基于多证据同步融合的目标辨识算法

为提高不同类型冲突证据融合结果的可靠性,提出基于多证据同步融合的目标辨识算法。新算法先是通过分析证据之间的冲突状况,选择适用的冲突衡量参数,并相应给出基于不同参数的证据及源自于不同证据焦元的权值计算公式;进一步,依据新的焦元权值对多证据局部冲突信息实行按权指派。实例和仿真应用结果显示,与现有常用相关算法比较,新算法具有稳定性高、使用范围广泛的优点。     

Combination of partially non-distinct beliefs: The cautious-adaptive rule

The combination rule is critical in an evidence based fusion process. The conjunctive rule is most common eventhough when the cognitive independence – distinctness – assumption is often questionable. A new combination rule is tested here in both discrete and continuous cases, accounting for a partial non-distinctness between evidences. It is based on ‘generalized discounting’, that we define for separable basic belief assignments (bbas) or basic belief densities (bbds), to be applied to the source correlation derived from the cautious rule. This correlation can be specified in both considered cases of consonant bbas/bbds (as proposed by Dubois et al.) and separable bbas/bbds (as proposed by Denœux). Then, the so-called ‘cautious-adaptive’ rule varies between the conjunctive rule and the cautious one, depending on the discounting level. In the Gaussian case with standard deviation σ, the evidence non-distinctness will be parameterized by a factor [0,1] dividing σ. It leads to the generalized discounting needed in the cautious-adaptive formulation.     

Limit Distributions for Conflict Dynamical System with Point Spectra

Ukrainian Mathematical Journal - We construct a model of conflict dynamical system whose limit states are associated with singular distributions. It is proved that a criterion for the appearance of...     

积分因子在定性理论中的性质及其应用

在微分方程定性理论中.一次奇点的分类.高次奇点的分类,极限环的稳定性等,都是需要研究的重要问题,并且是用不同的方法来加以解决的.而高次奇点中焦点与中心的区分,至今还是一个未解决的问题.在本文中,我们从理论上阐明了.所有上述问题都可利用积分因子的概念而统一地加以处理.此外,我们并给出了判别中心与焦点的方法,这一方法对于一次奇点与高次奇点都是同样适用的.从而解决了关于高次奇点的中心与焦点的区分问题.     

域外奇源分布法场点解的唯一性

应用奇源解的核函数沿距离递减的条件和积分不等式,可证这类奇源在凸域外分布只要满足以它产生的响应来表达的边界条件时,所引起相应的域内场点解是唯一的。文中给出这类奇源的部分例子,如Kelvin的点力,点圆力偶(PRC)等。并给出PRC分布解回转体扭转问题的场点解的唯一性证明作为应用例。     

Piecewise-analytic interfaces with weakly singular points of arbitrary order always scatter

It is proved that an inhomogeneous medium whose boundary contains a weakly singular point of arbitrary order scatters every incoming wave. Similarly, a compactly supported source term with weakly singular points on the boundary always radiates acoustic waves. These results imply the absence of non-scattering energies and non-radiating sources in a domain whose boundary is piecewise analytic but not infinitely smooth. Local uniqueness results with a single far-field pattern are obtained for inverse source and inverse medium scattering problems. Our arguments provide a rather weak condition on scattering interfaces and refractive index functions to guarantee the scattering phenomena that the scattered fields cannot vanish identically.     

Robust D-stability analysis for linear discrete singular time-delay systems with structured and unstructured parameter uncertainties

In this paper, the robust D-stability problem (i.e. the robusteigenvalue-clustering in a specified circular region problem)of linear discrete singular time-delay systems with structured(elemental) and unstructured (norm-bounded) parameter uncertaintiesis investigated. Under the assumptions that the linear nominaldiscrete singular time-delay system is regular and impulse-free,and has all its finite eigenvalues lying inside a specifiedcircular region, a new sufficient condition is proposed to preservethe assumed properties when structured and unstructured parameteruncertainties are added into the linear nominal discrete singulartime-delay system. When all the finite eigenvalues are justrequired to locate inside the unit circle of the z-plane, theproposed criterion will become the stability robustness criterion.For the case that the linear discrete singular time-delay systemis only subject to structured parameter uncertainties, by anillustrative example, the presented sufficient condition isshown to be less conservative than the existing one reportedrecently in the literature.     

Decomposition of conflict as a distribution on hypotheses in the framework on belief functions

In this paper, we address the problem of identifying the potential sources of conflict between information sources in the framework of belief function theory. To this aim, we propose a decomposition of the global measure of conflict as a function defined over the power set of the discernment frame. This decomposition, which associates a part of the conflict to some hypotheses, allows identifying the origin of conflict, which is hence considered as “local” to some hypotheses. This is more informative than usual global measures of conflict or disagreement between sources. Having shown the unicity of this decomposition, we illustrate its use on two examples. The first one is a toy example where the fact that conflict is mainly brought by one hypothesis allows identifying its origin. The second example is a real application, namely robot localization, where we show that focusing the conflict measure on the “favored” hypothesis (the one that would be decided) helps us to robustify the fusion process.     

Oscillatory traveling waves of polytropic filtration equation with generalized Fisher–KPP sources

The polytropic filtration equation with generalized Fisher–KPP sources is considered. We will show that the equation may have finite times oscillatory traveling waves, and try to give a complete classification by virtue of a singular exponent in the source according to the finiteness of the oscillatory times of traveling waves.     

Some properties of the isolated invariant set of a flow

In this paper, several results involving m-chain are proved. At the same time, a criterion for the existence of trajectories joining singular points is given.     

The singular sources method for cracks

The singular sources method is given to detect the shape of a thin infinitely cylindrical obstacle from a knowledge of the TM‐polarized scattered electromagnetic field in large distance. The basic idea is based on the singular behaviour of the scattered field of the incident point source on the cross‐section of the cylinder. We assume that the scatterer is a perfect conductor which is possibly coated by a material and investigate two models with different boundary conditions. Also we give a uniqueness proof for the shape reconstruction. Copyright © 2006 John Wiley & Sons, Ltd.     

Uniqueness for a seismic inverse source problem modeling a subsonic rupture

We consider an inverse source problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. The inverse source problem, with an arbitrary source term on the right-hand side of the wave equation, is not uniquely solvable. Here we formulate conditions on the source term that allow us to show uniqueness and that provide a reasonable model for the application of interest. We assume that the source term is supported on a finite set of times and that the support in space moves with subsonic velocity. Moreover, we assume that the spatial part of the source is singular on a hypersurface, an application being a seismic rupture along a fault plane. Given data collected over time on a detection surface that encloses the spatial projection of the support of the source, we show how to recover the times and locations of sources microlocally and then reconstruct the smooth part of the source assuming that it is the same at each source location.     

Landau Damping to Partially Locked States in the Kuramoto Model

In the Kuramoto model of globally coupled oscillators, partially locked states (PLS) are stationary solutions that capture the emergence of partial synchrony when the interaction strength increases. While PLS have long been considered, existing results on their stability are limited to neutral stability of the linearized dynamics in strong topology or to specific invariant subspaces (obtained via the so‐called Ott‐Antonsen (OA) ansatz) with specific frequency distributions for the oscillators. In the mean‐field limit, the Kuramoto model shows various ingredients of the Landau damping mechanism in the Vlasov equation. This analogy has been a source of inspiration for stability proofs of regular Kuramoto equilibria. In addition, the major mathematical issue with PLS asymptotic stability is that these states consist of heterogeneous and singular measures. Here we establish an explicit criterion for their spectral stability and prove their local asymptotic stability in weak topology for a large class of analytic frequency marginals. The proof strongly relies on a suitable functional space that contains (Fourier transforms of) singular measures, and for which the linearized dynamics is well under control. For illustration, the stability criterion is evaluated in some standard examples. We confirm in particular that no loss of generality results in assuming the OA ansatz. To the best of our knowledge, our result provides the first proof of Landau damping to heterogeneous and irregular equilibria in the absence of dissipation. © 2018 Wiley Periodicals, Inc.     

多时滞退化微分系统指数稳定的代数判据

本文研究退化多时滞微分系统的指数稳定性,得到了退化多时滞微分系统指数稳定性的代数判据,给出的一个例子说明所得结果的应用,同时给出了中立型退化时滞微分系统指数稳定的判定方法.     

Design with L-splines

We recently obtained a criterion to decide whether a given space of parametrically continuous piecewise Chebyshevian splines (i.e., splines with pieces taken from different Extended Chebyshev spaces) could be used for geometric design. One important field of application is the class of L-splines, that is, splines with pieces taken from the null space of some fixed real linear differential operator, generally investigated under the strong requirement that the null space should be an Extended Chebyshev space on the support of each possible B-spline. In the present work, we want to show the practical interest of the criterion in question for designing with L-splines. With this in view, we apply it to a specific class of linear differential operators with real constant coefficients and odd/even characteristic polynomials. We will thus establish necessary and sufficient conditions for the associated splines to be suitable for design. Because our criterion was achieved via a blossoming approach, shape preservation will be inherent in the obtained conditions. One specific advantage of the class of operators we consider is that hyperbolic and trigonometric functions can be mixed within the null space on which the splines are based. We show that this produces interesting shape effects.     

A new development for the Tikhonov Theorem in nonlinear singular perturbation systems

This paper deals with the exponential stability of nonlinear perturbation systems under a new condition. A novel criterion of exponential stability of nonlinear systems is firstly given in a general form. In this criterion, a new kind of characteristic value is introduced, which makes the exponential stability measurable. Based on this criterion, a new development for the Tikhonov Theorem in nonlinear singular perturbation systems is presented.     

Lagrange's early contributions to the theory of first-order partial differential equations

In 1776, J. L. Lagrange gave a definition of the concept of a “complete solution” of a first-order partial differential equation. This definition was entirely different from the one given earlier by Euler. One of the sources for Lagrange's reformulation of this concept can be found in his attempt to explain the occurrence of singular solutions of ordinary differential equations. Another source of the new definition is contained in an earlier treatise of Lagrange [1774] in which he elaborated an approach to first-order partial differential equations briefly indicated by Euler. The method of “variation of constants,” which was fundamental to his argument, suggested to Lagrange the reformulation of the concept of a “complete solution.” In the present paper I shall discuss both sources of the new definition of “completeness.”     

二阶多项式系统固定奇点附近解的解析展开

研究二阶多项式系统所确定的通过固定奇点的解．利用牛顿图法研究了这种解在固定奇点处的幂级数展开式,给出有无穷多个解通过固定奇点的判据,并在只有有限个解通过固定奇点的情况下,给出了过固定奇点的解个数的上界．     

奇异黎曼度量之下分支问题的C0接触等价D决定性

本文使用奇点理论方法对奇异黎曼度量之下的分支问题进行了拓扑性质的研究,给出了分支问题中的Ｃ＾０接触等价的一个判别条件,推广了文献［１－３］中的有关结果。