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Mathematics Subject Classifications (2000):
"... The Berezin transform for complex multivariable domains D ⊂ Cn is important to harmonic analysis because of its covariance with respect to holomorphic transformations. It can be regarded as an analogue of the Poisson transform, replacing the boundary integration by integrating over the domain itself ..."
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The Berezin transform for complex multivariable domains D ⊂ Cn is important to harmonic analysis because of its covariance with respect to holomorphic transformations. It can be regarded as an analogue of the Poisson transform, replacing the boundary integration by integrating over the domain itself. This applies in particular
Mathematics Subject Classifications (2000): References
"... Abstract. We analyze an adaptive finite element method (AFEM) which does not require an exact computation of the Galerkin approximation at each mesh. We propose to approximate the Galerkin solution Uk+1 at step k + 1 of the adaptive process up to a tolerance dictated by the difference between Ũk an ..."
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Abstract. We analyze an adaptive finite element method (AFEM) which does not require an exact computation of the Galerkin approximation at each mesh. We propose to approximate the Galerkin solution Uk+1 at step k + 1 of the adaptive process up to a tolerance dictated by the difference between Ũk and Ũk+1. Here Ũk denotes the computed approximate solution at step k of the adaptive iteration. The adaptive algorithm is guided by Dörfler’s marking strategy [2], using the residualtype a posteriori error estimators for the inexact (computed) solutions Ũk. We prove a quasioptimality result analogous to those of Stevenson [3] and Cascón et. al. [1]. This turns out to be a theoretical result of optimality for a very practical and realistic adaptive method, which is computationally cheaper than the usual AFEM. Several numerical tests show that a few iterations of the iterative linear solver are needed to obtain the desired accuracy in each step of the adaptive loop.
MathematicsSubjectClassification:35Q30,35Q35
"... uratherthanthevelocityitself.Inlargeeddysimulation,weuseanaveragingoperatorwhichallowsfortheseparationoflargeandsmalllengthscalesintheflowfield. udenotestheeddiesof sizeO(ffi)andlarger.Applyinglocalspatialaveragingoperatorwith averagingradiusffitotheNavierStokesequationsgivesanewsystemofequationgov ..."
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uratherthanthevelocityitself.Inlargeeddysimulation,weuseanaveragingoperatorwhichallowsfortheseparationoflargeandsmalllengthscalesintheflowfield. udenotestheeddiesof sizeO(ffi)andlarger.Applyinglocalspatialaveragingoperatorwith averagingradiusffitotheNavierStokesequationsgivesanewsystemofequationgoverningthelargescales.However,ithasthewellknown problemofclosure.Oneapproachtotheclosureproblemwhicharisesfromaveragingthenonlineartermisuseofascalesimilarityhypothesis.Weconsideronesuchscalesimilaritymodel.Weproveexistence ofweaksolutionsfortheresultingsystem.
On irreducible algebras of conformal endomorphisms over a linear algebraic group, Mathematics Subject Classification
"... Abstract. We study the algebra of conformal endomorphisms Cend G,G n of a finitely generated free module Mn over the coordinate Hopf algebra H of a linear algebraic group G. It is shown that a conformal subalgebra of Cendn acting irreducibly on Mn generates an essential left ideal of Cend G,G n if e ..."
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Cited by 2 (1 self)
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Abstract. We study the algebra of conformal endomorphisms Cend G,G n of a finitely generated free module Mn over the coordinate Hopf algebra H of a linear algebraic group G. It is shown that a conformal subalgebra of Cendn acting irreducibly on Mn generates an essential left ideal of Cend G,G n if enriched with operators of multiplication on elements of H. In particular, we describe such subalgebras for the case when G is finite. Introduction. The notion of a conformal algebra was introduced in [1] as a tool for investigation of vertex algebras [2, 3]. From the formal point of view, a conformal algebra is a linear space C over a field k (chark = 0) endowed with a linear operator T: C → C and with a family of bilinear operations ( · n ·), n ∈ Z+ (where Z+ stands for the set of nonnegative integers), satisfying the following axioms:
(Mathematics Subject classification: Primary 11B75, 11D99; Secondary 05D10,
, 2004
"... A set A of positive integers is called a coprime Diophantine powerset if the shifted product ab + 1 of two different elements a and b of A is always a pure power, and the occuring pure powers are all coprime. We prove that each coprime Diophantine powerset A ⊂ {1,..., N} has A  ≤ 8000 log N / log ..."
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A set A of positive integers is called a coprime Diophantine powerset if the shifted product ab + 1 of two different elements a and b of A is always a pure power, and the occuring pure powers are all coprime. We prove that each coprime Diophantine powerset A ⊂ {1,..., N} has A  ≤ 8000 log N / log log N for sufficiently large N. The proof combines results from extremal graph theory with number theory. Assuming the famous abcconjecture, we are able to both drop the coprimality condition and reduce the upper bound to c log log N for a fixed constant c. 1.
The mathematics of infectious diseases
 SIAM Review
, 2000
"... Abstract. Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number R0, the contact number σ, and the replacement number R are reviewed for the classic SIR epidemic a ..."
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Cited by 465 (4 self)
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Abstract. Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number R0, the contact number σ, and the replacement number R are reviewed for the classic SIR epidemic
Integrating classification and association rule mining
 In Proc of KDD
, 1998
"... Classification rule mining aims to discover a small set of rules in the database that forms an accurate classifier. Association rule mining finds all the rules existing in the database that satisfy some minimum support and minimum confidence constraints. For association rule mining, the target of di ..."
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Cited by 561 (21 self)
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Classification rule mining aims to discover a small set of rules in the database that forms an accurate classifier. Association rule mining finds all the rules existing in the database that satisfy some minimum support and minimum confidence constraints. For association rule mining, the target
Assessing agreement on classification tasks: the kappa statistic
 Computational Linguistics
, 1996
"... Currently, computational linguists and cognitive scientists working in the area of discourse and dialogue argue that their subjective judgments are reliable using several different statistics, none of which are easily interpretable or comparable to each other. Meanwhile, researchers in content analy ..."
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Cited by 829 (9 self)
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Currently, computational linguists and cognitive scientists working in the area of discourse and dialogue argue that their subjective judgments are reliable using several different statistics, none of which are easily interpretable or comparable to each other. Meanwhile, researchers in content
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