自组织结构的变论域模糊控制

针对变论域模糊控制,提出一种新的自组织结构的变论域模糊控制方法。自组织结构算法可以调整变论域模糊系统结构以及动态获得模糊规则,进一步减小变论域模糊控制项的稳态逼近误差。通过进一步理论分析可知,自组织结构算法仅仅保证了系统瞬时的切换是平稳的,但不能保证系统的闭环稳定性。给出了所提出控制方法的适用条件。通过与固定模糊系统结构的变论域模糊控制比较,仿真结果表明,所提出控制方法不仅使得系统的稳态跟踪误差更平稳,而且使得输入控制信号更加平滑。     

Nonsingularity in second-order cone programming via the smoothing metric projector

Based on the differential properties of the smoothing metric projector onto the second-order cone,we prove that,for a locally optimal solution to a nonlinear second-order cone programming problem,the nonsingularity of the Clarke's generalized Jacobian of the smoothing Karush-Kuhn-Tucker system,constructed by the smoothing metric projector,is equivalent to the strong second-order sufficient condition and constraint nondegeneracy,which is in turn equivalent to the strong regularity of the Karush-Kuhn-Tucker p...     

基于奇异值分解的SGCMG操纵律分析

基于奇异值分解理论,对航天器姿态控制系统中使用的单框架控制力矩陀螺（SGCMG）的操纵律进行了分析和比较研究．借助于奇异值分解方法,分析了各种操纵律逃逸奇异的机理,重点分析了各种操纵律对陀螺构型奇异性、输出力矩误差的影响．通过仿真算例定量地分析与比较了各种操纵律的性能,所得结果可供工程设计人员参考．     

Nonexistence of self-similar singularities in the viscous magnetohydrodynamics with zero resistivity

We are concerned on the possibility of finite time singularity in a partially viscous magnetohydrodynamic equations in Rn, n=2,3, namely the MHD with positive viscosity and zero resistivity. In the special case of zero magnetic field the system reduces to the Navier-Stokes equations in Rn. In this paper we exclude the scenario of finite time singularity in the form of self-similarity, under suitable integrability conditions on the velocity and the magnetic field. We also prove the nonexistence of asymptotically self-similar singularity. This provides us information on the behavior of solutions near possible singularity of general type as described in Corollary 1.1.     

Nonsingularity of the difference and the sum of two idempotent matrices

Groß and Trenkler 1 pointed out that if a difference of idempotent matrices P and Q is nonsingular, then so is their sum, and Koliha et al2 expressed explicitly a condition, which combined with the nonsingularity of P+Q ensures the nonsingularity of P-Q. In the present paper, these results are strengthened by showing that the nonsingularity of P-Q is in fact equivalent to the nonsingularity of any combination aP+bQ-cPQ (where a≠0,b≠0,a+b=c), and the nonsingularity of P+Q is equivalent to the nonsingularity of any combination aP+bQ-cPQ (where a≠0,b≠0,a+b≠c).     

On the splash singularity for the free-surface of a Navier–Stokes fluid

In fluid dynamics, an interface splash singularity occurs when a locally smooth interface self-intersects in finite time. We prove that for d-dimensional flows, $d=2$ or 3, the free-surface of a viscous water wave, modeled by the incompressible Navier–Stokes equations with moving free-boundary, has a finite-time splash singularity for a large class of specially prepared initial data. In particular, we prove that given a sufficiently smooth initial boundary (which is close to self-intersection) and a divergence-free velocity field designed to push the boundary towards self-intersection, the interface will indeed self-intersect in finite time.     

On the Milnor Number of an Equivariant Singularity

Mathematical Notes -     

一类逻辑环站点双态转移的研究

本对于容量有限和具有优先队列的逻辑环随机运作系统,研究其站点双态转移的有关问题,转移规律的探讨,零转移和非零转移的判断及其数目函数的推导;中还提出若干相关的新概念。章有别于以往寻求传统的工作特性参数表达式的思路,从另一个侧面揭示该类系统的数学特征。     

含有约束的两个状态变量系统的转迁集计算

周期解的分岔广泛存在于实际的非线性动力学系统中．该文对两个状态变量系统的约束分岔进行了讨论．在约束条件下系统将产生新的转迁集．此外,以一个二维系统为例,对含有约束条件和不含有约束条件的分岔特性进行了比较．所得的结果可以为系统的设计和参数选择提供理论依据．     

Saddlepoint Approximation for the Distribution Function Near the Mean

We repair numerical difficulties in applying saddlepoint tail probability approximations when the ordinate at which the approximation is evaluated is near the mean of the distribution approximated. These modifications apply to double saddlepoint approximations to conditional distributions as well.     

Structuring the Universe of Universal Logic

How, why and what for we should combine logics is perfectly well explained in a number of works concerning this issue. But the interesting question seems to be the nature and the structure of the general universe of possible combinations of logical systems. Adopting the point of view of universal logic in the paper the categorical constructions are introduced which along with the coproducts underlying the fibring of logics describe the inner structure of the category of logical systems. It is shown that categorically the universe of universal logic turns out to be a topos and a paraconsistent complement topos. This work was supported by Russian Foundation for Humanities via the Project ”The structure of Universal Logics”, grant No 06-03-00195a.     

A note on noncommutative moment problems

Noncommutative moment problems for C*-algebras are studied. We generalize a result of Hadwin on tracial states to nontracial case. Our results are applied to obtain simple solutions to moment problems on the square and the circle as well as extend the positive unital functionals from a (discrete) complex group algebra to states on the group C*-algebra.     

Decomposition of Marsden–Weinstein Reductions for Representations of Quivers

We decompose the Marsden–Weinstein reductions for the moment map associated to representations of a quiver. The decomposition involves symmetric products of deformations of Kleinian singularities, as well as other terms. As a corollary we deduce that the Marsden–Weinstein reductions are irreducible varieties.     

Fundamental domains in Lorentzian geometry

We consider a discrete subgroup Γ of the simply connected Lie group of finite level, i.e. the subgroup intersects the centre of in a subgroup of finite index, this index is called the level of the group. The Killing form induces a Lorentzian metric of constant curvature on the Lie group . The discrete subgroup Γ acts on by left translations. We describe the Lorentz space form by constructing a fundamental domain F for Γ. We want F to be a polyhedron with totally geodesic faces. We construct such F for all Γ satisfying the following condition: The image of Γ in PSU(1,1) has a fixed point u in the unit disk of order larger than the index of Γ. The construction depends on the group Γ and on the orbit Γ(u) of the fixed point u.      

On Higher-Order Differential Operators with Singularity inside the Interval

Mathematical Notes -     

Analysis of the stress singularity for a bi-material V-notch by the boundary element method

A new algorithm coupling the boundary element technique with the characteristic expansion method is proposed for the computation of the singular stress field in the V-notched bi-material structure. After the stress asymptotic expansions are introduced into the linear elasticity equilibrium equations, the governing equations at the small sector dug out from the bi-material V-notch tip region are transformed into the ordinary differential eigen-equations. All the parameters in the asymptotic expansions except the combination coefficients can be achieved by solving the established eigen-equations with the interpolating matrix method. Furthermore, the conventional boundary element method is applied to modeling the remaining structure without the notch tip region. The combination coefficients in the asymptotic expansion forms can be computed by the discretized boundary integral equations. Thus, the singular stress field at the V-notch tip and the generalized stress intensity factors of the bi-material notch are successfully calculated. The accurate singular stress field obtained here is very useful in the evaluation of the fracture property and the fatigue life of the V-notched bi-material structure.