Real Hypersurfaces Having Many Pseudo-hyperplanes

Abstract

Let nand dbe natural integers satisfying n ≥ 3 and d ≥ 10. Let Xbe an irreducible real hypersurface Xin ? ⁿ of degree dhaving many pseudo-hyperplanes. Suppose that Xis not a projective cone. We show that the arrangement ? of all d ? 2 pseudo-hyperplanes of Xis trivial, i.e., there is a real projective linear subspace Lof ? ⁿ (?) of dimension n ? 2 such that L ? Hfor all H ∈ ?. As a consequence, the normalization of Xis fibered over ?¹in quadrics. Both statements are in sharp contrast with the case n = 2; the first statement also shows that there is no Brusotti-type result for hypersurfaces in ? ⁿ , for n ≥ 3.     

Some properties of third order differential operators

Consider the third order differential operator L given by and the related linear differential equation L(x)(t) + x(t) = 0. We study the relations between L, its adjoint operator, the canonical representation of L, the operator obtained by a cyclic permutation of coefficients a _i , i = 1,2,3, in L and the relations between the corresponding equations.We give the commutative diagrams for such equations and show some applications (oscillation, property A).     

Stability properties of cycles and tori of a simplest nonresonant wave-type equation

For a number of meaningful examples, nonresonant wave-type equations are shown to be characterized by periodic dynamics. Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 744–750, November, 1997. Translated by O. V. Sipacheva     

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The asymptotic formulae for the third and fourth power moments of Fourier coefficients of cusp forms are proved in this paper.     

On an extreme class of real interpolation spaces

We investigate the limit class of interpolation spaces that comes up by the choice θ=0 in the definition of the real method. These spaces arise naturally interpolating by the J-method associated to the unit square. Their duals coincide with the other extreme spaces obtained by the choice θ=1. We also study the behavior of compact operators under these two extreme interpolation methods. Moreover, we establish some interpolation formulae for function spaces and for spaces of operators.     

Canonical form of a nonlinear monetary system

This paper addresses an autonomous system of quadratic ordinary differential equations, which describes a monetary system involving interest rate, investment demand and price index. The canonical form of this system is derived, which is dependent on a single parameter. On this basis, it is proved that this system is not smoothly equivalent to the generalized Lorenz canonical form.     

编序式问卷调查的模糊偏序排序法

讨论了现有的编序式问卷调查排序方法的不足之处;提出了基于模糊偏序关系的编序式问卷调查的排序方法,给出了模糊偏序排序法的数学模型,论证了用模糊偏序关系对编序式问卷调查进行排序是一种较好的方法;并用实例分析了模糊偏序排序法应用于编序式问卷调查的具体操作步骤.     

Complementarity properties of the Lyapunov transformation over symmetric cones

The well-known Lyapunov's theorem in matrix theory/continuous dynamical systems asserts that a square matrix A is positive stable if and only if there exists a positive definite matrix X such that AX +XA* is positive definite. In this paper, we extend this theorem to the setting of any Euclidean Jordan algebra V . Given any element a ∈ V , we consider the corresponding Lyapunov transformation La and show that the P and S-properties are both equivalent to a being positive. Then we characterize the R0 -property for La and show that La has the R0 -property if and only if a is invertible. Finally, we provide La with some characterizations of the E0 -property and the nondegeneracy property.     

靶流形为球面子流形的调和映射的量子化现象(英文)

本文研究了调和映射和极小子流形的量子化性质.通过运用谱分解方法,获得了靶流形为球面子流形的调和映射的量子化性质,然后将其应用到球面的极小子流形的高斯映射,得到了极小子流形的第二基本形式的量子化性子.     

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