Principal forms X^2 + nY^2 representing many integers

In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers less than or equal to x which are represented by the quadratic form X^2+nY^2. Based on some numerical computations, they observed that the constant occurring in the main term appears to be the largest for n=2. In this paper, we prove that in fact this constant is unbounded as n runs through positive integers with a fixed number of prime divisors.Comment: 10 pages, title has been changed, Sections 2 and 3 are new, to appear in Abh. Math. Sem. Univ. Hambur

Super congruences and Euler numbers

Let $p>3$ be a prime. We prove that $$\sum_{k=0}^{p-1}\binom{2k}{k}/2^k=(-1)^{(p-1)/2}-p^2E_{p-3} (mod p^3),$$ $$\sum_{k=1}^{(p-1)/2}\binom{2k}{k}/k=(-1)^{(p+1)/2}8/3*pE_{p-3} (mod p^2),$$ $$\sum_{k=0}^{(p-1)/2}\binom{2k}{k}^2/16^k=(-1)^{(p-1)/2}+p^2E_{p-3} (mod p^3)$$, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by our investigation of super congruences, we also raise a conjecture on 7 new series for $\pi^2$, $\pi^{-2}$ and the constant $K:=\sum_{k>0}(k/3)/k^2$ (with (-) the Jacobi symbol), two of which are $$\sum_{k=1}^\infty(10k-3)8^k/(k^3\binom{2k}{k}^2\binom{3k}{k})=\pi^2/2$$ and $$\sum_{k>0}(15k-4)(-27)^{k-1}/(k^3\binom{2k}{k}^2\binom{3k}k)=K.$

Collection Development Policies in Public Libraries in Australia: A Qualitative Content Analysis

The role that public library collection development polices play inguiding selectors and informing users has been promoted as a pillar of good professional practice. While these policies purport to open up the methods and the criteria used in selection so as to promote transparency and a sense of professional objectivity, how they actually are developed and put into practice has remained largely implicit in the research literature. This analysis revealedthat policies tended to focus on local issues and remained heavily materials focused. How collections are developed to support user’s information needs and substantive issues associated with topicality are largely unarticulated

Character and environmental lability of cyanobacteria-derived dissolved organic matter

Autotrophic dissolved organic matter (DOM) is central to the carbon biogeochemistry of aquatic systems, and the full complexity of autotrophic DOM has not been extensively studied, particularly by high-resolution mass spectrometry (HRMS). Terrestrial DOM tends to dominate HRMS studies in freshwaters due to the propensity of such compounds to ionize by negative mode electrospray, and possibly also because ionizable DOM produced by autotrophy is decreased to low steady-state concentrations by heterotrophic bacteria. In this study, we investigated the character of DOM produced by the widespread cyanobacteriaMicrocystis aeruginosausing high-pressure liquid chromatography-electrospray ionization-high-resolution mass spectrometry.M. aeruginosaproduced thousands of detectable compounds in axenic culture. These compounds were chromatographically resolved and the majority were assigned to aliphatic formulas with a broad polarity range. We found that the DOM produced byM. aeruginosawas highly susceptible to removal by heterotrophic freshwater bacteria, supporting the hypothesis that this autotroph-derived organic material is highly labile and accordingly only seen at low concentrations in natural settings

Intramolecular hydrogen transfer reactions of thiyl radicals from glutathione: formation of carbon-centered radical at Glu, Cys and Gly

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Chemical Research in Toxicology, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://pubs.acs.org/doi/abs/10.1021/tx3000494Glutathione thiyl radicals (GS•) were generated in H2O and D2O by either exposure of GSH to AAPH#, photoirradiation of GSH in the presence of acetone, or photoirradiation of GSSG. Detailed interpretation of the fragmentation pathways of deuterated GSH and GSH-derivatives during mass spectrometry analysis allowed us to demonstrate that reversible intramolecular H-atom transfer reactions between GS• and C-H bonds at Cys[αC], Cys[βC], and Gly[αC] are possible

High Rates of Hepatitis C Virus Reinfection and Spontaneous Clearance of Reinfection in People Who Inject Drugs: A Prospective Cohort Study

Hepatitis C virus reinfection and spontaneous clearance of reinfection were examined in a highly characterisedcohort of 188 people who inject drugs over a five-year period. Nine confirmed reinfections and 17 possiblereinfections were identified (confirmed reinfections were those genetically distinct from the previous infection andpossible reinfections were used to define instances where genetic differences between infections could not beassessed due to lack of availability of hepatitis C virus sequence data). The incidence of confirmed reinfection was28.8 per 100 person-years (PY), 95%CI: 15.0-55.4; the combined incidence of confirmed and possible reinfectionwas 24.6 per 100 PY (95%CI: 16.8-36.1). The hazard of hepatitis C reinfection was approximately double that ofprimary hepatitis C infection; it did not reach statistical significance in confirmed reinfections alone (hazard ratio [HR]:2.45, 95%CI: 0.87-6.86, p=0.089), but did in confirmed and possible hepatitis C reinfections combined (HR: 1.93,95%CI: 1.01-3.69, p=0.047) and after adjustment for the number of recent injecting partners and duration of injecting.In multivariable analysis, shorter duration of injection (HR: 0.91; 95%CI: 0.83-0.98; p=0.019) and multiple recentinjecting partners (HR: 3.12; 95%CI: 1.08-9.00, p=0.035) were independent predictors of possible and confirmedreinfection. Time to spontaneous clearance was shorter in confirmed reinfection (HR: 5.34, 95%CI: 1.67-17.03,p=0.005) and confirmed and possible reinfection (HR: 3.10, 95%CI: 1.10-8.76, p-value=0.033) than primary infection.Nonetheless, 50% of confirmed reinfections and 41% of confirmed or possible reinfections did not spontaneouslyclear.Conclusions: Hepatitis C reinfection and spontaneous clearance of hepatitis C reinfection were observed at highrates, suggesting partial acquired natural immunity to hepatitis C virus. Public health campaigns about the risks ofhepatitis C reinfection are required

Identification of dissolved organic matter size components in freshwater and marine environments

Dissolved organic matter (DOM) in the transition zone from freshwater to marine systems was analyzed with a new approach for parameterizing the size distribution of organic compounds. We used size-exclusion chromatography for molecular size analysis and quantified colored DOM (CDOM) on samples from two coastal environments in the Baltic Sea (Roskilde Fjord, Denmark and Gulf of Gdansk, Poland). We applied a Gaussian decomposition method to identify peaks from the chromatograms, providing information beyond bulk size properties. This approach complements methods where DOM is separated into size classes with pre-defined filtering cutoffs, or methods where chromatograms are used only to infer average molecular weight. With this decomposition method, we extracted between three and five peaks from each chromatogram and clustered these into three size groups. To test the applicability of our method, we linked our decomposed peaks with salinity, a major environmental driver in the freshwater-marine continuum. Our results show that when moving from freshwater to low-salinity coastal waters, the observed steep decrease of apparent molecular weight is mostly due to loss of the high-molecular-weight fraction (HMW; >2 kDa) of CDOM. Furthermore, most of the CDOM absorbance in freshwater originates from HMW DOM, whereas the absorbing moieties are more equally distributed along the smaller size range (<2 kDa) in marine samples.Peer reviewe

Hydrogen Bonding Constrains Free Radical Reaction Dynamics at Serine and Threonine Residues in Peptides

Free radical-initiated peptide sequencing (FRIPS) mass spectrometry derives advantage from the introduction of highly selective low-energy dissociation pathways in target peptides. An acetyl radical, formed at the peptide N-terminus via collisional activation and subsequent dissociation of a covalently attached radical precursor, abstracts a hydrogen atom from diverse sites on the peptide, yielding sequence information through backbone cleavage as well as side-chain loss. Unique free-radical-initiated dissociation pathways observed at serine and threonine residues lead to cleavage of the neighboring N-terminal C_α–C or N–C_α bond rather than the typical Cα–C bond cleavage observed with other amino acids. These reactions were investigated by FRIPS of model peptides of the form AARAAAXAA, where X is the amino acid of interest. In combination with density functional theory (DFT) calculations, the experiments indicate the strong influence of hydrogen bonding at serine or threonine on the observed free radical chemistry. Hydrogen bonding of the side-chain hydroxyl group with a backbone carbonyl oxygen aligns the singly occupied π orbital on the β-carbon and the N–C_α bond, leading to low-barrier β-cleavage of the N–C_α bond. Interaction with the N-terminal carbonyl favors a hydrogen-atom transfer process to yield stable c and z• ions, whereas C-terminal interaction leads to effective cleavage of the C_α–C bond through rapid loss of isocyanic acid. Dissociation of the C_α–C bond may also occur via water loss followed by β-cleavage from a nitrogen-centered radical. These competitive dissociation pathways from a single residue illustrate the sensitivity of gas-phase free radical chemistry to subtle factors such as hydrogen bonding that affect the potential energy surface for these low-barrier processes

Winter weather controls net influx of atmospheric CO2 on the north-west European shelf

Shelf seas play an important role in the global carbon cycle, absorbing atmospheric carbon dioxide (CO2) and exporting carbon (C) to the open ocean and sediments. The magnitude of these processes is poorly constrained, because observations are typically interpolated over multiple years. Here, we used 298500 observations of CO2 fugacity (fCO2) from a single year (2015), to estimate the net influx of atmospheric CO2 as 26.2 ± 4.7 Tg C yr-1 over the open NW European shelf. CO2 influx from the atmosphere was dominated by influx during winter as a consequence of high winds, despite a smaller, thermally-driven, air-sea fCO2 gradient compared to the larger, biologically-driven summer gradient. In order to understand this climate regulation service, we constructed a carbon-budget supplemented by data from the literature, where the NW European shelf is treated as a box with carbon entering and leaving the box. This budget showed that net C-burial was a small sink of 1.3 ± 3.1 Tg C yr-1, while CO2 efflux from estuaries to the atmosphere, removed the majority of river C-inputs. In contrast, the input from the Baltic Sea likely contributes to net export via the continental shelf pump and advection (34.4 ± 6.0 Tg C yr-1)

Microbial Activities and Dissolved Organic Matter Dynamics in Oil-Contaminated Surface Seawater from the Deepwater Horizon Oil Spill Site

The Deepwater Horizon oil spill triggered a complex cascade of microbial responses that reshaped the dynamics of heterotrophic carbon degradation and the turnover of dissolved organic carbon (DOC) in oil contaminated waters. Our results from 21-day laboratory incubations in rotating glass bottles (roller bottles) demonstrate that microbial dynamics and carbon flux in oil-contaminated surface water sampled near the spill site two weeks after the onset of the blowout were greatly affected by activities of microbes associated with macroscopic oil aggregates. Roller bottles with oil-amended water showed rapid formation of oil aggregates that were similar in size and appearance compared to oil aggregates observed in surface waters near the spill site. Oil aggregates that formed in roller bottles were densely colonized by heterotrophic bacteria, exhibiting high rates of enzymatic activity (lipase hydrolysis) indicative of oil degradation. Ambient waters surrounding aggregates also showed enhanced microbial activities not directly associated with primary oil-degradation (β-glucosidase; peptidase), as well as a twofold increase in DOC. Concurrent changes in fluorescence properties of colored dissolved organic matter (CDOM) suggest an increase in oil-derived, aromatic hydrocarbons in the DOC pool. Thus our data indicate that oil aggregates mediate, by two distinct mechanisms, the transfer of hydrocarbons to the deep sea: a microbially-derived flux of oil-derived DOC from sinking oil aggregates into the ambient water column, and rapid sedimentation of the oil aggregates themselves, serving as vehicles for oily particulate matter as well as oil aggregate-associated microbial communities