Search results for "function"

Poincare Inequalities and Spectral Gap, Concentration Phenomenon for G-Measures

2002

We produce a new approach based upon inequalities of Poincare’s type for giving constructive estimates of the mixing rate for a family of mixing stationary processes continuously depending on their past called g-measures. We establish also exponential inequalities of Hoeffding’s type leading to a concentration phenomenon for a large class of observables; this last property permits in particular to give the typical behaviour of the n-orbits of a g-measure.

Saddle index properties, singular topology, and its relation to thermodynamic singularities for aϕ4mean-field model

2004

We investigate the potential energy surface of a ${\ensuremath{\phi}}^{4}$ model with infinite range interactions. All stationary points can be uniquely characterized by three real numbers ${\ensuremath{\alpha}}_{+},{\ensuremath{\alpha}}_{0},{\ensuremath{\alpha}}_{\ensuremath{-}}$ with ${\ensuremath{\alpha}}_{+}+{\ensuremath{\alpha}}_{0}+{\ensuremath{\alpha}}_{\ensuremath{-}}=1$, provided that the interaction strength $\ensuremath{\mu}$ is smaller than a critical value. The saddle index ${n}_{s}$ is equal to ${\ensuremath{\alpha}}_{0}$ and its distribution function has a maximum at ${n}_{s}^{\mathrm{max}}=1∕3$. The density $p(e)$ of stationary points with energy per particle $e$, as well as…

Special Functions for the Study of Economic Dynamics: The Case of the Lucas-Uzawa Model

2004

The special functions are intensively used in mathematical physics to solve differential systems. We argue that they should be most useful in economic dynamics, notably in the assessment of the transition dynamics of endogenous growth models. We illustrate our argument on the Lucas-Uzawa model, which we solve by the means of Gaussian hypergeometric functions. We show how the use of Gaussian hypergeometric functions allows for an explicit representation of the equilibrium dynamics of the variables in level. In contrast to the preexisting approaches, our method is global and does not rely on dimension reduction.

Robust H<inf>∞</inf> control of Markovian jump systems with mixed time delays

2010

In this paper, the problem of stability analysis and control synthesis for Markovian jump linear systems with time delays and norm-bounded uncertainties is studied. The model under consideration consists of different time-invariant discrete, neutral and distributed delays. Delay-dependent sufficient conditions for the design of a mode-dependent delayed state feedback H ∞ control are given in terms of linear matrix inequalities (LMIs). A controller which guarantees stochastic stability and a prescribed level of H ∞ performance for the closed-loop system is then developed. A Lyapunov-Krasovskii functional (LKF) method underlies the control design. A numerical example with simulation results i…

A Self-Contained Biometric Sensor for Ubiquitous Authentication

2007

This paper describes a real-life behavior framework in simulation game based on Probabilistic State Machine (PSM) with Gaussian random distribution. According to the dynamic environment information, NPC can generate behavior planning autonomously associated with defined FSM. After planning process, we illuminate Gaussian probabilistic function for real-life action simulation in time and spatial domains. The expected value of distribution is estimated during behavior planning process and variance is determined by NPC personality in order to realize real life behavior simulation. We experiment the framework and Gaussian PSM on a restaurant simulation game. Furthermore we give some suggestions…

Excitation energies and photoabsorption oscillator strengths of the Rydberg series in CF3Cl. A linear response and quantum defect study.

2007

Vertical excitation energies of the CF(3)Cl molecule have been obtained from a response function approach with a CC reference function to determine absolute photoabsorption oscillator strengths in the molecular-adapted quantum defect orbital formalism (MQDO). The present work covers more highly excited Rydberg states than have been experimentally reported. Assessing of the reliability of the present calculations is provided through a comparative analysis between the results of the molecule and the Cl atom. This can be used to allow for predictions of the same type of properties in other analogous systems.

A Stieltjes Approach to Static Hedges

2014

Static hedging of complicated payoff structures by standard instruments becomes increasingly popular in finance. The classical approach is developed for quite regular functions, while for less regular cases, generalized functions and approximation arguments are used. In this note, we discuss the regularity conditions in the classical decomposition formula due to P. Carr and D. Madan (in Jarrow ed, Volatility, pp. 417–427, Risk Publ., London, 1998) if the integrals in this formula are interpreted as Lebesgue integrals with respect to the Lebesgue measure. Furthermore, we show that if we replace these integrals by Lebesgue–Stieltjes integrals, the family of representable functions can be exte…

Constant inner potential DFT for modelling electrochemical systems under constant potential and bias

2021

Electrochemical interfaces and reactions play a decisive role in e.g. clean energy conversion but understanding their complex chemistry remains an outstanding challenge. Constant potential or grand canonical ensemble (GCE) simulations are indispensable for unraveling the properties of electrochemical processes as a function of the electrode potential. Currently, constant electrode potential calculations at the density functional theory (DFT) level are carried out by fixing the Fermi level of the simulation cell. However, the Fermi level from DFT calculations does does not always reflect the experimentally controlled electrode potential or describe the thermodynamic independent variable in G…

Operator (Quasi-)Similarity, Quasi-Hermitian Operators and All that

2016

Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity between operators and explore to what extent they preserve spectral properties. Then we study quasi-Hermitian operators, bounded or not, that is, operators that are quasi-similar to their adjoint and we discuss their application in pseudo-Hermitian quantum mechanics. Finally, we extend the analysis to operators in a partial inner product space (pip-space), in particular the scale of Hilbert space s generated by a single unbounded metric operator.

On Taylor coefficients of entire functions integrable against exponential weights

2001