In this paper, we characterize w -Noetherian rings and SM rings. More precisely, in terms of the id="M3"> u -operation on a commutative ring id="M4"> R , prove that id="M5"> is id="M6"> if only direct limit id="M7"> r GV -torsion-free injective id="M8"> -modules id="M9"> SM, whic...

In a numerical, isopycnal, ocean model the mixing is investigated with the environment of two idealized Agulhas rings, one that splits, and one that remains coherent. The evolution of a passive tracer, initially contained within the rings, shows that tracer leakage is associated with the formation of filaments in the early stage of ring evolution. These filaments reach down to the thermocline. ...

Coherent large-scale vortices in the open ocean can retain their structure and properties for periods as long several years. However, patterns of potential vorticity such suggest that they are baroclinically unstable therefore should rapidly disintegrate. This study proposes a plausible explanation longevity rings based on bottom roughness, which restricts flow lower layer thereby stabilizes ed...

Let (X,D) be a D-scheme in the sense of Beilinson and Bernstein, given by an algebraic variety X and a morphism OX → D of sheaves of rings on X. We consider noncommutative deformations of quasi-coherent sheaves of left D-modules on X, and show how to compute their pro-representing hulls. As an application, we compute the noncommutative deformations of the left DX -module OX when X is any ellipt...

We report on the recent progress in the investigation of the influence of hyperacoustic vibrations on the coherent electron-positron pair creation by high-energy photons in crystals. In dependence of the values for the parameters, the presence of the deformation field can either enhance or reduce the cross-section. This can be used to control the parameters of the positron sources for storage r...

A completely new approach to measure beam emittance is examined. It is based on measuring the decay rate of coherent betatron-oscillation through nonlinear filamentation caused by lattice nonlinearity. Experimental results, computer simulations and analytic approach using differential algebra (DA) [1] [2] are presented. This method may provide useful tools in measuring emittance at high brightn...

The electron cloud in positron storage rings is pinched when a bunch passes by. For short bunches, the radiation due to acceleration of electrons of the cloud is coherent. Detection of such radiation can be used to measure the density of the cloud. The estimate of the power and the time structure of the radiated signal is given in this paper. ∗Work supported by Department of Energy contract DE–...

In this paper we study wide subcategories. A full subcategory of R-modules is said to be wide if it is abelian and closed under extensions. Hovey [Hov01] gave a classification of wide subcategories of finitely presented modules over regular coherent rings in terms of certain specialisation closed subsets of Spec(R). We use this classification theorem to study K-theory and “Krull-Schmidt” decomp...

Unlike the Gorenstein projective and injective dimensions, the majority of results on the Gorenstein flat dimension have been established only over Noetherian (or coherent) rings. Naturally, one would like to generalize these results to any associative ring. In this direction, we show that the Gorenstein flat dimension is a refinement of the classical flat dimension over any ring; and we invest...