We give details of the “reducibility” part of our proof of the Four Color theorem [1]. 29 March 1995 Revised 27 January 1997 ∗ Research partially performed under a consulting agreement with Bellcore, and partially supported by DIMACS Center, Rutgers University, New Brunswick, New Jersey 08903, USA. 1 Partially supported by NSF under Grant No. DMS-8903132 and by ONR under Grant No. N0001492-J-19...

In the LFT approach to Exact Real Arithmetic, we study the question how many argument digits are needed to produce a certain number of result digits. We present upper and lower bounds for many simple functions and operations, and for exponential and square root.

We let G(n,m) denote the set of r-uniform hypergraphs with n vertices and m edges, and f (n,p,s) is the smallest m such that every member of G(n,m) contains a member of G(p,s). In this paper we are interested in fixed values r,p and s for which f (n,p,s) grows quadratically with n. A probabilistic construction of Brown, Erdős and T. Sós ([2]) implies that f (n,s(r−2)+2, s)=Ω(n). In the other di...

We look at extensions (i.e., stronger logics in the same language) of the Belnap-Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap-Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterize the reduced algebraic models of these new logics and prove a completeness result for the first ...

The objective of this new Brazilian consensus is to update and to continue the standardization of the principal terms and fundamental patterns in chest CT scans in Portuguese. There is a succinct definition of the principal terms used to describe chest CT findings, as well as illustrations of classic examples. The group of authors comprised radiologists specializing in chest radiology and holdi...

We generalize a theorem of Mazur concerning the universal norms of an abelian variety over a Zp-extension of a complete local field. Then we apply it to the proof of a control theorem for abelian varieties over global function fields.

ship of twenty-four defective or retarded pupils, comprising ten from the first grade, ten from the second, two from the third, and two from the fifth. The number varied from time to time through dismissals and recruits, until altogether forty-nine pupils have received special treatment adapted to their individual needs. I desire to invite your attention to several particularly interesting and ...

The robust stability problem of continuous-time singular systems with multiple state delays and bounded parametric uncertainties is considered. Both commensurate and non-commensurate delays are investigated. On the basis of the linear fractional transformations (LFTs) framework and -analysis, a systematic approach is derived to convert the robustness problem to a robust nonsingularity problem. ...

Participant sex and a theorized correlate of biological sex, relational interdependence, were tested as relative predictors of the extent to which daters 1) missed and 2) used emotional support to cope when geographically separated from their dating partners. One hundred twenty-four daters completed multiple measures of missing and coping during their colleges' winter breaks. Results from regre...

This study investigates the use of relative clauses in French children's narrative monologues. Narrative texts were collected from French-speaking monolinguals in four age groups (five, seven, ten years and adults). Twenty subjects from each group were asked to tell a story based on a picture book consisting of twenty-four images without text (Frog, Where are you?). Relative constructions were ...