A New Representation for Exact Real Numbers
... 2 The new representation of real numbers There are a number of equivalent de nitions of a computable real number. The most convenient one for us is to consider a real number as the intersection of a shrinking nested sequence of rational intervals; we then say that the real number is computable if th ...
... 2 The new representation of real numbers There are a number of equivalent de nitions of a computable real number. The most convenient one for us is to consider a real number as the intersection of a shrinking nested sequence of rational intervals; we then say that the real number is computable if th ...
CERES for Propositional Proof Schemata
... This will yield our notion of proof schemata: I Definition 2.4 (Proof schemata). Let ψ be a proof symbol and S(n) be a sequent. Then a proof schema pair for ψ is a pair of LKS-proofs (π, ν(k + 1)) with end-sequents S(0) and S(k + 1) respectively such that π may not contain proof links and ν(k + 1) m ...
... This will yield our notion of proof schemata: I Definition 2.4 (Proof schemata). Let ψ be a proof symbol and S(n) be a sequent. Then a proof schema pair for ψ is a pair of LKS-proofs (π, ν(k + 1)) with end-sequents S(0) and S(k + 1) respectively such that π may not contain proof links and ν(k + 1) m ...
The University of Ottawa First Year Math Survival Guide
... • Considerably less time in the classroom, considerably more time with the books. After making your weekly timetable for your first semester, You could be shocked how little you "physically" have to be on campus compared with your long days at high school. In most cases, your classes and labs (or D ...
... • Considerably less time in the classroom, considerably more time with the books. After making your weekly timetable for your first semester, You could be shocked how little you "physically" have to be on campus compared with your long days at high school. In most cases, your classes and labs (or D ...
Sequence entropy pairs and complexity pairs for a measure
... and maximal null factor. In this purpose we introduce sequence entropy tuples for a measure and vve show that the set of sequence entropy tuples for a measure is contained in the set of topological sequence entropy tuples. The reciprocal is not true. Moreover, we show that for each system there is a ...
... and maximal null factor. In this purpose we introduce sequence entropy tuples for a measure and vve show that the set of sequence entropy tuples for a measure is contained in the set of topological sequence entropy tuples. The reciprocal is not true. Moreover, we show that for each system there is a ...
Are monochromatic Pythagorean triples avoidable?
... Pythagorean triples. On the other hand, some structure on the considered colorings is needed, in order to have a more manageable function space size. This prompts us to consider maps f : N+ → G satisfying weaker conditions than morphisms, and which we now define. First, for any positive integer n, w ...
... Pythagorean triples. On the other hand, some structure on the considered colorings is needed, in order to have a more manageable function space size. This prompts us to consider maps f : N+ → G satisfying weaker conditions than morphisms, and which we now define. First, for any positive integer n, w ...
CENTRAL LIMIT THEOREM FOR THE EXCITED RANDOM WALK
... random walk, the key issue being to obtain good tail estimates for these regeneration times. Indeed, using estimates for the so-called tan points of the simple random walk, introduced in [1] and subsequently used in [6, 7], it is possible to prove that, when d ≥ 2, the number of distinct points visi ...
... random walk, the key issue being to obtain good tail estimates for these regeneration times. Indeed, using estimates for the so-called tan points of the simple random walk, introduced in [1] and subsequently used in [6, 7], it is possible to prove that, when d ≥ 2, the number of distinct points visi ...
Homeworks, with Solutions
... Now we might answer 300+128 = 428. But it would be a mistake because we would have counted some numbers twice! Which ones? Those divisible by both 3 and 7 (see 105 and 987) in the lists above. These are exactly the number divisible by 21 and there are (987 − 105)/21 + 1 = 43. So, to account for coun ...
... Now we might answer 300+128 = 428. But it would be a mistake because we would have counted some numbers twice! Which ones? Those divisible by both 3 and 7 (see 105 and 987) in the lists above. These are exactly the number divisible by 21 and there are (987 − 105)/21 + 1 = 43. So, to account for coun ...
Siegel Discs
... f is locally linearizable around z0 . z0 ∈ F(f ). The connected component U of F(f ) containing z0 is a Siegel disc. Proof. If f is locally linearizable around z0 , then the iterates of f in a suitable neighborhood of z0 correspond to iterated rotations of a small disc, and hence form a normal ...
... f is locally linearizable around z0 . z0 ∈ F(f ). The connected component U of F(f ) containing z0 is a Siegel disc. Proof. If f is locally linearizable around z0 , then the iterates of f in a suitable neighborhood of z0 correspond to iterated rotations of a small disc, and hence form a normal ...
