A survey of Skolem-type sequences and Rosa’s use of them

Let D be a set of positive integers. A Skolem-type sequence is a sequence of i ∈ D such that every i ∈ D appears exactly twice in the sequence at positions a _i and b _i , and |b _i − a _i | = i. These sequences might contain empty positions, which are filled with null elements. Thoralf A. Skolem defined and studied Skolem sequences in order to generate solutions to Heffter’s difference problems. Later, Skolem sequences were generalized in many ways to suit constructions of different combinatorial designs. Alexander Rosa made the use of these generalizations into a fine art. Here we give a survey of Skolem-type sequences and their applications. Supported by an NSERC Graduate fellowship. This work is in partial fulfillment of an M.Sc.     

Ergodicity conditions for a continuous one-dimensional loss network

One dimensional continuous loss networks are spatial birth-and-death processes which can be dominated by a multitype branching process. Using the Peron-Frobenius theory for sub-criticality of branching process we obtain a sufficient condition for ergodicity of one-dimensional loss networks on with arbitrary length distribution and cable capacity C.     

Asymptotic Size of Covering Arrays: An Application of Entropy Compression

A covering array is an array A such that each cell of A takes a value from a v‐set V, which is called the alphabet. Moreover, the set is contained in the set of rows of every subarray of A. The parameter N is called the size of an array and denotes the smallest N for which a exists. It is well known that  [10]. In this paper, we derive two upper bounds on using an algorithmic approach to the Lovász local lemma also known as entropy compression.     

Temperature-programmed reduction of lightly yttrium-doped Au/CeO<Subscript>2</Subscript> catalysts

The reducibility of Au catalysts on CeO₂ supports doped with 1 and 2.5 mass% Y₂O₃ by two types of preparation methods (impregnation and co-precipitation) has been studied by temperature-programmed reduction and compared with that of pure Au/CeO₂. The kinetic parameters of reduction were determined simulating each reduction process. The capacities of these catalysts to retain oxygen have been evaluated by temperature-programmed desorption. The catalytic activities in water gas shift reaction were determined measuring CO conversion between 413 and 623 K. The catalytic performances of all these catalysts were explained in terms of mobility of the oxygen ions of the CeO₂ lattice.     

Meson production in p + d reactions

Total and differential cross sections for the reactions p + d → ³He + m ⁰ with m=π, η and p + d → ³H+π⁺ were measured with the GEM detector at COSY for beam momenta between threshold and the maximum of the corresponding baryon resonance. For both reactions a strong forward-backward asymmetry was found. The data were compared with model calculations. The aspect of isospin symmetry breaking is studied. Representing the GEM Collaboration     

The origin of diastereoselectivity in the Michael addition reaction: a computational study of the interaction between CH-acidic Schiff base and α,β-unsaturated ketones

Theoretical quantum chemical computations were applied in answering a question set from the experiment: why the Michael addition to chalcones is a highly diastereoselective process? Density functional theory methods were used to examine the mechanistic pathways for the Michael reaction of [(diphenylmethylene)amino]acetonitrile—CH-acidic Schiff base with α,β-unsaturated ketones (enones). Transition state structures, prereactive complexes and reaction path energetics for different channels of the reaction are determined. The theoretical predictions reveal that the difference in the stabilization of the prereactive complex explains adequately the experimental findings for diastereoselectivity of the addition to benzylideneacetophenone (chalcone), compared to the nonselective process in the case of 4,4-dimethyl-1-phenyl-1-pentene-3-one.     

Adding Value to the Oil Cake as a Waste from Oil Processing Industry: Production of Lipase and Protease by <Emphasis Type="Italic">Candida utilis</Emphasis> in Solid State Fermentation

Olive oil cake is a by-product from the olive oil processing industry and can be used for the lipase and protease production by Candida utilis in solid state fermentation. Different carbon and nitrogen sources were evaluated, and the results showed that the supplementation of the substrate with maltose and starch as carbon sources and yeast extract as a nitrogen source significantly increased the lipase production. The best results were obtained with maltose, whereas rather low lipase and protease activities were found with glucose and oleic acid. Response surface methodology and a five-level–three-factor central composite rotatable design were used to evaluate the effects of the initial moisture content, inoculum size and fermentation time on both lipase and protease activity levels. A lipase activity value of ≈25 U g^-1 and a protease activity value of 110 U g^-1 were obtained under the optimized fermentation conditions. An alkaline treatment of the substrate appeared to be efficient, leading to increases of 39% and 133% in the lipase and protease production, respectively. The results showed that the olive cake could be a good source for enzyme production by solid state fermentation.     

Galanthamine and Related Alkaloids Production by <Emphasis Type="Italic">Leucojum aestivum</Emphasis> L. Shoot Culture using a Temporary Immersion Technology

The process of galanthamine and related alkaloids production by Leucojum aestivum shoot culture in a temporary immersion system was studied. It was established that temporary immersion approach is prospective for development of a biosynthetic process for obtaining valuable Amaryllidaceae alkaloids. Both immersion frequency and temperature had significant effect on biomass accumulation and the yields of galanthamine and related alkaloids. The maximal yield of galanthamine was achieved at the cultivation of L. aestivum shoot culture in temporary immersion RITA^® system at immersion frequency 15 min flooding and 8 h stand-by periods, at 26 °C. Data on the relationships in the biological system “Nutrient medium–L. aestivum shoot culture–galanthamine” are presented as well.