We prove several approximation theorems of the complex Monge-Ampère operator on a compact Kähler manifold. As an application we give a simple proof of a recent result of Guedj and Zeriahi on a complete description of the range of the complex Monge-Ampère operator in E(X,ω), which is the class of ω-plurisubharmonic functions with vanishing complex Monge-Ampère mass on all pluripolar sets. We als...

A general description of entanglement is suggested as an action realized by an arbitrary operator over given disentangled states. The related entanglement measure is defined. Because of its generality, this definition can be employed for any physical systems, pure or mixed, equilibrium or nonequilibrium, and characterized by any type of operators, whether these are statistical operators, field ...

This material contains the description of instrumental technique of operative assessment of the mental condition of computer-aided control systems operator. The assessment is based on the study of processes of formation and functioning of mental dynamic images when an operator becomes involved in an activity on the basis of observation by perception. The data concerning the structure and dynami...

This paper provides the Banach duality theory structure of the optimal two-block H∞ problem. Alignment conditions are obtained and show that the optimal solution is flat in general, and unique in the SISO case. It is also proved that under specific conditions a Hankel-Toepltiz operator achieves its norm on the discrete spectrum, therefore generalizing a similar result obtained formerly for fini...

The construction of discrete velocity models or numerical methods for the Boltzmann equation, may lead to the necessity of computing the collision operator as a sum over lattice points. The collision operator involves an integral over a sphere, which corresponds to the conservation of energy and momentum. In dimension two there are difficulties even in proving the convergence of such an approxi...

The problem of a correct quantum description of the phase difference is examined from the perspective of parameter estimation theory. It is shown that an optimum phase-shift measurement defines a phase difference operator which coincides with other approaches to the same problem. We also study the fundamental limit to the accuracy of a phase difference shift detection. We show that this limit c...

This paper provides the duality structure of the optimal two-block H∞ problem. The dual description leads naturally to a numerical solution based on convex programming for LTI (including infinite dimensional) systems. Alignment conditions are obtained and show that the optimal solution is flat in general, and unique in the SISO case. It is also proved that under specific conditions a well-known...

This review provides a comprehensive understanding of regularization theory from different perspectives, emphasizing smoothness and simplicity principles. Using the tools of operator theory and Fourier analysis, it is shown that the solution of the classical Tikhonov regularization problem can be derived from the regularized functional defined by a linear differential (integral) operator in the...

We study the behavior of the limit of the spectrum of a non self-adjoint Sturm-Liouville operator with analytic potential as the semiclassical parameter h → 0. We get a good description of the spectrum and limit spectrum near ∞. We also study the action of one special perturbation of the operator (adding a Heaviside function), and prove that the limit spectrum is very unstable. As an illustrati...

We describe CIPF 2.0, a propositional constructive learner which is able to cope with both noise and representation mismatch in training examples simultaneously. CIPF 2.0’s abilities stem from coupling the robust selective learner C4.5 (and its production rule generator) with a sophisticated constructive induction component. An important new general constructive operator incorporated into CIPF ...