Asymptotic properties of B -splines, Eulerian numbers and cube slicing

In this paper, we clarify the connections among B -splines, Eulerian numbers and cube slicing. We first show that the asymptotic formula for Eulerian numbers can be considered as a special case of the asymptotic properties of B -splines. The volume of cube slicing can be considered as a value of box...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational and applied mathematics 2011-10, Vol.236 (5), p.988-995
Main Authors: Xu, Yan, Wang, Ren-hong
Format: Article
Language:English
Subjects:
[formula omitted]-splines
Asymptotic approximation
Asymptotic properties
Cube slicing
Cubes
Eulerian numbers
Joints
Mathematical analysis
Mathematical models
Probabilistic methods
Slicing
Splines
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c329t-a78776f0d991fd44427bb0947edef3013ca9259ed5959ae41e5836859e25772f3
cites cdi_FETCH-LOGICAL-c329t-a78776f0d991fd44427bb0947edef3013ca9259ed5959ae41e5836859e25772f3
container_end_page 995
container_issue 5
container_start_page 988
container_title Journal of computational and applied mathematics
container_volume 236
creator Xu, Yan
Wang, Ren-hong
description In this paper, we clarify the connections among B -splines, Eulerian numbers and cube slicing. We first show that the asymptotic formula for Eulerian numbers can be considered as a special case of the asymptotic properties of B -splines. The volume of cube slicing can be considered as a value of box spline functions. Based on the connection, a very simple proof for Laplace and Pólya’s formulas, which were settled by probabilistic methods, is given by spline theory.
doi_str_mv 10.1016/j.cam.2011.08.003
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_963852582</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0377042711004420</els_id><sourcerecordid>963852582</sourcerecordid><originalsourceid>FETCH-LOGICAL-c329t-a78776f0d991fd44427bb0947edef3013ca9259ed5959ae41e5836859e25772f3</originalsourceid><addsrcrecordid>eNp9kE1LAzEQhoMoWKs_wFtuXtx1kuxuEjzV0qpQ8KLnkGZnJWW_THaF_nsj9expYHif4Z2HkFsGOQNWPRxyZ7ucA2M5qBxAnJEFU1JnTEp1ThYgpMyg4PKSXMV4AIBKs2JBtqt47MZpmLyjYxhGDJPHSIeGPtEsjq3vMd7Tzdxi8Lan_dztMURq-5q6eY80tt75_vOaXDS2jXjzN5fkY7t5X79ku7fn1_VqlznB9ZRZqaSsGqi1Zk1dFKnPfg-6kFhjI4AJZzUvNdalLrXFgmGpRKXShpdS8kYsyd3pbur6NWOcTOejw7a1PQ5zNLoSquSl4inJTkkXhhgDNmYMvrPhaBiYX2XmYJIy86vMgDJJWWIeTwymF749BhOdx95h7QO6ydSD_4f-ASpacvI</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>963852582</pqid></control><display><type>article</type><title>Asymptotic properties of B -splines, Eulerian numbers and cube slicing</title><source>Elsevier</source><creator>Xu, Yan ; Wang, Ren-hong</creator><creatorcontrib>Xu, Yan ; Wang, Ren-hong</creatorcontrib><description>In this paper, we clarify the connections among B -splines, Eulerian numbers and cube slicing. We first show that the asymptotic formula for Eulerian numbers can be considered as a special case of the asymptotic properties of B -splines. The volume of cube slicing can be considered as a value of box spline functions. Based on the connection, a very simple proof for Laplace and Pólya’s formulas, which were settled by probabilistic methods, is given by spline theory.</description><identifier>ISSN: 0377-0427</identifier><identifier>EISSN: 1879-1778</identifier><identifier>DOI: 10.1016/j.cam.2011.08.003</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>[formula omitted]-splines ; Asymptotic approximation ; Asymptotic properties ; Cube slicing ; Cubes ; Eulerian numbers ; Joints ; Mathematical analysis ; Mathematical models ; Probabilistic methods ; Slicing ; Splines</subject><ispartof>Journal of computational and applied mathematics, 2011-10, Vol.236 (5), p.988-995</ispartof><rights>2011</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c329t-a78776f0d991fd44427bb0947edef3013ca9259ed5959ae41e5836859e25772f3</citedby><cites>FETCH-LOGICAL-c329t-a78776f0d991fd44427bb0947edef3013ca9259ed5959ae41e5836859e25772f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Xu, Yan</creatorcontrib><creatorcontrib>Wang, Ren-hong</creatorcontrib><title>Asymptotic properties of B -splines, Eulerian numbers and cube slicing</title><title>Journal of computational and applied mathematics</title><description>In this paper, we clarify the connections among B -splines, Eulerian numbers and cube slicing. We first show that the asymptotic formula for Eulerian numbers can be considered as a special case of the asymptotic properties of B -splines. The volume of cube slicing can be considered as a value of box spline functions. Based on the connection, a very simple proof for Laplace and Pólya’s formulas, which were settled by probabilistic methods, is given by spline theory.</description><subject>[formula omitted]-splines</subject><subject>Asymptotic approximation</subject><subject>Asymptotic properties</subject><subject>Cube slicing</subject><subject>Cubes</subject><subject>Eulerian numbers</subject><subject>Joints</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Probabilistic methods</subject><subject>Slicing</subject><subject>Splines</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKs_wFtuXtx1kuxuEjzV0qpQ8KLnkGZnJWW_THaF_nsj9expYHif4Z2HkFsGOQNWPRxyZ7ucA2M5qBxAnJEFU1JnTEp1ThYgpMyg4PKSXMV4AIBKs2JBtqt47MZpmLyjYxhGDJPHSIeGPtEsjq3vMd7Tzdxi8Lan_dztMURq-5q6eY80tt75_vOaXDS2jXjzN5fkY7t5X79ku7fn1_VqlznB9ZRZqaSsGqi1Zk1dFKnPfg-6kFhjI4AJZzUvNdalLrXFgmGpRKXShpdS8kYsyd3pbur6NWOcTOejw7a1PQ5zNLoSquSl4inJTkkXhhgDNmYMvrPhaBiYX2XmYJIy86vMgDJJWWIeTwymF749BhOdx95h7QO6ydSD_4f-ASpacvI</recordid><startdate>20111001</startdate><enddate>20111001</enddate><creator>Xu, Yan</creator><creator>Wang, Ren-hong</creator><general>Elsevier B.V</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20111001</creationdate><title>Asymptotic properties of B -splines, Eulerian numbers and cube slicing</title><author>Xu, Yan ; Wang, Ren-hong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c329t-a78776f0d991fd44427bb0947edef3013ca9259ed5959ae41e5836859e25772f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>[formula omitted]-splines</topic><topic>Asymptotic approximation</topic><topic>Asymptotic properties</topic><topic>Cube slicing</topic><topic>Cubes</topic><topic>Eulerian numbers</topic><topic>Joints</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Probabilistic methods</topic><topic>Slicing</topic><topic>Splines</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xu, Yan</creatorcontrib><creatorcontrib>Wang, Ren-hong</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Xu, Yan</au><au>Wang, Ren-hong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Asymptotic properties of B -splines, Eulerian numbers and cube slicing</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>2011-10-01</date><risdate>2011</risdate><volume>236</volume><issue>5</issue><spage>988</spage><epage>995</epage><pages>988-995</pages><issn>0377-0427</issn><eissn>1879-1778</eissn><abstract>In this paper, we clarify the connections among B -splines, Eulerian numbers and cube slicing. We first show that the asymptotic formula for Eulerian numbers can be considered as a special case of the asymptotic properties of B -splines. The volume of cube slicing can be considered as a value of box spline functions. Based on the connection, a very simple proof for Laplace and Pólya’s formulas, which were settled by probabilistic methods, is given by spline theory.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.cam.2011.08.003</doi><tpages>8</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0377-0427
ispartof Journal of computational and applied mathematics, 2011-10, Vol.236 (5), p.988-995
issn 0377-0427
1879-1778
language eng
recordid cdi_proquest_miscellaneous_963852582
source Elsevier
subjects [formula omitted]-splines
Asymptotic approximation
Asymptotic properties
Cube slicing
Cubes
Eulerian numbers
Joints
Mathematical analysis
Mathematical models
Probabilistic methods
Slicing
Splines
title Asymptotic properties of B -splines, Eulerian numbers and cube slicing
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T18%3A29%3A17IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Asymptotic%20properties%20of%20B%20-splines,%20Eulerian%20numbers%20and%20cube%20slicing&rft.jtitle=Journal%20of%20computational%20and%20applied%20mathematics&rft.au=Xu,%20Yan&rft.date=2011-10-01&rft.volume=236&rft.issue=5&rft.spage=988&rft.epage=995&rft.pages=988-995&rft.issn=0377-0427&rft.eissn=1879-1778&rft_id=info:doi/10.1016/j.cam.2011.08.003&rft_dat=%3Cproquest_cross%3E963852582%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c329t-a78776f0d991fd44427bb0947edef3013ca9259ed5959ae41e5836859e25772f3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=963852582&rft_id=info:pmid/&rfr_iscdi=true