Hirzebruch–Milnor classes of complete intersections

We prove a new formula for the Hirzebruch–Milnor classes of global complete intersections with arbitrary singularities describing the difference between the Hirzebruch classes and the virtual ones. This generalizes a formula for the Chern–Milnor classes in the hypersurface case that was conjectured by S. Yokura and was proved by A. Parusiński and P. Pragacz. It also generalizes a formula of J. Seade and T. Suwa for the Chern–Milnor classes of complete intersections with isolated singularities.     

Monodromies and poincaré series of quasihomogeneous complete intersections

We give a formula connecting the Saito duals of the reduced zeta functions of the monodromies of defining equations of a quasihomogeneous complete intersection, the Poincaré series of its coordinate ring, and orbit invariants with respect to the natural ℂ*-action. The authors were partially supported by the DFG-programme ”Global methods in complex geometry” (Eb 102/4-2), grants RFBR-04-01-00762, INTAS-00-259, NWO-RFBR-047.008.005.     

Existence of the Kähler-Einstein metric on certain Fano complete intersections

For certain families of Fano complete intersections we prove an estimate from below for the global (log) canonical threshold, which implies the existence of Kähler-Einstein metric on generic varieties in these families.     

Decomposition of small diagonals and Chow rings of hypersurfaces and Calabi–Yau complete intersections

On the one hand, for a general Calabi–Yau complete intersection X$X$, we establish a decomposition, up to rational equivalence, of the small diagonal in X×X×X$X\times X\times X$, from which we deduce that any decomposable 0-cycle of degree 0 is in fact rationally equivalent to 0, up to torsion. On the other hand, we find a similar decomposition of the smallest diagonal in a higher power of a hypersurface, which provides us an analogous result on the multiplicative structure of its Chow ring.     

On the computation of the Galois group over the quotient field of ℂ[λ]

Summary We give an algorithm for the computation of the Galois group of the splitting field of polynomials in two variables with integer coefficients over the quotient field (), (the rational functions in ). The algorithm uses a constructive version of the Newton polygon method and analytic continuations.Supported in part by the Fonds National Suisse     

Factoriality of complete intersections in ℙ<Superscript>5</Superscript>

Let X be a complete intersection of two hypersurfaces F _n and F _k in ℙ⁵ of degree n and k, respectively, with n ≥ k, such that the singularities of X are nodal and F _k is smooth. We prove that if the threefold X has at most (n + k − 2)(n − 1) − 1 singular points, then it is factorial.     

环Z[X]不是中华环

设R是具有单位元1的交换环;A是R中的理想而a,b则是R中的任意元.定义a≡b(A)若Ra+A=Rb+A.称环R是中华环若a≡b(A+B),则存在c∈R使c≡a(A)及c≡b(B).环是中华环的充要条件是由K.Aubert与A.Beck二人于1980年找出的.显然,整数环Z必是中华环.Aubert与Beck二人亦证明了Z[x,y]不是中华环.但他们二人无法证明Z[X]是否中华环.本文用不同的手法处理,证明了Z[X]不可能是中华环.同时,我们进一步证明,对任意代数数a,环Z[a]均是中华环.因此,Aubert与Beck在1980年所提出的问题,在本文中得到圆满的解答.     

类W-KKM(X,Y,Z),几乎不动点定理和不动点定理

引进了相对弱$R$-子集和类($W$-)KKM$(X,Y,Z)$的概念,给出了相对KKM映射与相对弱$R$-子集之间的等价关系以及$W$-KKM$(X,Y,Z)$的一个性质,然后给出了两个连续选择定理并得到不动点定理和重合点定理, 最后,在一致拓扑空间上得到具有弱-KKM性质的映射的几乎不动点,不动点和重合点的存在定理.     

“A=X Y Z”的故事

据说,一个爱说空话而不爱用功的年轻人,整天缠着大科学家爱因斯坦,要他们公开成功的秘诀,爱因斯坦同意了,写下了这个公式:A=X Y Z,爱因斯坦对这位年轻人解释道:“A代表成功,X代表艰苦的劳动,Y代表正确的方法,……”,“ Z代表什么呢?”年轻人迫切地追     

Multiplicities of Pfaffian intersections,and the Łojasiewicz inequality

An effective estimate for the local multiplicity of a complete intersection of complex algebraic and Pfaffian varieties is given, based on a local complex analog of the Rolle-Khovanskii theorem. The estimate is valid also for the properly defined multiplicity of a non-isolated intersection. It implies, in particular, effective estimates for the exponents of the polar curves, and the exponents in the ojasiewicz inequalities for Pfaffian functions. For the intersections defined by sparse polynomials, the multiplicities outside the coordinate hyperplanes can be estimated in terms of the number of non-zero monomials, independent of degrees of the monomials.     

Z＝X＋Y概率密度的拉氏变换解法

本根据拉氏变换的卷积性质，给出了某些情形下，随机变量Z＝X＋Y概率密度的一种简易的拉氏解法。     

Z=X+Y概率密度的拉氏变换解法

本文根据拉氏变换的卷积性质 ,给出了某些情形下 ,随机变量 Z=X+Y概率密度的一种简易的拉氏解法     

On the number of divisors which are values of a polynomial

Let τ(n) be the number of positive divisors of an integer n, and for a polynomial P(X)∈ℤ[X], let

微分方程X=Q（X,Y）,Y=P（X）的极限环的存在性

ФИЛИППОВ在文（１）中，利用变换Ｌｉｅｎａｒｄ方程ｄｘ／ｄｙ＝ｙ－Ｆ（ｘ），ｄｙ／ｄｔ＝－ｇ（ｘ）在左右两平面上的轨线新方程在右半平面内的积分线的方法，得到了在一定条件下，方程（１）存在极限环的结论，本文应用文（１）的方法，对类型更为广泛的方程ｄｘ／ｄｙ＝Ｑ（ｘ，ｙ），ｄｙ／ｄｔ＝Ｐ（ｘ）进行了探讨，得到了（２）存在稳定极限环的充分条件。     

On the Bifurcations of a Hamiltonian Having Three Homoclinic Loops under Z3 Invariant Quintic Perturbations

A cubic system having three homoclinic loops perturbed by Z3 invariant quintic polynomials is considered. By applying the qualitative method of differential equations and the numeric computing method, the Hopf bifurcation, homoclinic loop bifurcation and heteroclinic loop bifurcation of the above perturbed system are studied. It is found that the above system has at least 12 limit cycles and the distributions of limit cycles are also given.     

Differential structure of certainC(X) xα Z

In this paper, we show that, without involving theC*-bundle theory, elementary differential topology can do the classification of homogeneousC*-crossed productC(X) x Z, whereX is a compact differentiable manifold of low dimension and is a diffeomorphism ofX. The motivation of this work is the Shultz's theorem which states that aC*-algebra can be identified with its pure state space carryingw*-topology and certain geometric structure.     

Finite groups in which elements of the same order outside the center are conjugate

We prove that if G is a finite group in which the elements of the same order outside the center are conjugate,then either G is abelian or G(?)S_3.     

Cubature formulae which are exact on spacesP,intermediate betweenP k andQ k′

Summary In this paper we search, from the orthogonal polynomial theory, for conditions which allow to obtain cubature formulae on compacts of ⁿ , with weight function, and which are exact on the spaceR( _{k 1}, k₂, ..., k_n) of all polynomials of degree k _i respectively to each variablex _i , 1in.