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30
A powerdomain construction
 SIAM J. of Computing
, 1976
"... Abstract. We develop a powerdomain construction, [.], which is analogous to the powerset construction and also fits in with the usual sum, product and exponentiation constructions on domains. The desire for such a construction arises when considering programming languages with nondeterministic featu ..."
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Cited by 225 (20 self)
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Abstract. We develop a powerdomain construction, [.], which is analogous to the powerset construction and also fits in with the usual sum, product and exponentiation constructions on domains. The desire for such a construction arises when considering programming languages with nondeterministic features or parallel features treated in a nondeterministic way. We hope to achieve a natural, fully abstract semantics in which such equivalences as (pparq)=(qparp) hold. The domain (D Truthvalues) is not the right one, and instead we take the (finitely) generable subsets of D. When D is discrete they are ordered in an elementwise fashion. In the general case they are given the coarsest ordering consistent, in an appropriate sense, with the ordering given in the discrete case. We then find a restricted class of algebraic inductive partial orders which is closed under [. as well as the sum, product and exponentiation constructions. This class permits the solution of recursive domain equations, and we give some illustrative semantics using 5[.]. It remains to be seen if our powerdomain construction does give rise to fully abstract semantics, although such natural equivalences as the above do hold. The major deficiency is the lack of a convincing treatment of the fair parallel construct. 1. Introduction. When one follows the ScottStrachey approach to the
Topological structures in Colombeau algebras: topological ˜ Cmodules and duality theory
 Acta. Appl. Math
"... We study modules over the ring ˜ C of complex generalized numbers from a topological point of view, introducing the notions of ˜ Clinear topology and locally convex ˜ Clinear topology. In this context particular attention is given to completeness, continuity of ˜ Clinear maps and elements of dual ..."
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Cited by 24 (10 self)
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We study modules over the ring ˜ C of complex generalized numbers from a topological point of view, introducing the notions of ˜ Clinear topology and locally convex ˜ Clinear topology. In this context particular attention is given to completeness, continuity of ˜ Clinear maps and elements of duality theory for topological ˜ Cmodules. As main examples we consider various Colombeau algebras of generalized functions. Key words: modules over the ring of complex generalized numbers, algebras of generalized functions, topology, duality theory
Completeness of quasiuniform and syntopological spaces
 J. London Math. Soc
, 1994
"... In this paper we begin to develop the filter approach to (completeness of) quasiuniform spaces, proposed in [8, Section V]. It will be seen that this permits a more powerful and elegant account of completion to be given than was feasible using sequences or nets [8]. ..."
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Cited by 14 (0 self)
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In this paper we begin to develop the filter approach to (completeness of) quasiuniform spaces, proposed in [8, Section V]. It will be seen that this permits a more powerful and elegant account of completion to be given than was feasible using sequences or nets [8].
The OverlappingGenerations Model. II: The Case of Pure Exchange with Money
 Journal of Economic Theory
, 1981
"... Government debt instruments (e.g., money and government bonds) serve many functions in the private sector. They can be stores of value, vehicles for the payment of taxes, media for transactions, and so forth. Their roles vary from economy to economy depending upon institutions and ..."
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Cited by 12 (4 self)
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Government debt instruments (e.g., money and government bonds) serve many functions in the private sector. They can be stores of value, vehicles for the payment of taxes, media for transactions, and so forth. Their roles vary from economy to economy depending upon institutions and
On Information Structures and Nonsequential Stochastic Control
 CWI QUARTERLY
, 1996
"... ... this paper, we first present a survey of existing results on nonsequential systems within the framework of Witsenhausen's intrinsic model; then, we discuss some open problems arising from the research performed so far. ..."
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Cited by 12 (1 self)
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... this paper, we first present a survey of existing results on nonsequential systems within the framework of Witsenhausen's intrinsic model; then, we discuss some open problems arising from the research performed so far.
S.: Applications of near sets
 Amer. Math. Soc. Notices
, 2012
"... Near sets are disjoint sets that resemble each other. Resemblance is determined by considering set descriptions defined by feature vectors (ndimensional vectors of numerical features that represent characteristics of objects such as digital image pixels). Near sets are useful in solving problems ba ..."
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Cited by 4 (2 self)
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Near sets are disjoint sets that resemble each other. Resemblance is determined by considering set descriptions defined by feature vectors (ndimensional vectors of numerical features that represent characteristics of objects such as digital image pixels). Near sets are useful in solving problems based on human perception [44, 76, 49, 51, 56] that arise in areas such as image analysis
The Kuratowski closurecomplement theorem
 New Zealand Journal of Mathematics
"... The Kuratowski ClosureComplement Theorem 1.1. [29] If (X,T) is a topological space and A ⊆ X then at most 14 sets can be obtained from A by taking closures and complements. Furthermore there is a space in which this bound is attained. ..."
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Cited by 3 (0 self)
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The Kuratowski ClosureComplement Theorem 1.1. [29] If (X,T) is a topological space and A ⊆ X then at most 14 sets can be obtained from A by taking closures and complements. Furthermore there is a space in which this bound is attained.
Positivity problems for loworder linear recurrence sequences
 In Proc. Symp. on Discrete Algorithms (SODA). ACMSIAM
, 2014
"... We consider two decision problems for linear recurrence sequences (LRS) over the integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the Ultimate Positivity Problem (are all but finitely many terms of a given LRS positive?). We show decidability of both problems for ..."
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Cited by 3 (2 self)
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We consider two decision problems for linear recurrence sequences (LRS) over the integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the Ultimate Positivity Problem (are all but finitely many terms of a given LRS positive?). We show decidability of both problems for LRS of order 5 or less, with complexity in the Counting Hierarchy for Positivity, and in polynomial time for Ultimate Positivity. Moreover, we show by way of hardness that extending the decidability of either problem to LRS of order 6 would entail major breakthroughs in analytic number theory, more precisely in the field of Diophantine approximation of transcendental numbers. 1
Topological regular variation. I. Slow variation.
, 2008
"... Motivated by the Category Embedding Theorem, as applied to convergent automorphisms [BOst11], we unify and extend the multivariate regular variation literature by a reformulation in the language of topological dynamics. Here the natural setting are metric groups, seen as normed groups (mimicking nor ..."
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Cited by 2 (2 self)
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Motivated by the Category Embedding Theorem, as applied to convergent automorphisms [BOst11], we unify and extend the multivariate regular variation literature by a reformulation in the language of topological dynamics. Here the natural setting are metric groups, seen as normed groups (mimicking normed vector spaces). We brie‡y study their properties as a preliminary to establishing that the Uniform Convergence Theorem (UCT) for Baire, groupvalued slowlyvarying functions has two natural metric generalizations linked by the natural duality between a homogenous space and its group of homeomorphisms. Each is derivable from the other by duality. One of these explicitly extends the (topological) group version of UCT due to Bajšanski and Karamata [BajKar] from groups to ‡ows on a group. A multiplicative representation of the ‡ow derived in [Ostknit] demonstrates equivalence of the ‡ow with the earlier group formulation. In 1 companion papers we extend the theory to regularly varying functions: we establish the calculus of regular variation in [BOst14] and we extend to locally compact,compact groups the fundamental theorems on characterization and representation [BOst15]. In [BOst16], working with topological ‡ows on homogeneous spaces, we identify an index of regular variation, which in a normedvector space context may be speci…ed using the Riesz representation theorem, and in a locally compact group setting may be connected with Haar measure. Classi…cation: 26A03
EXCISION IN BANACH SIMPLICIAL AND CYCLIC COHOMOLOGY
, 1996
"... Abstract. We prove that, for every extension of Banach algebras 0 → B → A → D → 0 such that B has a left or right bounded approximate identity, the existence of an associated long exact sequence of Banach simplicial or cyclic cohomology groups is equivalent to the existence of one for homology group ..."
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Cited by 1 (1 self)
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Abstract. We prove that, for every extension of Banach algebras 0 → B → A → D → 0 such that B has a left or right bounded approximate identity, the existence of an associated long exact sequence of Banach simplicial or cyclic cohomology groups is equivalent to the existence of one for homology groups. It follows from the continuous version of a result of Wodzicki that associated long exact sequences exist. In particular, they exist for every extension of C ∗algebras. 1.