On the Decay of Crossing Numbers of Sparse Graphs

Richter and Thomassen proved that every graph has an edge e such that the crossing number of is at least . Fox and Cs. Tóth proved that dense graphs have large sets of edges (proportional in the total number of edges) whose removal leaves a graph with crossing number proportional to the crossing number of the original graph; this result was later strenghthened by ?erný, Kyn?l, and G. Tóth. These results make our understanding of the decay of crossing numbers in dense graphs essentially complete. In this article we prove a similar result for large sparse graphs in which the number of edges is not artificially inflated by operations such as edge subdivisions. We also discuss the connection between the decay of crossing numbers and expected crossing numbers, a concept recently introduced by Mohar and Tamon.     

Index Theory, Gerbes, and Hamiltonian Quantization

We give an Atiyah-Patodi-Singer index theory construction of the bundle of fermionic Fock spaces parametrized by vector potentials in odd space dimensions and prove that this leads in a simple manner to the known Schwinger terms (Faddeev-Mickelsson cocycle) for the gauge group action. We relate the APS construction to the bundle gerbe approach discussed recently by Carey and Murray, including an explicit computation of the Dixmier-Douady class. An advantage of our method is that it can be applied whenever one has a form of the APS theorem at hand, as in the case of fermions in an external gravitational field. Received:     

A Q-factorial complete toric variety with Picard number 2 is projective

This paper is devoted to settle two still open problems, connected with the existence of ample and nef divisors on a $\mathbb{Q}$-factorial complete toric variety. The first problem is about the existence of ample divisors when the Picard number is 2: we give a positive answer to this question, by studying the secondary fan by means of $\mathbb{Z}$-linear Gale duality. The second problem is about the minimum value of the Picard number allowing the vanishing of the Nef cone: we present a 3-dimensional example showing that this value cannot be greater then 3, which, under the previous result, is also the minimum value guaranteeing the existence of non-projective examples.     

Nitroxide mediated polymerization of sustainably sourced isobornyl methacrylate and tridecyl methacrylate with acrylonitrile co-monomer

Nitroxide-mediated polymerization (NMP) of isobornyl methacrylate (IBOMA) and tridecyl methacrylate (TDMA), derived from sustainable feedstocks, with a low fraction of acrylonitrile (AN) co-monomer were conducted with unimolecular initiator BlocBuilder-MA™ (BB) and the succinimidyl ester-functionalized form, NHS-BB. IBOMA and TDMA-rich compositions were both polymerized at 100 °C in a controlled manner (i.e., linear increase in number average molecular weight [Mn] with conversion up to ∼40% and low dispersity, Đ < 1.5). SG1-terminated poly(IBOMA-stat-AN) macroinitiator was then cleanly chain-extended with poly(TDMA-stat-AN) and the diblock copolymers exhibited two distinct glass transition temperatures (Tgs), indicative of microphase separation. IBOMA/TDMA/AN terpolymers with different IBOMA/TDMA molar ratios were also synthesized where terpolymers with higher IBOMA content had higher apparent rate constants and higher Tgs. Moreover, chain growth was linear up to conversions of ∼60% and all Đs were 1.51 to 1.64. Finally, 2-hydroxyethyl methacrylate (HEMA) was incorporated into the IBOMA/TDMA/AN system, resulting in statistical quadripolymers. The quadripolymer Tg decreased with increasing TDMA content and Mn ranged from 12 to 15.4 kg mol⁻¹ and the Đ were 1.39 to 1.54, suggesting the successful incorporation of sustainably sourced monomers into quadripolymers with a broad range of tunable Tgs via NMP with additional functionalities from HEMA. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 2422–2436     

Removal of Cs,Sr, U and Pu species from simulated nuclear waste effluent using graphene oxide

This article reports the findings from a series of radioactive experimental trials which have examined the sorption properties of graphene oxide focused on four key radionuclides commonly linked to effluent challenges in the nuclear industry—Cs, Sr, U and Pu. Unlike previous experimental studies, simulated effluent waste solutions were utilised with compositions typical of those found at the Sellafield nuclear site, UK. Molecular dynamics simulations were performed in parallel to elucidate the functional groups to which radionuclides preferentially adsorb.     

BRCA1/2 mutation carriers: living with susceptibility

OBJECTIVES: To examine whether being a BRCA1/2 mutation carrier affects a wide array of aspects of life, and if so, how. METHODS: Participants were grouped according to their carrier status (carrier and noncarrier status), health status (affected or unaffected by cancer), and their enrollment at the counseling service (probands and other family members). One hundred and sixty-five women completed a self-administered questionnaire following their genetic consultation session. RESULTS: Probands/nonprobands and carriers/noncarriers did not differ with regard to demographic characteristics, health behaviors including medical checkups, the distress they experience or their resources (sense of coherence, social integration, religiosity). Individuals affected by cancer did differ on some of these aspects from participants without cancer. CONCLUSIONS: From the results of this study, being a carrier could not be considered a psychosocial risk factor, nor does it seem to have an effect on carriers' resources and lifestyle.     

Experimental Effectiveness Investigation of Liquid-to-air Membrane Energy Exchangers under Low Heat Capacity Rates Conditions

The liquid-to-air membrane energy exchanger is a novel membrane base energy exchanger that allows both heat and moisture transfer between air and a salt solution using a membrane. The heat and mass transfer performance of a single one is significantly dependent on two dimensionless parameters: number of heat transfer units and the ratio of heat capacity rates between solution flow and airflow (Cr^*). In this study, the effectiveness of a small-scale liquid-to-air membrane energy exchanger under low Cr^* conditions (i.e., Cr^* < 1) that has been not investigated previously is experimentally and numerically tested.     

Reaction auf Blaus?ure

Ohne Zusammenfassung     

Ueber die L?slichkeit einiger Silbersalze in L?sungen von citronensaurem Natron

Ohne Zusammenfassung