The dynamics of two nonlinear Bloch systems is studied from the viewpoint of bifurcation and a particular parameter space has been explored for the stability analysis based on stability criterion. This enables the choice of the desired unstable periodic orbit from the numerous unstable ones present within the attractor through the process of closed return pairs. A generalized active control met...

We deal with the problem of the final sign of the neutrino asymmetry generated by active-sterile neutrino oscillations in the Early Universe solving the full momentum dependent quantum kinetic equations. We study the parameter region 10−2 < ∼ |δm2|/eV 2 ≤ 103. For a large range of sin 2θ0 values the sign of the neutrino asymmetry is fixed and does not oscillate. For values of mixing parameters ...

In general, the value function associated with an exit time problem is a discontin-uous function. We prove that the lower (upper) semicontinuous envelope of the value function is a supersolution (subsolution) of the Hamilton-Jacobi equation involving the proximal subdiierentials (superdiierentials) with subdiierential type (superdiierential type) mixed boundary condition. We also show that if t...

Nijenhuis tensors N on Courant algebroids compatible with the pairing are studied. This compatibility condition turns out to be of the form N + N = λI for irreducible Courant algebroids, in particular for the extended tangent bundles T M = TM ⊕ TM . It is proved that compatible Nijenhuis tensors on irreducible Courant algebroids must satisfy quadratic relations N −λN + γI = 0, so that the corre...

In a recent article in Modern Physics Letters A, Gentry proposed a new static cosmological model that seeks to explain the Hubble relation as a combination of gravitational and Doppler red shifts. We show that Gentry's model, although supposedly based on general relativity, is inconsistent with the Einstein field equations; that it requires delicate fine tuning of initial conditions; that it is...

The evolution towards equipartition in the β-FPU chain is studied considering as initial condition the highest frequency mode. Above an analytically derived energy threshold, this zone-boundary mode is shown to be modulationally unstable and to give rise to a striking localization process. The spontaneously created excitations have strong similarity with moving exact breathers solutions. But th...

This project will study the concept of chaos from a mathematical viewpoint. Qualities which characterise chaos (e.g., sensitive dependence on initial conditions, presence of periodic orbits of all periods, uncountably many aperiodic orbits, and dense orbits) will be studied. Methods for analytically proving that a system is chaotic (presence of a “horseshoe,” intersection of stable and unstable...

In a recent article in Modern Physics Letters A, Gentry proposed a new static cosmological model that seeks to explain the Hubble relation as a combination of gravitational and Doppler red shifts. We show that Gentry's model, although supposedly based on general relativity, is inconsistent with the Einstein field equations; that it requires delicate fine tuning of initial conditions; that it is...

In developing countries, similar to other parts of the world, smartphones and social networks are highly popular. there are many challenges in use of social networks by the health system staff. Clinical photography plays an important role in the medical practice to determine the state, treatment and progression of a patient’s condition. ethical education is needed on how to take and share clini...

We investigate the probabilities of large deviations for the position of the front in a stochastic model of the reaction X + Y → 2X on the integer lattice in which Y particles do not move while X particles move as independent simple continuous time random walks of total jump rate 2. For a wide class of initial conditions, we prove that a large deviations principle holds and we show that the zer...