bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Priori Estimates for the Global Error Committed by Runge-Kutta Methods for a Nonlinear Oscillator
Authors: Niesen Jitse 
Published: August 2013

AbstractThe Alekseev–Gröbner lemma is combined with the theory of modified equations to obtain an a priori estimate for the global error of numerical integrators. This estimate is correct up to a remainder term of order h2p, where h denotes the step size and p the order of the method. It is applied to nonlinear oscillators whose behaviour is described by the Emden–Fowler equation y″+tνyn=0. The result shows explicitly that later terms sometimes blow up faster than the leading term of order hp, necessitating the whole computation. This is supported by numerical experiments.
Enumerating Branched Surface Coverings from Unbranched Ones
Authors: Kwak Jin Ho , Lee Jaeun , Mednykh Alexander 
Published: August 2013

AbstractThe number of non-isomorphic n-fold branched coverings of a given closed surface can be determined by the number of nonisomorphic n-fold unbranched coverings of the surface and the number of nonisomorphic connected n-fold graph coverings of a suitable bouquet of circles. A similar enumeration can also be done for regular branched coverings. Some explicit enumerations are also possible.
An Algorithm to Compute the Canonical Basis of an Irreducible Module Over a Quantized Enveloping Algebra
Authors: de Graaf Willem A. 
Published: August 2013

AbstractThe paper describes an algorithm to compute the canonical basis of an irreducible module over a quantized enveloping algebra of a finite-dimensional semisimple Lie algebra. The algorithm works for any module that is constructed as a submodule of a tensor product of modules with known canonical bases.
The Alperin Weight Conjecture and Dade's Conjecture for the Simple Group J4
Authors: An Jianbei , O'Brien E. A. , Wilson R. A. 
Published: August 2013

AbstractThe authors construct faithful permutation representations of maximal 2-local subgroups and classify the radical chains of the Janko simple group J4; hence the Alperin weight conjecture and the Dade reductive conjecture for J4 are verified.
Fast Constructive Recognition of Black-Box Unitary Groups
Authors: Brooksbank Peter A. 
Published: August 2013

AbstractIn this paper, the author presents a new algorithm to recognise, constructively, when a given black-box group is a homomorphic image of the unitary group SU(d, q) for knowndandq. The algorithm runs in polynomial time, assuming the existence of oracles for handling SL(2,q) subgroups, and for computing discrete logarithms in cyclic groups of orderq± 1.
The Relative Consistency of the Axiom of Choice Mechanized Using Isabelle⁄zf
Authors: Paulson Lawrence C. 
Published: August 2013

AbstractThe proof of the relative consistency of the axiom of choice has been mechanized using Isabelle⁄ZF, building on a previous mechanization of the reflection theorem. The heavy reliance on metatheory in the original proof makes the formalization unusually long, and not entirely satisfactory: two parts of the proof do not fit together. It seems impossible to solve these problems without formalizing the metatheory. However, the present development follows a standard textbook, Kenneth Kunen'sSet theory: an introduction to independence proofs, and could support the formalization of further material from that book. It also serves as an example of what to expect when deep mathematics is formalized.
Strong and Uniform Continuity – the Uniform Space Case
Authors: Bridges Douglas , Vîţă Luminiţa 
Published: August 2013

AbstractIt is proved, within the constructive theory of apartness spaces, that a strongly continuous mapping from a totally bounded uniform space with a countable base of entourages to a uniform space is uniformly continuous. This lifts a result of Ishihara and Schuster from metric to uniform apartness spaces. The paper is part of a systematic development of computable topology using apartness as the fundamental notion.
Note on the Contribution of Low Zeros to Weil's Explicit Formula for Minimal Discriminants
Authors: Omar Sami 
Published: August 2013

AbstractThe bulk of this paper consists of tables giving lower bounds for discriminants of number fields up to 48. The lower bounds are obtained by using two different inequalities for the discriminant, one due to Odlyzko, and the other due to Serre. These inequalities are derived from Weil's explicit formula by choosing suitable weight functions. The bounds are compared with actual values of the discriminants, and the relative errors are computed. The computations show that, at least for values computed, the bounds obtained via Odlyzko's inequality are better than those obtained via Serre's inequality, and are generally within a few percentage points of the true value. This difference can be attributed to a difference in the weighting given to the contribution of low zeros by the two inequalities.
Programming Combinations of Deduction and BDD-based Symbolic Calculation
Authors: Gordon Michael J. C. 
Published: August 2013

AbstractA generalisation of Milner's ‘LCF approach’ is described. This allows algorithms based on binary decision diagrams (BDDs) to be programmed as derived proof rules in a calculus of representation judgements. The derivation of representation judgements becomes an LCF-style proof by defining an abstract type for judgements analogous to the LCF type of theorems. The primitive inference rules for representation judgements correspond to the operations provided by an efficient BDD package coded in C (BuDDy). Proof can combine traditional inference with steps inferring representation judgements. The resulting system provides a platform to support a tight and principled integration of theorem proving and model checking. The methods are illustrated by using them to solve all instances of a generalised Missionaries and Cannibals problem.
Coset Enumeration Using Prefix Gröbner Bases: An Experimental Approach
Authors: Reinert Birgit , Zeckzer Dirk 
Published: August 2013

AbstractThe authors study a new method for coset enumeration in finitely presented groups. Their method uses prefix Gröbner basis computation in the monoid ring ${\mathbb{K}}[{\cal M}]$, where ${\mathbb{K}}$ is a computable field and ${\cal M}$ a monoid presented by a convergent string-rewriting system. The method is compared to well-known methods for Todd-Coxeter enumeration, using examples from the literature where studies of these methods are reported. New insights into coset enumeration were gained using three different kinds of orderings, combined with new frameworks and strategies implemented in MRC 1.2.
On a Result of Darboux
Authors: Chavarriga Javier , Llibre Jaume , Ollagnier Jean Moulin 
Published: August 2013

AbstractThis paper is concerned with a relation of Darboux in enumerative geometry, which has very useful applications in the study of polynomial vector fields. The original statement of Darboux was not correct. The present paper gives two different elementary proofs of this relation. The first one follows the ideas of Darboux, and uses basic facts about the intersection index of two plane algebraic curves; the second proof is rather more sophisticated, and gives a stronger result, which should also be very useful. The power of the relation of Darboux is then illustrated by the provision of new, simple proofs of two known results. First, it is shown that an irreducible invariant algebraic curve of degree n > 1 without multiple points for a polynomial vector field of degree m satisfies n ≤ m + 1. Second, a proof is given that quadratic polynomial vector fields have no algebraic limit cycles of degree 3.
Picard Groups and Refined Discrete Logarithms
Authors: Bley W. , Endres M. 
Published: August 2013

AbstractLet K denote a number field, and G a finite abelian group. The ring of algebraic integers in K is denoted in this paper by $/cal{O}_K$, and $/cal{A}$ denotes any $/cal{O}_K$-order in K[G]. The paper describes an algorithm that explicitly computes the Picard group Pic($/cal{A}$), and solves the corresponding (refined) discrete logarithm problem. A tamely ramified extension L/K of prime degree l of an imaginary quadratic number field K is used as an example; the class of $/cal{O}_L$ in Pic($/cal{O}_K[G]$) can be numerically determined.
Spectral Bounds Using Higher-Order Numerical Ranges
Authors: Davies E. B. 
Published: August 2013

AbstractThis paper describes how to obtain bounds on the spectrum of a non-self-adjoint operator by means of what are referred to here as ‘its higher-order numerical ranges’. Proofs of some of their basic properties are given, as well as an explanation of how to compute them. Finally, they are used to obtain new spectral insights into the non-self-adjoint Anderson model in one and two space dimensions.
A Diophantine Equation Associated to X0(5)
Authors: Chen Imin 
Published: August 2013

AbstractSeveral classes of Fermat-type diophantine equations have been successfully resolved using the method of galois representations and modularity. In each case, it is possible to view the proper solutions to the diophantine equation in question as corresponding to suitably defined integral points on a modular curve of level divisible by 2 or 3. Motivated by this point of view, an example of a diophantine equation associated to the modular curve X0(5) is discussed in this paper. The diophantine equation has four terms rather than the usual three terms characteristic of generalized Fermat equations.
Computing Modular Polynomials
Authors: Charles Denis , Lauter Kristin 
Published: August 2013

AbstractThis paper presents a new probabilistic algorithm to compute modular polynomials modulo a prime. Modular polynomials parameterize pairs of isogenous elliptic curves, and are useful in many aspects of computational number theory and cryptography. The algorithm presented here has the distinguishing feature that it does not involve the computation of Fourier coefficients of modular forms. The need to compute the exponentially large integral coefficients is avoided by working directly modulo a prime, and computing isogenies between elliptic curves via Vélu's formulas.
Computation of Sets of Rational Points of Genus-3 Curves via the Dem'Janenko–Manin Method
Authors: Girard Martine , Kulesz Leopoldo 
Published: August 2013

AbstractThe authors construct two families of genus-3 curves defined over Q(t) with three independent morphisms to an elliptic curve of rank at most two. They give explicit examples of an application of the Dem'janenko-Manin method that completely determines both the set of the Q(t)-rational points of the curves under consideration, and the set of Q-rational points of some specialisations.
On Homogenous Minimal Involutive Varieties
Authors: Almeida L. C. O. , Coutinho S. C. 
Published: August 2013

AbstractЅ(2n,k) be the variety of homogeneous polynomials of degree k in 2n variables. The authors of this paper give a computer-assisted proof that there is an analytic open set Ω of Ѕ(4,3) such that the surface F = 0 is a minimal homogeneous involutive variety of ℂ4 for all F ∈ Ω. As part of the proof, they give an explicit example of a polynomial with rational coefficients that belongs to Ω.
Computing the Decay of a Simple Reversible Sub-Markov Semigroup
Authors: Davies E. B. 
Published: August 2013

AbstractTwo different numerical methods for solving a non-self-adjoint evolution equation are compared in this paper. If the intial function lies in the domain of the operator, a recently proposed method that combines pseudospectral ideas and semigroup theory is shown to be considerably more accurate than a standard discretization method. One example is worked out in detail, but the methodsa used are of much wider applicability.
Upper Bounds for Norms of Products of Binomials
Authors: Cipu Mihai 
Published: August 2013

AbstractThis paper deals with the problem of finding the least length of a product of n binomials. A theorem of R. Maltby has shown that the problem is algorithmically solvable for any fixed n. Here, a different proof is presented for this result, and yields improved complexity. The author reports the results of computations of the upper bounds on the least length or Euclidean norm of a product of binomials.
On Tensor-Factorisation Problems,I: The Combinatorial Problem
Authors: Neumann Peter M. , Praeger Cheryl E. 
Published: August 2013

AbstractA k-multiset is an unordered k-tuple, perhaps with repetitions. If x is an r-multiset {x1, …, xr} and y is an s-multiset {y1, …, ys} with elements from an abelian group A the tensor product x ⊗ y is defined as the rs-multiset {xi yj | 1 ≤ i ≤ r, 1 ≤ j ≤ s}. The main focus of this paper is a polynomial-time algorithm to discover whether a given rs-multiset from A can be factorised. The algorithm is not guaranteed to succeed, but there is an acceptably small upper bound for the probability of failure. The paper also contains a description of the context of this factorisation problem, and the beginnings of an attack on the following division-problem: is a given rs-multiset divisible by a given r-multiset, and if so, how can division be achieved in polynomially bounded time?
Easy Decision Diffie-Hellman Groups
Authors: Galbraith Steven D. , Rotger Victor 
Published: August 2013

AbstractThe decision Diffie-Hellman problem (DDH) is a central computational problem in cryptography. It is known that the Weil and Tate pairings can be used to solve many DDH problems on elliptic curves. Distortion maps are an important tool for solving DDH problems using pairings, and it is known that distortion maps exist for all super-singular elliptic curves. An algorithm is presented here to construct suitable distortion maps. The algorithm is efficient on the curves that are usable in practice, and hence all DDH problems on these curves are easy. The issue of which DDH problems on ordinary curves are easy is also discussed.
Cross Orbits
Authors: Rowley Peter 
Published: August 2013

AbstractThis paper contains a variety of results about the action of Con way‘s largest simple group upon the crosses in the Leech lattice. These results are tailor-made for use in ‘A Monster Graph, I'(Proc. London Math. Soc. (3) 90 (2005) 42-60), where a graph related to the Monster simple group is studied.
An Algorithmic Analysis of the Intersection Property
Authors: Jacobs Pascale , Leemans Dimitri 
Published: August 2013

AbstractIn this paper, efficient algorithms are given to test the intersection property and some of its variations on flag-transitive coset geometries. These algorithms are then applied to geometries of some sporadic groups, namely the Mathieu groups M11, M12, M22and M23, the Janko groups J1, J2and J3 and the Higman-Sims group HS.
A Bound on the Number of Endpoints of the Cut Locus
Authors: Sinclair Robert , Tanaka Minoru 
Published: August 2013

AbstractWe provide strong experimental evidence for an upper bound on the number of endpoints of the cut locus from a point on a 2-surface of revolution. This bound is equal to the minimal number of intervals of monotone non-increasing or non-decreasing Gaussian curvature along one meridian from one pole to the other.
On Polynomial Interpolations related to Verheul Homomorphisms
Authors: Satoh Takakazu 
Published: August 2013

AbstractThe Verheul homomorphism is a group homomorphism from a finite subgroup of the multiplicative group of a field to an elliptic curve. The hardness of computation of the Verheul homomorphism was shown by Verheul to be closely related to the hardness of the computational Diffie-Hellman problem. Let p ≥ 5 be a prime, and let N be a prime satisfying √(12p) < N < 2p / √3, where N ≠ p. Let E be an ordinary elliptic curve over Fp, and let C ⊂ E be a cyclic subgroup of order N. Let H be the group of all Nth roots of unity (contained in the algebraic closure of Fp), and let phi be the Verheul isomorphism from H to C.We consider a polynomial P such that P(z) is the X-coordinate of phi(z) for all z ∈ H – {1}. We show that, for at least approximately 58% of pairs (E, C), none of the coefficients of the non-constant terms of P vanishes.
Simple Lie Algebras of Low Dimension Over GF (2)
Authors: Vaughan-Lee Michael 
Published: August 2013

AbstractWe classify the simple Lie algebras of dimension at most 9 over GF(2). There is one of dimension 3 and one of dimension 6, there are two of dimension 7 and two of dimension 8, and there is one of dimension 9. The two simple Lie algebras of dimension 8 are restricted Lie algebras. If we extend the ground field to GF(4), then the six-dimensional algebra is no longer simple, and if we extend the ground field to GF(8) then the nine-dimensional algebra is no longer simple. But the other algebras are all central simple.
Resolving the Multitude of Microscale Interactions Accurately Models Stochastic Partial Differential Equations
Authors: Roberts A. J. 
Published: August 2013

AbstractConstructing numerical models of noisy partial differential equations is a very delicate task. Our long-term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a second step, we consider here a small domain, representing a finite element, and derive a one-degree-of-freedom model for the dynamics in the element; stochastic centre manifold theory supports the model. The approach automatically parametrises the microscale structures induced by spatially varying stochastic noise within the element. The crucial aspect of this work is that we explore how a multitude of microscale noise processes may interact in nonlinear dynamical systems. The analysis finds that noise processes with coarse structure across a finite element are the significant noises for the modelling. Further, the nonlinear dynamics abstracts effectively new noise sources over the macroscale time-scales resolved by the model.
Lens Spaces, Isospectral on Forms but not on Functions
Authors: Gornet Ruth , McGowan Jeffrey 
Published: August 2013

AbstractWe study the p-form spectrum of the Laplace-Beltrami operator acting on lens spaces as considered by Ikeda [Geometry of manifolds (Academic Press, Boston, MA, 1989) 383–417]. Ikeda gave examples of such spaces that are non-isometric but isospectral for all p ≤ p0. In this paper we exhibit examples of such spaces that are not isometric, and are isospectral for various, but not for all. values of p. In particular, examples are given of non-isometric lens spaces that are isospectral for some values of p but not for the case p = 0.
Improved Bounds for the Spread of Sporadic Groups
Authors: Bradley J. D. , Holmes P. E. 
Published: August 2013

AbstractThe spread of a group G is the greatest number r such that, for every set of non-trivial elements {x1,…,xr}, there exists an element y with the property that 〈xi, y〉 = G for 1 ≤ i ≤ r. In this paper we obtain good upper bounds for the spread of fourteen sporadic simple groups computationally, and we determine the value of the spread of M11 by hand.
On the Computation of Integral Closures of Cyclic Extensions of Function Fields
Authors: Fraatz Robert 
Published: August 2013

AbstractLetSbe a non-empty proper subset of the set of places of a global function fieldFandEa cyclic Kummer or Artin–Schreier–Witt extension ofF. We present a method of efficiently computing the ring of elements ofEwhich are integral at all places ofS. As an important tool, we include an algorithmic version of the strong approximation theorem. We conclude with several examples.
The Character Table of a Maximal Subgroup of the Monster
Authors: Barraclough R. W. , Wilson R. A. 
Published: August 2013

AbstractWe calculate the character table of the maximal subgroup of the Monster N(3B) isomorphic to a group of shape 3+1+12 · 2 · Suz: 2, and also of the group 31+12 : 6 · Suz · 2, which has the former as a quotient. The strategy is to induce characters from the inertia groups in 31+12 : 6 · Suz : 2 of characters of 31+12. We obtain the quotient map to N(3B) computationally, and our careful concrete approach allows us to produce class fusions between our tables and various tables in the GAP library.
Categorical Models of Syntactic Control of Intereference Revisited, Revisited
Authors: McCusker Guy 
Published: August 2013

AbstractThe question of what categorical structure is required to give semantics to O‘Hearn et al.'s type system Syntactic Control of Interference Revisited (SCIR) is considered. The previously proposed notion of bireflective model is rejected as being too restrictive to accommodate important concrete models based on game semantics and object spaces; furthermore it is argued that the existing proof-sketch of the important property of coherence for these models is incorrect. A new, more general notion of model is proposed and the coherence property proved.
The Tropicalj-Invariant
Authors: Katz Eric , Markwig Hannah , Markwig Thomas 
Published: August 2013

AbstractIf (Q,A) is a marked polygon with one interior point, then a general polynomialfbelonging toK[x,y] with supportAdefines an elliptic curveCfon the toric surfaceXA. IfKhas a non-archimedean valuation intoRwe can tropicalizeCfto get a tropical curve Trop(Cf). If in the Newton subdivision induced byfis a triangulation and the interior point occurs as the vertex of a triangle, then Trop(Cf) will be a graph of genus one and we show that the lattice length of the cycle of that graph is the negative of the valuation of thej-invariant ofCf.
A Point Counting Algorithm Using Cohomology with Compact Support
Authors: Chatel Gweltaz , Lubicz David 
Published: August 2013

AbstractWe describe an algorithm to count the number of rational points of an hyperelliptic curve defined over a finite field of odd characteristic which is based upon the computation of the action of the Frobenius morphism on a basis of the Monsky-Washnitzer cohomology with compact support. This algorithm follows the vein of a systematic exploration of potential applications of cohomology theories to point counting.Our algorithm decomposes in two steps. A first step which consists of the computation of a basis of the cohomology and then a second step to obtain a representation of the Frobenius morphism. We achieve aÕ(g4n3) time complexity andO(g3n3) memory complexity wheregis the genus of the curve andnis the absolute degree of its base field. We give a detailed complexity analysis of the algorithm as well as a proof of correctness.
Single-class genera of positive integral lattices
Authors: Lorch David , Kirschmer Markus 
Published: August 2013

AbstractWe give an enumeration of all positive definite primitive $ \mathbb{Z} $-lattices in dimension $n\geq 3$ whose genus consists of a single isometry class. This is achieved by using bounds obtained from the Smith–Minkowski–Siegel mass formula to computationally construct the square-free determinant lattices with this property, and then repeatedly calculating pre-images under a mapping first introduced by G. L. Watson.We hereby complete the classification of single-class genera in dimensions 4 and 5 and correct some mistakes in Watson’s classifications in other dimensions. A list of all single-class primitive $ \mathbb{Z} $-lattices has been compiled and incorporated into the Catalogue of Lattices.