We show that the non-superstability (non-stability) of a theory T is equivalent to the condition that for every elementary chain of length u; (un) of saturated models Mi of T with ||M,+i|| > ||M;|| for all s < UJ(U/I), the union of the chain is not saturated. The cardinality of T is immaterial.

The t-concept lattice is introduced as a set of triples associated to graded tabular information interpreted in a non-commutative fuzzy logic. Following the general techniques of formal concept analysis, and based on the works by Georgescu and Popescu, given a non-commutative conjunctor it is possible to provide generalizations of the mappings for the intension and the extension in two differen...

An approach to fixed field acceleration using exclusively linear optical elements was first proposed[1, 2] and successfully developed[3, 4] to support rapid, large-emittance muon acceleration required by a Neutrino Factory or Muon Collider. This approach was termed, simply, a non-scaling, fixed field alternating gradient (FFAG) accelerator. Lattices have evolved from the simple F0D0-cell baseli...

It has recently been discovered that both quantum and classical propositional logics can be modelled by classes of non-orthomodular and thus non-distributive lattices that properly contain standard orthomodular and Boolean classes, respectively. In this paper we prove that these logics are complete even for those classes of the former lattices from which the standard orthomodular lattices and B...

Motivated by a recent generalization of the Balian-Low theorem and by new research in wireless communications we analyze the construction of Wilson bases for general time-frequency lattices. We show that orthonormal Wilson bases for L(R) can be constructed for any time-frequency lattice whose volume is 1 2 . While this may be expected, our second result may come as a surprise. Namely we prove t...

In large-vocabulary, multi-pass speech recognition systems, it is desirable to generate word lattices incorporating a large number of hypotheses while keeping the lattice sizes small. We describe two new techniques for reducing word lattice sizes without eliminating hypotheses. The first technique is an algorithm to reduce the size of non-deterministic bigram word lattices. The algorithm iterat...

in this work, one and two-dimensional lattices are studied theoretically by a statistical mechanical approach. the nearest and next-nearest neighbor interactions are both taken into account, and the approximate thermodynamic properties of the lattices are calculated. the results of our calculations show that: (1) even though the next-nearest neighbor interaction may have an insignificant effect...