of number principle asserts that the number of solutions of any ...
The energy of a graph is defined as the sum of the absolute values of its graph eigenvalues (i.e., the sum of its graph spectrum terms). Other varieties of graph energy are ...
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 Sombor energy of a graph is defined as the graph energy of its Sombor matrix, i.e., the sum of the absolute values of the eigenvalues of its Sombor matrix.
Let Omega be a space with measure mu>=0, and let Phi(P,Q) be a real function on the product space Omega×Omega. When (mu,nu) = intintPhi(P,Q)dmu(Q)dnu(P) (1) = ...
If x_1<x_2<...<x_n denote the zeros of p_n(x), there exist real numbers lambda_1,lambda_2,...,lambda_n such that ...
The Randić energy of a graph is defined as the graph energy of its Randić matrix, i.e., the sum of the absolute values of the eigenvalues of its Randić matrix.
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