background: induction chemotherapy for acute lymphoblastic leukemia achieves complete remis sion in over 90% of children. it is apparent therefore that many patients in clinical remission and with out residual disease detectable by conventional light microscopy of peripheral blood or bone marrow films still harbor viable cells of the original disease mrd analysis does have a useful role to play...

Classical logic is unfortunately defective with its problematic definition of implication relation, the “material implication”. This work presents a corrected definition of implication relation to replace material implication in classical logic. Common “paradoxes” of material implication are avoided while simplicity and usefulness of the system are reserved with this definition of implication r...

Abstract The floodable volume of longwall gob can be great importance in developing accurate coal mine operation plans, particularly for water management and environmental control strategies. Given the inaccessibility difficulty direct measurement characteristics following recompression, hydrologic, geomechanical, spatial data principles were used to solve porosity height residual using a mathe...

A structural semantics is developed for a first-order logic, with infinite disjunctions and conjunctions, that is characterised algebraically by quantales. The model structures involved combine the “covering systems” approach of Kripke-Joyal intuitionistic semantics from topos theory with the ordered groupoid structures used to model various connectives in substructural logics. The latter are u...

PR3 ANCA is a classic marker of granulomatosis with polyangiitis (GPA). There have been several recent reports of increased prevalence of PR3ANCA in ulcerative colitis (UC) patients, the clinical implication of which is not well defined. We are reporting a case of 27-year-old Caucasian male with 14-year history of UC presenting with unilateral proptosis, conjunctival congestion, and chemosis wh...

We use coalgebraic methods to describe finitely generated free Heyting algebras. Heyting algebras are axiomatized by rank 0-1 axioms. In the process of constructing free Heyting algebras we first apply existing methods to weak Heyting algebras—the rank 1 reducts of Heyting algebras—and then adjust them to the mixed rank 0-1 axioms. On the negative side, our work shows that one cannot use arbitr...

This paper deals with the problem of the aggregation of implication functions. After characterizing those binary operations which merge two implication functions into a new implication function, we study some aspects of the aggregated implication functions in terms of the two given ones. In particular, we are interested in aggregation processes such that properties of the implication functions ...