We are concerned with some conditions such as the trivial solution of a planar system of differential equations (including the Liénard system) that is globally attractive but not stable. We emphasize the connection with some nonoscillatory conditions. The results are related to the previous ones obtained by Hara in 1993. 2000 Mathematics Subject Classification. 34D45.

Let u; v be distin t verti es of a multigraph G with degrees d u and d v , respe tively. The number of edge-disjoint u; v-paths in G is bounded above by minfd u ; d v g. A multigraph G is optimally edgeonne ted if for all pairs of distin t verti es u and v this upper bound is a hieved. If G is a multigraph with degree sequen e D, then we say G is a realisation of D. We hara terize degree sequen...

Lagrangian Descriptors (LDs) are scalar quantities able to reveal separatrices, manifolds of hyperbolic saddles, and chaotic seas dynamical systems. A popular version the LDs consists in computing arc-length trajectories over a calibrated time-window. Herein we introduce exploit an intrinsic geometrical parametrisation LDs, free time variable, for 1 degree-of-freedom Hamiltonian The depends sol...

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in five dimensions, and to Takashi Hara for the pleasure of four years of collaboration and for permission to include unpublished joint work.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

Ligand bias is a recently introduced concept in the receptor signaling field that underlies innovative strategies for targeted drug design. Ligands, as a consequence of conformational selectivity, produce signaling bias in which some downstream biochemical pathways are favored over others, and this contributes to variability in physiological responsiveness. Though the concept of bias and its im...

Presented herein is a closed-form mathematical solution for the construction of an orthogonal cross section of intersecting cylinder surface geometry created from a single planar section. The geometry in its 3-dimensional state consists of the intersection of two cylindrical surfaces of equal radii which is bounded on all four sides by planes orthogonal to the primary cylinder axis. A multivari...