Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell’s field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a consistent Lagrangian for the theory. Then from the action principle we get both Maxwell’s equation and the equation of motion of a dyon moving in the electromagne...

The Connes formula giving the dual description for the distance between points of a Riemannian manifold is extended to the Lorentzian case. It resulted that its validity essentially depends on the global structure of spacetime. The duality principle classifying spacetimes is introduced. The algebraic account of the theory is suggested as a framework for quantization along the lines proposed by ...

Performance Limitations Ji King Abstract—This paper investigates performance limitations and tradeoffs in the control design for linear time-invariant systems. It is shown that control specifications in time domain and in frequency domain are always mutually exclusive determined by uncertainty relations. The uncertainty principle from quantum mechanics and harmonic analysis therefore embeds its...

Rigidity results are obtained for Riemannian d-manifolds with sec > 1 and spherical rank at least d − 2 > 0. Conjecturally, all such manifolds are locally isometric to a round sphere or complex projective space with the (symmetric) Fubini– Study metric. This conjecture is verified in all odd dimensions, for metrics on dspheres when d 6= 6, for Riemannian manifolds satisfying the Rakić duality p...

Extending our reduction construction in [15] to the Hamiltonian action of a Poisson Lie group, we show that generalized Kähler reduction exists even when only one generalized complex structure in the pair is preserved by the group action. We show that the constructions in string theory of the (geometrical) T -duality with H-fluxes for principle bundles naturally arise as reductions of factoriza...

Contexts where entity descriptions belong to a meet-semilattice are considered. When the entity set is finite, we show that nonempty extensions of concepts assigned to such contexts coincide, casewise, with strong or weak clusters associated with some pairwise or multiway dissimilarity measure. Moreover, by duality principle, a similar result holds when entity descriptions belong to a join-semi...

In this paper we construct elliptic boundary value problems whose standard finite element approximations converge arbitrarily slowly in the energy norm, and show that adaptive procedures cannot improve this slow convergence. We also show that the L2-norm and the nodal point errors converge arbitrarily slowly. With the L2-norm two cases need to be distinguished, and the usual duality principle d...

Classical morphology is built up in such a way that all operators occur in pairs, e.g., dilation and erosion, opening and closing, etc. This phenomenon, which is a straightforward consequence of the duality principle, often prohibits the construction of tools that treat foreground and background of signals in exactly the same way. In this paper we discuss an alternative framework for morphologi...

This talk addresses vector-valued subspace Gabor frames with rational time-frequency product. By introduction of a suitable Zak transform matrix, we characterize vector-valued subspace Gabor frames, Riesz bases and orthonorrmal bases, and the uniqueness of Gabor duals of type I and type II. Using the uniqueness results, we extend the classical Balian-Low theorem to vector-valued subspace Gabor ...