Let K/k be an abelian extension of number fields with a distinguished place of k that splits totally in K. In that situation, the abelian rank one Stark conjecture predicts the existence of a unit in K, called the Stark unit, constructed from the values of the L-functions attached to the extension. In this paper, assuming the Stark unit exists, we prove index formulae for it. In a second part, ...

In this paper we extend recent work about logical criteria for approximation properties of optimization problems. We focus on the relationship between logical expressibility and expected asymptotic growth of optimal solutions on random inputs. This further develops a probabilistic approach due to Behrendt, Compton and Grr adel showing that expected optimal solutions for any problem in the class...

There is a growing body of literature that shows internet search volume on a topic, such as fishing, is a viable measure of salience. Herein, internet search volume for ‘fishing’ and ‘angling’ is used as a measure of public interest in fishing, in particular, recreational fishing. An online tool, Google Insights for Search, which allows one to study internet search terms and their volume since ...

We construct excited states of fundamental strings that admit a semiclassical description as rotating circular loops of string. We identify them with the supergravity solutions for rotating dipole rings. The identification involves a precise match of the mass, radius and angular momentum of the two systems. Moreover, the degeneracy of the string state reproduces the parametric dependence of the...

As a member of the Annex 1 countries to the Kyoto Protocol of the United Nations Framework Convention on Climate Change, Japan is committed to reducing 6% of the greenhouse gas emissions. In order to achieve this commitment, Japan has undertaken several major mitigation measures, one of which is the domestic measure that includes ecologically friendly lifestyle programs, utilizing natural energ...

Symbolic Finite Transducers, or SFTs, is a representation of finite transducers that annotates transitions with logical formulae to denote sets of concrete transitions. This representation has practical advantages in applications for web security analysis, as it provides ways to succinctly represent web sanitizers that operate on large alphabets. More importantly, the representation is also con...

We analyze the interpretation of spherically symmetric perfect fluid solutions that admit a flat synchronization orthogonal to flow as thermodynamic in local thermal equilibrium. The ideal gas sonic condition is examined for this family metrics, and macroscopic conditions physical reality are accurately tested some specific solutions.

Abstract Velocity hodographs are of importance in weather analysis. A historically important case is the hodograph Kepler problem. Here, we explore analytical solutions for velocity projectile trajectories under a polynomial, velocity, hydrodynamic dissipation. General terms hypergeometric functions found odd powers monomial terms. The even have but do not find general expression them. For comp...

Four thoughtful commentaries identify important issues and insights pertaining to the pyramid of needs presented by Kenrick, Griskevicius, Neuberg, and Schaller (2010, this issue). Here, we offer additional thoughts on some of these issues and insights, with an emphasis on the logical implications that result from an evolutionary analysis of fundamental human needs.

This paper focuses on two aspects of piece resolution in backward chaining for conceptual graph rules 13]. First, as conceptual graphs admit a rst-order logic interpretation, inferences can be proven by classical theorem provers. Nevertheless, they do not use the notion of piece, which is a graph notion. So we deene piece resolution over a class of rst-order logical formulae: the logical rules....