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In this paper, we consider a quasilinear viscoelastic wave equation that features a distributed delay as well as logarithmic nonlinearity. We combine the potential well theory, Faedo‐Galerkin's approximation, and some energy estimates to construct the global existence of the solution. With weaker conditions on the relaxation function, we establish explicit and general decay rate results by using the multiplier method and some properties of convex functions. Our results improve and generalize several earlier related results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we consider a system of viscoelastic wave equations of Kirchhoff type with dynamic boundary conditions. Supposing the relaxation functions $ g_i $ $ (i = 1, 2, \cdots, l) $ satisfy $ g_i(t)\leq-\xi_i(t)G(g_i(t)) $ where $ G $ is an increasing and convex function near the origin and $ \xi_i $ are nonincreasing, we establish some optimal and general decay rates of the energy using the multiplier method and some properties of convex functions. Moreover, we obtain the finite time blow-up result of solution with nonpositive or arbitrary positive initial energy. The results in this paper are obtained without imposing any growth condition on weak damping term at the origin. Our results improve and generalize several earlier related results in the literature. [ABSTRACT FROM AUTHOR]

Alpha-glucosidase inhibitors play a key role in regulating the body's metabolic processes and are commonly used for the treatment of type II diabetes. This study investigated the effects of various extracts from black tea on α-glucosidase. The black tea extracts strongly inhibited α-glucosidase activity. The half inhibition rate (IC50) of ethyl acetate extract (EAE), n-butyl alcohol extract (NBAE) and water extract (WE) produced by ethanol extraction were 3.89, 2.92 and 78.28 μg/mL, respectively, and the IC50 values of the extracts produced by water extraction were 8.19, 4.50 and 6.98 μg/mL. These extracts had much better inhibitory effects than acarbose (IC50 = 1.04 mg/mL). The inhibitory kinetics of the EAE and NBAE from ethanol extraction and WE from water extraction on α-glucosidase were also studied. The results showed that NBAE had a noncompetitive inhibitory effect on α-glucosidase whereas EAE and WE had a mixed inhibitory effect on α-glucosidase. Practical Applications Tea has been widely consumed in China as a kind of traditional drink, and tea has many beneficial health functions, however, the application of tea products in the treatment of diseases is not widely used. The results showed that the extracts of Yixing black tea have a strong inhibition on α-glucosidase, more effective than acarbose, without side effects. Therefore, the extracts of Yixing black tea maybe developed as functional food additives in dietary therapy or a potential therapeutic agent in controlling and preventing type II diabetes. [ABSTRACT FROM AUTHOR]