Saturation of Berge hypergraphs

Given a graph $F$, a hypergraph is a Berge- $F$ if it can be obtained by expanding each edge in $F$ to a hyperedge containing it. A hypergraph $H$ is Berge-$F$-saturated if $H$ does not contain a subhypergraph that is a Berge-$F$, but for any edge $e\in E\left(\overline{H}\right)$, $H+e$ does. The $k$-uniform saturation number of Berge-$F$ is the minimum number of edges in a $k$-uniform Berge-$F$-saturated hypergraph on $n$ vertices. For $k=2$ this definition coincides with the classical definition of saturation for graphs. In this paper we study the saturation numbers for Berge triangles, paths, cycles, stars and matchings in $k$-uniform hypergraphs.     

Theories of mathematics education: European perspectives, commentaries and viable research directions

We briefly comment on different perspectives on (1) the role of mathematics education theories, (2) the issue of plurality and healthy heterogeneity versus consolidation; (3) underlying inquiry systems or the implicit role of philosophy in theories of mathematics education. This paper also outlines developments within the European research scene on theory usage in mathematics education research, which complement the discussion at the 29th PME research forum in Melbourne.     

Estimation of zeta potentials of titania nanoparticles by molecular simulation

Non-equilibrium molecular dynamics (NEMD) simulations have been performed for static electric fields for a range of positively charged spherical rutile-titania nanoparticles with radii of 1.5 to 2.9 nm for two different salt concentrations in water, in order to simulate electrophoresis directly. Using the observed limiting drag velocities, Helmholtz-Smoluchowski (HS) theory was used to estimate their ζ potentials. These estimates were compared to values from numerical solution of the non-linear Poisson-Boltzmann (PB) equation for representative configurations of the nanoparticles, in addition to idealised analytic and Debye-Hückel (DH) solutions about spherical particles of the same geometry and charge state, for the given salt concentrations. It was found that reasonable agreement was obtained between the various approaches, with the NEMD-HS results some 15%-15% smaller than the numerical PB results for more highly charged nanoparticles.     

Matrix spectra and ground-state vibrational frequency of Sn2

Two strong laser-excited fluorescence systems are observed in rare gas matrices containing Sn. Evidence is presented suggesting assignment of the emission to Sn₂. The fluorescence spectrum provides a value of 188 cm^?1 for the ground-state vibrational frequency of this diatomic molecule.     

Spectra of inert-gas matrices containing bismuth: ground-state frequency of Bi2

Bi, Bi₂, Bi₄, and possibly Bi₃ in inert-gas matrices were observed and characterized. Their spectra exhibit negligible shifts from matrix to matrix and, when known, from gas to matrix. The Bi₂ Raman frequency in Ne is measured at 173 ± 1 cm^?1, in excellent agreement with the gas phase.     

Superoxide dismutase targets NO from GSNO to Cysbeta93 of oxyhemoglobin in concentrated but not dilute solutions of the protein

The role of hemoglobin (Hb) in transmitting the vasodilatory property of NO throughout the vascular system is of much current interest. NO exchange between Hb and low-molecular-weight nitrosothiols such as S-nitrosoglutathione (GSNO) has been speculated and reported in vitro. Previously, we reported that NO delivery from GSNO to Cysbeta93 of human oxyHb is prevented in the presence of the Cu chelators, neocuproine, and DTPA.(1) In the present work, 5 mM solutions of commercial human Hb were found by ICP-MS to contain approximately 20 microM Cu and Zn, suggesting the presence of Cu,Zn-superoxide dismutase (CuZnSOD), which was confirmed by Western blotting. SOD activity measurements were consistent with the presence of approximately 20 microM CuZnSOD monomer in 5 mM Hb solutions, which is the physiological concentrations of these proteins in the red blood cell. Incubation of 3.75 mM oxyHb (15 mM heme; 7.5 mM Cysbeta93) with 3.75 or 7.5 mM GSNO gave rise to 50% or 100% S-nitrosation, respectively, of Cysbeta93 as monitored by FTIR nu(SH) absorption, whereas excess GSNO over Cysbeta93 converted oxyHb to metHb due to the reaction, oxyHb + NO<==>metHb + NO(3)(-). Removal of CuZnSOD by anion-exchange chromatography yielded an oxyHb sample that was unreactive toward GSNO, and replacement with bovine CuZnSOD restored reactivity. Addition of 1 microM GSNO (Cysbeta93/GSNO = 1) to solutions diluted 10(4)-fold from physiological concentrations of oxyHb and CuZnSOD resulted largely in metHb formation. Thus, this work reports the following key findings: CuZnSOD is an efficient catalyst of NO transfer between GSNO and Cysbeta93 of oxyHb; metHb is not detected in oxyHb/GSNO incubates containing close to the physiological concentration (5 mM) of Hb and CuZnSOD when the Cysbeta93/GSNO molar ratio is 0.5 to 1.0, but metHb is detected when the total Hb concentration is low micromolar. These results suggest that erythrocyte CuZnSOD may play a critical role in preserving the biological activity of NO by targeting it from GSNO to Cysbeta93 of oxyHb rather than to its oxyheme.     

Photolysis of pentacarbonyl(selenocarbonyl)chromium(0), Cr(CO)5(CSe), in an Argon matrix at 20 K

U. v. photolysis (254 and 366 nm) of Cr(CO)₅(CSe) isolated in an argon matrix at ca. 20 K produces a mixture of two isomeric forms of Cr(CO)₄(CSe), Cr(CO)₆ and molecular CO. The two Cr(CO)₄(CSe) isomers are assigned square pyramidal geometries (CSe group axial, C_4v symmetry; CSe group equatorial, C_s symmetry) by comparison with the results from a previous matrix isolation i.r. study of the products formed in the u.v. photolysis of the analogous thiocarbonyl complex, Cr(CO)₅(CS). On further irradiation of the Cr(CO)₄(CSe) species with visible light (λ > 425 nm), the parent Cr(CO)₅(CSe) molecule is regenerated.     

Dynamical and energetic properties of hydrogen and hydrogen-tetrahydrofuran clathrate hydrates

Classical equilibrium molecular dynamics (MD) simulations have been performed to investigate the dynamical and energetic properties in hydrogen and mixed hydrogen-tetrahydrofuran sII hydrates at 30 and 200 K and 0.05 kbar, and also at intermediate temperatures, using SPC/E and TIP4P-2005 water models. The potential model is found to have a large impact on overall density, with the TIP4P-2005 systems being on average 1% more dense than their SPC/E counterparts, due to the greater guest-host interaction energy. For the lightly-filled mixed H(2)-THF system, in which there is single H(2) occupation of the small cage (1s1l), we find that the largest contribution to the interaction energy of both types of guest is the van der Waals component with the surrounding water molecules in the constituent cavities. For the more densely-filled mixed H(2)-THF system, in which there is double H(2) occupation in the small cage (2s1l), we find that there is no dominant component (i.e., van der Waals or Coulombic) in the H(2) interaction energy with the rest of the system, but for the THF molecules, the dominant contribution is again the van der Waals interaction with the surrounding cage-water molecules; again, the Coulombic component increases in importance with increasing temperature. The lightly-filled pure H(2) hydrate (1s4l) system exhibits a similar pattern vis-à-vis the H(2) interaction energy as for the lightly-filled mixed H(2)-THF system, and for the more densely-filled pure H(2) system (2s4l), there is no dominant component of interaction energy, due to the multiple occupancy of the cavities. By consideration of Kubic harmonics, there is some evidence of preferential alignment of the THF molecules, particularly at 200 K; this was found to arise at higher temperatures due to transient hydrogen bonding of the oxygen atom in THF molecules with the surrounding cage-water molecules.