Suppose given a smooth, compact planar region S and a smooth inward pointing vector field on ∂S. It is known that there is a diffusion process Z which behaves like standard Brownian motion inside S and reflects instantaneously at the boundary in the direction specified by the vector field. It is also known Z has a stationary distribution p. We find a simple, general explicit formula for p in te...

Some years ago Koutras presented a method of constructing a conformal Killing tensor from a pair of orthogonal conformal Killing vectors. When the vector associated with the conformal Killing tensor is a gradient, a Killing tensor (in general irreducible) can then be constructed. In this paper it is shown that the severe restriction of orthogonality is unnecessary and thus it is possible that m...

Abstract The conformal anomaly for 4D gravity-matter theories, which are non-minimally coupled with the dilaton, is systematically studied. Special care is taken for: rescaling of fields, treatment of total derivatives, hermiticity of the system operator and choice of measure. Scalar, spinor and vector fields are taken as the matter quantum fields and their explicit conformal anomalies in the g...

We investigate a class of locally conformal almost Kähler structures and prove that, under some conditions, this is subclass structures. show that manifold admits canonical foliation whose leaves are hypersurfaces with the mean curvature vector field proportional to Lee field. The geodesibility also characterized, their minimality coincides incompressibility along leaves.

Abstract We give conditions for a conformal vector field to be tangent null hypersurface. particularize two important cases: Killing and closed field. In the first case, we obtain result ensuring that hypersurface is horizon. second one, gives rise foliation of manifold by totally umbilical hypersurfaces with constant mean curvature which can spacelike, timelike or null. prove several results e...

QSAR modeling is a method for predicting properties, e.g. the solubility or toxicity, of chemical compounds using statistical learning techniques. QSAR is in widespread use within the pharmaceutical industry to prioritize compounds for experimental testing or to alert for potential toxicity. However, predictions from a QSAR model are difficult to assess if their prediction intervals are unknown...