Nonlinear Instability for Nonhomogeneous Incompressible Viscous Fluids

We investigate the nonlinear instability of a smooth steady density profile solution of the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field, including a Rayleigh-Taylor steady-state solution with heavier density with increasing height (referred to the Rayleigh-Taylor instability). We first analyze the equations obtained from linearization around the steady density profile solution. Then we construct solutions of the linearized problem that grow in time in the Sobolev space Hk, thus leading to a global instability result for the linearized problem. With the help of the constructed unstable solutions and an existence theorem of classical solutions to the original nonlinear equations, we can then demonstrate the instability of the nonlinear problem in some sense. Our analysis shows that the third component of the velocity already induces the instability, this is different from the previous known results.Comment: 24 page

A Study on the Level of Market Efficiency in Five Markets

This paper examines the weak form market efficiency in five stock markets, China (CSI 300 index), Hong Kong (HSI), Japan (Nikkei 225), the US (NASDAQCOM) and Germany (DAX) from the perspective of random walk hypothesis. The methods for testing random walk are autocorrelation, runs test, strategy. This paper also examine three calendar effects in all stock markets: January effect, the-turn-of-the-month effect (the TOM effect), the day-of-the-week-effect (the DOW effect). The results are: (1)From the viewpoint of autocorrelation, the most efficient market among five stock markets is the market in Hong Kong while strong evidence of autocorrelation is found in China, CSI 300 and The US, NASDAQCOM. (2) The results of runs tests do not found evidence against randomness in daily returns for CSI 300, HSI from 2006 to 2020 but find a little evidence for Nikkei 225, NASDAQCOM, DAX. The higher level of efficient markets among five stock markets are the markets in China and Hong Kong. (3) The strategy analyzed in this paper does not find evidence indicating inefficient market for five indexes. (4) January effect did not exist in five indexes. (5) All five indexes are characterized with a TOM effect in different level and therefore the hypothesis of an efficient market is rejected for five markets. (6) All five indexed are found the-day-of-week effect which also indicates inefficient stock markets. we conclude that all five market are not efficient from 2006 to 2020. (7) After the consideration of time-varying volatility, we found January effect in Nikkei 225 in returns. Except Nikkei 225 all the other indexes are verified with the turn-of-the-month-effect and only CSI 300 are verified with the day-of-the-week-effect in returns.* Revised： [21-24 , 2021

A Study on the Level of Market Efficiency Based on CSI 300 and 300 Constituent Stocks

This paper analyzes CSI 300 index and its 300 constituent stocks with seven market efficiency measures: autocorrelation of daily returns, autocorrelation of absolute daily returns, runs test, forecast ability of other historical data on daily return (the predictive ability of yesterday’s change of trading volume on today’s return in this paper), the return of specific trading strategy, variance ratio and pricing errors contained in daily return. We do a Principal component analysis to convert these indicators to a single indicator representing the market efficiency. Then we try to find the co-movement among different measures through correlation coefficient and among different stocks through OLS regression: market efficiency values of individual stocks are regressed on market efficiency values of CSI 300 for seven measures respectively. We found that different market efficiency measures are indeed consistent to each other to some extent and the individual stocks are somewhat consistent with the whole market indicating there is a systematic market efficiency in stock market in China. Our finding also support the idea that the market efficiency in Chinese stock market is changing all time without showing a clear upward trend from 2005 to 2020. In the end, we set three hypotheses to explain relatively high level of market efficiency in 2005, 2012, 2017 and 2019: the ability of market detecting and reacting to pricing errors, public information or private information is becoming quickly and accurately. We found that when the market is in a bad condition, the market contains more pricing-errors in daily returns and the ability of market detecting and reacting to private information is also bad

A Study on Market Efficiency Using Data from Shanghai Stock Exchange and Shenzhen Stock Exchange

This paper studies market efficiency from weak form aspect using data of Shanghai Stock Exchange composite index (SSEC) and Shenzhen Stock Exchange composite index (SZSEC) under expected return theory. Some classical methods are used to examine the features of stock returns and a little evidence against mutually independency, random walk of returns, and sub-martingale of stock prices is found. A notion of a new simple statistical test based on information set for judgement of market efficiency is proposed. Through hypothesis tests, evidence indicating inefficient markets around 2008, 2011 and 2018 under expected return theory is found. It is a new finding that SZSEC is more sensitive to information and therefore may be more appealing to investors than SSEC. Moreover, there is an another new finding that when market extends in size the degree of whole market efficiency declines. From the relationship between market efficiency and volatility, volatility is not a very good criterion for market efficiency but some rough rules can be concluded to help investors make their decisions on what time to conduct their own strategies. Finally, the results suggest that it is the time to think about strategies

Analysis Method Research on the Importance of the Factors Influencing the Flow Safety of Heated Crude Pipelines

Analyzing the importance of the factors which influence the flow safety of the heated oil pipeline is an important part of the whole assessment process, which is of great significance on the results analysis, phenomenon explanation, and risk control after the assessment. Focusing on the problems in the influencing factors' importance analysis on crude oil pipeline flow assurance assessment, a new method to analyze the importance of the influencing factors is proposed which considers the factors' fluctuations. Based on the actual probability distribution of the influencing factors during the stable operation of the pipeline, a new measure standard of the factors' importance is defined which can measure different factors importance and realize the importance sorting of each factor. The influence of different factors on the inlet temperature is taken as an example. The importance analysis and sensitivity analysis of the influencing factors on the actual pipeline have been done, the results of which are also compared. The results show that this method can combine the pipeline actual operating conditions and the influencing factors' actual fluctuation, reflecting the effect on the results' importance in different values of each factor and different fluctuation. This method can make comprehensive analysis on the importance of the influencing factors effectively

Long-Term Prognostic Analysis after Endoscopic Endonasal Surgery for Olfactory Neuroblastoma: A Retrospective Study of 13 Cases.

To summarize the characteristics and long-term outcomes of olfactory neuroblastoma through the analysis of 13 cases in single institution, with the assessment of treatment modality, prognostic factors.A retrospective study of thirteen cases diagnosed as olfactory neuroblastoma and underwent combined treatments during the period 2000-2010. Statistical analysis was performed to search for prognostic factors and compared different treatment modalities.13 patients were enrolled in this study, including 8 male and 5 female, ranging from 15 to 69 (median 43) years old. One patient at stage A was only treated with endoscopic endonasal surgery (EES). Seven patients were treated with preoperative radiotherapy and EES, two with EES and postoperative radiotherapy, and the other three with combined radiotherapy and chemotherapy. The range of follow-up time varied from 23 to 116 months (median 65 months). The 5-year overall survival rate was 46.2% (6/13). To date, these thirteen patients have not suffered local recurrences while two patients had lymph node recurrences and one had distant metastasis in the bone marrow. In 13 patients, 61.5% were diagnosed as late T stage (T3/4), 69.2% late Kadish stage (C/D) and 53.8% were high Hyams grade (I/ II), which indicated poor prognosis. Related prognostic factors were the TNM stage (T stage P = 0.028, N stage P = 0.000, M stage P = 0.007), Kadish stage (P = 0.025) and treatment modality (P = 0.015).Late stage of TNM and Kadish staging system indicated a poor prognosis. Combined treatment modality, including endoscopic endonasal surgery, achieved a better outcome than non-surgical approach

Involvement of 5f Orbitals in the Covalent Bonding between the Uranyl Ion and Trialkyl Phosphine Oxide: Unraveled by Oxygen K-Edge X-ray Absorption Spectroscopy and Density Functional Theory.

Monodentate organophosphorus ligands have been used for the extraction of the uranyl ion (UO22+) for over half a century and have exhibited exceptional extractability and selectivity toward the uranyl ion due to the presence of the phosphoryl group (O═P). Tributyl phosphate (TBP) is the extractant of the world-renowned PUREX process, which selectively recovers uranium from spent nuclear fuel. Trialkyl phosphine oxide (TRPO) shows extractability toward the uranyl ion that far exceeds that for other metal ions, and it has been used in the TRPO process. To date, however, the mechanism of the high affinity of the phosphoryl group for UO22+ remains elusive. We herein investigate the bonding covalency in a series of complexes of UO22+ with TRPO by oxygen K-edge X-ray absorption spectroscopy (XAS) in combination with density functional theory (DFT) calculations. Four TRPO ligands with different R substituents are examined in this work, for which both the ligands and their uranyl complexes are crystallized and investigated. The study of the electronic structure of the TRPO ligands reveals that the two TRPO molecules, irrespective of their substituents, can engage in σ- and π-type interactions with U 5f and 6d orbitals in the UO2Cl2(TRPO)2 complexes. Although both the axial (Oyl) and equatorial (Oeq) oxygen atoms in the UO2Cl2(TRPO)2 complexes contribute to the X-ray absorption, the first pre-edge feature in the O K-edge XAS with a small intensity is exclusively contributed by Oeq and is assigned to the transition from Oeq 1s orbitals to the unoccupied molecular orbitals of 1b1u + 1b2u + 1b3u symmetries resulting from the σ- and π-type mixing between U 5f and Oeq 2p orbitals. The small intensity in the experimental spectra is consistent with the small amount of Oeq 2p character in these orbitals for the four UO2Cl2(TRPO)2 complexes as obtained by Mulliken population analysis. The DFT calculations demonstrate that the U 6d orbitals are also involved in the U-TRPO bonding interactions in the UO2Cl2(TRPO)2 complexes. The covalent bonding interactions between TRPO and UO22+, especially the contributions from U 5f orbitals, while appearing to be small, are sufficiently responsible for the exceptional extractability and selectivity of monodentate organophosphorus ligands for the uranyl ion. Our results provide valuable insight into the fundamental actinide chemistry and are expected to directly guide actinide separation schemes needed for the development of advanced nuclear fuel cycle technologies

CT scans, PET scans and MRI findings of the tumor and metastatic cervical lymph nodes.

<p>The tumor was seen in the left nasal cavity, maxillary and ethmoidal sinus on CT scans (A1, B1and C1, red stars) and PET scans (A2, B2 and C2, red stars). MRI T1-weighted image showed a low-intense mass (A3 and B3, red circles) while T2-weighted image showed a relatively high-intense mass (C3 and D3, red circles). Metastatic cervical lymph nodes can been seen on CT scans (C1 and D1, yellow arrows) but more prominent on the PET scans (C2 and D2, yellow arrows).</p