Unified Field Theory From Enlarged Transformation Group. The Covariant Derivative for Conservative Coordinate Transformations and Local Frame Transformations

Pandres has developed a theory in which the geometrical structure of a real four-dimensional space-time is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group called the conservation group. This paper extends the geometrical foundation for Pandres' theory by developing an appropriate covariant derivative which is covariant under all local Lorentz (frame) transformations, including complex Lorentz transformations, as well as conservative transformations. After defining this extended covariant derivative, an appropriate Lagrangian and its resulting field equations are derived. As in Pandres' theory, these field equations result in a stress-energy tensor that has terms which may automatically represent the electroweak field. Finally, the theory is extended to include 2-spinors and 4-spinors.Comment: Aug 25 replacement has corrected margin width

Automatic Abstraction for Congruences

One approach to verifying bit-twiddling algorithms is to derive invariants between the bits that constitute the variables of a program. Such invariants can often be described with systems of congruences where in each equation $\vec{c} \cdot \vec{x} = d \mod m$, (unknown variable m)$is a power of two,$\vec{c}$is a vector of integer coefficients, and$\vec{x}$ is a vector of propositional variables (bits). Because of the low-level nature of these invariants and the large number of bits that are involved, it is important that the transfer functions can be derived automatically. We address this problem, showing how an analysis for bit-level congruence relationships can be decoupled into two parts: (1) a SAT-based abstraction (compilation) step which can be automated, and (2) an interpretation step that requires no SAT-solving. We exploit triangular matrix forms to derive transfer functions efficiently, even in the presence of large numbers of bits. Finally we propose program transformations that improve the analysis results

The Composition Gradient in M101 Revisited. II. Electron Temperatures and Implications for the Nebular Abundance Scale

(Abridged) We use high S/N spectra of 20 HII regions in the giant spiral galaxy M101 to derive electron temperatures for the HII regions and robust metal abundances over radii R = 0.19-1.25 Ro (6-41 kpc). We compare the consistency of electron temperatures measured from the [O III]4363, [N II]5755, [S III]6312, and [O II]7325 auroral lines. Temperatures from [O III], [S III], and [N II] are correlated with relative offsets that are consistent with expectations from nebular photoionization models. However, the temperatures derived from the [O II]7325 line show a large scatter and are nearly uncorrelated with temperatures derived from other ions. Our derived oxygen abundances O/H are well fitted by an exponential distribution over six disk scale lengths, from approximately 1.3 solar in the center to 1/15 solar in the outermost region studied (for solar 12 + log (O/H)=8.7). We measure significant radial gradients in N/O and He/H abundance ratios, but relatively constant S/O and Ar/O. Our abundances are systematically lower by 0.2-0.5 dex than those derived from the most widely used strong-line "empirical" abundance indicators. We suspect that most of the disagreement with the strong-line abundances arises from uncertainties in the nebular models that are used to calibrate the "empirical" scale, and that strong-line abundances derived for HII regions and emission-line galaxies are as much as a factor of two higher than the actual oxygen abundances. However other explanations, such as the effects of temperature fluctuations on the auroral line based abundances cannot be completely ruled out. These results point to the need for direct abundance determinations of a larger sample of extragalactic HII regions, especially for objects more metal-rich than solar.Comment: 50 pages, 14 figures, 8 tables. Accepted by Ap

Observation of anomalous decoherence effect in a quantum bath at room temperature

Decoherence of quantum objects is critical to modern quantum sciences and technologies. It is generally believed that stronger noises cause faster decoherence. Strikingly, recent theoretical research discovers the opposite case for spins in quantum baths. Here we report experimental observation of the anomalous decoherence effect for the electron spin-1 of a nitrogen-vacancy centre in high-purity diamond at room temperature. We demonstrate that under dynamical decoupling, the double-transition can have longer coherence time than the single-transition, even though the former couples to the nuclear spin bath as twice strongly as the latter does. The excellent agreement between the experimental and the theoretical results confirms the controllability of the weakly coupled nuclear spins in the bath, which is useful in quantum information processing and quantum metrology.Comment: 22 pages, related paper at http://arxiv.org/abs/1102.557

Appearance concerns in ophthalmic patients

Aims: This study aimed to determine the psychosocial and appearance-related concerns of a sample of ophthalmic patients by measuring a range of psychological, social, and demographic factors. Methods: Standardized psychological measures including anxiety, depression, appearance-related distress, self-discrepancy, appearance salience and valence were administered to 98 participants attending ophthalmic outpatient clinics in either London, Bristol, Sheffield or Bradford. Differences between groups were explored using t-tests and ANOVA, relationships between all variables were investigated using Pearson's correlation coefficient. Results: Although mean scores for psychological adjustment were within the normal range, some participants were experiencing considerable levels of generalized anxiety. Being older, male, and married or living with a partner was related to significantly better adjustment. Better adjustment was also related to a less visible area of concern, greater disguisability of the affected area, a more positive evaluation of their own appearance, less engagement in comparing themselves with others, greater feelings of being accepted by others, appearance being less important to their self-concept, and a smaller discrepancy between the persons ideal and actual appearance. Conclusions: A majority of ophthalmic patients adjust positively to the demands placed on them. By identifying the variables that are associated with successful adaptation, the specific psychological interventions and appropriate systems of support can be put in place to help those who are adversely affected

Compositional reasoning for shared-variable concurrent programs

Scalable and automatic formal verification for concurrent systems is always demanding. In this paper, we propose a verification framework to support automated compositional reasoning for concurrent programs with shared variables. Our framework models concurrent programs as succinct automata and supports the verification of multiple important properties. Safety verification and simulations of succinct automata are parallel compositional, and safety properties of succinct automata are preserved under refinements. We generate succinct automata from infinite state concurrent programs in an automated manner. Furthermore, we propose the first automated approach to checking rely-guarantee based simulations between infinite state concurrent programs. We have prototyped our algorithms and applied our tool to the verification of multiple refinements

Scaling and criticality of the Kondo effect in a Luttinger liquid

A quantum Monte Carlo simulation method has been developed and applied to study the critical behavior of a single Kondo impurity in a Luttinger liquid. This numerically exact method has no finite-size limitations and allows to simulate the whole temperature range. Focusing on the impurity magnetic susceptibility, we determine the scaling functions, in particular for temperatures well below the Kondo temperature. In the absence of elastic potential scattering, we find Fermi-liquid behavior for strong electron-electron interactions, g_c < 1/2, and anomalous power laws for 1/2<g_c < 1, where g_c is the correlation parameter of the Luttinger liquid. These findings resolve a recent controversy. If elastic potential scattering is present, we find a logarithmically divergent impurity susceptibility at g_c<1/2 which can be rationalized in terms of the two-channel Kondo model.Comment: 11 pages REVTeX, incl. 9 PS figures, subm. to PR

On the Spiral Structure of the Milky Way Galaxy

We consider the possible pattern of the overall spiral structure of the Galaxy, using data on the distribution of neutral (atomic), molecular, and ionized hydrogen, on the base of the hypothesis of the spiral structure being symmetric, i.e. the assumption that spiral arms are translated into each other for a rotation around the galactic center by 180{\deg} (a two-arm pattern) or by 90{\deg} (a four-arm pattern). We demonstrate that, for the inner region, the observations are best represented with a four-arm scheme of the spiral pattern, associated with all-Galaxy spiral density waves. The basic position is that of the Carina arm, reliably determined from distances to HII regions and from HI and H2 radial velocities. This pattern is continued in the quadrants III and IV with weak outer HI arms; from their morphology, the Galaxy should be considered an asymmetric multi-arm spiral. The kneed shape of the outer arms that consist of straight segments can indicate that these arms are transient formations that appeared due to a gravitational instability in the gas disk. The distances between HI superclouds in the two arms that are the brightest in neutral hydrogen, the Carina arm and the Cygnus (Outer) arm, concentrate to two values, permitting to assume the presence of a regular magnetic field in these arms.Comment: 21 pages, 14 fugures; accepted for publication in Astronomichesky Journal (Astron. Rep.

Risk-shifting Through Issuer Liability and Corporate Monitoring

This article explores how issuer liability re-allocates fraud risk and how risk allocation may reduce the incidence of fraud. In the US, the apparent absence of individual liability of officeholders and insufficient monitoring by insurers under-mine the potential deterrent effect of securities litigation. The underlying reasons why both mechanisms remain ineffective are collective action problems under the prevailing dispersed ownership structure, which eliminates the incentives to moni-tor set by issuer liability. This article suggests that issuer liability could potentially have a stronger deterrent effect when it shifts risk to individuals or entities holding a larger financial stake. Thus, it would enlist large shareholders in monitoring in much of Europe. The same risk-shifting effect also has implications for the debate about the relationship between securities litigation and creditor interests. Credi-tors’ claims should not be given precedence over claims of defrauded investors (e.g., because of the capital maintenance principle), since bearing some of the fraud risk will more strongly incentivise large creditors, such as banks, to monitor the firm in jurisdictions where corporate debt is relatively concentrated

Thermally Activated Resonant Magnetization Tunneling in Molecular Magnets: Mn_12Ac and others

The dynamical theory of thermally activated resonant magnetization tunneling in uniaxially anisotropic magnetic molecules such as Mn_12Ac (S=10) is developed.The observed slow dynamics of the system is described by master equations for the populations of spin levels.The latter are obtained by the adiabatic elimination of fast degrees of freedom from the density matrix equation with the help of the perturbation theory developed earlier for the tunneling level splitting [D. A. Garanin, J. Phys. A, 24, L61 (1991)]. There exists a temperature range (thermally activated tunneling) where the escape rate follows the Arrhenius law, but has a nonmonotonic dependence on the bias field due to tunneling at the top of the barrier. At lower temperatures this regime crosses over to the non-Arrhenius law (thermally assisted tunneling). The transition between the two regimes can be first or second order, depending on the transverse field, which can be tested in experiments. In both regimes the resonant maxima of the rate occur when spin levels in the two potential wells match at certain field values. In the thermally activated regime at low dissipation each resonance has a multitower self-similar structure with progressively narrowing peaks mounting on top of each other.Comment: 18 pages, 8 figure