since 2005 a new powerful invariant of an algebra has emerged using the earlier work of horvath, hethelyi, kulshammer and murray. the authors studied morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. it was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...

In this thesis, we study the theory of Isotropic Multiresolution Analysis (IMRA) and its application to image analysis problems that require rotational invariance. Multiresolution Analysis (MRA) is a mathematical tool that gives us the ability to process a signal or an image at multiple levels of resolution and detail. IMRA is a new type of MRA for which the core resolution sub-space is invaria...

Supersymmetric extensions of the 1D and 2D Swanson models are investigated by applying conformal bridge transformation (CBT) to first order Berry-Keating Hamiltonian multiplied $i$ its conformally neutral enlargements. The CBT plays role Dyson map that transforms into supersymmetric generalizations harmonic oscillator systems, allowing us define pseudo-Hermitian conjugation a suitable inner pro...

The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges strongly to the solution operator of the Schrödinger equation with the averaged rotational invariant potential. 1. The model, rotating frames We consider the...

Rotablation (rotational atherectomy) is an acknowledged method of percutaneous treatment of highly calcified coronary artery lesions that cannot be treated with traditional angioplasty. The complexity of the technique and usage of very specific equipment can contribute to the development of uncommon complications. We present a case of percutaneous retrieval of a damaged rotational atherectomy b...

In this study, an local invariant generalized Houghtransform (LI-GHT) method is proposed for integrated circuit (IC) visual positioning. The original generalized Hough transform (GHT) is robust to external noise; however, it is not suitable for visual positioning of IC chips due to the four-dimensionality (4D) of parameter space which leads to the substantial storage requirement and high comput...

Two approaches to defining almost-invariant surfaces for magnetic-fields with imperfect magnetic surfaces are compared. Both methods are based on treating magnetic field-line flow as a 1 :-dimensional Hamiltonian (or Lagrangian) dynamical system. In the quadratic-flux minimizing surface approach. the integral of the square of the action gradient over the toroidal and poloidal angles is minimize...

At the beginning of the semester we motivated our investigation of symmetries by illustrating that, given differential equations which were symmetric, the solutions had to transform into each other under the symmetries as a representation of the symmetry. The first illustrations considered Schrödinger equations with symmetric potentials, such as the electrons in the spherically symmetric potent...

This paper presents a newl divide-and-conquer method to analyze geometric shapes, contours and trajectories extracted as a discrete sequence of points (or pixels) from images or spatial sensors such as GPS or transponders. The method converts contour point sequences into Circular Augmented Rotational Trajectories (CART) and uses a scale invariant analysis to extract invariant arc features. The ...

At the beginning of the semester we motivated our investigation of symmetries by illustrating that, given differential equations which were symmetric, the solutions had to transform into each other under the symmetries as a representation of the symmetry. The first illustrations considered Schrödinger equations with symmetric potentials, such as the electrons in the spherically symmetric potent...