Weakly definable languages of infinite trees are an expressive subclass of regular tree languages definable in terms of weak monadic second-order logic, or equivalently weak alternating automata. Our main result is that given a Büchi automaton, it is decidable whether the language is weakly definable. We also show that given a parity automaton, it is decidable whether the language is recognizab...

We provide several characterizations of unanimity decision rules, in a public choice model where preferences are constrained by attributes possessed by the alternatives (Nehring and Puppe, 2007a,b). Solidarity conditions require that when some parameters of the economy change, the agents whose parameters are kept fixed either all weakly lose or they all weakly win. Population-monotonicity (Thom...

There are well-known quasi-formal arguments that identity is a “strict” relation in at least the following three senses: (1) There is a single identity relation and a single distinctness relation; (2) There are no contingent cases of identity or distinctness; and (3) There are no vague or indeterminate cases of identity or distinctness. However, the situation is less clear cut than it at first ...

When subject to a weak magnetic impurity distribution, the order parameter and quasi-particle energy gap of a weakly disordered bulk s-wave superconductor are suppressed. In the Born scattering limit, recent investigations have shown that ‘optimal fluctuations’ of the random impurity potential can lead to the nucleation of ‘domains’ of localised states within the gap region predicted by the con...

We provide several characterizations of unanimity decision rules, in a public choice model where preferences are constrained by attributes possessed by the alternatives (Nehring and Puppe, 2007a,b). Solidarity conditions require that when some parameters of the economy change, the agents whose parameters are kept fixed either all weakly lose or they all weakly win. Population-monotonicity (Thom...

We study the roles played by four special types of bases (weakly uniform bases, ω-in-ω bases, open-in-finite bases, and sharp bases) in the classes of linearly ordered and generalized ordered spaces. For example, we show that a generalized ordered space has a weakly uniform base if and only if it is quasi-developable and has a Gδ-diagonal, that a linearly ordered space has a point-countable bas...

Interaction of impulsively generated MHD waves with a one-dimensional plasma inhomogeneity, transverse to the magnetic field, is considered in the three-dimensional regime. Because of the transverse inhomogeneity, MHD fluctuations, even if they do not include initially any density perturbation, evolve toward states where the compressible components tend to become predominant. The propagating MH...

The abstract economy defined by Debreu (1952) generalizes the Nash non-cooperative game in that a player’s strategy set depends on the strategy choices of all the other players. Debreu (1952) proved the existence of equilibrium in abstract economies with finitely many agents, finite dimensional strategy space, and quasi-concave utility functions. Since then, the Debreu’s result has been extende...

Weakly left ample semigroups form a class of semigroups that are (2; 1)-subalgebras of semigroups of partial transformations, where the unary operation takes a transformation to the identity map in the domain of. They are semigroups with commuting idempotents such that the e R-class of any element a contains a (necessarily unique) idempotent a + , e R is a left congruence, and the ample identit...

The Banach space E has the weakly compact approximation property (W.A.P. for short) if there is a constant C < ∞ so that for any weakly compact set D ⊂ E and ε > 0 there is a weakly compact operator V : E → E satisfying supx∈D ‖x − V x‖ < ε and ‖V ‖ ≤ C. We give several examples of Banach spaces both with and without this approximation property. Our main results demonstrate that the James-type ...