Although the spectrum of radially periodic images is often expressed in terms of finite or infinite series of Bessel functions, such expressions do not clearly reveal the exact impulsive structure of the spectrum. An alternative Fourier decomposition of radially periodic images, in terms of circular cosine functions, is presented, and its significant advantages are shown. It is shown that the F...

Since the development of three-dimensional helical reconstruction methods in the 1960's, advances in Fourier-Bessel methods have facilitated structure determination to near-atomic resolution. A recently developed iterative helical real-space reconstruction (IHRSR) method provides an alternative that uses single-particle analysis in conjunction with the imposition of helical symmetry. In this wo...

An analytical solution to the transient heat conduction for a two dimensional cylindrical fin with general boundary conditions is obtained by the principle of superposition and separation variables. In the analysis, homogeneous material properties and thickness, the convective heat transfer coefficient, the ambient temperature and the fin properties are assume to be constant. The closed form tr...

A rigorous analysis combining the orthogonal expansion method and Galerkin method for the higher order eigenmodes in a circular–rectangular (C-R) waveguide is presented in this paper. The Bessel–Fourier series is employed to merge the circular and rectangular coordinate systems used in the analysis. The cutoff frequencies of the higher order modes are determined with the singular value decompos...

Current methods for generating Bessel beams are limited to fixed beam sizes or, in the case of conventional adaptive optics, relatively long switching times between beam shapes. We analyze the multiscale Bessel beams created using an alternative rapidly switchable device: a tunable acoustic gradient index (TAG) lens. The shape of the beams and their nondiffracting, self-healing characteristics ...

Fourier multiplexed FLIM (FmFLIM) tomography enables multiplexed 3D lifetime imaging of whole embryos. In our previous FmFLIM system, the spatial resolution was limited to 25 μm because of the trade-off between the spatial resolution and the imaging depth. In order to achieve cellular resolution imaging of thick specimens, we built a tomography system with dual-color Bessel beam. In combination...

The standard method for computing values of Bessel functions has been to use the well-known ascending series for small argument |z|, and to use an asymptotic series for large |z|. In a recent paper, D. Borwein, J. Borwein, and R. Crandall [1] derived a series for an exp-arc integral which gave rise to an absolutely convergent series for the J and I Bessel functions with integral order. Such ser...

The lost of nonentun and stiffness due to ablation nay significantly influence the vibrations of a solid propellant grain. This paper presents an analytical study of the axial shear vibrations of a long hollow cylinder that is subjected to tine dependent body forces in the axial direction. The outer surface of the cylinder is bonded to a rigid case, and the inner radius increases monotonically ...

In the chemical potential Stokes-Einstein formulation, when acceleration of the molecule is accounted for, a law of diffusion a capite ad calcem concentration results. In cartesian one-dimensional heat conduction in semi-infinite coordinates, the governing equation for temperature or concentration was solved for by the method of Laplace transforms. The results are in terms of the modified Besse...

‎By observing the equivalence of assertions on determining the jump of a‎ ‎function by its differentiated or integrated Fourier series‎, ‎we generalize a‎ ‎previous result of Kvernadze‎, ‎Hagstrom and Shapiro to the whole class of‎ ‎functions of harmonic bounded variation‎. ‎This is achieved without the finiteness assumption on‎ ‎the number of discontinuities‎. ‎Two results on determination of ...