The vectorial extension of the Ribaucour transformation for the Lamé equations of orthogonal conjugates nets in multidimensions is given. We show that the composition of two vectorial Ribaucour transformations with appropriate transformation data is again a vectorial Ribaucour transformation, from which it follows the permutability of the vectorial Ribaucour transformations. Finally, as an exam...

The analytic expression of the momentum representation in terms of the associated Legendre function is determined by a direct integration of Fourier transform of the wave function of coordinates using the Levi-Civita transformation and 2 2 R R → the generating function method. A new generating function for the associated Legendre functions are obtained.

We study a Hamiltonian realization of the phase space of κ-Poincaré algebra that yields a definition of velocity consistent with the deformed Lorentz symmetry. We are also able to determine the laws of transformation of spacetime coordinates and to define an invariant spacetime metric, and discuss some possible experimental consequences.

In this paper, two often-employed alternatives to the semi-recursive method are described and compared in terms of velocity transformation. The text offers a simplified way understand theory behind approaches. Focusing on planar cases, particular attention is given reference joint coordinates. Consequently, multibody modeling analyst that familiar with global formulations can easily extend his/...

A connection between the conifold locus of the type II string on the W P 4 11226 Calabi-Yau manifold and the geometry of the quantum moduli of N =2 SU(2) super Yang-Mills is presented. This relation is obtained from the anomalous behaviour of the SU(2) super Yang-Mills special coordinates under S-duality transformation in Sl(2;Z)/Γ2.

Since Descartes, coordinates have been the standard mathematical construct for describing and manipulating geometric objects. In addition, indices are commonly used to label elements of discrete geometric structures, such as polygon meshes. Since the coordinates and indices are numbers, they can be manipulated algebraically. This sets the framework for the handling of geometric objects in algeb...

We study the structure of the phase space of generic models of deformed special relativity which gives rise to a definition of velocity consistent with the deformed Lorentz symmetry. As a byproduct we also determine the laws of transformation of spacetime coordinates.

The explicit multi-instanton solutions by ’tHooft and Jackiw, Nohl & Rebbi are generalized to curvilinear coordinates. The idea is that a gauge transformation can notably simplify the expressions obtained after the change of variables. The gauge transform generates a compensating addition to the gauge potential of pseudoparticles. Singularities of the compensating field are irrelevant for physi...

We study T-duality in the Green-Schwarz formalism to all orders in superspace coordinates. We find two analogs of Buscher rules for the supervielbein and clarify their meaning from the superstring point of view. The transformation rules for the dilaton, spin 1/2 fermions and Ramond-Ramond superfields are also derived. E-mail: [email protected] E-mail: [email protected]

We have solved a σ–model in curved background using the fact that the Poisson–Lie T-duality can transform the curved background into the flat one. For finding solution of the flat model we have used transformation of coordinates that makes the metric constant. The T-duality transform was then explicitly performed.