A variety of semigroups that is minimal with respect to being non-finitely based is said to be a limit variety. By Zorn’s Lemma, each non-finitely based variety contains at least one limit subvariety. Although many examples of non-finitely based varieties are known in the literature (see [3, 5]), explicit examples of limit varieties are very rarely discovered [1, 2, 4]. The objective of the pre...

The main aim of this paper is to deal with a fuzzy version of Farkas lemma involving trapezoidal fuzzy numbers. In turns to that the fuzzy linear programming and duality theory on these problems can be used to provide a constructive proof for Farkas lemma. Keywords Farkas Lemma, Fuzzy Linear Programming, Duality, Ranking Functions.

Let k be a field. We determine the ideals I in a finitely generated graded k-algebra A, whose associated graded rings ⊕ n≥0 I/I are isomorphic to A. Also we compute the graded local cohomologies of the Rees rings A[It] and give the condition for A[It] to be generalized Cohen-Macaulay under the condition that A is generalized Cohen-Macaulay. MSC: 13A30, 13D45 Introduction Let k be a field and S ...

Let I be a monomial ideal in a polynomial ring over a field k. If the Rees cone of I is quasi-ideal, we express the normalization of the Rees algebra of I in terms of an Ehrhart ring. We introduce the basis Rees cone of a matroid and study their facets. Then an application to Rees algebras is presented.

Given that the supply of several rare earth elements (REEs) is sometimes limited, recycling REEs used in various advanced materials, such as Nd magnets, is important for realizing efficient use of REE resources. In the present work, the feasibility of using DNA for REE recovery and separation was examined, along with the identification of the binding site of REEs in DNA. In particular, a DNA-...

A newly synthesized alkyl phosphinic acid resin (APAR) was used for on-line preconcentration of trace rare earth elements (REES, lanthanides including yttrium) and then determined by inductively coupled plasma mass spectrometry. REEs in seawater could be on-line concentrated on the APAR packed column (4.6mm i.d.x50mm in length), and eluted from the column with 0.5mL 0.1molL(-1) nitric acid with...

Recently, the worldwide supply of rare earth element (REE) resources will be severely restricted. On the other hand, coal fly ash particles emitted from coal-fired electric power plants contain relatively high concentrations of REEs. The contents of REEs in coal fly ash are regularly several hundreds of ppmw. In order to extract and recover REEs from coal fly ash particles, as a first step, we ...

In the present study, bioaccumulation of REEs in Zea mays L. (corn plant) has been analyzed. The role of Rare Earth Element (REEs) in physiology and biochemistry of corn plant have been studied. Physiological characters like peroxidase (POD) and superoxide dismutase (SOD) activities, biochemical analysis of chlorophyll, carotenoids and phenol contents have also been carried out. The plant growt...

The determination of trace rare-earth elements (REEs) can be used for the assessment of environmental pollution, and is of great significance to the study of toxicity and toxicology in animals and plants. N, N, N', N'-tetraoctyl diglycolamide (TODGA) is an environmental friendly extractant that is highly selective to REEs. In this study, an analytical method was developed for the simultaneous d...

This expository paper contains history, definitions, constructions, and the basic properties of Rees valuations of ideals. A section is devoted to one-fibered ideals, that is, ideals with only one Rees valuation. Cutkosky [5] proved that there exists a two-dimensional complete Noetherian local integrally closed domain in which no zero-dimensional ideal is one-fibered. However, no concrete ring ...