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81.
Rachid Rahouadj Jean-Franois Ganghoffer Christian Cunat 《Mechanics Research Communications》2003,30(2):119-123
In the first part of this contribution, the Lie-symmetries of the principle of least action associated to the constitutive equations of the DNLR formalism of relaxation have been presented. We examine in this second part the continuous symmetries corresponding to the simple case of stress relaxation under isothermal conditions. The well-known principle of time/temperature equivalence is discussed in terms of variational symmetry for the Jacobi’s action functional, and connected to the Onsager’s relation near the thermodynamic equilibrium. 相似文献
82.
Firdaus E. Udwadia 《International Journal of Non》1996,31(6):951-958
This paper presents a unified framework from which emerge the Lagrange equations, the Gibbs-Appell Equations and the Generalized Inverse Equations for describing the motion of constrained mechanical systems. The unified approach extends the applicability of the first two approaches to systems where the constraints are non-linear functions of the generalized velocities and are not necessarily independent. Furthermore, the approach leads to the Explicit Gibbs-Appell Equations. 相似文献
83.
Laurent Baratchart Monique Chyba Jean-Baptiste Pomet 《Journal of Dynamics and Differential Equations》2007,19(1):75-107
We consider the problem of locally linearizing a control system via topological transformations. According to [2,3], there is no naive generalization of the classical Grobman–Hartman theorem for ODEs to control systems: a generic control system, when viewed as a set of under-determined differential equations parametrized by the control, cannot be linearized using pointwise transformations on the state and the control values. However, if we allow the transformations to depend on the control at a functional level (open loop transformations), we are able to prove a version of the Grobman–Hartman theorem for control systems. 相似文献
84.
Recently Zheng & Hwang established a series of independence theorems concerning with planar effective elastic properties.
It is manifested that the estimation of the effective elastic properties of microcracked solids through the generalized self-consistent
method (GSCM) contradicts with these independence theorems. In this paper it is shown that such contradiction is actually
caused by the approximate algorithm adopted, while the exact solution of GSCM is consistent with these rigorously established
independence theorems. Since only an approximate algorithm in GCSM is available in dealing with problems involving non-circular
inclusions or holes, an intrinsic GSCM is proposed, which can be performed based on an approximate algorithm and the corresponding
estimations are consistent with the independence theorems. 相似文献
85.
L. V. Ovsyannikov 《Journal of Applied Mechanics and Technical Physics》2004,45(2):153-157
The problem of classification of ordinary differential equations of the form y = f(x,y) by admissible local Lie groups of transformations is solved. Standard equations are listed on the basis of the equivalence concept. The classes of equations admitting a oneparameter group and obtained from the standard equations by invariant extension are described. 相似文献
86.
Guoting?Chen Duo?WangEmail author Jiazhong?Yang 《Journal of Dynamics and Differential Equations》2005,17(1):3-20
Normal forms for vector fields of Hopf-zero singularity in R3 are studied. Multiple Lie bracket method is used to give unique normal forms under both conjugacy and orbital equivalence for such vector fields with a generic quadratic part.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday. 相似文献
87.
88.
Liviu P?unescu 《Journal of Functional Analysis》2011,261(9):2461-2485
The notion of sofic equivalence relation was introduced by Gabor Elek and Gabor Lippner. Their technics employ some graph theory. Here we define this notion in a more operator algebraic context, starting from Connes? Embedding Problem, and prove the equivalence of these two definitions. We introduce a notion of sofic action for an arbitrary group and prove that an amalgamated product of sofic actions over amenable groups is again sofic. We also prove that an amalgamated product of sofic groups over an amenable subgroup is again sofic. 相似文献
89.
The composition operators on H2 whose symbols are hyperbolic automorphisms of the unit disk fixing ±1 comprise a one-parameter group and the analytic Toeplitz operators coming from covering maps of annuli centered at the origin whose radii are reciprocals also form a one-parameter group. Using the eigenvectors of the composition operators and of the adjoints of the Toeplitz operators, a direct unitary equivalence is found between the restrictions to zH2 of the group of Toeplitz operators and the group of adjoints of these composition operators. On the other hand, it is shown that there is not a unitary equivalence of the groups of Toeplitz operators and the adjoints of the composition operators on the whole of H2, but there is a similarity between them. 相似文献
90.
Michael R. Kelly 《Topology and its Applications》2011,158(16):2210-2215
A fixed point detection theorem for a family of maps defined on the once punctured torus is proved. As a consequence, we produce an example of a homotopy class [f] of self-maps on the once punctured torus that illustrates the following: (i) there is a map in the homotopy class that has no fixed points, and (ii) if the image of f lies in a 1-complex that embeds as a homotopy equivalence, then f must have a fixed point. 相似文献