On the Number of Mutually Disjoint Cyclic Designs and Large Sets of Designs

Let N(t; v; k; ) be the maximum possible number of mutually disjoint cyclic t- (v; k; ) designs. In this paper we find the number N(t; v; k; ) for two sets of parameters, and give bounds for other sets of parameters. We also discuss optimization techniques for finding (mutually disjoint) cyclic designs and prove an extension theorem for large sets of designs. The results of this study show the existence of two new large sets of designs. keywords: combinatorial designs, t\Gammadesigns, large sets 1 Introduction Let D = fB 1 ; B 2 ; :::; B b g be a finite family of k-subsets (called blocks) of a point set X = X v = f1; 2; :::; vg. Then, (X; D) is a t-(v; k; ) design if every t-subset of X is contained in exactly blocks of D. Frequently, the point set X is implicit and we simply think of the design as the collection of blocks D. The set of all k-subsets of X v will be denoted here by X (k) v . We will use X (k) instead of X (k) v whenever the value of v is clear from the conte..

Chromium Phyto-transformation in Salt Marshes: The Role of Halophytes

Wetlands, in particular salt marshes, are very interesting field laboratories to study metal biogeochemistry, namely, Cr. Due to the heavily industrialized history of most of estuarine systems, salt marshes became large deposits of heavy metals. Due to the large affinity of Cr to the medium organic matter, the removal of Cr throughout natural or enhanced processes occurs throughout plant-mediated processes. Naturally, plants acquire during their life cycle nutrients from their sediments but also some non-nutritional elements, like Cr, and store them in their tissues. In the last decades, this natural ability attracted the attention of several projects focusing on the enhancement of this process throughout the application of transporter molecules, like LMWOA, in order to increase the sediment-plant Cr transport. Due to its chemistry, Cr presents to oxidation states, Cr (III) and Cr (VI), being this last very toxic. Thus it became important to study not only the plant accumulation capacity but also the root-mediated processes of phyto-conversion of Cr (VI) toxic form to the less toxic Cr (III). Again, halophytes acquire an important role with high conversion efficiencies. All these passive and enhanced processes point out to a promising biotechnology using halophytes as potential cleaners of Cr-contaminated sediments, using environmental-friendly and low-cost technologies.info:eu-repo/semantics/publishedVersio