GENERALIZED CANONICAL REALIZATION AND BIRKHOFF’S REALIZATION OF CHAPLYGIN’S NON HOLONOMIC SYSTEM

1995 ◽  
Vol 19 (2) ◽  
pp. 59-73
Author(s):  
F.X. Mei ◽  
B. Lévesque
Keyword(s):  
Holonomic System ◽  
Canonical Realization

A minimal canonical realization algorithm for impulse response matrix using moments

1975 ◽  
Vol 63 (3) ◽  
pp. 538-540 ◽  
Author(s):  
M. Lal ◽  
H. Singh ◽  
R. Parthasarathy
Keyword(s):  
Impulse Response ◽  
Response Matrix ◽  
Canonical Realization

Singular 2D Behaviors: Fornasini–Marchesini and Givone–Roesser Models

2009 ◽  
Vol 16 (1) ◽  
pp. 105-130
Author(s):  
Vakhtang Lomadze ◽  
Eric Rogers ◽  
Jeffrey Wood
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Roesser Models ◽  
Canonical Realization ◽  
Necessary And Sufficient

Abstract In this paper we study 2D Fornasini–Marchesini and 2D Givone–Roesser models from the viewpoint developed in our recent paper [Lomadze, Rogers, Wood, Georgian Math. J. 15: 139–157, 2008]. We give necessary and sufficient conditions for a behavior to be expressable in Fornasini–Marchesini or Givone–Roesser form, and a canonical realization when the conditions are met. We also study the regularity, controllability and autonomy of these models. In particular, we provide the concepts of controllability in the sense of Kalman for each model, and show that they agree with the behavioral controllability as defined in [Lomadze, Rogers, Wood, Georgian Math. J. 15: 139–157, 2008].

scholarly journals Equivalence of Models in Loop Quantum Cosmology and Group Field Theory

Universe ◽  
2019 ◽  
Vol 5 (2) ◽  
pp. 41 ◽  
Author(s):  
Bekir Baytaş ◽  
Martin Bojowald ◽  
Sean Crowe
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Loop Quantum Cosmology ◽  
Canonical Realization ◽  
Group Field Theory

The paradigmatic models often used to highlight cosmological features of loop quantum gravity and group field theory are shown to be equivalent, in the sense that they are different realizations of the same model given by harmonic cosmology. The loop version of harmonic cosmology is a canonical realization, while the group-field version is a bosonic realization. The existence of a large number of bosonic realizations suggests generalizations of models in group field cosmology.

scholarly journals A system of hypergeometric differential equations in two variables of rank 9

2017 ◽  
Vol 28 (03) ◽  
pp. 1750015 ◽  
Author(s):  
Jyoichi Kaneko ◽  
Keiji Matsumoto ◽  
Katsuyoshi Ohara
Keyword(s):  
Differential Equations ◽  
Fundamental Group ◽  
Hypergeometric Function ◽  
Hypergeometric Series ◽  
Fundamental System ◽  
Singular Locus ◽  
Holonomic System

We study a hypergeometric function in two variables and a system of hypergeometric differential equations associated with this function. This is a regular holonomic system of rank [Formula: see text]. We give a fundamental system of solutions to this system in terms of this hypergeometric series. We give circuit matrices along generators of the fundamental group of the complement of its singular locus with respect to our fundamental system.

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