In this paper we enumerate and classify the “simplest” pairs (M, G) where M is a closed orientable 3-manifold and G is a trivalent graph embedded in M . To enumerate the pairs we use a variation of Matveev’s definition of complexity for 3-manifolds, and we consider only (0, 1, 2)-irreducible pairs, namely pairs (M, G) such that any 2-sphere in M intersecting G transversely in at most 2 points b...

We study the representative consumer’s risk attitude and efficient risk-sharing rules in a singleperiod, single-good economy in which consumers have homogeneous probabilistic beliefs but heterogeneous risk attitudes. We prove that if all consumers have convex absolute risk tolerance, so must the representative consumer. We also identify a relationship between the curvature of an individual cons...

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in five dimensions, and to Takashi Hara for the pleasure of four years of collaboration and for permission to include unpublished joint work.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 ...

Some new examples of two–character sets with respect to planes of PG(3,q2), q odd, are constructed. They arise from three–dimensional hyperbolic quadrics, from the geometry of an orthogonal polarity commuting with a unitary polarity. The last examples arise from the geometry of the unitary group PSU(3,3) acting on the split Cayley hexagon H(2). Dedicated to the memory of András Gács (1969-2009)

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) ...

Models of rational addiction suggest that obesity is consistent with time-consistent preferences. Behavioral economists maintain that addictions such as alcoholism, smoking and over-eating represent examples of present-bias in decision making that is fundamentally irrational. In this article, conduct an experiment to test whether individual discount schedules are time-consistent and whether dis...

Deflection analysis of a simply supported microbeam subjected to a concentrated load at the middle is investigated on the basis of a shear deformable beam theory and non-classical theory. Effects of shear deformation and small size are taken into consideration by hyperbolic shear deformable beam theory and modified strain gradient theory, respectively. The governing differential equations and c...

1. Error calculus 2 1.1. Ulp calculus 2 1.2. Relative error analysis 4 1.3. Generic error of addition/subtraction 4 1.4. Generic error of multiplication 5 1.5. Generic error of inverse 5 1.6. Generic error of division 6 1.7. Generic error of square root 7 1.8. Generic error of the exponential 7 1.9. Generic error of the logarithm 8 1.10. Ulp calculus vs relative error 9 2. Low level functions 9...

1. Notations and Assumptions 2 2. Error calculus 2 2.1. Ulp calculus 2 2.2. Relative error analysis 4 2.3. Generic error of addition/subtraction 4 2.4. Generic error of multiplication 5 2.5. Generic error of inverse 5 2.6. Generic error of division 6 2.7. Generic error of square root 7 2.8. Generic error of the exponential 7 2.9. Generic error of the logarithm 8 2.10. Ulp calculus vs relative e...