An overview of two types of beam solutions is presented, Gaussian beams and Bessel beams. Gaussian beams are examples of non-localized or diffracting beam solutions, and Bessel beams are example of localized, non-diffracting beam solutions. Gaussian beams stay bounded over a certain propagation range after which they diverge. Bessel beams are among a class of solutions to the wave equation that...

human voyage to the world of ultra sense is a matter of discourses which was widely discussed between nations and the various schools of philosophy, language and many people including leaders of religions and thoughts branches confessed doing such voyages and left some literary reports of their mystical and dreamy travel. the oldest and newest of these reports are shown in this paper and them b...

Holonomic quantum computation makes use of non-abelian geometric phases, associated to the evolution a subspace states, encode logical gates. We identify special class subspaces, for which sequence rotations results in holonomy topological nature, so that it is invariant under any SO(3)-perturbation. Making Majorana-like stellar representation we give explicit examples topological-holonomic (or...

Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Given a spectrum for a desired fusion frame operator and dimensions for subspaces, one existing method for creating unitweight fusion frames with these properties is the flexible a...

some estimates are proved for the generalized fourier-bessel transform in the space (l^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

In this dissertation, we study the Feichtinger Conjecture(FC), which has been shown to be equivalent to the celebrated Kadison-Singer Problem. The FC states that every norm-bounded below Bessel sequence in a Hilbert space can be partitioned into finitely many Riesz basic sequences. This study is divided into two parts. In the first part, we explore the FC in the setting of reproducing kernel Hi...

Quadratic eigenvalue problems involving large matrices arise frequently in areas such as the vibration analysis of structures, MEMS simulation, and the solution of quadratically constrained least squares problems. The typical approach is to solve the quadratic eigenvalue problem using a mathematically equivalent linearized formulation, resulting in a doubled dimension and a lack of backward sta...

Using an extension of the Cox-Ingersoll-Ross [1] stochastic model of the short interest rate r, we study the convergence in law of the longterm return in order to make some approximations. We use the theory of Bessel processes and observe the convergence in law of the sequence (√ −2β3 δn ∫ nt 0 (Xu + δu 2β )du ) t≥0 with the X a generalized Besselsquare process with drift with stochastic revers...

Let Mn(R) and Sn(R) be the spaces of n × n real matrices and real symmetric matrices respectively. We continue to study d(n, n − 2,R): the minimal number such that every -dimensional subspace of Sn(R) contains a nonzero matrix of rank n−2 or less. We show that d(4, 2,R) = 5 and obtain some upper bounds and monotonicity properties of d(n, n − 2,R). We give upper bounds for the dimensions of n − ...

The theory of Generalized Bessel Functions is reviewed and their application to various problems in the study electro-magnetic processes presented. We consider cases emission bremsstrahlung radiation by ultra-relativistic electrons linearly polarized undulators, including also exotic configurations, aimed at enhancing harmonic content emitted radiation. analysis eventually extended generalizati...