Using the Frobenius map, we introduce a new invariant of a pair (R, a) of a ring R and an ideal a ⊂ R, which we call the F-pure threshold c(a) of a, and study its properties. We see that the F-pure threshold characterizes some ring theoretic properties. By virtue of Hara and Yoshida's result [HY], the F-pure threshold c(a) in characteristic zero corresponds to the log canonical threshold lc(a) ...

The dynamics of MHD non-Newtonian fluid flow past a cylinder with slip boundary condition and magnetic field is addressed in this study. (tangent hyperbolic) considered study are nail polish whipped cream. This article investigates the statistical analysis two-dimensional tangent hyperbolic over condition. partial differential equations describing problem later transformed into ordinary equatio...

in order to evaluate competition among some weed species and canola, a field experiment in astan ghods razavi's field in mashhad was done on 2007-2008. thirty 50×50 cm quadrates were used in two times (stem and flower production) to measure the canola dry weight, leaf area index and canola and weeds density with destruction and thirty similar quadrates were used for counting weed species a...

Aims of the study were 1) to compare Hudgel's hyperbolic with Rohrer's polynomial model in describing the pressure-flow relationship, 2) to use this pressure-flow relationship to describe these resistances and to evaluate the effects of sleep stages on pharyngeal resistances, and 3) to compare these resistances to the pressure-to-flow ratio (DeltaP/V). We studied 12 patients: three with upper a...

Data on the variation of crop volumes with time for blowflies (Phormia regina Meigen) fed various volumes and concentrations of fructose or sucrose (from Gelperin, 1966, and Edgecomb et al. 1987) were used to characterize energy processing rates to test the assumption of food energy addivity of optimal foraging theories. Six regression models (linear, square root, cube root, hyperbolic, inverse...

Hyperbolic trigonometry is developed and illustrated in this article along lines parallel to Euclidean trigonometry by exposing the hyperbolic trigonometric law of cosines and of sines in the Poincaré ball model of n-dimensional hyperbolic geometry, as well as their application. The Poincaré ball model of 3-dimensional hyperbolic geometry is becoming increasingly important in the construction o...

Hara [Ha3] and Smith [Sm2] independently proved that in a normal Q-Gorenstein ring of characteristic p ≫ 0, the test ideal coincides with the multiplier ideal associated to the trivial divisor. We extend this result for a pair (R,∆) of a normal ring R and an effective Q-Weil divisor ∆ on SpecR. As a corollary, we obtain the equivalence of strongly F-regular pairs and klt pairs.

Terra B. Jacobson is Public Services Manager in the Library at Prairie State College; e-mail: Terra.jacobson@ gmail.com. The author would like to thank Dr. Noriko Hara for all of her assistance and guidance with this paper. © Terra B. Jacobson As Facebook has come to dominate the social networking site arena, more libraries have created their own library pages on Facebook to create library awar...

In this paper, we present a multiple views approach for exploring relationships between ontology classes and their instances. We employ thumbnails, 2D and 2.5D hyperbolic trees, which capture the hierarchical feature of parts of the ontology, while preserving the different categories of relationships between classes. In 2.5D visualization, the ontology is displayed as a tree on a plane, represe...