The Limit of the Boltzmann Equation to the Euler Equations for Riemann Problems

The convergence of the Boltzmann equaiton to the compressible Euler equations when the Knudsen number tends to zero has been a long standing open problem in the kinetic theory. In the setting of Riemann solution that contains the generic superposition of shock, rarefaction wave and contact discontinuity to the Euler equations, we succeed in justifying this limit by introducing hyperbolic waves with different solution backgrounds to capture the extra masses carried by the hyperbolic approximation of the rarefaction wave and the diffusion approximation of contact discontinuity.Comment: 59 page

Features of the Three Dimensional Structure in the Pacific Sub-surface Layer in Summer

The anomaly of the summer sea temperature is analyzed by a spatial-temporal synthetically rotated orthogonal function (REOF) at three different depths (0 m, 40 m, and 120 m) over the area 110°E~100°W and 30°S~60°N. The spatial-temporal distribution shows that the “signal” of annual anomaly is stronger in the sub-surface layer than the surface layer, and it is stronger in the eastern equatorial Pacific than in the western area. The spatial structure of the sea temperature anomaly at different layers is related to both the ocean current and the interaction of ocean and atmosphere. The temporal changing trend of the sub-surface sea temperature in different areas shows that the annual mean sea temperature increases and the annual variability evidently increases from the 1980s, and these keep the same trend with the increasing El Nino phenomenon very well

Improved performance of diatomite-based dental nanocomposite ceramics using layer-by-layer assembly

To fabricate high-strength diatomite-based ceramics for dental applications, the layer-by-layer technique was used to coat diatomite particles with cationic [poly(allylamine hydrochloride)] and anionic [poly(sodium 4-styrenesulfonate)] polymers to improve the dispersion and adsorption of positively charged nano-ZrO2 (zirconia) as a reinforcing agent. The modified diatomite particles had reduced particle size, narrower size distribution, and were well dispersed, with good adsorption of nano-ZrO2. To determine the optimum addition levels for nano-ZrO2, ceramics containing 0, 20, 25, 30, and 35 wt% nano-ZrO2 were sintered and characterized by the three-point bending test and microhardness test. In addition to scanning electron microscopy, propagation phase-contrast synchrotron X-ray microtomography was used to examine the internal structure of the ceramics. The addition of 30 wt% nano-ZrO2 resulted in the highest flexural strength and fracture toughness with reduced porosity. Shear bond strength between the core and veneer of our diatomite ceramics and the most widely used dental ceramics were compared; the shear bond strength value for the diatomite-based ceramics was found to be significantly higher than for other groups (P < 0.05). Our results show that diatomite-based nanocomposite ceramics are good potential candidates for ceramic-based dental materials

Case report: A case study on the treatment using icaritin soft capsules in combination with lenvatinib achieving impressive PR and stage reduction in unresectable locally progressive pancreatic cancer and a literature review

Background: Pancreatic cancer is one of the most deadly malignancies in the world. It is characterized by rapid progression and a very poor prognosis. The five-year survival rate of pancreatic cancer in China is only 7.2%, which is the lowest among all cancers and the use of combined paclitaxel albumin, capecitabine, and digital has been the clinical standard treatment for advanced pancreatic cancer since 1997. Also, the application of multidrug combinations is often limited by the toxicity of chemotherapy. Therefore, there is an urgent need for a more appropriate and less toxic treatment modality for pancreatic cancer.Case presentation: The patient was a 79-year-old woman, admitted to the hospital with a diagnosis of unresectable locally advanced pancreatic cancer (T3N0M0, stage IIA), with its imaging showing overgrowth of SMV involvement and unresectable reconstruction of the posterior vein after evaluation. As the patient refused chemotherapy, lenvatinib (8 mg/time, qd) and icaritin soft capsules (three tablets/time, bid) were recommended according to our past experience and a few clinical research cases. The tumor lesion was greatly reduced by 57.5% after the treatment, and the extent of vascular involvement also decreased. The aforementioned medication resulted in a significant downstaging of the patient’s tumor.Conclusion: Better results were achieved in the treatment with icaritin soft capsules and lenvatinib in this case. Because of its less toxic effect on the liver and kidney and bone marrow suppression, it was suitable to combine icaritin soft capsules with targeted drugs for treating intermediate and advanced malignancies, which brings hope to patients who cannot or refuse to take chemotherapy

Structurally Diverse Polyketides From the Mangrove-Derived Fungus Diaporthe sp. SCSIO 41011 With Their Anti-influenza A Virus Activities

Influenza A virus (IAV) is a severe worldwide threat to public health and economic development due to its high morbidity and mortality. Marine-derived fungi have been evidenced as a prolific source for the discovery of pharmacologically-active lead compounds. During the course of our search for novel bioactive substances from marine microorganisms, six new polyketides, including two octaketides (1–2), one chromone derivative (13), two highly substituted phthalides (17–18), and one α-pyrone derivative (21) along with 22 known congeners were isolated from a mangrove-associated fungus Diaporthe sp. SCSIO 41011. Their structures were determined by spectroscopic analysis and by comparison with literature data. And the absolute configurations were established according to the specific rotation or electron circular dichroism method. Antiviral evaluation results revealed that compounds 14, 15, 26, and 5-chloroisorotiorin displayed significant anti-IAV activities against three influenza A virus subtypes, including A/Puerto Rico/8/34 H274Y (H1N1), A/FM-1/1/47 (H1N1), and A/Aichi/2/68 (H3N2), with IC50 values in the range of 2.52–39.97 μM. The preliminary structure-activity relationships (SARs) are also discussed. These findings expand the chemical and bioactive diversity of polyketides derived from the genus Diaporthe, and also provide a basis for further development and utilization of chromone, xanthone, and chloroazaphilone derivatives as source of potential anti-viral chemotherapy agents

Hydrodynamic Limit of the Boltzmann Equation with Contact Discontinuities

The hydrodynamic limit for the Boltzmann equation is studied in the case when the limit system, that is, the system of Euler equations contains contact discontinuities. When suitable initial data is chosen to avoid the initial layer, we prove that there exists a unique solution to the Boltzmann equation globally in time for any given Knudsen number. And this family of solutions converge to the local Maxwellian defined by the contact discontinuity of the Euler equations uniformly away from the discontinuity as the Knudsen number $\varepsilon$ tends to zero. The proof is obtained by an appropriately chosen scaling and the energy method through the micro-macro decomposition.Comment: 34 pages. submitte