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A

**band**over a fixed topological space X is represented by a cover X= union U_alpha, U_alpha subset= X, and for each alpha, a sheaf of groups K_alpha on U_alpha along with ...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 ...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) = ...

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.Let h be a real-valued harmonic function on a bounded domain Omega, then the Dirichlet

**energy**is defined as int_Omega|del h|^2dx, where del is the gradient.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 ...A topological transformation in which a surface is made out of an infinitely elastic material which, however, may not be torn or cut. Using this simple prescription gives the ...

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