Geometric Integrability of Two-Component Camassa-Holm and Hunter-Saxton Systems

It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are directly constructed. In addition, a class of nonlocal symmetries depending on the pseudo-potentials are obtained.     

Separation of Variables for a Lattice Integrable System and the Inverse Problem

We investigate the relation between the local variables of a discrete integrable lattice system and the corresponding separation variables, derived from the associated spectral curve. In particular, we have shown how the inverse transformation from the separation variables to the discrete lattice variables may be factorized as a sequence of canonical transformations.     

Solution of a Generalized Inverse Spectral Problem for Weakly Resolved Spectra Using a Coefficient of Correlation

We consider in a new statement the inverse problem of the theory of vibrational spectra of molecules, in which a theoretical spectral curve directly gets closer to the experimental one. A coefficient of correlation between the curves is used as a criterion of the closeness of the curves and as a functional of the inverse problem. The procedure developed for solving the inverse problem makes it possible to dispense with the preliminary referencing of frequencies in an experimental spectrum and with its expansion into elementary absorption bands.     

Hamiltonian System and Infinite Conservation Laws Associated with a New Discrete Spectral Problem

Starting from a new discrete spectral problem, the corresponding hierarchy of nonlinear lattice equations is proposed. It is shown that the lattice soliton hierarchy possesses the bi-Hamiltonian structures and infinitely many common commuting conserved functions. Further, infinite conservation laws of the hierarchy are presented.     

Inverse Scattering and Soliton Solutions for a New Integrable System

A new integrable system describing the process of self-induced transparency with spatial dispersion is analyzed from the viewpoint of inverse scattering transform. The coupled set of Gelfand–Levitan equation is established and solved for one soliton solutions. The explicit structure of the solutions are exhibited graphically.     

Vector Product and an Integrable Dynamical System

We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals. The connection with Nambu mechanics is established. The extension to higher dimensions is also discussed.     

用逐次逼近迭代法分析含空间滤波器的多程激光放大系统的逆问题

基于Ｆｒａｎｔｚ－Ｎｏｄｖｉｋ（Ｆ－Ｎ）方程和广义惠更斯－菲涅耳衍射积分，提出了解决含空间滤波器的多程激光放大系统的逆问题的迭代算法，并作了数值计算了，所得的数值计算方法和有关结果可用于高功率多程激光放大系统的设计。     

杆的离散系统的某些混合型振动反问题

研究杆的离散系统的混合型振动反问题,即由给定的部分频谱数据和部分模态数据构造一个杆的离散系统的刚度矩阵和质量矩阵.提出3个此类反问题,给出反问题的解法,讨论反问题的解的存在条件,给出相应的计算实例,并分析这类反问题的潜在价值.     

Stark Broadening of Ne II and Ne III Spectral Lines

Using a semiclassical approach, the widths and shifts of the spectral lines of three Ne II and six Ne III multiplets caused by collisions with electrons, protons, and helium ions at a density of perturbing particles of 10¹⁷ cm^–3 and different temperatures have been calculated. The results obtained have been compared with the known experimental and theoretical data.     

The Adjoint Method for an Inverse Design Problem in the Directional Solidification of Binary Alloys

This paper presents a systematic procedure based on the adjoint method for solving a class of inverse directional alloy solidification design problems in which a desired growth velocityv_fis achieved under stable growth conditions. To the best of our knowledge, this is the first time that a continuum adjoint formulation is proposed for the solution of an inverse problem with simultaneous heat and mass transfer, thermo-solutal convection, and phase change. In this paper, the interfacial stability is considered to imply a sharp solid–liquid freezing interface. This condition is enforced using the constitutional undercooling criterion in the form of an inequality constraint between the thermal and solute concentration gradients,GandG_c, respectively, at the freezing front. The main unknowns of the design problem are the heating and/or cooling boundary conditions on the mold walls. The inverse design problem is formulated as a functional optimization problem. The cost functional is defined by the square of theL₂norm of the deviation of the freezing interface temperature from the temperature corresponding to thermodynamic equilibrium. A continuum adjoint system is derived to calculate the adjoint temperature, concentration, and velocity fields such that the gradient of the cost functional can be expressed analytically. The cost functional minimization process is realized by the conjugate gradient method via the finite element method solutions of the continuum direct, sensitivity, and adjoint problems. The developed formulation is demonstrated with an example of designing the directional solidification of a binary aqueous solution in a rectangular mold such that a stable vertical interface advances from left to right with a desired growth velocity.     

Application of a Factorial Design Method to Determine the Accuracy of a Solution to an Inverse Heat Conduction Problem

A numerical/experimental inverse procedure was employed to estimate the temperature-dependent thermal conductivity of a solid body in which 1D heat conduction in a top heated cylindrical sample is assumed. The emphasis is focused on the issue of sensitivity of results to selected assumptions made in inverse calculations. It has been found that the accuracy of heat capacity evaluation brings the largest contribution to final errors (up to 74%). Density accounts for one-fourth to one-third of the total error of determination. The failure to ensure unidirectional heat conduction in a sample during an experiment is important only at elevated temperatures.     

Analysis of Spectral Reflectance Using Normalization Method from Endoscopic Spectroscopy System

Objective assessment of gastrointestinal mucosal color is extremely important in the endoscopic diagnosis of digestive tract disease. In this paper, we propose a method to clarify the spectral characteristics of gastric and colon cancer. A large number of spectral reflectance data of mucous membrane are measured by the endoscopic spectroscopy system (ESS) in the National Cancer Center Hospital East, Kashiwa, Japan and the Department of Internal Medicine, Self-Defense Force Center Hospital, Tokyo, Japan. We assume that early cancer appears primarily in the spectral data of short wavelength, because it is usually present in a superficial cell where short wavelength light is scattered more strongly than long wavelength light. To identify the features in the short wavelength components, the spectral reflectance was divided by the reflectance of a long wavelength. We investigated the possibility of distinguishing early cancer from normal spectral data through statistical analysis, employing the projection axis as the mean difference between them. Early cancer and normal spectral data were projected on the projection axis, and the Student’s T-test was applied to evaluate the mean of the distribution between these data.     

Fractal Dromion, Fractal Lump, and Multiple Peakon Excitations in a New (2+1)-Dimensional Long Dispersive Wave System

By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: λqt + qxx - 2q ∫ (qr)xdy ＝ 0, λrt - rxx + 2r ∫(qr)xdy ＝ 0, is derived. Some types of the usual localized excitations such as dromions, lumps, rings, and oscillating soliton excitations can be easily constructed by selecting the arbitrary functions appropriately. Besides these usual localized structures, some new localized excitations like fractal-dromion, farctal-lump, and multi-peakon excitations of this new system are found by selecting appropriate functions.     

Spectral anomalies and spectral switches of partially coherent and polychromatic light diffracted at an aperture

Inrecentyearsanewbranchofmodernphysicalopticscalledsingularoptics[1]hasbeendeveloped.In2002theworkinsingularopticswasextendedfrommonochromaticlighttospatiallyfullycoherentandpolychromaticlightbyGburetal.[2—4].Itwasfoundthat,whenaconverging,spatiallyfullycoherentandpolychromaticsphericalwaveisdiffractedatanaperture,anomalousspectralchangestakeplaceclosetozerosoftheintensityinthefarfield;i.e.thespectrumisredshiftedatsomepoints,blueshiftedatothers,andsplitintotwolineselsewhere.Thepredictionsofsp…     

Multi-component SC Lax Integrable Hierarchy of Soliton Equations and Its Multi-component Integrable Coupling System with Two Arbitrary Functions

A new simple loop algebra GM is constructed, which is devoted to establishing an isospectral problem.By making use of generalized Tu scheme, the multi-component SC hierarchy is obtained. Furthermore, an expanding loop algebra FM of the loop algebra GM is presented. Based on FM, the multi-component integrable coupling system of the multi-component SC hierarchy of soliton equations is worked out. How to design isospectral problem of mulitcomponent hierarchy of soliton equations is a technique and interesting topic. The method can be applied to other nonlinear evolution equations hierarchy.     

Experimental Design and Methodology for Estimation of Local Heat Transfer Coefficient in Jet Impingement Using Transient Inverse Heat Conduction Problem

Abstract

This article aims to employ a two-dimensional inverse heat conduction technique in designing an experiment for accurately estimating the local convective heat transfer coefficient in slot jet impingement, given temperature measurements at some interior locations in the target plate. The method uses a sequential procedure together with the Beck function specification approach. Solution accuracy and experimental errors are examined using simulated temperature data. It is concluded that a good estimation of the space variable heat transfer coefficient can be made from the knowledge of the transient temperature recordings. The technique is used in a series of numerical experiments to provide the optimum experimental design for a slot jet impingement heat transfer investigation.     

Upper Triangular Matrix of Lie Algebra and a New Discrete Integrable Coupling System

The upper triangular matrix of Lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice soliton equation spectral problem is obtained and leads to a novel hierarchy of the nonlinear lattice equation hierarchy. It indicates that the study of integrable couplings using upper triangular matrix of Lie algebra is an important step towards constructing integrable systems.     

智能手机的主要叶类蔬菜品质和新鲜度指标的光谱检测

蔬菜品质和新鲜度的高低不仅影响食用时的口感,而且营养程度也不一样。作为蔬菜品质和新鲜度重要参考指标之一的叶绿素和含水量的检测,已经越来越受到国内外学者的重视。相比于传统的肉眼目视判断的检验方法,可见-近红外光谱分析具有快速高效、无损、非接触等独特的优势,更加适合蔬菜的实时检测。目前相关研究主要集中在生长中植被叶绿素和含水量的反演,对市场上成品蔬菜的研究较少,或者研究对象单一,缺乏市场普适性。此外,光谱数据的获取需要专业的光谱仪采集,费时费力,各种生理生化指标的研究离实用化还有很长的距离。为了与实际相结合,基于智能手机光谱系统（SCSS)建立了快速、准确、普适性强的反演蔬菜叶绿素和含水量的模型,并通过地面光谱仪SVC数据验证了该系统的可靠性。选取市场典型的五种蔬菜（菠菜、小油菜、油麦菜、生菜和娃娃菜）作为实验样本,分别进行常温保存和冷藏保存来模拟现实中菜市场和超市的蔬菜储存环境。每隔24 h进行一次数据采集。对获取的原始光谱数据进行波段选择和小波变换去噪的预处理。构建蔬菜叶绿素反演指数(VCRI_{（m, n）})和蔬菜含水量反演指数(VWRI_{(i, j)}),分别提取该两个指数与叶绿素和含水量实测值的相关系数R作为权重系数,最终建立了叶绿素和含水量的加权平均反演模型。实验结果表明,SVC仪器和SCSS两者数据针对蔬菜叶绿素和含水量的敏感波段基本一致,叶绿素反演的敏感波段在730~980 nm之间,反演精度R2分别为0.863和0.808 1,标准差为8.679 5和8.892 5;含水量反演的敏感波段在水汽吸收波段950~1 000 nm之间,反演精度R2分别为0.742 9和0.712 9,标准差为8.789 9%和8.861 4%。SVC实验数据跟SCSS实验数据结果十分接近,验证了新型智能手机光谱系统实时监测蔬菜叶绿素和含水量的有效性。智能手机光谱系统具有体积小、价格便宜的优势,结合网络云端服务和实时数据反馈的特点,能够实现蔬菜品质和新鲜度指标的智能检测,让光谱分析真正应用于人们日常生活中。     

New Family of Exact Solutions and Chaotic Soltions of Generalized Breor-Kaup System in (2+1)-Dimensions via an Extended Mapping Approach

Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of generalized (2 1)-dimensional Broer-Kaup system (GBK) system is derived. Then based on the derived solitary wave solution, we obtain some specific chaotic solitons to the (2 1)-dimensional GBK system.