弹性力学求解体系的研究

证明了弹性力学求解体系的微分形式与积分形式的等价关系,建立了统一求解体系构架.新体系包括微分形式、积分形式及混合形式.利用微分形式与积分形式的等价关系,导出了各种变分原理.提出了广义虚功方程和广义虚函数的概念.     

OnV-Killing forms in a locally conformal Kähler manifold with the parallel lee form

Summary We shall introduce a 1-form which is called V-Killing form in a locally conformal K?hler manifold with the parallel Lee form and prove that this form has similar properties of C-Killing form in a Sasakian manifold. We obtain that a V-harmonic form is invariant by a V-Killing form. Entrata in Redazione il 4 agosto 1978.     

Hypersurfaces with a parallel higher fundamental form

By a “higher fundamental form” of a hypersurface is understood a form obtained by inserting a power of the shape operator into the first fundamental form. The hypersurfaces in a Riemannian space form or in a three-dimensional Bianchi–Cartan–Vranceanu space for which the covariant derivative of a higher fundamental form vanishes are classified.     

Towards Characterization of All 3 × 3 Extremal Quasiconvex Quadratic Forms

Given a d × d quasiconvex quadratic form, d ≥ 3, we prove that if the determinant of its acoustic tensor is an irreducible extremal polynomial that is not identically zero, then the form itself is an extremal quasiconvex quadratic form; i.e., it loses its quasiconvexity whenever a convex quadratic form is subtracted from it. In the special case d=3, we slightly weaken the condition; namely we prove that if the determinant of the acoustic tensor of the quadratic form is an extremal polynomial that is not a perfect square, then the form itself is an extremal quadratic form. In the case d=3 we also prove that if the determinant of the acoustic tensor of the form is identically zero, then the form is either extremal or polyconvex. Also, if the determinant of the acoustic tensor of the form is a perfect square, then the form is either extremal or polycovex, or is a sum of a rank‐1 form and an extremal whose acoustic tensor determinant is identically zero. Here we use the notion of extremality introduced by Milton in 1990. © 2017 Wiley Periodicals, Inc.     

浅谈正定二次型的习题课设计

在高等代数的实二次型内容中,正定二次型占有特殊的地位.本文从概念的回顾、正定二次型与正定矩阵的判断、二次型正定及矩阵正定的性质、其它类型二次型四个方面来设计正定二次型的习题课,并通过具体例子说明例题、习题精选的原则.     

张拉结构初始几何形状确定的形函数方法

提出了一个确定张拉结构初始几何形状的形状函数.基于该形状函数,通过对结构边界控制点的插值确定张拉结构的初始形状.该结构形状可随结构的双向张力比和边界控制点的坐标而进行自动调整.从而给出了几何上可行,力学上合理的高精度张拉曲面.通过有限元方法检查,大量例子表明该方法确定的初始形状对于实际常用边界及双向等拉或不等拉张结构均十分理想,误差很小.     

双线性型图与交错型图不是完美图

本文证明了双线性型图与交错型图都不是完美图,从而解决了双线性型图与交错型图的完美图判别问题.     

A relation between perfect equilibria in extensive form games and proper equilibria in normal form games

The concept of quasi-perfect equilibria for games in extensive form is introduced. It is shown that a proper equilibrium of a normal form game induces a quasi-perfect equilibrium in every extensive form game having this normal form.     

A new transvectant algorithm for nilpotent normal forms

We offer an algorithm to determine the form of the normal form for a vector field with a nilpotent linear part, when the form of the normal form is known for each Jordan block of the linear part taken separately. The algorithm is based on the notion of transvectant, from classical invariant theory.     

Computation of normal forms of Hamiltonian systems in the presence of Poisson commuting integrals

The aim of this paper is to show the role of first integrals in further reducing the normal form unfolding of Hamiltonian systems. Based on a work by Cicogna and Gaeta, the joint normal form approach for Hamiltonian vector fields is considered. This normal form procedure, couched in a Lie-Poincaré scheme, allows us to see that we can reduce simultaneously the Hamiltonian together with its Poisson commuting integrals to a simplified normal form - a joint normal form - which is given a simple characterization. In this algorithmic procedure, approximate first integrals can be constructed (and used to simplify the normal form) at the same time that we bring the Hamiltonian to normal form. Further, following Walcher, we show that we can derive the joint normal form via a structure preserving transformation (in a sense to be specified). The approach is discussed from an implementational standpoint and illustrated by a Liouville-integrable Hénon-Heiles system. This revised version was published online in June 2006 with corrections to the Cover Date.     

Pseudo-normal form near saddle-center or saddle-focus equilibria

In this paper we introduce the pseudo-normal form, which generalizes the notion of normal form around an equilibrium. Its convergence is proved for a general analytic system in a neighborhood of a saddle-center or a saddle-focus equilibrium point. If the system is Hamiltonian or reversible, this pseudo-normal form coincides with the Birkhoff normal form, so we present a new proof in these celebrated cases. From the convergence of the pseudo-normal form for a general analytic system several dynamical consequences are derived, like the existence of local invariant objects.     

Cauchy and mathematical induction

The standard form of the principle of mathematical induction (PMI) is well known. Here we compare the standard form to the Cauchy's form of PMI. We present some results proved by the Cauchy's form of PMI. Finally we indicate the relation between the two forms of PMI and the well‐ordering principle.     

Synthesis of linear systems with desired equivalent form

A method for feedback synthesis of linear control systems with desired linearly equivalent form of the closed loop system matrix is proposed. The method is based on the serial canonical form of linear multivariable systems which is an alternative to the Luenberger canonical form. A stable computational algorithm for finding the serial canonical form using orthogonal similarity transformations is described. The algorithm for synthesis involves a simple recurrent procedure and gives the possibility to achieve any attainable equivalent form of the closed loop system. The results obtained are extended to the synthesis of reduced order state observers.     

洛必达法则及斯铎兹定理的一种简便证法

针对∞/∞型的洛必达法则、数列极限∞/∞型的斯铎兹定理以及函数极限0/0型和∞/∞型的斯铎兹定理,分别建立相应的引理,为证明这些定理提供一种新的思路.对这些定理的传统证明是一种改进和补充.     

牛顿(Newton)后向插指

利用牛顿后向插指算子将牛顿(Newton)插值推广到牛顿后向插指,并得到了牛顿后向插指算子与牛顿后向插值算子之间的关系.     

有强法式的体上矩阵

设D为除环,A∈Dn×n,则可用初等变换将λI-A化简为对角阵A= diag(1,…,1,φ1,…,φr),其中(?)i为D上首1多项式并且φ1|…|φr.如果这个对角阵A在形状上是唯一的,则称A是有强法式的矩阵.本文应用中心原子因子与初等因子给出了体上有强法式的矩阵的本质刻画,给出了体上矩阵有强法式的一些充要条件.     

A direct proof of theorem on generalized Jordan form of linear operators

The present paper gives a direct proof of the following result: for any linear operator over arbitrary field there exists a basis in which it has a polyquasicyclic matrix, i.e. a generalized Jordan form of second kind. The polyquasicyclic form of a linear operator is uniquely determined up to the order of direct summands on the diagonal, and it is shown that the generalized Jordan form of second kind is a link that connects the classical Jordan form and the rational canonical form.     

复空间形式中具有共形MASLOV形式的拉格朗日子流形的一些例子

该文从实空间形式到复空间形式拉格朗日等距浸入中找到了一些非平凡的具有共形Maslov形式的拉格朗日子流形.     

Quantum Birkhoff normal forms

We consider quantum analogues of several theorems on Birkhoff normal forms and prove a quantum analogue of the theorem on reducing a Hamiltonian to the normal form and the analogue of the theorem on reducing a Hamiltonian to the real normal form. We obtain the normal form explicitly in the nonresonant case. We consider the uniqueness problems of the normal form and of the normalizing transformation in the nonresonant and resonant cases.