Mean values of multiplicative functions over function fields

We discuss the mean values of multiplicative functions over function fields. In particular, we adapt the authors’ new proof of Halász’s theorem on mean values to this simpler setting. Several of the technical difficulties that arise over the integers disappear in the function field setting, which helps bring out more clearly the main ideas of the proofs over number fields. We also obtain Lipschitz estimates showing the slow variation of mean values of multiplicative functions over function fields, which display some features that are not present in the integer situation

Potential application of mesh-free SPH method in turbulent river flows

A comprehensive review has been completed on the simulation of turbulent flow over rough beds using mesh-free particle models. Based on the outcomes of this review, an improved Smoothed Particle Hydrodynamics (SPH) method has been developed for open channel flows over a rough bed, in which a mixing length model is used for modeling the 2D turbulence and a drag force equation is proposed for treating the boundary shear. The proposed model was applied to simulate a depth-limited open channel flow over a rough bed surface. The results of the velocity profile and shear stress distribution show a good agreement with the experimental data and existing analytical solutions. This work reveals that in order to correctly model turbulent open channel flow over a rough bed, the treatment of both flow turbulence and bed roughness effect is equally important

CXCR4 expression on circulating pan-cytokeratin positive cells is associated with survival in patients with advanced non-small cell lung cancer

<p>Abstract</p> <p>Background</p> <p>The CXC chemokine, CXCL12, and its receptor, CXCR4 promote metastases of a variety of solid tumors, including non-small cell lung cancer (NSCLC). The expression of CXCR4 on tumor cells may represent a critical biomarker for their propensity to metastasize. This study was performed to evaluate the hypothesis that co-expression of pan-cytokeratin and CXCR4 may be a prognostic marker for patients with advanced NSCLC.</p> <p>Methods</p> <p>We evaluated CXCR4 levels on circulating pan-cytokeratin positive cells from patients with NSCLC. NSCLC tumor and metastases were also assessed for the presence of CXCR4.</p> <p>Results</p> <p>Pan-cytokeratin positive cells were increased in the circulation of patients with NSCLC, as compared to normal control subjects. Patients with pan-cytokeratin +/CXCR4+ = 2,500 cells/ml had a significant improvement in median survival when compared with patients with pan-cytokeratin +/CXCR4+ >2,500 cells/ml (not achieved versus 14 weeks). CXCR4 expression was found on NSCLC tumors and at sites of tumor metastasis.</p> <p>Conclusion</p> <p>This study suggests that CXCR4 may be a prognostic marker in NSCLC, and provides hypothesis-generating results, which may be important in determining metastatic potential. In future studies, we will prospectively evaluate the prognostic significance of pan-cytokeratin/CXCR4+ cells, and determine the mechanisms involved in the regulation of CXCR4 expression on tumor cells in a larger patient population.</p

Serpina3n attenuates granzyme B-mediated decorin cleavage and rupture in a murine model of aortic aneurysm

Granzyme B (GZMB) is a proapoptotic serine protease that is released by cytotoxic lymphocytes. However, GZMB can also be produced by other cell types and is capable of cleaving extracellular matrix (ECM) proteins. GZMB contributes to abdominal aortic aneurysm (AAA) through an extracellular, perforin-independent mechanism involving ECM cleavage. The murine serine protease inhibitor, Serpina3n (SA3N), is an extracellular inhibitor of GZMB. In the present study, administration of SA3N was assessed using a mouse Angiotensin II-induced AAA model. Mice were injected with SA3N (0–120 μg/kg) before pump implantation. A significant dose-dependent reduction in the frequency of aortic rupture and death was observed in mice that received SA3N treatment compared with controls. Reduced degradation of the proteoglycan decorin was observed while collagen density was increased in the aortas of mice receiving SA3N treatment compared with controls. In vitro studies confirmed that decorin, which regulates collagen spacing and fibrillogenesis, is cleaved by GZMB and that its cleavage can be prevented by SA3N. In conclusion, SA3N inhibits GZMB-mediated decorin degradation leading to enhanced collagen remodelling and reinforcement of the adventitia, thereby reducing the overall rate of rupture and death in a mouse model of AAA

Later life sex and Rubin’s ‘Charmed Circle'

Gayle Rubin’s now classic concept of the ‘charmed circle’ has been much used by scholars of sexuality to discuss the ways in which some types of sex are privileged over others. In this paper, I apply the concept of the charmed circle to a new topic– later life – in order both to add to theory about later life sex and to add an older-age lens to thinking about sex hierarchies. Traditional discursive resources around older people’s sexual activities, which treat older people’s sex as inherently beyond the charmed circle, now coexist with new imperatives for older people to remain sexually active as part of a wider project of ‘successful’ or ‘active’ ageing. Drawing on the now-substantial academic literature about later life sex, I discuss some of the ways in which redrawing the charmed circle to include some older people’s sex may paradoxically entail the use of technologies beyond the charmed circle of ‘good, normal, natural, blessed’ sex. Sex in later life also generates some noteworthy inversions in which types of sex are privileged and which treated as less desirable, in relation to marriage and procreation. Ageing may, furthermore, make available new possibilities to redefine what constitutes ‘good’ sex and to refuse compulsory sexuality altogether, without encountering stigma

A new proof of Halasz's theorem, and its consequences

Abstract. Hal´asz’s Theorem gives an upper bound for the mean value of a multiplicative function f. The bound is sharp for general such f, and, in particular, it implies that a multiplicative function with |f(n)| ≤ 1 has either mean value 0, or is “close to” n it for some fixed t. The proofs in the current literature have certain features that are difficult to motivate and which are not particularly flexible. In this article we supply a different, more flexible, proof, which indicates how one might obtain asymptotics, and can be modified to treat short intervals and arithmetic progressions. We use these results to obtain new, arguably simpler, proofs that there are always primes in short intervals (Hoheisel’s Theorem), and that there are always primes near to the start of an arithmetic progression (Linnik’s Theorem)