整(0,m_1,…,m_q)插值的逼近性质

关于整（0，m1，…，mq）插值的可解性条件已由刘永平给出，本文给出此插值算子在LP（IR）空间（1≤p＜＋∞）的饱和阶和饱和类。     

（0,m1,…,mq）缺项整插值算子在Besov空间中的逼近

本文研究了在Besov空间中，（0,m1，…,mq）整插值算子的逼近和饱和问题，确定了逼近的饱和类与饱和阶。     

2-周期整(m1,…,mp;m1′,…,mq′)插值的逼近性质

研究了一类等距结点上的2-周期整(m1,…,mp;m1′,…,mq′)插值算子的逼近性质,通过引入辅助算子得到了该插值算子在Lp(R)(1≤p＜∞)空间的饱和阶与饱和类.     

(0,m_1,…,m_q)缺项整插值算子在Besov空间中的逼近

本文研究了在Besov空间中 ,(0 ,m1,… ,mq)整插值算子的逼近和饱和问题 ,确定了逼近的饱和类与饱和阶     

一类指数型整函数插值算子的逼近性质(2)

本文研究了一类指数型整函数插值算子在C（R）和Lp(1≤p≤∞）空间上的饱和性质。     

一个双周期整(0,Δ_h~m)插值问题

本文研究等距结点上双周期整（０,Δｍｈ ）插值问题,得到它在 Ｂ２σ中有唯一解的充要条件,给出了这种插值函数的精确表达式,同时也考虑了该插值算子的收敛性     

某些修正有理插值在L_w~p空间的逼近(英文)

本文拓广了T．Herman和P．Vertes研究的有理插值，引入某些修正的有理插值，并给出它们在Lpw空间的逼近阶，其中W（x）＝（1-x2）1/2．     

(O,ml,…,mq)缺项整插值算子在Besov空间中的逼近

本文研究了在Besov空间中,(0,ml,…,mq)整插值算子的逼近和饱和问题,确定了逼近的饱和类与饱和阶.     

高次样条循环插值的收敛阶

样条函数的Hermite-Birkhoff插值是一类相当广泛的插值类型。循环插值是稍加限制的H-B插值。我们首先讨论了奇次插值样条的正则性问题,然后讨论了循环插值的收敛性问题,给出了循环插值样条逼近达到饱和阶的充分条件。     

基于xL（a）n－1（x）之零点的（0，1，…，m－2，m）插值

本文给出了基于xL^（a）_n－1（x）之零点的（０，１，…，ｍ－２，ｍ）插值的正则性的充要条件，其中xL^（a）_n－1（x）为（ｎ－１）次Ｌａｇｕｅｒｒｅ多项式。同时基函数（若存在的话）的明显表达式也在文中给出。再者，还证明了，若该插值问题有无穷多个解，则其解的一般形式为ｆ₀（ｘ）＋Ｃｆ₁（ｘ）这里Ｃ为任意常数。     

Differential-geometric Newton method for the best rank-(R1, R2, R3) approximation of tensors

An increasing number of applications are based on the manipulation of higher-order tensors. In this paper, we derive a differential-geometric Newton method for computing the best rank-(R ₁, R ₂, R ₃) approximation of a third-order tensor. The generalization to tensors of order higher than three is straightforward. We illustrate the fast quadratic convergence of the algorithm in a neighborhood of the solution and compare it with the known higher-order orthogonal iteration (De Lathauwer et al., SIAM J Matrix Anal Appl 21(4):1324–1342, 2000). This kind of algorithms are useful for many problems. This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with its authors. Research supported by: (1) Research Council K.U.Leuven: GOA-Ambiorics, CoE EF/05/006 Optimization in Engineering (OPTEC), (2) F.W.O.: (a) project G.0321.06, (b) Research Communities ICCoS, ANMMM and MLDM, (3) the Belgian Federal Science Policy Office: IUAP P6/04 (DYSCO, “Dynamical systems, control and optimization”, 2007–2011), (4) EU: ERNSI. M. Ishteva is supported by a K.U.Leuven doctoral scholarship (OE/06/25, OE/07/17, OE/08/007), L. De Lathauwer is supported by “Impulsfinanciering Campus Kortrijk (2007–2012)(CIF1)” and STRT1/08/023.     

A combinatorial interpretation of the recurrence fn+1 = 6fn − fn−1

Bonin et al. (1993) recalled an open problem related to the recurrence relation verified by NSW numbers. The recurrence relation is the following: f_n+1 = 6f_n − f_n−1, with f₁ = 1 and f₂ = 7, and no combinatorial interpretation seems to be known. In this note, we define a regular language L whose number of words having length n is equal to f_n+1. Then, by using L we give a direct combinatorial proof of the recurrence.     

Irreducible characters with equal roots in the groups Sn and An

We show that treating of (non-trivial) pairs of irreducible characters of the group S_n sharing the same set of roots on one of the sets A_n and S_n \ A_n is divided into three parts. This, in particular, implies that any pair of such characters χ^α and χ^β (α and β are respective partitions of a number n) possesses the following property: lengths d(α) and d(β) of principal diagonals of Young diagrams for α and β differ by at most 1. Supported by RFBR grant No. 04-01-00463 and by RFBR-NSFC grant No. 05-01-39000. __________ Translated from Algebra i Logika, Vol. 46, No. 1, pp. 3–25, January–February, 2007.     

When isf(x1, x2, ..., xn) =u1(x1) +u2(x2) + ... +un(xn)?

We discuss subsetsS of ℝⁿ such that every real valued functionf onS is of the formf(x₁, x₂, ..., x_n) =u ₁(x₁) +u ₂(x₂) +...+u _n(x_n), and the related concepts and situations in analysis.     

On K1 and K2 of Algebraic Surfaces

In this paper we study higher Chow groups of smooth, projective surfaces over a field k of characteristic zero, using some new Hodge theoretic methods which we develop for this purpose. In particular we investigate the subgroup of CH ^r+1 (X,r) with r = 1,2 consisting of cycles that are supported over a normal crossing divisor Z on X. In this case, the Hodge theory of the complement forms an interesting variation of mixed Hodge structures in any geometric deformation of the situation. Our main result is a structure theorem in the case where X is a very general hypersurface of degree d in projective 3-space for d sufficiently large and Z is a union of very general hypersurface sections of X. In this case we show that the subgroup of CH ^r+1 (X,r) we consider is generated by obvious cycles only arising from rational functions on X with poles along Z. This can be seen as a generalization of the Noether–Lefschetz theorem for r = 0. In the case r = 1 there is a similar generalization by Müller-Stach, but our result is more precise than it, since it is geometric and not only cohomological. The case r = 2 is entirely new and original in this paper. For small d, we construct some explicit examples for r = 1 and 2 where the corresponding higher Chow groups are indecomposable, i.e. not the image of certain products of lower order groups. In an appendix Alberto Collino constructs even more indecomposable examples in CH ³ (X,2) which move in a one-dimensional family on the surface X.Contribution to appendix.     

ON DEGENERATE WEAKLY （K1, K2）-QUASIREGULAR MAPPINGS

The authors first give the definition of degenerate weakly （K1,K2）-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a useful inequality is obtained, which can be used to derive the self-improving regularity.     

(F_1,F_2)-攀援集的一些注记

研究(F_1,F_2)-攀援集的迭代不变性.定义了与正整数k相关的Furstenberg族的性质P(k)和Q(k).指出:对任意介于0,1之间的实数s而言,Furstenberg族M(s)具有性质P(k)和Q(k),其中■(s)表示非负整数集的所有上密度不小于s的无限子集构成的集族.据此证明了:对任意正整数k,S为系统(X,f)的(■(s),■(t))-攀援集当且仅当S为系统(X,f~k)的(■(s),■(t))-攀援集,其中s,t是介于0,1之间的任意给定的实数.     

K2 and K3 of the circle

Let k be $\text{Z}\text{[}\text{1}\text{2}\text{]}$, $\text{Q}$ or $\text{R}$, and set $\text{A =}\text{k[x,y]}\text{(x}{}^2\text{+ y}{}^2\text{? 1)}$. We compute K₂(A) and K₃(A). Our method is to construct a map $\text{? : K}{}_1\text{(k[i])→K}{}_{\mathrm{1\; +\; 1}}\text{(A)}$ and compare this to a localization sequence.We give three applications. We show that ? accounts for the primitive elements in K₂(A), and compare our results to computations of Bloch [1] for group schemes. Secondly, we consider the problem of basepoint independence, and indicate the interplay of geometry upon the K-theory of affine schemes obtained by glueing points of Spec(A). Third, we can iterate the construction to compute the K-theory of the torus ring A ?_kA.     

行列式detVn-(x1,...,xn)的准确值及其应用

本文给出行列式Ｖ_n^-(x₁,...,x_n)的准确值，它是通常的Ｖａｎｄｅｒｍｏｄｅ行列式计算公式的推广，以及它在理论上的一些重要应用．