相关论文: Irrational Base Counting

We present two embeddings of infinite-valued Lukasiewicz logic L into Meyer and Slaney's abelian logic A, the logic of lattice-ordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding…

In this paper we develop symbolic computation algorithms to investigate finiteness of central configurations for the planar $n$-body problem. Our approach is based on Albouy-Kaloshin's work on finiteness of central configurations for the…

We propose a new algorithm for computing validated bounds for the solutions to the first order variational equations associated to ODEs. These validated solutions are the kernel of numerics computer-assisted proofs in dynamical systems…

We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reformulated as the existence of certain algorithmic reductions…

The purpose of [1] was as follows. ?We consider special sets of continuants which occur in applications. For these sets we solve the problem of finding maximal and minimal continuants. There are several methods for finding extremum such as…

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…

One of the main contributions which Volker Weispfenning made to mathematics is related to Groebner bases theory. In this paper we present an algorithm for computing all algebraic intermediate subfields in a separably generated unirational…

We introduce and discuss, through a computational algebraic geometry approach, the automatic reasoning handling of propositions that are simultaneously true and false over some relevant collections of instances. A rigorous, algorithmic…

We introduce and study non-uniform expansions of real numbers, given by two non-integer bases.

We propose a new no-go theorem by proving the impossibility of constructing a deterministic quantum circuit that iterates a unitary oracle by calling it only once. Different schemes are provided to bypass this result and to approximately…

This paper investigates the absolute values on $\mathbb{Z}$ valued in the upper reals (i.e. reals for which only a right Dedekind section is given). These necessarily include multiplicative seminorms corresponding to the finite prime fields…

The Carrell-Chapuy recurrence formulas dramatically improve the efficiency of counting orientable rooted maps by genus, either by number of edges alone or by number of edges and vertices. This paper presents an implementation of these…

In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…

In this paper, a geometric resolution of singularities algorithm is developed. This method is elementary in its statement and proof, using explicit coordinate systems as much as possible. Each coordinate change used in the resolution…

We discuss some examples that illustrate the countability of the positive rational numbers and related sets. Techniques include radix representations, Godel numbering, the fundamental theorem of arithmetic, continued fractions, Egyptian…

We motivate and study an infinite sequence of binary operations on the ordinal numbers, extending the standard arithmetic on the ordinals to higher degrees of iteration. Connections to the hyperoperations on the natural numbers are…

We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and…

We reprove the countable splitting lemma by adapting Nawrotzki's algorithm which produces a sequence that converges to a solution. Our algorithm combines Nawrotzki's approach with taking finite cuts. It is constructive in the sense that…

While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…

A method of determining two factors of an odd integer without need of multiplication or division operation in iterative portion of computation is presented. It is feasible for an implementing algorithm to use only integer addition and…