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Local characterizations of the Pinsker von Neumann algebra and its sequence entropy analogue are given in terms of combinatorial independence, ℓ1 geometry, and Voiculescu's completely positive approximation entropy.
To overcome this shortcoming, we introduce in this paper a theoretic framework based on rough set theory, which is called positive approximation and can be used to accelerate a heuristic process for feature selection from incomplete data.
To overcome this shortcoming, we introduce a theoretic framework based on rough set theory, called positive approximation, which can be used to accelerate a heuristic process of attribute reduction.
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These solutions, including a positive real approximation to the Wiener-Hopf solution, are illustrated through an extensive example for the free end of a dispersive Bernoulli-Euler beam.
With special regard to intrinsic suppression of disturbances, the theoretical justification of the superiority of this approach over point measurement schemes, and an appropriate mathematical method based on positive spline approximation operators for the computer internal representation and processing of empirical functions are established.
Therefore, we should modify Hessian matrix to yield a positive definite approximation.
Equation 6 is composed of three components, additive positive constant, approximation of Gaussian pdf, and cosine multiplied Q-function terms.
Next, schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous Hamiltonians.
For nonlinear methods, I will describe the spectral direction method, which uses a sparse positive definite Hessian approximation to "bend" the true gradient with the curvature of the spectral part of the objective.
Furthermore, we can not ignore the fact that brain processing mechanisms in the modification of emotions and behaviors, such as the activation of the left frontal pole related to positive thoughts and approximation behaviors, and the activation of the right frontal pole which is related to negative thoughts and avoidance behaviors.
To fulfill this necessity, very recently the well-known sequences of linear positive operators of approximation theory have been transferred to the ((p,q -calculus and the advantages of ((p,q -calculusof them hand been inthesively investigadvantages
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