We consider some second order quasilinear partial differential inequalities for real valued functions on the unit ball and find conditions under which there is a lower bound for the supremum of nonnegative solutions that do not vanish at the origin. As a consequence, for complex valued functions f(z) satisfying ∂f/∂z̄ = |f |α, 0 < α < 1, and f(0) = 0, there is also a lower bound for sup |f | on ...

We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold (M, J) admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in M and to give a sufficient condition for the complete hyperbolicity of a domain in (M, J). Finally we obtain the regul...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

Human observers cannot judge heading accurately in the presence of simulated gaze rotations under many conditions [Royden et al. (1994). Vision Research, 34, 3197-3214]. They make errors in the direction of rotation with magnitudes proportional to the rotation rate. Two hypotheses have been advanced to explain this phenomenon. The extra-retinal-signal hypothesis states that the observer's estim...

When we see a stimulus of a radial flow field (the target flow) overlapped with a lateral flow field or another radial flow field, the focus of expansion (FOE) of the target radial flow appears to be shifted in a direction. Royden and Conti [(2003). A model using MT-like motion-opponent operators explains an illusory transformation in the optic flow field. Vision Research, 43, 2811-2826] argued...

this paper gives a short survey of some of the known results generalizing the theorem, credited to i. schur, that if the central factor group is finite then the derived subgroup is also finite.

in this paper, after reviewing some results in minimal space, some new results in this setting are given. we prove a generalized form of the fan-kkm typetheorem in minimal vector spaces. as some applications, the open type of matching theorem and generalized form of the classical kkm theorem in minimal vector spaces are given.