Asymptotic expansion of the logarithm of the partition function

A method is presented permitting one to find in principle all the non-decreasing terms of the asymptotic expansion of the logarithm of the partition function when the volume of region increases. The constructions are carried out at low activity for lattice systems with generaln-body interactions, and continuous systems with two-body interactions.     

基于P范数的核最小对数绝对差自适应滤波算法

为了进一步提高在a稳定分布噪声背景下非线性自适应滤波算法的收敛速度,本文提出了一种新的基于p范数的核最小对数绝对差自适应滤波算法(kernel least logarithm absolute difference algorithm based on p-norm, P-KLLAD).该算法结合核最小对数绝对差算法和p范数,一方面利用最小对数绝对差准则保证了算法在a稳定分布噪声环境下良好的鲁棒性,另一方面在误差的绝对值上添加p范数,通过p范数和一个正常数a来控制算法的陡峭程度,从而提高该算法的收敛速度.在非线性系统辨识和Mackey-Glass混沌时间序列预测的仿真结果表明,本文算法在保证鲁棒性能的同时提高了收敛速度,并且在收敛速度和鲁棒性方面优于核最小均方误差算法、核分式低次幂算法、核最小对数绝对差算法和核最小平均p范数算法.     

基于对数解调的递变能量CT成像方法

复杂结构件由于有效厚度差异大和成像系统动态范围受限, 单一能量下的投影数据信息不完整, 常用CT重建算法及不完全数据重建算法无法在数据缺失严重的情况, 有效实现复杂结构件的CT重建. 为此论文提出基于对数解调的递变能量CT成像方法. 该方法在分析直接高动态CT成像所存在问题的基础上, 提出利用对数变换压缩递变能量投影序列动态范围, 并利用现有的基于图像灰度一致性的融合方法, 计算融合加权系数, 再经常规重建算法实现复杂构件的CT成像. 论文并以某复杂仪表为对象, 进行实验, 相比传统的固定能量成像方式, CT信息完整, 质量高. 从而说明论文所提出的方法, 能够实现CT系统动态范围的扩展, 实现复杂结构件的高动态CT成像.     

Flux confinement in the leading logarithm model

We study the statics of quasi-abelian quark and antiquark source charges in the approximation in which leading logarithm radiative corrections are retained in the gauge gluon effective action functional. We show that the partial differential equation for the flux function is of degenerating elliptic type, leading to flux confinement within a free boundary which is a characteristic. The static potential increases linearly for large source separations, with a logarithmic subdominant term.     

A gray-natural logarithm ratio bilateral filtering method for image processing

A new method based on gray-natural logarithm ratio bilateral filtering is presented for image smoothing in this work. A new gray-natural logarithm ratio range filter kernel, leading to adaptive magnitude from image gray distinction information, is pointed out for the bilateral filtering. The new method can not only well restrain noise but also keep much more weak edges and details of an image, and preserve the original color transition of color images. Experimental results show the effectiveness for image denoising with our method.     

基于分窗Gram-Schmidt变换和PSO-SVR算法的水稻纹枯病病情指数检测

纹枯病是水稻的主要病害之一,其防治对于保证水稻产量、质量具有重要意义,以高光谱检测水稻病害得到了广泛应用,并且高光谱降维是光谱分析的重要环节。该研究在2019年沈农水稻试验基地获取水稻低空遥感冠层与地面冠层高光谱,并对其进行以窗口宽度为15和阶数为3的Savitzky-Golay平滑处理和光谱变换（得到原始光谱、一阶微分光谱和倒数之对数光谱）,分窗口对这3种光谱分别进行Gram-Schmidt变换,找到投影空间并映射出主基底,实现高光谱数据降维,绘制具有显著性概率的主基底,其极大极小值为特征波段。此外3种光谱还采用了主成分分析和连续投影法降维。以降维后的数据与水稻纹枯病病情指数进行支持向量机回归建模,其中支持向量机回归进行粒子群优化,并以径向基为核函数,对比分析了3种降维方式的降维效果。结果表明：水稻地面冠层尺度建模效果高于低空遥感尺度建模;在光谱处理方面,低空冠层高光谱进行倒数之对数变换效果较好,地面冠层所得高光谱数据进行一阶微分变换效果较好;分窗Gram-Schmidt变换算法优于主成分分析和连续投影法;粒子群算法可以优化支持向量机中的惩罚系数和核函数参数,提高其反演精度;无人机低空遥感尺度中,高光谱进行倒数之对数处理,以分窗Gram-Schmidt变换降维,敏感波段为427.3,539.6,749.5和825.4 nm,PSO-SVR建模决定系数R2为0.731,均方根误差RMSE为0.151;地面冠层尺度中,高光谱进行一阶微分处理,以分窗Gram-Schmidt变换降维,敏感波段为552,607,702和730 nm,PSO-SVR模型决定系数R2为0.778,均方根误差RMSE为0.147。因此,高光谱技术可以有效地检测水稻纹枯病,并且其病情指数可用冠层高光谱进行反演,分窗Gram-Schmidt变换对于高光谱数据降维有较好的效果,PSO-SVR建模对于水稻纹枯病病情指数的反演有明显提高,结果可为冠层尺度检测水稻纹枯病与病害发生情况提供一定的理论基础和技术支撑。     

Energy spectra of abundant nuclei of primary cosmic rays from the data of ATIC-2 experiment: Final results

The final results of processing the data from the balloon-born experiment ATIC-2 (Antarctica, 2002–2003) for the energy spectra of protons and He, C, O, Ne, Mg, Si, and Fe nuclei, the spectrum of all particles, and the mean logarithm of atomic weight of primary cosmic rays as a function of energy are presented. The final results are based on improvement of the methods used earlier, in particular, considerably increased resolution of the charge spectrum. The preliminary conclusions on the significant difference in the spectra of protons and helium nuclei (the proton spectrum is steeper) and the non-power character of the spectra of protons and heavier nuclei (flattening of carbon spectrum at energies above 10 TeV) are confirmed. A complex structure of the energy dependence of the mean logarithm of atomic weight is found.     

On the Discrete Spectrum of a Spatial Quantum Waveguide with a Disc Window

In this study we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width d. We impose the Neumann boundary condition on a disc window of radius a and Dirichlet boundary conditions on the remained part of the boundary of the strip. We prove that such system exhibits discrete eigenvalues below the essential spectrum for any a > 0. We give also a numeric estimation of the number of discrete eigenvalue as a function of \fracad\frac{a}{d}. When a tends to the infinity, the asymptotic of the eigenvalue is given.     

Simulation and optimization of a polymer directional coupler electro-optic switch with push-pull electrodes

Structural model and design technique are proposed for a polymer directional coupler electro-optic switch with rib waveguides and push-pull electrodes, of which the electric field distribution is analyzed by the conformal transforming method and image method. In order to get the minimum mode loss and the minimum switching voltage, the parameters of the waveguide and electrode are optimized, such as the core with, core thickness, buffer layer between the core and the electrode, coupling gap between the waveguides, electrode thickness, electrode width and electrode gap. Switching Characteristics are analyzed, which include the output power, insertion loss, and crosstalk. To realize normal switching function, the fabrication error, spectrum shift, and coupling loss between a single mode fiber (SMF) and the waveguide are discussed. Simulation results show that the coupling length is 3082 μm, push-pull switching voltage is 2.14 V, insertion loss is less than 1.17 dB, and crosstalk is less than −30 dB for the designed device.     

Bethe logarithm and QED shift for lithium

A novel finite basis set method is used to calculate the Bethe logarithm for the ground 2 (2)S(1/2) and excited 3 (2)S(1/2) states of lithium. The basis sets are constructed to span a huge range of distance scales within a single calculation, leading to well-converged values for the Bethe logarithm. The results are used to calculate an accurate value for the complete quantum electrodynamic energy shift up to order alpha(3) Ry. The calculated 3 (2)S(1/2)-2 (2)S(1/2) transition frequency for 7Li is 27 206.092 6(9) cm(-1), and the ionization potential for the 2 (2)S(1/2) state is 43 487.158 3(6) cm(-1). The 7Li-6Li isotope shift is also considered, and all the results compared with experiment.     

Quantization of plasma density irregularities under the action of a powerful electromagnetic wave: The spectrum of upper hybrid oscillations self-consistently trapped in density cavities

We present a theoretical model of the self-localization of the upper hybrid (UH) oscillations in plasma density depletions due to thermal nonlinearities driven by a homogeneous and monochromatic pump electric field. The Bohr-Sommerfeld condition for the trapped UH oscillations demands that the parameters of the density cavity be quantized. The depth and square of the depletion width across the magnetic field is proportional to an integer. The depth of the parabolically shaped cavity is proportional to the square of its width. The characteristic relative value of the density minimum is a few percent and the width is of the order of one meter for the pump wave amplitudes used in the ionospheric F-region experiments. We consider also the parametric decay of primary, localized UH oscillations trapped in the quantized plasma density depletions into secondary UH oscillations and lower-hybrid waves. We calculated the spectrum of the non-linear stabilized secondary UH oscillations which are also self-consistently trapped in the same density cavity. The spectrum of the UH oscillations is consistent with the observed spectrum of the downshifted (DM) and upshifted (UM) maximum in the stimulated electromagnetic emissions (SEE). Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 7, pp. 641–650, July 1999.     

滤波片透过率曲线测量中棱镜单色仪参数的选取

从理论上分析了入射、出射狭缝大小对出射光的光谱宽度和透过率曲线的影响，得到了入射、出射狭缝大小的最佳匹配条件，并通过实验验证了这一结论，分析了鼓轮每次转动格数对测得的透过率曲线的影响，给出了鼓轮每次转动的最佳格数值．     

Spectral study of light with a very low intensity by means of the measurement of laplace or fourier transform of the time-interval probability

In this work we intend the analysis of light with a very low intensity be means of the measurement of Laplace or Fourier transform of the probability of the time-intervals between two successive photons. The method is applied to the particular case of light of lorentzian spectrum and the error with which the spectral width would be obtained is studied (with a theoretical model and simulating through a computer). This error is confronted with that which might be attained if the spectral width were determined from the intensity correlation function. Results are discussed.     

分数阶对数耦合系统在非周期外力作用下的定向输运现象

本文讨论了分数阶对数耦合系统在非周期外力作用情况下, 耦合粒子链的定向输运现象. 由于粒子在黏性介质中的运动具有“记忆性”, 所以本文通过将系统建模为分数阶对数耦合模型来研究各个系统参数对粒子链运动状态的影响. 数值仿真表明: 1)对于此类系统, 只有在存在外力作用的情况下粒子链才能够产生定向输运现象, 并且粒子链平均流速随着外力的增大而增大. 2)对于分数阶阶数较小的系统, 阻尼记忆性对粒子链的运动状态有显著的影响, 具体表现为: 粒子链的平均流速存在上界(这个上界非常小), 无论外力、耦合力以及噪声强度如何变化, 粒子链的平均流速都不会超过这个上界. 当系统的阻尼力很大且外力为零时, 粒子链不会产生定向输运现象. 3) 当系统的阶数与外力较大时, 虽然粒子链能够产生定向流, 但是此时系统对耦合力与噪声具有免疫性. 4) 耦合力与噪声强度对粒子链运动的影响只在外力较小的情况下有所表现. 在这种情况下, 当系统阶数充分大时, 粒子链的平均流速随着耦合力与噪声强度的变化而变化, 并且伴随着定向流的产生.     

An exact solution to the Helmholtz equation for a quasi-Gaussian beam in the form of a superposition of two sources and sinks with complex coordinates

An exact solution to the Helmholtz equation is proposed. The solution describes a quasi-Gaussian beam with an arbitrary width and has the form of a superposition of sources and sinks with complex coordinates. It is shown that such a beam always lacks a component that propagates against the principal propagation direction. In addition, when the diameter of the beam exceeds the wavelength, the beam becomes directional in the broad sense: the radiation condition is satisfied with respect to the beam waist plane. For the beam under study, expressions for the angular spectrum and the spherical harmonic expansion coefficients are derived.     

Strong "quantum" chaos in the global ballooning mode spectrum of three-dimensional plasmas

The spectrum of ideal magnetohydrodynamic (MHD) pressure-driven (ballooning) modes in strongly nonaxisymmetric toroidal systems is difficult to analyze numerically owing to the singular nature of ideal MHD caused by lack of an inherent scale length. In this paper, ideal MHD is regularized by using a k-space cutoff, making the ray tracing for the WKB ballooning formalism a chaotic Hamiltonian billiard problem. The minimum width of the toroidal Fourier spectrum needed for resolving toroidally localized ballooning modes with a global eigenvalue code is estimated from the Weyl formula. This phase-space-volume estimation method is applied to two stellarator cases.     

The generalized Bethe logarithm for tightly bound electrons

We derive a closed relativistic expression that makes it possible to calculate the self-energy of multiply charged ions in an external Coulomb field without resorting to a series expansion in powers of αZ. The expression contains the generalized Bethe logarithm for tightly bound electrons. We do numerical calculations of the self-energy for the 1s _1/2-electrons of multiply charged hydrogenlike ions. The proposed method allows for self-energy calculations for any values of the nuclear charge Z. Zh. éksp. Teor. Fiz. 112, 1197–1208 (October 1997)     

An echolocation model for the restoration of an acoustic image from a single-emission echo

Bats can form a fine acoustic image of an object using frequency-modulated echolocation sound. The acoustic image is an impulse response, known as a reflected-intensity distribution, which is composed of amplitude and phase spectra over a range of frequencies. However, bats detect only the amplitude spectrum due to the low-time resolution of their peripheral auditory system, and the frequency range of emission is restricted. It is therefore necessary to restore the acoustic image from limited information. The amplitude spectrum varies with the changes in the configuration of the reflected-intensity distribution, while the phase spectrum varies with the changes in its configuration and location. Here, by introducing some reasonable constraints, a method is proposed for restoring an acoustic image from the echo. The configuration is extrapolated from the amplitude spectrum of the restricted frequency range by using the continuity condition of the amplitude spectrum at the minimum frequency of the emission and the minimum phase condition. The determination of the location requires extracting the amplitude spectra, which vary with its location. For this purpose, the Gaussian chirplets with a carrier frequency compatible with bat emission sweep rates were used. The location is estimated from the temporal changes of the amplitude spectra.