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Topic: Bell numbers

	Kids.Net.Au - Encyclopedia > Bell numbers
		The Bell numbers, named in honor of Eric Temple Bell, are a sequence of integers arising in combinatorics that begins thus:
		Each Bell number is a sum of "Stirling numbers of the second kind"
		The Stirling number S(n, k) is the number of ways to partition a set of cardinality n into exactly k nonempty subsets.
	www.kids.net.au /encyclopedia-wiki/be/Bell_numbers (0 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal
		In combinatorial mathematics, the nth Bell number, named in honor of Eric Temple Bell, is the number of partitions of a set with n members, or equivalently, the number of equivalence relations on it.
		The nth Bell number is also the sum of the coefficients in the polynomial that expresses the nth moment of any probability distribution as a function of the first n cumulants; this way of enumerating partitions is not as coarse as that given by the Stirling numbers.
		The number in the nth row and kth column is the number of partitions of {1,..., n} such that n is not together in one class with any of the elements k, k + 1,..., n − 1.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Bell_number (0 words)

	Bell's Numbers
		Bell Numbers, or Bell's Numbers, are the sequence {1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147....}.
		The Bell numbers are named for mathematician and writer Eric Temple Bell (1883-1960) because he was one of the first to do in-depth analysis of the sequence.
		Bell was a contributor to number theory, but is better known for his many books on the History of Mathematics.
	www.pballew.net /Bellno.html (0 words)

	Bell's numbers are bubbling over - The Boston Globe
		Once the Bells knew their baby was going to be a boy, Bill Bell decided to nickname his son "Bubba." He would take his father's name on his birth certificate, but he would be known as Bubba Bell.
		LANCASTER, Calif. -- Once the Bells knew their baby was going to be a boy, Bill Bell decided to nickname his son "Bubba." He would take his father's name on his birth certificate, but he would be known as Bubba Bell.
		Bell has done about all he can to take advantage of the conditions at Lancaster -- which routinely has 30-mile-per-hour winds blowing out to right field -- and hit on the road.
	www.boston.com /sports/baseball/articles/2007/06/29/bells_numbers_are_bubbling_over (540 words)

	Welcome to Powerball
		The lucky group of co-workers are Christine Bell of Imperial, Cheri Schmitt of Lebanon, Ill., Donna Jansberg of St. Louis, Arthur Duy and Sharon Martin-Reibe of St. Louis.
		Bell checked their numbers on Sunday and couldn't believe it when she saw that they had won the second-level prize.
		Bell said most of the five lucky winners have young children, and they're planning to save their prize money for the future, and they have talked about taking vacations.
	www.powerball.com (0 words)

	Verizon \| SOUTH JERSEY TO GET NEW AREA CODE
		Bell Atlantic computes its rates by measuring the distance between the origin of the call and the place of completion.
		Numbers in the 609 area are expected to exhaust in the second quarter of 1998.
		Bell Atlantic also owns a substantial interest in Telecom Corporation of New Zealand and is actively developing high-growth national and international business opportunities in all phases of the industry.
	newscenter.verizon.com /press-releases/bell-atlantic/1996/page.jsp?itemID=29606181 (1103 words)

	faqchangeringing
		Since there are both place numbers and bell numbers it can be confusing until you get it sorted out as to which set of numbers are being spoken of at any moment.
		Rounds are rung from the #1 bell to the nth bell.
		Have the ringer passing their bell to the left be under the person passing their bell to the right.
	www.knology.net /~jkearns/faqchangeringing.htm (1046 words)

	Dynamics And Hierarchies
		A tree structure of Bell number diagrams allows recursive partitioning to be displayed in a less visually confusing manner that displaying it with a standard tree graph.
		Partitions with 1 or 2 items are not displayed as their own separate Bell number diagram since no additional information would be forthcoming; a single item can’t be sub-partitioned, and two items can only be recursively partitioned in one way due to the prohibition against placing all items in a single partition.
		The reason for forbidding Bell number diagram with a single partition in classification diagrams becomes clear, the terms are absent from the right hand side of the equation as they are the terms we wish to solve for.
	www.tetration.org /Dynamics/DynamicsAndHierarchies.htm (6678 words)

	Bell Numbers (Site not responding. Last check: )
		The GF for the Bell numbers is 1 + x/(1-x) + x^2/(1-x)(1-2x) + x^3/(1-x)(1-2x)(1-3x) +...
		The Bell GF uses 1/(1-2x) for example, and this can be considered to be saying there are two distinct copies of the SAME unit, and again we write 1 and 1', although for clarity a different symbol should be used.
		The number of symmetric patterns is the number of patterns from one stem.
	www.users.globalnet.co.uk /~perry/maths/bellnumbers/bellnumbers.htm (1254 words)

	Welcome to BachBrass.com
		For an instrument without a bell number stamped on it, it’s obviously more difficult to determine with certainty which bell was used.
		By knowing an instrument's serial number, which may indicate about when the instrument was made, and its bore size, a person can make a reasonable assumption about which bell is on it, even when the bell number is omitted.
		This is the only number found by the authors to date that relates a specific brass alloy produced by a brass manufacturer to a corresponding bell brass code.
	www.bachbrass.com /content/bachology/ref_article1.php (4498 words)

	Ma Bell Short of Numbers Again (Site not responding. Last check: )
		Skyrocketing growth in the number of telephones, faxes, cellular phones, pagers and Internet accounts in the Toronto area over the past several years is quickly exhausting the supply of available 416 numbers, said Ginny Dybenko, vice-president of communications for Bell Canada.
		Bell's Dybenko said her company may reconsider the reserved telephone number service in light of the current number crunch.
		Bell's Dybenko wouldn't provide the estimated cost of the changeover, but did say it would be significant.
	www.areacode-info.com /headline/1999/on990107.htm (872 words)

	Bell Helicopter - Support (Site not responding. Last check: )
		Bell is committed to quality and therefore is concerned that operators have and use genuine Bell helicopters.
		To ensure that you have a genuine Bell aircraft and not a counterfeit Bell, which are classified as destroyed by the appropriate investigative agency are considered to no longer exist as manufactured by Bell.
		Bell requests that the certification authority remove the aircraft serial number from the Type Certificate Data Sheet for each aircraft determined by the investigating government agency to have been destroyed.
	www.bellhelicopter.textron.com /en/support/index.cfm?content=flightsafety/counterfeit.cfm&g_folder=header_10 (581 words)

	Telecom Order CRTC 2005-397
		In its application, Bell Canada stated that it has identified system constraints, which were inadvertently not identified at product launch, that preclude the support of this number portability option at this time.
		Bell Canada indicated that it planned to implement a manual solution for LNP for out-of-territory primary numbers within four months, but that it was reluctant to undertake system modifications for LNP for secondary numbers.
		The Commission further considers that a six-month period is reasonable for Bell Canada to implement the necessary solution(s) with regard to fully supporting LNP for both primary and secondary numbers used in conjunction with its Bell Digital Voice Lite service.
	www.crtc.gc.ca /archive/ENG/Orders/2005/o2005-397.htm (0 words)

	Robert M. Dickau - Diagrams relating to Bell Numbers
		The Bell numbers (1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597,...) describe the number of ways a set with n elements can be partitioned into disjoint, non-empty subsets.
		Bell number can be computed using the formula
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /advanced/robertd/bell.html (0 words)

	Bell 'Numbers' gullbuy review
		Bell released this CD and a 12" single to little notice last year.
		I believe that timing is everything, and that they were just a bit on the wrong side of the bell curve.
		Bell is really for fans of music on labels such as Erstatz Audio, Bpitch Control, WMF, and International DeeJay Gigolo.
	www.gullbuy.com /buy/2002/4_9/bell.cfm (371 words)

	Bell numbers (Site not responding. Last check: )
		The Bell numbers, named in honor of Eric Temple Bell, are a sequence of integers arising in combinatorics that begins thus:
		The Stirling number S(n, k) is the number of ways to partition a set of cardinality n into exactly k nonempty subsets.
		The nth Bell number is also the sum of the coefficients in the polynomial that expresses the nth moment of any probability distribution as a function of the first n cumulants; this way of enumerating partitions isn't as coarse as that given by the Stirling numbers.
	www.news-server.org /b/be/bell_numbers.html (199 words)

	Bell Weights
		number to reflect the entire range of practical tower bell * * A bourdon code number is used to give a general indication
		bell instrument which has a C key connected to a bell of * * numbers and notes using approximate bell weights in kilo-
		The code numbering scheme is a free adaptation of one originally developed by carillon architect Frederick C. Mayer.
	www.gcna.org /data/Weights.html (3788 words)

	Notable Properties of Specific Numbers at MROB
		It is widely acknowledged that 60 was used in a number system because it has lots of factors; in fact it sets a record for having more factors than any smaller number.
		The Fibonacci sequence is the first recursive sequence studied in Europe; the relationship to phi was noticed in the 18th century and the occurrances of Fibonacci numbers in nature (such as flower petals) in the 19th century.
		After 100, 1000 and 1000000, the answer to "what's the biggest number you've heard of?" will usually be one or more of: billion, trillion, Avagadro's number, googol and googolplex.
	home.earthlink.net /~mrob/pub/math/numbers-6.html (2477 words)

	Tales of Statisticians \| Eric Temple Bell
		The Bell numbers (1, 1, 2, 5, 15, 52, and so on), a series of whole numbers arising in the theory of partitions, were first investigated by him, and are named for him.
		Bell's conviction at the time, that Fermat's unmatched insight into the character of numbers did not mislead him as to the existence of a proof, was vindicated recently when a proof was finally found.
		Bell's infectious love of number, his sense of the large sweep of mathematical history, and his generous anger at the fools and poopheads who all too densely populate that history, are his great legacy to posterity.
	www.umass.edu /wsp/statistics/tales/bell.html (1394 words)

	Nick Sherman > Articles > Bell Centennial
		Bell Centennial is a family of four weights, designed by Matthew Carter at Mergenthaler, to take advantage of the then-newer composing and printing technologies, while still compensating for the limitations that did exist.
		Bell Centennial is a condensed sans-serif design that maintains legibility at very small sizes, allows for clear information structures, is economical on space, and accommodates for adverse production conditions; all while keeping to an intended typographic style.
		Bell Gothic worked fine when the directories were still being composed in hot metal on a Linotype machine and printed on a letterpress, but because it was designed for those production methods, it didn't hold up under the set of limitations presented by newer technologies.
	www.nicksherman.com /articles/bellCentennial.html (1804 words)

	Ma Bell's Numbers
		The technology exists to reduce the number of phone numbers to blocks of 100 or so, but the phone companies are unwilling to invest in the new technology.
		Update (April 99): There are now 10 phone numbers for every man, woman, and child in the United States and Canada, (a total of 265 area codes) and the FCC still does not think it is enough.
		The number of assigned area codes has more than doubled in the past few years owing to skyrocketing use of cellular phones and pagers along with the growth of competitive local phone carriers.
	members.cox.net /mathmistakes/phone.htm (886 words)

	Strad_Bell_Markings (Site not responding. Last check: )
		In some cases, the last two digits of the trumpet or cornet's bore size are appended to the bell numbers.
		For example, the number six (6) bell was based on the bell flare of a French Besson trumpet owned by Harry Glantz, the famous principal of the New York Philharmonic.
		The bell numbers markings for these instruments follow the same general ideas as those of the Bb instruments.
	www.vintagecornets.com /html/strad_bell_markings.htm (4586 words)

	Browse by Artist: BELL
		Bell are a duo from London and this release is brilliant' -- Muzik.
		Bell recently played alongside ESG at the last 1977 and have got fans from the likes of Andy Weatherall and Gilles Peterson.
		Bell are Dan Crouch and Adrian Stephens and both are from London."
	www.forcedexposure.com /artists/bell.html (0 words)

	Casting Numbers
		In 1965, this number was changed to C5AE-6015-E for the 289 2V, 4V and Hi-Po (note the change to full size Ford designation and 6 bolt bell housings).
		Casting numbers can be helpful, but some blocks used several different casting numbers, and in some cases, one casting is not interchangeable with the other.
		Casting numbers are usually the same or nearly the same as the part number.
	www.classicmustang.com /casting_numbers.htm (634 words)

	Bell court bid claims the buck stops here - Christopher Webb - Opinion
		Bell Commodities is seeking a Supreme Court order that Buck provide its audit working papers for the three financial years to 2003.
		Bell Commodities reckons William Buck did not detect the reporting error and gave positive assurances that Bell's internal control procedures were adequate.
		Bell got an opinion from accountants BDO about whether it might have a claim against Buck for the 2001, 2002 and 2003 audits.
	www.theage.com.au /news/christopher-webb/bell-court-bid-claims-the-buck-stops-here/2006/07/22/1153166631126.html?from=rss (620 words)

	US-Based Bicycle Helmet Manufacturers
		Bell Helmets published in their 1994 stock prospectus an estimate of their own worldwide sales at about 11 million annually at that time, and the popular saying is that they have 70 per cent or more of the world market.
		Bell's staff members have been among the most active in promoting standards, particularly VP emeritus Dean Fisher, who has for years contributed a great deal to the standards effort, along with Thom Parks in Corporate Affairs.
		Bell also funds bicycle helmet promotion activities of the Safe Kids, whose local chapters are the country's most active lobby for mandatory helmet laws.
	www.bhsi.org /manufacs.htm (1201 words)

	Math Forum - Ask Dr. Math
		These numbers are famous, and even have a name.
		One remarkable formula for the Bell Numbers b(n) is infinity b(n) = (1/e)* SUM r^n/r!, n >= 1.
		Better is to know that the exponential generating function B(x) for the Bell Numbers is infinity B(x) = e^(e^x-1) = SUM b(n)*x^n/n!, n=0 so b(n) is the nth derivative of e^(e^x-1) evaluated at x = 0.
	www.mathforum.org /library/drmath/view/52270.html (0 words)

	Recent Articles and Reviews (Site not responding. Last check: )
		The Numbers' recording is live, restored from the '70s, the record of a relentless jam band taking cues from Kidney's hip-man vocals.
		Though the Numbers Band continued on and are still active today, the remarkable lineup that recorded Jimmy Bell split shortly after its release.
		The Numbers Band's insistence on minimalist rhythms, innovative use of brass and the ability to make disparate genres feel like natural relations, has kept their music sounding fresh, perhaps even visionary.
	www.numbersband.com /2000_review.html (2668 words)

	Focus: Tatum Bell - Fantasy Football Cafe 2005
		Bell was able to play 41 total games at OSU, racking up 3,409 yards on just 634 carries.
		With this skill, Bell found a way onto the Broncos’ draft board, and he was selected with the 41st overall pick in the 2004 draft.
		Bell will consistently get his 10-15 carries a game, and he will continue to break out big runs, which is what you’re looking for if you have him on your team.
	www.fantasyfootballcafe.com /2005/tips_bell.php (1589 words)

	Set Partitions
		As a matter of curiosity, the Bell number for a set with N members, B(N), is the sum of the number of ways that it can be partitioned into 1, 2, 3,...
		The number of partitions increases rapidly with set size - more than a billion for 15 items - so it's not practical to count the number of ways by actually generating them.
		The program will generate Bell numbers up to the limit of the 64 bit integer type, about set size 25.
	www.delphiforfun.org /Programs/Math_Topics/set_partitions.htm (641 words)

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