拉格朗日插值算子的L_p收敛速度

本文得到了以第二类Ｔｃｈｅｂｙｃｈｅｆ多项式的零点为插值结点组的拉格朗日插值于Ｌｐ（１＜ｐ＜２）下的收敛速度     

赋范线性空间中的最佳共逼近的一点注记

本文用例子表明最佳共逼近与最佳逼近间有着区别．指出强共逼近的元未必是唯一的;凸集未必是共太阳集和强共Ｋｏｌｍｏｇｏｒｏｖ集;而在最佳逼近论中它们的相应回答均是肯定的．     

广义对角占优阵的一个等价条件

给出了实方阵为广义对角占优阵的充要条件,同时给出了判断广义对角占优阵可靠,可行,较简单方法。     

非球面检测中最佳入射球面波和最佳参考球面波的确定

为了能够对非球面光学元件面型进行高精度的干涉检测,提出了一种确定最佳入射球面波和最佳参考球面波的新方法。该方法通过计算分析入射球面波与非球面反射波干涉条纹密度,确定最佳入射球面波的波源位置;通过计算分析在干涉图记录平面CCD上干涉条纹的密度,确定非球面检测时参考球面波波源的最佳位置。应用该理论与方法,不仅可明确非球面检测时CCD等光路元件选型的具体策略,而且可用于指导非球面检测调试过程,并能够通过对干涉图的深入分析,获得更多被测非球面的信息。     

On the Approximation of Functions on Locally Compact Abelian Groups

Questions of approximative nature are considered for a space of functions L ^p(G, ), 1 p , defined on a locally compact abelian Hausdorff group G with Haar measure . The approximating subspaces which are analogs of the space of exponential type entire functions are introduced.     

Non-cooperative implementation: A survey of recent results

Strategic decentralization of collective decision-making is considered when the agents' behaviour is non-cooperative. Specifically they use dominant, maximin risk-avert or sophisticated strategies. The existing results applying these equilibrium concepts are reviewed in three familiar economically meaningful contexts: ordinal (as in voting), random (as in bargaining) and quasilinear (as in public goods problems).     

Weak Type Inequalities for Best Simultaneous Approximation in Banach Spaces

For arbitrary Banach spaces Butzer and Scherer in 1968 showed that the approximation order of best approximation can characterized by the order of certain K-functionals. This general theorem has many applications such as the characterization of the best approximation of algebraic polynomials by moduli of smoothness involving the Legendre, Chebyshev, or more general the Jacobi transform. In this paper we introduce a family of seminorms on the underlying approximation space which leads to a generalization of the Butzer–Scherer theorems. Now the characterization of the weighted best algebraic approximation in terms of the so-called main part modulus of Ditzian and Totik is included in our frame as another particular application. The goal of the paper is to show that for the characterization of the orders of best approximation, simultaneous approximation (in different spaces), reduction theorems, and K-functionals one has (essentially) only to verify three types of inequalities, namely inequalities of Jackson-, Bernstein-type and an equivalence condition which guarantees the equivalence of the seminorm and the underlying norm on certain subspaces. All the results are given in weak-type estimates for almost arbitrary approximation orders, the proofs use only functional analytic methods.     

Accurate computation of the smallest eigenvalue of a diagonally dominant -matrix

If each off-diagonal entry and the sum of each row of a diagonally dominant -matrix are known to certain relative accuracy, then its smallest eigenvalue and the entries of its inverse are known to the same order relative accuracy independent of any condition numbers. In this paper, we devise algorithms that compute these quantities with relative errors in the magnitude of the machine precision. Rounding error analysis and numerical examples are presented to demonstrate the numerical behaviour of the algorithms.

     

On copositive approximation in some classical spaces of sequences

In this paper the author writes a simple characterization for the best copositive approximation in c; the space of convergent sequences, by elements of finite dimensional Chebyshev subspaces, and shows that it is unique.     

Evidence for ion–ion interactions between peptides and anions (HSO4− or ClO4−) derived from high‐acidity acids

The existence of gas‐phase electrostatic ion–ion interactions between protonated sites on peptides ([Glu] Fibrinopeptide B, Angiotensin I and [Asn¹, Val⁵]‐Angiotensin II) and attaching anions (ClO₄^? and HSO₄^?) derived from strong inorganic acids has been confirmed by CID MS/MS. Evidence for ion–ion interactions comes especially from the product ions formed during the first dissociation step, where, in addition to the expected loss of the anion or neutral acid, other product ions are also observed that require covalent bond cleavage (i.e. H₂O loss when several carboxylate groups are present, or NH₃ loss when only one carboxylate group is present). For [[Glu] Fibrinopeptide B + HSO₄]^?, under CID, H₂O water loss was found to require less energy than H₂SO₄ departure. This indicates that the interaction between HSO₄^? and the peptide is stronger than the covalent bond holding the hydroxyl group, and must be an ion–ion interaction. The strength and stability of this type of ion‐pairing interaction are highly dependent on the accessibility of additional mobile charges to the site. Positive mobile charges such as protons from the peptide can be transferred to the attaching anion to possibly form a neutral that may depart from the complex. Alternatively, an ion–ion interaction can be disrupted by a competing proximal additional negatively charged site of the peptide that can potentially form a salt bridge with the positively charged site and thereby facilitate the attaching anion's departure. Copyright © 2014 John Wiley & Sons, Ltd.