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Resolution of singularities and geometric proofs of the Lojasiewicz inequalities
Get PDFThe Łojasiewicz inequalities for real analytic functions on Euclidean space were first proved by Stanisław Łojasiewicz in [83, 84, 87] using methods of semianalytic and subanalytic sets, arguments later simplified by Bierstone and Milman [7]. In this article, we first give an elementary geometric, coordinate-based proof of the Łojasiewicz inequalities in the special case where the function is C^1 with simple normal crossings. We then prove, partly following Bierstone and Milman [9, Section 2] and using resolution of singularities for real analytic varieties, that the gradient inequality for an arbitrary real analytic function follows from the special case where it has simple normal crossings. In addition, we give elementary proofs of the the Łojasiewicz inequalities when the function is C^2 and Morse–Bott or C^N and Morse–Bott of order N ≥ 2
Quantised relativistic membranes and non-perturbative checks of gauge/gravity duality
Get PDFWe test the background geometry of the BFSS model using a D4–brane probe. This proves a sensitive test of the geometry and we find excellent agreement with the D4–brane predictions based on the solution of a membrane corresponding to the D4–brane propagating on this background
Variations and controls on crustal thermal regimes in Southeastern Australia
No full textThe surface heat flow field in Australia has for many years been poorly constrained compared to continental regions elsewhere. 182 recent heat flow determinations and 66 new heat production measurements for Southeastern Australia significantly increase our understanding of local and regional lithospheric thermal regimes and allow for detailed thermal modelling. The new data give a mean surface heat flow for Victoria of 71 ± 15 mW m-2 which fits within the 61–77 mW m-2 range reported for Phanerozoic-aged crust globally. These data reveal three new thermally and compositionally distinct heat flow sub-provinces within the previously defined Eastern Heat Flow Province: the Delamerian heat flow sub-province (average surface heat flow 60 ± 9 mW m- 2); the Lachlan heat flow sub-province (average surface heat flow 74 ± 13 mW m- 2); and the Newer Volcanics heat flow sub-province (average surface heat flow 72 ± 16 mW m- 2) which includes extreme values that locally exceed 100 mW m- 2. Inversions of reduced heat flow and crustal differentiation find that the Delamerian sub-province has experienced significant crustal reworking compared to the Lachlan and Newer Volcanics sub-provinces. The latter has experienced volcanism within the last 8 Ma and the degree of variability observed in surface heat flow points (up to 8 mW m-2 per kilometre laterally) cannot be replicated with steady-state thermal models through this sub-province. In the absence of a strong palaeoclimate signal, aquifer disturbances, or highly enriched granites, we suggest that this high variability arises from localised transient perturbations to the upper crust associated with recent intraplate volcanism. This is supported by a strong spatial correlation of high surface heat flow and known eruption points within the Newer Volcanics heat flow sub-province
The development and typology of number suppletion in adjectives
Get PDFThis paper looks at the cross-linguistically rare phenomenon of suppletion in number in adjectives. I consider how such suppletion arises by looking at six known examples with a special focus on the Brittonic languages (Breton, Cornish and Welsh) which are discussed as an extended case study. Three generalisations are suggested on the basis of the typological study. First, adjectives denoting size (“small” and “big”) are at the centre of this phenomenon. Second, where the etymology of the adjectives is known, the plural member of the suppletive pair for “small” develops from a lexeme denoting something having been divided into or consisting of small parts. These lexemes can also be used with some singular nouns and in such cases their reference is to the component structure of the referent. Finally, adjectives with number suppletion tend to mark plural number consistently in environments in which plural marking is otherwise optional or rare
Galactic Cosmic Rays - Theory and Interpretation
Get PDFThe arguments surrounding the Galactic component of the cosmic rays, the energy budget, ques- tions of composition, spectral features, anisotropy, sources etc, will be critically examined. We are moving into a new phase in the study of the Galactic cosmic rays where it is becoming clear that precision measurements are revealing new, and in some cases unexpected, features which are forcing us to develop more sophisticated models for their production and propagation. The fundamental concepts however appear to be quite solid and have changed remarkably little in the more than fifty years since Ginzburg and Syrovatskii’s classic "The Origin of Cosmic Rays"
Spherical Transverse M5-Branes from the Plane Wave Matrix Model
Get PDFWe consider matrix theoretical description of transverse M5-branes in M-theory on the 11-dimensional maximally supersymmetric pp-wave background. We apply the localization to the plane wave matrix model (PWMM) and show that the transverse spherical fivebranes with zero light cone energy in M-theory are realized as the distribution of low energy moduli of the SO(6) scalar fields in PWMM
Magnetic Monopoles and Symmetries in Noncommutative Space
Get PDFIn this paper, we review the progress in the analysis of magnetic monopoles as generalized states in quantum mechanics. We show that the considered model contains rich algebraic structure that generates symmetries which have been utilized in different physical contexts. Even though are we focused on quantum mechanics in noncommutative space R^3_λ , the results can be reconstructed in ordinary quantum mechanics in R^3 as well
The Mile High Magic Pyramid
Get PDFUsing a unified formulation of N=1,2,4,8, super Yang-Mills theories in D=3 spacetime dimensions with fields valued respectively in R,C,H,O, it was shown that tensoring left and right multiplets yields a Freudenthal magic square of D=3 supergravities. When tied in with the more familiar R,C,H,O description of super Yang-Mills in D=3,4,6,10 this results in a magic pyramid of supergravities: the known 4×4 magic square at the base in D=3, a 3×3 square in D=4, a 2×2 square in D=6 and Type II supergravity at the apex in D=10
Crustal structure of southern Burkina Faso inferred from magnetotelluric, gravity and magnetic data
Get PDFUnderstanding the architecture of the West African craton at depth is essential to be able to reconstruct its evolution. Our study focuses on the crustal imaging of structures and geometries characterizing the crust of the Leo-Man shield with broadband and long period magnetotelluric data collected in southern Burkina Faso and covering a 220 km long profile. The resulting 3D resistivity crustal model highlights the distribution of the granite-greenstone assemblages with depth showing excellent correlation with mapped surficial lithologies. The whole crust of southern Burkina Faso is resistive, with lateral as opposed to vertical major resistivity contrasts, reflecting the location of major-scale shear zones characterizing this part of the Baoulé-Mossi domain. Ground gravity data acquired along the same line as the MT data were also modeled and show relatively good correspondence with the resistivity model. The new resistivity and gravity models compared with results from joint inversion of gravity and aeromagnetic data highlight significant changes between the greenstone belts and granitoid domains along the profile. The comparison of the geophysics with the geology enables us to define new depth constraints of the main tectonic features in the area. The observed large scale dipping shear zones favour the model of crustal building through major parallel thrust faults
