An Application of Nash-Moser Theorem to Smooth Solutions of One-Dimensional Compressible Euler Equation with Gravity

We study one-dimensional motions of polytropic gas governed by the compressible Euler equations. The problem on the half space under a constant gravity gives an equilibrium which has free boundary touching the vacuum and the linearized approximation at this equilibrium gives time periodic solutions. But it is not easy to justify the existence of long-time true solutions for which this time periodic solution is the first approximation. The situation is in contrast to the problem of free motions without gravity. The reason is that the usual iteration method for quasilinear hyperbolic problem cannot be used because of the loss of regularities which causes from the touch with the vacuum. Interestingly, the equation can be transformed to a nonlinear wave equation on a higher dimensional space, for which the space dimension, being larger than 4, is related to the adiabatic exponent of the original one-dimensional problem. We try to find a family of solutions expanded by a small parameter. Applying the Nash-Moser theory, we justify this expansion.The application of the Nash-Moser theory is necessary for the sake of conquest of the trouble with loss of regularities, and the justification of the applicability requires a very delicate analysis of the problem

The integration of storm water flooding and thermal stress potential in Tainan (Taiwan) and Groningen (Netherlands)

Stormwater flooding and thermal stresses of citizens are two important phenomena for most of the dense urban area. Due to the climate change, these two phenomena will occur more frequently and cause serious problems. Therefore, the sectors for public health and disaster management should be able to assess the vulnerability to stormwater flooding and thermal stress. To achieve this goal, two cities in different climate regions and with different urban context have been selected as the pilot areas, i.eY., Tainan, Taiwan and Groningen, Netherlands. Stormwater flooding and thermal stress maps will be produced for both cities for further comparison. The flooding map indicates vulnerable low lying areas, where the thermal stress map indicates high Physiological Equivalent Temperature (PET) values (thermal comfort) in open areas without shading. The combined map indicates the problem areas of flooding and thermal stress and can be used by urban planners and other stakeholders to improve the living environment

Enhancement of polar phases in PVDF by forming PVDF/SiC nanowire composite

Different contents of silicon carbide (SiC) nanowires were mixed with Poly(vinylidene fluoride) (PVDF) to facilitate the polar phase crystallization. It was shown that the annealing temperature and SiC content affected on the phase and crystalline structures of PVDF/SiC samples. Furthermore, the addition of SiC nanowire enhanced the transformation of non-polar α phase to polar phases and increased the relative fraction of β phase in PVDF. Due to the nucleating agent mechanism of SiC nanowires, the ion-dipole interaction between the negatively charged surface of SiC nanowires and the positive CH2 groups in PVDF facilitated the formation of polar phases in PVDF

Evaluation of structural transformation in 2D metal–organic frameworks based on a 4,4′-sulfonyldibenzoate linker: microwave-assisted solvothermal synthesis, characterization and applications

Structural transformation has been observed in 2D MOFs.</p

Gastric adenocarcinoma of the fundic gland: A review of clinicopathological characteristics, treatment and prognosis

Gastric adenocarcinoma of the fundic gland is a rare, well-differentiated gastric cancer entity, and very few patients transition to poorly differentiated tubular adenocarcinoma during progression. Gastric adenocarcinoma of the fundic gland originates from the mucosa of the gastric fundic gland, usually without chronic gastritis or intestinal metaplasia. Histologically, the tumor cells are closely arranged to form anastomosing tubular glands, and more than 95% of tumor cells differentiate towards chief cells. Most gastric adenocarcinoma of the fundic gland cases are characterized by submucosal involvement, but the tumor volume is usually small, with lymphatic and vascular invasion rarely observed. Therefore, endoscopic submucosal dissection can be an ideal treatment, leading to a favorable prognosis, and recurrence and metastasis of the disease are uncommon