Kepler's third law of n-body system

正Newton’s gravitational law and its derived Kapler’s orbit of planetary motions are the very first triumph of science,which confirms that a purely human’s invention of mathematics is able to accurately describe observations in nature.For the     

Cephalotanins A–D,Four Norditerpenoids Represent Three Highly Rigid Carbon Skeletons from Cephalotaxus sinensis

Four polycyclic norditerpenoids, cephalotanins A–D ( 1 – 4 ) representing three unprecedented carbon skeletons with highly rigid ring systems, were isolated from Cephalotaxus sinensis and structurally characterized by a combination of various methods. Compounds 1 and 2 are new skeletal norditerpenoid trilactones, while 3 and 4 are two norditerpenoids featuring different new carbon skeletons. Biosynthetic pathways for 1 – 4 were proposed by involving diverse and very fascinating chemical events with the coexisting cephalotane troponoids as the precursors. Compound 1 exhibited good NF‐κB inhibition with an IC₅₀ value of 4.12±0.61 μΜ.     

Recent studies of agent incentives in internet resource allocation and pricing

Market makers choose and design market rules to serve certain objectives, such as to maximize revenue from the sales in the case of a single seller and multiple buyers. Given such rules, market participants play against each other to maximize their utility function values on goods acquired, possibly by hiding or misrepresenting their information needed in the implementation of market rules. Today’s Internet economy has changed the information collection process and may make some of the assumptions of market rule implementation obsolete. Here we make a fresh review of works on this challenge on the Internet where new economic systems operate.     

Stacking‐Induced Diamagnetic/Paramagnetic Conversion of Imidazo[1,2‐a]pyridin‐2(3 H)‐one Derivatives: Near‐Infrared Absorption and Magnetic Properties in the Solid State

Herein, we present three imidazo[1,2‐a]pyridin‐2(3 H)‐one derivatives that are diamagnetic in solution, but paramagnetic in the solid state, possibly owing to a stacking‐induced formation of phenoxide‐type radicals. Notably, a larger bathochromic shift of the absorption (even up to the near‐ infrared region) of these three compounds was observed in the solid state than in solution, which was attributable to the ordered columnar stacking arrangements or their single‐electron character as radicals in the solid state. Interestingly, compared to that in solution, (E)‐3‐(pyridin‐4′‐ylmethylene)imidazo[1,2‐a]pyridine 2(3 H)‐one displayed a largely red‐shifted emission (centered at 660 nm, with tailing above 800 nm) in the solid state. A larger bathochromic shift (260 nm) of the emission is an indication of better order and tight stacking in the solid state, which is brought about by the rigid and polar acceptor. These three compounds also reveal different magnetic susceptibilities at 300 K, thus implying that they possess various columnar stacking structures. Most interestingly, these three radicals exhibit unusual ferromagnetic‐to‐antiferromagnetic phase transitions, which can be attributed to anisotropic contraction and non‐uniform slippage of the columnar stacking chains.     

Synthesis and Characterization of Iron Nanowires

The iron nanowires can be fabricated via the process in which sodium borohydride reduces iron salts in external magnetic field. The iron nanowires are found to be covered by passivated layers of iron oxide which prevent the oxidation of iron nanowires. In this process, the boron will include in iron nanowires. The average length and diameter of iron nanowires is around 1.2 micrometers and 60 nanometers, respectively. According to ICP results, the contents of B and Fe are about 1.98 wt% and 87.04 wt%, respectively, in iron nanowires. A wide variety of equipment is used to investigate the morphological, microchemical, and structural characteristics of the newly synthesized iron nanowires ––– e.g., XRD, FE‐SEM, HR‐TEM, VSM and XANES. XANES analysis indicates the boron in iron nanowires exists in the form of B₂O₃. The saturation magnetization and the coercive force of iron nanowires are 157.93 emu/g and 9.74 Oe, respectively. In‐situ images of synthesized iron nanowires during reduction process in magnetic field are observed by NSRRC transmission X‐ray microscope. Thus, this study develop a novel process to produce iron nanowires with large quantitates and can control its length and diameter by various the concentration of precursors for various applications.