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# Topic: Set of uniqueness

###### In the News (Mon 22 Jul 19)

 Wikinfo | Empty set In the axiomatization of set theory known as Zermelo-Fraenkel set theory, the existence of the empty set is assured by the axiom of empty set. As a result, the empty set is the unique initial object of the category of sets and functions. The empty set can be turned into a topological space in just one way (by defining the empty set to be open); this empty topological space is the unique initial object in the category of topological spaces with continuous maps. www.wikinfo.org /wiki.php?title=Empty_set   (1080 words)

 Set of uniqueness - Wikipedia, the free encyclopedia "a set of uniqueness with respect to summing over balls". In Fourier analysis there is no question of uniqueness, since the coefficients c(n) are derived by integrating the function. The empty set is a set of uniqueness. en.wikipedia.org /wiki/Set_of_uniqueness   (827 words)

 Sudoku Players' Forums :: View topic - Standardizing the Uniqueness descriptions...   (Site not responding. Last check: 2007-10-14) If you're looking for naked sets of the extras, or hidden sets of the originals, you actually won't be able to find one that includes the others if you set the "quantum values" of the two cells to extras and original+extras. Uniqueness 3 guarantees it because a partial subset can only be found in situations where one of the cells has the roof candidates, making it part of the full hidden set which complements the full naked set. Uniqueness 4 guarantees it because one of the roof candidates is already known to occur only within the two floor cells. www.sudoku.com /forums/viewtopic.php?p=13002   (3007 words)

 C++Course: The Set Data Structure Keep in mind that the number of elements in the set, numElements, is not the same thing as the size of the pvector. The Set constructor takes a single parameter, which is the initial size of the pvector. It is the number of elements in the set, of course, but it is also the index of the next element to be added. www.vias.org /cppcourse/chap23_07.html   (730 words)

 Uniqueness of Pitch Class Spaces, Minimal Bases and Z Partners   (Site not responding. Last check: 2007-10-14) The synonyms above all refer to a set class whose representatives are of cardinality M. The cardinality of the set class itself is not the same as the cardinality of its members. Given sets (set classes) X and Y, X and Y are in the Z relation with respect to M-decomposition iff the M-class vectors of X and Y are equal. Given sets X and Y, X and Y are in the Z relation with respect to C-decomposition iff the C-vectors of X and Y are equal. www.axp.mdx.ac.uk /~nicholas15/musictheorypaper/diderotmusictheory.htm   (4875 words)

 Springer Online Reference Works The theory of trigonometric series can conditionally be divided into two main branches: the theory of Fourier series, in which it is supposed that the series (1) is the Fourier series of some function, and the theory of general trigonometric series, where this hypothesis is not made. Therefore the problem on the representation of functions that can take infinite values on a set of positive measure has been considered for the case when convergence almost-everywhere is replaced by a weaker condition, namely, convergence in measure. In the uniqueness problem, an important role is played by very precise characteristics of sets of measure zero. eom.springer.de /t/t094240.htm   (1620 words)

 Springer Online Reference Works These concepts are related to the problem of the uniqueness of the representation of a function by a trigonometric series converging to it everywhere, except perhaps on a given set Cantor (1872) showed that a finite set (including the empty set) is a set of uniqueness, and the extension of this result to infinite sets led him to the creation of set theory. relating uniqueness sets with Helson sets and sets of spectral synthesis (cf. eom.springer.de /u/u095440.htm   (373 words)

 Erroll Garner Archives   (Site not responding. Last check: 2007-10-14) The set ranks as an essential resource for jazz historians, instructors, students, fans, and pianists of every stripe. Out-of-print for some twenty years, the body of the set (circa 1959-1973) is replete with marvelous stories Garner tells with his inherent melodic and lyrical music -- entirely improvised. Gamer's uniqueness is a trademark of instant recognition and is guaranteed to arouse pleasures, respect, and admiration. errollgarner.com /review_boxset2.html   (206 words)

 [No title] The set of $\gamma(a_0,a_1)$ corresponding to nonrecurrent Pisot sequences is actually dense on the interval $[(1+\sqrt 5)/2,+\infty]$. Riemann's result states that the empty set $\varnothing$ is a set of uniqueness. So the problem was left to decide whether sets of measure 0 had to be sets of uniqueness or not. www.ams.org /journals/bull/pre-1996-data/199329-2/France   (1503 words)

 Set Machine Help In this case, Set Machine examines the current input stream value and considers only whether or not the value is in the current set and whether the maximum number of occurrences for the current subpattern has been attained. A subpattern is defined as a minimum and maximum number of occurrences of elements of a set, or occurrences of a variable. A Tag is a unique textual identifier for an object such as a node or a pattern. www.setmachine.com /sm.htm   (10378 words)

 Appendix A - EXPRESS Model of Static Work Environment   (Site not responding. Last check: 2007-10-14) Set of uniqueness constraints on combinations of one or more unique attributes, including constraints inherited from supertypes. A uniqueness rule specifies a combination of attributes whose values, when taken jointly, uniquely identify a single instance of the declaring entity. The surface is specified using an irregularly connected set of nodes and edges (mesh), or a regularly connected set of nodes and edges (2d grid), or a set of contours. www.posc.org /Epicentre.2_2/DataAccessAndExchange/DAESpecification/dl_appa.html   (4778 words)

 Set Theory And Uniqueness For Trigonometric Series (ResearchIndex) Abstract: this paper is to give a basic introduction to the application of set theoretic methods to problems concerning uniqueness for trigonometric series. It is written in the style of informal lecture notes for a course or seminar on this subject and, in particular, contains several exercises. The treatment is as elementary as possible and only assumes some familiarity with the most basic results of general topology, measure theory, functional analysis, and descriptive set theory. citeseer.ist.psu.edu /463215.html   (313 words)

 Set of uniqueness   (Site not responding. Last check: 2007-10-14) We recognize the uniqueness of the child in the 11-14 age group and the need for an easy transition from childhood to adolescence. A set of commercial and civil barristers in Lincoln's Inn, with a focus on professional liability. Advocate the uniqueness of the profession of ophthalmology by educating both its members and the public in order to enable ophthalmologists to provide the highest quality of service to the public. omniknow.com /common/wiki.php?in=en&term=set%20of%20uniqueness   (2263 words)

 TNTsdk: rvc/descriptor.h Source File   (Site not responding. Last check: 2007-10-14) Set the object description 00178 void SetDescription (00179 const MISTRINGand Description //!< The MISTRING containing the long description 00180) { m_Description = Description; } 00181 00182 //! Set the object source 00188 void SetSource (00189 const OBJECTNAMEand Source //!< The OBJECTNAME containing the source string 00190) { m_Source = Source; } 00191 00192 //! Pass NULL for the 'Source' parameter to set to MsysGetAppName(). www.microimages.com /tntsdk71/descriptor_8h-source.html   (714 words)

 SONIC ARTS - Nick Collins : Uniqueness of pitch class spaces, minimal bases and Z partners Given sets (set classes) X and Y, X and Y are in the Z relation with respect to M-decomposition iff the M-class vectors of Uniqueness U((S,IVLS,int))= supremum { u(X) : X Ì S}where u(X) is the uniqueness of a set X. By proposition 4.3 U((S,IVLS,int))= sup { u(X) : X Ì S}= The use of the term permutation refers to the successive difference representation of a pc set, formally set out in Appendix A. Solving a decomposition backwards requires the "fitting together" of a group of lower cardinality pc sets into a larger cardinality one. www.sonic.mdx.ac.uk /research/nickpitch.html   (4971 words)

 Lego Set Review: 1817 - Forest Flyer   (Site not responding. Last check: 2007-10-14) My first introduction to the 1817 set was a very cool POV picture of the set's plane located on Anton Raves gallery page. The best part of the set (though I quite like the cabin) is the one-man plane in white with red highlights and landing pontoons. There were a strange amount of leftover pieces when I was finished (some 1x4 and 1x1 tiles) and the instructions came as two separate booklets (one for the cabin and boat and one for the plane) but this just adds to the uniqueness of the set. www.adequate.com /lego/reviews/Details/214.html   (473 words)

 Parameters in the Route Choice Model   (Site not responding. Last check: 2007-10-14) Another set of shortest paths are now computed, and appended to the existing set. Once the choice set has been defined, DynaMIT is ready to compute the probability with which an individual might choose each of the available alternatives. An alternative approach would be to focus on the calibration of a subset of key route choice coefficients while holding all other parameters in the model fixed at their initial values. web.mit.edu /~rama/main/node103.html   (521 words)

 Terra Nova: Uniqueness in Virtual Worlds There would be no way of telling which of those unique items is better, just from the name, you'd have to check info of each one...Furthermore, item uniqueness wouldn't sit well with market "buy" orders. Sep 21, 2004 7:50:24 AM In real life, almost every item is 'unique' in some way, but that doesn't mean that they can't be categorised in a lot of useful ways, such as 'televisions', which mostly all do the same kind of thing and so. In my opinion, a universe in which all items are unique would be far more interesting than the standard mmo affair, especially if the differences aren't always obvious to an untrained eye. terranova.blogs.com /terra_nova/2004/09/uniqueness_in_v.html   (901 words)

 Citebase - Ordinary differential equations and descriptive set theory: uniqueness and globality of solutions of Cauchy ...   (Site not responding. Last check: 2007-10-14) Ordinary differential equations and descriptive set theory: uniqueness and globality of solutions of Cauchy problems in one dimension We study some natural sets arising in the theory of ordinary differential equations in one variable from the point of view of descriptive set theory and in particular classify them within the Borel hierarchy. We prove that the set of Cauchy problems for ordinary differential equations which have a unique solution is Π citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/9609204   (212 words)

 Empty set - Wikipedia, the free encyclopedia The empty set is the set containing no elements. x ≠ x}, which can be defined to be the empty set. It is used to emphasise that nothing should be added to the noun. en.wikipedia.org /wiki/Empty_set   (1534 words)

 Amazon.com: Three Colors Trilogy (Blue / White / Red): DVD: Juliette Binoche,Benoît Régent,Florence Pernel,Charlotte ...   (Site not responding. Last check: 2007-10-14) The DVD set has numerous extras spread throughout the three discs; the end result is a superior collection. In BLUE, the first of the trilogy, a widow tries to set herself free (and gain liberty) from her emotional baggages. The three films are set not just in France, but also in Poland and Switzerland, and WHITE has primarily Polish dialogs. www.amazon.com /Three-Colors-Trilogy-Blue-White/dp/B000083C5F   (3630 words)

 Entity DAE_ENTITY_DEFINITION   (Site not responding. Last check: 2007-10-14) The set of authorizations which have been granted for this entity. Each entity must be explicitly assigned all "default" authorizations (e.g., to the data store creator and the system administrator) at the time of creation of the entity. Defines the set of data stores which share this entity. www.posc.org /Epicentre.2_2/DataAccessAndExchange/DAESpecification/LogicalDictionary/DAE_E/dae_entity_definition.html   (449 words)

 Woot : Motorola 802.11g Enhanced Networking Set But Motorola's own sales copy tries to paint the wireless vs. wired question as the next coming of Ali-Frazier, peddling some line about how all-fired wonderful this WR850GP router is because it’s both a wireless access point and a wired Ethernet router. We’re not going to puff up this set's uniqueness just to meet our copy quota. Either you want it (and you click the big orange button) or you don't (and you proclaim that fact in a forum post that will quickly be deleted). www.woot.com /Blog/BlogEntry.aspx?BlogEntryId=805   (396 words)

 Adding new element to the Set object doesn't preserve the set uniqueness.   (Site not responding. Last check: 2007-10-14) Adding new element to the Set object doesn't preserve the set uniqueness. We are using both Lists and Sets in our STEP application and according to the Reference manual we should be able to add items to a Set only if they don't already exist in the set. However, it looks like when I add something to our sets, it gets added no matter what. www.steptools.com /support/kb/articles/0028.htm   (130 words)

 TNTsdk: RVC::DESCRIPTOR Class Reference   (Site not responding. Last check: 2007-10-14) Will set the description field if the resulting short name is different than 'name' Presets the 'source' field from MsysGetAppName(). Set the object source Pass NULL for the 'Source' parameter to set to MsysGetAppName(). The documentation for this class was generated from the following file: www.microimages.com /tntsdk71/classRVC_1_1DESCRIPTOR.html   (242 words)

 Barlow, Perkins: On pathwise uniqueness and expansion of filtrations Barlow, Perkins: On pathwise uniqueness and expansion of filtrations Barlow, Martin T. Perkins, Edwin A. On pathwise uniqueness and expansion of filtrations. : Weak and strong solutions of stochastic differential equations: Existence and uniqueness. www.numdam.org /numdam-bin/item?id=SPS_1990__24__194_0   (134 words)

 Quartz Clock and Pen Set - $25-$50 This genuine walnut desk set will compliment any desk. This desk set also comes with a high quality writing instrument. Gold trim highlights the uniqueness of this set. www.lazerdesigns.com /promotionalitems/prods/DA2201.html   (97 words)

 U NATO phonetic alphabet University of Utah University calendar Nancy Mitford mathematics operator set of uniqueness ...   (Site not responding. Last check: 2007-10-14) U NATO phonetic alphabet University of Utah University calendar Nancy Mitford mathematics operator set of uniqueness military science Unicode British novelist Nancy Mitford brought to popular attention the linguistic terminology "U" and "non-U" to indicate the speech markers of upper class and non-upper class British speakers respectively. stands for intersection (both are operators on sets). en.powerwissen.com /ucEjEAAY6ojfvQc5NHWXhg==_U.html   (378 words)

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