Hydraulic and geometrical relationships of lay-flat irrigation tubing /

Caption title.

Geometrical optics /

Mode of access: Internet.

Euclid's Elements of geometry, chiefly from the text of Dr. Simson...together with a selection of geometrical exercises from the Senate-house and college examination papers ...

Mode of access: Internet.

Ad quadratum; a study of the geometrical bases of classic & medieval religious architecture, with special reference to their application in the restoration of the cathedral of Nidaros (Throndhjem) Norway,

"Rules of religious architecture were a secret science in the middle ages, just as they were in classic times ... Through this secrecy, the rules became forgotten ... It is this forgotten science which we have discovered, and which we develop in this work."--p. xxii.

Disposition kinetics of propranolol isomers in the perfused rat liver

The aim of this study was to define the determinants of the linear hepatic disposition kinetics of propranolol optical isomers using a perfused rat liver. Monensin was used to abolish the lysosomal proton gradient to allow an estimation of propranolol ion trapping by hepatic acidic vesicles. In vitro studies were used for independent estimates of microsomal binding and intrinsic clearance. Hepatic extraction and mean transit time were determined from outflow-concentration profiles using a nonparametric method. Kinetic parameters were derived from a physiologically based pharmacokinetic model. Modeling showed an approximate 34-fold decrease in ion trapping following monensin treatment. The observed model-derived ion trapping was similar to estimated theoretical values. No differences in ion-trapping values was found between R(+)- and S(-)- propranolol. Hepatic propranolol extraction was sensitive to changes in liver perfusate flow, permeability-surface area product, and intrinsic clearance. Ion trapping, microsomal and nonspecific binding, and distribution of unbound propranolol accounted for 47.4, 47.1, and 5.5% of the sequestration of propranolol in the liver, respectively. It is concluded that the physiologically more active S(-)- propranolol differs from the R(+)- isomer in higher permeability-surface area product, intrinsic clearance, and intracellular binding site values.

Evaluating the potential neurotoxicity of hexanedione isomers:an in vitro approach

2,5-hexanedione (2,5HD) is the neurotoxic metabolite of the aliphatic hydrocarbon n-Hexane. The isomers, 2,3-hexanedione (2,3HD) and 3,4-hexanedione (3,4HD) are used as food additives. Although the neurotoxicity of 2,5HD is well established, there are no human data of the possible toxicity of the 2,3- and 3,4- isomers. MTT and flow cytometry were utilised to determine the cytotoxicity of hexanedione isomers in neuroblastoma cells. The neuroblastoma cell lines SK-N-SH and SH-SY5Y are sufficiently neuron-like to provide preliminary assessment of the neurotoxic potential of these isomers, in comparison with toxicity towards human non-neuronal cells. Initial studies showed that 2,5HD was the least toxic in all cell lines at all times (4, 24 and 48h). Although considerably lower than for 2,5HD, in general the IC50s for the α isomers were not significantly different from each other and, besides 4h exposure, the SH-SY5Y cells were significantly more sensitive to 2,3HD and 3,4HD than the SK-N-SH cells. All three isomers caused varying degrees of apoptosis in the neuroblastoma lines, with 3,4HD more potent than 2,3HD. Flow cytometry highlighted cell cycle arrest indicative of DNA damage with 2,3- and 3,4HD. The toxicity of the isomers towards 3 non-neuronal cell lines (MCF7, HepG2 and CaCo-2) was assessed by MTT assay. All 3 hexanedione isomers proved to be cytotoxic in all non-neuronal cell lines at all time points. These data suggest cytotoxicity of 2,3- and 3,4HD (mM range), but it is difficult to define this as specific neurotoxicity in the absence of specific neurotoxic endpoints. However, the neuroblastomas were significantly more susceptible to the cytotoxic effects of the α hexanedione isomers at exposures of 4 and 24 hours, compared to non-neuronal lines. Finally, a mechanism of toxicity is suggested for the α HD isomers whereby inhibition of the oxoglutarate carrier (OGC) releases apoptosis inducing factor (AIF), causing apoptosis-like cell death.

The toxicity of hexanedione isomers in neural and astrocytic cell lines

The metabolite 2,5-hexanedione (HD) is the cause of neurotoxicity linked with chronic n-hexane exposure. Acute exposure to high levels of 2,5-HD, have also shown toxic effects in neuronal cells and non-neuronal cells. Isomers of 2,5-HD, 2,3- and 3,4-HD, added to foodstuffs, are reported to be non-toxic. The acute cytotoxic effects of 2,5-, 2,3- and 3,4-HD were evaluated in neural (NT2.N, SK-N-SH), astrocytic (CCF-STTG1) and non-neural (NT2.D1) cell lines. All the cell lines were highly resistant to 2,5-HD (34-426 mM) at 4-h exposure, although sensitivity was greatest with NT2.D1, then SK-N-SH, NT2.N and finally the CCF-STTG1 line. At 24-h exposure, cell vulnerability increased 5-10-fold. The NT2.D1 cells were again the most sensitive, followed by NT2.N, SK-N-SH and then the CCF-STTG1 cells. 2,3- and 3,4-HD (8-84 mM), were significantly more toxic towards all four cell lines compared with 2,5-HD, after 4-h exposure. After 24-h exposure there was a 12-fold increase in inhibition of MTT turnover in the SK-N-SH cells and a 4-fold increase in the CCF-STTG1 cells, compared with 2,5-HD exposure. 2,3- and 3,4-HD, were significantly less toxic to the NT2.N cells than the SK-N-SH cells after 24-h exposure to the compounds, demonstrating a differing toxin vulnerability between these neural and neuroblastoma cell lines. This study indicates that these non-neuronal and neuronal cells are acutely resistant to 2,5-HD cytotoxicity, whilst the previously unreported sensitivity of all four cell lines to the 2,3- and 3,4- isomers of HD to has been shown to be significantly greater than that of 2,5-HD. © 2006 Elsevier B.V. All rights reserved.

A Geometrical Interpretation to Define Contradiction Degrees between Two Fuzzy Sets

For inference purposes in both classical and fuzzy logic, neither the information itself should be contradictory, nor should any of the items of available information contradict each other. In order to avoid these troubles in fuzzy logic, a study about contradiction was initiated by Trillas et al. in [5] and [6]. They introduced the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Moreover, the need to study not only contradiction but also the degree of such contradiction is pointed out in [1] and [2], suggesting some measures for this purpose. Nevertheless, contradiction could have been measured in some other way. This paper focuses on the study of contradiction between two fuzzy sets dealing with the problem from a geometrical point of view that allow us to find out new ways to measure the contradiction degree. To do this, the two fuzzy sets are interpreted as a subset of the unit square, and the so called contradiction region is determined. Specially we tackle the case in which both sets represent a curve in [0,1]2. This new geometrical approach allows us to obtain different functions to measure contradiction throughout distances. Moreover, some properties of these contradiction measure functions are established and, in some particular case, the relations among these different functions are obtained.

A Geometrical Construction for the Polynomial Invariants of some Reflection Groups

2000 Mathematics Subject Classification: Primary 20F55, 13F20; Secondary 14L30.