Algebraic numbers
On the density function of the distribution of real algebraic numbers
... for algebraic numbers of higher ...real algebraic numbers are distributed uniformly, he also brought some natural heuristic arguments in favour of his ...
23
Zero-Sum Stochastic Games over the Field of Real Algebraic Numbers
... In this paper, we constructively solve the above problem over the ordered field F of real algebraic numbers. This is shown without any structural assumptions on the game and applies to both discounted and ...
17
On the algebraic numbers computable by some generalized Ehrenfest urns
... of numbers, some algebraic numbers as ”simple” (on a computational point of view) as 1/5 are not com- ...certain algebraic structure which is consistent with computability? In other words: ...
15
Formalized algebraic numbers: construction and first-order theory.
... John Harrison [ 51 ] made the following observation: “There isn’t a perfect match between what humans find easy and what proof assistants find easy, so it’s pos- sible that a proof that a human would regard as more ...
165
Logarithms of algebraic numbers
... Abstract. This article is devoted to a new proof of transcen- dence for evaluations of the archimedean logarithm at all algebraic numbers except unity. As in other proofs of the same theorem, a sort of Padé ...
38
Rational approximations to ${\@root 3 \of {2}}$ and other algebraic numbers revisited
... As Ramaré and Rumely note, considerable roundoff error can arise in the sum of so many floating point numbers. We handled this issue in a similar way to them. We multiply each log by 10 6 , round the resulting ...
27
Fast Computation with Two Algebraic Numbers
... Unité de recherche INRIA Rocquencourt Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex France Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois -[r] ...
26
On the binary expansions of algebraic numbers
... in [14]. (In doing so, they effectively solved research Problem 1.88 of [10], which asks for a fast method.) Might there be a similar, fast construction for C 0 ? • In recent times has emerged the field of “experimental ...
33
Real Algebraic Numbers: Complexity Analysis and Experimentations
... Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex France Unité de recherche INRIA Futurs : Parc Club Orsay Université - ZAC des Vi[r] ...
24
Algebraic numbers and automorphisms of free groups
... The reason is probably that, in the case of an automorphism whose associated matrix has k > 1 expanding eigenvalues, instead of considering a map (or the tiling flow of which this map[r] ...
44
Best simultaneous diophantine approximations of some cubic algebraic numbers
... Proposition 2. Suppose a is a real algebraic number of degree 3 over Q whose conjugates are not real. There exist a unit C of the ring of integer of K = Q(a), two positive integers al and a2 and euclidean norm on ...
13
Problems and results on the distribution of algebraic points on algebraic varieties
... non-zero algebraic num- ber not a root of ...on algebraic numbers and algebraic varieties over number fields and, as such, it deserves a lot of ...
18
Z-numbers as Generalized Probability Boxes
... “(X is A) has probability B”, like the statement “it is probable that my income will he high this year”. Zadeh introduced this kind of probability-qualified statements much earlier, when introducing a general framework ...
18
Cluster algebras and Markoff numbers
... Markoff numbers, which have been introduced in the work of ...are numbers that satisfy the Diophantine Equation a 2 + b 2 + c 2 = ...Markoff numbers is an important subject in combinatorics and plays ...
10
A new class of identities involving Cauchy numbers, harmonic numbers and zeta values
... Improving an old idea of Hermite, we associate to each natural number k a modified zeta function of order k. The evaluation of the values of these functions F k at positive integers reveals a wide class of identities ...
24
Quartic Salem numbers which are Mahler measures of non-reciprocal 2-Pisot numbers
... given algebraic integer is a Mahler measure of an algebraic number, and some related results may be found in [4], [8] and ...Salem numbers for every degree of the form 2 + 4n (n ∈ N) and also for ...
14
Algebraic-Closure-Based Moment Method for Unsteady Eulerian Simulations of Non-Isothermal Particle-Laden Turbulent Flows at Moderate Stokes Numbers in Dilute Regime
... Stokes numbers in high shear zones of the ...Stokes numbers (St < ...Stokes numbers, a ACBMM ap- proach involving higher-order-moment conservation equations or QBMM/KBMM approaches should be ...
27
The CAML numbers reference manual
... L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r] ...
162
Algebraic-Closure-Based Moment Method for Unsteady Eulerian Simulations of Non-Isothermal Particle-Laden Turbulent Flows at Moderate Stokes Numbers in Dilute Regime
... ς which are functions of the invariants of the dimensionless S + and + . Using the Cayley-Hamilton theorem, Pope [ 41 ] showed that a set of ten (ς = 10) tensors T (ς ) is needed to form an integrity basis [ 58 ] in ...
26
A squirmer across Reynolds numbers
... University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK (Received 21 May 2015; revised 22 February 2016; accepted 30 March 2016; first published online 29 April 2016) The self-propulsion of a spherical squirmer ...
25