scholarly journals On quantum additive Gaussian noise channels

2017 ◽  
Vol 17 (3&4) ◽  
pp. 283-302
Author(s):  
Martin Idel ◽  
Robert Konig
Keyword(s):  
Normal Form ◽  
Gaussian Noise ◽  
Quantum Channel ◽  
Sufficient Conditions ◽  
The State ◽  
Input And Output ◽  
Necessary And Sufficient ◽  
Gaussian Noise Channels ◽  
Multi Mode ◽  
Additive Channel

We give necessary and sufficient conditions for a Gaussian quantum channel to have a dilation involving a passive, i.e., number-preserving unitary. We then establish a normal form of such channels: any passively dilatable channel is the result of applying passive unitaries to the input and output of a Gaussian additive channel. The latter combine the state of the system with that of the environment by means of a multi-mode beamsplitter.

scholarly journals A Note on Decomposable and Reducible Integer Matrices

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1125
Author(s):  
Carlos Marijuán ◽  
Ignacio Ojeda ◽  
Alberto Vigneron-Tenorio
Keyword(s):  
Normal Form ◽  
Linear Algebra ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Integer Matrix ◽  
Hermite Normal Form ◽  
Necessary And Sufficient

We propose necessary and sufficient conditions for an integer matrix to be decomposable in terms of its Hermite normal form. Specifically, to each integer matrix, we associate a symmetric integer matrix whose reducibility can be efficiently determined by elementary linear algebra techniques, and which completely determines the decomposability of the first one.

scholarly journals Zeroing of state variables in fractional descriptor electrical circuits by state-feedbacks

2014 ◽  
Vol 63 (3) ◽  
pp. 321-333
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Closed Loop ◽  
Sufficient Conditions ◽  
The State ◽  
Necessary And Sufficient Conditions ◽  
State Variables ◽  
Electrical Circuits ◽  
Closed Loop Systems ◽  
Necessary And Sufficient

Abstract The problem of zeroing of the state variables in fractional descriptor electrical circuits by state-feedbacks is formulated and solved. Necessary and sufficient conditions for the existence of gain matrices such that the state variables of closed-loop systems are zero for time greater zero are established. The procedure of choice of the gain matrices is demonstrated on simple descriptor electrical circuits with regular pencils

The Pointwise Ergodic Theorem for Transformations whose Orbits contain or are contained in the Orbits of a Measure-Preserving Transformation

1982 ◽  
Vol 34 (6) ◽  
pp. 1303-1318 ◽  
Author(s):  
John C. Kieffer ◽  
Maurice Rahe
Keyword(s):  
Information Theory ◽  
Ergodic Theory ◽  
Probability Space ◽  
Sufficient Conditions ◽  
Measurable Transformation ◽  
Input And Output ◽  
Measure Preserving Transformation ◽  
Image Position ◽  
Necessary And Sufficient ◽  
Measure Preserving Transformations

1. Introduction. Let be a probability space with standard. Let T be a bimeasurable one-to-one map of Ω onto itself. Let U: Ω → Ω be another measurable transformation whose orbits are contained in the T-orbits; that is,where Z denotes the set of integers. (This is equivalent to saying that there is a measurable mapping L: Ω → Z such that U(ω) = TL(ω)(ω), ω ∈ Ω.) Such pairs (T, U) arise quite naturally in ergodic theory and information theory. (For example, in ergodic theory, one can see such pairs in the study of the full group of a transformation [1]; in information theory, such a pair can be associated with the input and output of a variable-length source encoder [2] [3].) Neveu [4] obtained necessary and sufficient conditions for U to be measure-preserving if T is measure-preserving. However, if U fails to be measure-preserving, U might still possess many of the features of measure-preserving transformations.

Generalized semi-Markov decision processes

1979 ◽  
Vol 16 (03) ◽  
pp. 618-630
Author(s):  
Bharat T. Doshi
Keyword(s):  
Markov Decision Processes ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
The State ◽  
Service Rate ◽  
Storage Model ◽  
Sample Paths ◽  
Markov Decision ◽  
Sufficient Conditions For Optimality ◽  
Necessary And Sufficient

Various authors have derived the necessary and sufficient conditions for optimality in semi-Markov decision processes in which the state remains constant between jumps. In this paper similar results are presented for a generalized semi-Markov decision process in which the state varies between jumps according to a Markov process with continuous sample paths. These results are specialized to a general storage model and an application to the service rate control in a GI/G/1 queue is indicated.

scholarly journals Lagrangian for Circuits with Higher-Order Elements

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1059 ◽  
Author(s):  
Zdenek Biolek ◽  
Dalibor Biolek ◽  
Viera Biolkova
Keyword(s):  
Variational Principle ◽  
Equations Of Motion ◽  
Sufficient Conditions ◽  
Higher Order ◽  
The State ◽  
Even Order ◽  
Independent Variable ◽  
Necessary And Sufficient ◽  
Derivatives Of ◽  
State Functions

The necessary and sufficient conditions of the validity of Hamilton’s variational principle for circuits consisting of (α,β) elements from Chua’s periodical table are derived. It is shown that the principle holds if and only if all the circuit elements lie on the so-called Σ-diagonal with a constant sum of the indices α and β. In this case, the Lagrangian is the sum of the state functions of the elements of the L or +R types minus the sum of the state functions of the elements of the C or −R types. The equations of motion generated by this Lagrangian are always of even-order. If all the elements are linear, the equations of motion contain only even-order derivatives of the independent variable. Conclusions are illustrated on an example of the synthesis of the Pais–Uhlenbeck oscillator via the elements from Chua’s table.

scholarly journals The geometry of modified Riemannian extensions

2009 ◽  
Vol 465 (2107) ◽  
pp. 2023-2040 ◽  
Author(s):  
E. Calviño-Louzao ◽  
E. García-Río ◽  
P. Gilkey ◽  
R. Vázquez-Lorenzo
Keyword(s):  
Normal Form ◽  
Space Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Jordan Normal Form ◽  
Jacobi Operators ◽  
Necessary And Sufficient

We show that every paracomplex space form is locally isometric to a modified Riemannian extension and gives necessary and sufficient conditions for a modified Riemannian extension to be Einstein. We exhibit Riemannian extension Osserman manifolds of signature (3, 3), whose Jacobi operators have non-trivial Jordan normal form and which are not nilpotent. We present new four-dimensional results in Osserman geometry.

Synchronization of switched Boolean networks with impulsive effects

2018 ◽  
Vol 11 (06) ◽  
pp. 1850080 ◽  
Author(s):  
Xiaojing Xu ◽  
Yansheng Liu ◽  
Haitao Li ◽  
Fuad E. Alsaadi
Keyword(s):  
Sufficient Conditions ◽  
Boolean Networks ◽  
The State ◽  
Impulsive Effects ◽  
Space Representation ◽  
Algebraic Form ◽  
State Space Representation ◽  
Switching Signal ◽  
Output Synchronization ◽  
Necessary And Sufficient

This paper studies the state/output synchronization of switched Boolean networks (SBNs) with impulsive effects via the algebraic state space representation (ASSR) approach. First, an algebraic form is established for SBNs with impulsive effects via ASSR. Second, based on the algebraic form, some necessary and sufficient conditions are presented for the state/output synchronization of SBNs with impulsive effects under arbitrary switching signals. Third, two special kinds of switching signals, that is, free switching signal and feedback switching signal, are considered for the state synchronization of SBNs with impulsive effects. Finally, two illustrative examples are worked out to show the effectiveness of the obtained results.

CONTROLLABILITY OF A LINEAR DISCRETE SYSTEM WITH CHANGE OF THE STATE VECTOR DIMENSION

2021 ◽  
pp. 173-178
Author(s):  
V. V. Pichkur ◽  
D. A. Mazur ◽  
V. V. Sobchuk
Keyword(s):  
State Vector ◽  
Discrete System ◽  
Sufficient Conditions ◽  
The State ◽  
Functional Stability ◽  
Final State ◽  
Technological Processes ◽  
Linear Discrete System ◽  
Necessary And Sufficient ◽  
Vector Dimension

The paper proposes an analysis of controllability of a linear discrete system with change of the state vector dimension. We offer necessary and sufficient conditions of controllability and design the control that guarantees the decision of a problem of moving of such system to an arbitrary final state. It provides functional stability of technological processes described by a linear discrete system with change of the state vector dimension.

Necessary and sufficient conditions for stability of fractional discrete-time linear state-space systems

2013 ◽  
Vol 61 (4) ◽  
pp. 779-786 ◽  
Author(s):  
M. Busłowicz ◽  
A. Ruszewski
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
The State ◽  
Necessary And Sufficient Conditions ◽  
Practical Stability ◽  
State Matrix ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract In the paper the problems of practical stability and asymptotic stability of fractional discrete-time linear systems are addressed. Necessary and sufficient conditions for practical stability and for asymptotic stability are established. The conditions are given in terms of eigenvalues of the state matrix of the system. In particular, it is shown that (similarly as in the case of fractional continuous-time linear systems) in the complex plane exists such a region, that location of all eigenvalues of the state matrix in this region is necessary and sufficient for asymptotic stability. The parametric description of boundary of this region is given. Moreover, it is shown that Schur stability of the state matrix (all eigenvalues have absolute values less than 1) is not necessary nor sufficient for asymptotic stability of the fractional discrete-time system. The considerations are illustrated by numerical examples.

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