The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Coincidence Wecken homotopies versus Wecken homotopies relative to a fixed homotopy in one of the maps

We study the 1-parameter Wecken problem versus the restricted Wecken problem, for coincidence free pairs of maps between surfaces. For this we use properties of the function space between two surfaces and of the pure braid group on two strings of a surface. When the target surface is either the 2-sphere or the torus it is known that the two problems are the same. We classify most pairs of homotopy classes of maps according to the answer of the two problems are either the same or different when the target is either projective space or the Klein bottle. Some partial results are given for surfaces of negative Euler characteristic. (C) 2010 Elsevier B.V. All rights reserved.

Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani)

We prove that the symplectic group Sp(2n, Z) and the mapping class group Mod(S) of a compact surface S satisfy the R(infinity) property. We also show that B(n)(S), the full braid group on n-strings of a surface S, satisfies the R(infinity) property in the cases where S is either the compact disk D, or the sphere S(2). This means that for any automorphism phi of G, where G is one of the above groups, the number of twisted phi-conjugacy classes is infinite.

Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane

We classify the ( finite and infinite) virtually cyclic subgroups of the pure braid groups P(n)(RP(2)) of the projective plane. The maximal finite subgroups of P(n)(RP(2)) are isomorphic to the quaternion group of order 8 if n = 3, and to Z(4) if n >= 4. Further, for all n >= 3, the following groups are, up to isomorphism, the infinite virtually cyclic subgroups of P(n)(RP(2)): Z, Z(2) x Z and the amalgamated product Z(4)*(Z2)Z(4).

Boutet de Monvel`s calculus and groupoids I

Can Boutet de Monvel`s algebra on a compact manifold with boundary be obtained as the algebra Psi(0)(G) of pseudodifferential operators on some Lie groupoid G? If it could, the kernel G of the principal symbol homomorphism would be isomorphic to the groupoid C*-algebra C*(G). While the answer to the above question remains open, we exhibit in this paper a groupoid G such that C*(G) possesses an ideal I isomorphic to G. In fact, we prove first that G similar or equal to Psi circle times K with the C*-algebra Psi generated by the zero order pseudodifferential operators on the boundary and the algebra K of compact operators. As both Psi circle times K and I are extensions of C(S*Y) circle times K by K (S*Y is the co-sphere bundle over the boundary) we infer from a theorem by Voiculescu that both are isomorphic.

Construction of Hamiltonian-Minimal Lagrangian submanifolds in Complex Euclidean Space

We describe several families of Lagrangian submanifolds in complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odd-dimensional unit sphere.

Spherical space forms - Homotopy self-equivalences and homotopy types, the case of the groups Z/a x (Z/b x TL(2)(F(p)))

Let G = Z/a x(mu) (Z/b x TL(2)(F(p))) and X(n) be an n-dimensional CW-complex with the homotopy type of the n-sphere. We determine the automorphism group Aut(G) and then compute the number of distinct homotopy types of spherical space forms with respect to free and cellular G-actions on all CW-complexes X(2dn - 1), where 2d is a period of G. Next, the group E(X(2dn - 1)/alpha) of homotopy self-equivalences of spherical space forms X(2dn - 1)/alpha, associated with such G-actions alpha on X(2dn - 1) are studied. Similar results for the rest of finite periodic groups have been obtained recently and they are described in the introduction. (C) 2009 Elsevier B.V. All rights reserved.

Intralamellar structural modifications related to the proton exchanging in K(4)Nb(6)O(17) layered phase

Basic structural aspects about the layered hexaniobate of K(4)Nb(6)O(17) composition and its proton-exchanged form were investigated mainly by spectroscopic techniques. Raman spectra of hydrous K(4)Nb(6)O(17) and H(2)K(2)Nb(6)O(17)center dot H(2)O show significant modifications in the 950-800 cm(-1) region (Nb-O stretching mode of highly distorted NbO(6) octahedra). The band at 900 cm(-1) shifts to 940 cm(-1) after the replacement of K(+) ion by proton. Raman spectra of the original materials and the related deuterated samples are similar suggesting that no isotopic effect occurs. Major modifications were observed when H(2)K(2)Nb(6)O(17) was dehydrated: the relative intensity of the band at 940 cm(-1) decreases and new bands seems to be present at about 860-890 cm(-1). The H(+) ions should be shielded by the hydration sphere what preclude the interaction with the layers. Removing the water molecules, H(+) ions can establish a strong interaction with oxygen atoms, decreasing the bond order of Nb-O linkage. X-ray absorption near edge structure studies performed at Nb K-edge indicate that the niobium coordination number and oxidation state remain identical after the replacement of potassium by proton. From the refinement of the fine structure, it appears that the Nb-Nb coordination shell is divided into two main contributions of about 0.33 and 0.39 nm, and interestingly the population, i.e., the number of backscattering atoms is inversed between the two hexaniobate materials. 2009 Elsevier Ltd. All rights reserved.

Application of Microelectrode Voltammetry to Study the Properties of Surfactant Solutions: Alkyltrimethylammonium Bromides

Microelectrode cyclic voltammetry (MV) has been employed to investigate the micellar properties of solutions of homologous alkyltrimethylammonium bromides, RMe(3)ABr, R = C(10), C(12), and C(14), in water and in the presence of added NaBr. The micellar self-diffusion coefficient was calculated from the limiting current for the reversible electron transfer of micelle-bound ferrocene. From the values of this property, other parameters were calculated, including the micellar hydrodynamic radius, RH, and aggregation number, N(agg); the latter was also theoretically calculated. We determined the values of the diffusion coefficient as a function of various experimental variables and observed the following trends: The diffusion coefficient decreases as a function of increasing surfactant concentration (no additional electrolyte added); it decreases as a function of increasing surfactant concentration at fixed NaBr concentration; and it shows a complex dependence (increase then decrease) on the NaBr concentration at a fixed RMe(3)ABr concentration. The value of the intermicellar interaction parameter decreases and then increases as a function of increasing NaBr concentration. These results are discussed in terms of intermicellar,interactions and the effect of NaBr on the micellar surface charge density and sphere-to-rod geometry change. The NaBr concentration required to induce the latter change increases rapidly as a function of decreasing the length of R: no geometry change was detected for C(10)Me(3)ABr. Values of N(agg) increase as I function of increasing the length of R and are in good agreement with both literature values and values that were calculated theoretically. Thus, MV is a convenient and simple technique for obtaining fundamental properties of surfactant solutions, including additive-induced changes of micellar parameters (N(agg)) and morphology changes.

Synthesis, characterization and spectroscopic investigation of new tetrakis(acetylacetonato)thulate(III) complexes containing alkaline metals as countercations

In this work a series of tetrakis complexes C[Tm(acac)(4)] where C(+) = Li(+) Na(+) and K(+) countercations and acac = acetylacetonate ligand were synthesized and characterized for photoluminescence investigation The relevant aspect is that these complexes are water-free in the first coordination sphere The emission spectra of the tetrakis Tm(3+)-complexes present narrow bands characteristic of the (1)G(4)->(3)H(6) (479 nm) (1)G(4)->(3)F(4) (650 nm) and (1)G(4) ->(3)H(5) (779 nm) transitions of the Tm(3+) ion with the blue emission color at 479 nm as the most prominent one The lifetime values (tau) of the emitting (1)G(4) level of the C[Tm(acac)(4)] complexes were 344 360 and 400 ns for the Li(+) Na(+) and K(+) countercations respectively showing an increasing linear behavior versus the ionic radius of the alkaline ion An efficient intramolecular energy transfer process from the triplet state (T) of the ligands to the emitting (1)G(4) state of the Tm(3+) ion is observed This fact together with the absence of water molecules in first coordination sphere allows these tetrakis Tm(3+)-complexes to act as efficient blue light conversion molecular devices (c) 2010 Elsevier B V All rights reserved

Luminescence enhancement of the Tb(III) ion with the thenoyltrifluoroacetonate ligand acting as an efficient sensitizer

The synthesis, structural investigation, and photophysical properties of the complex [Tb(TTA)(2)(NO(3)) (TPPO)(2)] are reported. Unlike the analog tris-diketonate complex [Tb(TTA)(3)(TPPO)(2)], the new complex presents abnormally high luminescence intensity centered on the terbium ion. Our results clearly suggest a higher energy transfer efficiency from the TEA antenna ligand to the Tb(III) ion in the bis-diketonate complex compared with that in the tris-diketonate complex. A mechanism involving the increasing of triplet state energy when one TTA ligand is replaced by the NO(3)(-) group in the first coordination sphere is suggested and experimentally investigated to explain the anomalous luminescence properties of the new complex [Tb(TTA)(2)(NO(3))(TPPO)(2)]. (C) 2010 Elsevier B.V. All rights reserved.

A theoretical study on the XeF(2) molecule

A relativistic four-component study was performed for the XeF(2) molecule by using the Dirac-Coulomb (DC) Hamiltonian and the relativistic adapted Gaussian basis sets (RAGBSs). The comparison of bond lengths obtained showed that relativistic effects on this property are small (increase of only 0.01 angstrom) while the contribution of electron correlation, obtained at CCSD(T) or CCSD-T levels, is more important (increase of 0.05 angstrom). Electron correlation is also dominant over relativistic effects for dissociation energies. Moreover, the correlation-relativity interaction is shown to be negligible for these properties. The electron affinity, the first ionization potential and the double ionization potential are obtained by means of the Fock-space coupled cluster (FSCC) method, resulting in DC-CCSD-T values of 0.3 eV, 12.5 eV and 32.3 eV, respectively. Vibrational frequencies and some anharmonicity constants were also calculated under the four-component formalism by means of standard perturbation equations. All these molecular properties are, in general, ill satisfactory agreement with available experimental results. Finally, a partition in terms of charge-charge flux-dipole flux (CCFDF) contributions derived by means of the quantum theory of atoms in molecules (QTAIM) in non-relativistic QCISD(FC)/3-21G* calculations was carried out for XeF(2) and KrF(2). This analysis showed that the most remarkable difference between both molecules lies on the charge flux contribution to the asymmetric stretching mode, which is negligible in KrF(2) but important in XeF(2). (c) 2008 Elsevier B.V. All rights reserved.

Cationic and neutral phenylmercury(II) complexes with heterocyclic thione ligands. X-ray structures of [HgPh(dmpymtH)][BF(4)] center dot H(2)O and [{HgPh}(2)(mu-dtu)]

The neutral complex [HgPh(dmpymt)] 1 (dmpymtH = 4,6-dimethylpyrimidine-2(1H)-thione) reacts with HBF(4) to give the cationic complex [HgPh(dmpymtH)][BF(4)] 2. The X-ray molecular structure of the later revealed a [2+1] coordination sphere about the mercury(II) atom (C-Hg-S and Hg center dot center dot center dot N). In the dinuclear complex [(HgPh)(2)(mu-dtu)] 3 [dtuH(2) = 2,4(1H,3H)-pyrimidinedithione or dithiouracil] the coordination spheres are also [2+1] although dissimilar regarding the Hg center dot center dot center dot N secondary bonds. NMR spectroscopy ((1)H, (13)C and (199)Hg) studies were undertaken in solution and the results discussed in the light of the X-ray structures. (C) 2008 Elsevier B. V. All rights reserved.

Oxotechnetium(V) Complexes with a Novel Class of Tridentate Thiosemicarbazide Ligands

A novel tridentate thiosemicarbazide-type ligand class with an SNS donor set, H(2)L(1), was prepared by reactions of N-[N`,N`-dialkylamino(thiocarbonyl)]benzimidoyl chlorides with thiosemicarbazides. H(2)L(1) ligands readily react with (NBu(4))[TcOCl(4)] in MeOH under the formation of red oxotechnetium(V) complexes of composition [TcOCl(L(1))]. The monomeric, five-coordinate compounds are air-stable and bind (L(1))(2-) tridentate in the equatorial coordination sphere. The compounds represent the first examples of oxotechnetium(V) complexes with NS chelate-bonded thiosemicarbazones.

Öppna arenor och slutna rum : några kommunikationskonsulter i Dalarna ser på opinionsbildning

Syftet med denna uppsats är att ta reda på hur lokala kommunikationskonsulter i Falun/Borlänge-regionen ser på opinionsbildning via professionella konsulter. De centrala begrepp som avhandlas är PR, opinionsbildning och lobbying.Den teoretiska ram som omger undersökningen består av de teoribyggen som skapats av Jürgen Habermas, James E. Grunig och Larsåke Larsson. Habermas ställer sig tveksam till den demokratiska nyttan av professionell opinionsbildning, Grunig är mer positiv och Larsson ser både för- och nackdelar med PR-verksamheten. Larssons undersökning av opinionskonsulter från 2005 refereras också.Undersökningen bygger på intervjuer med ett antal kommunikationskonsulter verksamma i Falun och Borlänge. Den lokala marknaden för opinionsbildande uppdrag diskuteras, men också huruvida politiska uppdrag förser byråerna med politisk färg. Huruvida medarbetarnas engagemang är viktigt och hur hög statusen på opinionsbildande uppdrag är ventileras, samt vilka arbetsmetoder som används. Intervjuerna behandlar också förekomsten av lobbying på lokal nivå. Till slut redogör de intervjuade för sin syn på hur opinionsbildning, PR och lobbying via konsulter påverkar demokratin.Under slutsatser diskuteras resultatet i relation till den teoretiska ramen. Att PR- och reklambranscherna alltmer växer samman och att opinionsbildning är ett vanligt inslag i många projekt är ett faktum som också skymtat fram i den teoretiska ramen. Men reklam- och PR-metoder integreras också i politiken, på gott och ont. Följaktligen växer den gråzon som finns mellan de olika typerna av kommunikation och mellan opinionsbildande och icke-opinionsbildande uppdrag. Det försvårar gränsdragning och tydlighet, men skapar nya kreativa möjligheter.Att den ökade användningen av kommunikationskonsulter kanske kan bidra till en orättvis fördel för resursstarka organisationer diskuteras. Ny teknik, t.ex. Internet, kan dock eventuellt vara den motvikt som gör det möjligt även för resurssvaga grupper att höras i det offentliga samtalet. Kommunikation som maktfaktor tas även upp utifrån termer som lobbying och medias dagordningsfunktion.Några aspekter av den outnyttjade potential som PR har ventileras också. PR som metod är en outnyttjad resurs på det lokala planet, något som kan bero både på okunskap hos de lokala kunderna och ett traditionellt arbetssätt hos byråerna. Utifrån intervjusvaren framkommer att både byråerna, deras kunder och media på landsorten skulle gynnas av ett större samarbete.Resultaten av intervjuerna stöder mycket i den teoretiska ramen, medan somligt förkastas. Som sammanfattning kan sägas att opinionsbildning via konsulter kan användas för både gott och ont. Vilket som blir resultatet handlar som oftast om etik, ansvar, öppenhet och professionalitet.ABSTRACTThe primary target for this report is to find out how communication consultants in the region of Falun and Borlänge views the practice of establishing public opinions by using professional public relations consultants. The concepts in focus are PR, the moulding of public opinion and lobbying.The theoretical framework surrounding this report is the writings by Jürgen Habermas, James E. Grunig and Larsåke Larsson. Habermas has doubts as to the democratic use of professional consultants working with public opinions, Grunig has a somewhat more positive approach and Larsson sees both advantages and disadvantages in a democratic sense with the PR industry. Larssons research concerning consultants working with the moulding of public opinions from 2005 is also reviewed. The research is carried out by interviewing some communication consultants working in the Falun /Borlänge- area. The local market for commissions concerning public opinions is discussed, but also if and how political commissions are forcing a political stamp upon the firms engaging in such commissions. The importance of personal commitment in the consultants and the level of prominence commissions concerning public opinion has in the business is discussed, but also which methods is used and preferred. The interviews also deal with the practice of lobbying in the local arena. Finally the participants state their views on how the moulding of public opinion, PR and lobbying effects the democracy. Conclusively, the result is put in relation to the theories earlier mentioned. The public relations market is merging with the advertising business, that is a fact, and establishing public opinion is a common element in a lot of projects. But methods used for advertising and PR are also integrated in the political sphere, for good and bad. That has made the distinction between different kinds of communication harder, thereby enhancing the difficulties of establishing boundaries and achieving clarity. Yet at the same time it facilitates new creative opportunities.The growing use of communication consultants may contribute to unfair advantages for organisations with large economic resources. New technical development though, such as the Internet for example, may prove to simplify communication for groups with lesser economic power. Communication as an aspect of power is being discussed in terms of lobbying and the agenda setting power of media.Some aspects of the unused potential that lies within PR are also in focus in this report. PR as a method is an unused resource in the local market, which can be due to the local clients lack of knowledge but also to the traditional work carried out by the communication firms. The findings of the interviews show that both communication firms, their clients and the local media would benefit from greater cooperation.The theoretical base in this work is mostly supported by the interviews, though a few of the findings does not agree. The moulding of public opinions by professional consultants can be used for both good and bad. What the result will be is, not surprisingly, a question of ethics, responsibility, openness and professionalism.