The most perceptually important features in images are geometrical, the most prevalent being the smooth contours (“edges”) that separate different homogeneous regions and delineate distinct objects. Although wavelet based algorithms have enjoyed success in many areas of image processing, they have significant shortcomings in their treatment of edges. Wavelets do not parsimoniously capture even ...

Institut de recherche en informatique de Toulouse y Abstract The heart of our thesis is that matrices of incidence can be used for mechanical theorem proving in projective geometry. To every geometrical statement of projective geometry is associated a matrix of incidence whose normal form is computed after successive identiications of rows and columns. Our main result is that the geometrical st...

As it is known, the closed inexact exterior form and associated closed dual form make up a differential-geometrical structure. Such a differential-geometrical structure describes a physical structure, namely, a pseudostructure on which conservation laws are fulfilled (A closed dual form describes a pseudostructure. And a closed exterior form, as it is known, describes a conservative quantity, s...

In the paper the main attention is paid to conditions on algebras from a given variety Θ which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.

We consider the problem of stability of equilibrium points in Hamiltonian systems of two degrees of freedom under resonances. Determining the stability or instability is based on a geometrical criterion based on how two surfaces, related with the normal form, intersect one another. The equivalence of this criterion with a result of Cabral and Meyer is proved. With this geometrical procedure, th...

In this paper we investigate (using AM1 semi-empirical as well as HF methods at the STO-3G, 3-21G, 6-31G, 6-31G* and 6-31+G** level) the conformations, geometrical parameters, Mulliken charges, and solvation effects of the triphosphate form of AZT (AZTTP), as well as the thymidine nucleotide (dTTP) structure. Our calculated geometrical parameters and Mulliken charges, with and without solvation...

By means of an analogy with Classical Mechanics and Geometrical Optics, we are able to reduce Lagrangians to a kinetic term only. This form enables us to examine the extended solution set of field theories by finding the geodesics of this kinetic term’s metric. This new geometrical standpoint sheds light on some foundational issues of QFT and brings to the forefront core aspects of field theory.

Geometry has been present in medicine in various aspects for many years. Information on geometrical form of particular anatomic structures should not be underestimated since it is both basic and key information in many clinical cases, beginning from fractures to radiotherapy. Technical apparatuses and devices used in doctors’ practice also require comprehension of technical documentation in nec...