Optical image encryption using fractional Fourier transform and chaos

We propose a new method for image encryption using fractional Fourier transform and chaos theory. Random phase masks are generated using iterative chaos functions. The input image is combined with the first random phase mask at the object plane and is then transformed using the fractional Fourier transform. After the first fractional Fourier transform, the second random phase mask, again generated by using the chaos functions, is used at the fractional plane. The second fractional Fourier transform operation is then carried out to obtain the encrypted image. Three types of chaos functions have been used: the logistic map, the tent map and the Kaplan–Yorke map. The mean square error and the signal-to-noise ratio between the decrypted image and the input image for the correct order and the incorrect order of the fractional Fourier transform have been calculated. The computer simulations are presented to verify the validity of the proposed technique.     

用等离子体粒子能谱拟合温度的新方法

用最小二乘法拟合等离子体粒子能谱实验数据时，通常使拟合函数与实验能谱数据之间的误差平方和极小化。如果将能谱实验数据的对数拟合成直线以求得粒子温度，则最好对温度误差的平方和极小化。给出了这种拟合方法的计算公式，并对两种不同方法得到的结果进行了比较。     

经济预测中的正交回归分析

本文介绍了一种新的线性模型参数回归分析方法即正交回归，并以建立经济模型为例，对正交回归和经典回归的结果进行了比较。     

离差平方和分解的投影分析

以双因素协方差分析为例,介绍如何用代数中投影的方法进行离差平方和分解.结果表明:这种分解方法比通常采用的分析方法更简洁明了.     

用偶幂级数处理Abel变换问题

本文提出了用偶幂级数代替对称分布函数,使其线积分成为递推可积,从而简化了Abel逆变换。引进权函数使本方法简单地过渡到非对称问题。对一组假想相移信号进行变换,获得了可靠的密度分布结果,并对影响变换精度的各种因素作了讨论。     

A compact high‐order HLL solver for nonlinear hyperbolic systems

We present a new finite‐volume method for calculating complex flows on non‐uniform meshes. This method is designed to be highly compact and to accurately capture all discontinuities that may arise within the solution of a nonlinear hyperbolic system. In the first step, we devise a fourth‐degree Hermite polynomial to interpolate the solution. The coefficients defining this polynomial are calculated by using a least‐square method. To introduce monotonicity conditions within the procedure, two constraints are added into the least‐square system. Those constraints are derived by locally matching the high‐order Hermite polynomial with a low‐order TVD polynomial. To emulate these constraints only in regions of discontinuities, data‐depending weights are defined; these weights are based upon normalized indicators of smoothness of the solution and are parameterized by an O(1) quantity. The reconstruction so generated is highly compact and is fifth‐order accurate when the solution is smooth; this reconstruction becomes first order in regions of discontinuities. In the second step, this reconstruction is inserted in an HLL approximate Riemann solver. This solver is designed to correctly capture all discontinuities that may arise into the solution. To this aim, we introduce the contribution of a possible contact discontinuity into the HLL Riemann solver. Thus, a spatially fifth‐order non‐oscillatory method is generated. This method evolves in time the solution and its first derivative. In a one‐dimensional context, a linear spectral analysis and extensive numerical experiments make it possible to assess the robustness and the advantages of the method in computing multi‐scale problems with embedded discontinuities. Copyright © 2008 John Wiley & Sons, Ltd.     

非素数阶幻方的构造

基于矩阵运算,给出任意双偶数阶和非素数阶幻方的新构造方法:1)由任一低阶m(m为偶数且m≠2)幻方生成一高阶2m阶幻方;2)利用已知的m(m≠2)阶和n(n≠2)阶两个幻方,构造任意的非素数mn阶幻方,加强一些条件后,进一步提出构造两类高级幻方(泛对角线幻方和关联幻方)的新方法.     

Transition to chaos in lid-driven square cavity flow

To date, there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity, due to the difficulties in theoretical analysis and numerical simulations. In this paper, we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us. We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of (13944.7021,13946.5333) by the method of bisection. Through Fourier analysis, it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval. Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram, Kolmogorov entropy and maximal Lyapunov exponent. The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic.     

Characterization of Chickpea Flour by Near Infrared Spectroscopy and Chemometrics

Near infrared (NIR) spectrometry was used for the rapid characterization of quality parameters in desi chickpea flour (besan). Partial least square regression, principal component regression (PCR), interval partial least squares (iPLS), and synergy interval partial least squares (siPLS) were used to determine the protein, carbohydrate, fat, and moisture concentrations of besan. Spectra were collected in reflectance mode using a lab-built predispersive filter-based instrument from 700 to 2500?nm. The quality parameters were also determined by standard methods. The root mean square error (RMSE) for the calibration and validation sets was used to evaluate the performance of the models. The correlation coefficients for moisture, fat, protein, and carbohydrates in chickpea flour exceeded 0.96 using PLS and PCR models using the full spectral range. Wavelengths from 2100 to 2345?nm had the lowest RMSE for quality parameters by iPLS. The error was further decreased by 0.41, 0.1, and 1.1% for carbohydrates, fats, and proteins by siPLS. The NIR spectral regions yielding the lowest RMSE of prediction were 1620–2345?nm for carbohydrates, 1180–1590?nm and 1860–2094?nm for fat, and 1700–2345?nm for proteins. The study shows that chickpea flour quality parameters were accurately determined using the optimized wavelengths.