Gaussian DCT Coefficient Models

It has been known that the distribution of the discrete cosine transform (DCT) coefficients of most natural images follow a Laplace distribution. However, recent work has shown that the Laplace distribution may not be a good fit for certain type of images and that the Gaussian distribution will be a realistic model in such cases. Assuming this alternative model, we derive a comprehensive collection of formulas for the distribution of the actual DCT coefficient. The corresponding estimation procedures are derived by the method of moments and the method of maximum likelihood. Finally, the superior performance of the derived distributions over the Gaussian model is illustrated. It is expected that this work could serve as a useful reference and lead to improved modeling with respect to image analysis and image coding.     

Mathematical modelling of swirling flow in hydraulic turbines for the full operating range

We introduce and validate a novel mathematical model for computing the radial profiles of both axial and circumferential velocity components, respectively, of the swirling flow exiting the runner of hydraulic turbines within the full operating range. We assume an incompressible, inviscid, axisymmetrical, and steady swirling flow, with vanishing radial velocity at runner outlet. First we find the correlation between the flux of moment of momentum downstream the turbine runner and the operating regime given by turbine’s discharge and head. Second, we express the relationship between the axial and circumferential velocity components, corresponding to the fixed pitch runner blades, using the swirl-free velocity instead of the traditional relative flow angle at runner outlet. It is shown that the swirl-free velocity profile practically does not change with the operating regime. Third, we introduce a constrained variational problem corresponding to the minimization of the flow force while maintaining the prescribed discharge and flux of moment of momentum. This formulation also accounts for a possible central stagnant region to develop when operating the turbine far from the best efficiency point. Fourth, we show that by representing the unknown axial velocity profile with a suitable Fourier–Bessel series, the discharge constraint can be automatically satisfied. The resulting numerical algorithm is robust and produces results in good agreement with available data for both axial and circumferential velocity profiles measured on a model Francis turbine at several operating regimes. Our mathematical model is suitable for the early optimization stages of the runner design, as it provides the swirling flow configuration at runner outlet without actually computing the runner. By optimizing the parameterized swirl-free velocity profile one can achieve through the inverse design approaches the most suitable runner blades configuration at the trailing edge.     

体视显微镜与CCD成像系统在高阶贝塞尔光束光斑测量中的应用

主要对光学测量仪器体视显微镜与CCD成像系统在高阶贝塞尔光束光斑测量中的应用进行分析,通过以非相干LED绿光经过螺旋相位板和轴棱锥产生的高阶贝塞尔(Bessel)光束为例,模拟出沿轴向不同距离处的截面光强分布图,并与相应的实验参数(如:最大无衍射距离、中心暗斑直径等)进行比较。实验结果表明,体视显微镜与CCD成像系统的测量结果相吻合,但是体视显微镜测量误差较大会影响测量结果的准确度。     

Enhancement of single mode operation in coaxial optical waveguide using DB boundary conditions

In this study, a competent numerical strategy to compute the dispersion of optical waveguides is presented and propagation of electromagnetic waves in a coaxial optical waveguide with DB boundary conditions is instigated. For this intend, cylindrical coordinates are here being used to derive the DB boundary conditions and to obtain field components for the modes. The propagation constant for the waveguide to be studied is determined by solving the Bessel and the modified Bessel functions. The cutoff frequencies for various lower order modes have been calculated and their dispersion characteristics are plotted correspondingly. The behavior of the coaxial optical waveguide under DB boundary conditions is shown to be significantly different from that of coaxial optical waveguide and conventional optical waveguide under traditional or tangential boundary conditions. Finally, the effect of waveguide dimensions on the mode cutoff frequencies and fabrication issues are also addressed.     

On Bessel distributions for quasi-split groups

We show that the Bessel distribution attached by Gelfand and Kazhdan and by Shalika to a generic representation of a quasi-split reductive group over a local field is given by a function when it is restricted to the open Bruhat cell. As in the case of the character distribution, this function is real analytic for archimedean fields and locally constant for non-archimidean fields.

     

变截面梁柱刚度方程的Bessel函数解

本文提出了一个计算Bessel函数Jp(x)及Np(x)的近似方法并在－∞＜P＜∞和X＞0的范围内验证了方法的适用性,进而提出了截面按幂涵数变化的变截面梁柱的刚度方程并研究了其临床其临界力。∞     

A new explicit Bessel and Neumann fitted eighth algebraic order method for the numerical solution of the Schrödinger equation

An explicit eighth algebraic order Bessel and Neumann fitted method is developed in this paper for the numerical solution of the Schrödinger equation. The new method has free parameters which are defined in order the method is fitted to spherical Bessel and Neumann functions. A variable-step procedure is obtained based on the newly developed method and the method of Simos [17]. Numerical illustrations based on the numerical solution of the radial Schrödinger equation and of coupled differential equations arising from the Schrödinger equation indicate that this new approach is more efficient than other well known methods.     

Direct recursion of the ratio of Bessel functions with applications to Mie scattering calculations

The primary goal of this paper is to describe a method to directly calculate the ratios between the Bessel functions of the first and second kind. This new method is introduced and discussed under the context of Mie scattering calculations. Past work on Mie calculations has mostly relied on calculating the Bessel functions separately, then taking the ratio. This technique fails when the order of the functions becomes appreciably larger than the argument. To solve this problem, we developed a stable method to directly calculate the ratio. When applied to Mie scattering calculations, the new method improves the control of the desired accuracy and enables calculations with higher precision. Since many other wave propagation problems also involve the ratios of Bessel functions and our method provides reliable and accurate calculations over a wide range of conditions, we expect it to find applications beyond Mie calculations.     

Time Average Geometric Moiré—Back to the Basics

Applicability of time average geometric moiré for elastic oscillating structures is analysed in this paper. Mathematical and numerical models describing the formation of time averaged fringes are carefully constructed without the assumption that dynamic deflections are described by a slowly varying function. Though time average geometric moiré is considered as a classical optical experimental technique, we show that well known relationship between the fringe order, amplitude of oscillation and pitch of the grating in state of equilibrium can be used only when the amplitude is small. Otherwise the inverse problem of fringe interpretation becomes much more complicated and is the object of analysis in this paper. We describe the interpretation of fringes produced by time average geometric moiré in detail and illustrate the complexity of the problem by numerical examples.