Lebens- und Regierungsgeschichte Friedrich Wilhelm's III., Königs von Preußen

Hrsg. von L. Weyl

Petrology and origin of basalts at DSDP Hole 66-487

The volcanism of Central America, according to current theory (Pichler and Weyl, 1973; Stoiber and Carr, 1974; Hey, 1977), is related to the subduction of the Cocos Plate under the North American lithospheric plate and the melting of ocean crust material in the subduction zone (Green and Ringwood, 1968; Dickinson, 1970, Fitton, 1971). Since Cocos Plate subduction occurs at the rate of more than 7 cm/y. (Hey et al., 1977), basalts underlying upper Miocene sediments of the Middle America Trench outer slope, penetrated in Hole 487 (Fig. 1) during Leg 66 (Moore et al., 1979), should have formed far from their present position if current theory is accurate. Present manifestations of basaltic magmatism in adjacent areas of the Pacific derive from the axial part of the East Pacific Rise, the Galapagos spreading center, and transform fracture zones. The question arises: Are there analogs of the Middle America Trench basalts among magmatic cock associated with these modern features, or do the trench basalts have some other origin?

Topological invariance and spatial scaling of surface roughness in two highly eroded zones of Mexico: a comparative study

The Fractal Image Informatics toolbox (Oleschko et al., 2008 a; Torres-Argüelles et al., 2010) was applied to extract, classify and model the topological structure and dynamics of surface roughness in two highly eroded catchments of Mexico. Both areas are affected by gully erosion (Sidorchuk, 2005) and characterized by avalanche-like matter transport. Five contrasting morphological patterns were distinguished across the slope of the bare eroded surface of Faeozem (Queretaro State) while only one (apparently independent on the slope) roughness pattern was documented for Andosol (Michoacan State). We called these patterns ?the roughness clusters? and compared them in terms of metrizability, continuity, compactness, topological connectedness (global and local) and invariance, separability, and degree of ramification (Weyl, 1937). All mentioned topological measurands were correlated with the variance, skewness and kurtosis of the gray-level distribution of digital images. The morphology0 spatial dynamics of roughness clusters was measured and mapped with high precision in terms of fractal descriptors. The Hurst exponent was especially suitable to distinguish between the structure of ?turtle shell? and ?ramification? patterns (sediment producing zone A of the slope); as well as ?honeycomb? (sediment transport zone B) and ?dinosaur steps? and ?corals? (sediment deposition zone C) roughness clusters. Some other structural attributes of studied patterns were also statistically different and correlated with the variance, skewness and kurtosis of gray distribution of multiscale digital images. The scale invariance of classified roughness patterns was documented inside the range of five image resolutions. We conjectured that the geometrization of erosion patterns in terms of roughness clustering might benefit the most semi-quantitative models developed for erosion and sediment yield assessments (de Vente and Poesen, 2005).

Einstein-like geometric structures on surfaces

An AH (affine hypersurface) structure is a pair comprising a projective equivalence class of torsion-free connections and a conformal structure satisfying a compatibility condition which is automatic in two dimensions. They generalize Weyl structures, and a pair of AH structures is induced on a co-oriented non-degenerate immersed hypersurface in flat affine space. The author has defined for AH structures Einstein equations, which specialize on the one hand to the usual Einstein Weyl equations and, on the other hand, to the equations for affine hyperspheres. Here these equations are solved for Riemannian signature AH structures on compact orientable surfaces, the deformation spaces of solutions are described, and some aspects of the geometry of these structures are related. Every such structure is either Einstein Weyl (in the sense defined for surfaces by Calderbank) or is determined by a pair comprising a conformal structure and a cubic holomorphic differential, and so by a convex flat real projective structure. In the latter case it can be identified with a solution of the Abelian vortex equations on an appropriate power of the canonical bundle. On the cone over a surface of genus at least two carrying an Einstein AH structure there are Monge-Amp`ere metrics of Lorentzian and Riemannian signature and a Riemannian Einstein K"ahler affine metric. A mean curvature zero spacelike immersed Lagrangian submanifold of a para-K"ahler four-manifold with constant para-holomorphic sectional curvature inherits an Einstein AH structure, and this is used to deduce some restrictions on such immersions.

La paradoja de Mies : las simetrías invisibles a través del Pabellón de Barcelona

El vínculo de Mies van der Rohe con la simetría es un invariante que se intuye en toda su obra más allá de su pretendida invisibilidad. Partiendo del proyecto moderno como proceso paradójico, que Mies lo expresa en sus conocidos aforismos, como el célebre “menos es más”, la tesis pretende ser una aproximación a este concepto clave de la arquitectura a través de una de sus obras más importantes: el Pabellón Alemán para la Exposición Universal de 1.929 en Barcelona. Ejemplo de planta asimétrica según Bruno Zevi y un “auténtico caballo de Troya cargado de simetrías” como lo definió Robin Evans. El Pabellón representó para la modernidad, la culminación de una década que cambió radicalmente la visión de la arquitectura hasta ese momento, gracias al carácter inclusivo de lo paradójico y las innumerables conexiones que hubo entre distintas disciplinas, tan antagónicas, como el arte y la ciencia. De esta última, se propone una definición ampliada de la simetría como principio de equivalencia entre elementos desde la invariancia. En esta definición se incorpora el sentido recogido por Lederman como “expresión de igualdad”, así como el planteado por Hermann Weyl en su libro Simetría como “invariancia de una configuración bajo un grupo de automorfismos” (libro que Mies tenía en su biblioteca privada). Precisamente para Weyl, el espacio vacío tiene un alto grado de simetría. “Cada punto es igual que los otros, y en ninguno hay diferencias intrínsecas entre las diversas direcciones." A partir de este nuevo significado, la obra de Mies adquiere otro sentido encaminado a la materialización de ese espacio, que él pretendía que “reflejase” el espíritu de la época y cuya génesis se postula en el Teorema de Noether que establece que “por cada simetría continua de las leyes físicas ha de existir una ley de conservación”. Estas simetrías continúas son las simetrías invisibles del espacio vacío que se desvelan “aparentemente” como oposición a las estructuras de orden de las simetrías de la materia, de lo lleno, pero que participan de la misma lógica aporética miesiana, de considerarlo otro material, y que se definen como: (i)limitado, (in)grávido, (in)acabado e (in)material. Finalmente, una paradoja más: El “espacio universal” que buscó Mies, no lo encontró en América sino en este pabellón. Como bien lo han intuido arquitectos contemporáneos como Kazuyo Sejima + Ryue Nishizawa (SANAA) legítimos herederos del maestro alemán. ABSTRACT The relationship between Mies van der Rohe with the symmetry is an invariant which is intuited in his entire work beyond his intentional invisibility. Based on the modern project as a paradoxical process, which Mies expresses in his aphorisms know as the famous “less is more”, the thesis is intended to approach this key concept in architecture through one of his most important works: The German Pavilion for the World Expo in 1929 in Barcelona, an example of asymmetric floor according to Bruno Zevi and a “real Trojan horse loaded with symmetries”. As defined by Robin Evans. For modernity, this Pavilion represented the culmination of a decade which radically changed the vision of architecture so far, thanks to the inclusive character of the paradoxical and the innumerable connections that there were amongst the different disciplines, as antagonistic as Art and Science. Of the latter, an expanded definition of symmetry is proposed as the principle of equivalence between elements from the invariance. Incorporated into this definition is the sense defined by Leterman as “expression of equality,” like the one proposed by Hermann Weyl in his book Symmetry as “configuration invariance under a group of automorphisms” (a book which Mies had in his private library). Precisely for Weyl, the empty space has a high degree of symmetry. “Each point is equal to the other, and in none are there intrinsic differences among the diverse directions.” Based on this new meaning, Mies’ work acquires another meaning approaching the materialization of that space, which he intended to “reflect” the spirit of the time and whose genesis is postulated in the Noether’s theorem which establishes that “for every continuous symmetry of physical laws, there must be a law of conservation.” These continuous symmetries are the invisible empty space symmetries which reveal themselves “apparently” as opposition to the structures of matter symmetries, of those which are full, but which participate in the same Mies aporetic logic, if deemed other material, and which is defined as (un)limited, weight(less), (un)finished and (im)material. Finally, one more paradox: the “universal space” which Mies search for, he did not find it in America, but at this pavilion, just as the contemporary architects like Kazuyo Sejima + Ryue Nishizawa (SANAA) rightfully intuited, as legitimate heirs of the German master.

Schwermineraltabelle

Die Altersbestimmung von Sedimentärgeschieben, die nicht durch ihren Fossilgehalt hinreichend gekennzeichnet sind, ist nur auf dem Wege eines petrographischen Vergleiches mit bekannten Geschieben oder dem anstehenden Vorkommen der betreffenden Gesteine möglich. In vielen Fällen Iäßt zwar schon das makroskopische Bild sichere Aussagen zu, wie z. B. ein fossilfreier roter Orthocerenkalk oder ein Juraoolith ohne Schwierigkeiten erkannt und damit auch richtig eingestuft werden können. Zuweilen ist dieser makroskopische Vergleich aber doch recht unsicher und Iäßt keine eindeutige Entscheidung zu. Hier können mikroskopische Methoden mit Aussicht auf Erfolg weiterhelfen. Im Laufe der letzten Jahrzehnte hat sich zur Kennzeichnung klastischer Sedimente die Untersuchung der spezifisch schweren Minerale in zunehmendem Maße bewährt, wobei einmal das Auftreten bestimmter Minerale in einzelnen Schichtgruppen, zum andern das relative Mengenverhältnis gleicher Minerale in verschiedenen Ablagerungen herangezogen wurde. Eine Übertragung dieser Methoden auf die Geschiebeforschung ist bisher noch nicht versucht worden, obwohl hier gerade ein dankbares Objekt vorliegt, da auch sehr geringe Mengen von Untersuchungssubstanz eine hinreichende Charakterisierung des Schwermineralbestandes gestatten, also auch kleine und kleinste Geschiebe der Untersuchung zugänglich sind.

Die Betriebsführung von Wasserwerken.

Mode of access: Internet.

Research in the service of national purpose; proceedings of the Office of Naval Research Vicennial Convocation.

Mode of access: Internet.

I was Castro's prisoner: an American tells his story.

Mode of access: Internet.

The constitution of glasses : a dynamic interpretation /

Bibliography: p. 1520-1542.

Lehrbuch der organischen Chemie für Mediciner /

On spine: Organ. Chemie

A brief history of the church in Upper Canada : containing the acts of Parliament, imperial and provincial, royal instructions, proceedings of the deputation, correspondence with the government, clergy reserves' question, &c. &c. /

Mode of access: Internet.

1931 UM Track Team

Top Row: William Klein, William Hill, Roger Howell

3rd Row: George Weyl, Edwin Jackson, Leo Draveling, Donald Haefele, David Gafill, Francis Hazen, Robert Feustel

2nd Row: Hawley Eggleston, Charles DeBaker, Edwin Turner, Roderick Cox, Ben Glading, Charles Eknovich, Howard Braden, Harmon Wolfe

Front Row: John Campbell, Joseph Austin, Ralph Mueller, John Noyes, John Pottle, coach Charles Hoyt, Edwin Russell, Eddie Tolan, J. Clifford Murray

A class of perfect fluids in general relativity

This thesis is concerned with exact solutions of Einstein's field equations of general relativity, in particular, when the source of the gravitational field is a perfect fluid with a purely electric Weyl tensor. General relativity, cosmology and computer algebra are discussed briefly. A mathematical introduction to Riemannian geometry and the tetrad formalism is then given. This is followed by a review of some previous results and known solutions concerning purely electric perfect fluids. In addition, some orthonormal and null tetrad equations of the Ricci and Bianchi identities are displayed in a form suitable for investigating these space-times. Conformally flat perfect fluids are characterised by the vanishing of the Weyl tensor and form a sub-class of the purely electric fields in which all solutions are known (Stephani 1967). The number of Killing vectors in these space-times is investigated and results presented for the non-expanding space-times. The existence of stationary fields that may also admit 0, 1 or 3 spacelike Killing vectors is demonstrated. Shear-free fluids in the class under consideration are shown to be either non-expanding or irrotational (Collins 1984) using both orthonormal and null tetrads. A discrepancy between Collins (1984) and Wolf (1986) is resolved by explicitly solving the field equations to prove that the only purely electric, shear-free, geodesic but rotating perfect fluid is the Godel (1949) solution. The irrotational fluids with shear are then studied and solutions due to Szafron (1977) and Allnutt (1982) are characterised. The metric is simplified in several cases where new solutions may be found. The geodesic space-times in this class and all Bianchi type 1 perfect fluid metrics are shown to have a metric expressible in a diagonal form. The position of spherically symmetric and Bianchi type 1 space-times in relation to the general case is also illustrated.

New Vacuum Solutions for Quadratic Metric-Affine Gravity - a Metric Affine Model for the Massless Neutrino?

AMS Subj. Classification: 83C15, 83C35