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...

Background and Purpose—Little is known of the acute, subacute, and longer-term energy demands of stroke, information essential to appropriate clinical and nutritional management. The goals of this study were to (1) determine the resting energy expenditure (REE) of stroke patients from stroke onset to 3 months, (2) examine relations between stroke size, type, location, severity, and REE, and (3)...

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...

‎There is a flatness property of acts over monoids called Condition $(PWP)$ which‎, ‎so far‎, ‎has received‎ ‎much attention‎. ‎In this paper‎, ‎we introduce Condition GP-$(P)$‎, ‎which is a generalization of Condition $(PWP)$‎. ‎Firstly‎, ‎some  characterizations of monoids by Condition GP-$(P)$ of their‎ ‎(cyclic‎, ‎Rees factor) acts are given‎, ‎and many known results are generalized‎. ‎More...

Brown coal remains an important energy source in Europe, including countries such as Germany, Poland, the Czech Republic, and Greece. Open-pit mines disturb environment terms of air quality, hydrology, chemical biological transformations rivers receiving mine waters. In present study, we assessed impact waters from four brown open-pit on contamination river sediments. Chemical analysis included...

Rare earth elements (REEs) have undergone a steady spread in several industrial, agriculture and medical applications. With the aim of exploring a sensitive and reliable indicator of estimating exposure level to REEs, a simple, accurate and specific ICP-MS method for simultaneous direct quantification of 15 REEs ((89)Y, (139)La, (140)Ce, (141)Pr, (146)Nd, (147)Sm, (153)Eu, (157)Gd, (159)Tb, (16...