Search

In this paper, we introduce some monotonicity rules for the ratio of integrals. Furthermore, we demonstrate that the function $-T_{\nu ,\alpha ,\beta }(s)$ is completely monotonic in $s$ and absolutely monotonic in $\nu $ if and only if $\beta \ge 1$, where $T_{\nu ,\alpha ,\beta }(s)=K_{\nu }^2(s)-\beta K_{\nu -\alpha }(s)K_{\nu +\alpha }(s)$ defined on $s>0$ and $K_{\nu }(s)$ is the modified Bessel function of the second kind of order $\nu $. Finally, we determine the necessary and sufficient conditions for the functions $s \mapsto T_{\mu ,\alpha ,1}(s)/T_{\nu ,\alpha ,1}(s)$, $s \mapsto (T_{\mu ,\alpha ,1}(s) + T_{\nu ,\alpha ,1}(s))/(2T_{(\mu +\nu )/2,\alpha ,1}(s))$, and $s \mapsto \frac{\mathrm{d}^{n_1}}{\mathrm{d} \nu ^{n_1}} T_{\nu ,\alpha ,1}(s)/\frac{\mathrm{d}^{n_2}}{\mathrm{d} \nu ^{n_2}} T_{\nu ,\alpha ,1}(s)$ to be monotonic in $s\in (0,\infty )$ by employing the monotonicity rules.

In this paper, we investigate the monotonicity of the functions t \mapsto \frac {\sum _{k=0}^\infty a_k w_k(t)}{\sum _{k=0}^\infty b_k w_k(t)} and x \mapsto \frac {\int _\alpha ^\beta f(t) w(t,x) \mathrm {d} t}{\int _\alpha ^\beta g(t) w(t,x) \mathrm {d} t}, focusing on case where the monotonicity of a_k/b_k and f(t)/g(t) change once. The results presented also provide insights into the monotonicity of the ratios of two power series, two \mathcal {Z}-transforms, two discrete Laplace transforms, two discrete Mellin transforms, two Laplace transforms, and two Mellin transforms. Finally, we employ these monotonicity rules to present several applications in the realm of special functions and stochastic orders. [ABSTRACT FROM AUTHOR]

Objective: To evaluate the effect of Coflex interspinous stabilization and vertebral arch pedicle screw implant on the stability and motion of the lumbar spine., Methods: The range of motion (ROM) of 6 fresh adult human cadaver lumbar spine specimens (L(1) approximately S(1)) was biomechanically tested in forward flexion/extension stretch, left/right lateral bending and left/right axial rotation. The ROM and neutral zone (NZ) of the segments L(2/3), L(3/4), and L(4/5) were measured and compared in 3 conditions, namely intact condition (a), rigid fixation of the segment L(4/5) with vertebral arch pedicle screw (b), and condition b plus L(3/4) stabilization with Coflex device (c)., Results: The ROM of segment L(4/5) was significantly smaller in conditions b and c than in condition a in all the directions (P<0.05). The ROM of segment L(3/4) was significantly smaller in conditions a and c than in condition b in extension stretch (P<0.01), smaller in condition a than in conditions b and c in left/right lateral bending (P<0.01), and decreased significantly in the order of a0.05)., Conclusions: The ROM of the segment superior to the lumbar spine with rigid fixation increases in all the directions, but can be reduced with Coflex device implanted in the superior segment, which results in only increased ROM of the segment superior to Coflex device in extension stretch.

Objective: To determine the concentrations of interleukin-18 (IL-18), IL-6, IL-8, and prostaglandin E2 (PGE2) in the synovial fluid in patients with osteoarthritis (OA), and explore the role of IL-18 in the pathogenesis of OA., Methods: The synovial fluid was collected from 30 patients with knee OA, and the concentrations of IL-18 and the other cytokines were measured using enzyme-linked immunosorbent assay (ELISA). A linear regression was performed between IL-18 and the other cytokines., Results: The average IL-18 and PGE2 concentrations were 220-/+304 pg/ml and 89-/+104 pg/ml in the synovial fluid, respectively, and the two cytokines showed a positive correlation in the synovial fluid (r=0.628, P=0.001). The IL-18 concentration was also correlated to the concentrations of IL-6 (1200-/+1587 pg/ml, n=22; r=0.590, P=0.008) and IL-8 (5190-/+6024 pg/ml, n=9; r=0.776, P=0.014)., Conclusion: IL-18 can promote PGE2 production, which causes cartilage degradation in OA, thus therapies targeting this cytokine may prove an effective approach to early OA treatment.