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Realization of Frobenius manifolds as submanifolds in pseudo-Euclidean spaces
k-potential submanifolds partial differential equations pseudo-Euclidean spaces
2010/4/8
We introduce a class of k-potential submanifolds in pseudo-Euclidean spaces and prove that for an arbitrary positive integer k and an arbitrary nonnegative integer p, each N-dimensional Frobenius mani...
Analytical Determination of Fractal Structure in Stochastic Time Series
Fractal Structure Stochastic Time Series
2010/4/8
Current methods for determining whether a time series exhibits fractal structure (FS) rely on subjective assessments on estimators of the Hurst exponent (H). Here, I introduce the Bayesian Assessment ...
有理Bezier曲面的光滑拼接
有理曲面 Bezier三角曲面 曲面造型 几何连续性
2009/11/12
本文考虑有理Bezier曲面片的光滑拼接问题，培出了有理Bezier三角曲面片的一阶与二阶几何连续的简明条件。同l时还给出了有理Bezier三角曲面片与有理Bezier矩形曲面片的几何连续拼接算法．
Fractal Weyl law behavior in an open, chaotic Hamiltonian system
chaotic Hamiltonian system Fractal Weyl law
2010/4/8
We numerically show fractal Weyl law behavior in an open Hamiltonian system that is described by a smooth potential and which supports numerous above-barrier resonances. This behavior holds even relat...
The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann--Hilbert problems
multi-component 2D Toda hierarchy orthogonal polynomials Riemann--Hilbert problems
2010/4/7
We consider the relation of the multi-component 2D Toda hierarchy with matrix orthogonal and biorthogonal polynomials. The multi-graded Hankel reduction of this hierarchy is considered and the corresp...
由于传统的兴趣和多种原因,几何定理的机器证明在自动推理的研究中占有重要的地位.自吴法发表至今30年,几何定理机器证明的研究和实践有了很大的进展.对无序几何命题而言,代数方法、数值方法均能有效地判定其真假,面积法(消点法)、搜索法更能生成其可读的证明.几何不等式机器证明的研究,由于多项式完全判别系统的建立,也有了突破.研究领域已由机器证明扩展为包括几何作图在内的一般几何问题的机器求解,并有了实际的应...
二元插值的几何特征与插值结点平面构形
二元插值 插值结点组的几何特征 GCn集合亏量
2012/11/20
插值结点组的几何特征(GC)决定二元插值问题的解的存在性与唯一性.通过引入亏量的概念对满足GC5条件的集合进行讨论，得到了猜想在n=5时的几何平面构形.该构形确定的二元Lagrange公式最终表示成一次因子乘积的形式，进一步验证了该猜想的正确性.
Normal del Pezzo surfaces containing a nonrational singularity
Normal del Pezzo surfaces nonrational singularity
2010/10/29
Working over a perfect field, I classify normal del Pezzo surfaces with base number one that contain a nonrational singularity. They form a huge infinite hierarchy; contractions of ruled surfaces lie ...
Homogeneous Hypersurfaces with Isotropy in Affine Four-space
Homogeneous Hypersurfaces Affine Four-space
2010/10/29
We classify the non-degenerate homogeneous hypersurfaces in real and complex affine four-space whose symmetry group is at least four-dimensional.
Reflexive polyhedra, weights and toric Calabi-Yau fibrations
Reflexive polyhedra weights toric Calabi-Yau fibrations
2010/10/29
During the last years we have generated a large number of data related to Calabi-Yau hypersurfaces in toric varieties which can be described by reflexive polyhedra. We classified all reflexive polyhe...
Random unitaries in non-commutative tori, and an asymptotic model for q-circular systems
non-commutative tori asymptotic model q-circular systems
2010/10/29
We consider the concept of a q-circular system, which is a deformation of the circular system from free probability, taking place in the framework of the so-called 'q-commutation relations'. We show ...
We classify coproducts on matrix algebra in terms of solutions to some modification of pentagon equation. The construction of Baaj and Skandalis describing finite dimensional unitary solutions of pen...
The trace formula for transversally elliptic operators on Riemannian foliations
The trace formula transversally elliptic Riemannian foliations
2010/11/1
We prove a Duistermaat-Guillemin trace formula for transversally elliptic operators on a compact foliated manifold.
Hierarchy Structure of Graphs and Weighted Condensations
Hierarchy Structure Graphs Weighted Condensations
2010/11/1
By natural way the hierarchy structure is introduced on directed graphs with weighted adjacencies. Embedded system of algebras of subsets of the set of vertices of such digraph and it's consolidation...