MacMahon's sum-of-divisors functions, Chebyshev polynomials, and Quasi-modular forms

We investigate a relationship between MacMahon's generalized sum-of-divisors functions and Chebyshev polynomials of the first kind. This determines a recurrence relation to compute these functions, as well as proving a conjecture of MacMahon about their general form by relating them to quasi-modular forms. These functions arise as solutions to a curve-counting problem on Abelian surfaces.Comment: 6 Page

The Use and Abuse of Special-Purpose Entities in Public Finance

States increasingly are raising financing indirectly through special-purpose entities (SPEs), variously referred to as authorities, special authorities, or public authorities. Notwithstanding their long history and increasingly widespread use, relatively little is known or has been written about these entities. This article examines state SPEs and their functions, comparing them to SPEs used in corporate finance. States, even more than corporations, use these entities to reduce financial transparency and avoid public scrutiny, seriously threatening the integrity of public finance. The article analyzes how regulation could be designed in order to control that threat while maintaining the legitimate financing benefits provided by these state entities

The determinants of health related quality of life of patients on maintenance haemodialysis at Kenyatta National Hospital, Kenya

Background: Health related quality of life (HRQOL) is increasingly being recognised as a primary outcome measure in the treatment of end stage renal disease. In addition to being an important surrogate marker of quality of care in patients on maintenance haemodialysis, HRQOL measures have being shown to be robust predictors of mortality and morbidity.Objective: To determine the health related quality of life and its determinants in patients on maintenance haemodialysis at the Kenyatta National Hospital.Design: A cross-sectional descriptive study.Setting: Renal unit, Kenyatta National HospitalSubjects: Adult patients with end stage renal disease on maintenance haemodialysis.Results: The mean physical composite summary and mental composite summary scores were 39.09±9.49 and 41.87±10.56 respectively. The burden of kidney disease sub-scale, symptom and problems sub-scale and effect of kidney disease on daily life sub-scale scores were 16.15±21.83, 73.46±18.06 and 67.63±23.45 respectively. No significant correlations were found between the health-related quality of life scores, socio-demographic and clinical factors assessed.Conclusion: The health-related quality of life of patients on maintenance haemodialysis is reduced. The physical quality of life is more affected than the mental quality of life. No independent determinants of health-related quality of life were identified

A phase field formulation for hydrogen assisted cracking

We present a phase field modeling framework for hydrogen assisted cracking. The model builds upon a coupled mechanical and hydrogen diffusion response, driven by chemical potential gradients, and a hydrogen-dependent fracture energy degradation law grounded on first principles calculations. The coupled problem is solved in an implicit time integration scheme, where displacements, phase field order parameter and hydrogen concentration are the primary variables. We show that phase field formulations for fracture are particularly suitable to capture material degradation due to hydrogen. Specifically, we model (i) unstable crack growth in the presence of hydrogen, (ii) failure stress sensitivity to hydrogen content in notched specimens, (iii) cracking thresholds under constant load, (iv) internal hydrogen assisted fracture in cracked specimens, and (v) complex crack paths arising from corrosion pits. Computations reveal a good agreement with experiments, highlighting the predictive capabilities of the present scheme. The work could have important implications for the prediction and prevention of catastrophic failures in corrosive environments. The finite element code developed can be downloaded from www.empaneda.com/code

A phase field model for elastic-gradient-plastic solids undergoing hydrogen embrittlement

We present a gradient-based theoretical framework for predicting hydrogen assisted fracture in elastic-plastic solids. The novelty of the model lies in the combination of: (i) stress-assisted diffusion of solute species, (ii) strain gradient plasticity, and (iii) a hydrogen-sensitive phase field fracture formulation, inspired by first principles calculations. The theoretical model is numerically implemented using a mixed finite element formulation and several boundary value problems are addressed to gain physical insight and showcase model predictions. The results reveal the critical role of plastic strain gradients in rationalising decohesion-based arguments and capturing the transition to brittle fracture observed in hydrogen-rich environments. Large crack tip stresses are predicted, which in turn raise the hydrogen concentration and reduce the fracture energy. The computation of the steady state fracture toughness as a function of the cohesive strength shows that cleavage fracture can be predicted in otherwise ductile metals using sensible values for the material parameters and the hydrogen concentration. In addition, we compute crack growth resistance curves in a wide variety of scenarios and demonstrate that the model can appropriately capture the sensitivity to: the plastic length scales, the fracture length scale, the loading rate and the hydrogen concentration. Model predictions are also compared with fracture experiments on a modern ultra-high strength steel, AerMet100. A promising agreement is observed with experimental measurements of threshold stress intensity factor $K_{th}$ over a wide range of applied potentials

Elevated expression of artemis in human fibroblast cells is associated with cellular radiosensitivity and increased apoptosis

Copyright @ 2012 Nature Publishing GroupThis article has been made available through the Brunel Open Access Publishing Fund.Background: The objective of this study was to determine the molecular mechanism(s) responsible for cellular radiosensitivity in two human fibroblast cell lines 84BR and 175BR derived from two cancer patients. Methods: Clonogenic assays were performed following exposure to increasing doses of gamma radiation to confirm radiosensitivity. γ-H2AX foci assays were used to determine the efficiency of DNA double strand break (DSB) repair in cells. Quantitative-PCR (Q-PCR) established the expression levels of key DNA DSB repair proteins. Imaging flow cytometry using Annexin V-FITC was used to compare artemis expression and apoptosis in cells. Results: Clonogenic cellular hypersensitivity in the 84BR and 175BR cell lines was associated with a defect in DNA DSB repair measured by the γ-H2AX foci assay. Q-PCR analysis and imaging flow cytometry revealed a two-fold overexpression of the artemis DNA repair gene which was associated with an increased level of apoptosis in the cells before and after radiation exposure. Over-expression of normal artemis protein in a normal immortalised fibroblast cell line NB1-Tert resulted in increased radiosensitivity and apoptosis. Conclusion: We conclude elevated expression of artemis is associated with higher levels of DNA DSB, radiosensitivity and elevated apoptosis in two radio-hypersensitive cell lines. These data reveal a potentially novel mechanism responsible for radiosensitivity and show that increased artemis expression in cells can result in either radiation resistance or enhanced sensitivity.This work was supported in part by The Vidal Sassoon Foundation USA. This article is made available through the Brunel Open Access Publishing Fund

Lack of plasma albumin impairs intravascular lipolysis and explains the associated free fatty acids deficiency and hypertriglyceridemia

<p>Abstract</p> <p>Background</p> <p>Abnormalities in lipid metabolism and transport are hallmarks in analbuminemic Nagase rats (NAR) and humans. Triglyceridemia is nearly 3- to 5-fold higher in female NAR than in control Sprague-Dawley rats (SDR). Also, NAR present with a severe plasma free fatty acid (FFA) deficit. There are conflicting results regarding the mechanisms underlying NAR hypertriglyceridemia.</p> <p>Objective</p> <p>We aimed at investigating whether liver lipogenesis and triglyceride secretion rates into the plasma contribute to the hypertriglyceridemia in NAR. We also studied whether heparin or albumin administration would release the hypothesized lipolysis inhibition in NAR.</p> <p>Methods</p> <p>The incorporation of tritiated water into lipids and the linear accumulation rate of plasma triglycerides after Triton WR1339 injection were the measures of liver lipogenesis and triglyceride secretion rates.</p> <p>Results</p> <p>Lipogenesis (596 ± 40 vs. 929 ± 124 μmol ³H₂O/g/h) and triglyceride (4.25 ± 1.00 vs. 7.04 ± 1.68 mg/dL/min) secretion rates were slower (<it>P </it>≤ 0.05) in fasted NAR than in control SDR. The injection of either heparin or albumin elicited an increase in NAR plasma FFA levels over time. FFA levels reached control levels 90 min after the albumin administration, increasing from 0.36 ± 0.05 to 1.34 ± 0.16 mEq/L (<it>P </it>≤ 0.05). These results indicate that the lack of plasma albumin inhibits intravascular lipolysis and causes the FFA deficit observed in NAR.</p> <p>Conclusion</p> <p>NAR hepatic triglyceride synthesis and output do not contribute to NAR hypertriglyceridemia. We propose that the lack of albumin diminishes intravascular lipolysis which reduces the plasma triglyceride removal rate and explain both NAR hypertriglyceridemia and FFA deficiency.</p

The role of plastic strain gradients in the crack growth resistance of metals

Crack advance from short or long pre-cracks is predicted by the progressive failure of a cohesive zone in a strain gradient, elasto-plastic solid. The presence of strain gradients leads to the existence of an elastic zone at the tip of a stationary crack, for both the long crack and the short crack cases. This is in sharp contrast with previous asymptotic analyses of gradient solids, where elastic strains were neglected. The presence of an elastic singularity at the crack tip generates stresses which are sufficiently high to activate quasi-cleavage. For the long crack case, crack growth resistance curves are predicted for a wide range of ratios of cohesive zone strength to yield strength. Remarkably, this feature of an elastic singularity is preserved for short cracks, leading to a severe reduction in tensile ductility. In qualitative terms, these predictions resemble those of discrete dislocation calculations, including the concept of a dislocation-free zone at the crack tip

Pancreatic cancer-associated diabetes mellitus: an open field for proteomic applications.

Background: Diabetes mellitus is associated with pancreatic cancer in more than 80% of the cases. Clinical, epidemiological, and experimental data indicate that pancreatic cancer causes diabetes mellitus by releasing soluble mediators which interfere with both beta-cell function and liver and muscle glucose metabolism. Methods: We analysed, by matrix-assisted laser desorption ionization time of flight (MALDI-TOF), a series of pancreatic cancer cell lines conditioned media, pancreatic cancer patients' peripheral and portal sera, comparing them with controls and chronic pancreatitis patients' sera. Results: MALDI-TOF analysis of pancreatic cancer cells conditioned media and patients' sera indicated a low molecular weight peptide to be the putative pancreatic cancer-associated diabetogenic factor. The sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) analysis of tumor samples from diabetic and non-diabetic patients revealed the presence of a 1500 Da peptide only in diabetic patients. The amino acid sequence of this peptide corresponded to the N-terminal of an S-100 calcium binding protein, which was therefore suggested to be the pancreatic cancer-associated diabetogenic factor. Conclusions: We identified a tumor-derived peptide of 14 amino acids sharing a 100% homology with an S-100 calcium binding protein, which is probably the pancreatic cancer-associated diabetogenic facto