The vacuum expectation value of the Wilson loop in the dual representation is calculated in the dual Higgs model with dual Dirac strings. It is shown that the averaged value of the Wilson loop in the dual representation obeys the area– law falloff. Quantum fluctuations of the dual–vector and the Higgs field around Abrikosov flux lines induced by dual Dirac strings in a dual superconducting vacu...

Remember that any linear map is fully determined by its action on an (arbitrary) basis. In fact, for ~v = ∑ 1≤k≤n λk~vk one gets νi(~v) = λi ∈ R (i = 1, . . . , n). We prove that ν1, . . . , νn ∈ V ∗ are linearly independent. Assume that the vector α := ∑ 1≤k≤n μkνk ∈ V ∗ is the zero map. I.e. ν(~v) = 0 ∈ R holds for all ~v ∈ V . Since this holds for all ~v ∈ V , it follows that μ1 = μ2 = · · ·...

This paper provides a new variational paradigm to measure the smoothness of unit vector fields on spatial domains, leading to new methods for smoothing and interpolating such datasets. Our point of view is to consider unit vector fields as linear forms acting on reproducing kernel Hilbert spaces of vector fields or tensors and work with the dual norm, leading to new variational problems and alg...

We show that coarse graining arguments invented for the analysis of multi-spin systems on a randomly triangulated surface apply also to the O(n) model on a random lattice. These arguments imply that if the model has a critical point with diverging string susceptibility, then either γ = + 1 2 or there exists a dual critical point with negative string susceptibility exponent, ˜ γ, related to γ by...

In a first course in functional analysis, a great deal of time is spent with Banach spaces, especially the interaction between such spaces and their dual spaces. Banach spaces are a special type of topological vector space, and there are important topological vector spaces which do not lie in the Banach category, such as the Schwartz spaces. The most fundamental theorem about Banach spaces is t...

This article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. It is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...

We consider the separable nonlinear and strictly convex single-commodity network flow problem (SSCNFP). We develop a computational scheme for generating a primal feasible solution from any Lagrangian dual vector; this is referred to as “early primal recovery”. It is motivated by the desire to obtain a primal feasible vector before convergence of a Lagrangian scheme; such a vector is not availab...

We consider a generalized ε-vector equilibrium problem which contain vector equilibrium problems and vector variational inequalities as special cases. By using the KKM theorem,we obtain some existence theorems for the generalized ε-vector equilibrium problem. We also investigate the duality of this generalized ε-vector equilibrium problem and discuss the equivalence relation between solutions o...

A class of boundary conditions for canonical general relativity are proposed and studied at the quasi-local level. It is shown that for un-trapped or marginal surfaces, fixing the area element on the 2-surface (rather than the induced 2-metric) and the angular momentum surface density are enough to have a functionally differentiable Hamiltonian, thus provide definition of conserved quantities f...

A class of boundary conditions for canonical general relativity are proposed and studied at the quasi-local level. It is shown that for untrapped or marginal surfaces, fixing the area element on the 2-surface (rather than the induced 2-metric) and the angular momentum surface density is enough to have a functionally differentiable Hamiltonian, thus providing definition of conserved quantities f...