Mathematics with Only Rods

We discuss in this expository paper the rod system used in ancient China based on the mathematical classic work of Sun Zi, with a focus on application to solving systems of linear equations. The mathematics involved is authentic and beautiful, and we believe it is also of interest from historical, cultural, and pedagogical perspectives

Mathematics with Only Rods

We discuss in this expository paper the rod system used in ancient China based on the mathematical classic work of Sun Zi, with a focus on application to solving systems of linear equations. The mathematics involved is authentic and beautiful, and we believe it is also of interest from historical, cultural, and pedagogical perspectives

Study on compressive stress-strain relationship of ultra-high performance concrete with coarse aggregates under and after high temperatures

Uniaxial compression tests are conducted on ultra-high performance concrete (UHPC) with different volume fractions of coarse aggregates (0 %, 10 %, 20 %, and 30 %) at temperatures ranging from room temperature to 900°C, both during and after high-temperature exposure. The compressive failure modes and the stress-strain curves of the ultra-high performance concrete with coarse aggregates (CA-UHPC) under and after high temperatures are obtained. A systematic analysis of the key characteristic parameters of the stress-strain curve, including axial compressive strength, elastic modulus, and peak strain, is carried out, and respective temperature-dependent calculation formulas are proposed. Experimental results show that the failure modes under and after high temperatures are similar, both exhibiting shear failure. It is found that both the temperature and the coarse aggregate contents affect the shape of the stress-strain curve. The uniaxial compressive performance of the CA-UHPC under and after high temperatures is compared. Finally, the uniaxial compressive stress-strain relationships of the CA-UHPC under and after high temperatures are established, considering the temperature, coarse aggregate content, and steel fiber content

Geothermal driving force: A new additional non-gravity action driving the migration of geothermal water in the Xinzhou geothermal field of Yangjiang, Guangdong

The "nested multilevel flow system" summarized by Tóth and the gravity driven groundwater flow system theory summarized by Zhang Renquan et al are the important theoretical basis for groundwater migration.Groundwater flow may be affected by gravitational potential, compaction potential and tectonic compression force.However, the anomalous phenomenon that the groundwater recharge area is lower than the groundwater drainage area is found in the convective hydrothermal system.As the temperature rises, the density of geothermal water decreases and the pressure increases, and the actual pressure head of geothermal water increases, which is the physical basis for this abnormal phenomenon.This paper defines the additional pressure head as "geothermal driving force", which is related to the temperature, salinity and viscosity of geothermal water.And we propose a quantitative calculation method.In the case of Xinzhou geothermal field in Yangjiang, Guangdong Province, the starting point of the geothermal driving force is located at the deepest part of the geothermal water cycle of 4.34 km, where the standard head of the geothermal driving force generated by temperature rise is +351.59 m, and the standard head of the geothermal driving force generated by salinity increase is -2.78 m, and the standard head of total geothermal driving force is +348.81 m.The higher the geothermal water temperature is, the greater the geothermal driving force is.The greater the salinity, the smaller the geothermal driving force.The additional supporting effect of geothermal driving force can accelerate the circulation of groundwater in hydrothermal system

Optimal social welfare: A many-to-many data transaction mechanism based on double auctions

With the development of Big Data and the Internet of Things (IoT), the data value is more significant in both academia and industry. Trading can achieve maximal data value and prepare data for smart city services. Due to data's unique characteristics, such as dispersion, heterogeneity and distributed storage, an unbiased platform is necessary for the data trading market with rational trading entities. Meanwhile, there are multiple buyers and sellers in a practical data trading market, and this makes it challenging to maximize social welfare. To solve these problems, this paper proposes a Social-Welfare-Oriented Many-to-Many Trading Mechanism (SOMTM), which integrates three entities, a trading process and an algorithm named Many-to-Many Trading Algorithm (MMTA). Based on the market scale, market dominated-side and market fixed-side, simulations verify the convergency, economic properties and efficiency of SOMTM

Comparison of the Transcriptomes of Mouse Skin Derived Precursors (SKPs) and SKP-Derived Fibroblasts (SFBs) by RNA-Seq

<div><p>Skin-derived precursors (SKPs) from dermis possess the capacities of self-renewal and multipotency. <i>In vitro</i> and <i>in vivo</i> studies demonstrated that they can differentiate into fibroblasts. However, little is known about the molecular mechanism of the differentiation of SKPs into fibroblasts. Here we compare the transcriptomes of mouse SKPs and SKP-derived fibroblasts (SFBs) by RNA-Seq analysis, trying to find differences in gene expression between the two kinds of cells and then elucidate the candidate genes that may play important roles in the differentiation of SKPs into fibroblasts. A total of 1971 differentially expressed genes (DEGs) were identified by RNA-Seq, which provided abundant data for further analysis. Gene Ontology enrichment analysis revealed that genes related to cell differentiation, cell proliferation, protein binding, transporter activity and membrane were significantly enriched. The most significantly up-regulated genes <i>Wnt4</i>, <i>Wisp2</i> and <i>Tsp-1</i> and down-regulated genes <i>Slitrk1</i>, <i>Klk6</i>, <i>Agtr2</i>, <i>Ivl</i>, <i>Msx1</i>, <i>IL15</i>, <i>Atp6v0d2</i>, <i>Kcne1l</i> and <i>Thbs4</i> may play important roles in the differentiation of SKPs into fibroblasts. KEGG analysis showed that DEGs were significantly enriched in the TGF-β signaling pathway, Wnt signaling pathway and Notch signaling pathway, which have been previously proven to regulate the differentiation and self-renewal of various stem cells. These identified DEGs and pathways could facilitate further investigations of the detailed molecular mechanisms, making it possible to take advantage of the potential therapeutic applications of SKPs in skin regeneration in the future.</p></div

DEGs between SKPs and SFBs.

<p>(A) The numbers of DEGs.(B) Scattered plot of DEGs.</p