Properly coloured copies and rainbow copies of large graphs with small maximum degree

Let G be a graph on n vertices with maximum degree ?. We use the Lovasz local lemma to show the following two results about colourings ? of the edges of the complete graph Kn. If for each vertex v of Kn the colouring ? assigns each colour to at most (n - 2)/(22.4?2) edges emanating from v, then there is a copy of G in Kn which is properly edge-coloured by ?. This improves on a result of Alon, Jiang, Miller, and Pritikin [Random Struct. Algorithms 23(4), 409433, 2003]. On the other hand, if ? assigns each colour to at most n/(51?2) edges of Kn, then there is a copy of G in Kn such that each edge of G receives a different colour from ?. This proves a conjecture of Frieze and Krivelevich [Electron. J. Comb. 15(1), R59, 2008]. Our proofs rely on a framework developed by Lu and Szekely [Electron. J. Comb. 14(1), R63, 2007] for applying the local lemma to random injections. In order to improve the constants in our results we use a version of the local lemma due to Bissacot, Fernandez, Procacci, and Scoppola [preprint, arXiv:0910.1824]. (c) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 425436, 2012

Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

Experimental evidence for the sensitivity of the air-shower radio signal to the longitudinal shower development

We observe a correlation between the slope of radio lateral distributions and the mean muon pseudorapidity of 59 individual cosmic-ray-air-shower events. The radio lateral distributions are measured with LOPES, a digital radio interferometer colocated with the multidetector-air-shower array KASCADE-Grande, which includes a muon-tracking detector. The result proves experimentally that radio measurements are sensitive to the longitudinal development of cosmic-ray air showers. This is one of the main prerequisites for using radio arrays for ultra-high-energy particle physics and astrophysics.

TRANSITIVITY AND ROTATION SETS WITH NONEMPTY INTERIOR FOR HOMEOMORPHISMS OF THE 2-TORUS

We show that if f is a homeomorphism of the 2-torus isotopic to the identity and its lift (f) over tilde is transitive, or even if it is transitive outside the lift of the elliptic islands, then (0,0) is in the interior of the rotation set of (f) over tilde. This proves a particular case of Boyland's conjecture.

Subdivision of Hysteresis Loss in Mn-Zn Ferrite Toroidal Cores

The hysteresis loss subdivision method proved to be a strong tool to help in the analysis of different energy dissipation mechanisms along the quasi-static hysteresis loop measured on electrical steels. This paper used the samemethod to discuss the mechanisms involving the energy loss dissipation in Mn-Zn ferrite toroidal cores. The samples, sintered under controlled atmosphere in industrial conditions, were measured under triangular waveform excitation at very low frequency (5 mHz) and peak flux densities varying from 0.05 T to 0.45 T. The results show a different behavior between the low inductions hysteresis loss (WLI) and the high induction hysteresis loss (WHI) which proves the existence of different energy dissipation mechanisms affecting these loss components.

Origin of the heavy elements in HD 140283 Measurement of europium abundance

Context. HD 140283 is a nearby (V = 7.7) subgiant metal-poor star, extensively analysed in the literature. Although many spectra have been obtained for this star, none showed a signal-to-noise (S/N) ratio high enough to enable a very accurate derivation of abundances from weak lines. Aims. The detection of europium proves that the neutron-capture elements in this star originate in the r-process, and not in the s-process, as recently claimed in the literature. Methods. Based on the OSMARCS 1D LTE atmospheric model and with a consistent approach based on the spectrum synthesis code Turbospectrum, we measured the europium lines at 4129 angstrom and 4205 angstrom, taking into account the hyperfine structure of the transitions. The spectrum, obtained with a long exposure time of seven hours at the Canada-France-Hawaii Telescope (CFHT), has a resolving power of 81 000 and a S/N ratio of 800 at 4100 angstrom. Results. We were able to determine the abundance A(Eu) = -2.35 +/- 0.07 dex, compatible with the value predicted for the europium from the r-process. The abundance ratio [Eu/Ba] = +0.58 +/- 0.15 dex agrees with the trend observed in metal-poor stars and is also compatible with a strong r-process contribution to the origin of the neutron-capture elements in HD 140283.

Interpolation estimate for a finite-element space with embedded discontinuities

We consider a recently proposed finite-element space that consists of piecewise affine functions with discontinuities across a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite element methodologies, the space is a variant of the standard conforming Formula space that can be implemented element by element. Further, it neither introduces new unknowns nor deteriorates the sparsity structure. It is proved that, for u arbitrary in Formula, the interpolant Formula defined by this new space satisfies Graphic where h is the mesh size, Formula is the domain, Formula, Formula, Formula and standard notation has been adopted for the function spaces. This result proves the good approximation properties of the finite-element space as compared to any space consisting of functions that are continuous across Γ, which would yield an error in the Formula-norm of order Graphic. These properties make this space especially attractive for approximating the pressure in problems with surface tension or other immersed interfaces that lead to discontinuities in the pressure field. Furthermore, the result still holds for interfaces that end within the domain, as happens for example in cracked domains.

A further note on the college admission game

When a stable matching rule is used for a college admission market, questions on incentives facing agents of both sides of the market naturally emerge. This note states and proves four important results which fill a gap in the theory of incentives for the college admission model. Two of them have never been demonstrated but have been used along the years and are responsible for the success that this theory has had in explaining empirical economic phenomena.

Fermentative production of ribonucleotides from whey by Kluyveromyces marxianus: effect of temperature and pH

Ribonucleotides have shown many promising applications in food and pharmaceutical industries. The aim of the present study was to produce ribonucleotides (RNA) by Kluyveromyces marxianus ATCC 8,554 utilizing cheese whey, a dairy industry waste, as a main substrate under batch fermentation conditions. The effects of temperature, pH, aeration rate, agitation and initial cellular concentration were studied simultaneously through factorial design for RNA, biomass production and lactose consumption. The maximum RNA production (28.66 mg/g of dry biomass) was observed at temperature 30°C, pH 5.0 and 1 g/l of initial cellular concentration after 2 h of fermentation. Agitation and aeration rate did not influence on RNA concentration (p >0.05). Maximum lactose consumption (98.7%) and biomass production (6.0 g/l) was observed after 12 h of incubation. This study proves that cheese whey can be used as an adequate medium for RNA production by K. marxianus under the optimized conditions at industrial scale.

Origin of the heavy elements in HD 140283: measurement of europium abundance

Context. HD140283 is a nearby (V = 7:7) subgiant metal-poor star, extensively analysed in the literature. Although many spectra have been obtained for this star, none showed a signal-to-noise (S/N) ratio high enough to enable a very accurate derivation of abundances from weak lines. Aims. The detection of europium proves that the neutron-capture elements in this star originate in the r-process, and not in the s-process, as recently claimed in the literature. Methods. Based on the OSMARCS 1D LTE atmospheric model and with a consistent approach based on the spectrum synthesis code Turbospectrum, we measured the europium lines at 4129 Å and 4205 Å, taking into account the hyperfine structure of the transitions. The spectrum, obtained with a long exposure time of seven hours at the Canada-France-Hawaii Telescope (CFHT), has a resolving power of 81 000 and a S/N ratio of 800 at 4100 Å. Results. We were able to determine the abundance A(Eu) =

Measurement and model calculation of the temperature dependence of ligand-to-metal energy transfer rates in lanthanide complexes

Temperature dependent transient curves of excited levels of a model Eu3+ complex have been measured for the first time. A coincidence between the temperature dependent rise time of the 5D0 emitting level and decay time of the 5D1 excited level in the [Eu(tta)3(H2O)2] complex has been found, which unambiguously proves the T1→5D1→5D0 sensitization pathway. A theoretical approach for the temperature dependent energy transfer rates has been successfully applied to the rationalization of the experimental data.