On the Smarandache reciprocal function and its mean value

The main purpose of this paper is using the elementary and analytic methods to study the mean value distribution properties of Sc(n), and give two interesting mean value formulas for it

A NEW FUNCTION AND ITS MEAN VALUE

The main purpose of this paper is using the elementary method to study the mean value properties of a new function for n, and give a sharp asymptotic formula for it

Developing pedagogic theory: the case of geometry proof teaching

This paper compares the teaching of proof in geometry at the lower secondary school level in the East (China, Japan) and in the West (UK). The aim is to seek to identify teaching strategies that might inform new pedagogic approaches for teaching deductive proof and proving. In the West, much theory focuses on examining the nature of classroom tasks. In the East, the heuristic nature of teaching and the theory of variation are useful as they focus on the dynamic role of the teacher. The paper suggests that the main need is for deeper thinking on the relationship between teachers’ instructional practices and the development of students’ mathematical reasoning

Instructional strategies in explicating the discovery function of proof for lower secondary school students

In this paper, we report on the analysis of teaching episodes selected from our pedagogical and cognitive research on geometry teaching that illustrate how carefully-chosen instructional strategies can guide Grade 8 students to see and appreciate the discovery function of proof in geometr

Improved spectral processing for a multi-mode pulse compression Ka–Ku-band cloud radar system

Cloud radars are widely used in observing clouds and precipitation. However, the raw data products of cloud radars are usually affected by multiple factors, which may lead to misinterpretation of cloud and precipitation processes. In this study, we present a Doppler-spectra-based data processing framework to improve the data quality of a multi-mode pulse-compressed Ka–Ku radar system. Firstly, non-meteorological signal close to the ground was identified with enhanced Doppler spectral ratios between different observing modes. Then, for the Doppler spectrum affected by the range sidelobe due to the implementation of the pulse compression technique, the characteristics of the probability density distribution of the spectral power were used to identify the sidelobe artifacts. Finally, the Doppler spectra observations from different modes were merged via the shift-then-average approach. The new radar moment products were generated based on the merged Doppler spectrum data. The presented spectral processing framework was applied to radar observations of a stratiform precipitation event, and the quantitative evaluation shows good performance of clutter or sidelobe suppression and spectral merging.</p

Improved spectral processing for a multi-mode pulse compression Ka-Ku-band cloud radar system

Cloud radars are widely used in observing clouds and precipitation. However, the raw data products of cloud radars are usually affected by multiple factors, which may lead to misinterpretation of cloud and precipitation processes. In this study, we present a Doppler-spectra-based data processing framework to improve the data quality of a multi-mode pulse-compressed Ka-Ku radar system. Firstly, non-meteorological signal close to the ground was identified with enhanced Doppler spectral ratios between different observing modes. Then, for the Doppler spectrum affected by the range sidelobe due to the implementation of the pulse compression technique, the characteristics of the probability density distribution of the spectral power were used to identify the sidelobe artifacts. Finally, the Doppler spectra observations from different modes were merged via the shift-then-average approach. The new radar moment products were generated based on the merged Doppler spectrum data. The presented spectral processing framework was applied to radar observations of a stratiform precipitation event, and the quantitative evaluation shows good performance of clutter or sidelobe suppression and spectral merging.Peer reviewe

The Marine-Derived Oligosaccharide Sulfate (MdOS), a Novel Multiple Tyrosine Kinase Inhibitor, Combats Tumor Angiogenesis both In Vitro and In Vivo

Despite the emerging success of multi-targeted protein tyrosine kinase (PTK) inhibitors in cancer therapy, significant side effects and resistance concerns seems to be avoided unlikely. The aim of the present study was to identify novel multi-targeting PTK inhibitors. The kinase enzymatic activities were measured by enzyme-linked immunosorbent assay (ELISA). The antiproliferative activities in human microvascular endothelial cells (HMECs) were evaluated by sulforhodamine (SRB) assay. The phosphorylation of kinases and their downstream molecules was probed by western blot analysis. The binding mode between MdOS and PTKs was profiled by surface plasmon resonance (SPR) approach and molecular simulation. Tube formation assay, rat aortic ring method and chicken chorioallantoic membrane assay were combined to illustrate the in vitro and in vivo anti-angiogenic effects. Results indicated that MdOS, a novel marine-derived oligosaccharide sulfate, exhibited a broad-spectrum PTK inhibitory action. At an enzymatic level, MdOS inhibited HER2, EGFR, VEGFR, PDGFR, c-Kit, FGFR1 and c-Src, with little impact on FGFR2. In cellular settings, MdOS inhibited phosphorylation of PTKs, exemplified by HER2, EGFR and VEGFR2, and downstream molecules of Erk1/2 and AKT. Further studies demonstrated that MdOS acted as an ATP-competitive inhibitor via directly binding to the residues of entrance rather than those of the ATP-binding pocket. Furthermore, MdOS inhibited proliferation and tube formation of HMECs, arrested microvessel outgrowth of rat aortic rings and hindered the neovascularization of chick allantoic membrane. Taken together, results presented here indicated that MdOS exhibited anti-angiogenic activity in a PTK-dependent manner and make it a promising agent for further evaluation in PTK-associated cancer therapy