This paper studies FA-presentable structures and gives a complete classification of the finitely generated FA-presentable cancellative semigroups. We show that a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group.

in this article, we study the artin-rees property in  c(x), in the  rings of fractions of  c(x) and in the factor rings of c(x) . we show that c(x)/(f) is an artin-rees ring if and only if  z(f)  is an open p-space. a necessary and sufficient condition for the local rings of  c(x)   to be artin-rees rings is that each prime ideal in  c(x)  becomes minimal and it turns out that every local ring ...

Inspired by recent work in the theory of central projections onto hypersurfaces, we characterize self-linked perfect ideals of grade 2 as those with a Hilbert–Burch matrix that has a maximal symmetric subblock. We also prove that every Gorenstein perfect algebra of grade 1 can be presented, as a module, by a symmetric matrix. Both results are derived from the same elementary lemma about symmetr...

Different alloying concepts to trace deoxidation products, mainly aluminium oxides, using rare earth elements (REEs), were tested on the laboratory scale by melting trials with a high-frequency remelting furnace. Lanthanum and Cerium, which belong group of light REEs, used for these experiments. The formed multiphase inclusions characterized scanning electron microscopy energy dispersive spectr...

Rare earth elements (REEs) have been increasingly emitted into the 8 atmosphere with a worldwide increase in use of these metals. However, the research 9 on REEs in atmospheric particulates is fairly limited. In this paper, atmospheric 10 particulates including total suspended particulate (TSP) matter and particles with an 11 equivalent aerodynamic diameter less than 10 μm (PM10) were collected...

We consider partial differential operators H = − div(C∇) in divergence form on R with a positive-semidefinite, symmetric, matrix C of real L∞-coefficients and establish that H is strongly elliptic if and only if the associated semigroup kernel satisfies local lower bounds, or, if and only if the kernel satisfies Gaussian upper and lower bounds.

Weak uniqueness is established for the martingale problem associated to a family of catalytic branching networks. This martingale problem corresponds to a stochastic differential equation with a degenerate Hölder continuous diffusion matrix. Our approach uses the semigroup perturbation method of Stroock and Varadhan and a modification of a Banach space of weighted Hölder continuous functions in...

It has long been observed that rare earth elements (REEs) regulate multiple facets of plant growth and development. However, the underlying mechanisms remain largely unclear. Here, using electron microscopic autoradiography, we show the life cycle of a light REE (lanthanum) and a heavy REE (terbium) in horseradish leaf cells. Our data indicate that REEs were first anchored on the plasma membran...

Given two determinantal rings over a field k, we consider the Rees algebra of the diagonal ideal, the kernel of the multiplication map. The special fiber ring of the diagonal ideal is the homogeneous coordinate ring of the secant variety. When the Rees algebra and the symmetric algebra coincide, we show that the Rees algebra is CohenMacaulay.