In the event in which a quantum mechanical particle can pass from an initial state to a final state along two possible paths, the duality principle states that "the simultaneous observation of wave and particle behavior is prohibited" [Scully MO, Englert B-G, Walther H (1991) Nature 351:111-116]. Whereas wave behavior is associated with the observation of interference fringes, particle behavior...

The main objectives of this article are 1) to derive a field theory of weak interactions, 2) to study the duality of weak interactions, and 3) to derive the long overdue weak potential and force formula. The new field equations for weak interactions is derived by applying the principle of interaction dynamics (PID) and the principle of representation invariance (PRI) to a standard SU(2) gauge a...

There are many geometric algorithms based on computation of intersection of lines, planes etc. Sometimes, very complex mathematical notations are used to express simple mathematical solutions, even if their formulation in the projective space offers much more simple solution. This paper presents solution of selected problems using principle of duality and projective space representation. It wil...

In general, duality implies a situation in which two different languages give an accurate description of Nature. While one may be more convenient than the other in certain situations, both are correct. If we are interested in hadronic reactions, the two relevant pictures are the quark-gluon picture and the hadronic picture. In principle, we can describe any hadronic reaction in terms of quarks ...

Virtual reality and haptic systems use geometric transformations with points represented in homogeneous coordinates extensively. In many cases interpolation and barycentric coordinates are used. However, developers do not fully use properties of projective representation to make algorithms stable, robust and faster. This paper describes geometric transformations and principle of duality which e...

We propose a Lagrangian density for M-Theory which is purely topological using Gelfand-Fuchs cohomology which characterises up to homotopy Γq-structures and hence foliations in particular. Then, using a physical principle and S-duality, we conjecture on the existence of certain plane fields on S. PACS classification: 11.10.-z; 11.15.-q; 11.30.-Ly

Depth contours are a well-known technique for visualizing the distribution of multidimensional point data sets. We present an image-space algorithm for drawing the depth contours of a set of planar points. The algorithm is an improvement on existing algorithms based on the duality principle, implemented using 3D graphics rendering techniques.

Variational principle for probabilistic learning Yet another justification More simplification of updates for mean-field family Examples Dirichlet Process Mixture On minimization of divergence measures Energy minimization justifications Variational learning with exponential family Mean parametrization and marginal polytopes Convex dualities The log-partition function and conjugate duality Belie...

We present an extension of Naimark’s duality principle which states that complete systems in a Hilbert space are projections of ω-linearly independent systems of elements of an ambient Hilbert space. This result is presented in the context of other known extensions of Naimark’s theorem.

In this article we show the existence of solutions to a mixed boundary-value problem of second-order differential systems with a p-Laplacian. The associated Hamiltonian actions are indefinite and the discussion of the existence of solutions is due to the application of duality principle.