R3中一类四次可逆系统的周期轨与极限环问题

本文研究了R3中一类四次可逆系统及其扰动系统的周期轨与极限环问题,利用Poincáre紧化理论讨论了相关平面系统的定性性质,证明了所考虑的系统存在无穷多对称周期轨的结论.然后借助一系列技巧性变换,并利用平均方法证明了R3中这类四次可逆系统的扰动系统在其某周期轨邻域至少存在两个具有不同稳定性的极限环的结论.     

基础R0-代数与基础L*系统

研究了王国俊教授建立的模糊命题演算的形式演绎系统L^*和与之在语义上相匹配的R0-代数，以及：Petr Hajek建立的模糊命题演算系统BL和BL-代数，提出了基础R0-代数和基础L^*系统的观点，讨论了基础L^*代数与BL代数，基础L^*系统与BL系统之间．的相互关系及相对独立性，讨论了基础L^*系统关于基础风一代数的完备性问题，证明了MV-代数是特殊的基础R0-代数，指出了Lukasiewicz模糊命题演算系统是基础L^*系统的扩张，最后作为基础R0-代数与基础L^*系统的一个应用，证明了L^*系统关于语义Ωw的完备性，并在将模糊命题演算系统中的推演证明转化为相应逻辑代数中的代数运算方面作了一些尝试．     

Orbits of Curves on Certain K3 Surfaces

In this paper, we study the family of algebraic K3 surfaces generated by the smooth intersection of a (1, 1) form and a (2, 2) form in defined over and with Picard number 3. We describe the group of automorphisms on V. For an ample divisor D and an arbitrary curve C ₀ on V, we investigate the asymptotic behavior of the quantity . We show that the limit

Orbits of Lagrangian Subalgebras of the Double sl(2, R)

We describe the variety of Lagrangian subalgebras of the Drinfeld double for an arbitrary bialgebra structure on sl(2, R). We determine the irreducible components and the orbit structure under the natural action of the group SL(2, R)     

On Closed Orbits of Morse-Smale Flows on 3-Manifolds

Any link in a 3-manifold is the closed orbits of a non-singularMorse-Smale flow after taking the split sum with the unlinkand the connected sum with S² x S¹s. Current address: Department of Mathematics, University of Toronto,Toronto, Ontario M5S 1A1, Canada     

Orbits of points on certain K3 surfaces

In this paper we show that, for a K3 surface within a certain class of surfaces and over a number field, the orbit of a point under the group of automorphisms is either finite or its exponent of growth is exactly the Hausdorff dimension of a fractal associated to the ample cone. In particular, the exponent depends on the geometry of the surface and not its arithmetic. For surfaces in this class, the exponent is 0.6527±0.0012.     

Orbits in symmetric spaces

We characterize those elements in fully symmetric spaces on the interval (0,1) or on the semi-axis (0,∞) whose orbits are the norm-closed convex hull of their extreme points.     

Orbits in max-min algebra

Properties of orbits in max-min algebra are described, mainly the properties of periodic orbits. An O(n³) algorithm computing the period of a periodic orbit is presented. As a consequence, an O(n³ log n) algorithm computing the period of arbitrary orbit is obtained, as the pre-periodic part of the orbit has length at most (n − 1)² + 1.     

R~3中一类Kolmogorov系统的空间周期解

本文对一类具有相同增长率的三种群广义的Ｋｏｌｍｏｇｏｒｏｖ系统的空间周期解 存在条件进行研究,得到存在非常数空间周期解的判定条件．     

3-Sasakian Geometry, Nilpotent Orbits, and Exceptional Quotients

Using 3-Sasakian reduction techniques we obtain infinite familiesof new 3-Sasakian manifolds M (p ₁,p ₂, p ₃) andM (p ₁,p ₂, p ₃, p ₄) in dimension 11 and 15 respectively. The metric cone on (p ₁,p ₂, p ₃) is a generalization ofthe Kronheimer hyperkähler metric on the regular maximalnilpotent orbit of sl (3, C)whereas the cone on M (p ₁,p ₂, p ₃, p ₄)generalizes the hyperkähler metric onthe 16-dimensional orbit of so(6, C).These are the first examples of 3-Sasakian metrics which are neither homogeneous nor toric. In addition we consider some further U(1)-reductions of M(p ₁,p ₂, p ₃).These yield examples of nontoric 3-Sasakian orbifold metrics in dimensions 7. As a result we obtain explicit families O() of compact self-dual positivescalar curvature Einstein metrics with orbifoldsingularities and with only one Killing vector field.     

16种基础R0-代数结构的相对独立公理系统

在对R0-代数和基础R0-代数结构研究的基础上,讨论了基础R0-代数结构与并(交)半格及有界并(交)半格上的等价性命题系统,进而证明了16种基础R0-代数公理系统的相对独立性,同时指出了相应R0-代数结构的公理系统的相对独立性.     

Orbits in finite incidence structures

Geometriae Dedicata -     

Orbits of subsystem stabilizers

Let Φ be a reduced irreducible root system. We consider pairs (S, X (S)), where S is a closed set of roots, X(S) is its stabilizer in the Weyl group W(Φ). We are interested in such pairs maximal with respect to the following order: (S₁, X (S₁)) ≤ (S₂, X (S₂)) if S₁ ⊆ S₂ and X(S₁) ≤ X(S₂). The main theorem asserts that if Δ is a root subsystem such that (Δ, X (Δ)) is maximal with respect to the above order, then X (Δ) acts transitively both on the long and short roots in Φ \ Δ. This result is a wide generalization of the transitivity of the Weyl group on roots of a given length. Bibliography: 23 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 338, 2006, pp. 98–124.     

Orbits of Nilpotent Matrices

The action under conjugation of invertible lower triangular n×n matrices (over an infinite field) on lower triangular nilpotent matrices, N_n, divides N_n into orbits. We show that for n?6 the number of orbits is infinite.     

The Numbers of Permutation Groups Orbits and of the Wreath Product Orbits

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Geometric Separation in $$mathbb {R}^3$$ R 3

Journal of Fourier Analysis and Applications - The geometric separation problem, initially posed by Donoho and Kutyniok (Commun Pure Appl Math 66:1–47, 2013), aims to separate a distribution...     

Bi-Invariant Domains in Semisimple Groups: Nonprincipal Orbits and Boundaries

Let G be a complex semisimple group with real form G . For the action of G × G on G by left and right translation, we define and study an orbit-type stratification of G. In particular, we compute the dimension of an arbitrary stratum; we identify certain strata of low codimension in G, the union of whose closures contains every nonprincipal stratum; and we describe the boundaries and adjacency relations of the maximal connected domains in G that contain only principal orbits.