Identification of Boundary Conditions Using Natural Frequencies

The present investigation concerns a disc of varying thickness of whose flexural stiffness $D$ varies with the radius $r$ according to the law $D=D_0 r^m$, where $D_0$ and $m$ are constants. The problem of finding boundary conditions for fastening this disc, which are inaccessible to direct observation, from the natural frequencies of its axisymmetric flexural oscillations is considered. The problem in question belongs to the class of inverse problems and is a completely natural problem of identification of boundary conditions. The search for the unknown conditions for fastening the disc is equivalent to finding the span of the vectors of unknown conditions coefficients. It is shown that this inverse problem is well posed. Two theorems on the uniqueness and a theorem on stability of the solution of this problem are proved, and a method for establishing the unknown conditions for fastening the disc to the walls is indicated. An approximate formula for determining the unknown conditions is obtained using first three natural frequencies. The method of approximate calculation of unknown boundary conditions is explained with the help of three examples of different cases for the fastening the disc (rigid clamping, free support, elastic fixing). Keywords: Boundary conditions, a disc of varying thickness,inverse problem, Plucker condition.Comment: 19 page

Post epidemic giardiasis and gastrointestinal symptoms among preschool children in Bergen, Norway. A cross-sectional study

<p>Abstract</p> <p>Background</p> <p>A surprisingly low number of children became ill with giardiasis during the large waterborne outbreak of <it>Giardia lamblia </it>in Bergen, Norway during autumn 2004. The aim of the present study was to evaluate the prevalence of giardiasis among exposed children one year after an outbreak and compare faecal carriage of <it>Giardia </it>and abdominal symptoms among exposed versus unexposed children one year after the epidemic.</p> <p>Methods</p> <p>Children between 1 and 6 years old were recruited from the local health care centres in Bergen municipality in the period between June 2005 and January 2006. One faecal sample per child was collected and examined for presence of <it>Giardia </it>with a rapid immunoassay antigen test, and parents were asked to answer a questionnaire. A total of 513 children participated, 378 in the group exposed to contaminated water, and 135 in the in the group not exposed.</p> <p>Results</p> <p>In the exposed group eleven children had been treated for giardiasis during the epidemic and none in the unexposed group. <it>Giardia </it>positive faecal tests were found in six children, all in the exposed group, but the difference between the groups did not reach statistical significance. All six <it>Giardia </it>positive children were asymptomatic. No differences were found between the groups regarding demographic data, nausea, vomiting, different odour from stools and eructation. However, the reported scores of abdominal symptoms (diarrhoea, bloating and stomach ache) during the last year were higher in the exposed group than in the unexposed group.</p> <p>Conclusions</p> <p>A low prevalence of asymptomatic <it>Giardia </it>infection (1.7%) was found among exposed children around one year after the epidemic (1.2% overall prevalence in the study). In the present setting, pre-school children were therefore unlikely to be an important reservoir for continued transmission in the general population.</p

Understanding the benefit of metformin use in cancer treatment

Biguanides have been developed for the treatment of hyperglycemia and type 2 diabetes. Recently, metformin, the most widely prescribed biguanide, has emerged as a potential anticancer agent. Epidemiological, preclinical and clinical evidence supports the use of metformin as a cancer therapeutic. The ability of metformin to lower circulating insulin may be particularly important for the treatment of cancers known to be associated with hyperinsulinemia, such as those of the breast and colon. Moreover, metformin may exhibit direct inhibitory effects on cancer cells by inhibiting mammalian target of rapamycin (mTOR) signaling and protein synthesis. The evidence supporting a role for metformin in cancer therapy and its potential molecular mechanisms of action are discussed

Toxic but Drank: Gustatory Aversive Compounds Induce Post-ingestional Malaise in Harnessed Honeybees

BACKGROUND: Deterrent substances produced by plants are relevant due to their potential toxicity. The fact that most of these substances have an unpalatable taste for humans and other mammals contrasts with the fact that honeybees do not reject them in the range of concentrations in which these compounds are present in flower nectars. Here we asked whether honeybees detect and ingest deterrent substances and whether these substances are really toxic to them. RESULTS: We show that pairing aversive substances with an odor retards learning of this odor when it is subsequently paired with sucrose. Harnessed honeybees in the laboratory ingest without reluctance a considerable volume (20 µl) of various aversive substances, even if some of them induce significant post-ingestional mortality. These substances do not seem, therefore, to be unpalatable to harnessed bees but induce a malaise-like state that in some cases results in death. Consistently with this finding, bees learning that one odor is associated with sugar, and experiencing in a subsequent phase that the sugar was paired with 20 µl of an aversive substance (devaluation phase), respond less than control bees to the odor and the sugar. Such stimulus devaluation can be accounted for by the malaise-like state induced by the aversive substances. CONCLUSION: Our results indicate that substances that taste bitter to humans as well as concentrated saline solutions base their aversive effect on the physiological consequences that their ingestion generates in harnessed bees rather than on an unpalatable taste. This conclusion is only valid for harnessed bees in the laboratory as freely-moving bees might react differently to aversive compounds could actively reject aversive substances. Our results open a new possibility to study conditioned taste aversion based on post-ingestional malaise and thus broaden the spectrum of aversive learning protocols available in honeybees