We show that the free precession of a triaxial body can naturally explain the anomalously rapid change of the X-ray pulse profile of Her X-1 observed by the HEAO-1 in September 1978 without requiring a large change in the moment of inertia.

It is well known that a closed universe with a minimally coupled massive scalar field always collapses to a singularity unless the initial conditions are extremely fine tuned. We show that the corrections to the equations of motion for the massive scalar field, given by loop quantum gravity in high curvature regime, always lead to a bounce independently of the initial conditions. In contrast to the previous works in loop quantum cosmology, we note that the singularity can be avoided even at the semi-classical level of effective dynamical equations with non-perturbative quantum gravity modifications, without using a discrete quantum evolution.

Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic Prandtl numbers. It is argued that all the different cases show similarities at intermediate length scales. On the other hand, in the presence of helicity of the turbulence, power develops on large scales, which is not present in non-helical small-scale turbulent dynamos. At small length scales, differences occur in connection with the dissipation cutoff scales associated with the respective value of the magnetic Prandtl number. These differences are found to be independent of whether or not there is large-scale dynamo action. However, large-scale dynamos in homogeneous systems are shown to suffer from resistive slow-down even at intermediate length scales. The results from simulations are connected to mean field theory and its applications. Recent work on helicity fluxes to alleviate large-scale dynamo quenching, shear dynamos, nonlocal effects and magnetic structures from strong density stratification are highlighted. Several insights which arise from analytic considerations of small-scale dynamos are discussed.

We consider initial conditions leading to Starobinsky inflation in the general quadratic gravity, where the action of the theory contains one more curvature square invariant in addition to $R^2$. We have chosen corresponding coefficients in a way so that the inflationary solution keeps to be stable. Our numerical results show that despite the configuration of initial conditions in the $(H,R)$ plane, leading to Starobinsky inflation can change considerably from the $R^2$ theory, realization of inflation does not need a fine-tuning of the initial conditions.

The injection of magnetic helicity into the heliosphere during solar cycle 24 and the early phase of cycle 25 has been calculated based on the analysis of a series of synoptic magnetic charts. During the cycle, the injected magnetic helicity is found to be mainly contributed by the magnetic field in active regions. According to Hale's law, the polarities of active regions statistically reverse between solar cycles 24 and 25. We suggest that the dominant source of injected magnetic helicity likely arises from the relatively strong magnetic fields of the leading polarity of active regions. This occurs as part of the magnetic field that migrates to high latitudes and the polar regions of the Sun due to the effect of meridional circulation inferred from a series of HMI/SDO magnetic synoptic charts. Significant fluctuations of the injected magnetic helicity from the subsurface layers may reflect the complex processes of how the twist from the convection zone ejects magnetic fields through a series of active regions on different temporal and spatial scales at the solar surface.

We present a model of set theory, in which, for a given $n\ge2$, there exists a non-ROD-uniformizable planar lightface $\varPi^1_n$ set in $\mathbb R\times\mathbb R$, whose all vertical cross-sections are countable sets (and in fact Vitali classes), while all planar boldface $\bf\Sigma^1_n$ sets with countable cross-sections are $\bf\Delta^1_{n+1}$-uniformizable. Thus it is true in this model, that the ROD-uniformization principle for sets with countable cross-sections first fails precisely at a given projective level.