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THE SPLITTING OF OPERATOR ALGEBRAS
"... We say the singly generated C*algebra, C*(Tt®Tt)9 splits if C*(TΊ φ Γ2)=C*(Γ1) φ C*(T2). A necessary and sufficient condition is derived for the splitting of C*(T λ φ T2) in terms of the topological structure of the primitive ideal space of C*CZ \ φ T2). In particular, when C*(2 \ φ T2) is strongl ..."
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Cited by 1 (1 self)
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We say the singly generated C*algebra, C*(Tt®Tt)9 splits if C*(TΊ φ Γ2)=C*(Γ1) φ C*(T2). A necessary and sufficient condition is derived for the splitting of C*(T λ φ T2) in terms of the topological structure of the primitive ideal space of C*CZ \ φ T2). In particular, when C*(2 \ φ T2
SIGNAL RECOVERY BY PROXIMAL FORWARDBACKWARD SPLITTING
 MULTISCALE MODEL. SIMUL. TO APPEAR
"... We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulation makes it possible to derive existence, uniqueness, characterization, and stability results in a unifi ..."
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Cited by 509 (24 self)
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unified and standardized fashion for a large class of apparently disparate problems. Recent results on monotone operator splitting methods are applied to establish the convergence of a forwardbackward algorithm to solve the generic problem. In turn, we recover, extend, and provide a simplified analysis
SPLITTING OF OPERATIONS FOR ALTERNATIVE AND MALCEV STRUCTURES
"... Abstract. In this paper we define preMalcev algebras and alternative quadrialgebras and prove that they generalize preLie algebras and quadrialgebras respectively to the alternative setting. Constructions in terms bimodules, splitting of operations, and RotaBaxter operators are discussed. 1. ..."
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Abstract. In this paper we define preMalcev algebras and alternative quadrialgebras and prove that they generalize preLie algebras and quadrialgebras respectively to the alternative setting. Constructions in terms bimodules, splitting of operations, and RotaBaxter operators are discussed. 1.
On the DouglasRachford splitting method and the proximal point algorithm for maximal monotone operators
, 1992
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Splitting of operations, Manin products and RotaBaxter operators
 Int. Math. Res. Not. IMRN
"... ar ..."
On the simplest splitmerge operator on the infinitedimensional simplex
, 2001
"... We consider the simplest splitmerge Markov operator T on the infinitedimensional simplex Σ1 of monotone nonnegative sequences with unit sum. For a sequence x ∈ Σ1, it picks a sizebiased sample (with replacement) of two elements of x; if these elements are distinct, it merges them and reorders th ..."
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Cited by 4 (0 self)
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We consider the simplest splitmerge Markov operator T on the infinitedimensional simplex Σ1 of monotone nonnegative sequences with unit sum. For a sequence x ∈ Σ1, it picks a sizebiased sample (with replacement) of two elements of x; if these elements are distinct, it merges them and reorders
PointSplit Lattice Operators for B Decays
, 1992
"... The matrix element which determines the B meson decay constant can be measured on the lattice using an effective field theory for heavy quarks. Various discretizations of the heavylight bilinears which appear in this and other B decay matrix elements are possible. The heavylight bilinear currently ..."
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, and discuss their application. Several weak matrix elements involving heavy mesons can be studied on the lattice [1][2]. The relationship of the lattice operators to the operators coming from the continuum electroweak theory must be calculated in order to make use of the lattice results. While these short
Erratum to “Splitting an Operator: Algebraic Modularity Results for logics with
"... In [Vennekens et al. 2006], we defined a class of stratified autoepistemic theories and made the claim that the models of such theories under a number of different semantics (namely, (partial) expansions, (partial) extensions, KripkeKleene model and wellfounded model) can be constructed in an inc ..."
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In [Vennekens et al. 2006], we defined a class of stratified autoepistemic theories and made the claim that the models of such theories under a number of different semantics (namely, (partial) expansions, (partial) extensions, KripkeKleene model and wellfounded model) can be constructed in an incremental way, following the stratification of the theory. However, it turns out that this result only holds as long as the constructed models are consistent. This can be demonstrated by the following example. Let T be the theory {¬p; q ∧ ¬Kp}. This T is stratifiable with respect to the partition Σ0 = {p}, Σ1 = {q} of its alphabet. The least precise partial expansion, i.e., the KripkeKleene model, of this theory is the pair of possible world structures ({{q}}, {}). However, the stratified construction would first consider only the formula ¬p in alphabet Σ0 and construct the exact pair ({{}}, {{}}), i.e., p would be known to be false. Next, it would consider the formula q ∧ ¬Kp in alphabet Σ1 and substitute Kp by its truth value in the possible world structure {{}} for Σ0, thus arriving at q ∧ ¬f. The only partial expansion of this formula is the exact
Splitting an operator: Algebraic modularity results for logics with fixpoint semantics
 ACM Transactions on computational logic (TOCL
, 2005
"... Abstract. It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different “levels”, such that the models of the entire program can be constructed by incrementally constructing models for ea ..."
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Cited by 9 (7 self)
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for arbitrary operators, this gives us a uniform and powerful way of deriving splitting results for each logic with a fixpoint semantics. We demonstrate the usefulness of these results, by generalizing existing results for logic programming, autoepistemic logic and default logic. 1
Splitting an operator: An algebraic modularity result and its application to autoepistemic logic
 In Proceedings of International Workshop on NonMonotonic Reasoning
, 2004
"... It is well known that it is possible to split certain autoepistemic theories under the semantics of expansions, i.e. to divide such a theory into a number of different “levels”, such that the models of the entire theory can be constructed by incrementally constructing models for each level. Similar ..."
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Cited by 7 (4 self)
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results exist for other nonmonotonic formalisms, such as logic programming and default logic. In this work, we present a general, algebraic theory of splitting under a fixpoint semantics. Together with the framework of approximation theory, a general fixpoint theory for arbitrary operators, this gives us
Results 1  10
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4,557