Given a vector space of microscopic quantum observables, density functional theory is formulated on its dual space. A generalized Hohenberg-Kohn theorem and the existence of the universal energy functional in the dual space are proven. In this context ordinary density functional theory corresponds to the space of one-body multiplication operators. When the operators close under commutation to f...

The Kneser-Hecke-operator is a linear operator defined on the complex vector space spanned by the equivalence classes of a family of self-dual codes of fixed length. It maps a linear self-dual code C over a finite field to the formal sum of the equivalence classes of those self-dual codes that intersect C in a codimension 1 subspace. The eigenspaces of this self-adjoint linear operator may be d...

Support vector data description (SVDD), proposed by [1], is a useful method for outlier detection. Its model is obtained by solving the dual optimization problem. In this paper, we point out some issues in their derivations. For example, they formulate SVDD as a non-convex problem and derive the dual problem only under some parameter settings. Given the wide use of SVDD, it is important to addr...

Let V be the representation of the quantized enveloping algebra of gl(n) which is the q-analogue of the vector representation and let V ∗ be the dual representation. We construct a basis for ⊗r (V ⊕ V ∗) with favorable properties similar to those of Lusztig’s dual canonical basis. In particular our basis is invariant under the bar involution and contains a basis for the subspace of invariant te...

Dual field theory realisations are given for linearised gravity in terms of gauge fields in exotic representations of the Lorentz group. The field equations and dual representations are discussed for a wide class of higher spin gauge fields. For non-linear Einstein gravity, such transformations can be implemented locally in light-cone gauge, or partially implemented in the presence of a Killing...

This paper is concerned with some methods that attempt to provide simultaneous representation of dual relationships, such as ties of membership that connect persons and groups, or connections between organizations and agendas. We focus on vector space and lattice representations, and on techniques for simplifying the structure of dual networks. We demonstrate some fundamental similarities among...

We convert the self-dual model of Townsend, Pilch, and Nieuwenhuizen to a first-class system using the generalized canonical formalism of Batalin, Fradkin, and Tyutin and show that gauge-invariant fields in the embedded model can be identified with observables in the Maxwell-Chern-Simons theory as well as with the fundamental fields of the self-dual model. We construct the phase-space partition...

This paper presents a numerical method for quasi-static contact problems with the Coulomb friction. The is based on primal-dual algorithm convex optimization. As noteworthy feature, this free from solutions of linear equations systems; it consists matrix-vector multiplications, vector additions, and projections vectors onto friction cone. Numerical experiments show that requires smaller computa...

Let A be a 0 − 1 matrix with precisely two 1’s in each column and let 1 be the all-one vector. We show that the problems of deciding whether the linear system Ax ≥ 1, x ≥ 0 (1) defines an integral polyhedron, (2) is totally dual integral (TDI), and (3) is box-totally dual integral (box-TDI) are all co-NP-complete, thereby confirming the conjecture on NP-hardness of recognizing TDI systems made ...

The braid groups map homomorphically into the Temperley-Lieb algebras. Recently, Zinno showed that the homomorphic images of the simple elements arising from the dual presentation of the braid groups form a basis for the vector space underlying the Temperley-Lieb algebras. We give a simple geometric proof of his theorem, using a new presentation of the Temperley-Lieb algebras that corresponds t...