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In this paper, by using Schwarz rearrangement and isoperimetric inequalities, we prove comparison results for the solutions of Poisson equations on complete Riemannian manifolds with Ric ≥ (n − 1) κ , κ = 0 or 1 , which extends the results in [A. Alvino, C. Nitsch and C. Trombetti, A Talenti comparison result for solutions to elliptic problems with Robin boundary conditions, Comm. Pure Appl. Math. 76(3) (2023) 585–603]. Furthermore, as applications of our comparison results, we obtain the Saint-Venant inequality and Bossel–Daners inequality for Robin Laplacian. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the Faber-Krahn inequality for the first eigenvalue of the Robin Laplacian on bounded domain in Riemannian manifolds whose Ricci curvature satisfies Ric g ≥ (n − 1). The Faber-Krahn inequality also holds for the Robin Laplacian on bounded domain in hyperbolic space H n. [ABSTRACT FROM AUTHOR]

In this paper, we use the inverse mean curvature flow to establish an optimal Minkowski type inequality, a weighted Alexandrov-Fenchel inequality for the mean convex star-shaped hypersurfaces in the Reissner-Nordström-anti-deSitter manifold, and a Penrose type inequality for asymptotically locally hyperbolic manifolds which can be realized as graphs over the Reissner-Nordström-anti-deSitter manifold. [ABSTRACT FROM AUTHOR]

In this short note we obtain some gradient estimates for the positive solution to the doubly nonlinear diffusion equation on closed Riemannian manifold with Ricci curvature bounded below by a non-positive constant. As applications, we also derive corresponding Harnack inequalities. [ABSTRACT FROM AUTHOR]

In this article we study surfaces in S3(1) × R for which the R-direction makes a constant angle with the normal plane. We give a complete classification for such surfaces with parallel mean curvature vector. [ABSTRACT FROM AUTHOR]

Abstract: Let Ω be a bounded domain in an n-dimensional Euclidean space . We study eigenvalues of an eigenvalue problem of a system of elliptic equations: Estimates for eigenvalues of the above eigenvalue problem are obtained. Furthermore, we obtain an upper bound on the th eigenvalue . We also obtain sharp lower bound for the first eigenvalue of two kinds of eigenvalue problems of the biharmonic operator on compact manifolds with boundary and positive Ricci curvature. [Copyright &y& Elsevier]

In this paper, we investigate universal inequalities for eigenvalues of the Dirichlet Laplacian and the clamped plate problem on a bounded domain in an n-dimensional polydisk 픻n. Moreover, from the domain monotonicity of the eigenvalue, we can prove that if the first eigenvalue of the Dirichlet Laplacian tends to $\frac n4$ when the domain tends to the polydisk 픻n, then all of the eigenvalues tend to $\frac n4$. [ABSTRACT FROM AUTHOR]

For n ≥ 7, we give the optimal estimate for the second eigenvalue of Paneitz operators for compact n-dimensional submanifolds in an ( n + p)-dimensional space form in terms of the mean curvature and the Q-curvature. [ABSTRACT FROM AUTHOR]

Abstract: For a bounded planar region in , we obtain the ratios of lower order eigenvalues of Laplace operator. Combining our results with the recursive formula in Cheng and Yang (2007) , we can obtain better upper bound of the -th () membrane eigenvalues. [Copyright &y& Elsevier]

Abstract: Under two boundary conditions, the generalized Atiyah–Patodi–Singer boundary condition and the modified generalized Atiyah–Patodi–Singer boundary condition, we get the lower bounds for the eigenvalues of the fundamental Dirac operator on compact spin manifolds with nonempty boundary. [Copyright &y& Elsevier]

To evaluate the effect of nalbuphine on emergence agitation (EA) in children undergoing adenotonsillectomy. Multicenter, prospective, double-blind, randomized controlled trial. The First People's Hospital of Foshan and three other participating institutions in China, from April 2020 to December 2021. Eight hundred patients, 3–9 years of age, American Society of Anesthesiologists (ASA) classification I or II, undergoing elective adenotonsillectomy were included. Nalbuphine (0.1 mg/kg) or saline was administered intravenously. The incidence of EA; the pediatric anesthesia emergence delirium (PAED) scale; and the faces, legs, activity, cry, and consolability (FLACC) scales. Extubation time, duration of post-anesthesia care unit (PACU) stay, anesthesia nurses' and parents' satisfaction, and other side effects. The incidence of EA in the nalbuphine group was lower than that in the saline group 30 min after extubation (10.28% vs. 28.39%, P = 0.000). In addition, the FLACC scores in the nalbuphine group were lower than those in the saline group 30 min after extubation (P < 0.05). Furthermore, the proportion of moderate-to-severe pain cases (FLACC scores >3) was significantly lower in the nalbuphine group than in the saline group (33.58% vs. 60.05%, P = 0.000). Adjusting the imbalance of postoperative pain intensity, the risk of EA was still lower in the nalbuphine group at 0 min (OR, 0.39; 95% CI, 0.26–0.60; P = 0.000), (OR, odds ratio; CI, confidence interval), 10 min (OR, 0.39; 95% CI, 0.19–0.79; P = 0.01), and 20 min (OR, 0.27; 95% CI, 0.08–0.99; P = 0.046) than in the saline group. There were no significant differences in extubation time, duration of PACU stay, nausea and vomiting, or respiratory depression between the two groups (P > 0.05). Nalbuphine reduced the incidence of EA in children after adenotonsillectomy under general anesthesia, which may be involved in both analgesic and non-analgesic pathways. • Nalbuphine could reduce emergence agitation in children after general anesthesia. • Nalbuphine did not increase extubation time and duration of PACU stay. • Nalbuphine did not increase the incidence of breath depression and nausea and vomiting. [ABSTRACT FROM AUTHOR]

Protein kinase C (PKC)-dependent regulation of voltage-gated Ca (Cav; with α1β1Bα2/δ subunits) channel 2.3 was investigated using phorbol 12-myristate 13-acetate (PMA), or by M1 muscarinic receptor activation in Xenopus oocytes. The inward Ca2+-current with Ba2+ (IBa) as the charge carrier was potentiated by PMA or acetyl-β-methylcholine (MCh). The inactivating [I(inact)] and non-inactivating [I(noninact)] components of IBa and the time constant of inactivation τ(inact) were all increased by MCh or PMA. This may be a PKC-dependent action since the effect of MCh and PMA was blocked by Ro-31-8425 or β-pseudosubstrate. MCh effect was blocked by atropine, guanosine-5′-O-(2-thiodiphosphate) trilithium (GDPβS) or U-73122. The effect of MCh but not PMA was blocked by the inhibition of inositol-1,4,5-trisphosphate (IP3) receptors, intracellular Ca2+ ([Ca2+]i) or the translocation of conventional PKC (cPKC) with heparin, BAPTA and βC2.4, respectively. While a lower concentration (25 nM) of Ro-31-8425 blocked MCh, a higher concentration (500 nM) of Ro-31-8425 was required to block PMA action. This differential susceptibility of MCh and PMA to heparin, BAPTA, βC2.4 or Ro-31-8425 is suggestive of the involvement of Ca2+-dependent cPKC in MCh action, whereas cPKC and Ca2+-independent novel PKC (nPKC) in PMA action. PMA led to additional increase in IBa that was already potentiated by preadministered MCh (1 or 10 μM), leading to the suggestion that differential phosphorylation sites for cPKC and nPKC may be present in the α12.3 subunit of Cav 2.3 channels. [Copyright &y& Elsevier]

Focuses on the study which examines the efficacy of the drug captopril in the prevention of hypertrophy-dependent gene expression in the hearts of spontaneously hypertensive rats. Methodology of the study; Causes of ventricular hypertrophy; Discussion of results of the study; Physiologic effects of captopril.