Andreev's Theorem on hyperbolic polyhedra

In 1970, E. M. Andreev published a classification of all three-dimensional compact hyperbolic polyhedra having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, $C$, Andreev's Theorem provides five classes of linear inequalities, depending on $C$, for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing $C$ with the assigned dihedral angles. Andreev's Theorem also shows that the resulting polyhedron is unique, up to hyperbolic isometry. Andreev's Theorem is both an interesting statement about the geometry of hyperbolic 3-dimensional space, as well as a fundamental tool used in the proof for Thurston's Hyperbolization Theorem for 3-dimensional Haken manifolds. It is also remarkable to what level the proof of Andreev's Theorem resembles (in a simpler way) the proof of Thurston. We correct a fundamental error in Andreev's proof of existence and also provide a readable new proof of the other parts of the proof of Andreev's Theorem, because Andreev's paper has the reputation of being ``unreadable''.Comment: To appear les Annales de l'Institut Fourier. 47 pages and many figures. Revision includes significant modification to section 4, making it shorter and more rigorous. Many new references include

Research on physical and physiological aspects of visual optics in space flight

Physical and physiological aspects of visual optics in space fligh

Spherical structures on torus knots and links

The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found in terms of cone angles and volume formul{\ae} are presented.Comment: 17 pages, 5 figures; typo

The stopping cross section of gases for protons, 30-600 kev

The stopping cross section of H2, He, O2, air, N2, Ne, A, Kr, Xe, H2O, NH3, NO, N2O, CH4, C2H2, C2H4, and C6H6 for protons has been measured over the energy range Ep=30-600 kev. An electrostatic analyzer measures the energy of protons incident on a gas cell, and the transmitted beam energy is measured with a magnetic spectrometer. The gas cell is closed off with thin aluminum windows. Comparison of the molecular stopping cross section of the compounds with the values obtained by summing the constituent atomic cross sections shows that Bragg's rule does not hold for any of these compounds below Ep=150 kev; for NO the additive rule does not hold at any energy studied. Above 150 kev the stopping cross section of carbon is obtained by subtracting the hydrogen contribution from the values measured for the hydrocarbons. Average ionization potentials are calculated from these measurements. A range energy relation for protons in air is included. Sources of error are discussed; the probable error of the stopping cross section measurements varies between 2-4 percent

Nudges and other moral technologies in the context of power: Assigning and accepting responsibility

Strawson argues that we should understand moral responsibility in terms of our practices of holding responsible and taking responsibility. The former covers what is commonly referred to as backward-looking responsibility , while the latter covers what is commonly referred to as forward-looking responsibility . We consider new technologies and interventions that facilitate assignment of responsibility. Assigning responsibility is best understood as the second- or third-personal analogue of taking responsibility. It establishes forward-looking responsibility. But unlike taking responsibility, it establishes forward-looking responsibility in someone else. When such assignments are accepted, they function in such a way that those to whom responsibility has been assigned face the same obligations and are susceptible to the same reactive attitudes as someone who takes responsibility. One family of interventions interests us in particular: nudges. We contend that many instances of nudging tacitly assign responsibility to nudgees for actions, values, and relationships that they might not otherwise have taken responsibility for. To the extent that nudgees tacitly accept such assignments, they become responsible for upholding norms that would otherwise have fallen under the purview of other actors. While this may be empowering in some cases, it can also function in such a way that it burdens people with more responsibility that they can (reasonably be expected to) manage

Poincare Polynomials and Level Rank Dualities in the N=2N=2 Coset Construction

We review the coset construction of conformal field theories; the emphasis is on the construction of the Hilbert spaces for these models, especially if fixed points occur. This is applied to the $N=2$ superconformal cosets constructed by Kazama and Suzuki. To calculate heterotic string spectra we reformulate the Gepner con- struction in terms of simple currents and introduce the so-called extended Poincar\'e polynomial. We finally comment on the various equivalences arising between models of this class, which can be expressed as level rank dualities. (Invited talk given at the III. International Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta, Ukraine, June 1993. To appear in Theor. Math. Phys.)Comment: 14 pages in LaTeX, HD-THEP-93-4

Benchmark Problems in Eddy-Current NDE

Inversion of eddy-current data and the reconstruction of flaws is the preeminent problem in electromagnetic nondestructive evaluation (NDE). This places a premium on developing good forward models for computing field-flaw interactions, because all inversion algorithms must, of necessity, rely on such calculations. There has evolved in recent years several sophisticated computational models for the forward problem [1–4], but these models differ significantly in their theoretical and numerical approaches. For example, [1-3] use a volume-integral approach that incorporates fast Fourier transforms with conjugate gradients to solve the resulting linear system of equations, whereas [4] uses finite-elements

An R^4 non-renormalisation theorem in N=4 supergravity

We consider the four-graviton amplitudes in CHL constructions providing four-dimensional N=4 models with various numbers of vector multiplets. We show that in these models the two-loop amplitude has a prefactor of d^2R^4. This implies a non-renormalisation theorem for the R^4 term, which forbids the appearance of a three-loop ultraviolet divergence in four dimensions in the four-graviton amplitude. We connect the special nature of the R^4 term to the U(1) anomaly of pure N=4 supergravity.Comment: v2: added comments about one-loop UV divergences. Assorted stylistic corrections. Added references. v3: Eq. III.21 corrected and assorted minor corrections and clarifications. Version to be published. v4: minor corrections. 18 pages. one figur

The 7.68-Mev state in C12

Magnetic analysis of the alpha-particle spectrum from N14(d, α)C12 covering the excitation energy range from 4.4 to 9.2 Mev in C12 shows a level at 7.68±0.03 Mev. At Ed=620 kev, θlab=90°, transitions to this state are only 6 percent of those to the level at 4.43 Mev

Multiloop Calculations in the String-Inspired Formalism: The Single Spinor-Loop in QED

We use the worldline path-integral approach to the Bern-Kosower formalism for developing a new algorithm for calculation of the sum of all diagrams with one spinor loop and fixed numbers of external and internal photons. The method is based on worldline supersymmetry, and on the construction of generalized worldline Green functions. The two-loop QED $\beta$ -- function is calculated as an example.Comment: uuencoded ps-file, 20 pages, 2 figures, final revised version to appear in Phys. Rev.