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Correlation of clusters: Partially truncated correlation functions and their decay
Get PDFIn this article, we investigate partially truncated correlation functions (PTCF) of infinite continuous systems of classical point particles with pair interaction. We derive Kirkwood-Salsburg-type equations for the PTCF and write the solutions of these equations as a sum of contributions labelled by certain forests graphs, the connected components of which are tree graphs. We generalize the method introduced by R.A. Minlos and S.K. Pogosyan (1977) in the case of truncated correlations. These solutions make it possible to derive strong cluster properties for PTCF which were obtained earlier for lattice spin systems
On the Morse-Bott Property of Analytic Functions on Banach Spaces with Lojasiewicz Exponent One Half
Get PDFIt is a consequence of the Morse–Bott Lemma (see Theorems 2.10 and 2.14) that a C^2 Morse–Bott function on an open neighborhood of a critical point in a Banach space obeys a Łojasiewicz gradient inequality with the optimal exponent one half. In this article we prove converses (Theorems 1, 2, and Corollary 3) for analytic functions on Banach spaces: If the Łojasiewicz exponent of an analytic function is equal to one half at a critical point, then the function is Morse–Bott and thus its critical set nearby is an analytic submanifold. The main ingredients in our proofs are the Łojasiewicz gradient inequality for an analytic function on a finite-dimensional vector space [58] and the Morse Lemma (Theorems 4 and 5) for functions on Banach spaces with degenerate critical points that generalize previous versions in the literature, and which we also use to give streamlined proofs of the Łojasiewicz–Simon gradient inequalities for analytic functions on Banach spaces (Theorems 8 and 9)
Review: Hayden and Russell, Grammatica, Gramadach and Gramadeg: Vernacular Grammar and Grammarians in Medieval Ireland and Wales
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Ar drywydd Magna, ‘chwaer Dewi Sant’, ac eglwys ddiflanedig yn Nyffryn Teifi
Get PDFThis article investigates the fragmentary evidence for a lost church called Llanfawr, or Landa Magna in Latin, which lay in the Teifi valley in Ceredigion. It is argued that the Latin name of this church gave rise to stories about a character called Magna or Magnus. This fictional personage appears as the subject of a miracle performed by St David, and in Ireland was even transformed into a sister of David. Sources discussed include Bonedd y Saint, Progenies Keredic, the Breton-Latin Life of St Brioc, Rhygyfarch’s Life of St David, the Life of St Maur by Odo of Glanfeuil, and the tract on the Mothers of Irish Saints. Possible locations of Llanfawr are discussed, but it remains uncertain where precisely it was and whether it corresponds to any church known today
Retrieving robust noise-based seismic velocity changes from sparse data sets: synthetic tests and application to Klyuchevskoy volcanic group (Kamchatka)
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Alternative Description of Magnetic Monopoles in Quantum Mechanics
Get PDFWe present an alternative description of magnetic monopoles by lifting quantum mechanics from 3-dimensional space into a one with 2 complex dimensions. Magnetic monopoles are realized by generalization of the considered states. Usual algebraic relations and magnetic fields describing monopoles are reproduced, with the Dirac quantisation condition satisfied naturally
Probabilistic surface heat flow estimates assimilating palaeoclimate history: new implications for the thermochemical structure of Ireland
No full textRegions where surface temperature has increased since past glaciation events, such as Ireland, underestimate the heat output of the Earth unless palaeoclimate corrections are applied. We apply probabilistic techniques to quantify the uncertainty of 22 palaeoclimate-corrected heat flow estimates in Ireland, which assimilate multiple surface temperature histories associated with 130 ka of glacial oscillation in the British Isles. Heat flow values increase by ~15 mW m-2 after a palaeoclimate correction and provide new insights into the thermochemical structure of the lithosphere.
The heat flow regime is broadly delineated by the Iapetus Suture Zone (ISZ) that separates Laurentian to the North and Avalonian terranes to the South (mean surface heat flow of 73 +/- 14 and 65 +/- 14 mW m-2, respectively). The degree to which heat-producing elements are partitioned into the uppermost crust is described by the differentiation index of a heat flow province. From Bayesian inversion, we determine that radiogenic elements are substantially more differentiated in the uppermost crust of Laurentia (DI=2.8 +/- 1.4) than Avalonia (DI=1.5 +/- 1.3), despite a moderately enriched lower crust (0.8 +/- 0.3 uW m-3). This is facilitated by a thin yet highly radiogenic layer in the uppermost crust of Laurentia (3.9 +/- 1.8 uW m-3). Extrapolating these results across the British Isles and Newfoundland suggests that heat-producing elements have been more successfully reworked into the upper crust to the north of the ISZ during continental accretion between Laurentia and Avalonia
