Exact Finite-Dimensional Filter for Exponential Functionals of the State of Beneš Systems

2015 ◽  
Vol 33 (6) ◽  
pp. 1056-1067
Author(s):  
Patrick Florchinger
Keyword(s):  
The State ◽  
Finite Dimensional

scholarly journals On Uncertainty Relations and Entanglement Detection with Mutually Unbiased Measurements

2015 ◽  
Vol 22 (01) ◽  
pp. 1550005 ◽  
Author(s):  
Alexey E. Rastegin
Keyword(s):  
The State ◽  
Uncertainty Relations ◽  
Trade Off ◽  
Entropic Uncertainty Relations ◽  
Finite Dimensional ◽  
State Dependent ◽  
Entanglement Detection

We formulate some properties of a set of several mutually unbiased measurements. These properties are used for deriving entropic uncertainty relations. Applications of mutually unbiased measurements in entanglement detection are also revisited. First, we estimate from above the sum of the indices of coincidence for several mutually unbiased measurements. Further, we derive entropic uncertainty relations in terms of the Rényi and Tsallis entropies. Both the state-dependent and state-independent formulations are obtained. Using the two sets of local mutually unbiased measurements, a method of entanglement detection in bipartite finite-dimensional systems may be realized. A certain trade-off between a sensitivity of the scheme and its experimental complexity is discussed.

scholarly journals Characteristic phenomena in combustion

1997 ◽  
Vol 1 (2) ◽  
pp. 147-159
Author(s):  
Dirk Meinköhn
Keyword(s):  
State Space ◽  
Reaction Diffusion ◽  
Stationary Solutions ◽  
The State ◽  
State Variable ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Singularity Order ◽  
The Relationship ◽  
Stable Stationary Solutions

For the case of a reaction–diffusion system, the stationary states may be represented by means of a state surface in a finite-dimensional state space. In the simplest example of a single semi-linear model equation given. in terms of a Fredholm operator, and under the assumption of a centre of symmetry, the state space is spanned by a single state variable and a number of independent control parameters, whereby the singularities in the set of stationary solutions are necessarily of the cuspoid type. Certain singularities among them represent critical states in that they form the boundaries of sheets of regular stable stationary solutions. Critical solutions provide ignition and extinction criteria, and thus are of particular physical interest. It is shown how a surface may be derived which is below the state surface at any location in state space. Its contours comprise singularities which correspond to similar singularities in the contours of the state surface, i.e., which are of the same singularity order. The relationship between corresponding singularities is in terms of lower bounds with respect to a certain distinguished control parameter associated with the name of Frank-Kamenetzkii.

scholarly journals State Feedback Regulation Problem to the Reaction-Diffusion Equation

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1983
Author(s):  
Francisco Jurado ◽  
Andrés A. Ramírez
Keyword(s):  
State Feedback ◽  
Feedback Regulation ◽  
Parabolic Type ◽  
Reaction Diffusion ◽  
The State ◽  
Reaction Diffusion Equation ◽  
Finite Dimensional ◽  
Sturm Liouville ◽  
Bounded Input ◽  
Feedback Regulator

In this work, we explore the state feedback regulator problem (SFRP) in order to achieve the goal for trajectory tracking with harmonic disturbance rejection to one-dimensional (1-D) reaction-diffusion (R-D) equation, namely, a partial differential equation of parabolic type, while taking into account bounded input, output, and disturbance operators, a finite-dimensional exosystem (exogenous system), and the state of the exosystem as the state to the feedback law. As is well-known, the SFRP can be solved only if the so-called Francis (regulator) equations have solution. In our work, we try with the solution of the Francis equations from the 1-D R-D equation following given criteria to the eigenvalues from the exosystem and transfer function of the system, but the state operator is here defined in terms of the Sturm–Liouville differential operator (SLDO). Within this framework, the SFRP is then solved for the 1-D R-D equation. The numerical simulation results validate the performance of the regulator.

State estimation for stochastic polynomial systems with switching in the state equation

2017 ◽  
Vol 40 (9) ◽  
pp. 2732-2739
Author(s):  
Miguel Hernandez-Gonzalez ◽  
Michael V Basin
Keyword(s):  
Covariance Matrix ◽  
Polynomial System ◽  
Random Variable ◽  
Polynomial Systems ◽  
State Equation ◽  
The State ◽  
Nonlinear Functions ◽  
Degree Polynomial ◽  
Error Covariance ◽  
Finite Dimensional

The problem of designing a mean-square filter has been studied for stochastic polynomial systems, where the state equation switches between two different nonlinear functions, over linear observations. A switching signal depends on a random variable modelled as a Bernoulli distributed sequence that takes the quantities of zero and one. The differential equations for the state estimate and the error covariance matrix are obtained in a closed form by expressing the conditional expectation of polynomial terms as functions of the estimate and covariance matrix. Finite-dimensional filtering equations are obtained for a particular case of a third-degree polynomial system. Numerical simulations are carried out in two cases of switching between different linear and second degree polynomial functions.

NONCLASSICAL EFFECTS OF THE STATES GENERATED BY EXCITATIONS ON A COHERENT STATE OF A HARMONIC OSCILLATOR IN A FINITE-DIMENSIONAL HILBERT SPACE

2005 ◽  
Vol 19 (16) ◽  
pp. 779-784
Author(s):  
YUAN-XING LI ◽  
QIN-MEI WANG ◽  
JING-BO XU
Keyword(s):  
Hilbert Space ◽  
Coherent State ◽  
Harmonic Oscillator ◽  
Physical Properties ◽  
The State ◽  
Photon Statistics ◽  
Finite Dimensional ◽  
Dimensional Hilbert Space ◽  
Finite Dimensional Hilbert Space

The mathematical and physical properties of the states which are generated by excitations on the coherent state of a harmonic oscillator in a finite-dimensional Hilbert space are studied. It is shown that the state exhibits squeezing in one of the quadratures of the field and sub-Poissonian photon statistics.

Entropy fluctuations to quantify mixedness

2019 ◽  
Vol 17 (08) ◽  
pp. 1941007
Author(s):  
J. A. Anaya-Contreras ◽  
A. Zúñiga-Segundo ◽  
H. M. Moya-Cessa
Keyword(s):  
Hilbert Spaces ◽  
The State ◽  
Field Interaction ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Level Atom ◽  
Final Dimension

We propose a mixedness quantifier based on entropy fluctuations. It provides information about the degree of mixedness either for finite dimensional and infinite dimensional Hilbert spaces (HS). It may be used to determine the reduction of the HS as it becomes maximum when either the state is maximally mixed, or when the HS effectively reduces its dimensions, such as in the atom field interaction where the two-level atom dictates the final dimension of the field.

Geometric description of time-dependent finite-dimensional mechanical systems

2020 ◽  
Vol 25 (11) ◽  
pp. 2050-2075
Author(s):  
Simon R. Eugster ◽  
Giuseppe Capobianco ◽  
Tom Winandy
Keyword(s):  
State Space ◽  
Degrees Of Freedom ◽  
Vector Fields ◽  
Mechanical Systems ◽  
Second Order ◽  
The State ◽  
Time Dependent ◽  
Finite Dimensional ◽  
Affine Bundle ◽  
Time Position

Using the non-standard geometric structure proposed by Loos, we present a coordinate-free formulation of the theory for time-dependent finite-dimensional mechanical systems with n degrees of freedom. The state space containing the system’s information on time, position and velocity is defined as a (2 n+1)-dimensional affine bundle over an ( n+1)-dimensional generalized space-time. The main goal is to present a geometric postulate that characterizes a second-order vector field whose integral curves describe the motions of a time-dependent finite-dimensional mechanical system. The core objects of the postulate are differential two-forms on the state space, called action forms, which are in a bijective relation with second-order vector fields. The requirements for a differential two-form to be an action form allow for a coordinate-free definition of non-potential forces, which may depend on time, position and velocity. Finally, we show that not only Lagrange’s equations but also Hamilton’s equations follow directly as mere coordinate representations of the same coordinate-free postulate.

PAIRS OF SIMPLE DIMENSION GROUPS

1999 ◽  
Vol 10 (06) ◽  
pp. 739-761 ◽  
Author(s):  
A. KISHIMOTO
Keyword(s):  
The State ◽  
Crossed Product ◽  
Real Rank ◽  
Real Rank Zero ◽  
State Spaces ◽  
Rank Zero ◽  
C Algebra ◽  
Finite Dimensional ◽  
Dimension Groups

Given a pair of simple dimension groups with isomorphic state spaces we try to express it as the pair K0(A),K0(A×αR) of K0 groups for a C*-algebra A with an action α of R, where both A and the crossed product A×αR are supposed to be simple AT algebras of real rank zero. We solve this when the state spaces are finite-dimensional.

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