here, the concept of quantum potential that has been illustrated in extended phase space (eps) in previous works is explored for its marginal behavior. unlike in configuration space, different representations of the quantum mechanics can be found in eps when exploiting appropriate canonical transformations. these canonical transformations revealed that there exist several representations in whi...

in this paper, the concept of canonical representation is proposed to find fuzzy roots of fuzzy polynomial equations. we transform fuzzy polynomial equations to system of crisp polynomial equations, this transformation is perform by using canonical representation based on three parameters value, ambiguity and fuzziness.

In this paper, the concept of canonical representation is proposed to find fuzzy roots of fuzzy polynomial equations. We transform fuzzy polynomial equations to system of crisp polynomial equations, this transformation is perform by using canonical representation based on three parameters Value, Ambiguity and Fuzziness. 

using the riemann-liouville fractional differintegral operator, the lie theory is reformulated. the fractional poisson bracket over the fractional phase space as 3n state vector is defined to be the fractional lie derivative. its properties are outlined and proved. a theorem for the canonicity of the transformation using the exponential operator is proved. the conservation of its generator is p...

The generalization of the classical Poisson sum formula, by replacing the ordinary Fourier transform by the canonical transformation, has been derived in the linear canonical transform sense. Firstly, a new sum formula of Chirp-periodic property has been introduced, and then the relationship between this new sum and the original signal is derived. Secondly, the generalization of the classical P...

This note describes a numerically stable procedure to derive a canonical coordinate system for a 2D linear transformation. The determinant of the transformation from the given coordinate system to the canonical coordinate system is 1; thus area is preserved. The transformation is composed of a short sequence of rotations and areapreserving nonuniform scales. If the eigenvectors are real, they m...

We generalize the prescription realizing classical Poisson–Lie T–duality as canonical transformation to Poisson–Lie T–plurality. The key ingredient is the transformation of left–invariant fields under Poisson–Lie T–plurality. Explicit formulae realizing canonical transformation are presented and the preservation of canonical Poisson brackets and Hamiltonian density is shown. PACS: 02.30.Ik, 04....