Addendum to ``Reconciling grand unification with strings by anisotropic compactifications''

In this brief addendum, we clarify a point which we left unaddressed in a previous publication [Phys. Rev. D 78, 066006 (2008)]. In particular, we show that a specific vacuum configuration constructed in one of our models satisfies the condition D=0. In the previous publication, we only showed F=0. Both D=0 and F=0 are necessary to ensure that supersymmetry survives to the weak scale.

Embedding Of Non-Simple Lie-Groups, Coupling-Constant Relations And Non-Uniqueness Of Models Of Unification

A general derivation of the coupling constant relations which result on embedding a non-simple group like SU L (2) @ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin~0=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons like E 6, while addition of extra charged fermion singlets can reduce the value of sin ~ 0 to 1/4. We point out that at the present time the models of grand unification are far from unique.

Seyfert Galaxies: Nuclear Radio Structure And Unification

A radio study of a carefully selected sample of 20 Seyfert galaxies that are matched in orientation-independent parameters, which are measures of intrinsic active galactic nucleus power and host galaxy properties, is presented to test the predictions of the unified scheme hypothesis. Our sample sources have core flux densities greater than 8 mJy at 5 GHz on arcsec scales due to the feasibility requirements. These simultaneous parsec-scale and kiloparsec-scale radio observations reveal (1) that Seyfert 1 and Seyfert 2 galaxies have an equal tendency to show compact radio structures on milliarcsecond scales, (2) the distributions of parsec-scale and kiloparsec-scale radio luminosities are similar for both Seyfert 1 and Seyfert 2 galaxies, (3) there is no evidence for relativistic beaming in Seyfert galaxies, (4) similar distributions of source spectral indices in spite of the fact that Seyferts show nuclear radio flux density variations, and (5) the distributions of the projected linear size for Seyfert 1 and Seyfert 2 galaxies are not significantly different as would be expected in the unified scheme. The latter could be mainly due to a relatively large spread in the intrinsic sizes. We also find that a starburst alone cannot power these radio sources. Finally, an analysis of the kiloparsec-scale radio properties of the CfA Seyfert galaxy sample shows results consistent with the predictions of the unified scheme.

A unification-based decision procedure for cryptographic protocol analysis

We present a sound and complete decision procedure for the bounded process cryptographic protocol insecurity problem, based on the notion of normal proofs [2] and classical unification. We also show a result about the existence of attacks with “high” normal cuts. Our proof of correctness provides an alternate proof and new insights into the fundamental result of Rusinowitch and Turuani [9] for the same setting.

Proceedings of Sixth International Workshop on Unification

Swiss National Science Foundation; Austrian Federal Ministry of Science and Research; Deutsche Forschungsgemeinschaft (SFB 314); Christ Church, Oxford; Oxford University Computing Laboratory

A General Theory of Semi-Unification

Various restrictions on the terms allowed for substitution give rise to different cases of semi-unification. Semi-unification on finite and regular terms has already been considered in the literature. We introduce a general case of semi-unification where substitutions are allowed on non-regular terms, and we prove the equivalence of this general case to a well-known undecidable data base dependency problem, thus establishing the undecidability of general semi-unification. We present a unified way of looking at the various problems of semi-unification. We give some properties that are common to all the cases of semi-unification. We also the principality property and the solution set for those problems. We prove that semi-unification on general terms has the principality property. Finally, we present a recursive inseparability result between semi-unification on regular terms and semi-unification on general terms.

Beta-Reduction As Unification

We define a unification problem ^UP with the property that, given a pure lambda-term M, we can derive an instance Gamma(M) of ^UP from M such that Gamma(M) has a solution if and only if M is beta-strongly normalizable. There is a type discipline for pure lambda-terms that characterizes beta-strong normalization; this is the system of intersection types (without a "top" type that can be assigned to every lambda-term). In this report, we use a lean version LAMBDA of the usual system of intersection types. Hence, ^UP is also an appropriate unification problem to characterize typability of lambda-terms in LAMBDA. It also follows that ^UP is an undecidable problem, which can in turn be related to semi-unification and second-order unification (both known to be undecidable).

The Unification of Asymmetry Signatures of Type Ia Supernovae

We present a compilation of the geometry measures acquired using optical and IR spectroscopy and optical spectropolarimetry to probe the explosion geometry of Type Ia supernovae (SNe Ia). Polarization measurements are sensitive to asymmetries in the plane of the sky, whereas line profiles in nebular phase spectra are expected to trace asymmetries perpendicular to the plane of the sky. The combination of these two measures can overcome their respective projection effects, completely probing the structures of these events. For nine normal SNe Ia, we find that the polarization of Si II ?6355 at 5 days before maximum (p Si II ) is well correlated with its velocity evolution (\dot{v}_Si II), implying that \dot{v}_Si II is predominantly due to the asymmetry of the SNe. We find only a weak correlation between the polarization of Si II and the reported velocities (v neb) for peak emission of optical Fe II and Ni II lines in nebular spectra. Our sample is biased, with polarization measurements being only available for normal SNe that subsequently exhibited positive (i.e., redshifted) v neb. In unison these indicators are consistent with an explosion in which the outer layers are dominated by a spherical oxygen layer, mixed with an asymmetric distribution of intermediate-mass elements. The combination of spectroscopic and spectropolarimetric indicators suggests a single geometric configuration for normal SNe Ia, with some of the diversity of observed properties arising from orientation effects.

ECONOMIC AND POLITICAL UNIFICATION OF GERMANY: 1815-1871. PART 2: THE SHARE OF THE PUBLIC SECTOR IN THE ECONOMY..

Rapport de recherche

Vers une grammaire d'unification Sens-Texte du français : le temps verbal dans l'interface sémantique-syntaxe

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

The unification of Germany, 1815-1919.

Su contenido, revisado y actualizado, se adapta a la especificación AS para AQA y Edexcel. Estudia la evolución de Alemania en el siglo XIX y los factores que influyeron en el movimiento hacia la unidad nacional. Examina la Alemania de Bismarck y su caída, así como las políticas y los cambios producidos en el nuevo estado alemán hasta la formación de la República de Weimar en 1919. Incluye fechas clave, términos y temas, perfiles biográficos, resúmenes esquemáticos, fuentes literarias y síntesis de los principales debates historiográficos.