Irrational Stable Commutator Length in Finitely Presented Groups

We give examples of finitely presented groups containing elements with irrational (in fact, transcendental) stable commutator length, thus answering in the negative a question of M. Gromov. Our examples come from 1-dimensional dynamics, and are related to the generalized Thompson groups studied by M. Stein, I. Liousse and others.Comment: 8 pages, 1 figur

Selective Laser Sintering Process Management Using a Relational Database

With more and more materials used in the Selective Laser Sintering (SLS) process, it is becoming necessary to use a database to manage the process efficiently. In this paper, a relational database for the SLS process is described. The database includes powdered material data, sintering parameters, machine characteristics, mechanical properties and surface quality of prototypes. Use ofthis database will make it is easy to store and retrieve processing information and make decisions for planning the SLS. This paper will go on to describe how the database can be extended to include other RP technologies.Mechanical Engineerin

Stable W-length

We study stable W-length in groups, especially for W equal to the n-fold commutator gamma_n:=[x_1,[x_2, . . . [x_{n-1},x_n]] . . . ]. We prove that in any perfect group, for any n at least 2 and any element g, the stable commutator length of g is at least as big as 2^{2-n} times the stable gamma_n-length of g. We also establish analogues of Bavard duality for words gamma_n and for beta_2:=[[x,y],[z,w]]. Our proofs make use of geometric properties of the asymptotic cones of verbal subgroups with respect to bi-invariant metrics. In particular, we show that for suitable W, these asymptotic cones contain certain subgroups that are normed vector spaces.Comment: 24 pages; version 2 incorporates referee's comment

Femtosecond dynamics of flavoproteins: Charge separation and recombination in riboflavine (vitamin B_2)-binding protein and in glucose oxidase enzyme

Flavoproteins can function as hydrophobic sites for vitamin B_2 (riboflavin) or, in other structures, with cofactors for catalytic reactions such as glucose oxidation. In this contribution, we report direct observation of charge separation and recombination in two flavoproteins: riboflavin-binding protein and glucose oxidase. With femtosecond resolution, we observed the ultrafast electron transfer from tryptophan(s) to riboflavin in the riboflavin-binding protein, with two reaction times: approx 100 fs (86% component) and 700 fs (14%). The charge recombination was observed to take place in 8 ps, as probed by the decay of the charge-separated state and the recovery of the ground state. The time scale for charge separation and recombination indicates the local structural tightness for the dynamics to occur that fast and with efficiency of more than 99%. In contrast, in glucose oxidase, electron transfer between flavin-adenine-dinucleotide and tryptophan(s)/tyrosine(s) takes much longer times, 1.8 ps (75%) and 10 ps (25%); the corresponding charge recombination occurs on two time scales, 30 ps and nanoseconds, and the efficiency is still more than 97%. The contrast in time scales for the two structurally different proteins (of the same family) correlates with the distinction in function: hydrophobic recognition of the vitamin in the former requires a tightly bound structure (ultrafast dynamics), and oxidation-reduction reactions in the latter prefer the formation of a charge-separated state that lives long enough for chemistry to occur efficiently. Finally, we also studied the influence on the dynamics of protein conformations at different ionic strengths and denaturant concentrations and observed the sharp collapse of the hydrophobic cleft and, in contrast, the gradual change of glucose oxidase

Teachers as coaches: A teachers' perceptions and actions in a game-based virtual learning environment

Identification of how a teacher can facilitate learning within virtual environments is critical if use is to become a valued student learning experience. Through an ethnographic case study, a teacher’s perception of her role and her actions in classrooms and the virtual world along with attributes used to facilitate inquiry were described. Comparisons were also made to determine if transfer of pedagogical techniques from traditional to virtual environments were possible. Understanding how game-based complex virtual worlds work and where knowledge that the student is to acquire exists, as well teacher’s value of virtual environments, were key for facilitation and teacher buy-in

A Geometric Study of Commutator Subgroups

Let G be a group and G' its commutator subgroup. Commutator length (cl) and stable commutator length (scl) are naturally defined concepts for elements of G'. We study cl and scl for two classes of groups. First, we compute scl in generalized Thompson's groups and their central extensions. As a consequence, we find examples of finitely presented groups in which scl takes irrational (in fact, transcendental) values. Second, we study large scale geometry of the Cayley graph of a commutator subgroup with respect to the canonical generating set of all commutators. When G is a non-elementary hyperbolic group, we prove that, for any n, there exists a quasi-isometrically embedded, dimension n integral lattice in this graph. Thus this graph is not hyperbolic, has infinite asymptotic dimension, and has only one end. For a general finitely presented group, we show that this graph is large scale simply connected