Calderon-Zygmund Operators, Local Mean Oscillation and Certain Automorphisms of the Toeplitz Algebra

1995 ◽  
Vol 117 (5) ◽  
pp. 1157 ◽  
Author(s):  
Paul S. Muhly ◽  
Jingbo Xia
Keyword(s):  
Toeplitz Algebra ◽  
Mean Oscillation ◽  
Local Mean

Joint Mean Oscillation and Local Ideals in the Toeplitz Algebra II: Local Commutivity and Essential Commutant

2002 ◽  
Vol 45 (2) ◽  
pp. 309-318
Author(s):  
Jingbo Xia
Keyword(s):  
Local Analysis ◽  
Toeplitz Algebra ◽  
Calkin Algebra ◽  
Algebra Ii ◽  
Mean Oscillation ◽  
Essential Commutant ◽  
Double Commutant ◽  
Local Ideals

AbstractA well-known theorem of Sarason [11] asserts that if [Tf, Th] is compact for every h ∈ H∞, then f ∈ H∞ + C(T). Using local analysis in the full Toeplitz algebra τ = τ(L∞), we show that the membership f ∈ H∞ + C(T) can be inferred from the compactness of a much smaller collection of commutators [Tf, Th]. Using this strengthened result and a theorem of Davidson [2], we construct a proper C*-subalgebra τ(L)) of τ which has the same essential commutant as that of τ. Thus the image of τ(ℒ) in the Calkin algebra does not satisfy the double commutant relation [12], [1]. We will also show that no separable subalgebra Ѕ of τ is capable of conferring the membership f ∈ H∞ + C(T) through the compactness of the commutators {[Tf, S] : S ∈ Ѕ}.

Performance analysis of global local mean square error criterion of stochastic linearization for nonlinear oscillator

2019 ◽  
Author(s):  
Nguyen Cao Thang ◽  
Luu Xuan Hung
Keyword(s):  
Performance Analysis ◽  
Mean Square Error ◽  
Nonlinear Oscillators ◽  
Degree Of Freedom ◽  
Equivalent Linearization ◽  
Mean Square ◽  
Error Criterion ◽  
Stochastic Linearization ◽  
Local Mean ◽  
Mean Square Error Criterion

The paper presents a performance analysis of global-local mean square error criterion of stochastic linearization for some nonlinear oscillators. This criterion of stochastic linearization for nonlinear oscillators bases on dual conception to the local mean square error criterion (LOMSEC). The algorithm is generally built to multi degree of freedom (MDOF) nonlinear oscillators. Then, the performance analysis is carried out for two applications which comprise a rolling ship oscillation and two degree of freedom one. The improvement on accuracy of the proposed criterion has been shown in comparison with the conventional Gaussian equivalent linearization (GEL).

scholarly journals Hexagonal-Shaped Spin Crossover Nanoparticles Studied by Ising-Like Model Solved by Local Mean Field Approximation

2021 ◽  
Vol 7 (5) ◽  
pp. 69
Author(s):  
Catherine Cazelles ◽  
Jorge Linares ◽  
Mamadou Ndiaye ◽  
Pierre-Richard Dahoo ◽  
Kamel Boukheddaden
Keyword(s):  
Spin Crossover ◽  
Hexagonal Lattice ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ligand Field ◽  
Order And Disorder ◽  
The Matrix ◽  
Local Mean ◽  
Parameter Values

The properties of spin crossover (SCO) nanoparticles were studied for five 2D hexagonal lattice structures of increasing sizes embedded in a matrix, thus affecting the thermal properties of the SCO region. These effects were modeled using the Ising-like model in the framework of local mean field approximation (LMFA). The systematic combined effect of the different types of couplings, consisting of (i) bulk short- and long-range interactions and (ii) edge and corner interactions at the surface mediated by the matrix environment, were investigated by using parameter values typical of SCO complexes. Gradual two and three hysteretic transition curves from the LS to HS states were obtained. The results were interpreted in terms of the competition between the structure-dependent order and disorder temperatures (TO.D.) of internal coupling origin and the ligand field-dependent equilibrium temperatures (Teq) of external origin.

scholarly journals Some estimates for the commutators of multilinear maximal function on Morrey-type space

2021 ◽  
Vol 19 (1) ◽  
pp. 515-530
Author(s):  
Xiao Yu ◽  
Pu Zhang ◽  
Hongliang Li
Keyword(s):  
Maximal Function ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Generalized Morrey Spaces ◽  
Type Space ◽  
Bmo Function ◽  
Mean Oscillation ◽  
Multilinear Maximal Function ◽  
Equivalent Conditions

Abstract In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space. Moreover, the endpoint estimate for such operators on generalized Morrey spaces is also given.

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