We study enumerative and homological properties of the Rees product of the cubical lattice with the chain. We give a bijective proof that the Möbius function of this poset can be expressed as n times the permanent of a matrix. This gives a new bijective proof of Jonsson’s result that the Möbius function of the Rees product of the Boolean algebra with the chain is given by a derangement number. ...

INTRODUCTION Through leaching experiments and simulated rainfall experiments, characteristics of vertical leaching of exogenous rare earth elements (REEs) and phosphorus (P) and their losses with surface runoff during simulated rainfall in different types of soils (terra nera soil, cinnamon soil, red soil, loess soil, and purple soil) were investigated. RESULTS AND ANALYSES Results of the lea...

We introduce techniques to derive estimates for the degrees of the generators of the integral closure of several classes of Rees algebras of modules, and to bound the length of normalization processes. In the case of regular base rings, the bounds are expressed in terms of Buchsbaum–Rim multiplicities and a module version of Briançon–Skoda numbers. Normalization of modules is the study of the i...

Rare earth elements (REE) are widely used in advanced technology. Praseodymium (Pr), neodymium (Nd), samarium (Sm) and dysprosium (Dy) are used in high-power permanent magnets. Ytterbium (Yb), erbium (Er) and holmium (Ho) are used in lasers. Lanthanum (La), gadolinium (Gd), terbium (Tb), europium (Eu) and Yb are components of luminescent and fluorescent phosphors, used in fluorescent lamps, rad...

In ring and module theory, the concept of an exact sequence is commonly employed. The generalized into U-exact V-coexact sequence. Rough set theory has also been applied to a variety algebraic structures, including groups, rings, modules, others. this study, we investigated characteristics rough in groups

the dalir phosphate horizon is located ~57 km southwest of chalous, mazandaran province. the horizon developed as stratiform within upper shale of soltanieh formation (late neoproterozoic - early cambrian). according to mineralogical data, the major minerals of the phosphate horizon are calcite, fluorapatite, dolomite, quartz, pyrite, muscovite, and illite. microscopic evidence such as existenc...