This paper presents the effective control of the formation and competition of cellular patterns. Simulation and theoretical analyses are carried out for pattern formation in a confined circular domain. The Cahn–Hilliard equation is solved with the zero-flux boundary condition to describe the phase separation of binary mixtures. A wavelet-based discrete singular convolution algorithm is employed...

in this paper we develop a natural generalization of schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. we prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. we prove that the operators of a dual ov-basis are continuous. we also de ne the concepts of bessel, hilbert ov-basis and obt...

We report on an interferometry-based measurement of the phase and group velocities of optical Bessel beams, providing confirmation of their superluminal character in the non-diffractive region. The measurements were performed in free space with a continuous wave laser and femtosecond pulses for phase and group velocities respectively. The Bessel beams were produced using a conical mirror. Einst...

We report the first experimental realization of all-optical trapping and manipulation of plasmonic nanowires in three dimensions. The optical beam used for trapping is the Fourier transform of a linearly polarized Bessel beam (termed FT-Bessel). The extended depth of focus of this beam enables the use of a retroreflection geometry to cancel radiation pressure in the beam propagation direction, ...

We consider systems of vectors of the form {Ahi : i ∈ I, n ≥ 0} where {hi}i∈I is a countable (finite or infinite) system of vectors in a separable Hilbert space H and A ∈ B(H) is a bounded operator. We show that a system of that form can never be both complete and minimal, and find conditions that the operator A needs to satisfy for the system to be a frame or a complete Bessel system. We also ...

Abstract This manuscript contains a small portion of the algebraic theory orthogonal polynomials developed by Maroni and their applicability to study characterization classical families, namely Hermite, Laguerre, Jacobi, Bessel polynomials. It is presented cyclical proof some most relevant characterizations, particularly those due Al-Salam Chihara, Bochner, Hahn, Maroni, McCarthy. Two apparentl...

In this paper, we introduce the concept of dual frame of g-p-frame, and give the sufficient condition for a g-p-frame to have dual frames. Using operator theory and methods of functional analysis, we get some new properties of g-p-frame. In addition, we also characterize g-p-frame and g-q-Riesz bases by using analysis operator of g-p-Bessel sequence. c ©2017 All rights reserved.