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Magnolol (MG) is one of the primary active components of Magnoliae officinalis cortex, which has been widely used in traditional Chinese and Japanese herbal medicine and possesses a wide range of pharmacological activities. In recent years, attention has been drawn to this component due to its potential as an anti-inflammatory and antitumor drug. To summarize the new biological and pharmacological data on MG, we screened the literature from January 2011 to October 2020. In this review, we provide an actualization of already known anti-inflammatory, cardiovascular protection, antiangiogenesis, antidiabetes, hypoglycemic, antioxidation, neuroprotection, gastrointestinal protection, and antibacterial activities of MG. Besides, results from studies on antitumor activity are presented. We also summarized the molecular mechanisms, toxicity, bioavailability, and formulations of MG. Therefore, we provide a valid cognition of MG.

We consider the following inverse problem of finding the evolution parameter p(r) dnd the solution ~( x .I ) such thdt (a,,(x3 [ ) U , , + b,(x, t , U ) ) x v,(x) = g ( x , t , U ) on Sr,.,=I and I,, q ( x , t)u(x, t ) dx= E(t) Osts Twhere Qr= C2 X (0, T I , T>O and 52 is an open bounded region in R" with boundary 8D as smooth as needed throughout this paper; v ( x ) = ( v , ( x ) , vz(x), ..., v J x ) ) is the outward pointing normal direction on asl; uir, g, F, a,,, b,. q and E are given functions. The notion of a weak solution for the pair ( U , p ) is formulated. The existence, uniqueness and continuous dependence upon the data of the solution ( U , p ) are demonstrated for F(x, t , U ) = G(x, t , U ) + H ( x , t)p(r) and F(x, t , U ) = G ( x . t , U ) + ~( x , t ) p ( t ) .

The authors consider in this paper the inverse problem of finding a pair of functions (w, p) such thatwhere F, f, E, s, a,-, /?,-, y t , g t , i = 1, 2 , are given functions.The existence and uniqueness of a smooth global solution pair (u, p) which depends continuously upon the data are demonstrated under certain assumptions on the data.

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It is well-known that a circular cylindrical tube may not stay circular cylindrical after eversion and it may prefer to adopt a wrinkled configuration. A linear analysis using the method of adjacent equilibria followed by a numerical computation shows that for a neo-Hookean tube, a wrinkled configuration is possible when the ratio of the inner radius to the outer radius is approximately equal to 0.4232. The wrinkles have a circumferential mode number approximately equal to 14. In this paper the WKB method is used to derive an asymptotic expression for the critical ratio of the inner radius to the outer radius, with the mode number used as a large parameter. A turning point is found to exist in the eigenmodes, and is used to explain the difficulties experienced in previous numerical computations.