19,141 research outputs found
On the Star Class Group of a Pullback
For the domain arising from the construction , we relate the star
class groups of to those of and . More precisely, let be an
integral domain, a nonzero maximal ideal of , a proper subring of
, the natural projection, and let .
For each star operation on , we define the star operation
on , i.e., the ``projection'' of under , and the star operation
on , i.e., the ``extension'' of to . Then we
show that, under a mild hypothesis on the group of units of , if is a
star operation of finite type, 0\to \Cl^{\ast_{\phi}}(D) \to \Cl^\ast(R) \to
\Cl^{{(\ast)}_{_{T}}}(T)\to 0 is split exact. In particular, when , we deduce that the sequence 0\to \Cl^{t_{D}}(D) {\to} \Cl^{t_{R}}(R)
{\to}\Cl^{(t_{R})_{_{T}}}(T) \to 0 is split exact. The relation between
and (and between \Cl^{(t_{R})_{_{T}}}(T) and
\Cl^{t_{T}}(T)) is also investigated.Comment: J. Algebra (to appear
Towards Interactive Logic Programming
Linear logic programming uses provability as the basis for computation. In
the operational semantics based on provability, executing the
additive-conjunctive goal from a program simply terminates
with a success if both and are solvable from . This is an
unsatisfactory situation, as a central action of \& -- the action of choosing
either or by the user -- is missing in this semantics.
We propose to modify the operational semantics above to allow for more active
participation from the user. We illustrate our idea via muProlog, an extension
of Prolog with additive goals.Comment: 8 pages. It describes two execution models for interactive logic
programmin
Different Behavior of Magnetic Impurities in Crystalline and Ammorphous States of Superconductors
It has been observed that the effect of magnetic impurities in a
superconductor is drastically different depending on whether the host
superconductor is in a crystalline or an amorphous state. Based on the recent
theory of Kim and Overhauser (KO), it is shown that as the system is getting
disordered, the initial slope of the depression is decreasing by a
factor , when the mean free path becomes smaller
than the BCS coherence length , which is in agreement with
experimental findings. In addition, for a superconductor in a crystalline state
in the presence of magnetic impurities the superconducting transition
temperature drops sharply from about 50% of (for a pure
system) to zero near the critical impurity concentration. This {\sl pure limit
behavior} was indeed found by Roden and Zimmermeyer in crystalline Cd.
Recently, Porto and Parpia have also found the same {\sl pure limit behavior}
in superfluid He-3 in aerogel, which may be understood within the framework of
the KO theory.Comment: 7 figures, 20 pages, latex, to appear in Superconductor Science and
Technolog
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