Three-Convex Approximation by Free Knot Splines in C [0, 1]

A Jackson-type estimate is obtained for the approximation of 3 -convex functions by 3 -convex splines with free knots. The order of approximation is the same as for the Jackson-type estimate for unconstrained approximation by splines with free knots. Shape-preserving free knot spline approximation of k -convex functions, k > 3 , is also considered. January 15, 1996. Date revised: December 9, 1996.     

σ-相关同伦元素的非平凡性

本文中,通过几何方法证明了σ相关同伦元素在球面稳定同伦群π_mS中是非平凡的,其中m=p~(n+1)q+2p~nq+(s+3)p~2q+(s+3)pq+(s+3)q-8,p≥7是奇素数,n3,0≤sp-3,且q=2(p-1).该σ相关同伦元素在Adams谱序列的E_2-项中由■_s+3■_ng0表示.     

Detection of Some Elements in the Stable Homotopy Groups of Spheres

Let A be the mod p Steenrod algebra and S be the sphere spectrum localized at an odd prime p. To determine the stable homotopy groups of spheres π＊S is one of the central problems in homotopy theory. This paper constructs a new nontrivial family of homotopy elements in the stable homotopy groups of spheres πp^nq＋2pq＋q-3S which isof order p and is represented by kohn ∈ ExtA^3,P^nq＋2pq＋q（Zp,Zp） in the Adams spectral sequence, wherep 〉 5 is an odd prime, n ≥3 and q = 2（p-1）. In the course of the proof, a new family of homotopy elements in πp^nq＋（p＋1）q-1V（1） which is represented by β＊i＇＊i＊（hn） ∈ ExtA^2,pnq＋（p＋1）q＋1 （H^＊V（1）, Zp） in the Adams sequence is detected.     

On L p Extremal Polynomials

A Turán-type inequality for L _p extremal polynomials is given and mean convergence of Lagrange interpolation based on the zeros of L _p extremal polynomials is investigated. November 8, 1994. Date revised: January 23, 1997.     

A NEW FAMILY OF FILTRATION S ＋ 5 IN THE STABLE HOMOTOPY GROUPS OF SPHERES

In this article, by the algebraic method, the author proves the existence of a new nontrivial family of filtration s ＋ 5 in the stable homotopy groups of spheres πrS,which is represented by 0 ≠γ^-s＋3hnhm∈Ext^s＋5,A ^t（Zp,Zp）in the Adams spectral sequence,where r=q（p^m＋p^n＋（s＋3）p^2＋（s＋2）p＋（s＋1））-5,t=p^mq＋p^nq＋（s＋3）p^2q＋（s＋2）pq＋（s＋1）q＋s,p≥7,m≥n＋2〉5,0≤s〈p-3,q=2（p-1）.     

On an Infinite Family in πS

In this paper, a new family of homotopy elements in the stable homotopy groups of spheres represented by

n−2≥m≥5 and 3≤s<p.$n-2\ge m\ge 5\hspace{0.17em}\text{and}\hspace{0.17em}3\le s<p.$

in the Adams spectral sequence is detected, where n − 2 ≥ m ≥ 5 and 3 ≤ s < p.     

球面稳定同伦群中的$\xi_n$-相关元素的非平凡性

利用Adams谱序列与May谱序列, 发掘了球面稳定同伦群中一族$\xi_n$的相关元素. 这里$\xi_n\in\pi_* M$在Adams 谱序列中由$h_0h_n\in \ext_A^{2,p^n q+q}(H^* M,\zz_p)$所表示, 其中$p\geqslant 7,\ n>3,\ q=2(p-1).$     

Discrete May–Leonard Competition Models I

The local dynamics of two discrete-time models applicable to three competing plant species are shown to have properties similar to the May–Leonard (M-L) differential equation model. The dynamics of the two discrete models are shown to be similar. However, they are not dynamically consistent with the continuous M-L model. Unlike the continuous M-L model, the Hopf bifurcations of the discrete M-L models are not degenerate. The continuous M-L model is the limiting case of the discrete models.     

Gaussian Versus Optimal Integration of Analytic Functions

We consider error estimates for optimal and Gaussian quadrature formulas if the integrand is analytic and bounded in a certain complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented. This method is applied to Szeg?-type weight functions and ellipses as regions of analyticity. In this situation, the error constants for the Gaussian formulas are close to the obtained lower bounds, which proves the quality of the Gaussian formulas and also of the lower bounds. In the sequel, different regions of analyticity are investigated. It turns out that almost exclusively for ellipses, the Gaussian formulas are near-optimal. For classes of simply connected regions of analyticity, which are additionally symmetric to the real axis, the asymptotic of the worst ratio between the error constants of the Gaussian formulas and the optimal error constants is calculated. As a by-product, we prove explicit lower bounds for the Christoffel-function for the constant weight function and arguments outside the interval of integration. September 7, 1995. Date revised: October 25, 1996.     

球面稳定同伦群的γ_tl_1g_0新元素族

首先给出了May谱序列E_1~(s,t,u)项的几个结果,然后利用这些结果和关于Ext_P~(s,t)(Z_p,Z_p)的一个估计(P为由mod p Steenrod代数A的所有循环缩减幂P~i(i≥0)生成的子代数)得出了乘积(?)t (?)g0∈Ext_A~(*,*)(Z_p,Z_p)(3≤t相似文献