Sentence examples for duality product from inspiring English sources

This result implicitly gives new characterizations for both the convergence in the sense of obstacles of a weakly convergent sequence of positive functions and for the weak l.s.c. of the duality product.

Given a weakly convergent sequence of positive functions in W1,p0, we prove the equivalence between its convergence in the sense of obstacles and the lower semi-continuity of the term by term duality product associated to (the p-Laplacian of) weakly convergent sequences of p-superharmonic functions of W1,p0.

Denote by the duality product.

Here denotes the duality product.

where 〈·,·〉denotes the usual duality product.

where 〈 ⋅, ⋅ 〉 stands for the duality product.

Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces, spectral theorem, counting techniques, and linear algebra methods in discrete mathematics including spectral graph theory and dimension arguments.

Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces, spectral theorem, metric spaces, differentiation in Euclidean space, submanifolds of Euclidean space, inverse and implicit function theorems, and many examples.

Uncertainty theory is a branch of mathematics based on normality, duality, subadditivity, and product axioms.

In order to study the belief degree, an uncertainty theory was founded by Liu [8] in 2007 and revised by Liu [9] in 2010 based on normality, duality, subadditivity, and product axioms.

To this end we prove an integral formula for the duality between tensor products and polynomials.