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。     

多元三角阵列插值多项式

本文研究多元三角阵列的多项式插值问题,多元Newton插值,多元Abel-Goncarov插值以及Kergin插值都是三角阵列插值的特殊情况,本文首先得到了多元三角阵列插值多项式及其余项的具体表达式;在此基础上,证明了插值问题的存在唯一性;给出了三角阵列插值余项的估计式,进而得到一个有关多元复变函数插值级数的收敛性定理。     

(Ⅱ)型三角剖分下带边界条件的二元二次样条插值

本文研究(Ⅱ)型三角剖分下带边界条件的二元二次样条插值问题的存在唯一性与插值节点分布的关系,并且在证明了中心插值、角点插值和偏心插值问题解的存在唯一性的基础上,给出了这三种插值函数的构造方法.     

矩形网格上的Thiele重心型连分式混合有理插值

1引言众所周知,有理插值是非线性逼近的一种重要方法,但由于其复杂性,主要表现在有理插值问题有解是有条件的或者说有理插值问题不是总是有解的.熟知的有理插值格式(包括向量有理插值、矩阵有理插值)函数构造方法,都是假定有理插值问题有解的条件下给出的,为实际应用带来一定的困难.目前,构造有理插值常用方法之一是基于连分式给出的,应用混合方法或分块方     

广义Vandermonde行列式及其应用

1 广义Vandermonde行列式的定义 1966年,I.J.Schoenberg在文[1]中明确提出具有一般性的Hermite-Birkhoff插值及其插值适定性问题.而一般的Hermite-Birkhoff插值问题则未必是适定的,关于这方面目前已有许多工作,见[2]—[7].我们知道,Hermite-Birkhoff插值问题是 Hermite插值问题的推     

关于球面上的Lagrange插值

1引 言 单位球面上的插值问题一直是三元插值问题中比较受关注的部分.近年来,球面上的 Lagrange插值问题已经得到了很好地解决.例如[1]中给出了构造单位球面上的Lagrange 插值适定结点组的一种方法：添加圆周法.[2]和[3]中研究了单位球面上的多项式插值问题,给出了构造单位球面上的插值适定结点组的另外两种方法.     

多元零次有理插值的构造性理论及算法

<正>1引言有理插值问题是由一组给定数据构造分子、分母均属于同一有限维多项式空间的有理函数R的插值问题.一元有理插值已经多年研究,理论比较成熟[1].然而,多元有理插值问题比一元情形复杂得多,加之研究工具和方法的制约,至今理论还远非完善.作为一次十分有益的尝试,[5]依据多元多项式插值的构造性代数理论,证明了多元Cauchy型有理插值的存在性并给出了插值函数的一般表达式.     

插值(切触)分式表的构造

用插值分式表或切触插值分式表来讨论有理插值或切触有理插值问题的一些算法的条件是比较方便的(参看[3],[6]).但关于这两个表的结构,至今未见充要的结果.为解决此问题,先引入有关术语及记号,并首先考虑有理插值的情况.     

复插值逼近

本文着重地介绍复数域上各类插值多项式(有时也提到有理函数)的收敛性与发散性问题的近代成果,适当地介绍了复插值逼近阶的估计。文章共分七节,其中§1为问题的提出;§2介绍紧集上解析函数的Lagrange插值多项式收敛的充要条件;§3介绍A(|z|≤1)上函数的Lagrange插值的收敛及发散问题;§4是一般区域上Lagrange插值的收敛问题;§5介绍调和多项式的插值;§6介绍Hermite及Hermite-Fejer插值的收敛与发散性问题;§7介绍有理函数插值的收敛性问题。     

关于球面上的一种Hermite插值

本文旨在提出单位球面上的一种Hermite插值格式.为此,本文首先研究了沿球面同轴圆周组上的Hermite插值问题,给出了三种适定的插值泛函组.然后研究了球面上的Hermite插值问题,给出了球面上Hermite插值的一种叠加插值法,即添加圆周组法.进一步将二者结合,导出了一类球面上Hermite插值的适定插值泛函组.为了说明这类适定插值泛函组的构造方法,在本文最后还给出了构造球面上低次Hermite适定插值泛函组的一些具体例子和数值算例.     

BOOK REVIEWS

Book reviewed in this article: Beloved Scientist , by David O. Woodbury. Physics , A Textbook for Colleges , by Oscar M. Stewart. Modern Physics , by Charles E. Dull. Experiments in Organic Chemistry , by E. Wertheim. Dynamical Analogies , by Harry F. Olson, E.E., Ph.D. A Peimer of Electronics , by Don P. Caverly. Applied Mechanics and Heat , by L. Raymond Smith. An Elementary Course in Qualitative Analysis , by William Lloyd Evans, Jesse Erwin Day, and Alfred Benjamin Garrett. Fundamentals of Machines , by John A. Clark. Fundamentals of Machines , by Charles E. Dull. Algebra (Mathematics for Technical Training ), by Paul L. Evans. Geometry with Military and Naval Applications , by Willis F. Kern and James R. Bland. Plane Trigonometry with Tables , by Paul L. Evans. Elementary Applied Electricity , by L. Raymond Smith. Fundamentals of Electricity , Based on Material Developed for the Teaching of Learners and Apprentices of the Carnegie -Illinois Steel Corporation . Rewritten to Conform to the Preinduction Training Course in Fundamentals of Electricity as Prepared by the War Department . Fundamental Jobs in Electricity , by Edgar C. Perry, A. M. and Harry V. Schafebook.     

Quasi-planar graphs have a linear number of edges

A graph is calledquasi-planar if it can be drawn in the plane so that no three of its edges are pairwise crossing. It is shown that the maximum number of edges of a quasi-planar graph withn vertices isO(n).Work on this paper by Pankaj K. Agarwal, Boris Aronov and Micha Sharir has been supported by a grant from the U.S.-Israeli Binational Science Foundation. Work on this paper by Pankaj K. Agarwal has also been supported by NSF Grant CCR-93-01259, by an Army Research Office MURI grant DAAH04-96-1-0013, by an NYI award, and by matching funds from Xerox Corporation. Work on this paper by Boris Aronov has also been supported by NSF Grant CCR-92-11541 and by a Sloan Research Fellowship. Work on this paper by János Pach, Richard Pollack, and Micha Sharir has been supported by NSF Grants CCR-91-22103 and CCR-94-24398. Work by János Pach was also supported by Grant OTKA-4269 and by a CUNY Research Award. Work by Richard Pollack was also supported by NSF Grants CCR-94-02640 and DMS-94-00293. Work by Micha Sharir was also supported by NSF Grant CCR-93-11127, by a Max-Planck Research Award, and by grants from the Israel Science Fund administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development. Part of the work on this paper was done during the participation of the first four authors in the Special Semester on Computational and Combinatorial Geometry organized by the Mathematical Research Institute of Tel Aviv University, Spring 1995.     

Intrinsic regular submanifolds in Heisenberg groups are differentiable graphs

We characterize intrinsic regular submanifolds in the Heisenberg group as intrinsic differentiable graphs. G. Arena is supported by MIUR (Italy), by INDAM and by University of Trento. R. Serapioni is supported by MIUR (Italy), by GALA project of the Sixth Framework Programme of European Community and by University of Trento.     

BOOK REVIEWS

Book reviewed in this article: Galaxies , by Harlow Shapley, Director of the Harvard College Observatory. Modern Chemistry , by Charles E. Dull. Essentials of Plane and Spherical Trigonometry with Tables , by Clifford Bell and Tracy Y. Thomas Solid Geometry , by A. M. Welchons and. W. R. Keickenberger. General Chemistry , (Fifth Edition) by Horace G. Deming. The Science of Explosives , by Martin Meyer. Biology for High Schools , by Sister M. Dafrose, O.P. Manual of Wartime Hygiene . Supplement to “A College Textbook of Hygiene” by Dean Franklin Smiley, A.B., M.D. Plane and Spherical Trigonometry , by Alfred L. Nelson and Karl W. Folley. Mathematics for Machinists , by R. W. Burnham. Calculus , by Lyman M. Kells.     

BOOK REVIEWS

Book reviewed in this article: Electronics : Today and Tomorrow , by John Mills. General Physics , A Textbook for Colleges , by Oswald Blackwood, Ph.D. Essentials of Astronomy , by John Charles Duncan, Ph.D. Basic Air Navigation , by Eibert F. Blackburn. How to Pass Radio License Examinations , by Charles E. Drew. Introductory Astronomy , A Guide for Night Watchers , by J. B. Sidgwick. Plane and Spherical Trigonometry , by Donald H. Ballou, Ph.D. and Frederick, H. Steen, Ph.D. How to Pass a Written Examination , by Harry C. McKown. Military Applications of Mathematics , by Paul P. Hanson, M.A. Calculus Refresher for Technical Men , by Albert Klaf, B.S., M.E. Mathematics for Aircraft Engine Mechanics , by Harold Griffiths. Essentials of Business Arithmetic , Revised Edition, by Edward M. Kanzer. Mathematics for the Emergency , a text-workbook in essential mathematics. By C. J. Lapp. Liberal Education , by Mark Van Doren.     

BOOK REVIEWS

Book reviewed in this article: The Science of Nutrition , by Henry C. Sherman. Laboratory Explorations in General Zoology , by Karl A. Stiles, M.S., Ph.D. An Introduction to Navigation and Nautical Astronomy , By William George Shute, William Wright Shirk, George Forbes Porter, and Courtenay Hemenway. Electrical Essentials of Radio , by Morris Slurzberg, B.S., M.A., and William Osterheld, B.S., M.A. Fools and Foolishness , by Harry C. McKown. Principles of Air Navigation , by Bert A, Shields. Radio Material Guide , by Francis E. Almstead, Lieut. Illustrated Technical Dictionary , Edited by Maxim Newmark. Vitalized Physics , by Robert H. Carleton. First -Year Algebra , by Raleigh Schorling and Rolland R. Smith. Plane Geometry , by A. D. Theissen and Louis A. McCoy. Mathematics for Victory , by Virgil S. Mallory. A Mathematics Refresher , by A. Hooper. Arithmetic for the Emergency , a text-workbook. By G. M. Ruch, F. B. Knight and John W. Studebaker. Complexity of Mental Processes in Science Testing , by Frederick Thomas Howard, Ph.D. Consumer Education , by James E. Mendenhall and Henry Harap.     

On Solvability of Lie Rings with an Automorphism of Finite Order

A new criterion for a Lie ring with a semisimple automorphism of finite order to be solvable is proved. It generalizes the effective version of Winter's criterion obtained earlier by Khukhro and Shumyatsky and by Bergen and Grzeszczuk in replacing the ideal generated by a certain set by the subring generated by this set. The proof is inspired by the original theorem of Kreknin on solvability of Lie rings with regular automorphisms of finite order and is conducted mostly in terms of Lie rings graded by a finite cyclic group.     

带干扰的Erlang(2)过程

本篇论文主要讨论带干扰的E rlang(2)过程,首先通过指数分布的可加性来推得生存概率所满足的积分微分方程,进而得到破产概率(由干扰引起和由索赔引起)所满足的积分微分方程,最后得到破产概率的拉氏变换所满足的方程.     

BOOK REVIEWS

Book reviewed in this article: The Origin of the Carolina Bays , by Douglas Johnson. A Guide to Naval Aviation , by Lt. Wallace W. Elton, USNR; Lt. Alfred H. Driscoll, USNR; Lt. Robert N. Burchmore, USNR; and Lt. Gray B. Larkum, USNR. Mathematics for Navigators , by Delwyn Hyatt, Commander, USN, (Ret.) and Bennett M. Dodson, Commander, USNR. The Text -Activity Books . Elementary Topography and Map Reading , by Samuel L. Greitzer. Earth Science , A Physiography, by Gustave L. Fletcher. Shopwork , by Edward C. Wicks, Instructor of Industrial Arts, Morristown High School, New Jersey, John Poljacik, Jr., Instructor of Industrial Arts, Morrislown High School, and John Ellberg, author of Tales of A Rambler. Shop Practice , by William J. Kennedy. Plane Trigonometry and Statics , by Norman Miller. The Story of Flying , by Archibald Black. Electricity for Everyone , by Joseph R. Lunt, late Professor of Science at Rhode Island College of Education, and William T. Wyman. Air Navigation for Beginners , A Ground School Primer for Aerial Navigators , by Scott G. Lamb, B.S., M.S. Essentials of Algebra (Complete Second Year Course ), by Walter W. Hart. Solid Geometry , by F. Eugene Seymour, Supervisor of Mathematics, New York State Department of Education, and Paul James Smith, Head of Department of Mathematics, East High School, Rochester, New York. Modern Science Series , by Charles E. Dull. Organic Chemistry , by C. W. Porter and T. D. Stewart. Man's Physical Universe , by Arthur Talbot Bawden. Man and His Physical Universe , by Frank Covert, Jean Ezra Clarence Harrah, and Fred Louis Herman. Elementary Electricity , by Edgar P. Slack.     

Symmetry Reductions of the Combined KdV—mKdV Equation

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