We study the group properties and similarity solutions for constraint conditions of anti-self-dual null K\"{a}hler four-dimensional manifolds with at least a Killing symmetry vector. Specifically we apply theory Lie symmetries to determine all infinitesimal generators one-parameter point transformations which leave system invariant. use these define invariant are used simplify differential equa...

We investigate the foliation defined by kernel of an exact presymplectic form dα rank 2n on a (2n + r)-dimensional closed manifold M. For r = 2, we prove that has at least two leaves which are homeomorphic to 2-dimensional torus, if M admits locally free T2-action preserves and satisfies function α(Z2) is constant, where Z1, Z2 infinitesimal generators T2-action. also give its generalization fo...

Certain phase space path integrals can be evaluated exactly using equivariant cohomology and localization in the canonical loop space. Here we extend this to a general class of models. We consider hamiltonians which are a priori arbitrary functions of the Cartan subalgebra generators of a Lie group which is defined on the phase space. We evaluate the corresponding path integral and find that it...

The Noether symmetry of a generic f(R) cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generators of the desired symmetry. We explicitly calculate the form of f(R) for which such symmetries exist. It is shown that the resulting form of f(R) yields a power law expansion for the cosmological scale factor. We also obtain the effe...

The paper presents passivity conditions for a class of stochastic Hopfield neural networks with state-dependent noise and with Markovian jumps. Our contributions are mainly based on the stability analysis of the class of stochastic neural networks considered, using infinitesimal generators of appropriate stochastic Lyapunov-type functions. The passivity conditions derived are expressed in terms...

We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by Colombeau’s theory of algebras of generalized functions. We show that under some mild conditions on the differential equations, symmetries of classical solutions...

The continuous extension of the discrete duality symmetry of the SchwarzSen model is studied. The corresponding infinitesimal generator Q turns out to be local, gauge invariant and metric independent. Furthermore, Q commutes with all the conformal group generators. We also show that Q is equivalent to the non—local duality transformation generator found in the Hamiltonian formulation of Maxwell...

We discuss an example from quantum physics of “positive system” in which the state (a density operator) is a square matrix constrained to be positive semidefinite (plus Hermitian and of unit trace). The positivity constraint is captured by the notion of complete positivity of the corresponding flow. The infinitesimal generators of all possible admissible ODEs can be characterized explicitly in ...

For the action of a Lie group, which can be given by its infinitesimal generators only, we characterize a generating set of differential invariants of bounded cardinality and show how to rewrite any other differential invariants in terms of them. Those invariants carry geometrical significance and have been used in equivalence problem in differential geometry. http://hal.inria.fr/inria-00194528...

Starting from the forward and backward infinitesimal generators of bilateral, timehomogeneous Markov processes, the self-adjoint Hamiltonians of the generalized Schrödinger equations are first introduced by means of suitable Doob transformations. Then, by broadening with the aid of the Dirichlet forms, the results of the Nelson stochastic mechanics, we prove that it is possible to associate bil...