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...

We investigate the generalized derivations and show that every generalized derivation on a simple Hilbert C∗-module either is closable or has a dense range. We also describe dynamical systems on a full Hilbert C∗-module M over a C∗-algebra A as a oneparameter group of unitaries on M and prove that if α : R → U(M) is a dynamical system, where U(M) denotes the set of all unitary operator on M, th...

1550-7998=20 The conservative dynamics of two point masses given in harmonic coordinates up to the third postNewtonian order is treated within the framework of constrained canonical dynamics. A representation of the approximate Poincaré algebra is constructed with the aid of Dirac brackets. Uniqueness of the generators of the Poincaré group or the integrals of motion is achieved by imposing the...

The relations between linear system theory and mathematical morphology are mainly understood on a pure convolution / dilation level. A formal connection on the level of differential or pseudodifferential equations is still missing. In our paper we close this gap. We establish the sought relation by means of infinitesimal generators, exploring essential properties of the slope and a modified Cra...

A strong inspiration for studying perturbation theory fractional evolution equations comes from the fact that they have proven to be useful tools in modeling many physical processes. We study of order \(\alpha \in (1,2)\) associated with infinitesimal generator an operator cosine (sine) function generated by bounded time-dependent perturbations a Banach space. show abstract Cauchy problem stron...

The ten dimensional heterotic string effective action with graviton, dilaton and antisymmetric tensor fields is dimensionally reduced to two spacetime dimensions. The resulting theory, with some constraints on backgrounds, admits infinite sequence of conserved nonlocal currents. It is shown that generators of the infinitesimal transformations associated with these currents satisfy Kac-Moody alg...

In this study, the Lie symmetry analysis is given for time-fractional telegraph equation with Riemann–Liouville derivative. This useable to describe physical processes of models possessing memory. By applying classical and nonclassical α , β derivatives some technical computations, new infinitesimal gen...

We study Hilbert space valued Ornstein-Uhlenbeck processes (Y (t), t ≥ 0) which arise as weak solutions of stochastic differential equations of the type dY = JY + CdX(t) where J generates a C0 semigroup in the Hilbert space H, C is a bounded operator and (X(t), t ≥ 0) is an H-valued Lévy process. The associated Markov semigroup is of generalised Mehler type. We discuss an analogue of the Feller...