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	Aliquot - Wikipedia, the free encyclopedia
		For instance, 2 is an aliquot of 12.
		The sum of all the aliquots of an integer n is the value σ(n) of the divisor function σ at n.
		In chemistry, an aliquot is usually a portion of a total amount of a solution.
	en.wikipedia.org /wiki/Aliquot (103 words)

	Aliquot sequence - Wikipedia, the free encyclopedia
		For instance, the aliquot sequence of 220 is 220, 284, 220, 284,....
		For instance, the aliquot sequence of 95 is 95, 25, 6, 6, 6,....
		An important conjecture due to Catalan with respect to aliquot sequences is that every aliquot sequence ends in a prime number, perfect number, or a set of sociable numbers.
	en.wikipedia.org /wiki/Aliquot_sequence (384 words)

	Aliquot stringing - Wikipedia, the free encyclopedia
		Aliquot stringing is the use of extra unstruck strings in the piano for the purpose of enriching the tone.
		Aliquot stringing and the duplex scale are not equivalent.
		In mathematics "aliquot" means "an exact part or divisor", reflecting the fact that the length of an aliquot string forms an exact division of the length of longer strings with which it vibrates sympathetically.
	en.wikipedia.org /wiki/Aliquot_stringing (412 words)

	Aliquot Sequences
		The aliquot divisors of a number are all of its divisors except itself.
		The aliquot divisors of 10 are 1, 2, and 5.
		An aliquot sequence is a sequence of numbers where each number is the sum of the previous number’s aliquot divisors.
	home.netcom.com /~jrhowell/math/aliquot.htm (562 words)

	Lesson #2
		Hence the aliquot divisors of 28 are 1, 2, 4, 7, and 14.
		The sum of the aliquot divisors of 20 is 1 + 2 + 4 + 5 + 10 = 22.
		The sum of the aliquot divisors of 22 is 1 + 2 + 11 = 14.
	www.mccallie.org /math/lesson_1.htm (937 words)

	Aliquot game
		Aliquot part is another name for a proper divisor, i.e.
		1, 2, 3, 4, 6 are all aliquot parts of 12.
		In the Aliquot game, players take turns subtracting an aliquot part of the number left by their opponent.
	www.cut-the-knot.org /SimpleGames/Aliquot.shtml (360 words)

	Patent 6,733,748
		The electromagnetic emission stressor is suitably applied by irradiating the aliquot under treatment from a source of electromagnetic emission while the aliquot is maintained at the aforementioned temperature and while the oxygen/ozone gaseous mixture is being bubbled through the aliquot.
		It is preferred to subject the aliquot to the oxidative environment stressor, the UV light stressor and the temperature stressor simultaneously, following the subjection of the aliquot to the mechanical stress, e.g.
		When the oxidative environment in the form of a gaseous mixture of oxygen and ozone applied to the aliquot is chosen as one of the two stressors, the concentration of the oxidizing agent and the rate at which it is supplied to the aliquot may affect the preferred temperature.
	www.pharmcast.com /Patents100/Yr2004/May2004/051104/6733748_Leukemia051104.htm (2948 words)

	Standard dimension pallet assembly formed of separate abutted segments - Patent 4694962
		2, each aliquot portion, such as the half portion 4 shown, is comprised of a substantially planar cargo bearing surface, such as the surface formed by the upward facing surfaces of each of a plurality of support members, such as slats or boards 6.
		Normally an aliquot portion of a splittable cargo would be borne by each pallet segment and maintained on each segment by means, such as by using a corrugated paper cover or envelope, or more likely, a plastic shrink wrap which protectively covers the sub-section of cargo and maintains it on its respective pallet segment.
		Each of the aliquot segments 112 of the cargo bearing members are provided with a rigidifying locating and spacing means, such as members 120, which coact with upper portions of stringers 116 to aid in maintaining the members 112 properly located on the base.
	www.freepatentsonline.com /4694962.html (4471 words)

	Midwest Research Institute (MRI) Laboratory Methods
		Summary: A one gram aliquot of the dried soil is transferred to a beaker and metalsare extracted using nitric acid and hydrogen peroxide (1).
		Summary: A 50-mL aliquot of water is digested with nitric acid and hydrochloric acid in a heating block at 95 C for 3 hours and the sample is diluted to 50 mL.
		Summary: A 0.5-g aliquot of dry sediment is digested with nitric acid (and optionally hydrochloric acid) in a microwave oven at a temperature of 170-180*C for 20 minutes and the sample is diluted to 50 mL.
	www.fws.gov /chemistry/methods_mri_lab.htm (3639 words)

	Patent 6,569,467
		The autovaccine is prepared by exposing the blood aliquot to at least one stressor, in controlled amounts, the stressor being selected from among oxidizing agents such as ozone, ultraviolet radiation and elevated temperature, and combinations of two or more of such stressors.
		In preparing the autovaccine according to the invention, by modification of a blood aliquot extracted from the patient, the blood cells are stressed.
		The ultraviolet radiation stressor is suitably applied by irradiating the aliquot under treatment from an appropriate source of UV radiation, while the aliquot is maintained at the aforementioned temperature and while the oxygen/ozone gaseous mixture is being bubbled through the aliquot.
	www.pharmcast.com /Patents/Yr2003/May2003/052703/6569467_Autoimmune052703.htm (2996 words)

	Aliquot sequences (Site not responding. Last check: 2007-10-25)
		Aliquot sequences arise in iterating the sum-of-divisors function s, which assigns to a positive integer the sum of its proper divisors (i.e., excluding the number itself).
		The main open question in the area is given by the Catalan-Dickson conjecture, which states that for any starting value n one of two things happens: either the sequence ends in a cycle, or it reaches 1 after finitely many steps (and is said to terminate then).
		All this is ongoing work as part of a bigger effort by several people (see the aliquot page of Wolfgang Creyaufmüller, or the page of Juan Varona, or the aliquot page of Paul Zimmermann).
	www.math.ru.nl /~bosma/research/nuth/ali.html (404 words)

	aliquot part
		For instance, the aliquot parts of 12 are 1, 2, 3, 4, and 6.
		An aliquot sequence is formed by taking the sum of the aliquot parts of a number, adding them to form a new number, then repeating this process on the next number and so on.
		For some numbers, the result loops back immediately to the original number; in such cases the two numbers are called amicable numbers.
	www.daviddarling.info /encyclopedia/A/aliquot_part.html (265 words)

	Problem 23.- Divisors (V) Aliquot sequences, Sociable Numbers.
		As we saw in the Problem 22, one possible end of an aliquot sequence is to reach to a cycle of numbers.
		Moews and I have exhaustively searched for all aliquot cycles of length greater than 2 such that the number preceding the largest number of the cycle is below 1.54*10^11.
		I have verified the existence of some of these cycles, and found that the least number that generates - in some instant of the develop of the aliquot sequence - the cycle of order k = 5 is n = 9464.
	www.primepuzzles.net /problems/prob_023.htm (480 words)

	Pražské znění (Site not responding. Last check: 2007-10-25)
		Aliquot singing is based on conscious highlighting of individual spectral tones, it’s amplification and separation from the ground singed tone.
		Aliquot singing is a dateless way of singing, nowadays still usual in Mongolia, Tuva or Tibet.
		In every culture were aliquots used for healing, in rituals and prayers, because they’re a powerful way of physical, mental end emotional ordeal.
	www.alikvotnifestival.cz /en_aliquot.htm (424 words)

	In the matter of Aliquot Asset Management Limited [2003] ATP 19 – Aliquot Asset Management Limited (20/05/2003)
		Aliquot Asset Management Limited and its management system was recognised by other shareholders during the year and an attempt was made to change the board of Aliquot Asset Management Limited.
		According to the response of Aliquot and EquitiLink, the reference to "an arrangement" was a reference to the matters referred to above in paragraph 19.
		The Panel considers that the application does not disclose matters that come within the Panel's area of concern and that having regard to the nature of the issues raised in the application it is not appropriate for the Panel to commence proceedings.
	www.takeovers.gov.au /display.asp?ContentID=88 (1407 words)

	ALIQUOT PAGE - Prime families - Primzahlfamilien
		An aliquot sequence is a sequence of integers, built with the sigma function.
		Normally the end of an aliquot sequence is a prime.
		ALIQUOT is written by Ivo Duentsch in Turbo Pascal and available in its original version at the ftp-server.
	www.aliquot.de /aliquote.htm (3166 words)

	Emblemata aliquot selectiora amatoria: Introduction
		The Emblemata aliquot selectiora amatoria was first published in 1618, as a result of un ungoing competition by two Amsterdam publishers.
		The selection made in the Emblemata aliquot selectiora amatoria (only 70 of the original 124 emblems were selected for this anthology) led to a collection that hardly differs in order from the Amorum emblemata of 1608.
		in the Emblemata aliquot selectiora amatoria ware taken from a not corresponding position in the Amorum emblemata (namely emblem 18, and 19 and 79).
	emblems.let.uu.nl /emblems/html/va1618ei.html (691 words)

	Aliquot
		Aliquot : A measured portion of a sample taken for analysis.
		Reduced aliquot size for a plasma organochlorine assay for use in...
		Gamma analysis used an aliquot of the sample and was analyzed by gamma...
	www.mongabay.com /reference/environment/Aliquot.html (374 words)

	Tests to evaluate the Anti-virus Effect of Polymer OCT 57
		Aliquot 1 plus TV1 was mixed with the normally growing Aliquot 2 and held at 26-30 C. 10 hours.
		Aliquot 5 plus the test Antiviral agent was a normally growing culture – microscopic examination revealed normally dividing mobile cells indistinguishable from the control culture.
		Since active growth occurred in these aliquots it is clear that the Polymer OCT 57 stopped the action of the bacteriophage to B. Coli.
	www.malleus.net /HCWA4.htm (1418 words)

	Triturations and Aliquots
		Select the size of the aliquot portion to be taken to contain the 6 mg of drug.
		Determine the weight of lactose which must be added to the aliquot portion of trituration to complete the prescription, so that each capsule weighs 200 mg.
		Both the total volume of solution and the aliquot volume should be such that they are easily and accurately measured (preferably whole number multiples of 5 ml).
	pharmlabs.unc.edu /triturations/text.htm (854 words)

	Aliquot Form
		After filtering the aliquots using the standard filtering and sorting methods (use the right click menu and the toolbar buttons), you may print out the results in either form view or datasheet view.
		The combo boxes for selecting aliquot positions are populated by advanced querying procedures.
		Providing these 'dummy' locations enables the aliquot records to appear in the treeviews of the Storage Tree Form, where they may subsequently be dragged to their correct locations.
	cryoma.com /BioDataWorks/HelpFiles/BioDataWorks_help/aliquot_form.htm (1040 words)

	Aliquot Sums
		The aliquot divisors of a number are all of its divisors except the number itself.
		The aliquot sum is the sum of the aliquot divisors so, for example, the aliquot divisors of 12 are 1, 2, 3, 4, and 6 and it's aliquot sum is 16.
		If we denote the aliquot sum by ASUM, then the condition for a perfect number is ASum(N)=N. Numbers A and B with the property that ASum(A)=B and ASum(B)=A are called AMICABLE numbers.
	www.delphiforfun.org /Programs/AliquotSums.htm (732 words)

	Pražské znění
		To teach aliquot techniques is possible only in the choirs that are systematically working on the voice education as well.
		Although even only one song with aliquot techniques can enrich the concept of the concert really much, apart from the fact, that during the rehearsal learns the choir to hear it’s sound from quite new point of view.
		The aliquot choir Spektrum from Prague is going to perform on the planned lecture, illustrating with instances the possibilities of the work with the sound-color.
	www.alikvotnifestival.cz /en_lecture.htm (449 words)

	Chlamydia/Gonococcus - Client provided Cytyc Aliquot (Site not responding. Last check: 2007-10-25)
		It is recommended to use powder-free gloves and an individually wrapped, disposable pipetting device with an aerosol barrier tip that is sized appropriately for the volume being withdrawn and dispensed.
		Aliquot Removal from low-cellularity may leave insufficient material in the PreservCyt sample vial for preparation of a satisfactory ThinPrep Pap Test slide.
		Aliquot Removal may leave insufficient material in the PreservCyt sample vial for performance of ancillary testing (e.g., reflexive HPV testing) using the residual specimen following preparation of a ThinPrep Pap Test slide.
	www.labcorp.com /datasets/labcorp/html/chapter/mono/nf10011680.htm (1805 words)

	Aliquot sequences
		If you are interested in this subject, you can found pre-print with our results (in tex, dvi and pdf formats), the last term for any doubtful sequence, and the present state of the calculus by using anonymous ftp from mat.unirioja.es/pub/aliquot.
		Wolfgang Creyaufmueller, from Aachen, is cumputing aliquot sequences starting a in number between 10^5 and 10^6 up to a minimum of 60 digits.
		Wieb Bosma is working with aliquot sequences starting between 10000 and 50000.
	www.unirioja.es /dptos/dmc/jvarona/aliquot.html (990 words)

	World's Longest Unitary Aliquot Sequence
		On 11 July 2001, the longest known terminating unitary aliquot sequence was computed to its termination.
		A unitary aliquot sequence is constructed similarly to a "standard" aliquot sequence, except that instead of adding divisors, one adds up unitary divisors.
		It is conjectured that all unitary aliquot sequences eventually either enter a closed cycle, or terminate by reaching the number 1.
	www.brennen.net /primes/151244562.html (420 words)

	Perfect numbers
		Today the usual definition of a perfect number is in terms of its divisors, but early definitions were in terms of the 'aliquot parts' of a number.
		An aliquot part of a number is a proper quotient of the number.
		Note that 10 is not an aliquot part of 10 since it is not a proper quotient, i.e.
	www-history.mcs.st-and.ac.uk /history/HistTopics/Perfect_numbers.html (4360 words)

	Genetix - Instruments - aliQuot
		The aliQuot is an automated, low volume liquid dispensing platform optimised to deliver volumes of between 1-350ul with high accuracy and reproducibility.
		The aliQuot can be supplied with an extended plate stage which allows portrait and landscape accessibility for robotic arms.
		The footprint of the aliQuot is small, allowing the instrument to be placed in a laminar flow cabinet to maintain a sterile environment.
	www.genetix.com /instr/aliquot.asp (300 words)

	Curious Properties of 153 By Shyam Sunder Gupta
		The sum of aliquot divisors of 153 is also a perfect square:
		Aliquot divisors of a number are all the divisors of that number excluding the number itself but including 1.
		It is seen that the sum of aliquot divisors of 153 is the square of the sum of the digits of 153.
	www.shyamsundergupta.com /c153.htm (691 words)

	Divisor Sums
		An Aliquot sequence is a sequence of integers of the form
		People have been particularly fascinated in Aliquot sequences that are periodic.
		This problem is not that different from the problem of Aliquot sequences; yet, small observations in the data lead to a solution for the
	www.math.okstate.edu /~wrightd/PARI/NumberTheoryandPARI/Divisor_Sums.html (411 words)

	Aliquot Sequences from the Trenches
		This progression led some to question the fate of sequences in which each member was the sum of the aliquot parts of its predecessor, where the aliquot parts of n consist of the divisors of n excluding n itself.
		In particular, an aliquot sequence beginning with a randomly chosen even number would, in all probability, be expected to increase without bound.
		Advances in Aliquot Sequences which was published in the journal Mathematics of Computation.
	www.lafn.org /~ax810/aliquot.htm (2703 words)

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