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259,949
Relations and their basic properties
 Journal of Formalized Mathematics
, 1989
"... Summary. We define here: mode Relation as a set of pairs, the domain, the codomain, and the field of relation; the empty and the identity relations, the composition of relations, the image and the inverse image of a set under a relation. Two predicates, = and ⊆, and three functions, ∪, ∩ and \ are ..."
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Cited by 1060 (6 self)
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, ∪, ∩ and \ are redefined. Basic facts about the above mentioned notions are presented.
Functions and their basic properties
 JOURNAL OF FORMALIZED MATHEMATICS
, 2003
"... The definitions of the mode Function and the graph of a function are introduced. The graph of a function is defined to be identical with the function. The following concepts are also defined: the domain of a function, the range of a function, the identity function, the composition of functions, the ..."
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Cited by 1336 (32 self)
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, the 11 function, the inverse function, the restriction of a function, the image and the inverse image. Certain basic facts about functions and the notions defined in the article are proved.
On the Resemblance and Containment of Documents
 In Compression and Complexity of Sequences (SEQUENCES’97
, 1997
"... Given two documents A and B we define two mathematical notions: their resemblance r(A, B)andtheircontainment c(A, B) that seem to capture well the informal notions of "roughly the same" and "roughly contained." The basic idea is to reduce these issues to set intersection probl ..."
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Cited by 506 (6 self)
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Given two documents A and B we define two mathematical notions: their resemblance r(A, B)andtheircontainment c(A, B) that seem to capture well the informal notions of "roughly the same" and "roughly contained." The basic idea is to reduce these issues to set intersection
USER’S GUIDE TO VISCOSITY SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
, 1992
"... The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking argume ..."
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Cited by 1399 (16 self)
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The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking
Compressed sensing
, 2004
"... We study the notion of Compressed Sensing (CS) as put forward in [14] and related work [20, 3, 4]. The basic idea behind CS is that a signal or image, unknown but supposed to be compressible by a known transform, (eg. wavelet or Fourier), can be subjected to fewer measurements than the nominal numbe ..."
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Cited by 3625 (22 self)
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We study the notion of Compressed Sensing (CS) as put forward in [14] and related work [20, 3, 4]. The basic idea behind CS is that a signal or image, unknown but supposed to be compressible by a known transform, (eg. wavelet or Fourier), can be subjected to fewer measurements than the nominal
ScaleSpace Theory in Computer Vision
, 1994
"... A basic problem when deriving information from measured data, such as images, originates from the fact that objects in the world, and hence image structures, exist as meaningful entities only over certain ranges of scale. "ScaleSpace Theory in Computer Vision" describes a formal theory fo ..."
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Cited by 625 (21 self)
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A basic problem when deriving information from measured data, such as images, originates from the fact that objects in the world, and hence image structures, exist as meaningful entities only over certain ranges of scale. "ScaleSpace Theory in Computer Vision" describes a formal theory
Concurrent Constraint Programming
, 1993
"... This paper presents a new and very rich class of (concurrent) programming languages, based on the notion of comput.ing with parhal information, and the concommitant notions of consistency and entailment. ’ In this framework, computation emerges from the interaction of concurrently executing agent ..."
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Cited by 502 (16 self)
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This paper presents a new and very rich class of (concurrent) programming languages, based on the notion of comput.ing with parhal information, and the concommitant notions of consistency and entailment. ’ In this framework, computation emerges from the interaction of concurrently executing
Qualitative process theory
 MIT AI Lab Memo
, 1982
"... Objects move, collide, flow, bend, heat up, cool down, stretch, compress. and boil. These and other things that cause changes in objects over time are intuitively characterized as processes. To understand commonsense physical reasoning and make programs that interact with the physical world as well ..."
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Cited by 899 (92 self)
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as people do we must understand qualitative reasoning about processes, when they will occur, their effects, and when they will stop. Qualitative process theory defines a simple notion of physical process that appears useful as a language in which to write dynamical theories. Reasoning about processes also
Engineering and Theoretical Underpinnings of Retrenchment
, 2001
"... Refinement is reviewed in a partial correctness framework, highlighting in particular the distinction between its use as a specification constructor at a high level, and its use as an implementation mechanism at a low level. Some of its shortcomings as specification constructor at high levels of ..."
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Cited by 25 (16 self)
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of abstraction are pointed out, and these are used to motivate the adoption of retrenchment for certain high level development steps. Basic properties of retrenchment are described, including a justification of the operation PO, simple examples, simulation properties, and compositionality for both the basic
Universal coalgebra: a theory of systems
, 2000
"... In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certa ..."
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Cited by 408 (42 self)
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the notion of coalgebra homomorphism, the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras. Thus, the three basic notions of universal algebra: algebra, homomorphism of algebras, and congruence, turn out to correspond to coalgebra, homomorphism
Results 1  10
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259,949