Variational methods for boundary integral equations deal with the weak formulations of boundary integral equations. Their numerical discretizations are known as the boundary element methods. The later has become one of the most popular numerical schemes in recent years. In this expository paper, we discuss some of the essential features of the methods, their intimate relations with the variational formulations of the corresponding partial differential equations and recent developments with respect to applications in domain composition from both mathematical and numerical points of view. Variational Formulations for Boundary Integral EquationsIt is well known that the reduction of boundary value problems to integral equations is by no means a unique process. In spite of many formulations, there are two kinds of boundary integral equations, the first and the second kind boundary integral equations either from the direct or indirect approach. The variational formulations of boundary integral equations in general may depend upon the types of boundary integral equations under consideration. In the following we shall systematically discuss these formulations through simple model problems and present some of the basic theorems and indicate typical ways for obtaining these results which may be employed in general for the variational methods concerning boundary integral equations.

No abstract

Antrodia camphorata (A. camphorata) is well-known in Taiwan as a traditional Chinese medicine. The purpose of this study was to evaluate the ability of A. camphorata extracts to protect against oxidative stress in vitro and against carbon tetrachloride (CCl(4))-induced hepatic injury in vivo. An extract of A. camphorata inhibited nonenzymatic iron-induced lipid peroxidation in rat brain homogenates with an IC(50) value about 3.1 mg/mL. It also scavenged the stable free radical 1,1-diphenyl-2-picrylhydrazyl (DPPH). The dose of the A. camphorata extract resulting in a decrease of 0.20 in the absorbance of DPPH was about 31 +/- 0.7 microg/mL. Furthermore, an A. camphorata extract dose-dependently (250-1250 mg/kg) ameliorated the increase in plasma aspartate aminotransferase (GOT) and alanine aminotransferase (GPT) levels caused by chronic repeated CCl(4) intoxication in mice. Moreover, A. camphorata extract significantly improved the CCl(4)-induced increase in hepatic glutathione peroxidase, reductase, and CCl(4)-induced decrease in superoxide dismutase activities. It also restored the decrement in the glutathione content and catalase activity of hepatic tissues in CCl(4)-intoxicated mice. Furthermore, it also dose-dependently inhibited the formation of lipid peroxidative products during CCl(4) treatment. Histopathological changes of hepatic lesions induced by CCl(4) were significantly ameliorated by treatment with an A. camphorata extract in a dose-dependent manner. These results suggest that A. camphorata extract exerts effective protection against chronic chemical-induced hepatic injury in vivo, by mediating antioxidative and free radical scavenging activities.

No abstract

Clathrin-dependent endocytosis is believed to be involved in TGFβ-stimulated cellular responses, but the subcellular locus at which TGFβ induces signaling remains unclear. Here, we demonstrate that inhibitors of clathrin-dependent endocytosis, which are known to arrest the progression of endocytosis at coated-pit stages, inhibit internalization of cell-surface-bound TGFβ and promote colocalization and accumulation of TβR-I and SARA at the plasma membrane. These inhibitors enhance TGFβ-induced signaling and cellular responses (Smad2 phosphorylation/nuclear localization and expression of PAI-1). Dynasore, a newly identified inhibitor of dynamin GTPase activity, is one of the most potent inhibitors among those tested and, furthermore, is a potent enhancer of TGFβ. Dynasore ameliorates atherosclerosis in the aortic endothelium of hypercholesterolemic ApoE-null mice by counteracting the suppressed TGFβ responsiveness caused by the hypercholesterolemia, presumably acting through its effect on TGFβ endocytosis and signaling in vascular cells.

Abstract-It has been suggested that tetrahydrobiopterin (H 4 B), a cofactor of NO synthase, can reverse endothelial dysfunction caused by cardiovascular diseases, including atherosclerosis, coronary artery disease, and hypertension. Moreover, an impairment of H 4 B biosynthesis in spontaneously hypertensive rats (SHR) was observed. Thus, we hypothesized that the defect of the H 4 B synthesis system may play an important role in the development of hypertension in SHR. In the present study H 4 B (10 mg/kg per day IP) was used to treat SHR and Wistar-Kyoto rats (WKY) from the age of 5 through 16 weeks. Results demonstrated that chronic treatment with H 4 B significantly improved the impaired vascular responses to acetylcholine and suppressed the development of hypertension in SHR but did not affect WKY. The increase of inducible NO synthase expression, nitrotyrosine immunostaining, NO production, and superoxide anion formation in adult SHR were also significantly suppressed by chronic treatment with H 4 B. In contrast, H 4 B had no effect on WKY.In conclusion, this study demonstrated that H 4 B significantly attenuated the development of hypertension in SHR. The antihypertensive effect of H 4 B might be mediated through its direct antioxidant activity and/or decreasing oxygen free radical production from NO synthase, thereby reducing inducible NO synthase expression and peroxynitrite formation. Thus, the present study proposed that supplementation with H 4 B might be beneficial in preventing pathological conditions such as essential hypertension. Key Words: nitric oxide synthase Ⅲ peroxynitrite Ⅲ rats, inbred SHR Ⅲ superoxide Ⅲ biopterin I ncreased superoxide formation occurs in spontaneously hypertensive rats (SHR). 1 Superoxide may induce inducible NO synthase (iNOS) and then cause overproduction of NO. 2 The formation of massive amounts of NO via iNOS has a potentially cytotoxic effect, whereas relatively small amounts of NO formed via endothelial NO synthase (eNOS) have a cytoprotective action on the cardiovascular system. 3 In addition, the parallel time course of the generation of superoxide anion and iNOS indicates an efficient simultaneous reaction: NOϩO 2 *3 ONOOϪ (peroxynitrite). 4 Peroxynitrite is a short-lived and potently damaging oxidant that contributes significantly to pathological oxidative stress in living tissues. 5 Moreover, the unique chemical reactions of peroxynitrite, such as protein nitration, DNA single-strand breakage, and guanidine nitration, are not only cytotoxic but also mutagenic. 6 These findings suggest that increased production of superoxide in SHR may lead to the development of hypertension through chronic damage of the cardiovascular system, especially endothelium, induced by massive amounts of NO and peroxynitrite. Because peroxynitrite formation was previously identified through immunostaining of nitrotyrosine at the local site of infected organs, 4 in the present study we used a Western blotting assay to detect nitrotyrosine expression in the thoracic aorta as indirect eviden...

Variational methods for boundary integral equations deal with the weak formulations of boundary integral equations. Their numerical discretizations are known as the boundary element methods. The later has become one of the most popular numerical schemes in recent years. In this expository paper, we discuss some of the essential features of the methods, their intimate relations with the variational formulations of the corresponding partial differential equations and recent developments with respect to applications in domain composition from both mathematical and numerical points of view.

SummaryThis paper is concerned with the recent developments in the solution of boundary value problems by integral equations of the first kind. Basic results for weakly singular and hypersingular boundary integral operators will be discussed. Emphases will be given to the mathematical foundation of the method' as well as to the physical interpretations of various side conditions derived for the unique solvability of the integral equations of the first kind.