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SIMPLIFIED PROOF OF THE THEOREM OF VAROPOULOS IN THE COMMUTATIVE CASE
, 802
"... Abstract. We give continuity properties of bitraces on (possibly noncommutative) Banach ∗algebras based on the Closed Graph Theorem, leading to a simplified proof of the Theorem of Varopoulos in the commutative case. 1. ..."
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Abstract. We give continuity properties of bitraces on (possibly noncommutative) Banach ∗algebras based on the Closed Graph Theorem, leading to a simplified proof of the Theorem of Varopoulos in the commutative case. 1.
Gravity coupled with matter and the foundation of non commutative geometry
, 1996
"... We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D i ..."
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Cited by 343 (17 self)
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We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D
Mixed succession rules: the commutative case
, 2008
"... We begin a systematic study of the enumerative combinatorics of mixed succession rules, which are succession rules such that, in the associated generating tree, the nodes are allowed to produce their sons at several different levels according to different production rules. Here we deal with a specif ..."
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Cited by 1 (1 self)
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specific case, namely that of two different production rules whose rule operators commute. In this situation, we are able to give a general formula expressing the sequence associated with the mixed succession rules in terms of the sequences associated with the component production rules. We end
Homological Characterization of Rings: The Commutative Case
, 2002
"... A large number of finiteness properties of commutative rings have homological characterizations. For example, it is well known that for a ring to be Noetherian a condition most commonly described by the finite generation of the ideals of the ring, it is necessary and su ¢ cient that arbitrary dire ..."
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A large number of finiteness properties of commutative rings have homological characterizations. For example, it is well known that for a ring to be Noetherian a condition most commonly described by the finite generation of the ideals of the ring, it is necessary and su ¢ cient that arbitrary
Cartier isomorphism and Hodge theory in the noncommutative case
 in Arithmetic geometry, Clay Math. Proc. 8, AMS
, 2009
"... ..."
LevelSpacing Distributions and the Airy Kernel
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 1994
"... Scaling levelspacing distribution functions in the "bulk of the spectrum" in random matrix models of N x N hermitian matrices and then going to the limit N — » oo leads to the Fredholm determinant of the sine kernel sinπ(x — y)/π(x — y). Similarly a scaling limit at the "edge o ..."
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Cited by 430 (24 self)
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;quot;edge of the spectrum " leads to the Airy kernel [Ai(x) Ai(y) — Ai (x) Ai(y)]/(x — y). In this paper we derive analogues for this Airy kernel of the following properties of the sine kernel: the completely integrable system of P.D.E.'s found by Jimbo, Miwa, Mori, and Sato; the expression, in the case of a
MValgebras with operators (the commutative and the noncommutative case)
"... In the present paper we define the (pseudo) MValgebras with nary operators, generalizing MVmodules and product MValgebras. Our main results assert that there are bijective correspondences between the operators defined on a pseudo MValgebra and the operators defined on the corresponding ℓgroup. ..."
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Cited by 3 (1 self)
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In the present paper we define the (pseudo) MValgebras with nary operators, generalizing MVmodules and product MValgebras. Our main results assert that there are bijective correspondences between the operators defined on a pseudo MValgebra and the operators defined on the corresponding ℓgroup. We also provide a categorical framework and we prove the analogue of Mundici’s categorical equivalence between MValgebras
THE STANDARD MODEL – THE COMMUTATIVE CASE: SPINORS, DIRAC OPERATOR AND DE RHAM ALGEBRA
, 2000
"... Abstract. The present paper is a short survey on the mathematical basics of Classical Field Theory including the SerreSwan ’ theorem, Clifford algebra bundles and spinor bundles over smooth Riemannian manifolds, Spin Cstructures, Dirac operators, exterior algebra bundles and Connes ’ differential ..."
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algebras in the commutative case, among other elements. We avoid the introduction of principal bundles and put the emphasis on a modulebased approach using SerreSwan’s theorem, Hermitian structures and module frames. A new proof (due to Harald Upmeier) of the differential algebra isomorphism between
A Classification of the Projective Lines over Small Rings II. NonCommutative Case
"... A list of different types of a projective line over noncommutative rings with unity of order up to thirtyone inclusive is given. Eight different types of such a line are found. With a single exception, the basic characteristics of the lines are identical to those of their commutative counterparts. ..."
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Cited by 11 (7 self)
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A list of different types of a projective line over noncommutative rings with unity of order up to thirtyone inclusive is given. Eight different types of such a line are found. With a single exception, the basic characteristics of the lines are identical to those of their commutative counterparts
Binary operations applied to functions
 Journal of Formalized Mathematics
, 1989
"... Summary. In the article we introduce functors yielding to a binary operation its composition with an arbitrary functions on its left side, its right side or both. We prove theorems describing the basic properties of these functors. We introduce also constant functions and converse of a function. The ..."
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Cited by 299 (43 self)
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. The recent concept is defined for an arbitrary function, however is meaningful in the case of functions which range is a subset of a Cartesian product of two sets. Then the converse of a function has the same domain as the function itself and assigns to an element of the domain the mirror image
Results 1  10
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