scholarly journals Regarding three link road train model moving reverse non-holonomic system steering laws synthesis

2018 ◽  
pp. 127-139
Author(s):  
D. Tatievskyi ◽  
Keyword(s):  
Holonomic System

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.

scholarly journals Selberg integrals, super-hypergeometric functions and applications to β-ensembles of random matrices

2015 ◽  
Vol 04 (02) ◽  
pp. 1550007 ◽  
Author(s):  
Patrick Desrosiers ◽  
Dang-Zheng Liu
Keyword(s):  
Hypergeometric Functions ◽  
Matrix Theory ◽  
Direct Application ◽  
Holonomic System ◽  
Expectation Value ◽  
Linear Partial Differential Equations ◽  
Integral Formulas ◽  
Duality Relations ◽  
Selberg Integrals ◽  
Type Integral

We study a new Selberg-type integral with n + m indeterminates, which turns out to be related to the deformed Calogero–Sutherland systems. We show that the integral satisfies a holonomic system of n + m non-symmetric linear partial differential equations. We also prove that a particular hypergeometric function defined in terms of super-Jack polynomials is the unique solution of the system. Some properties such as duality relations, integral formulas, Pfaff–Euler and Kummer transformations are also established. As a direct application, we evaluate the expectation value of ratios of characteristic polynomials in the classical β-ensembles of Random Matrix Theory.

Lie Symmetry and Approximate Hojman Conserved Quantity of Lagrange Equations for a Weakly Nonholonomic System

2013 ◽  
Vol 30 (1) ◽  
pp. 21-27 ◽  
Author(s):  
Y.-L. Han ◽  
X.-X. Wang ◽  
M.-L. Zhang ◽  
L.-Q. Jia
Keyword(s):  
Nonholonomic System ◽  
Equations Of Motion ◽  
Lie Symmetry ◽  
Conserved Quantity ◽  
Holonomic System ◽  
Lagrange Equations ◽  
Definition Of ◽  
Weakly Nonholonomic System ◽  
Infinitesimal Transformations ◽  
Hojman Conserved Quantity

ABSTRACTThe Lie symmetry and Hojman conserved quantity of Lagrange equations for a weakly nonholonomic system and its first-degree approximate holonomic system are studied. The differential equations of motion for the system are established. Under the special infinitesimal transformations of group in which the time is invariable, the definition of the Lie symmetry for the weakly nonholonomic system and its first-degree approximate holonomic system are given, and the exact and approximate Hojman conserved quantities deduced directly from the Lie symmetry are obtained. Finally, an example is given to study the exact and approximate Hojman conserved quantity for the system.

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