Using the Frobenius map, we introduce a new invariant for 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 several 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...

lace expansion and suggesting that it might converge in five dimensions, and to Takashi Hara for the pleasure of four years of collaboration and for permission to include unpublished joint work. We gratefully acknowledge financial support from the Natural Sciences and Engineering Reearch Council of Canada. Finally we offer our thanks and deep appreciation to Joyce Kruskal and Joanne Nakonechny ...

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) ...

For time-to-event data, when the hazards are non-proportional, in addition to the hazard ratio, the absolute risk reduction and the restricted mean survival difference can be used to describe the time-dependent treatment effect. The absolute risk reduction measures the direct impact of the treatment on event rate or survival, and the restricted mean survival difference provides a way to evaluat...

aims: the occurrence of fire in residential buildings , commercial complexes and large and small industries cause physical, environmental and financial damages to many different communities. fire safety in hospitals is sensitive and it is believed that the society takes the responsibility to care sick people . the goal of this study was to use fire risk assessment method for engineering (frame)...

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...