Computation of Integral Bases

Let $A$ be a Dedekind domain, $K$ the fraction field of $A$, and $f\in A[x]$ a monic irreducible separable polynomial. For a given non-zero prime ideal $\mathfrak{p}$ of $A$ we present in this paper a new method to compute a $\mathfrak{p}$-integral basis of the extension of $K$ determined by $f$. Our method is based on the use of simple multipliers that can be constructed with the data that occurs along the flow of the Montes Algorithm. Our construction of a $\mathfrak{p}$-integral basis is significantly faster than the similar approach from $[7]$ and provides in many cases a priori a triangular basis.Comment: 22 pages, 4 figure

Numerical Explorations of the Ngai-Pissarides Model of Growth and Structural Change

In this paper we specialize the Ngai-Pissarides model of growth and structural change [American Economic Review 97 (2007), 429-443] to the case of three sectors, representing the primary (agriculture, mining), secondary (construction, manufacturing) and tertiary (services) sectors. On that basis we explore the dynamic properties of the model along the transition path to the steady-state equilibrium by numerical methods. Our explorations show that the model misses several stylized facts of structural change among these sectors. We propose several extensions of the model to align the model more closely with the facts.economic growth, structural change, transition path

What Java Developers Know About Compatibility, And Why This Matters

Real-world programs are neither monolithic nor static -- they are constructed using platform and third party libraries, and both programs and libraries continuously evolve in response to change pressure. In case of the Java language, rules defined in the Java Language and Java Virtual Machine Specifications define when library evolution is safe. These rules distinguish between three types of compatibility - binary, source and behavioural. We claim that some of these rules are counter intuitive and not well-understood by many developers. We present the results of a survey where we quizzed developers about their understanding of the various types of compatibility. 414 developers responded to our survey. We find that while most programmers are familiar with the rules of source compatibility, they generally lack knowledge about the rules of binary and behavioural compatibility. This can be problematic when organisations switch from integration builds to technologies that require dynamic linking, such as OSGi. We have assessed the gravity of the problem by studying how often linkage-related problems are referenced in issue tracking systems, and find that they are common

Zero-temperature equation of state of mass-imbalanced resonant Fermi gases

We calculate the zero-temperature equation of state of mass-imbalanced resonant Fermi gases in an ab initio fashion, by implementing the recent proposal of imaginary-valued mass difference to bypass the sign problem in lattice Monte Carlo calculations. The fully non-perturbative results thus obtained are analytically continued to real mass imbalance to yield the physical equation of state, providing predictions for upcoming experiments with mass-imbalanced atomic Fermi gases. In addition, we present an exact relation for the rate of change of the equation of state at small mass imbalances, showing that it is fully determined by the energy of the mass-balanced system.Comment: 5 pages, 2 figures, 2 table

Inhomogeneous phases in one-dimensional mass- and spin-imbalanced Fermi gases

We compute the phase diagram of strongly interacting fermions in one dimension at finite temperature, with mass and spin imbalance. By including the possibility of the existence of a spatially inhomogeneous ground state, we find regions where spatially varying superfluid phases are favored over homogeneous phases. We obtain estimates for critical values of the temperature, mass and spin imbalance, above which these phases disappear. Finally, we show that an intriguing relation exists between the general structure of the phase diagram and the binding energies of the underlying two-body bound-state problem.Comment: 5 pages, 3 figure

Phase structure of mass- and spin-imbalanced unitary Fermi gases

We study the phase diagram of mass- and spin-imbalanced unitary Fermi gases, in search for the emergence of spatially inhomogeneous phases. To account for fluctuation effects beyond the mean-field approximation, we employ renormalization group techniques. We thus obtain estimates for critical values of the temperature, mass and spin imbalance, above which the system is in the normal phase. In the unpolarized, equal-mass limit, our result for the critical temperature is in accordance with state-of-the-art Monte Carlo calculations. In addition, we estimate the location of regions in the phase diagram where inhomogeneous phases are likely to exist. We show that an intriguing relation exists between the general structure of the many-body phase diagram and the binding energies of the underlying two-body bound-state problem, which further supports our findings. Our results suggest that inhomogeneous condensates form for mass ratios of the spin-down and spin-up fermions greater than three. The extent of the inhomogeneous phase in parameter space increases with increasing mass imbalance.Comment: 17 pages, 7 figure

On the compactness of nonmonotonic logics

A weak concept of compactness for nonmonotonic logics is proposed, which is suitable for several nonmonotonic logics, for which Makinsons smallest cumulative extension as well as Freund/Lehmanns canonical extension fail

Crystalline Ground States in Polyakov-loop extended Nambu--Jona-Lasinio Models

Nambu--Jona-Lasinio-type models have been used extensively to study the dynamics of the theory of the strong interaction at finite temperature and quark chemical potential on a phenomenological level. In addition to these studies, which are often performed under the assumption that the ground state of the theory is homogeneous, searches for the existence of crystalline phases associated with inhomogeneous ground states have attracted a lot of interest in recent years. In this work, we study the Polyakov-loop extended Nambu--Jona-Lasinio model and find that the existence of a crystalline phase is stable against a variation of the parametrization of the underlying Polyakov loop potential. To this end, we adopt two prominent parametrizations. Moreover, we observe that the existence of a quarkyonic phase depends crucially on the parametrization, in particular in the regime of the phase diagram where inhomogeneous chiral condensation is favored.Comment: 7 pages, 3 figure