Rigidity Theorem for Degenerated Singular Points of Germs of Holomorphic Vector Fields in the Complex Plane

We consider the class _n of germs of holomorphic vector fields in ( , 0) with vanishing (n – 1)-jet at zero. We prove that the formal equivalence of two generic germs in _n implies their analytic equivalence. This result is analogous to the one obtained in [16] for the case of orbital analytic equivalence.     

A Complete Classification for Pairs of Real Analytic Curves in the Complex Plane with Tangential Intersection

We study the group structure of centralizers of a holomorphic mapping that is tangent to the identity. We give a complete classification for pairs of real analytic curves intersecting tangentially via the Ecalle—Voronin theory. We also classify pairs of one-dimensional holomorphic involutions that have a high-order tangency, real analytic mappings on the real line, and exceptional non-Abelian subgroups of Cerveau and Moussu. Consequently, we prove the existence of holomorphic mappings z z + O(2) that are reversible by a formal antiholomorphic mapping, but not by any (convergent) antiholomorphic one. We also prove the existence of local real analytic mappings on the real line that are not equivalent with respect to any local real analytic diffeomorphism and yet whose complexifications are holomorphically equivalent.2000 Mathematics Subject Classification. 30C35, 32B10.Research of the second author was partially supported by the NSF grant DMS-0305474.     

Twin Vector Fields and Independence of Spectra for Quadratic Vector Fields

The object of this paper is to address the following question: when is a polynomial vector field on \(\mathbb {C}^{2}\) completely determined (up to affine equivalence) by the spectra of its singularities? We will see that for quadratic vector fields, this is not the case: given a generic quadratic vector field there is, up to affine equivalence, exactly one other vector field which has the same spectra of singularities. Let us say that two distinct vector fields are twin vector fields if they have the same singular locus and the same spectrum at each singularity. Our main result is as follows: any two generic quadratic vector fields with the same spectra of singularities (yet possibly different singular locus) can be transformed by suitable affine maps to be either the same vector field or a pair of twin vector fields. Moreover, a generic quadratic vector field has exactly one twin vector field. We later analyze the case of quadratic Hamiltonian vector fields in more detail and find necessary and sufficient conditions for a collection of non-zero complex numbers to arise as the spectra of singularities of a quadratic Hamiltonian vector field. Lastly, we show that a generic quadratic vector field is completely determined (up to affine equivalence) by the spectra of its singularities together with the characteristic numbers of its singular points at infinity.     

Nonoscillating Projections for Trajectories of Vector Fields

The properties of oscillation for trajectories of three-dimensional vector fields are “visible” in the sense that they can be detected by means of plane projections. We also recover a three-dimensional version of the classical dichotomy “nonoscillation” versus “spiralling” for plane vector fields.      

On First Integrals for Holomorphic Vector Fields

It is proven that a generic vector field in \(\mathbb {C}^{3}\) having a formal first integral or non-enumerable many invariant hypersurfaces and closed leaves off the singularity has a holomorphic first integral.     

Groups of Germs of Analytic Diffeomorphisms in (C2, 0)

Let G be a group of germs of analytic diffeomorphisms in (C², 0). We find some remarkable properties supposing that G is finite, linearizable, abelian, nilpotent, and solvable. In particular, if the group is abelian and has a generic dicritic diffeomorphisms, then the group is a subgroup of a 1-parametric group. In addition, we study the topological behavior of the orbits of a dicritic diffeomorphisms. Last, we find some invariants in order to know when two diffeomorphisms are formally conjugate.     

Analytical Classification of Singular Saddle-Node Vector Fields

We consider the set Z_SNof germs of holomorphic saddlenode (or degenerate resonant) vector fields at the origin of C²and study the local analytical classi.cation, i.e., describing the set of orbits of Diiff(C², 0) acting by change of coordinates on Z_SN. J. Martinet and J.-P. Ramis studied this classi.cation problem in the case of the underlying foliation, leading to functional invariants. When two vector fields induce the same foliation, we show that conjugating them is equivalent to solving some homological equation associated with one of these vector fields. Therefore, we can read the existence of such a change of coordinates in some integrals along asymptotic cycles of the foliation, providing a complete set of functional invariants in addition to Martinet—Ramis invariants.     

Topological Equivalence of Dicritical Holomorphic Vector Fields

In this paper we study the topological equivalence between holomorphic vector fields with dicritical isolated singularity and without singularities at the divisor.     

Limit Cycles for Multidimensional Vector Fields. The Elliptic Case

We consider polynomial vector fields of the form and their polynomial perturbations of degree n. We present a sufficient condition that the perturbed system has an invariant surface close to the plane z = 0. We study limit cycles which appear on this surface. The linearized condition for limit cycles, bifurcating from the curves y ² – x ³ + 3x = h, leads to a certain 2- dimensional integral (which generalizes the elliptic integrals). We show that this integral has a representation R ₁(h)I ₁ + + R _e(h)I _e, where R _j (h) are rational functions with degrees of numerators and denominators bounded by O(n). In the case of constant and one-dimensional matrix A(x,y) we estimate the number of zeros of the integral by const n.     

Accurate Computation of Axisymmetric Vector Potential Fields with the Finite Element Method

A highly efficient formulation is described for implementing the finite element method for axisymmetric vector field analysis. The method was tested to investigate its full potential for the solution of steady-state and transient electromagnetic fields before application to specific problems. Computational tests show that the method requires comparable computing time to the equivalent Cartesian coordinate problem. The results of some numerical examples are presented including problems with different time-dependent source vectors. Results obtained are compared, where possible, against analytical solutions, as well as experimental results. An error analysis confirms that the accuracy is very good even for elements placed near the axis. Hence the singularity problem is effectively removed, as expected.     

用当量叶栅求解亚音速可压缩平面叶栅流场的边界元法

本文把物理平面内的亚音速可压缩流平面叶栅变换为计算平面内的不可压缩流当量叶栅,再用边界元法进行计算,得到了良好的结果。     

Normalizability, Synchronicity, and Relative Exactness for Vector Fields in C2

In this paper, we study the necessary and su.cient condition under which an orbitally normalizable vector field of saddle or saddle-node type in C²is analytically conjugate to its formal normal form (i.e., normalizable) by a transformation fixing the leaves of the foliation locally.First, we express this condition in terms of the relative exactness of a certain 1-form derived from comparing the time-form of the vector field with the time-form of the normal form. Then we show that this condition is equivalent to a synchronicity condition: the vanishing of the integral of this 1-form along certain asymptotic cycles de.ned by the vector field. This can be seen as a generalization of the classical Poincaré theorem saying that a center is isochronous (i.e., synchronous to the linear center) if and only if it is linearizable.The results, in fact, allow us in many cases to compare any two vector fields which differ by a multiplicative factor. In these cases we show that the two vector fields are analytically conjugate by a transformation fixing the leaves of the foliation locally if and only if their time-forms are synchronous.     

提高微型汽车白车身扭转刚度的研究

采用有限元法研究了某种微型汽车白车身的扭转刚度。采用3节点和4节点空间板壳单元离散整个白车身,建立了有限元模型,通过有限元分析,找出了对白车身扭转刚度影响显著的部位,提出了提高扭转刚度的最佳方案。     

Analytic solution for the non-linear drying problem

Recently, Landman, Pel and Kaasschieter proposed an analytic solution for a non-linear drying problem using a quasi-steady state solution. This analytic model for drying is explained here. An important consequence of this model is that the drying front has a constant speed when it is entering the material. This is also observed in experiments. On the basis of this constant drying front speed comparisons are made between the analytic model and numerical simulations. Finally comparisons are made between measured moisture profiles during drying and the analytic model.     

行星齿轮啮合刚度对其振动特性的影响

建立了单级直齿行星齿轮传动多自由度数学模型。在该系统中,根据行星齿轮固有频率和振动模态的特点,指导了特征值对于啮合刚度的敏感度公式及其与啮合应变能之间的关系式。分析结果表明,啮合刚度对两个旋转模态、两组位移模态和两个行星模态的固有特性影响较大;根据啮合应变能分布,可以清楚地了解啮合刚度变化对于系统固有特性的影响。     

Nonlinear Vector Potential Formulation and Experimental Verification of Newton-Raphson Solution of Three Dimensional Magnetostatic Fields in Electrical Devices

An iterative technique, based on magnetic vector potential formulation and the Newton-Raphson method, for the determination of the three dimensional magnetostatic field distributions in electrical devices is given. The proper degrees of magnetic saturation in the various materials within a given volume under consideration are obtained by repeated evaluation of the reluctivities in that volume, using a cubic spline representation of the B-H magnetization characteristics of composite materials (laminations). The formulation has been applied to a practical example of determining the field in and around a shell type 1.5 kva single phase transformer. The convergence and implementation characteristics of the developed method are given in this paper which show a saving of about 34% in CPU solution time in comparison with previously published methods. Experimental verification is given in terms of a comparison between computed and experimentally obtained values of flux densities surrounding the transformer core and winding, under heavily saturated conditions. Excellent agreement between test and calculated flux densities was achieved. This method is thus quite applicable to the solution of a wide class of three dimensional magnetostatic field problems associated with electrical apparatus.     

Normal Forms of Germs of Contact Sub-Lorentzian Structures on R3. Differentiability of the Sub-Lorentzian Distance Function

The aim of this paper is to construct certain normal forms for germs of contract sub-Lorentzian metrics in R³. Using them we show that there are regions in which longest curves are necessarily timelike, and where the local sub-Lorentzian distance function is smooth. By the way, we compute the null conjugate locus of a point.     

基于支持向量回归算法的汽轮机热耗率模型

利用支持向量回归算法,建立了汽轮机热耗率计算模型.介绍了支持向量回归算法的原理,对算法中的参数选择进行了探讨.对某300MW机组汽轮机热耗率计算进行了建模,并与RBF神经网络回归模型进行了比较.结果表明:基于支持向量回归算法的模型具有较强的泛化能力,适于在线应用.通过对输入参数添加随机扰动量分析表明,该模型比传统计算模型具有更好的稳定性,能更准确地计算汽轮机热耗率.     

锅炉钢构架中梁柱刚性接点设计的几点探讨

目前锅炉钢构架中梁柱的刚性连接形式大部分采用梁腹板以螺栓连接,梁翼缘板采用全焊透的形式连接与柱的传统的连接形式,本文以H型钢为研究对象,通过对这种传统的梁柱连接及其它共四种不同的连接形式进行非线性有限元分析,研究其分析结果,总结规律,从而提出了新的梁柱刚性连接节点的设计思想,即在梁柱连接区梁端采取扩大翼缘板宽度,同时柱端增加加强筋,这样就避免了在连接焊缝区域产生应力集中的现象,使因应力过大而产生的塑性铰远离连接区,从而大大提高了节点的承载性能。这一思想值得其他从事锅炉刚构架的设计人员参考应用和推广。