Group SO3 Research Articles

Kinematics and dynamics of quantum walks in terms of systems of imprimitivity

We build systems of imprimitivity (SI) in the context of quantum walks and provide geometric constructions for their configuration space. We consider three systems, an evolution of unitaries from the group SO3 on a low dimensional de Sitter space where the walk happens on the dual of SO3, a standard quantum walk whose SI live on the orbits of stabilizer subgroups (little groups) of semidirect products describing the symmetries of 1 + 1 spacetime, and automorphisms (walks are specific automorphisms) on distance-transitive graphs as an application of the constructions.

Formula omitted]-adic cofiltration of [formula omitted

We prove that the group SO3(Q) of rational rotations is the inverse limit of a family of finite solvable groups of order 23k−2⋅3, whose 2-Sylow subgroups have nilpotency class 2k−3, exponent 2k−1, and Frattini subgroups coinciding with the commutator subgroups, and we give generators for these groups.

FTIR spectroscopic study of the complex formation between H+ and DMSO in Nafion

Nafion membranes plasticized with dimethyl sulfoxide (DMSO) have been examined at room temperature using the vacuum ATR - FTIR spectroscopic technique in the range 50–4000cm−1. The amount of the plasticizer corresponds to the molecular ratio n=DMSO/H+=1.2, 2.3, 4.8, 7.0, 9.7 and 13.3. The medium intensity band with two maxima at 780 and 853cm−1 have been assigned to the ν(SO) stretching vibrations of the H+(DMSO)2 complex. The possible reason of ν(SO) splitting is symmetry decrease of hydrogen bond under the influence of the anion group SO3− electric field. Whereas the mutual association of free DMSO molecules in Nafion leads to appearance of weak band at 86cm−1 assigned to the dipole-dipole interactions.

Synthesis of graphene/polystyrene nanocomposite by microemulsion polymerization

Graphene/polystyrene nanocomposites were prepared by water-based in situ microemulsion polymerization. Graphene was synthesized from graphite oxide, and then modified by diazonium salt of sulfanilic acid. FT-IR spectrum indicated the presence of functional group SO3- on the surface of graphene. It helps graphene not aggregate in water after reduced by NaBH4, which supported water-based microemulsion process. Ranman spectrum and Tramission Electronic Microscopy (TEM) showed graphene dispersed well in polystyrene matrix. However, there were still some tactoids where graphene had multilayer. The addition of GO increased the glass transition temperature of the PS/GO composites. The storage modulus and thermal stability of the nanocomposites were also improved compared with PS.

Anisotropic developments for homogeneous shear flows

The general decomposition of the spectral correlation tensor Rij(k) by Cambon et al. [J. Fluid Mech. 202, 295 (1989); 337, 303 (1997)] into directional and polarization components is applied to the representation of Rij(k) by spherically averaged quantities. The decomposition splits the deviatoric part Hij(k) of the spherical average of Rij(k) into directional and polarization components Hij(e)(k) and Hij(z)(k). A self-consistent representation of the spectral tensor is constructed in terms of these spherically averaged quantities. The directional and polarization components must be treated independently: representation of the spectral tensor using the spherical average Hij(k) alone proves to be inconsistent with Navier-Stokes dynamics. In particular, a spectral tensor consistent with a prescribed Reynolds stress is not unique. Since spherical averaging entails a loss of information, the description of an anisotropic correlation tensor by spherical averages is limited to weak departures from isotropy. The degree of anisotropy permitted is restricted by realizability requirements. More general descriptions can be given using a higher-order expansion of the spectral tensor. Directionality is described by a conventional expansion in spherical harmonics, but polarization requires an expansion in special tensorial quantities generated by irreducible representations of the rotation group SO3. These expansions are considered in more detail in the special case of axial symmetry.

Introduction to Symmetry Analysis

Introduction to Symmetry Analysis

Permeation of n-butane, 1-butene and 1,3-butadiene through anhydrated Ag +-doped perfluorocarbon-type ion-exchange membranes

The characterization of anhydrated Ag+-doped polyperfluorosulfonate membrane (PSM) was made by using EDS, positron annihilation lifetime measurement and AFM. It was confirmed that the distribution of doped Ag+ in the membrane was homogeneous, the membranes were rather dense ones and the concentration of doped Ag+ was about twice as much as that of charged group SO3− in the membrane. The permeation experiments were also carried out for n-butane, 1-butene and 1,3-butadiene. Anhydrated Ag+-doped PSM exhibited relatively high permeability for 1-butene compared with n-butane and 1,3-butadiene. The ideal separation factor of 1-butene/n-butane, which was the permeability coefficient ratio of 1-butene to n-butane, was about 5400 in the membranes exchanged by AgNO3 aqueous solution at 25°C. Both the permeability of 1-butene and selectivity of 1-butene/n-butane increased with decrease of temperature. On the other hand for 1-butene/1,3-butadiene system, the highest ideal separation factor 11.7 was obtained at 70°C while permeability increased with decrease of temperature. The permeation behaviour of alkenes through anhydrated Ag+-doped PSM could be explained by a swelling model suggested in this paper. Based on such swelling mechanism, the diffusivity and permeability of alkenes were strongly affected by the amount of alkenes absorbed in the membrane.

One Fixed Point Actions and Homology 3-Spheres

One of the best known three-dimensional manifolds is the Poincare homology three-sphere 1(2, 3,5); this closed 3-manifold has the same homology groups as the standard sphere S3 but is not simply connected (see [Pnc, p. 106] or [Br2, Section 1.8]). Numerous investigations during the past century have shown that this manifold has many remarkable properties; several equivalent descriptions of 1(2,3,5) are summarized in [KiS]. From the viewpoint of transformation groups, one noteworthy property is that 1(2, 3, 5) is the only nonsimply connected homology sphere admitting a transitive action of a compact Lie group [Brl]. The manifold 1(2, 3,5) also figures importantly in regularity questions for group actions on spherelike manifolds. Linear (or orthogonal) actions of finite groups on spheres are generally viewed as the simplest and most regular examples of such actions, and one of the themes of transformation groups is to determine the extent to which arbitrary actions on spherelike manifolds resemble linear actions. One distinguishing feature of linear actions is that their fixed point sets (if nonempty) are also spheres. The well-known results of P. A. Smith (cf. [Br2]) show that continuous p-group actions on homology spheres all resemble linear actions in this respect; i.e., the fixed point sets are always Zp-homology (cohomology) spheres. On the other hand, outside the family of p-groups, there are many exotic group actions. Perhaps the most elementary example of this type involves 1(2, 3,5). If A is the subgroup of the rotation group SO3 given by the symmetries of a regular icosahedron (so that A is isomorphic to the alternating group A5), then the quotient space S03/A is the Poincare homology 3-sphere and the induced action of A5 ? A has exactly one fixed point. This example suggests that general actions of finite groups on homology spheres can be quite different from linear actions, and much of the work on exotic finite group actions during the past three decades was at least partially motivated by the existence of this group action.

New results on conjectures by Lichnerowicz and Caratheodory

Every stationary universe model, with asymptotically Euclidean behaviour, for which the lines of the matter flow (considered as a perfect fluid) coincide with the time lines, is spherically symmetric (that is, the group SO3 acts on the space section as an isometry group). Every regular surface (that is, of class Ck with k sufficiently large), diffeomorphic to the sphere S2, strictly convex, possesses at least two umbilical points.

Application of Raman spectroscopy to industrial membranes. Part 2–Perfluorosulphonic membrane

AbstractThe Raman spectrum of a Nafion 117 membrane immersed in aqueous solution was recorded. Assignments are proposed for the fundamental vibrations observed for this material. The interaction of counter ions (cations) and also of sorbed electrolytes with the antagonist group SO3− of the membrane were studied. For this purpose, intensity measurements were made of selected appropriate signals versus the nature and type of counter ions (monovalent, divalent). The intensity of the symmetric stretching vibration band of the SO3− group can be used to monitor the variation of the conductivity of the membrane studied.

Interferometry in a space-time with torsion

The phase shift in neutron interference due to the gravitational field containing torsion is obtained, by using a WKB approximation of Dirac’s equation. It is then shown that, an upper limit on torsion of about 1-7 m-1 may be placed, for the first time, in principle, by neutron interferometry. This phase shift can also be obtained by a path-ordered operator, which is an element of the anti-De Sitter group SO3,2 that determines the evolution of the wave function. This is somewhat analogous to the determination of the corresponding phase shift for gauge fields by means of parallel transports which are elements of the gauge group.