Search results for "FUNCTIONALS"
showing 10 items of 45 documents
Symmetry of minimizers with a level surface parallel to the boundary
2015
We consider the functional $$I_\Omega(v) = \int_\Omega [f(|Dv|) - v] dx,$$ where $\Omega$ is a bounded domain and $f$ is a convex function. Under general assumptions on $f$, G. Crasta [Cr1] has shown that if $I_\Omega$ admits a minimizer in $W_0^{1,1}(\Omega)$ depending only on the distance from the boundary of $\Omega$, then $\Omega$ must be a ball. With some restrictions on $f$, we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these results extend to more general settings, in particular to functionals that are not differenti…
Information dynamics: Temporal behavior of uncertainty measures
2008
We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tool are the information theory methods and inequalities satisfied by Fisher and Shannon information measures. We focus on a compatibility of these inequalities with the prescribed (deterministic, random or quantum) temporal behavior of pertinent probability densities.
Observer-Based Stabilization of Stochastic Systems with Limited Communication
2012
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from Hindawi: http://dx.doi.org/10.1155/2012/781542 Open Access This paper studies the problem of observer-based stabilization of stochastic nonlinear systems with limited communication. A communication channel exists between the output of the plant and the input of the dynamic controller, which is considered network-induced delays, data packet dropouts, and measurement quantization. A new stability criterion is derived for the stochastic nonlinear system by using the Lyapunov functional approach. Based on this, the design procedure of observer-based controller is presented,which ensures asy…
A Viscosity Equation for Minimizers of a Class of Very Degenerate Elliptic Functionals
2013
We consider the functional $$J(v) = \int_\varOmega\bigl[f\bigl(|\nabla v|\bigr) - v\bigr] dx, $$ where Ω is a bounded domain and f:[0,+∞)→ℝ is a convex function vanishing for s∈[0,σ], with σ>0. We prove that a minimizer u of J satisfies an equation of the form $$\min\bigl(F\bigl(\nabla u, D^2 u\bigr), |\nabla u|-\sigma\bigr)=0 $$ in the viscosity sense.
Additive functionals and push forward measures under Veretennikov's flow
2014
16 pages; In this work, we will be interested in the push forward measure $(\vf_t)_*\gamma$, where $\vf_t$ is defined by the stochastic differential equation \begin{equation*} d\vf_t(x)=dW_t + \ba(\vf_t(x))dt, \quad \vf_0(x)=x\in\mbR^m, \end{equation*} and $\gamma$ is the standard Gaussian measure. We will prove the existence of density under the hypothesis that the divergence $\div(\ba)$ is not a function, but a signed measure belonging to a Kato class; the density will be expressed with help of the additive functional associated to $\div(\ba)$.
Nonlocal van der Waals Approach Merged with Double-Hybrid Density Functionals: Toward the Accurate Treatment of Noncovalent Interactions
2015
Noncovalent interactions drive the self-assembly of weakly interacting molecular systems to form supramolecular aggregates, which play a major role in nanotechnology and biochemistry. In this work, we present a thorough assessment of the performance of different double-hybrid density functionals (PBE0-DH-NL, revPBE0-DH-NL, B2PLYP-NL, and TPSS0-DH-NL), as well as their parent hybrid and (meta)GGA functionals, in combination with the most modern version of the nonlocal (NL) van der Waals correction. It is shown that this nonlocal correction can be successfully coupled with double-hybrid density functionals thanks to the short-range attenuation parameter b, which has been optimized against ref…
Robust delay-dependent H∞ control of uncertain time-delay systems with mixed neutral, discrete, and distributed time-delays and Markovian switching p…
2011
Author's version of an article published in the journal: IEEE Transactions on Circuits and Systems I: Regular Papers. Also available from the publisher at: http://dx.doi.org/10.1109/tcsi.2011.2106090 The problem of robust mode-dependent delayed state feedback H ∞ control is investigated for a class of uncertain time-delay systems with Markovian switching parameters and mixed discrete, neutral, and distributed delays. Based on the LyapunovKrasovskii functional theory, new required sufficient conditions are established in terms of delay-dependent linear matrix inequalities for the stochastic stability and stabilization of the considered system using some free matrices. The desired control is …
Katalizatory i proces koordynacyjnej polimeryzacji etylenu - eksperyment i teoria
2004
Badania eksperymentalne i teoretyczne koordynacyjnej polimeryzacji etylenu przeprowadzono wobec katalizatorów otrzymanych z prekursorów - kompleksów halogenków Ti, Zr, Hf, V z organicznymi zasadami Lewisa, nośnika magnezowego [MgCl2(THF)2] i związków glinoorganicznych. Określono zależnosć pomiędzy rodzajem halogenków w prekursorze a aktywnością katalizatora wanadowego. Ustalono profile energetyczne reakcji insercji i terminacji (beta-eliminacji) oraz przeniesienia atomu wodoru beta. Obliczone wartości barier insercji, a także energii wiązania etylenu do centrum aktywnego dobrze korelują z wynikami polimeryzacji. Stwierdzono występowanie w centrach aktywnych oddziaływań agostycznych, które o…
Calculation of magnetic coupling constants with hybrid density functionals
2013
The currently available computational methods for the calculation of magnetic coupling constants with density functional theory have been reviewed. These methods include modern approximations to the exchangecorrelation functional, such as hybrid, range-separated and double-hybrid functionals, as well as approaches to treat the severe spin symmetry problems encountered in density functional calculations of magnetic interactions. In addition to the commonly used unrestricted Kohn–Sham formalism, density functional methods based on multireference wave functions and ensemble densities are also discussed. Performance of these models based on various studies has been summarized. The results indic…
Higher-order energy density functionals in nuclear self-consistent theory
2011
In this thesis consisting of two publications and an overview part, a study of two aspects of energy density functionals has been performed. Firstly, we have linked the next-to-next-to-next-to-leading order nuclear energy density functional to a zero-range pseudopotential that includes all possible terms up to sixth order in derivatives. Within the Hartree-Fock approximation, the quasi-local nuclear Energy Density Functional (EDF) has been calculated as the average energy obtained from the pseudopotential. The direct reference of the EDF to the pseudopotential acts as a constraint that allows for expressing the isovector coupling constants functional in terms of the isoscalar ones, or vice …