A conjecture on triangles of graphs

We give various results related to the following conjecture: If a graphG does not contain more thank pairwise edge-disjoint triangles, then there exists a set of at most 2k edges that meets all triangles ofG. Some of the results were presented at the Conference on Combinatorics, Optimization and Statistics, Srinagar, India, August 1987. Research supported in part by the AKA Research Fund of the Hungarian Academy of Sciences, grant 1-3-86-264.     

Application of plutonium radiochronometry to the analysis of plutonium age dating reference materials

Journal of Radioanalytical and Nuclear Chemistry - Radiochronometry is an important tool for nuclear forensic analysis. Plutonium has a wide array of parent/progeny pairs that can be measured to...     

Determination of nuclear graphite impurities by prompt gamma activation analysis to support decommissioning operations

Journal of Radioanalytical and Nuclear Chemistry - Elemental composition of non-irradiated nuclear grade graphite was determined by Prompt Gamma Activation Analysis (PGAA) to quantitively assess...     

A two‐dimensional numerical scheme of dry/wet fronts for the Saint‐Venant system of shallow water equations

We propose a new two‐dimensional numerical scheme to solve the Saint‐Venant system of shallow water equations in the presence of partially flooded cells. Our method is well balanced, positivity preserving, and handles dry states. The latter is ensured by using the draining time step technique in the time integration process, which guarantees non‐negative water depths. Unlike previous schemes, our technique does not generate high velocities at the dry/wet boundaries, which are responsible for small time step sizes and slow simulation runs. We prove that the new scheme preserves ‘lake at rest’ steady states and guarantees the positivity of the computed fluid depth in the partially flooded cells. We test the new scheme, along with another recent scheme from the literature, against the analytical solution for a parabolic basin and show the improved simulation performance of the new scheme for two real‐world scenarios. Copyright © 2014 John Wiley & Sons, Ltd.     

Rapid Identification of Potential Drug Candidates from Multi-Million Compounds’ Repositories. Combination of 2D Similarity Search with 3D Ligand/Structure Based Methods and In Vitro Screening

Rapid in silico selection of target focused libraries from commercial repositories is an attractive and cost-effective approach in early drug discovery. If structures of active compounds are available, rapid 2D similarity search can be performed on multimillion compounds’ databases. This approach can be combined with physico-chemical parameter and diversity filtering, bioisosteric replacements, and fragment-based approaches for performing a first round biological screening. Our objectives were to investigate the combination of 2D similarity search with various 3D ligand and structure-based methods for hit expansion and validation, in order to increase the hit rate and novelty. In the present account, six case studies are described and the efficiency of mixing is evaluated. While sequentially combined 2D/3D similarity approach increases the hit rate significantly, sequential combination of 2D similarity with pharmacophore model or 3D docking enriched the resulting focused library with novel chemotypes. Parallel integrated approaches allowed the comparison of the various 2D and 3D methods and revealed that 2D similarity-based and 3D ligand and structure-based techniques are often complementary, and their combinations represent a powerful synergy. Finally, the lessons we learnt including the advantages and pitfalls of the described approaches are discussed.     

NMR Analysis and Regiochemical Structure of Some Selectively 13C‐Enriched Poly(propylene)s

Summary: The regiochemical structures of poly(propylene)s obtained in the presence of three single‐site catalysts, Cp*Ti(CH₃)₃ + B(C₆F₅)₃ (I + III), CpTi(CH₃)₃ + B(C₆F₅)₃ (II + III), and VCl₄ + anisole + Al(C₂H₅)₂Cl (V + A), are investigated by ¹³C NMR analysis. Polymer 1 , obtained in the presence of I + III is, seemingly, fully regioregular, while, surprisingly, polymer 2 , obtained in the presence of II + III, appears to be alternating sequence of primary and secondary regioblocks, very much like polymer 3 , obtained in the presence of V + A. The stereochemical structure of the polymer obtained in the presence of I + III is in excellent agreement with a Bernoullian statistical model of the stereoselective propagation, while those of the other two polymers possibly require a Coleman‐Fox model.

¹³C NMR spectra of 10%‐enriched poly[(2‐¹³C)propylene], 1′ and 2′ , prepared under the conditions reported in Table 1 for the corresponding poly(propylene)s, 1 and 2 . The resonances of the tertiary carbons are diagnostic of the regioblock structure of sample 2′ .     

Minimally Non-Preperfect Graphs of Small Maximum Degree

 A graph G is called preperfect if each induced subgraph G ^′⊆G of order at least 2 has two vertices x, y such that either all maximum cliques of G ^′ containing x contain y, or all maximum independent sets of G ^′ containing y contain x, too. Giving a partial answer to a problem of Hammer and Maffray [Combinatorica 13 (1993), 199–208], we describe new classes of minimally non-preperfect graphs, and prove the following characterizations: (i) A graph of maximum degree 4 is minimally non-preperfect if and only if it is an odd cycle of length at least 5, or the complement of a cycle of length 7, or the line graph of a 3-regular 3-connected bipartite graph. (ii) If a graph G is not an odd cycle and has no isolated vertices, then its line graph is minimally non-preperfect if and only if G is bipartite, 3-edge-connected, regular of degree d for some d≥3, and contains no 3-edge-connected d ^′-regular subgraph for any 3≤d ^′<d. Received: March 4, 1998 Final version received: August 14, 1999     

Determination of gadolinium‐based magnetic resonance imaging contrast agents by micellar electrokinetic capillary chromatography

MEKC with DAD was applied to detect six Gd‐based contrasting agents (CAs) (Gd‐DTPA‐BMA (Omniscan), Gd‐HPDO3A (ProHance), Gd‐DOTA (Dotarem), Gd‐AAZTA, Gd‐BOPTA (Multihance) and Gd‐DTPA (Magnevist)) commonly used in MRI diagnostics. The achieved LODs ranged between 0.40 and 20 μM and the optimized method gave excellent precision, especially when two internal standards were applied (less than 0.34 RSD% for migration time). The MEKC technique made it possible to determine the CAs in urine and serum samples of patients having a therapeutic dose. Due to the SDS content of the running buffer, the serum samples can be directly injected to analyze Gd‐based CAs without interference of high protein content.     

Buckling Models for Higher Catastrophes∗

Abstract

An illustrative study of higher order catastrophes (elliptic umbilic and two kinds of double cusp) is presented on a simple elastic structure using polar co-ordinates. The bifurcation paths are analyzed for both perfect and imperfect structures.