Abstract:
This introduction presentation addresses in a general way the historical invention of Nuclear Magnetic Resonance and its general aspects and characteristics: sensitivity and its consequences, nature of the interactions, observation methods, sophistications, longitudinal and transverse relaxation, and principle of Magnetic Resonance Imaging.

Abstract:
The impact of economic recessions on business strategy and marketinghas recently received increased research attention. However, thesecontributions are limited, especially with respect to sports marketingbusinesses and those operating in emerging markets. The main aim ofthis study was to examine the impact of the global recession on the businessmodels of sports marketing businesses. Qualitative data were collectedvia semi-structured interviews with executives at market-leadingsports marketing businesses in South Africa. Grounded theory dataanalysis was conducted to understand the common patterns within thedata. The results of the research point to four significant business modelshifts, influencing the customer value proposition, agency relationships,revenue models and staffing approaches of sports marketingfirms. Theoretical and practical implications are discussed includingthe suggestion to revisit the business model upon which sports marketingbusinesses compete in a post-crisis world.

Abstract:
The spectra emitted from clouds near the Galactic Centre are investigated calculating the UV-optical-IR lines using the physical parameters and the element abundances constrained by the fit of mid-IR observations. The characteristic line ratios are compared with those observed in active galaxies. We have found that the physical conditions in the nebulae near the GC are different from those of starburst galaxies and AGN, namely, gas velocities and densities as well as the photoionization fluxes are relatively low. The geometrical thickness of the emitting nebulae is particularly small suggesting that matter is strongly fragmented by instabilities leading to an underlying shock-generated turbulence.

Abstract:
This paper gives an elementary proof of the result that the conjugacy classes of pairs (X,Y) of unimodular 2x2 complex matrices is an affine 3-space, parametrized by the traces of X, Y and XY. Identities for triples of elements of SL(2,C) are also derived.

Abstract:
The SL(2)-character variety X of a closed surface M enjoys a natural complex-symplectic structure invariant under the mapping class group G of M. Using the ergodicity of G on the SU(2)-character variety, we deduce that every G-invariant meromorphic function on X is constant. The trace functions of closed curves on M determine regular functions which generate complex Hamiltonian flows. For simple closed curves, these complex Hamiltonian flows arise from holomorphic flows on the representation variety generalizing the Fenchel-Nielsen twist flows on Teichmueller space and the complex quakebend flows on quasi-Fuchsian space. Closed curves in the complex trajectories of these flows lift to paths in the deformation space of complex-projective structures between different projective structures with the same holonomy (grafting). A pants decomposition determines a holomorphic completely integrable system on X. This integrable system is related to the complex Fenchel-Nielsen coordinates on quasi-Fuchsian space developed by Tan and Kourouniotis, and relate to recent formulas of Platis and Series on complex-length functions and complex twist flows.

Abstract:
This paper concerns the relationship between locally homogeneous geometric structures on topological surfaces and the moduli of polystable Higgs bundles on Riemann surfaces, due to Hitchin and Simpson. In particular we discuss the uniformization of Riemann surfaces by hyperbolic geometry from this viewpoint, and survey more recent developments in this theory.

Abstract:
The conjugacy class of a generic unimodular 2 by 2 complex matrix is determined by its trace, which may be an arbitrary complex number. In the nineteenth century, it was known that a generic pair (X,Y) of such pairs is determined up to conjugacy by the triple of traces (tr(X),tr(Y),tr(XY), which may be an arbitary element of C^3. This paper gives an elementary and detailed proof of this fact, which was published by Vogt in 1889. The folk theorem describing the extension of a representation to a representation of the index-two supergroup which is a free product of three groups of order two, is described in detail, and related to hyperbolic geometry. When n > 2, the classification of conjugacy-classes of n-tuples in SL(2,C) is more complicated. We describe it in detail when n= 3. The deformation spaces of hyperbolic structures on some simple surfaces S whose fundamental group is free of rank two or three are computed in trace coordinates. (We only consider the two orientable surfaces whose fundamental group has rank 3.)

Abstract:
We survey developments arising from Milnor's 1958 paper, "On the existence of a connection with curvature zero" and his 1977 paper, "On fundamental groups of complete affinely flat manifolds".

Abstract:
Crooked planes were defined by Drumm to bound fundamental polyhedra in Minkowski space for Margulis spacetimes. They were extended by Frances to closed polyhedral surfaces in the conformal compactification of Minkowski space (Einstein space) which we call crooked surfaces. The conformal model of anti-de Sitter space is the interior of the quotient of Einstein space by an involution fixing an Einstein plane. The purpose of this note is to show that the crooked planes defined in anti-de Sitter space recently by Danciger-Gu\'eritaud-Kassel lift to restrictions of crooked surfaces in Einstein space which are adapted under the involution of Einstein space defining anti-de Sitter space.