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	[No title] (Site not responding. Last check: 2007-10-21)
		Lessons on Dual Numbers This is an outline of some lessons on dual numbers, suitable for a second-year algebra course after a chapter on the algebra of complex numbers.
		We think of D as a very small number whose square is "too small to be seen." Naturally no real numbers have this property, but since the students have studied complex numbers already, this should not cause them to fall out of their chairs.
		With complex numbers we use the fact that (0 -1)^2 (-1 0) (1 0) = (0 -1) to identify the complex number a + b*i with the matrix (a -b) (b a).
	www.rexx.com /~oinkoink/dual_numbers.txt (2060 words)

	Dual space - Wikipedia, the free encyclopedia
		In the language of category theory, taking the dual of vector spaces and the transpose of linear maps is therefore a contravariant functor from the category of vector spaces over F to itself.
		The continuous dual V′ of a normed vector space V (e.g., a Banach space or a Hilbert space) forms a normed vector space.
		This turns the continuous dual into a normed vector space, indeed into a Banach space so long as the underlying field is complete which is often included in the definition of the normed vector space.
	en.wikipedia.org /wiki/Dual_space (998 words)

	Dual numbers - Wikipedia, the free encyclopedia
		The plane of all dual numbers is an "alternative complex plane" that complements the ordinary complex number plane C and the plane of split-complex numbers.
		The "unit circle" of dual numbers consists of those with a = 1 or -1 since these satisfy z z * = 1 where z * = a - bε.
		As a consequence, we see that the dual numbers over any field (or any commutative local ring) form a local ring.
	en.wikipedia.org /wiki/Dual_numbers (436 words)

	Center for Immigration Studies
		The 2001 legal immigration number is expected to be actually something like 1.5 million, just legal immigrants, not even counting illegal immigrants, and 90 percent of them come from countries that allow some form of dual citizenship.
		So dual citizenship in the nineteenth century context was akin to putting individuals in a situation similar to contested territory, and states ended up fighting over their claim to individuals and these dispute could be quite intense.
		Dual citizenship involves people who are here as permanent residents already, so when we're looking at assimilation questions we're facing those questions outside of the citizenship context.
	www.cis.org /articles/2002/dualcitpanel.html (9662 words)

	Community College Review: A comparison of learning outcomes for dual-enrollment mathematics students taught by high ...
		Dual enrollment courses were not offered during the summer terms at the district high schools; therefore, no summer terms are included in the study.
		Of the 1,833 students identified as having taken a dual enrollment mathematics course during the five-year period studied, 754 students were found to have taken subsequent coursework in mathematics at one of Florida's 10 state universities as of spring 2000.
		Dual enrollment students taught by high school teachers were better prepared for subsequent coursework at the university level than were those taught by college faculty.
	www.findarticles.com /p/articles/mi_m0HCZ/is_3_29/ai_83315685/pg_3 (1405 words)

	Dual Citizenship in Australia (Current Issues Brief 5 2000-01)
		The strongest argument in favour of dual citizenship at the beginning of the new millennium in Australia is the estimated 4-5 million Australians-people who have migrated and taken out Australian citizenship, and their children-who are already dual citizens.
		Australian governments have in the past resisted dual citizenship, because of the notion that citizenship reflects a person's allegiance and commitment to the nation, and perhaps to allay concerns regarding the incorporation of large numbers of immigrants from increasingly diverse sources.
		While dual (or multiple) citizenship may pay off for awhile in the global marketplace, and at the individual level, it continues to add to a sense in the broader community of erosion of social values and political and legal structures.
	www.aph.gov.au /library/pubs/cib/2000-01/01cib05.htm (5271 words)

	Center for Immigration Studies
		Dual citizenship, especially when it entails active participation in the political life of an immigrant's home country, leads to conflicts of interest, attention, and attachment.
		An American dual citizen domiciled in a foreign country would have to return to this country one year prior to the election in which he or she wished to vote, or not be able to do so.
		The problem of dual citizens, or even American citizens with strong homeland feelings, entering into combat in one form or another in their countries of origin is certainly not as large a problem numerically as the issue of foreign voting; the numbers are most likely very small.
	www.cis.org /articles/2005/dualcitizenship.html (14491 words)

	THE H.A.M.B. - 348/409 Dual Quad question
		Buick dual quad carbs are often confused with the 409 carbs.
		The numbers for 409 2X4 carbs are front 3361 and rear 3362 (early) or 3804 (late).
		They are the same carbs, but for the "numbers matching" 60's Chevy 409 restorer crowd, they want the carbs without the "S" at the end of the carb number.
	www.jalopyjournal.com /forum/showthread.php?t=42979 (758 words)

	Citizens of the World - The Harvard Political Review - Cover (Site not responding. Last check: 2007-10-21)
		Their sheer numbers give dual citizens the potential to profoundly influence the character of today's nations-the real question is how.
		In 1915, Theodore Roosevelt called the "theory of dual nationality" a "self-evident absurdity." After nearly a century, attitudes have changed dramatically: in 2002, 92 countries allowed some form of dual citizenship, and more are added to the list every year.
		Most significantly, dual citizens owe allegiance and obedience to more than one country, which sometimes entails obligations to laws, taxes, and military service.
	hpronline.org /news/2005/02/01/Cover/Citizens.Of.The.World-858057.shtml (799 words)

	Dual-eligibles
		Even if the pharmacist informs a NJ dual eligible that his/her medication is denied by the Medicare drug plan, the dual eligible should never leave the pharmacy without at least a temporary (6-day) supply of their prescription medication -- paid for by our state's wrap -around.
		If you are a dual eligible (or a caregiver), and you have not received the yellow letter, it is suggested that you contact the Medicare hotline to request this information.
		When the caller is connected to a Social Security agent, the caller should request confirmation of the dual eligible's date of first entitlement for Medicare (and the caller may want to add that this information is necessary to switch drug plans in the Medicare Part D system).
	www.arcnj.org /html/dual-eligibles.html (1900 words)

	AskTom "All about the DUAL table " (Site not responding. Last check: 2007-10-21)
		The advantage to dual is the optimizer understands dual is a special one row, one column table -- when you use it in queries, it uses this knowledge when developing the plan.
		select * from dual, dual; would be the same as: select dual.dummy, dual.dummy from dual, dual; where as: select * from dual, (select * from dual) is the same as: select dual.dummy, .dummy from dual, (select * from dual); where anonymous is like "null" - no anonymous equates to anyother anonymous.
		I find dual to be no used in "real queries" and when it is, it is in a construct like: select * from t where x = (select foo() from dual); meaning, the cardinality of dual is not excessively relevant.
	asktom.oracle.com /pls/ask/f?p=4950:8:::::F4950_P8_DISPLAYID:1562813956388 (6460 words)

	Good Math, Bad Math : Introducing the Surreal Numbers
		Surreal numbers are a beautiful, simple, set-based construction that allows you to create and represent all real numbers, so that they behave properly; and in addition, it allows you to create infinitely large and infinitely small values, and have them...
		Surreal numbers are a beautiful, simple, set-based construction that allows you to create and represent all real numbers, so that they behave properly; and in addition, it allows you to create infinitely large and infinitely small values, and have them behave and interact in a consistent way with the real numbers in their surreal representation.
		Given any surreal number {LR}, the value that it represents is the value between the largest value in L and the smallest value in R with the earliest birthday (or, equivalently, the lowest ordinal).
	scienceblogs.com /goodmath/2006/08/introducing_the_surreal_number.php (2440 words)

	Advanced Animation Techniques in VRML 97
		Dual quaternions are known since the early days of quaternion algebra in the 18th century.
		In the first case the dual part of the dual angle is zero, in case of a translation the real part is zero.
		Finally, the dual quaternions are multiplied with the quaternion describing the initial transformation and rotational and translational part are extracted.
	www.cse.unsw.edu.au /~cs9018/vrml98/dualquat.html (1499 words)

	Unit 2
		The first part of the dual number is the unit number, and the second part is the sequence number of the section within the unit.
		dual numbers: the first part of the dual number is the unit number, and the second part is the sequence number for the figure.
		Number any figures you wish to use in UREs or CEs as T–1, T–2, and so forth (see appendix), and refer to them as such in your proposed multiple-choice test questions.
	www.au.af.mil /au/afiadl/curriculum/guide/unit2.htm (4945 words)

	Dual_space (Site not responding. Last check: 2007-10-21)
		Given any vector space V over some field F, we define the dual space V* to be the set of all linear functionals on F, i.e., scalar-valued linear transformations on V (in this context, a "scalar" is a member of the base-field F).
		This turns the continuous dual into a normed vector space, indeed into a Banach space.
		In analogy with the case of the algebraic double dual, there is always a naturally defined injective continuous linear operator Ψ : V → V '' from V into its continuous double dual V ''.
	www.freecaviar.com /search.php?title=Dual_space (995 words)

	1st-order Hypercomplex Numbers (Site not responding. Last check: 2007-10-21)
		This might seem like this means that there should be an infinite number of different kinds of 2nd-order hypercomplex numbers, but it turns out that they can all be reduced to three species.
		In general, division is not defined for the dual and double numbers.
		Complex numbers are therefore unique in being the only division system which can be made up from two real numbers being coupled in the form a + bi.
	math.hyperjeff.net /hypercomplex/1st_order.html (303 words)

	Maths - Multivector transforms - Martin Baker
		An example of the first case is G+3,0,1 (dual quaternion) which represents both the linear and rotational movement as bivectors which are associated with planes, or quantities associated with them like rotations, we would expect a linier displacement to be represented by a vector.
		A dual whose elements are complex numbers or a complex numbern whose elements are duals, (its the same thing).
		A dual whose elements are quaternions or a quaternion whose elements are duals, (its the same thing).
	www.euclideanspace.com /maths/algebra/clifford/transforms (842 words)

	Pro forma profits
		The article was trying to make sense of Cisco's dual numbers, both posted in the same financial press release, and the recent trend toward firms reporting "pro forma" financials to the public.
		But again, pro forma numbers are for "public" consumption only and are not accepted by the SEC as "real" numbers.
		To be fair, pro forma numbers can sometimes be useful to help a firm restate previous numbers or provide additional guidance on overall numbers.
	www.networkworld.com /columnists/2001/0730current.html (659 words)

	Southwest Virginia Community College News
		The numbers of dual enrolled students has increased dramatically in the past several years.
		“Dual enrollment helps students broaden their knowledge by taking courses that are not offered at their high school(s).
		With dual credit classes, students actually get to take classes on the campus of their high school(s), making it very accessible.
	www.sw.vccs.edu /news05/dualenrollmentdec.htm (640 words)

	Dual-specific T cells combine proliferation and antitumor activity - Nature Biotechnology
		The transfer of large numbers of alloreactive T cells, and the further generation of alloreactive T cells in vivo after immunization, could conceivably lead to the activation of T cells cross-reactive with autoantigens.
		We have focused on the effect of immunization on the numbers of dual-specific T cells in vivo, and it is likely that the increase in these cells contributes to the observed antitumor effect.
		In our approach, large numbers of adoptively transferred T cells persist (and probably expand), and in vitro reactivity is high; however, improvements could perhaps be achieved by modifying the culture or transduction conditions or by minimizing in vitro culture.
	www.nature.com /cgi-taf/DynaPage.taf?file=/nbt/journal/v20/n12/full/nbt756.html (6539 words)

	Articles - Grammatical number (Site not responding. Last check: 2007-10-21)
		As we have seen, in many languages number is limited to two categories: singular number, distinguishing between one referent and plural number, distinguishing more than one referent.
		dual number, for two instances of the referent (e.g.
		A very common situation is that plural number is not marked if there is any other overt indication of number (as for example in Hungarian: virág "flower"; virágok "flowers"; hat virág "six flowers").
	www.gaple.com /articles/Grammatical_number (1472 words)

	DUAL CITIZENSHIP EXPLODES IN U.S. [Free Republic]
		Dual citizens "can be loyal to two countries," she says, explaining that to her dual citizenship means being connected to her homeland, which she loves.
		Teddy Roosevelt was quoted on dual citizenship during his presidency to the effect that you show me a dual citizen who loves the US as much as his home country and I'll show you a philanderer who claims he loves his wife as much as his mistress.
		"Dual nationality" in the U.S. is very different from in most any other country for two simple reasons - the U.S. borders a country that is the source of many such "dual nationals" and that the U.S. is quite accepting of further immigration compared to most other countries.
	www.freerepublic.com /forum/a382fc17f0cae.htm (5677 words)

	3D ANALYSIS OF HUMAN LOCOMOTION USING DUAL-VECTORS AND GRAPH THEORY (Site not responding. Last check: 2007-10-21)
		In the dual- vector approach, the two domains are combined and system variables are expressed using a spatial mathematical entity consisting of a vector and an associated moment.
		It is shown by (5) that the pelvic twist V4 is the sum of the absolute twist of the left foot V1, and the relative twists of the ankle V8, knee V9 and hip V10.
		It is also shown by (7) that the internal forces, F13 is automatically eliminated from the motion equation thus reducing number of the unknowns and hence, number of the equations.
	www.asb-biomech.org /onlineabs/NACOB98/277 (1249 words)

	Numbers, Numbers -- But What Do They Mean?
		One of the latest trends these days is for crawler-based search engines to flaunt both how many pages they have in their index plus the larger number of pages they visited to create that index.
		Citing dual numbers is a marketing spin we haven't seen since the first search engine size wars of 1996, when Lycos used to say it "knew" of millions of URLs even though its index contained only some of these.
		By citing the larger number of pages visited, the search engines are able to answer this question in a better light.
	searchenginewatch.com /showPage.html?page=2162421 (2273 words)

	Compare Prices and Read Reviews on Casio DB70D-7V Wrist Watch at Epinions.com
		When the color mode is red on blue, the red numbers shine with an almost holographic quality, which is cool to watch.
		When you enter Dual time, your home time moves to the top 1/3 of the screen the bottom 2/3 is then local time.
		Dual time is very easy to set, but also very easy to change by accident since there is no "set mode".
	www.epinions.com /content_175634943620 (572 words)

	Decimal Encoding Specification - Overview
		The finite numbers are defined by a sign, an exponent (which is a power of ten), and a decimal integer coefficient.
		The combination field requires 30 states out of a possible 32 for the finite numbers; the other two states are used to identify the special values.
		This localization of the special values means that only the first few bits of a number have to be inspected in order to determine whether it is finite or is a special value.
	www2.hursley.ibm.com /decimal/dbover.html (637 words)

	CGTalk - Dual processesor motherboards - where to buy?
		Most of the dual boards from newegg are EATX form factor and require a whopper of a PSU.
		It seems that back in the day, dual mobo's could handle a variety of different proc's so long as the pair were the same.
		I've been looking to buy a Dual Xeon system for some time now, I asked the people at boxxtech what they put in their Dual 800MHz 3.0GHz Xeons and they choose the Supermicro X6DAx mainboard...
	forums.cgsociety.org /printthread.php?t=172057 (823 words)

	Dual space : Duality (linear algebra) (Site not responding. Last check: 2007-10-21)
		In mathematics the existence of a 'dual' vector space reflects in an abstract way the relationship between row vectors (1xn) and column vectors (nx1).
		Given any vector space V over some field F, we define the dual space V* to be the set of all linear functions from V to F. These linear functions to the base field are also called linear functionals.
		One may also talk about the continuous dual of an arbitrary topological vector space.
	www.city-search.org /du/duality-(linear-algebra).html (1294 words)

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