Boundary behaviour of the unique solution to a singular Dirichlet problem with a convection term

AbstractBy Karamata regular variation theory and constructing comparison functions, we derive that the boundary behaviour of the unique solution to a singular Dirichlet problem −Δu=b(x)g(u)+λ|∇u|q, u>0, x∈Ω, u|∂Ω=0, which is independent of λ|∇uλ|q, where Ω is a bounded domain with smooth boundary in RN, λ∈R, q∈(0,2], lims→0+g(s)=+∞, and b is non-negative on Ω, which may be vanishing on the boundary

The LpL_p Chord Minkowski problem in a critical interval

Chord measures and $L_p$ chord measures were recently introduced by Lutwak-Xi-Yang-Zhang by establishing a variational formula regarding a family of fundamental integral geometric invariants called chord integrals. Prescribing the $L_p$ chord measure is known as the $L_p$ chord Minkowski problem, which includes the $L_p$ Minkowski problem heavily studied in the past 2 decades as special cases. In the current work, we solve the $L_p$ chord Minkowski problem when $0\leq p<1$, without symmetry assumptions.Comment: revised and to appear in Math. An

Tribulus terrestris extracts alleviate muscle damage and promote anaerobic performance of trained male boxers and its mechanisms: Roles of androgen, IGF-1, and IGF binding protein-3

AbstractPurposeTo investigate the effects of Tribulus terrestris (TT) extracts on muscle mass, muscle damage, and anaerobic performances of trained male boxers and its mechanisms: roles of plasma androgen, IGF-1, and IGF-1 binding protein-3 (IGFBP-3).MethodsFifteen male boxers were divided into exercise group (E, n = 7) and exercise plus TT group (E + TT, n = 8). The two groups both undertook 3-week high intensity and 3-week high volume trainings separated by a 4-week rest. TT extracts (1250 mg/day) were orally administered by boxers in E + TT group. TT extract compositions were detected by UHPLC–Q-TOF/MS. Before and at the end of the two trainings, muscle mass, anaerobic performance, and blood indicators were explored.ResultsCompared with E group, decreases of plasma CK (1591.50 ± 909.55 vs. 2719.86 ± 832.47 U/L) and IGFBP-3 (3075.53 ± 1072.45 vs. 3950.83 ± 479.25 ng/mL) as well as increases of mean power (MP, 459.42 ± 122.25 vs. 434.60 ± 69.47 W) and MP/body weight (MP/BW, 7.54 ± 0.85 vs. 7.07 ± 1.09 W/kg) were detected in E + TT group after a high intensity training. For high volume training, reduction of IGFBP-3 (2946.38 ± 974.07 vs. 3632.67 ± 470.06 ng/mL) and increases of MP (508.71 ± 103.21 vs. 477.81 ± 49.90 W) and MP/BW (8.24 ± 0.29 vs. 7.52 ± 0.92 W/kg) were detected in E + TT group. Muscle mass, blood levels of testosterone, dihydrotestosterone (DHT), and IGF-1 were unchanged between the two groups.ConclusionTaking 1250 mg capsules containing TT extracts did not change muscle mass and plasma levels of testosterone, DHT, and IGF-1 but significantly alleviated muscle damage and promoted anaerobic performance of trained male boxers, which may be related to the decrease of plasma IGFBP-3 rather than androgen in plasma