Representations of the Riemann zeta function: A probabilistic approach

In this paper, we give a short elementary proof of the well known Euler's recurrence formula for the Riemann zeta function at positive even integers and integral representations of the Riemann zeta function at positive integers and at fractional points by means of probabilistic approach. The proof is based on the moment generating function and the characteristic function of logistic and half-logistic distributions in probability theory

Exploring the use of phenocams and satellite data to better inform the pasture phenology and aerobiology of allergenic grass pollen in eastern Australia

University of Technology Sydney. Faculty of Science.Phenological studies of grassland/ pastures have attracted increased attention for their sensitivity to climate change with associated impacts on allergenic pollen release and public health. Allergenic pollen exposure is expected to increase with global warming following extended grass growing and grass pollen seasons and the prevalence of allergic diseases in Australia is among the highest globally. The primary aims of this thesis were to integrate phenocam and satellite imagery with pollen concentration data, over subtropical to temperate grassland sites in Australia, in order to address critical knowledge gaps in our understanding of the ecological drivers of grass pollen aerobiology. Phenocams were used to investigate the diurnal and daily greenness variations across solar zenith angles, solar intensity, and direct/ diffuse sky conditions. This information was used to develop an optimised daily compositing methodology. Next, I successfully registered a 3×3 window of Sentinel-2 pixels at 10 m resolution with the phenocam measurement footprint to conduct upscaling analyses. The relationships between Sentinel-2 Enhanced Vegetation Index (EVI) and phenocam green chromatic coordinate (GCC) index were strong and independent of the time of year and grass phenophases. This enabled the more sparse temporal sampling of Sentinel-2 greenness to be converted to daily values. Relationships between seasonal grass pollen concentrations and phenocam GCC and satellite EVI phenology were also strong with pollen concentration peaks in phase with grass greenness peaks, including multiple sub-seasonal pollen and greenness peaks. The grass greenness amplitudes, a surrogate of biomass, were found to be correlated with total pollen concentrations. Finally, I investigated grass pollen sources at more detailed, 10 m resolution, by generating a neural net grass map, from the Sentinel-2 sensor. This enabled urban, peri-urban and regional grass sources to be quantified based on distance and orientation to the pollen sampler, providing new insights for pollen forecasting. This thesis highlights the ability of near-surface and satellite remote sensing to achieve more accurate grassland/ pasture phenology to improve upon the understanding of ecologically relevant factors for grass pollen aerobiology in Australia

Successive one-sided Hodrick-Prescott filter with incremental filtering algorithm for nonlinear economic time series

We propose a successive one-sided Hodrick-Prescott (SOHP) filter from multiple time scale decomposition perspective to derive trend estimate for a time series. The idea is to apply the one-sided HP (OHP) filter recursively on the updated cyclical component to extract the trend residual on multiple time scales, thereby to improve the trend estimate. To address the issue of optimization with a moving horizon as that of the SOHP filter, we present an incremental HP filtering algorithm, which greatly simplifies the involved inverse matrix operation and reduces the computational demand of the basic HP filtering. Actually, the new algorithm also applies effectively to other HP-type filters, especially for large-size or expanding data scenario. Numerical examples on real economic data show the better performance of the SOHP filter in comparison with other known HP-type filters

Adsorption Properties of Copper (II) Ion From Aqueous Solution by Starch-Grafted Polyacrylamide and Crosslinked Starch-Grafted Polyacrylamide

Starch-grafted polyacrylamide (SA) and cross-linked starch-grafted polyacrylamide (CSA) had been synthesized via grafting polymerization from corn starch and used as adsorbents for the removal of Cu(II) ion from aqueous solution. The equilibrium, kinetics and thermodynamics of adsorption processes of SA and CSA were investigated and compared. It was found that the adsorption capacity of Cu(II) of SA and CSA could reach the maximum within 60 min when the pH was 6. The adsorption kinetics of CSA and SA for Cu(II) was favorably described by the pseudo-second-order kinetic model and the adsorption isotherm was described well with the Freundlich isotherm model. Thermodynamic studies indicated that the adsorption was a spontaneous and endothermic process with increased entropy, and the rise of temperature would benefit the adsorption; the enthalpy change(ΔH), the entropy change (ΔS) and free energy change (ΔG) of the adsorption process of Cu(II) on SA and CSA were calculated with adsorption isotherm data and basic thermodynamic relations

De novo transcriptome sequencing and comprehensive analysis of the drought-responsive genes in the desert plant Cynanchum komarovii

The figure of an agarose gel with PCR products. (TIFF 11899 kb

Proteomic Analysis of Serum in Lung Cancer Induced by 3-Methylcholanthrene

Lung cancer remains the leading cause of cancer-related mortality worldwide. Early detection of lung cancer is problematic due to the lack of a marker with high diagnosis sensitivity and specificity. To determine the differently expressed proteins in the serum of lung cancer and figure out the function of the proteins, two-dimensional electrophoresis (2DE) and matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS) were used to screen the serum proteins of lung cancer model induced by 3-methylcholanthrene (MCA). From optimized 2DE image, 455 spots in the normal sera and 716 spots in the lung cancers sera were detected. Among them, 141 protein spots were differentially expressed when comparing the serum from normal rat and serum from lung cancer model, including 82 overexpressed proteins and 59 underexpressed proteins. Changes of haptoglobin, transthyretin, and TNF superfamily member 8 (TNFRS8) were confirmed in sera from lung cancer by MALDI-TOF-MS. Proteomics technology leads to identify changes of haptoglobin, transthyretin, and TNFRS8 in serum of rat lung cancer model and represents a powerful tool in searching for candidate proteins as biomarkers