Representations of integers by certain positive definite binary quadratic forms

We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n=x^2+Ny^2 for a squarefree integer N.Comment: 8 pages, submitte

Economics of agroforestry (1996)

Agroforestry provides a landowner the opportunity to develop a portfolio of short- and long-term investments that allow for some spreading of financial risk through diversification. In general, diversification of investment provides financial advantages, although it also introduces the need for additional management expertise to deal with the added complexity of the farm operation. For farms with land particularly unsuitable for crops, agroforestry provides a way to remove the unsuitable land from crop production over an extended period as the trees mature. Agroforestry also provides social benefits by functioning as a protective system that ensures resource conservation, although some of these benefits are not directly measurable.New 5/96/5M

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

Shifts in the source and composition of dissolved organic matter in Southwest Greenland lakes along a regional hydro-climatic gradient

Dissolved organic matter (DOM) concentration and quality were examined from Arctic lakes located in three clusters across south-west (SW) Greenland, covering the regional climatic gradient: cool, wet coastal zone; dry inland interior; and cool, dry ice-marginal areas. We hypothesized that differences in mean annual precipitation between sites would result in a reduced hydrological connectivity between lakes and their catchments and that this concentrates degraded DOM. The DOM in the inland lake group was characterized by a lower aromaticity and molecular weight, a low soil-like fluorescence, and carbon stable isotope (δ 13 C-DOC) values enriched by ~2‰ relative to the coastal group. DOC-specific absorbance (SUVA 254 ) and DOC-specific soil-like fluorescence (SUVF C1 ) revealed seasonal and climatic gradients across which DOM exhibited a dynamic we term “pulse-process”: Pulses of DOM exported from soils to lakes during snow and ice melt were followed by pulses of autochthonous DOM inputs (possibly from macrophytes), and their subsequent photochemical and microbial processing. These effects regulated the dynamics of DOM in the inland lakes and suggested that if circumpolar lakes currently situated in cool wetter climatic regimes with strong hydrological connectivity have reduced connectivity under a drier future climate, they may evolve toward an end-point of large stocks of highly degraded DOC, equivalent to the inland lakes in the present study. The regional climatic gradient across SW Greenland and its influence on DOM properties in these lakes provide a model of possible future changes to lake C cycling in high-latitude systems where climatic changes are most pronounced

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.$

Plasma deconvolution identifies broadly neutralizing antibodies associated with hepatitis C virus clearance

A vaccine for hepatitis C virus (HCV) is urgently needed. Development of broadly neutralizing plasma antibodies during acute infection is associated with HCV clearance, but the viral epitopes of these plasma antibodies are unknown. Identifying these epitopes could define the specificity and function of neutralizing antibodies (NAbs) that should be induced by a vaccine. Here, we present the development and application of a high-throughput method that deconvolutes polyclonal anti-HCV NAbs in plasma, delineating the epitope specificities of anti-HCV NAbs in acute-infection plasma of 44 humans with subsequent clearance or persistence of HCV. Remarkably, we identified multiple broadly neutralizing antibody combinations that were associated with greater plasma neutralizing breadth and with HCV clearance. These studies have the potential to inform new strategies for vaccine development by identifying broadly neutralizing antibody combinations in plasma associated with the natural clearance of HCV, while also providing a high-throughput assay that could identify these responses after vaccination trials

The contribution of algae to freshwater dissolved organic matter: implications for UV spectroscopic analysis

Dissolved organic matter (DOM) is an important constituent of freshwater that participates in a number of key ecological and biogeochemical processes but can be problematic during water treatment. Thus, the demand for rapid and reliable monitoring is growing, and spectroscopic methods are potentially useful. A model with 3 components—2 that absorb in the ultraviolet (UV) range and are present at variable concentrations and a third that does not absorb light and is present at a low constant concentration—was previously found to yield reliable predictions of dissolved organic carbon concentration [DOC]. The model underestimated [DOC] in shallow eutrophic lakes in the Yangtze Basin, China, however, raising the possibility that DOM derived from algae might be poorly estimated, an idea supported by new data reported here for eutrophic British lakes. We estimated the extinction coefficients in the UV range of algae-derived DOM from published data on algal cultures and from new data from outdoor mesocosm experiments in which high concentrations of DOC were generated under conditions comparable to those in eutrophic freshwaters. The results demonstrate the weak UV absorbance of DOM from algae compared to DOM from terrestrial sources. A modified model, in which the third component represents algae-derived DOM present at variable concentrations, allowed contributions of such DOM to be estimated by combining the spectroscopic data with [DOC] measured by laboratory combustion. Estimated concentrations of algae-derived DOC in 77 surface freshwater samples ranged from 0 to 8.6 mg L−1, and the fraction of algae-derived DOM ranged from 0% to 100%

Controls on the composition and lability of dissolved organic matter in Siberia's Kolyma River basin

High-latitude northern rivers export globally significant quantities of dissolved organic carbon (DOC) to the Arctic Ocean. Climate change, and its associated impacts on hydrology and potential mobilization of ancient organic matter from permafrost, is likely to modify the flux, composition, and thus biogeochemical cycling and fate of exported DOC in the Arctic. This study examined DOC concentration and the composition of dissolved organic matter (DOM) across the hydrograph in Siberia's Kolyma River, with a particular focus on the spring freshet period when the majority of the annual DOC load is exported. The composition of DOM within the Kolyma basin was characterized using absorbance-derived measurements (absorbance coefficienta330, specific UV absorbance (SUVA254), and spectral slope ratio SR) and fluorescence spectroscopy (fluorescence index and excitation-emission matrices (EEMs)), including parallel factor analyses of EEMs. Increased surface runoff during the spring freshet led to DOM optical properties indicative of terrestrial soil inputs with high humic-like fluorescence, SUVA254, and low SRand fluorescence index (FI). Under-ice waters, in contrast, displayed opposing trends in optical properties representing less aromatic, lower molecular weight DOM. We demonstrate that substantial losses of DOC can occur via biological (∼30% over 28 days) and photochemical pathways (>29% over 14 days), particularly in samples collected during the spring freshet. The emerging view is therefore that of a more dynamic and labile carbon pool than previously thought, where DOM composition plays a fundamental role in controlling the fate and removal of DOC at a pan-Arctic scale