On graphs containing a given graph as center

We examine the problem of embedding a graph H as the center of a supergraph G, and we consider what properties one can restrict G to have. Letting A(H) denote the smallest difference ∣V(G)∣ - ∣V(H)∣ over graphs G having center isomorphic to H it is demonstrated that A(H) ≤ 4 for all H, and for 0 ≤ i ≤ 4 we characterize the class of trees T with A(T) = i. for n ≥ 2 and any graph H, we demonstrate a graph G with point and edge connectivity equal to n, with chromatic number X(G) = n + X(H), and whose center is isomorphic to H. Finally, if ∣V(H)∣ ≥ 9 and k ≥ ∣V(H)∣ + 1, then for n sufficiently large (with n even when k is odd) we can construct a k-regular graph on n vertices whose center is isomorphic to H.     

Admissible measures in one dimension

In this note we show that -admissible measures in one dimension (i.e. doubling measures admitting a -Poincaré inequality) are precisely the Muckenhoupt -weights.

     

How can we test the neutrino mass seesaw mechanism experimentally?

The seesaw mechanism for the small neutrino mass has been a popular paradigm, yet it has been believed that there is no way to test it experimentally. We present a conceivable outcome from future experiments that would convince us of the seesaw mechanism. It would involve data from the CERN Large Hadron Collider, International Linear Collider, cosmology, underground, and low-energy flavor experiments to establish the case.     

Microstructural changes in irradiated silica based glasses

High voltage electron microscopy studies have been performed on irradiated pure silica and borosilicate glasses to check their long-term stability when these materials are employed near high energy radioactive sources, such as in fusion reactors and during the storage of nuclear waste. The intense energetic beam of electrons produced by the Harwell 1 MeV microscope, ranging from 10¹⁷ to 10²⁰ e/cm²/s has been focused upon specimens of various composition and impurity content at different temperatures up to about 850°C. Pure silica samples have also been bombarded with 46.5 MeV Ni+6 ions at the Variable Energy Cyclotron. It is found that while no significant changes are detectable in pure irradiated silica, clear evidence is present in complex borosilicate glasses for the growing of large defect clusters (over 1000 Å, resembling gas bubbles) after electron doses of about 8.5 × 10¹⁹ e/cm² and dose rates exceeding 2 × 10¹⁸ e/cm²/sec. Moreover, small regions, about 100 Å wide, scattering electrons more than the matrix are also present. The nature of this fine microstructure has been established as a phase separation into crystalline tridymite. The observations are discussed in terms of their dependence on temperature, sample thickness, dose and dose rates.     

The preparation and characterization of silica gels doped with copper complexes

Silica gels doped with [Cu(C₅H₅N)₄]²⁺ (C₅H₅N = Py), CuCl₂-HOCH₂CH₂OH and Cu(CH₃COO)₂-NH₂(CH₂)₃Si-(OC₂H₅)₃ (CH₃COO = OAc, C₂H₅ = Et) have been prepared and examined by X-ray diffraction, electron spin resonance, transmission electron microscopy (TEM), thermal gravimetric analysis and Fourier transform infrared spectroscopy. Different dopants have different interactions with the silica alcogels depending on the chemistry of the dopants: [Cu(Py)₄]²⁺ forms chemical bonds with the hydroxyl oxygens on the surface of the silica matrix; in Cu(OAc)₂-NH₂(CH₂)₃Si(OEt)₃-doped alcogels, the siloamine enters into the sol-gel reaction and Cu(OAc)₂ coordinates to the -NH₂(CH₂)₃ ligand of the precursor. However, there is no evidence for bond formation between copper and the hydroxyl groups on the silica surface in the CuCl₂-HOCH₂CH₂OH-doped alcogels. The TEM images show a homogeneous and uniform distribution of copper particles on the reduced CuCl₂-HOCH₂CH₂OH- and Cu(OAc)₂-NH₂(CH₂)₃Si(OEt)₃-doped xerogel surface. The type of nitrogen adsorption isotherms of doped silica xerogels are unaffected by the dopant concentration. However, their surface areas do depend on the level of dopant. The microstructure of the silica matrix is primarily determined by the pH of the initial reactants, at least in the [Cu(Py)₄]²⁺-doped case.     

Human urinary metabolite profile of tea polyphenols analyzed by liquid chromatography/electrospray ionization tandem mass spectrometry with data-dependent acquisition

Tea is rich in polyphenols and has a variety of biological activities. In order to better understand the biological effects of tea constituents on human health, markers for their exposure and their metabolic fates are needed. Previously, we have characterized several catechin metabolites in the blood and urine, but more information on the metabolite profile of tea polyphenols is needed. In the present study, the human urinary metabolite profile of tea polyphenols was investigated using liquid chromatography/electrospray ionization tandem mass spectrometry with data-dependent acquisition. With data-dependent MS/MS analysis by collecting the MS2 and MS3 spectra of the most intense ions in the sample, we identified more than twenty metabolites of tea polyphenols from human urine samples. (-)-Epigallocatechin (EGC) glucuronide, methylated EGC glucuronide, methylated EGC sulfate, (-)-epicatechin (EC) glucruronide, EC sulfate, methylated EC sulfate, as well as the glucuronide and sulfate metabolites of the ring-fission metabolites of tea catechins, 5-(3',4',5'-trihydroxyphenyl)-gamma-valerolactone (M4), 5-(3',4'-dihydroxyphenyl)-gamma-valerolactone (M6) and 5-(3',5'-dihydroxyphenyl)-gamma-valerolactone (M6'), were the major human urinary metabolites of tea polyphenols. To our knowledge, this is the first report of the direct simultaneous analysis of the human urinary metabolite profile of tea polyphenols using single sample analysis. This method can also be used for thorough investigations of the metabolite profiles of many other dietary constituents.     

Multiple ionization of argon in coincidence with projectile ions in 60–120 MeV Si q+-Ar collisions

A projectile ion-recoil ion coincidence technique has been employed to study the multiple ionization and the charge transfer processes in collisions of 60–120 MeV Si ^q+ (q = 4−14) ions with neutral argon atoms. The relative contribution of different ionization channels, namely; direct ionization, electron capture and electron loss leading to the production of slow moving multiply charged argon recoil ions have been investigated. The data reported on the present collision system result from a direct measurement in the considered impact energy for the first time. The total ionization cross-sections for the recoil ions are shown to scale as q ^1.7/E _p ^0.5 , where E _p is the energy in MeV of the projectile and q its charge state. The recoil fractions for the cases of total- and direct ionizations are found to decrease with increasing recoil charge state j. The total ionization fractions of the recoils are seen to depend on q and to show the presence of a ‘shell-effect’ of the target. Further, the fractions are found to vary as 1/j ² upto j = 8+. The average recoil charge state 〈j〉 increases slowly with q and with the number of lost or captured electrons from or into the projectile respectively. The projectile charge changing cross-sections σ _qq′ are found to decrease with increasing q for loss ionization and to increase with q for direct-and capture ionization processes respectively. The physics behind various scaling rules that are found to follow our data for different ionization processes is reviewed and discussed.     

Transfer measurements for the Ti+Ni systems at near barrier energies

Large enhancements have been observed in the sub-barrier fusion cross sections for Ti+Ni systems in our previous studies. Coupled channel calculations incorporating couplings to 2⁺ and 3⁻ states failed to explain these enhancements completely. A possibilty of transfer channels contributing to the residual enhancements had been suggested. In order to investigate the role of relevant transfer channels, measurements of one- and two-nucleon transfer were carried out for ^46,48Ti+⁶¹Ni systems. The present paper gives the results of these studies.     

Crystal thickness distributions from melting homopolymers or random copolymers

Differential scanning calorimetry (DSC) can be used to infer the distribution of lamellar crystal thickness l. For homopolymers, the relation between melting temperature T and thickness is described by the Gibbs relation. In this case the weight distribution function of thickness g(l) ∝ P(T)(T − T)², where P(T) is DSC power and T is the melting temperature of an infinitely thick crystal. Copolymer melting is affected by the concentration of noncrystallizable comonomer in the melt as well as lamellar thickness. Unknown melt composition in copolymers with nonequilibrium crystallinity makes determination of the correct distribution g(l) from DSC impossible. An approximate distribution g₂(l) ∝ P(T)(T − T)² is proposed, where T is based on Flory's equilibrium crystallization theory. This approximate distribution is most accurate when crystallinity is small, that is, near the upper end of the melting range. Results are reported for polyethylene homopolymer and model ethylene–butene random copolymers. Corrections were not made for distortion of the DSC endotherms by thermal lag or by melting and recrystallization; these experiments are primarily to illustrate the effect of analysis in terms of an incorrect g₃(l) ∝ P(T). Average crystal thicknesses are about 20 nm for polyethylene and 5 nm for the copolymers. Distributions are characterized by l_w /l_n ≤ 1.1 in all cases. Width of the melting range is not a reliable indicator of the breadth of the thickness distribution. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3131–3140, 1999