scholarly journals Oscillation theorems for self-adjoint matrix Hamiltonian systems involving general means

2004 ◽  
Vol 295 (2) ◽  
pp. 355-377 ◽  
Author(s):  
Qigui Yang ◽  
Yun Tang
Keyword(s):  
Hamiltonian Systems ◽  
Adjoint Matrix ◽  
Oscillation Theorems

scholarly journals Oscillation theorems for self-adjoint matrix Hamiltonian systems

2003 ◽  
Vol 190 (1) ◽  
pp. 306-329 ◽  
Author(s):  
Qigui Yang ◽  
Ronald Mathsen ◽  
Siming Zhu
Keyword(s):  
Hamiltonian Systems ◽  
Adjoint Matrix ◽  
Oscillation Theorems

Interval oscillation criteria for self-adjoint matrix Hamiltonian systems

2005 ◽  
Vol 135 (5) ◽  
pp. 1085-1108 ◽  
Author(s):  
Qigui Yang ◽  
Yun Tang
Keyword(s):  
Hamiltonian Systems ◽  
Half Line ◽  
Linear Functionals ◽  
Matrix Space ◽  
Differential Systems ◽  
Adjoint Matrix ◽  
Oscillation Criteria ◽  
Positive Linear Functionals ◽  
Interval Oscillation ◽  
New Criteria

By using a monotonic functional on a suitable matrix space, some new oscillation criteria for self-adjoint matrix Hamiltonian systems are obtained. They are different from most known results in the sense that the results of this paper are based on information only for a sequence of subintervals of [t0, ∞), rather than for the whole half-line. We develop new criteria for oscillations involving monotonic functionals instead of positive linear functionals or the largest eigenvalue. The results are new, even for the particular case of self-adjoint second-differential systems which can be applied to extreme cases such as

scholarly journals ON THE OSCILLATION OF SELF-ADJOINT MATRIX HAMILTONIAN SYSTEMS

2003 ◽  
Vol 46 (3) ◽  
pp. 609-625 ◽  
Author(s):  
Qigui Yang ◽  
Sui Sun Cheng
Keyword(s):  
Hamiltonian Systems ◽  
Subject Classification ◽  
Hamiltonian Matrix ◽  
Linear Functionals ◽  
Adjoint Matrix ◽  
Oscillation Criteria ◽  
Positive Linear Functionals ◽  
Matrix Spaces

AbstractBy means of monotone functionals and positive linear functionals defined on suitable matrix spaces as well as new generalized Riccati transformations, oscillation criteria for self-adjoint linear Hamiltonian matrix systems are obtained. Our results are generalizations and improvements of many existing results.AMS 2000 Mathematics subject classification: Primary 34A30; 34C10

Interval oscillation criteria for self-adjoint matrix Hamiltonian systems

2005 ◽  
Vol 135 (5) ◽  
pp. 1085-1108
Author(s):  
Qigui Yang ◽  
Yun Tang
Keyword(s):  
Hamiltonian Systems ◽  
Half Line ◽  
Linear Functionals ◽  
Matrix Space ◽  
Differential Systems ◽  
Adjoint Matrix ◽  
Oscillation Criteria ◽  
Positive Linear Functionals ◽  
Interval Oscillation ◽  
New Criteria

By using a monotonic functional on a suitable matrix space, some new oscillation criteria for self-adjoint matrix Hamiltonian systems are obtained. They are different from most known results in the sense that the results of this paper are based on information only for a sequence of subintervals of [t0, ∞), rather than for the whole half-line. We develop new criteria for oscillations involving monotonic functionals instead of positive linear functionals or the largest eigenvalue. The results are new, even for the particular case of self-adjoint second-differential systems which can be applied to extreme cases such as

Riccati techniques and oscillation for self-adjoint matrix Hamiltonian systems

2009 ◽  
Vol 58 (6) ◽  
pp. 1211-1222 ◽  
Author(s):  
Qi-Ru Wang ◽  
Yuan-Tong Xu ◽  
Ronald M. Mathsen
Keyword(s):  
Hamiltonian Systems ◽  
Adjoint Matrix ◽  
Riccati Techniques

Oscillation theorems for linear matrix Hamiltonian systems

2015 ◽  
Vol 253 ◽  
pp. 402-409 ◽  
Author(s):  
Jing Shao ◽  
Fanwei Meng ◽  
Zhaowen Zheng
Keyword(s):  
Hamiltonian Systems ◽  
Linear Matrix ◽  
Oscillation Theorems

Deterministic Mechanism of Irreversibility

2018 ◽  
Vol 14 (3) ◽  
pp. 5708-5733 ◽  
Author(s):  
Vyacheslav Michailovich Somsikov
Keyword(s):  
Internal Energy ◽  
Hamiltonian Systems ◽  
Classical Mechanics ◽  
Motion Equation ◽  
Holonomic Constraints ◽  
Dissipative Processes ◽  
Motion Energy ◽  
Analytical Review ◽  
History Of ◽  
Material Points

The analytical review of the papers devoted to the deterministic mechanism of irreversibility (DMI) is presented. The history of solving of the irreversibility problem is briefly described. It is shown, how the DMI was found basing on the motion equation for a structured body. The structured body was given by a set of potentially interacting material points. The taking into account of the body’s structure led to the possibility of describing dissipative processes. This possibility caused by the transformation of the body’s motion energy into internal energy. It is shown, that the condition of holonomic constraints, which used for obtaining of the canonical formalisms of classical mechanics, is excluding the DMI in Hamiltonian systems. The concepts of D-entropy and evolutionary non-linearity are discussed. The connection between thermodynamics and the laws of classical mechanics is shown. Extended forms of the Lagrange, Hamilton, Liouville, and Schrödinger equations, which describe dissipative processes, are presented.

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