Local uniqueness of vortices for 2D steady Euler flow

We study the steady planar Euler flow in a bounded simply connected domain, where the vortex function is $f=t_+^p$ with $p>0$ and the vorticity strength is prescribed. By studying the location and local uniqueness of vortices, we prove that the vorticity method and the stream function method actually give the same solution. We also show that if the vorticity of flow is located near an isolated minimum point and non-degenerate critical point of the Kirchhoff-Routh function, it must be stable in the nonlinear sense.Comment: 47 pages. arXiv admin note: text overlap with arXiv:1703.0986

Overdetermined boundary value problems with strongly nonlinear elliptic PDE

We consider the strongly nonlinear elliptic Dirichlet problem in a connected bounded domain, overdetermined with the constant Neumann condition F(∇u) = c on the boundary. Here F is convex and positively homogeneous of degree 1, and its polar F ∗ represents the anisotropic norm on R n. We prove that, if this overdetermined boundary value problem admits a solution in a suitable weak sense, then Ω must be of Wulff shape

On a nonlocal problem for a confined plasma in a Tokamak

summary:The paper deals with a nonlocal problem related to the equilibrium of a confined plasma in a Tokamak machine. This problem involves terms $u'_{\ast }(|u>u(x)|)$ and $|u>u(x)|$, which are neither local, nor continuous, nor monotone. By using the Galerkin approximate method and establishing some properties of the decreasing rearrangement, we prove the existence of solutions to such problem

Effects of the combination of loxoprofen sodium and sodium hyaluronate on osteoarthritis and knee function

Purpose: To determine the treatment efficacy of the combination of loxoprofen sodium and sodium hyaluronate in osteoarthritis (OA), and its role in knee joint function. Methods: 98 patients with OA admitted to Guang'an People's Hospital, Sichuan, China were allocated into control group (CNG, given loxoprofen sodium n, = 51) and study group (SG, given loxoprofen sodium and sodium hyaluronate, n = 47). Both groups were compared in terms of the levels of inflammatory factor, Lysholm, VAS, WOMAC scores, treatment effects, serum MDA, NO, SOD levels, adverse effects, and blood rheology indices. Results: The study group had higher SOD levels, and higher BALP and BGP than CNG (p < 0.05). SG had lower TRACP-5b and blood rheological indices than CNG (p < 0.05). The difference in the incidence of adverse reactions was not statistically significant between the two groups (p > 0.05). Conclusion: The combination of loxoprofen sodium and sodium hyaluronate effectively improves the function and blood rheological indices of knee joints. It reduces the occurrence of adverse reactions and the level of pain in patients with OA, and improves OA prognosis. However further clinical trials are required prior to application in clinical practice

Methylprednisolone as Adjunct to Endovascular Thrombectomy for Large-Vessel Occlusion Stroke

Importance It is uncertain whether intravenous methylprednisolone improves outcomes for patients with acute ischemic stroke due to large-vessel occlusion (LVO) undergoing endovascular thrombectomy. Objective To assess the efficacy and adverse events of adjunctive intravenous low-dose methylprednisolone to endovascular thrombectomy for acute ischemic stroke secondary to LVO. Design, Setting, and Participants This investigator-initiated, randomized, double-blind, placebo-controlled trial was implemented at 82 hospitals in China, enrolling 1680 patients with stroke and proximal intracranial LVO presenting within 24 hours of time last known to be well. Recruitment took place between February 9, 2022, and June 30, 2023, with a final follow-up on September 30, 2023.InterventionsEligible patients were randomly assigned to intravenous methylprednisolone (n = 839) at 2 mg/kg/d or placebo (n = 841) for 3 days adjunctive to endovascular thrombectomy. Main Outcomes and Measures The primary efficacy outcome was disability level at 90 days as measured by the overall distribution of the modified Rankin Scale scores (range, 0 [no symptoms] to 6 [death]). The primary safety outcomes included mortality at 90 days and the incidence of symptomatic intracranial hemorrhage within 48 hours. Results Among 1680 patients randomized (median age, 69 years; 727 female [43.3%]), 1673 (99.6%) completed the trial. The median 90-day modified Rankin Scale score was 3 (IQR, 1-5) in the methylprednisolone group vs 3 (IQR, 1-6) in the placebo group (adjusted generalized odds ratio for a lower level of disability, 1.10 [95% CI, 0.96-1.25]; P = .17). In the methylprednisolone group, there was a lower mortality rate (23.2% vs 28.5%; adjusted risk ratio, 0.84 [95% CI, 0.71-0.98]; P = .03) and a lower rate of symptomatic intracranial hemorrhage (8.6% vs 11.7%; adjusted risk ratio, 0.74 [95% CI, 0.55-0.99]; P = .04) compared with placebo. Conclusions and Relevance Among patients with acute ischemic stroke due to LVO undergoing endovascular thrombectomy, adjunctive methylprednisolone added to endovascular thrombectomy did not significantly improve the degree of overall disability.Trial RegistrationChiCTR.org.cn Identifier: ChiCTR210005172

Existence results for nonlinear degenerate elliptic equations with lower order terms

In this paper, we prove the existence and regularity of solutions of the homogeneous Dirichlet initial-boundary value problem for a class of degenerate elliptic equations with lower order terms. The results we obtained here, extend some existing ones of [2, 9, 11] in some sense

Hydrogen Production by Catalytic Partial Oxidation of Coke Oven Gas in BaCo

The BaCo0.7Fe0.3-xZrxO3-δ (BCFZ, x = 0.04–0.12) mixed ionic–electronic conducting (MIEC) membranes were synthesized with a sol–gel method and evaluated as potential membrane reactor materials for the partial oxidation of coke oven gas (COG). The effect of zirconium content on the phase structure, microstructure and performance of the BCFZ membrane under He or COG atmosphere were systemically investigated. The BaCo0.7Fe0.24Zr0.06O3-δ membrane exhibited the best oxygen permeability and good operation stability, which could be a potential candidate of the membrane materials for hydrogen production through the partial oxidation of COG