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Topic: Domain calculus

	Tuple relational calculus - Wikipedia, the free encyclopedia
		The tuple calculus is a calculus that was introduced by Edgar F. Codd as part of the relational model in order to give a declarative database query language for this data model.
		Along with the tuple calculus Codd also introduced the domain calculus which is closer to first-order logic and showed that these two calculi (and the relational algebra) are equivalent in expressive power.
		Since the calculus is a query language for relational databases we first have to define a relational database.
	www.wikipedia.org /wiki/Tuple_calculus (1951 words)

	domain (magnetism) - Hutchinson encyclopedia article about domain (magnetism) (Site not responding. Last check: 2007-10-09)
		The magnetism of the material is due to the movement of electrons in the atoms of the domain.
		In an unmagnetized sample of material, the domains point in random directions, or form closed loops, so that there is no overall magnetization of the sample.
		In a magnetized sample, the domains are aligned so that their magnetic effects combine to produce a strong overall magnetism.
	encyclopedia.farlex.com /domain+(magnetism) (139 words)

	Class Notes for Chapter 9 (part II)
		Relational calculus is a formal query language where we write one declarative expression to specify a retrieval request and hence there is no description of how to evaluate a query; a calculus expression specifies what is to be retrieved rather than how to retrieve it.
		A safe expression in relational calculus is one that is guaranteed to yield a finite number of tuples as its result; otherwise, the expression is called unsafe.
		The domain calculus differs from the tuple calculus in the type of variables used in formulas: rather than having variables range over tuples, the variables range over single values from domains of attributes.
	ranger.uta.edu /~alp/db1/ch9TupleAndDomainRelationalCalculus.htm (3563 words)

	Domain relational calculus - Wikipedia, the free encyclopedia
		In computer science, domain relational calculus is a calculus that was introduced by Edgar F. Codd as part of the relational model in order to give a declarative database query language for this data model.
		is either a domain variable or constant, and p() denotes a DRC Formula.
		This language uses the same operators as tuple calculus; Logicial operators ∧ (and), ∨ (or) and ¬ (not), and we can use the existential quantifier (∃) and the universal quantifier (∀) to bind the variables.
	en.wikipedia.org /wiki/Domain_calculus (240 words)

	01. Introduction
		Calculus has a property in common with many other skills in life — it is a bit more complicated than picking up a rock.
		They don't tell you Calculus is an enriching addition to your personal intellectual toolkit — that is not in their interest.
		As the rock begins to fall, it leaves the domain of algebra and enters the domain of Calculus, because Calculus is the mathematics of motion and change.
	arachnoid.com /calculus (595 words)

	Data model - Wikipedia, the free encyclopedia
		For example in the relational model all data is represented by mathematical relations (or, to be precise, a slightly generalized version thereof).
		There exists a general language for specifying constraints (first-order logic), and for manipulations and querying the data the relational algebra, tuple calculus and domain calculus are introduced.
		The Entity-Relationship Model method is used to establish a domain specific data model.
	en.wikipedia.org /wiki/Data_model (375 words)

	Atlas: Domain Theory, Computational Geometry and Differential Calculus (A short course) by Abbas Edalat
		Domain theory is a mathematical theory of computation, which was originally developed in the late 1960's to model the semantics of programming languages, but later found applications in mainstream mathematical computation.
		Then a domain for continuously differentiable functions is constructed as a subset of the product of two copies of the function space of the real line with the interval domain.
		We introduce a domain for geometric objects in the n-dimensional Euclidean space, which consists of pairs of disjoint open subsets representing the interior and exterior of subsets.
	atlas-conferences.com /cgi-bin/abstract/capi-10 (1010 words)

	Domain and Range
		The rule is to first square the number in the domain and then take the principal square root (positive answer only) of the answer.
		When numbers are placed in the f function, the results, f(x), must be in the domain of the g function.
		If the domain and range are not handled carefully you may work with an incorrect graph.
	mathrahn.tripod.com /domainandrange.htm (212 words)

	Math Forum - Ask Dr. Math
		Date: 10/13/98 at 11:56:25 From: Doctor Rob Subject: Re: Pre-Calculus The domain of a function is the set of values you can substitute for the variable and get a sensible answer.
		Usually it is a subset of some implicitly agreed-upon set, such as the real numbers, or the complex numbers, or the integers.
		The range of a function is the set of values you get as results when you substitute the values in the domain for the variable.
	mathforum.org /library/drmath/view/54477.html (306 words)

	Fundamentals of Database Systems
		Domain calculus was thought of as a way to explain what QBE does.
		lDomain calculus differs from tuple calculus in the type of variables used in formulas: rather than having variables range over tuples, the variables range over single values from domains of attributes.
		., xn+m are domain variables that range over domains (of attributes) and COND is a condition or formula of the domain relational calculus.
	www.ecst.csuchico.edu /~melody/courses/Fall2003CSCI273/CourseNotes/ENCh06_files/slide0145.htm (154 words)

	domain calculus : Definition from the Online Dictionary at Datasegment.com (Site not responding. Last check: 2007-10-09)
		1 definition found domain calculus - Free On-line Dictionary of Computing (19 Sep 2003) : domain calculus A form of relational calculus in which scalar variables take values drawn from a given domain.
		Examples of the domain calculus are ILL, FQL, DEDUCE and the well known Query By Example (QBE).
		INGRES is a relational DBMS whose DML is based on the relational calculus.
	onlinedictionary.datasegment.com /word/domain+calculus (74 words)

	CCH Chapter 1--Functions: Roots, Domain & Range I (Site not responding. Last check: 2007-10-09)
		As we delve further into our study of calculus we'll be dealing extensively with the study of functions.
		The natural domain of a function is the set of all real numbers that its independent variable may assume.
		Finally, the range of the function is the set of all output values generated by the function when the domain values are evaluated by it.
	calculuslab.deltacollege.edu /CalcIMMA/CalcIMMA-1/CalcIMMA-1-1-1.html (621 words)

	DOM from FOLDOC (Site not responding. Last check: 2007-10-09)
		The domain engineering activity in which domain knowledge is studied and formalised as a domain definition and a domain specification.
		A domain architecture can be adapted to create designs for software systems within a domain and also provides a framework for configuring assets within individual software systems.
		Said of a domain address (as opposed to a bang path) because the part to the right of the "@" specifies a nested series of "domains"; for example, esr@snark.thyrsus.com specifies the machine called snark in the subdomain called thyrsus within the top-level domain called com.
	www.instantweb.com /d/dictionary/foldoc.cgi?query=DOM (1464 words)

	Erwin Data Model (Site not responding. Last check: 2007-10-09)
		The ER model is part of design methods used to create a domain specific data model especially for relational databases.
		Conceptual data models, sometimes called domain models, are an abstract representation typically used to explore domain entity types and the relationships between them.
		In fact "conceptual model" or "domain model" are more appropriate names than "conceptual data model" because they don't bias you towards just using a data-oriented notation.
	www.blownspeakers.com /pages3/30/erwin-data-model.html (1527 words)

	Visual Calculus - Graphs and Derivatives (Site not responding. Last check: 2007-10-09)
		Suppose that a is in the domain of the function f such that, for all x in the domain of f,
		Suppose that a is in the domain of the function f and suppose that there is an open interval I containing a which is contained in the domain of f such that, for all x in I,
		Suppose that a is in the domain of the function f and suppose that there is an open interval I containing a which is also contained in the domain of f such that, for all x in I,
	archives.math.utk.edu /visual.calculus/3/graphing.13/index.html (292 words)

	FreePOOMA: DomainCalculus.h File Reference
		These routines are not part of the main user API, they are mainly for the domain calculus implementation.
		findIntersectionEndpoints is used by the domain calculus routines to find the endpoints and stride of an intersection domain given two other strided domains defined by [a0:a1:s] and [b0:b1:t].
		If this is possible, this return true and the min, max, stride of the resulting domain [i0,i1,is] in the final arguments.
	www.tat.physik.uni-tuebingen.de /~rguenth/pooma/reference/DomainCalculus_8h.html (277 words)

	Domain Calculus (Site not responding. Last check: 2007-10-09)
		As its name suggests, domain calculus focuses on the columns of a relation.
		Since both calculi use the same operators, we're going to translate the tuple calculus queries into their domain calculus equivalents.
		To transform this query into domain calculus we must explicitly assign a variable name to each attribute use in the query.
	www.iwu.edu /~sander/CS314/Lectures/algebra/calculus2.html (277 words)

	Inverse Functions, No Domain Restrictions, Example 3
		Recall that a function is a rule that links an element in the domain to just one number in the range.
		Therefore, the domain of the original function must be restricted so that the inverse will be unique.
		Review an example of finding the inverse of a function where the domain of the original function needs to be restricted.
	www.sosmath.com /algebra/invfunc/fnc2.3.html (419 words)

	Domain Independence and the Relational Calculus - Hull, Su (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		Abstract: Several alternative semantics (or interpretations) of the relational (domain) calculus are studied here.
		It is shown that they all have the same expressive power, i.e., the selection of any of the semantics neither gains nor loses expressive power.
		Since the domain is potentially infinite, the answer to a relational calculus query is sometimes infinite (and hence not a relation).
	citeseer.lcs.mit.edu /hull93domain.html (568 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		Note: The term "calculus" signifies merely a system of computation (the Latin word calculus means a pebble, perhaps used in counting or some other form of reckoning).
		In a real computer system, however, all domains and relations are necessarily finite, and the predicate calculus thus degeneratesÄÄat least in principleÄÄto the simpler propositional calculus.
		You might be tempted to think, therefore, that the reason the query can't be handled in the calculus or the algebra is that calculus and algebra expressions are relation-valued, not truth-valued.
	www.cis.uab.edu /cs426/files/CHAP08.DOC (2807 words)

	Implied Domain (Site not responding. Last check: 2007-10-09)
		If the text or your instructor only states the rule for a function, then the domain will be
		That domain is the largest set of real numbers that can be used in that rule.
		g(x) = sqrt(x-4) has the implied domain of R - reals smaller than 4 or all x >= 4 or { x
	www.cs.georgiasouthern.edu /faculty/mac/calculus/implied_domain.html (103 words)

	[No title]
		By having students continue to study algebraic structures throughout their degree program the program ensures that they have the breadth and depth of knowledge and skills to teach algebra and to provide students with a wide variety of problem solving situations.
		Calculus The calculus core of the program consists of the Calculus Sequence (MATH 131, 132, & 234).
		Calculus and its relationship to the high school curriculum is revisited in Senior Seminar for Future Mathematics Educators (MATH 493).
	myweb.lmu.edu /cbennett/ctc/master/mastdoc.doc (15420 words)

	relational calculus (Site not responding. Last check: 2007-10-09)
		Codd's reduction algorithm can convert from relational calculus to relational algebra.
		The relational calculus refers to the two calculi, the tuple calculus and the domain calculus, that are part of the...
		The relational calculus refers to the two calculi, the tuple calculus and the domain calculus, that are part of the relational model for databases and...
	www.mathscoacher.com /articles/31/relational-calculus.html (347 words)

	The Math Forum - Math Library - Functions
		An illustrated introductions to the concept of functions, a relationship or correlation where each element of the domain corresponds to one and only one element of the range.
		(The domain is made up of all possible inputs; the range is made up of all possible outputs of the function but may contain other elements also.) From a required math course for majors in Elementary Education, Special Education and Early Childhood Education.
		A selection of answers to questions about the domain and range of a function, as well as determining the domain and range of a function from its graph.
	forum.swarthmore.edu /library/topics/functions (2089 words)

	VLDB Journal 4(4): 727-794 (1995) (Site not responding. Last check: 2007-10-09)
		The notion of domain independence (from relational databases) is defined, and syntactic restrictions (referred to as safety conditions) on calculus queries are formulated to guarantee domain independence.
		The main results are: The domain-indenpendent calculus, the safe calculus, the algebra, and the logic-programming oriented language have equivalent expressive power.
		A more restricted version of safety is presented, such that the restricted safe calculus is equivalent to the algebra without powerset.
	researchsmp2.cc.vt.edu /DB/db/journals/vldb/AbiteboulB95.html (214 words)

	BRICS Mini-Course: Domain-theoretic Models of Differential Calculus and Geometry (Site not responding. Last check: 2007-10-09)
		Then a continuous Scott domain for continuously differentiable functions is constructed which is composed of consistent pairs of Scott continuous functions, each pair providing a function approximation and a derivative approximation for a classical continuously differentiable function.
		Given a continuous vector field, uniformly Lipschitz in the space component, and an initial value, a domain-theoretic generalization of the classical Picard operator is defined on the domain for continuously differentiable functions.
		We present a domain for geometric objects in the n-dimensional Euclidean space, which for the first time enables us to define the notions of a computable geometric object and operation.
	www.brics.dk /MC/03/DifferentialCalculus/index.html (397 words)

	[No title]
		y(t1, t2,..., tn) } where y is a safe relational calculus expression By Lemmata: can assume neither Ù or " occurs in y enough to show for each subformula w of y of form { t1t2...tm
		6óM¨-From domain relational calculus to algebra 17¨\Have proved the equivalence of relational algebra and domain / tuple relational calculus...
		Theorems 1, 2 and 3 together prove relational algebra domain relational calculus tuple relational calculus all have the same expressive power.
	www.dcs.warwick.ac.uk /~wmb/CS319/ppt/drelcalc.ppt (343 words)

	Relational Algebra (Site not responding. Last check: 2007-10-09)
		Relational calculus uses operators that are derived from symbolic logic.
		Domain Calculus As its name implies, this calculus focuses on the columns in the relational schema.
		Each field in one instance must be of the same domain as the corresponding field in the second instance.
	www.iwu.edu /~sander/CS314/Lectures/algebra/algebra.html (805 words)

	AMCA: Interplay between formal languages and domain mu-calculus by Guo-Qiang Zhang (Site not responding. Last check: 2007-10-09)
		This talk provides an improved formulation of a fragment of the domain mu-calculus and presents open problems related to this mu-calculus, such as decidability and expressive power.
		Our formulation is based on the recent work of Leiss, who established a sophisticated framework for solving language equations using Boolean automata and a generalized notion of language derivatives.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/k/b/84.htm (195 words)

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