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路易斯安那大学拉法耶艺术博物馆美国路易斯安那州拉法耶

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世界建筑导报 2024年第1期39卷 70-73页

作者：无 Timothy Hurlsey(摄影) Philip gould(摄影) EDR建筑事务所乔恩·艾默生建筑事务所不详

新博物馆紧邻1967年竣工的大学艺术博物馆,是其有益扩充,并界定出新的雕塑公园和广场。新馆功能包括门厅和公共空间,永久收藏品展厅和临时藏品展厅,行政办公以及艺术维护和档案用房。新博物馆像一个紧密包裹的体块,结构形式与老建筑的... 详细信息

新博物馆紧邻1967年竣工的大学艺术博物馆,是其有益扩充,并界定出新的雕塑公园和广场。新馆功能包括门厅和公共空间,永久收藏品展厅和临时藏品展厅,行政办公以及艺术维护和档案用房。新博物馆像一个紧密包裹的体块,结构形式与老建筑的相呼应,以便在全新的场地中获得清晰的组织架构。盘旋于参观者进入博物馆时头上的玻璃立面,将现有的优美的海斯小镇建筑物和雕塑公园周围的橡树反射出来。随着位置和一天中时间的不同,玻璃面在全反射和透明之间变幻。夜晚,玻璃立面被穿孔金属天花板上的筒灯染成光亮的深蓝色,使新博物馆与其老邻居形成鲜明对比。

关键词：艺术博物馆行政办公雕塑公园路易斯安那州深蓝色公共空间全反射组织架构

Powers of the Catalan generating Function and Lagrange's 1770 Trinomial Equation Series

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Journal of Mathematical Research with Applications 2019年第6期39卷 603-606页

作者： H.w.gould Department of Mathematics West Virginia University

The Catalan numbers 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862,... are given by C（n）=■for n ≥ 0. They are named for Eugene Catalan who studied them as early as *** were also found by Leonhard Euler（1758）, Nicholas von Fuss（1795）, and Andreas von Segner（1758）. The Catalan numbers have the binomial generating function ■It is known that powers of the generating function C（z） are given by ■The above formula is not as widely known as it should be. we observe that it is an immediate, simple consequence of expansions first studied by J. L. Lagrange. Such series were used later by Heinrich August Rothe in 1793 to find remarkable generalizations of the Vandermonde convolution. For the equation x-3x + 1 = 0, the numbers ■analogous to Catalan numbers occur of course. Here we discuss the history of these expansions. and formulas due to L. C. Hsu and the author.

关键词： Catalan numbers Vandermonde convolution Lagrange and Bürmann series Rothe’s formula(or general identity of Rothe-Hagen)

Characterization of (c)-Riordan Arrays, gegenbauer-Humbert-Type Polynomial Sequences, and (c)-Bell Polynomials

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Journal of Mathematical Research with Applications 2013年第5期33卷 505-527页

作者： Henry w. gould Tianxiao HE Department of Mathematics West Virginia University Department of Mathematics Illinois Wesleyan University

Here presented are the definitions of(c)-Riordan arrays and(c)-Bell polynomials which are extensions of the classical Riordan arrays and Bell *** characterization of(c)-Riordan arrays by means of the A-and Z-sequences is given,which corresponds to a horizontal construction of a(c)-Riordan array rather than its definition approach through column generating *** exists a one-to-one correspondence between gegenbauerHumbert-type polynomial sequences and the set of(c)-Riordan arrays,which generates the sequence characterization of gegenbauer-Humbert-type polynomial *** sequence characterization is applied to construct readily a(c)-Riordan *** addition,subgrouping of(c)-Riordan arrays by using the characterizations is ***(c)-Bell polynomials and its identities by means of convolution families are also ***,the characterization of(c)-Riordan arrays in terms of the convolution families and(c)-Bell polynomials is presented.

关键词： Riordan arrays (c)-Riordan arrays A-sequence Z-sequence (c)-Bell polynomials (c)-hitting-time subgroup.

Characterization of Polynomial Systems Satisfying generalized Convolution Differential-Difference Equations

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数学研究与评论 1989年第2期9卷 159-172页

作者： H.w.gould w.Y.Kerr Department of Mathematics’ west Virginia Vniversity

I. Introduction. The present paper has been motivated by the desire to find all polynomial solutions of the convolution type differential -difference equation （1.1） Dxgn（x）=sum from i=1 to n-1 (gi（x）gn-i（x）,n≥2,) where g1（x） is assumed to be a constant. This problem arose in work by one of the authors （Kerr） with a differential equation arising in a coal research project

关键词： Characterization of Polynomial Systems Satisfying generalized Convolution Differential-Difference Equations

Annihilation Coefficients, Binomial Expansions and q-Analogs

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Journal of Mathematical Research and Exposition 2010年第2期30卷 191-204页

作者： H.w.gould J.QUAINTANCE Department of Mathematics West Virginia UniversityMorgantownW.Va.26506U.S.A.

Let {An}∞n=0 be an arbitary sequence of natural numbers. we say A（n,k;A） are the Convolution Annihilation Coefficients for {An}n∞=0 if and only if n∑κ=0A（n,k;A）（x-Aκ）n-k=xn. （0.1） Similary, we define B（n,k;A） to be the Dot Product Annihilation Coefficients for {An}n∞=0 if and only if n∑κ=0A（n,k;A）（x-Aκ）n-k=xn. （0.2） The main result of this paper is an explicit formula for B（n,k;A）, which depends on both k and {An}∞n=0. This paper also discusses binomial and q-analogs of Equations （0.1） and （0.2）.

关键词： Annihilation coefficient Binomial expansion stirling number of the first kind stirling number of the second kind vadermonde convolution.

Masses for free-floating planets and dwarf planets

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Research in Astronomy and Astrophysics 2021年第6期21卷 207-221页

作者： Andrew gould wei-Cheng Zang Shude Mao Su-Bo Dong Max-Planck-Institute for Astronomy Konigstuhl 17D-69117 HeidelbergGermany Department of Astronomy Ohio State University140 W.18th Ave.ColumbusOH 43210USA Department of Astronomy Tsinghua UniversityBeijing 100084China National Astronomical Observatories Chinese Academy of SciencesBeijing 100101China Kavli Institute for Astronomy and Astrophysics Peking UniversityBeijing 100871China

The mass and distance functions of free-floating planets(FFPs) would give major insights into the formation and evolution of planetary systems, including any systematic differences between those in the disk and bulge. we show that the only way to measure the mass and distance of individual FFPs over a broad range of distances is to observe them simultaneously from two observatories separated by D ~ O(0.01 au)(to measure their microlens parallax πE) and to focus on the finite-source point-lens(FSPL) events(which yield the Einstein radius θE). By combining the existing KMTNet 3-telescope observatory with a 0.3 m 4 deg2 telescope at L2, of order 130 such measurements could be made over four years, down to about M ~ 6 M⊕for bulge FFPs and M ~ 0.7 M⊕for disk FFPs. The same experiment would return masses and distances for many bound planetary systems. A more ambitious experiment, with two 0.5 m satellites(one at L2 and the other nearer Earth) and similar camera layout but in the infrared, could measure masses and distances of sub-Moon mass objects, and thereby probe(and distinguish between) genuine sub-Moon FFPs and sub-Moon "dwarf planets" in exo-Kuiper Belts and exo-Oort Clouds.

关键词： gravitational lensing:micro

New Inverse Series Relations for Finite and Infinite Series with Applications

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数学研究与评论 1984年第2期 119-130页

作者： H.w.gould west Virginia University USA

Some new series inversion formulas of the general form F（n）=sum form k=0 to r(Ak,mf（n-mk）) if and only if f（n）=sum form k=0 to r(Bk,nF（ro-mk）) valid for either r=[n/m]or r=∞ are presented. These relations generalize many of those given by the author in a long series of preceding papers. An interesting example is given by Ak,n=（-y）kAk（p-λn,t（1+λm）） and Bk,n=ykAk（p-λn,（1-t）（1+λm）） where Ak（a,b）=a/（a+bk） in terms of binomial coefficients. Here p,t,y and λ are arbitrary complex numbers. A corresponding Abel coefficient case occurs which uses numbers of the form a（a+bi）（i-1）/i!. An application to special functions studied by Singhal and Kumari is given, and it is also shown that sum form k=0 to ∞（zkAk（a+ck,b））=xa（x-b（x-1））/（x-（b+c）（x-1））, where z=（x-1）x-b-c, with a corresponding case for the Abel coefficients sum from k=0 to ∞（zkBk（a+ck,b））=xo（1-b logx）/（1-（b+c）log x）,where z=（log x）x-b-c From these expansions we then have easily the new convolution formula for Rothe coeffici

关键词： New Inverse Series Relations for Finite and Infinite Series with Applications