On maximum-overlap orbitals in nuclei

A formulation of the maximum overlap requirement is given which brings the scheme conceptually closer to the Hartree-Fock method. A procedure of solving the necessary condition for the maximum overlap is suggested and the stability conditions for the solutions as well as some symmetry aspects to the method are discussed.Using the suggested procedure the hyperspherical wave function of⁴He as well as the shell model wave function of¹⁸F are analyzed.     

Note on the 3-graph counting lemma

Szemerédi's regularity lemma proved to be a powerful tool in extremal graph theory. Many of its applications are based on the so-called counting lemma: if G is a k-partite graph with k-partition V₁∪?∪V_k, |V₁|=?=|V_k|=n, where all induced bipartite graphs G[V_i,V_j] are (d,ε)-regular, then the number of k-cliques K_k in G is . Frankl and Rödl extended Szemerédi's regularity lemma to 3-graphs and Nagle and Rödl established an accompanying 3-graph counting lemma analogous to the graph counting lemma above. In this paper, we provide a new proof of the 3-graph counting lemma.     

Application of computer imaging,stripping voltammetry and mass spectrometry to study the effect of lead (Pb-EDTA) on the growth and viability of early somatic embryos of Norway spruce (<Emphasis Type="Italic">Picea abies</Emphasis> /L./ Karst.)

Image analysis (IA) was used to determine the areas and circumferences of clusters of early somatic embryos (ESEs) of the Norway spruce (Picea abies /L./Karst.). Results obtained from IA were compared with the fresh weights of the ESE clusters and their esterase activities. The areas of the ESE clusters correlated well with both the increases in fresh weight (R ²=0.99) of the ESEs and their esterase activities (R ²=0.99). In addition, we studied the viability of the ESEs, which was determined by (a) double staining with fluorescein diacetate and propidium iodide (the resulting fluorescence was quantified by IA) and (b) determining esterase activity using a spectrofluorimetric detector. The results obtained with IA and esterase assay were comparable (the deviation between the tangents of the bisectors was 6.4%). IA was also used to study the effect of Pb–EDTA chelate (50, 250 and 500 μM) on the viability of the ESEs and on the growth of clusters. The presence of Pb–EDTA markedly slowed the growth of ESEs clusters (by more than 65% with 250 μM of Pb–EDTA after 288 h of cultivation) and decreased the viability of ESEs (by more than 30% with 500 μM of Pb–EDTA after 288 h of cultivation). The lead concentration in the ESEs was determined by differential pulse anodic stripping voltammetry and increased with the external lead concentration and the time of treatment from 100 to 600 pg Pb/100 mg of fresh weight of ESEs. Glutathione is a diagnostic marker of the influence of Pb–EDTA on ESEs and its content was determined by high–performance liquid chromatography coupled with mass spectrometry. The glutathione content changed linearly with treatment time and the applied external lead concentration. The highest glutathione content was obtained at 250 μM of Pb–EDTA after 192 h of cultivation.     

Nearly bipartite graphs with large chromatic number

P. Erdős and A. Hajnal asked the following question. Does there exist a constant ε>0 with the following property: If every subgraphH of a graphG can be made bipartite by the omission of at most ε|H| edges where |H| denotes the number of vertices ofH thenx(H) ≦ 3. The aim of this note is to give a negative answer to this question and consider the analogous problem for hypergraphs. The first was done also by L. Lovász who used a different construction.     

Monotone paths in ordered graphs

LetV _fin andE _fin resp. denote the classes of graphsG with the property that no matter how we label the vertices (edges, resp.) ofG by members of a linearly ordered set, there will exist paths of arbitrary finite lengths with monotonically increasing labels. The classesV _inf andE _inf are defined similarly by requiring the existence of an infinite path with increasing labels. We proveE _inf ⫋V _inf ⫋V _fin ⫋E _fin. Finally we consider labellings by positive integers and characterize the class corresponding toV _inf.     

On ramsey families of sets

The main result of this paper is a lemma which can be used to prove the existence of highchromatic subhypergraphs of large girth in various hypergraphs. In the last part of the paper we use amalgamation techniques to prove the existence for everyl, k 3 of a setA of integers such that the hypergraph having as edges all the arithmetic progressions of lengthk inA has both chromatic number and girth greater thanl.     

Über die simultanen diophantischen Approximationen

Ohne Zusammenfassung     

Biodegradable polyhydroxybutyrate as a polyol for elastomeric polyurethanes

In the proposed work, new elastomeric bio-polyol based polyurethanes (bio-PUs) with specific mechanical properties were prepared by a one-shot process without the presence of a solvent. Commercial non-degradable polyether polyol derived from petrochemical feed stock was partly (in the amount of 1 mass %, 5 mass %, and 10 mass %) substituted by the biodegradable polyhydroxybutyrate (PHB). Morphology of elastomeric PU composites was evaluated by scanning electron microscopy and mechanical properties of the prepared samples were obtained by both tensile measurements and prediction via the Mooney-Rivlin equation. Electron microscopy proved that the prepared materials have the character of a particle filled composite material, where PHB particles are regular with their size of about 1?C2 ??m in diameter. Tensile measurements demonstrated that the Young??s modulus, tensile stress at break, and tensile strain at break of each sample increase with the increase of the volume fraction of the filler. From the measured stress-strain data, the first and the second term of the Mooney-Rivlin equation were calculated. The obtained constants were applied to recalculate the stress-strain curves. It was found that the Mooney-Rivlin equation corresponds well with the stress-strain behavior of the prepared specimens.     

Supersaturation For Ramsey-Turán Problems

For an l-graph , the Turán number is the maximum number of edges in an n-vertex l-graph containing no copy of . The limit is known to exist [8]. The Ramsey–Turán density is defined similarly to except that we restrict to only those with independence number o(n). A result of Erdős and Sós [3] states that as long as for every edge E of there is another edge E′of for which |E∩E′|≥2. Therefore a natural question is whether there exists for which . Another variant proposed in [3] requires the stronger condition that every set of vertices of of size at least εn (0<ε<1) has density bounded below by some threshold. By definition, for every . However, even is not known for very many l-graphs when l>2. We prove the existence of a phenomenon similar to supersaturation for Turán problems for hypergraphs. As a consequence, we construct, for each l≥3, infinitely many l-graphs for which . We also prove that the 3-graph with triples 12a, 12b, 12c, 13a, 13b, 13c, 23a, 23b, 23c, abc, satisfies . The existence of a hypergraph satisfying was conjectured by Erdős and Sós [3], proved by Frankl and R?dl [6], and later by Sidorenko [14]. Our short proof is based on different ideas and is simpler than these earlier proofs. * Research supported in part by the National Science Foundation under grants DMS-9970325 and DMS-0400812, and an Alfred P. Sloan Research Fellowship. † Research supported in part by the National Science Foundation under grants DMS-0071261 and DMS-0300529.