A logarithmically completely monotonic function is completely monotonic. The function 1 − ln x + 1x ln Γ (x + 1) is strictly completely monotonic on (0, ∞). The function x √ Γ (x + 1)/x is strictly logarithmically completely monotonic on (0, ∞).

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Peptidoglycan (PGN), the major component of the cell wall of Gram-positive bacteria, activates the innate immune system of the host and induces the release of cytokines and chemokines. We investigated the signaling pathway involved in IL-6 production stimulated by PGN in rheumatoid arthritis synovial fibroblasts. PGN caused concentration- and time-dependent increases in IL-6 production. PGN-mediated IL-6 production was attenuated by TLR2 small interfering RNA and nucleotide-binding oligomerization domain 2 small interfering RNA. Pretreatment with PI3K inhibitor (Ly294002 and wortmannin), Akt inhibitor, and AP-1 inhibitor (tanshinone IIA) also inhibited the potentiating action of PGN. PGN increased the focal adhesion kinase (FAK), PI3K, and Akt phosphorylation. Stimulation of rheumatoid arthritis synovial fibroblast cells with PGN increased the accumulation of phosphorylated c-Jun in the nucleus, AP-1-luciferase activity, and c-Jun binding to the AP-1 element on the IL-6 promoter. PGN mediated an increase in the accumulation of phosphorylated c-Jun in the nucleus, AP-1-luciferase activity, and c-Jun binding to AP-1 element was inhibited by Ly294002, Akt inhibitor, and FAK mutant. Our results suggest that PGN increased IL-6 production in human synovial fibroblasts via the TLR2 receptor/FAK/PI3K/Akt and AP-1 signaling pathway.

The function [V(x + l)]

Articular adipose tissue is a ubiquitous component of human joints, and adiponectin is a protein hormone secreted predominantly by differentiated adipocytes and involved in energy homeostasis. The adiponectin is significantly higher in synovial fluid of patients with osteoarthritis and rheumatoid arthritis. Matrix metalloproteinases (MMP)-3 may contribute to the breakdown of articular cartilage during arthritis. We investigated the signaling pathway involved in MMP-3 caused by adiponectin in human chondrocytes. Adiponectin increased the secretion of MMP-3 in cultured human chondrocytes, as shown by qPCR, Western blot, and ELISA analysis. Adiponectin-mediated MMP-3 expression was attenuated by AdipoR1 but not AdipoR2 siRNA. Pretreatment with 5'-AMP-activated protein kinase (AMPK) inhibitor (araA and compound C), p38 inhibitor (SB203580), and NF-κB inhibitor (PDTC and TPCK) also inhibited the potentiating action of adiponectin. Activations of p38, AMPK, and NF-κB pathways after adiponectin treatment were demonstrated. Taken together, our results provide evidence that adiponectin acts through AdipoR1 to activate p38 and AMPK, resulting in the activations of NF-κB on the MMP-3 promoter and contribute cartilage destruction during arthritis.

Objectives Despite the ease of health care access and the waiver of copayments for cancer patients, treatment is delayed in a small proportion of Taiwanese patients diagnosed with cervical cancer. In this study, we explored the relationship between the time interval from diagnosis to treatment and survival in cervical cancer patients. Material and methods The study was a retrospective population-based observational study conducted between 2004 and 2010. In Taiwan, 12,020 patients were newly diagnosed with cervical cancer from 2004 to 2010, and 9,693 patients (80.6%) were enrolled in our final analysis. Results Most of the patients received treatment within 90 days of diagnosis (n = 9,341, 96.37%). After adjustment for other variables, patients who received treatment between 90 and 180 days and >180 days after diagnosis had a 1.33 (95% CI: 1.02–1.72, P < 0.05) and 1.36 (95% CI: 1.12–1.65, P < 0.05) times higher risk of death, respectively, than those who received treatment within 90 days. Kaplan–Meier analysis showed that the patients treated after 90 days from diagnosis had a lower overall survival rate than those treated within 90 days. In analysis stratifying the patients according to their initial tumor stage, namely stages I and II and stage III and IV, the time interval from diagnosis to treatment remained a significant prognosticator in those who received treatment >180 days after diagnosis. Conclusion A longer interval between diagnosis and treatment is associated with poorer prognosis among cervical cancer patients.

By using the first Binet's formula the strictly completely monotonic properties of functions involving the psi and polygamma functions are obtained. As direct consequences, two inequalities are proved. As an application, the best lower and upper bounds of the nth harmonic number are established.  2005 Elsevier Inc. All rights reserved.

Abstract. By employing the convolution theorem of Laplace transforms, some asymptotic formulas and integral representations of the gamma, psi and polygamma functions, and other analytic techniques, this note provides an alternative proof of a monotonicity and convexity property by N. Elezović, C. Giordano and J. Pečarić in [4] to establish the best bounds in Gautschi-Kershaw inequalities. Moreover, some (logarithmically) complete monotonicity results on functions related to Gautschi-Kershaw inequalities are remarked.Mathematics subject classification (2000): 33B15, 26A48, 26A51, 26D20.