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Topic: Ultrafilter

	Ultrafilter - Wikipedia, the free encyclopedia
		In this case, ultrafilters are characterized by containing, for each element a of the Boolean algebra, exactly one of the elements a and ¬a (the latter being the Boolean complement of a).
		Ultrafilters on sets are useful in topology, especially in relation to compact Hausdorff spaces, and in model theory in the construction of ultraproducts and ultrapowers.
		Ultrafilters on sets are used in the ultrapower construction of certain fields of hyperreal numbers.
	en.wikipedia.org /wiki/Ultrafilter (683 words)

	Ultrafilter Info - Bored Net - Boredom (Site not responding. Last check: 2007-10-07)
		Equivalently, an ultrafilter F on a set S is a filter on S with the additional property that for every subset A of S, either A is in F or S \\ A is in F.
		Ultrafilters are useful in topology, especially in relation to compact Hausdorff spaces.
		Ultrafilters are also used in the construction of hyperreal numbers.
	www.borednet.com /e/n/encyclopedia/u/ul/ultrafilter.html (274 words)

	Ultrafilter lemma - Wikipedia, the free encyclopedia
		In mathematics, the ultrafilter lemma states that every filter is a subset of some ultrafilter, i.e.
		This statement is in fact an easy consequence of the Boolean prime ideal theorem that is commonly used in order theory.
		The Ultrafilter Lemma cannot be proven from ZF (the Zermelo-Fraenkel axioms) alone, and it cannot be used to prove the axiom of choice, so it is properly weaker.
	en.wikipedia.org /wiki/Ultrafilter_Lemma (353 words)

	Ultrafilter -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-07)
		Another way of looking at ultrafilters on a set S is to define a function m on the (Click link for more info and facts about power set) power set of S by setting m(A) = 1 if A is contained in F and m(A) = 0 otherwise.
		Likewise, ultrafilters on posets are most important if the poset is a Boolean algebra, since in this case the ultrafilters coincide with the (Click link for more info and facts about prime filter) prime filters.
		Ultrafilters on sets are used in the ultrapower construction of certain fields of (Click link for more info and facts about hyperreal numbers) hyperreal numbers.
	www.absoluteastronomy.com /encyclopedia/U/Ul/Ultrafilter.htm (695 words)

	PlanetMath: every filter is contained in an ultrafilter (Site not responding. Last check: 2007-10-07)
		An importance consequnce of this theorem is the existence of free ultrafilters on infinite sets.
		Acoording to the theorem, there must exist an ultrafilter which is finer than the cofinite filter.
		This is version 2 of every filter is contained in an ultrafilter, born on 2004-10-06, modified 2004-10-07.
	planetmath.org /encyclopedia/EveryFilterIsContainedInAnUltrafilter.html (137 words)

	Membranes of acrylonitrile polymers for ultrafilter and method for producing the same - United States Patent 3,933,653
		More particularly, it relates to a high performance membranes of acrylonitrile polymers for ultrafilter having a large water-permeability, in which size of pore are extremely small and distribution of size is narrow and the method for producing the same.
		An object of the present invention is to provide novel membranes for ultrafilter having a large water-permeability being capable of affording a high filtration rate; hardly causing the clogging of pores and hence, enabling to carry out continuous filtration operation for a long period of time with the same material.
		It is also possible to prepare a membrane of ultrafilter on a supporting material such as cloth, porous plate, porous tube and they should be construed to be included in the membrane of the present invention.
	xrint.com /patents/us/3933653 (4330 words)

	United States Patent: 4,708,713 - UltraPheresis (Site not responding. Last check: 2007-10-07)
		The effective pore size of ultrafiltered media having pores with non-circular cross sections shall be the diameter of a circular pore which will pass molecules or other components of an equivalent size to the molecules or other components which pass through the filter medium in question.
		Blood should be pumped through the ultrafilter unit at sufficient pressure to cause the blood components having the immunosuppressive effects to pass through the filter but at a velocity which will not excessively shear or otherwise damage the blood cells passing over the membrane.
		The permeate pump was adjusted to withdraw 2 cc's per minute of permeate from the ultrafilter, and a second pump withdrew plasma from a source bottle and pumped the plasma into the discharge conduit of the ultrafilter at the same rate as the permeate was withdrawn from the ultrafilter.
	www.ultrapheresis.com /patent_4708713.htm (5147 words)

	PlanetMath: alternative characterization of ultrafilter (Site not responding. Last check: 2007-10-07)
		"alternative characterization of ultrafilter" is owned by yark.
		Cross-references: finite, propositions, theorem, union, disjoint union, satisfies, ultrafilter, filter
		This is version 7 of alternative characterization of ultrafilter, born on 2004-10-08, modified 2005-08-31.
	planetmath.org /encyclopedia/AlternativeCharacterizationOfUltrafilter.html (122 words)

	Ultrafilter Lemma - Wikipedia
		An ultrafilter is a maximal filter -- for every set, either that set or its complement are in the filter.
		The Ultrafilter Lemma says that every filter is a subset of some ultrafilter.
		The Ultrafilter Lemma cannot be proven from ZF (the Zermelo-Frankel axioms) alone, and it cannot be used to prove the axiom of choice, so it is properly weaker.
	nostalgia.wikipedia.org /wiki/Ultrafilter_Lemma (262 words)

	Stevens Point Journal - Donaldson Co. to acquire Ultrafilter International (Site not responding. Last check: 2007-10-07)
		With roughly $94.5 million in sales, Ultrafilter is a global leader in the design and manufacture of components, replacement parts and complete systems for the compressed air purification industry.
		"Ultrafilter's direct selling approach is similar to Donaldson's dust collection business, which has the highest market share in its industry,"he said.
		Dirk G. Kronsbein, chairman, CEO and founder of ultrafilter, said that the transaction was the culmination of seven years of discussions with Donaldson.
	www.wisinfo.com /journal/spjbusiness/275177867555701.shtml (457 words)

	Pneumofore: Company: Subpage (Site not responding. Last check: 2007-10-07)
		For several years, Ultrafilter has supplied Pneumofore with the industry's best treatment technologies, such as filters and dryer components.
		Based in Germany, Ultrafilter is a global company with 14 branch offices and 76 distribution partners.
		Ultrafilter equipment supports the lowest possible life cycle cost, perfectly fitting with Pneumofore units and guaranteeing optimal results over long periods.
	www.pneumofore.com /main/company_partners.htm (345 words)

	Ultrafilter (Site not responding. Last check: 2007-10-07)
		En este caso, los ultrafilters son caracterizados conteniendo, para cada elemento a de la álgebra boleana, exactamente una de los elementos a y ¬a (el último ser el complemento boleano de a).
		Los ultrafilters en grupos son útiles en topología, especialmente en relación a los espacios compactos de Hausdorff, y en la teoría modelo en del la construcción ultraproducts y los ultrapowers.
		Cada ultrafilter en un espacio de Hausdorff del acuerdo converge a exactamente un punto.
	www.yotor.net /wiki/es/ul/Ultrafilter.htm (756 words)

	Compressor Opening Paragraph
		Donaldson Ultrafilter manufacturers a complete line of refrigerated, desiccant and membrane compressed air dryers to meet your specific air quality requirements.
		Donaldson Ultrafilter oil/water separators process condensate to a residual oil content as low as 5 ppm, allowing the processed water to be discharged into most municipal waste water treatment systems.
		Where quality requirements are exceptionally high, Donaldson Ultrafilter offers a selection of process filters that enable you to reach the maximum purity standards required by your process.
	www.donaldson.com /en/compressor/products (399 words)

	Ultrafilter India Pvt Ltd Disclaimer
		Ultrafilter India Pvt Ltd does not warrant that functions contained on this site will be uninterrupted or error-free, that defects will be corrected, or that this site or the server are free of viruses or other harmful components.
		Ultrafilter India Pvt Ltd does not warrant or represent the use of the materials on this site in terms of their correctness, accuracy, reliability, or otherwise.
		Ultrafilter India Pvt Ltd makes no representation or warranty regarding the standing, credit or otherwise of any person, firm or company mentioned in the information, nor the suitability of the information for any purpose.
	snsvo4.seekandsource.com /ultrafilter/disclaimer.html (245 words)

	Industrial Dryers, Donaldson Ultrafilter Dryers, Compressor Filters, California
		Donaldson Ultrafilter International AG is a world leading group of companies in compressed air purification, using compressed air efficiently and with minimal environmental impact.
		ultrafilter is a member of the Compressed Air and Gas Institute (CAGI) and is compliant with ISO 9001 and ISO 8573.1 standards throughout the product line.
		ultrafilter was the first German producer of separation systems, filters and dryers to be awarded the DQS, the German Quality Control Certificate for successful quality control.
	www.californiacompressor.com /accessories.html (395 words)

	Effective and Reliable The HRE and HRS Adsorption Dryers (Site not responding. Last check: 2007-10-07)
		The ultrafilter HRE-SGD and HRE-MSD externally heat-regenerated dryers are designed for the economical and, above all, low-cost treatment of large volume flows of compressed air.
		The user-friendly ultrafilter software coupled with ultrafilter's worldwide guarantee and customer service ensure the high availability of ultrafilter systems and components.
		Have a chat with your ultrafilter engineer and ask for a free analysis to show you how to reduce your operating and energy costs.
	www.tahas.com /adsorption.htm (524 words)

	Ultrafilter
		Equivalently, an ultrafilter F on a set S...
		ultrafilter international AG is in 1972 opgericht te Dsseldorf (Duitsland) en snel uitgegroeid tot een krachtige, wereldwijde onderneming op het gebied van zuivering van perslucht, andere gecomprimeerde gassen en vloeistoffen.
		The benefits of added organic matter to the soil have long been known and are usually attributed to increased nitrogen, greater water-holding capacity and an increase in activity of soil earthworms and microbes.
	all-about-air-quality.info /resources/ultrafilter.html (1442 words)

	Air Purification - Air Response (Site not responding. Last check: 2007-10-07)
		Ultrafilter are acknowledged as one of the worlds premier manufacturers of air purification equipment.
		The Ultrafilter dryer is distinctive with it's unique low pressure drop, outstanding performance and low energy consumption.
		Everywhere from compressors, air receivers and filters to dryers efficient drainage of condensate is imperative.
	www.air-response.demon.co.uk /air.htm (551 words)

	Introducing Electrocoat
		ULTRAFILTER: Ultrafilter is primarily used to produce permeate for rinsing and recovery of paint solids.
		The paint flows through the ultrafilter and water is removed from the paint.
		The secondary use of the ultrafilter is to help maintain the conductivity of the main bath as and when required.
	in.geocities.com /coatecindia (2055 words)

	Karting Challenge 1998
		The race then settled down in to the usual rhythm and the majority of drivers knew that conservation and caution at this stage of the race were the things to be concentrating on.
		At the 30 minute mark Ultrafilter were a lap up on DT Racing and FHM-Parker who had climbed quickly through the field.
		P.S. We have with discussions been informed by Buckmore Park that this is the only the 4th incident of this type in the last 6 years and that onus is on the pit crew to deal with a fire and that the driver on the extinguisher is not held liable.
	pages.britishlibrary.net /racingsnakes/report_round5.html (1231 words)

	Concentration and Detection of Cryptosporidium Oocysts in Surface Water Samples by Method 1622 Using Ultrafiltration ...
		from 11 to 86% (average, 42%) with the ultrafilters and 21 to
		There are advantages and disadvantages associated with both the capsule filters and ultrafilters.
		the ultrafilters is much less (approximately $35 per filter).
	aem.asm.org /cgi/content/full/67/3/1123 (3457 words)

	Ultrafilter Filters
		That's why you need ultrafilter filters to protect your business.
		With ultrafiter there are no more compromises, ultrafilter makes a clean sweep because the high performance filter elements ensure pure compressed air.
		Ultrafilter has developed two different types, the filtration material of the standard PE type consists of ultrapoly®, a sintered polyethylene.
	www.broadcom.com.au /core/content/compressors/uf-filters.html (545 words)

	Ultrafilter GmbH, Haan, Germany
		Formed in Düsseldorf in 1972, ultrafilter swiftly expanded to become an international company whose headquarters are now located in Haan.
		Since we always planned to do more than just produce filters and separators, ultrafilter not only stands for numerous patents but has also given birth to ultratrockner GmbH.
		In short, you can benefit from ultrafilter technology in the whole field of compressed air, gas and fluids separation.
	www.chemie.de /firmen/e/1017/ultrafilter_gmbh.html (67 words)

	Optimization of a Reusable Hollow-Fiber Ultrafilter for Simultaneous Concentration of Enteric Bacteria, Protozoa, and ...
		Optimization of a Reusable Hollow-Fiber Ultrafilter for Simultaneous Concentration of Enteric Bacteria, Protozoa, and Viruses from Water -- Morales-Morales et al.
		Optimization of a Reusable Hollow-Fiber Ultrafilter for Simultaneous Concentration of Enteric Bacteria, Protozoa, and Viruses from Water
		Procedure for the evaluation of the reusable hollow-fiber ultrafilter for the concentration of viral, bacterial, and protozoal pathogens from 10-liter water samples.
	aem.asm.org /cgi/content/full/69/7/4098 (2928 words)

	Light Reading - Networking the Telecom Industry
		Based upon the company’s proprietary technology, the UltraFilter UF50-POF provides the capability of independently equalizing, attenuating and blocking any or all wavelengths in the C-band at 50 GHz channel spacings.
		The UltraFilter UF50-POF ultimately reduces network complexity as well as operating and capital costs by enabling remote, dynamic channel reconfiguration and eliminating the need for multiple discrete wavelength filtering components.
		The company is also developing an UltraFilter platform to address Metro and Regional network applications featuring an ultra small form factor and 100 GHz channel spacings, and is planning to officially announce the product later this year.
	www.lightreading.com /document.asp?doc_id=40210 (475 words)

	Programmable Optical Filter (Site not responding. Last check: 2007-10-07)
		Based on the company’s proprietary technology, the UltraFilter UF50-POF provides the capability of independently equalizing, attenuating and blocking any or all wavelengths in the C-band at 50-GHz channel spacings.
		The company said UltraFilter UF50-POF ultimately reduces network complexity as well as operating and capital costs by enabling remote, dynamic channel reconfiguration and eliminating the need for multiple discrete wavelength filtering components.
		The company said it is also developing an UltraFilter platform to address metro and regional network applications, featuring an ultrasmall form factor and 100-GHz channel spacings, later this year.
	www.photonics.com /fiber/XQ/ASP/url.readprod/prodid.511/QX/readprod.htm (274 words)

	Water Chillers have capacities to 58 tons., Ultrafilter, Inc. (Site not responding. Last check: 2007-10-07)
		ultrafilter, inc. is pleased to announce the launch of it's ultracool process water chiller product line into the North American market.
		ultrafilter's North American headquarters is located in Norcross, Georgia while it's world headquarters is in Haan, Germany.
		Other ultrafilter inc. products include compressed air and gas purification equipment such as refrigerated and desiccant air dryers, particulate and coalescing filters and related products.
	news.thomasnet.com /fullstory/7022/1029 (320 words)

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