Singular solutions of fully nonlinear elliptic equations and applications

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of $\mathbb{R}^n$, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragm\'en-Lindel\"of result as well as a principle of positive singularities in certain Lipschitz domains.Comment: 41 pages, 2 figure

Gastric cancer and Helicobacter pylori: a combined analysis of 12 case control studies nested within prospective cohorts

BACKGROUND: The magnitude of the association between Helicobacter pylori and incidence of gastric cancer is unclear. H pylori infection and the circulating antibody response can be lost with development of cancer; thus retrospective studies are subject to bias resulting from classifi- cation of cases as H pylori negative when they were infected in the past. AIMS: To combine data from all case control studies nested within prospective cohorts to assess more reliably the relative risk of gastric cancer associated with H pylori infection.To investigate variation in relative risk by age, sex, cancer type and subsite, and interval between blood sampling and cancer diagnosis. METHODS: Studies were eligible if blood samples for H pylori serology were collected before diagnosis of gastric cancer in cases. Identified published studies and two unpublished studies were included. Individual subject data were obtained for each. Matched odds ratios (ORs) and 95% confidence intervals (95% CI) were calculated for the association between H pylori and gastric cancer. RESULTS: Twelve studies with 1228 gastric cancer cases were considered. The association with H pylori was restricted to noncardia cancers (OR 3.0; 95% CI 2.3–3.8) and was stronger when blood samples for H pylori serology were collected 10+ years before cancer diagnosis (5.9; 3.4–10.3). H pylori infection was not associated with an altered overall risk of cardia cancer (1.0; 0.7–1.4). CONCLUSIONS: These results suggest that 5.9 is the best estimate of the relative risk of non-cardia cancer associated with H pylori infection and that H pylori does not increase the risk of cardia cancer. They also support the idea that when H pylori status is assessed close to cancer diagnosis, the magnitude of the non-cardia association may be underestimated

Nonadiabatic approach to dimerization gap and optical absorption coefficient of the Su-Schrieffer-Heeger model

An analytical nonadiabatic approach has been developed to study the dimerization gap and the optical absorption coefficient of the Su-Schrieffer-Heeger model where the electrons interact with dispersive quantum phonons. By investigating quantitatively the effects of quantum phonon fluctuations on the gap order and the optical responses in this system, we show that the dimerization gap is much more reduced by the quantum lattice fluctuations than the optical absorption coefficient is. The calculated optical absorption coefficient and the density of states do not have the inverse-square-root singularity, but have a peak above the gap edge and there exist a significant tail below the peak. The peak of optical absorption spectrum is not directly corresponding to the dimerized gap. Our results of the optical absorption coefficient agree well with those of the experiments in both the shape and the peak position of the optical absorption spectrum.Comment: 14 pages, 7 figures. to be published in PR

Sideward flow of K+ mesons in Ru+Ru and Ni+Ni reactions near threshold

Experimental data on K+ meson and proton sideward flow measured with the FOPI detector at SIS/GSI in the reactions Ru+Ru at 1.69 AGeV and Ni+Ni at 1.93 AGeV are presented. The K+ sideward flow is found to be anti-correlated (correlated) with the one of protons at low (high) transverse momenta. When compared to the predictions of a transport model, the data favour the existence of an in-medium repulsive K+ nucleon potential.Comment: 16 pages Revtex, 3 ps-figures, submitted to Phys. Lett.

A ballistic motion disrupted by quantum reflections

I study a Lindblad dynamics modeling a quantum test particle in a Dirac comb that collides with particles from a background gas. The main result is a homogenization theorem in an adiabatic limiting regime involving large initial momentum for the test particle. Over the time interval considered, the particle would exhibit essentially ballistic motion if either the singular periodic potential or the kicks from the gas were removed. However, the particle behaves diffusively when both sources of forcing are present. The conversion of the motion from ballistic to diffusive is generated by occasional quantum reflections that result when the test particle's momentum is driven through a collision near to an element of the half-spaced reciprocal lattice of the Dirac comb.Comment: 54 pages. I rewrote the introduction and simplified some of the presentatio

SPACA3gene variants in a New Zealand cohort of infertile and fertile couples

SPRASA (also referred to as SLLP1) is a protein identified in the acrosome of human sperm and encoded by the gene SPACA3. SPRASA is associated with sperm-oocyte recognition and binding, and may play a role in fertility. In order to determine whether variants in the SPACA3 gene are associated with human infertility, we undertook a genetic analysis of 102 infertile and 104 fertile couples. Three gene variants were identified using PCR-based DNA sequencing; 1) an insertion of TGC within a quadruple tri-nucleotide (TGC) repeat region in the 5’ untranslated region (UTR) (g.–22TGC(4_5), 2) a guanine to adenosine transition at position 239 (c.239G> A) resulting in a non-synonymous amino acid substitution from cysteine to tyrosine (p.C80Y) at position 80 in the putative transmembrane region, and 3) a novel nucleotide variant (c.691G> C) located in the 3’UTR. A functional effect of the g.–22TGC (4_5) was confirmed by a luciferase expression assay, while the effects of the variants c.239G> A and c.691G> C were predicted using in silico analysis. Although the frequencies of these variants were not significantly different between the infertile and fertile populations, we present evidence that the variants could affect the expression levels or function of SPRASA, thereby affecting a couple's fertility. Larger populations, especially individuals/couples with unexplained infertility, need to be screened for these variants to validate a relationship with fertility

Towards an understanding of neuroscience for science educators

Advances in neuroscience have brought new insights to the development of cognitive functions. These data are of considerable interest to educators concerned with how students learn. This review documents some of the recent findings in neuroscience, which is richer in describing cognitive functions than affective aspects of learning. A brief overview is presented here of the techniques used to generate data from imaging and how these findings have the possibility to inform educators. There are implications for considering the impact of neuroscience at all levels of education – from the classroom teacher and practitioner to policy. This relatively new cross-disciplinary area of research implies a need for educators and scientists to engage with each other. What questions are emerging through such dialogues between educators and scientists are likely to shed light on, for example, reward, motivation, working memory, learning difficulties, bilingualism and child development. The sciences of learning are entering a new paradigm

Mendelian randomisation study of height and body mass index as modifiers of ovarian cancer risk in 22,588 BRCA1 and BRCA2 mutation carriers

Item does not contain fulltextBACKGROUND: Height and body mass index (BMI) are associated with higher ovarian cancer risk in the general population, but whether such associations exist among BRCA1/2 mutation carriers is unknown. METHODS: We applied a Mendelian randomisation approach to examine height/BMI with ovarian cancer risk using the Consortium of Investigators for the Modifiers of BRCA1/2 (CIMBA) data set, comprising 14,676 BRCA1 and 7912 BRCA2 mutation carriers, with 2923 ovarian cancer cases. We created a height genetic score (height-GS) using 586 height-associated variants and a BMI genetic score (BMI-GS) using 93 BMI-associated variants. Associations were assessed using weighted Cox models. RESULTS: Observed height was not associated with ovarian cancer risk (hazard ratio [HR]: 1.07 per 10-cm increase in height, 95% confidence interval [CI]: 0.94-1.23). Height-GS showed similar results (HR = 1.02, 95% CI: 0.85-1.23). Higher BMI was significantly associated with increased risk in premenopausal women with HR = 1.25 (95% CI: 1.06-1.48) and HR = 1.59 (95% CI: 1.08-2.33) per 5-kg/m(2) increase in observed and genetically determined BMI, respectively. No association was found for postmenopausal women. Interaction between menopausal status and BMI was significant (Pinteraction < 0.05). CONCLUSION: Our observation of a positive association between BMI and ovarian cancer risk in premenopausal BRCA1/2 mutation carriers is consistent with findings in the general population

MRI and 2D-CSI MR spectroscopy of the brain in the evaluation of patients with acute onset of neuropsychiatric systemic lupus erythematosus

MRI and 2D-CSI spectroscopy were performed in eight patients with systemic lupus erythematosus who presented with acute onset of neuropsychiatric lupus (NP-SLE), and in seven normal controls to evaluate for differences in metabolic peaks and metabolic ratios between the two groups. Also, the interval change of the metabolic peaks and their ratios during treatment in the NP-SLE patient group was evaluated. Metabolic peaks for N -acetyl-aspartate (NAA), choline (Cho), creatine (Cr), and lactate/lipids (LL) and their ratios (NAA/Cr, NAA/Cho, Cho/Cr, LL/Cr) were determined at initial presentation and 3 and 6 months later. In the eight lupus patients compared to the seven normal controls, NAA/Cho ratios were lower at presentation (1.05 vs 1.25; p  = 0.004) and decreased even further at the three month follow-up (0.92 vs 1.05; p  = 0.008). In contrast, both Cho/Cr (1.42 vs 1.26; p  = 0.026) and LL/Cr ratios (0.26 vs 0.19; p  = 0.002) were higher in the lupus patients at presentation compared to the controls and did not significantly change at three and six months follow-up. The NAA/Cr ratios were lower in the lupus patients compared to the controls at presentation but the difference was not statistically significant. However, the mean NAA/Cr significantly decreased from the initial examination to the three month follow-up (1.42 vs 1.32; p  = 0.049) but did not significantly change from the three to the six month follow-up examinations. The NAA/Cr, Cho/Cr, and NAA/Cho ratios varied significantly ( p  < 0.05, p  < 0.05, p  < 0.05, respectively) between the 17 different locations measured in the brain in all eight patients and seven controls. Both the NAA/Cr ratios and the Cho/Cr ratios were also significantly lower in the gray matter than in the white matter ( p  < 0.0001) in both patients and controls, whereas the LL/Cr and NAA/Cho ratios were not significantly different. In conclusion, 2D-CSI MR spectroscopy may be useful in the early detection of metabolic CNS changes in NP-SLE patients with acute onset of new neurological symptoms as well as in the follow-up after treatment to assess presence and changes in metabolic brain injury. However, although there are detectable differences between normal individuals and lupus patients it is currently unclear whether these relate to the acute episode. Future studies are needed comparing NP-SLE patients with active CNS involvement with those inactive disease.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46668/1/234_2005_Article_1371.pd