Partially Ordered Models

We provide a formal definition and study the basic properties of partially ordered random fields (PORF). These systems were proposed to model textures in image processing and to represent independence relations between random variables in statistics (in the latter case they are known as Bayesian networks). Our random fields are a generalization of probabilistic cellular automata (PCA) and their theory has features intermediate between that of discrete-time processes and the theory of statistical mechanical lattice fields. Its proper definition is based on the notion of partially ordered specification (POS), in close analogy to the theory of Gibbs measures. This paper contains two types of results. First, we present the basic elements of the general theory of PORFs: basic geometrical issues, definition in terms of conditional probability kernels, extremal decomposition, extremality and triviality, reconstruction starting from single-site kernels, relations between POM and Gibbs fields. Second, we prove three uniqueness criteria that correspond to the criteria known as uniform boundedness, Dobrushin uniqueness and disagreement percolation in the theory of Gibbs measures.     

Calculation of the linear kernel of the collision integral for the hard-sphere potential

The expansion of a distribution function in spherical harmonics transforms the Boltzmann equation into a system of integro-differential equations with kernels depending only of the magnitudes of velocities. The kernels can be expressed in terms of the sums including the matrix elements (MEs) of the collision integral. The kernels are constructed using new results of ME calculations; analysis of errors is carried out with the help of analytic expressions for kernels, which were derived by Hilbert and Hecke for the hard-sphere model. The concept of generalized matrix elements is introduced and their asymptotic representation is constructed for large values of indices. Analytic expressions for the contribution from MEs with large indices to the kernels are constructed. The high accuracy of the construction of a kernel using MEs is demonstrated.     

On the rate of convergence of the Legendre spectral collocation method for multi-dimensional nonlinear Volterra-Fredholm integral equations

While the approximate solutions of one-dimensional nonlinear Volterra-Fredholm integral equations with smooth kermels are now well understood,no systematic studies of the numerical solutions of their multi-dimensional counterparts exist.In this paper,we provide an efficient numerical approach for the multi-dimensional nonlinear Volterra-Fredholm integral equations based on the multi-variate Legendre-collocation approach.Spectral collocation methods for multi-dimensional nonlinear integral equations are known to cause major difficulties from a convergence analysis point of view.Consequently,rigorous error estimates are provided in the weighted Sobolev space showing the exponential decay of the numerical errors.The existence and uniqueness of the numerical solution are established.Numerical experiments are provided to support the theoretical convergence analysis.The results indicate that our spectral collocation method is more flexible with better accuracy than the existing ones.     

Lyapunov-type inequalities for fractional difference operators with discrete Mittag-Leffler kernel of order 2 &lt; <Emphasis Type="Italic">α</Emphasis> &lt; 5/2

Fractional difference operators with discrete-Mittag-Leffler kernels of order α > 1 are defined and their corresponding fractional sum operators are confirmed. We prove existence and uniqueness theorems for the discrete fractional initial value problems in the frame of discrete Caputo (ABC) and Riemann (ABR) operators by using Banach contraction theorem. Then, we prove Lyapunov type inequality for a Riemann type fractional difference boundary value problem of order 2 < α < 5∕2 within discrete Mittag-Leffler kernels, where the limiting case α → 2⁺ results in the ordinary difference Lyapunov inequality. Examples are given to clarify the applicability of our results and an application about the discrete fractional Sturm-Liouville eigenvalue problem is analyzed.     

基于可见光光谱高效鉴别玉米单倍体籽粒

单倍体技术已发展成为玉米遗传研究及现代玉米育种的重要技术之一,单倍体籽粒的鉴别筛选是其中的重要环节。目前单倍体籽粒主要是依赖于籽粒的R1-nj遗传标记通过人工肉眼观察颜色的有或无进行鉴别,费时费工。而且部分材料由于标记颜色很难从籽粒外部观察到,导致人工筛选准确率较低。基于可见光光谱分析建立玉米单倍体籽粒鉴别方法,探索利用可见光光谱鉴别玉米单倍体籽粒的可行性。同时,由于每季用于诱导单倍体的育种材料不尽相同,模型须能够鉴别未参加建模的材料的单倍体。本研究以9个遗传背景的单倍体和杂交籽粒共284粒作为试验材料,利用便携式紫外-可见光光纤光谱仪采集单个玉米籽粒的可见光漫透射光谱。光谱数据经平滑、矢量归一化预处理和主成分分析,基于支持向量机方法建立单倍体和杂交籽粒判别模型。每次选择1个背景的样本作为测试集,其余背景的样本作为建模集对模型进行交叉验证。模型交叉验证平均正确判别率达到92.06%。其中8次测试正确判别率在85%以上。结果表明利用可见光光谱分析建立玉米单倍体籽粒鉴别方法,并使模型可鉴别未参与建模材料的单倍体具有可行性。并且基于该方法有望建立玉米单倍体籽粒的自动化快速筛选系统,提高玉米单倍体育种效率。     

Approximations of exchange-correlation energy by functionals with kernels depends on difference of coordinates

An area has been found containing for any given electron density all possible values of exchange-correlation energy approximated by nonlocal expressions with kernels depends on the difference of coordinates. It is assumed that such functionals satisfy but a few evident physical restrictions.Subsystem of valent electrons of germanium has been considered for sake of illustration. The details of kernels behaviour have been shown to weakly affect the total exchange-correlation energy.     

Identification and dosimetry of irradiated walnuts (Juglans regia) using EPR

Electron paramagnetic resonance (EPR) is an easy, fast, and reliable tool for identification of irradiated food. Untreated nuts may encounter hazards of carrying several pathogens or microbial contamination; walnuts are of specific importance due to their nutritional and medicinal values, and hence walnut processing via gamma irradiation is a necessary step. EPR was employed for the identification and dosimetry of Cs-137 gamma-irradiated walnuts (shells and kernels). Several important parameters were studied, such as spectral features, microwave power dependence of signal intensities, and short- and long-term time dependences. Responses of walnut shells and kernels to different radiation doses in the range 0–10 kGy were investigated. Results confirmed that EPR is a suitable tool for the identification and dosimetry of irradiated walnuts using either their shells or only kernels.     

Exact series expansions, recurrence relations, properties and integrals of the generalized exponential integral functions

Generalized exponential integral functions (GEIF) are encountered in multi-dimensional thermal radiative transfer problems in the integral equation kernels. Several series expansions for the first-order generalized exponential integral function, along with a series expansion for the general nth order GEIF, are derived. The convergence issues of these series expansions are investigated numerically as well as theoretically, and a recurrence relation which does not require derivatives of the GEIF is developed. The exact series expansions of the two dimensional cylindrical and/or two-dimensional planar integral kernels as well as their spatial moments have been explicitly derived and compared with numerical values.     

Uniqueness of Self-similar Solutions to Smoluchowski’s Coagulation Equations for Kernels that are Close to Constant

We consider self-similar solutions to Smoluchowski’s coagulation equation for kernels \(K=K(x,y)\) that are homogeneous of degree zero and close to constant in the sense that $$\begin{aligned} -\varepsilon \le K(x,y)-2 \le \varepsilon \Big ( \Big (\frac{x}{y}\Big )^{\alpha } + \Big (\frac{y}{x}\Big )^{\alpha }\Big ) \end{aligned}$$ for \(\alpha \in [0,1)\) . We prove that self-similar solutions with given mass are unique if \(\varepsilon \) is sufficiently small which is the first such uniqueness result for kernels that are not solvable. Our proof relies on a contraction argument in a norm that measures the distance of solutions with respect to the weak topology of measures.     

A remark on the low-temperature behavior of the SOS interface in half-space

We investigate the low-temperature phase diagram of thed-dimensional (d2) solid-on-solid (SOS) interface constrained to lie above a rigid wall to which it is attracted by a constant force. We prove uniqueness of the Gibbs state and exponentially fast convergence (in the diameter of the domain) of the finite-volume expectation of local observables, for all values of parameters where uniqueness in the class of translation-periodic limit Gibbs states was established previously. These domains of uniqueness are bordered by lines on which the system undergoes a layering transition.     

Acceleration-induced nonlocality: uniqueness of the kernel

We consider the problem of uniqueness of the kernel in the nonlocal theory of accelerated observers. In a recent work [Ann. Phys. (Leipzig) 11 (2002) 309], we showed that the convolution kernel is ruled out as it can lead to divergences for nonuniform accelerated motion. Here we determine the general form of bounded continuous kernels and use observational data regarding spin-rotation coupling to argue that the kinetic kernel given by K(τ,τ′)=k(τ′) is the only physically acceptable solution.     

Singular Values of Products of Ginibre Random Matrices,Multiple Orthogonal Polynomials and Hard Edge Scaling Limits

Akemann, Ipsen and Kieburg recently showed that the squared singular values of products of M rectangular random matrices with independent complex Gaussian entries are distributed according to a determinantal point process with a correlation kernel that can be expressed in terms of Meijer G-functions. We show that this point process can be interpreted as a multiple orthogonal polynomial ensemble. We give integral representations for the relevant multiple orthogonal polynomials and a new double contour integral for the correlation kernel, which allows us to find its scaling limits at the origin (hard edge). The limiting kernels generalize the classical Bessel kernels. For M = 2 they coincide with the scaling limits found by Bertola, Gekhtman, and Szmigielski in the Cauchy–Laguerre two-matrix model, which indicates that these kernels represent a new universality class in random matrix theory.     

Cusp kernels for velocity-changing collisions

We introduce an analytical kernel, the "cusp" kernel, to model the effects of velocity-changing collisions on optically pumped atoms in low-pressure buffer gases. Like the widely used Keilson-Storer kernel [J. Keilson and J.?E. Storer, Q. Appl. Math. 10, 243 (1952)], cusp kernels are characterized by a single parameter and preserve a Maxwellian velocity distribution. Cusp kernels and their superpositions are more useful than Keilson-Storer kernels, because they are more similar to real kernels inferred from measurements or theory and are easier to invert to find steady-state velocity distributions.     

Coupling Between the Group—Related Coherent States

When two representations of the Lie algebra are coupled,the coupling integral kernels are presented to relate the coupled to uncoupled group-related coherent states,These kernels have a connection with usual coupling coefficients.The explicit expressions of these kernels for SU(2),SO(4) and SUq(2) are given.When the direct product of three representations is formed in two ways,the recoupling integral kernels relating to the coupled group-related coherent states corresponding to two different schemes are introduced,and the relations between these kernels and the general recoupling coefficients are obtained.The properties of these kerels are discussed.     

基于稀疏先验的空间目标图像盲反演方法

针对图像盲反演算法未考虑空间目标图像自身特性,致使对空间目标图像细节信息恢复不理想、重构图像中易产生边界伪像等不足之处,提出了一种基于稀疏表示的联合稀疏先验约束盲反演算法.首先,结合空间目标图像梯度的稀疏特性,采用图像梯度的L 0范数提取有利于模糊核估计的图像显著边缘信息;其次,采用L p范数和L 0范数对图像的梯度分布和空间域进行稀疏约束,以保证反演图像的像素点间具有显著的对比度,同时保证图像中包含边缘和纹理等细节信息;最后,采用拉普拉斯分布先验对模糊核进行约束,以保证模糊核的稀疏特性.采取交替迭代策略对所提出的模型进行优化求解,从而得到模糊核和空间目标图像的估计值.实验结果表明,相比于几种具有代表性的盲反演算法,提出的方法能估计出更准确的模糊核,对图像边缘和纹理等细节信息具有更好的恢复能力,在主观评价和客观评价方面均取得了较好的反演性能.     

Generalized thermostatistics based on the Sharma-Mittal entropy and escort mean values

A generalized thermostatistics is developed for an entropy measure introduced by Sharma and Mittal. A maximum-entropy scheme involving the maximization of the Sharma and Mittal entropy under appropriate constraints expressed as escort mean values is advanced. Maximum-entropy distributions exhibiting a power law behavior in the asymptotic limit are obtained. Thus, results previously derived for the Renyi entropy and the Tsallis entropy are generalized. In addition, it is shown that for almost deterministic systems among all possible composable entropies with kernels that are described by power laws the Sharma-Mittal entropy is the only entropy measure that gives rise to a thermostatistics based on escort mean values and admitting of a partition function. Received 27 June 2002 Published online 31 December 2002     

On the global “two-sided” characteristic Cauchy problem for linear wave equations on manifolds

The global characteristic Cauchy problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown that, if geometrically well-motivated restrictions are placed on the supports of the (smooth) initial datum and of the (smooth) inhomogeneous term, then there exists a continuous global solution which is smooth “on each side” of the initial value hypersurface. A uniqueness result in Sobolev regularity \(H^{1/2+\varepsilon }_{\mathrm {loc}}\) is proved among solutions supported in the union of the causal past and future of the initial value hypersurface, and whose product with the indicator function of the causal future (resp. past) of the hypersurface is past compact (resp. future compact). An explicit representation formula for solutions is obtained, which prominently features an invariantly defined, densitised version of the null expansion of the hypersurface. Finally, applications to quantum field theory on curved spacetimes are briefly discussed.     

Coherent state map quantization in a Hermitian-like setting

For vector bundles having an involution on the base space, Hermitian-like structures are defined in terms of such an involution. We prove a universality theorem for suitable self-involutive reproducing kernels on Hermitian-like vector bundles. This result relies on pullback operations involving the tautological bundle on the Grassmann manifold of a Hilbert space and exhibits the aforementioned reproducing kernels as pullbacks of universal reproducing kernels that live on the Hermitian-like tautological bundle. To this end we use a certain type of classifying morphisms, which are geometric versions of the coherent state maps from quantum theory. As a consequence of that theorem, we obtain some differential geometric properties of these reproducing kernels in this setting.     

THz技术在农产品/食品品质检测中的应用

农产品/食品的质量和品质问题越来越受人们关注。探索实际可行的农产品/食品的无损检测与品质评估技术正在成为研究热点。太赫兹(THz)辐射是位于中红外和微波波段之间的一段电磁波,具有非常重要的科学研究和应用价值。长期以来由于缺乏可行的THz波产生方法与探测手段,该波段相关领域的研究滞缓。THz光谱传感和成像技术是THz波的两个主要应用技术。THz光谱检测技术作为一种新型检测技术能够获得传统检测无法获得的信息。近十几年来,THz波用于来研究固、液、气相等各种物质的光电特性、分子内部振动和组成信息,在生物分析、医疗诊断、安全检测、环境控制等领域,THz技术显示出广阔的应用前景。文章介绍了THz波的主要性质、THz波检测技术的特点,论述了THz技术在农产品、食品质量与品质检测中的最新进展及其应用的潜力。     

The ultraviolet behaviour of integrable quantum field theories,affine Toda field theory

We investigate the thermodynamic Bethe ansatz (TBA) equations for a system of particles which dynamically interacts via the scattering matrix of affine Toda field theory and whose statistical interaction is of a general Haldane type. Up to the first leading order, we provide general approximated analytical expressions for the solutions of these equations from which we derive general formulae for the ultraviolet scaling functions for theories in which the underlying Lie algebra is simply laced. For several explicit models we compare the quality of the approximated analytical solutions against the numerical solutions. We address the question of existence and uniqueness of the solutions of the TBA equations, derive precise error estimates and determine the rate of convergence for the applied numerical procedure. A general expression for the Fourier transformed kernels of the TBA equations allows one to derive the related Y-systems and a reformulation of the equations into a universal form.