We show by elementary combinatorial arguments that any non-zero homogeneous quasimorphism on a given group can be realized as the relative growth of some bi-invariant partial order on that group. Thereby we provide a link between quasimorphisms, bounded cohomology and partial orders. This yields existence results for bi-invariant partial orders, e.g. for non-elementary Gromov hyperbolic groups....

A left order on a magma (e.g., semigroup) is a total order of its elements that is left invariant under the magma operation. A natural topology can be introduced on the set of all left orders of an arbitrary magma. We prove that this topological space is compact. Interesting examples of nonassociative magmas, whose spaces of right orders we analyze, come from knot theory and are called quandles...

OBJECTIVE This study considers three hypotheses regarding the impact of extended involuntary outpatient commitment orders on services utilization. METHOD Service utilization of Victorian Psychiatric Case Register (VPCR) patients with extended (> or =180 day) outpatient commitment orders was compared to that of a diagnostically-matched treatment compliant group with similarly extended (> or =1...

Let n be an ordinal number, let L be an add-associative right complementable right zeroed unital distributive non empty double loop structure, and let m1, m2 be monomials of n, L. Note that m1 ∗m2 is monomial-like. Let n be an ordinal number, let L be an add-associative right complementable right zeroed distributive non empty double loop structure, and let c1, c2 be constant polynomials of n, L...

Viruses catch a wave cientists know from looking at fixed cells that viruses frequently associate with filopodia and microvilli. Using video microscopy, Lehmann et al. (page 317) find that after a virus attaches to the filopodial membrane, it surfs down the plasma membrane toward the cell body. Entry into the cell occurs only after the virus has reached the base of the filopodium. Retroviruses ...

Let F={P1,...,Pm} be a family of sets. A partial order P(F, <) on F is naturally defined by the condition Pi< Pj iff Pi is contained in Pj. When the elements of F are disks (i.e. circles together with their interiors), P(F, <) is called a circle order; if the elements of F are n-polygons, P(F, <) is called an n-gon order. In this paper we study circle orders and n-gon orders. The crossing numbe...

suppose that  is a finite group. then the set of all prime divisors of  is denoted by  and the set of element orders of  is denoted by . suppose that . then the number of elements of order  in  is denoted by  and the sizes of the set of elements with the same order is denoted by ; that is, . in this paper, we prove that if  is a group such that , where , then . here  denotes the family of suzuk...