The Invariant Fields of the Sylow groups of Classical Groups in the natural characteristic

Let X be any finite classical group defined over a finite field of characteristic p>0. In this paper we determine the fields of rational invariants for the Sylow p-subgroups of X, acting on the natural module. In particular we prove that these fields are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant linear forms defining X.Comment: 33 page

The invariant rings of the Sylow groups of GU(3,q2), GU(4,q2), Sp(4,q) and O+(4,q) in the natural characteristic

Let G be a Sylow p-subgroup of the unitary groups GU(3, q2), GU(4, q2), the symplectic group Sp(4, q) and, for q odd, the orthogonal group O +(4, q). In this paper we construct a presenta tion for the invariant ring of G acting on the natural module. In particular we prove that these rings are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant form defining the corresponding classical group. We also show that these generators form a SAGBI basis and the invariant ring for G is a complete intersection.info:eu-repo/semantics/publishedVersio

The invariant fields of the Sylow groups of classical groups in the natural characteristic

Let X be any finite classical group defined over a finite field of characteristic p > 0. In this article, we determine the fields of rational invariants for the Sylow p-subgroups of X, acting on the natural module. In particular, we prove that these fields are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant linear forms defining X.info:eu-repo/semantics/publishedVersio

Graphene growth on h-BN by Molecular Beam Epitaxy

The growth of single layer graphene nanometer size domains by solid carbon source molecular beam epitaxy on hexagonal boron nitride (h-BN) flakes is demonstrated. Formation of single-layer graphene is clearly apparent in Raman spectra which display sharp optical phonon bands. Atomic-force microscope images and Raman maps reveal that the graphene grown depends on the surface morphology of the h-BN substrates. The growth is governed by the high mobility of the carbon atoms on the h-BN surface, in a manner that is consistent with van der Waals epitaxy. The successful growth of graphene layers depends on the substrate temperature, but is independent of the incident flux of carbon atoms.Comment: Solid State Communications, 201

Molecular beam growth of graphene nanocrystals on dielectric substrates

We demonstrate the growth of graphene nanocrystals by molecular beam methods that employ a solid carbon source, and that can be used on a diverse class of large area dielectric substrates. Characterization by Raman and Near Edge X-ray Absorption Fine Structure spectroscopies reveal a sp2 hybridized hexagonal carbon lattice in the nanocrystals. Lower growth rates favor the formation of higher quality, larger size multi-layer graphene crystallites on all investigated substrates. The surface morphology is determined by the roughness of the underlying substrate and graphitic monolayer steps are observed by ambient scanning tunneling microscopy.Comment: Accepted in Carbon; Discussion section added; 20 pages, 6 figures (1 updated

Field-induced Ordering in Critical Antiferromagnets

Transfer-matrix scaling methods have been used to study critical properties of field-induced phase transitions of two distinct two-dimensional antiferromagnets with discrete-symmetry order parameters: triangular-lattice Ising systems (TIAF) and the square-lattice three-state Potts model (SPAF-3). Our main findings are summarised as follows. For TIAF, we have shown that the critical line leaves the zero-temperature, zero -field fixed point at a finite angle. Our best estimate of the slope at the origin is $(dT_c/dH)_{T=H=0} = 4.74 \pm 0.15$. For SPAF-3 we provided evidence that the zero-field correlation length diverges as $\xi(T \to 0, H=0) \simeq \exp (a/T^{x})$, with $x=1.08 \pm 0.13$, through analysis of the critical curve at $H \neq 0$ plus crossover arguments. For SPAF-3 we have also ascertained that the conformal anomaly and decay-of-correlations exponent behave as: (a) H=0: $c=1, \eta=1/3$; (b) $H \neq 0: c=1/2, \eta=1/4$.Comment: RevTex, 7 pages, 4 eps figures, to be published in Phys. Rev.

Research and development project assessment and social impact

Nowadays, organisations increasingly need to adapt to the fast evolution of markets and societies in our globalised world in order to be competitive. Therefore, it is essential to take the right decisions when it comes to invest in research and development (R & D) projects. However, an issue that has not been given much attention is how to measure the social impact (or return) of R & D projects. In this exploratory study, the findings of an analysis of how R & D projects are assessed and selected, including this social perspective, are presented. The methodology which has been used in this research includes both interviews and analysis of the data obtained through them. The major finding is that in the current situation the social impact is not taken into account, but is growing the awareness of this perspective among different types of organizations dealing with R & D activities.(undefined)info:eu-repo/semantics/publishedVersio