Triads, Flocks of Conics and Q -(5,q)

We show that if an ovoid of Q (4,q),q even, admits a flock of conics then that flock must be linear. It follows that an ovoid of PG (3,q),q even, which admits a flock of conics must be an elliptic quadric. This latter result is used to give a characterisation of the classical example Q ^-(5,q) among the generalized quadrangles T ₃( ), where is an ovoid of PG (3q) and q is even, in terms of the geometric configuration of the centres of certain triads.     

Structure in the classical knot concordance group

We provide new information about the structure of the abelian group of topological concordance classes of knots in $S^3$. One consequence is that there is a subgroup of infinite rank consisting entirely of knots with vanishing Casson-Gordon invariants but whose non-triviality is detected by von Neumann signatures.     

Groups with infinitely many types of fixed subgroups

It is a theorem of Shor that ifG is a word-hyperbolic group, then up to isomrphism, only finitely many groups appear as fixed subgroups of automorphisms ofG. We give an example of a groupG acting freely and cocompactly on a CAT(0) square complex such that infinitely many non-isomorphic groups appear as fixed subgroups of automorphisms ofG. Consequently, Shor’s finiteness result does not hold if the negative curvature condition is relaxed to either biautomaticity or nonpositive curvature. D. T. Wise was supported by grants from FCAR and NSERC.     

Free group representations from vector-valued multiplicative functions,I

Let Γ denote a noncommutative free group and let Ω stand for its boundary. We construct a large class of unitary representations of Γ. This class contains many previously studied representations, and is closed under several natural operations. Each of the constructed representations is in fact a representation of Γ ⋉_λ C(Ω). We prove here that each of them is irreducible as a representation of Γ ⋉_λ C(Ω). Actually, as will be shown in further work, each of them is irreducible as a representation of Γ, or is the direct sum of exactly two irreducible, inequivalent Γ-representations. This research was supported by the Italian CNR.     

Isoperimetric inequalities for nilpotent groups

We prove that every finitely generated nilpotent group of class c admits a polynomial isoperimetric function of degree c + 1 and a linear upper bound on its filling length function.     

A Class of Orthogonal Refinable Functions and Wavelets

We give a construction, for any n 2, of a space S of spline functions of degree n – 1 with simple knots in (1/4)Z which is generated by a triple of refinable, orthogonal functions with compact support. Indeed, the result holds more generally by replacing the B-spline of degree n – 1 with simple knots at the integers by any continuous refinable function whose mask is a Hurwitz polynomial of degree n. A simple construction is also given for the corresponding wavelets.     

Organizations and Complexity: Searching for the Edge of Chaos

Traditional organizational theory advocates increased differentiation and horizontal integration for organizations in unstable environments or with uncertain technologies. This paper seeks to develop a better understanding of the relationship of group structure and the level of interdependency between individuals on group performance under various task complexities. Complexity theory in general, and NK models in particular, are introduced as theoretical frameworks that offer an explanation for group performance. Simulation models are developed, based on the communication network research of Bavelas (1948) and Leavitt (1952), to explore the effects of decentralization and interdependence. The simulation model developed here shows general consistency with previous human subject experiments. However, contrary to predictions, not all decentralized group structures perform well when undertaking complex task assignments. Structures that are highly connected (actors communicating with all others) perform much worse than those with a lower level of connection. Further experiments varying both the number of actors and the degree of interdependence between them find evidence of the edge of chaos. This research advances our understanding of organizations beyond earlier models by suggesting that there is an optimal range of interconnectedness between actors or tasks that explains the variation in performance. An intriguing result is that this optimal level of interdependence is fairly low, regardless of the size of the group.     

Synthesis of SnO2−x nanoparticles tuned between 0 x 1 in a premixed low pressure H2/O2/Ar flame

The transition from tin monoxide to tin dioxide is investigated by doping a low pressure premixed H₂/O₂/Ar flame with dilute concentrations of tetramethyl tin (TMT) Sn(CH₃)₄. The H₂/O₂ ratio was varied between 1.97 and 0.97; the reactor pressure was set to 30 mbar. The inlet gas velocity was kept constant and the precursor concentration was varied between 200 and 700 ppm. Mean particle diameters between 3 nm d_p 7 nm were measured using a particle mass spectrometer (PMS), while X-ray diffraction (XRD) and transmission electron microscope (TEM) analysis revealed information on crystal structure as well as morphology of the synthesized oxides. A gray SnO film was observed in the reactor at low oxygen concentrations, while for higher oxygen concentrations light yellow sub-stoichiometric tin oxides and white SnO₂ were obtained. Further analysis of the sub-stoichiometric oxides, using atomic electron spectroscopy AES revealed that SnO_2−x (0.2 x 0.6) was obtained. Furthermore, electrical characterization of all materials, deposited on interdigital capacitors, showed a decrease in the conductivity of the nanoparticles with increasing oxidation (decreasing x).     

Intermolecular Electron Spin Transfer between Naphthalene π-Systems Separated by a Variable Number of Spirobonded Cyclobutane Rings,An. ESR and ENDOR Study

The radical anions of the compounds N1N, N3N and N5N , in which two naphthalen π-systems are separated by 1, 3 and 5 spirobonded cyclobutane rings, respectively, and tha tof the reference compound N1 , containing one naphthalene π-system and one cyclobutane ring, have been studied by ESR and ENDOR spectroscopy under a variety of experimental conditions. The intramolecular electrons spin transfer between the two π-moieties in N3N and N5N is slow on the hyperfine time-scale, irrespective of the applied conditions. It is also slow in N1N , except for media of high solvating power. In such media, with a slight reduction of N1N to its radical anion, a paramagnetic species is observed, the hyperfine data for which are consistent with N1N to its radical anion, a paramagnetic species is observed, the hyperfine data of which are consistent with N1N , undergoing a fast intramolecular electron spin tansfer. The ESR and ENDOR spectra of this species are superimposed on those characteristic of a slow transfer. It is suggested that the fast and slow transfer involve the syn- and anti-conformations, respectively, since the distance, r, between the two naphthalene π-systems of N1N is considerably shorter in the former than in the latter (r = 740 vs. 880 Pm for the distance between the centres of the π-systems). Glassy solutions of exhaustively reduced N1N display signals of the dianion triplet state, whereas no such signals are found for N3N and N5N . The zero-field splitting parameter, D , is 4.7 mT, corresponding to r ≈ 480 pm.