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In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

Rain clusters are mesoscale disaster weather systems, and some of rain clusters have spiral structures. In this paper, a theoretical model of spiral rain cluster is established under pseudo-adiabatic approximation, and its horizontal structure equation is obtained. The study shows that the horizontal structure with spiral arm rain clusters has the following characteristics: at locations close e...

We carried out three-dimensional global resistive magnetohydrodynamic (MHD) simulations of the cooling instability in optically thin hot black hole accretion flows by assuming bremsstrahlung cooling. General relativistic effects are simulated by using the pseudo-Newtonian potential. Cooling instability grows when the density of the accretion disk becomes sufficiently large. We found that as the...

A case study of a double dryline on 22 May 2002 is presented. Mobile, 3-mm-wavelength Doppler radars from the University of Massachusetts and the University of Wyoming (Wyoming cloud radar) were used to collect very fine resolution vertical-velocity data in the vicinity of each of the moisture gradients associated with the drylines. Very narrow (50–100 m wide) channels of strong upward vertical...

The application of the seismic reflection method is often limited in complex terrain areas. The problem is the incorrect correction of time-shifts caused by topography. To apply normal moveout (NMO) correction to reflection data correctly, static corrections are necessary to be applied in advance for the compensation of the time distortions of topography and the time-delays from near-surface we...

relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $m$, called {em $tau$-rank of} $m$, which coincides with the reduced rank of $m$ whenever $tau$ is the goldie torsion theory. it is shown that the $tau$-rank of $m$ is measured by the length of certain decompositions of the $tau$-injective hull of $m$. moreover, some relations between the $tau$-rank of $m$ and c...

Two-sided incompressible surfaces in Seifert fiber spaces with isolated singular fibers are well-understood. Frohman [3] and Rannard [6] have shown that one-sided which either pseudo-horizontal or psuedo-vertical. We extend their result to characterise essential may surfaces, i.e., S1-foliated 3-manifolds fibered model neighbourhoods isomorphic a solid torus Klein bottle.