Even subgraphs of bridgeless graphs and 2-factors of line graphs

By Petersen's theorem, a bridgeless cubic multigraph has a 2-factor. Fleischner generalised this result to bridgeless multigraphs of minimum degree at least three by showing that every such multigraph has a spanning even subgraph. Our main result is that every bridgeless simple graph with minimum degree at least three has a spanning even subgraph in which every component has at least four vertices. We deduce that if G is a simple bridgeless graph with n vertices and minimum degree at least three, then its line graph has a 2-factor with at most max{1,(3n-4)/10} components. This upper bound is best possible.     

The effect of some possible factors in c-peptide immunoreactivity in urine on the quality of the results

About 15% of CPR-U did not correspond between two kinds of kits in the routine assay, which were produced by different pharmaceutical firms, and also it is realised that the effect of the preservative, storage condition and buffer dilutions can not be overlooked in quality control programmes. Based on these problems, following results are concluded; (1) Urine preservative: NaN3 is better than toluene. (2) Urine CPR was stable for added preservative at 4 degrees C for two weeks. (3) Diluents may effect the CPR-U results, if not kept in good condition. The role of the makers in supporting improved quality in clinical laboratory tests will be expected.     

SOLVENT EFFECTS ON TRIPLET-STATE BACTERIOCHLOROPHYLL a AS DETECTED BY TRANSIENT RAMAN SPECTROSCOPY AND THE ENVIRONMENT OF BACTERIOCHLOROPHYLL a IN THE LIGHT-HARVESTING COMPLEX OF Rhodobacter sphaeroides R26

The frequency of BChl that was bound to the light-harvesting complex (LHC) of Rhodobacter sphaeroides R26 was found to be 1598 cm^-1, a result which suggests that a pair of BChl molecules form a dimer in the LHC in the T₁ state.     

Photocatalytic activity of R3MO7 and R2Ti2O7 (R=Y, Gd, La; M=Nb, Ta) for water splitting into H2 and O2

The photocatalytic activities of R3MO7 and R2Ti2O7 (R=Y, Gd, La; M=Nb, Ta) strongly depended on the crystal structure. Overall, photocatalytic water splitting into H2 and O2 proceeded over La3TaO7 and La3NbO7, which have an orthorhombic weberite structure, Y2Ti2O7 and Gd2Ti2O7, which have a cubic pyrochlore structure, and La2Ti2O7, which has a monoclinic perovskite structure. All of these materials are composed of a network of corner-shared octahedral units of metal cations (TaO6, NbO6, or TiO6); materials without such a network were inactive. The octahedral network certainly increased the mobility of electrons and holes, thereby enhancing photocatalytic activity.     

Closure concept for 2-factors in claw-free graphs

We introduce a closure concept for 2-factors in claw-free graphs that generalizes the closure introduced by the first author. The 2-factor closure of a graph is uniquely determined and the closure operation turns a claw-free graph into the line graph of a graph containing no cycles of length at most 5 and no cycles of length 6 satisfying a certain condition. A graph has a 2-factor if and only if its closure has a 2-factor; however, the closure operation preserves neither the minimum number of components of a 2-factor nor the hamiltonicity or nonhamiltonicity of a graph.     

Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge

Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word problems was found to have only a limited impact. Instead, removing contextual constraints from the problem goal was found to motivate students to validate their problem solving in terms of their everyday experiences. Based on these findings, what determines the authenticity and relevance of a mathematical problem seems to be whether the problem allows students to freely reconstruct the problem situation by making use of their imagination and everyday experiences. In short, the basic principle seems to be “less is more”; that is, fewer constraints in problem goals could function to help students personally associate problem solving with their everyday experiences.     

Farey Series and the Riemann Hypothesis III

In this paper we shall make a further study on the the equivalence problem, i.e., equivalent conditions to the Riemann hypothesis in terms of Farey series by developing a rather analytical (-arithmetical) method to establish unexpected short interval results, namely results, therewith simultaneously clarifying the underlying reasons for results obtained in Part I.