On the fast Khintchine spectrum in continued fractions

For $x\in [0,1)$, let $x=[a_1(x), a_2(x),...]$ be its continued fraction expansion with partial quotients ${a_n(x), n\ge 1}$. Let $\psi : \mathbb{N} \rightarrow \mathbb{N}$ be a function with $\psi(n)/n\to \infty$ as $n\to \infty$. In this note, the fast Khintchine spectrum, i.e., the Hausdorff dimension of the set E(\psi):=\Big{x\in [0,1): \lim_{n\to\infty}\frac{1}{\psi(n)}\sum_{j=1}^n\log a_j(x)=1\Big} is completely determined without any extra condition on $\psi$.Comment: 10 page

On Khintchine exponents and Lyapunov exponents of continued fractions

Assume that $x\in [0,1)$ admits its continued fraction expansion $x=[a_1(x), a_2(x),...]$. The Khintchine exponent $\gamma(x)$ of $x$ is defined by $\gamma(x):=\lim\limits_{n\to \infty}\frac{1}{n}\sum_{j=1}^n \log a_j(x)$ when the limit exists. Khintchine spectrum $\dim E_\xi$ is fully studied, where $E_{\xi}:=\{x\in [0,1):\gamma(x)=\xi\} (\xi \geq 0)$ and $\dim$ denotes the Hausdorff dimension. In particular, we prove the remarkable fact that the Khintchine spectrum $\dim E_{\xi}$, as function of $\xi \in [0, +\infty)$, is neither concave nor convex. This is a new phenomenon from the usual point of view of multifractal analysis. Fast Khintchine exponents defined by $\gamma^{\phi}(x):=\lim\limits_{n\to\infty}\frac{1}{\phi(n)} \sum_{j=1}^n \log a_j(x)$ are also studied, where $\phi (n)$ tends to the infinity faster than $n$ does. Under some regular conditions on $\phi$, it is proved that the fast Khintchine spectrum $\dim (\{x\in [0,1]: \gamma^{\phi}(x)= \xi \})$ is a constant function. Our method also works for other spectra like the Lyapunov spectrum and the fast Lyapunov spectrum.Comment: 37 pages, 5 figures, accepted by Ergodic Theory and Dyanmical System

Usnic acid ameliorates bleomycin-induced pulmonary fibrosis in mice via inhibition of inflammatory responses and oxidative stress

Purpose: To Investigate the effect of usnic acid (UA) on bleomycin (BLM)-induced pulmonary fibrosis in mice, and the underlying mechanism. Methods: Male Kunming mice with bleomycin-induced pulmonary fibrosis (PF) were exposed to different concentrations of usnic acid. Lung coefficient and histopathological changes were determined, while MDA, superoxide dismutase (SOD) activity, and expression levels of hydroxyproline, tumor necrosis factor-α, interleukins-1β & 6, and transforming growth factor-β1 were assayed in lung homogenates. Results: UA significantly mitigated lung coefficient and histopathological changes in mice. Compared to the bleomycin group, MDA level was significantly reduced while the content of SOD markedly increased after UA pretreatment (p < 0.05). Moreover, UA significantly reduced the expression levels of all the parameters, relative to bleomycin group (p < 0.05). Conclusion: These results indicate that UA protects mice against bleomycin-induced PF via a mechanism associated with attenuation of pro-oxidant stress and inflammation. Therefore, UA has therapeutic potential for the management of pulmonary fibrosis

The Characteristics of Seebeck Coefficient in Silicon Nanowires Manufactured by CMOS Compatible Process

Silicon nanowires are patterned down to 30 nm using complementary metal-oxide-semiconductor (CMOS) compatible process. The electrical conductivities of n-/p-leg nanowires are extracted with the variation of width. Using this structure, Seebeck coefficients are measured. The obtained maximum Seebeck coefficient values are 122 μV/K for p-leg and −94 μV/K for n-leg. The maximum attainable power factor is 0.74 mW/m K2 at room temperature

Comparative Proteomic Approach Identifies Pkm2 and Cofilin-1 as Potential Diagnostic, Prognostic and Therapeutic Targets for Pulmonary Adenocarcinoma

Lung cancer is the leading cause of cancer-related death in the world. Non-small cell lung carcinomas (Non-SCLC) account for almost 80% of lung cancers, of which 40% were adenocarcinomas. For a better understanding of the molecular mechanisms behind the development and progression of lung cancer, particularly lung adenocarcinoma, we have used proteomics technology to search for candidate prognostic and therapeutic targets in pulmonary adenocarcinoma. The protein profile changes between human pulmonary adenocarcinoma tissue and paired surrounding normal tissue were analyzed using two-dimensional polyacrylamide gel electrophoresis (2-DE) based approach. Differentially expressed protein-spots were identified with ESI-Q-TOF MS/MS instruments. As a result, thirty two differentially expressed proteins (over 2-fold, p<0.05) were identified in pulmonary adenocarcinoma compared to normal tissues. Among them, two proteins (PKM2 and cofilin-1), significantly up-regulated in adenocarcinoma, were selected for detailed analysis. Immunohistochemical examination indicated that enhanced expression of PKM2 and cofilin-1 were correlated with the severity of epithelial dysplasia, as well as a relatively poor prognosis. Knockdown of PKM2 expression by RNA interference led to a significant suppression of cell growth and induction of apoptosis in pulmonary adenocarcinoma SPC-A1 cells in vitro, and tumor growth inhibition in vivo xenograft model (P<0.05). In addition, the shRNA expressing plasmid targeting cofilin-1 significantly inhibited tumor metastases and prolonged survival in LL/2 metastatic model. While additional works are needed to elucidate the biological significance and molecular mechanisms of these altered proteins identified in this study, PKM2 and cofilin-1 may serve as potential diagnostic and prognostic biomarkers, as well as therapeutic targets for pulmonary adenocarcinoma

A mass vaccination campaign targeting adults and children to prevent typhoid fever in Hechi; Expanding the use of Vi polysaccharide vaccine in Southeast China: A cluster-randomized trial

BACKGROUND: One of the goals of this study was to learn the coverage, safety and logistics of a mass vaccination campaign against typhoid fever in children and adults using locally produced typhoid Vi polysaccharide (PS) and group A meningococcal PS vaccines in southern China. METHODS: The vaccination campaign targeted 118,588 persons in Hechi, Guangxi Province, aged between 5 to 60 years, in 2003. The study area was divided into 107 geographic clusters, which were randomly allocated to receive one of the single-dose parenteral vaccines. All aspects regarding vaccination logistics, feasibility and safety were documented and systematically recorded. Results of the logistics, feasibility and safety are reported. RESULTS: The campaign lasted 5 weeks and the overall vaccination coverage was 78%. On average, the 30 vaccine teams gave immunizations on 23 days. Vaccine rates were higher in those aged ≤ 15 years (90%) than in adolescents and young adults (70%). Planned mop-up activities increased the coverage by 17%. The overall vaccine wastage was 11%. The cold chain was maintained and documented. 66 individuals reported of adverse events out of all vaccinees, where fever (21%), malaise (19%) and local redness (19%) were the major symptoms; no life-threatening event occurred. Three needle-sharp events were reported. CONCLUSION: The mass immunization proved feasible and safe, and vaccine coverage was high. Emphasis should be placed on: injection safety measures, community involvement and incorporation of mop-up strategies into any vaccination campaign. School-based and all-age Vi mass immunizations programs are potentially important public health strategies for prevention of typhoid fever in high-risk populations in southern China