bluuebunny/crossref_metadata_2025 huggingface dataset:
Unavoidable systems of functions
Authors: Hayman W. K. , Rubel Lee A.
Published: November 2008

Suppose that D is a plane domain and that f(z), g(z) are meromorphic in D and f(z) ╪ g(z) for all z in D. Then following Rubel and Yang [11], we say that f(z) avoids g(z) in D. A system of functions g1(z), …, gn(z) is said to be unavoidable if, whenever f is meromorphic in D, at least one of the equations f(z) = gv(z) has a root in D. Rubel and Yang [11] proved that if D is the open plane, then any two functions form an avoidable system, but three distinct polynomials a1, a2, a3 such that a1−a2 and a2−a3 are not both constant form an unavoidable system.
Cubic systems with four real line invariants
Authors: Kooij Robert E.
Published: November 2008

A polynomial system is a real autonomous system of ordinary differential equations on the plane with polynomial nonlinearities:

with aij, bij ∈ ℝ and where x = x(t) and y = y(t) are real-valued functions.

The problem of analysing limit cycles (isolated periodic solutions) in polynomial systems was first discussed by Poincaré[16]. Then, in the famous list of 23 mathematical problems stated in 1900, Hilbert[9] asked in the second part of the 16th problem for an upper bound for the number of limit cycles for nth degree polynomial systems, in terms of n. Recently, it has been proved that, given a particular choice of coefficients for a system of form (1·1), the number of limit cycles is finite. This result is known as Dulac's theorem, see Ecalle[8] or Il'yashenko[10]. However, it is unknown whether or not there exists an upper bound for the number of limit cycles in system (1·1) in terms of n. Even for quadratic systems (i.e. polynomial systems with quadratic nonlinearities) this remains an open question.
Some remarks on Gauss sums associated with kth powers
Authors: Montgomery H. L. , Vaughan R. C. , Wooley T. D.
Published: November 2008

Estimates for rational trigonometric sums are of great importance in analysing the local aspects of many additive problems. Indeed, bounds for the sums

in which e(α) denotes exp (2πiα), play a fundamental rôle in the application of the Hardy–Littlewood method to Waring's problem (see [11]), and also in the analysis of the local solubility of systems of additive equations (see, for example, [2]). When k ≥ 2 is an integer, and p is a prime number it is well known (see [5] or [11, lemma 4·3]) that
Homotopical algebra and triangulated categories
Authors: Grandis Marco
Published: November 2008

We study here the connections between the well known Puppe-Verdier notion of triangulated category and an abstract setting for homotopical algebra, based on homotopy kernels and cokernels, which was expounded by the author in [11, 13[.

We show that a right-homotopical category A (having well-behaved homotopy cokernels, i.e. mapping cones) has a sort of weak triangulated structure with regard to the suspension endofunctor σ, called σ-homotopical category. If A is homotopical and h-stable (in a sense related to the suspension-loop adjunction), this structure is also h-stable, i.e. satisfies ‘up to homotopy’ the axioms of Verdier[29[ for a triangulated category, excepting the octahedral one which depends on some further elementary conditions on the cone endofunctor of A. Every σ-homotopical category can be stabilized, by two universal procedures, respectively initial and terminal.
On arithmetically realizable classes
Authors: Burns D.
Published: November 2008

We fix a number field L and a finite group G, and write Cl (ℤL[G]) for the reduced Grothendieck group of the category of finitely generated projective ℤL[G]-modules. We let RG denote the ring of complex characters of G, with SG the additive subgroup which is generated by the irreducible symplectic characters. We shall say that an element c ∈ Cl (ℤL[G]) is ‘(arithmetically) realizable’ if there exists a tamely ramified Galois extension N/K of number fields with L ⊆ K and an identification Gal (N/K) →˜ G via which c is the class of some Gal (N/K)-stble ℤN-ideal. We let RL(G) denote the subgroup of Cl (ℤL[G]) which is generated by the realizable elements for varying N/K. Our interest in RL(G) arises from the fact that it is the largest subset of Cl (ℤL[G]) upon which the results of Chinburg and the author in [Bu, Ch] can be used to give an explicit module theoretic description of the action of the integral semi-group ring AL, G of the Adams-Cassou-Noguès-Taylor operators (ΨL, k): k ∈ ℤ, 2 × k if SG ≠ {0}}. Whilst the results of [Bu, Ch] can (at least partially) be understood ‘geometrically’ via the action of Bott cannibalistic elements on suitable Grothendieck groups (cf. [Ch, E, P, T], [Bu]), the underlying problem of finding an explicit module theoretic interpretation of the action of AL, G on all elements of Cl(ℤL[G]) is of course essentially algebraic in nature. It is in this context that we were originally motivated to investigate RL(G).
Asymptotic distribution of the zeros of Faber polynomials
Authors: Kuijlaars A. B. J. , Saff E. B.
Published: November 2008

Using potential theoretic methods and exploiting the connection with eigenvalues of Toeplitz matrices, we investigate the limiting behaviour of zeros of Faber polynomials generated by a Laurent series. Our results build upon fundamental work of J. L. Ullman. For example, we show that if E is a compact set with simply connected complement and connected interior whose boundary is either (i) not a piecewise analytic curve or (ii) a piecewise analytic curve but with a singularity other than an outward cusp, then the equilibrium distribution for E is a limit measure of the sequence of normalized zero counting measures for the Faber polynomials associated with E.
Counterexamples to the modified Weyl–Berry conjecture on fractal drums
Authors: Lapidus Michel L. , Pomerance Carl
Published: November 2008

Let Ω be a non-empty open set in ℝn with finite ‘volume’ (n-dimensional Lebesgue measure). Let be the Laplacian operator. Consider the eigenvalue problem (with Dirichlet boundary conditions):

where λ ∈ ℝ and u is a non-zero member of (the closure in the Sobolev space H1(Ω) of the set of smooth functions with compact support contained in Ω). It is well known that the values of λ∈ℝ for which (1·1) has a non-zero solution are positive and form a discrete set. Moreover, for each λ, the associated eigenspace is finite dimensional. Let the spectrum of (1·1) be denoted where 0 < λ1 ≤ λ2 ≤ … and where the multiplicity of each λ in the sequence is the dimension of the associated eigenspace. Let
Embedding knots and links in an open book II. Bounds on arc index
Authors: Cromwell Peter R. , Nutt Ian J.
Published: November 2008

There is an open-book decomposition of the 3-sphere which has open discs as pages and an unknotted circle as the binding. We can think of the 3-sphere as ℝ3 ∪ {∞} and of the circle as the z–axis ∪ {∞}. The pages are then half-planes Hθ at angle θ when the x–y plane has polar coordinates. In their investigation of the braid index of satellite links, Birman and Menasco [B–M] embed the companion knot in finitely many such half-planes so that the knot meets each half-plane in a single simple arc, and therefore meets the axis in a finite number of points. At the end of their paper they mention that the minimum number of planes required to present a given knot in this manner is a knot invariant and that it seems to have escaped attention. (Jósef Przytycki has since pointed out to us that the phenomenon is evident in a one-hundred-year-old paper by H. Brunn[Br].) We call this invariant the arc index of a link and denote it by α(L).
Towards a higher-dimensional MacLane class
Authors: Rippon P. J.
Published: November 2008

Let D be a bounded region in ℝm, m ≥ 2. We say that a function u defined in D has asymptotic value α if there is a boundary path Γ:x(t), 0≤t<1, in D (that is, dist (x(t), ∂D)→0 as t→1), such that u(x(t))→α as t→1. If in addition, x(t)→ξ as t→1, then u has asymptotic value α at ξ.
Countable partitions of Euclidean space
Authors: Schmerl James H.
Published: November 2008

Erdös has asked whether the plane ℝ2, or more generally n-dimensional Euclidean space ℝn, can be partitioned into countably many sets none of which contains the vertices of an isosceles triangle. Assuming the Continuum Hypothesis (CH), Davies[2] (for n = 2) and Kunen[10] (for arbitrary n) proved that such partitions exist. Assuming Martin's Axiom, Erdös and Komjáth proved in [5] that such partitions exist for n = 2. We will prove here, without additional set-theoretic hypotheses, that there are such partitions in all dimensions.

Let ‖x‖ denote the usual Euclidean norm of a point x ∈ ℝn, so that ‖x − y‖ is the distance between x and y.
Uniqueness theorems for left-symmetric enveloping algebras
Authors: Bolgar J. R.
Published: November 2008

Let L be a Lie algebra over a field of characteristic zero. We study the uni versai left-symmetric enveloping algebra U(L) introduced Dan Segal in [9]. We prove some uniqueness results for these algebras and determine their automorphism groups, both as left-symmetric algebras and as Lie algebras.
Transfer maps for fibrations
Authors: Dwyer W. G.
Published: November 2008

Let f: E → B be a fibration with fibre F over a connected space B. If F is homotopy equivalent to a finite complex, Becker and Gottlieb [2, 3] and others have constructed a transfer map

where for simplicity X+ denotes the suspension spectrum of the space obtained from X adding a disjoint basepoint. One key property of τ(f) is the fact that the composite map f+. τ(f): B+ → B+ induces a map on integral homology which is multiplication the Euler characteristic X(F).
An algebraic condition to determine whether a knot is prime
Authors: Ryder Hayley
Published: November 2008

A quandle is the algebraic distillation of the second and third Reidemeister moves, on unframed links. Quandles have been studied by many people including Kauffman[K], Fenn and Rourke[F-R] and Joyce [J]. Joyce defines the fundamental quandle, which is a classifying invariant of irreducible, unframed links. Fenn and Rourke, who study generalised quandles or racks in [F—R], show that the natural map from the fundamental quandle of a knot K to the knot group is never injective if K is a connected sum. We now prove that the natural map from the fundamental quandle to the fundamental group of the complement of a link in S3 is injective if and only if the link is prime.
Geometrical conditions for the stability of orbits in planar systems
Authors: Garcia R. A. , Gasull A. , Guillamon A.
Published: November 2008

Given a vector field X on the real plane, we study the influence of the curvature of the orbits of ẋ = X┴(x) in the stability of those of the system x˙ = X(x). We pay special attention to the case in which this curvature is negative in the whole plane. Under this assumption, we classify the possible critical points and give a criterion for a point to be globally asymptotically stable. In the general case, we also provide expressions for the first three derivatives of the Poincaré map associated to a periodic orbit in terms of geometrical quantities.
Almost all Bianchi groups have free, non-cyclic quotients
Authors: Mason A. W. , Odoni R. W. K. , Stothers W. W.
Published: November 2008

Let d be a square-free positive integer and let O (= Od) be the ring of integers of the imaginary quadratic number field ℚ(-d). The groups PSL2(O) are called the Bianchi groups after Luigi Bianchi who made the first important contribution 1 to their study in 1892. Since then they have attracted considerable attention particularly during the last thirty years. Their importance stems primarily from their action as discrete groups of isometries on hyperbolic 3-space, H3. As a consequence they play an important role in hyperbolic geometry, low-dimensional topology together with the theory of discontinuous groups and automorphic forms. In addition they are of particular significance in the class of linear groups over Dedekind rings of arithmetic type. Serre9 has proved that in this class the Bianchi groups (along with, for example, the modular group, PSL2(z), where z is the ring of rational integers) have an exceptionally complicated (non-congruence) subgroup structure.
Modular symbols for 1(N) and elliptic curves with everywhere good reduction
Authors: Cremona J. E.
Published: November 2008

The modular symbols method developed by the author in 4 for the computation of cusp forms for 0(N) and related elliptic curves is here extended to 1(N). Two applications are given: the verification of a conjecture of Stevens 14 on modular curves parametrized by 1(N); and the study of certain elliptic curves with everywhere good reduction over real quadratic fields of prime discriminant, introduced by Shimura and related to Pinch's thesis 10.
Modular structure of algebras of unbounded operators
Authors: Inoue Atsushi
Published: November 2008

A systematic analysis of standard systems and modular systems for which one can develop TomitaTakesaki theory for algebras of unbounded operators is presented. Such systems arise in the Wightman quantum field theory. The connection between such systems and the theory of local nets of von Neumann algebras initiated by Araki and HaagKastler is discussed.
Singular n-tuples and Hausdorff dimension. II
Authors: Baker R. C.
Published: November 2008

Let n be a natural number, with n ≥ 2. Let Kn denote the set of θ in Euclidean space Rn for which θ1, …, θn, 1 are linearly independent over the rational numbers. We denote points of the set of integer n-tuples Zn by x, y,…. We write

Inner product is denoted by θø. In Rl, ‖θ‖ denotes distance to the nearest integer.
Translation-invariant linear operators
Authors: Dales H. G. , Millinoton A.
Published: November 2008

The theory of translation-invariant operators on various spaces of functions (or measures or distributions) is a well-trodden field. The problem is to decide, first, whether or not a linear operator between two function spaces on, say, ℝ or ℝ+ which commutes with one or many translations on the two spaces is necessarily continuous, and, second, to give a canonical form for all such continuous operators. In some cases each such operator is zero. The second problem is essentially the ‘multiplier problem’, and it has been extensively discussed; see [7], for example.
Separation of points by classes of harmonic functions
Authors: Armitage D. H. , Gardiner S. J. , Netuka I.
Published: November 2008

We characterize those domains Ω in ℝN for which the positive harmonic functions on Ω separate the points of Ω.
Double point surfaces of smooth immersions Mn → ℝ2n−2
Authors: Szücs András
Published: November 2008

In recent years many papers have dealt with the zero-dimensional multiple point sets of smooth immersions of closed manifolds in Euclidean spaces (see, for example, [2, 6, 7, 8, 9, 10, 13, 14, 15, 21]). In the present paper we deal with the case when the double points form a two-dimensional surface and consider the following question: Which surfaces can occur as double point surfaces of self-transverse immersions of closed n-manifolds in ℝ2n−2? We prove the following
On the homomorphisms of sequences
Authors: Cockcroft W. H.
Published: November 2008

The algebraic classification problem with which I shall be concerned in this paper is suggested by the algebraic theory of homomorphisms of free crossed modules whose groups of operators are free groups. This theory arises in the study of the homotopy theory of two-dimensional C.W. complexes*. It is shown in (3) that the homotopy theory of such complexes, including the homotopy classification of mappings, is equivalent to this purely algebraic theory.
An integral of hypergeometric type
Authors: Slater L. J.
Published: November 2008

In a recent paper (2) I gave some integrals which represented general transformations of hypergeometric series of both ordinary and basic types. In this paper I give the most general form of this kind of integral, from which all the previously known general basic transformations can be deduced.

In the usual notation for basic series,

where x may be a function of n, for example,

and Π is written for ‘Idem (a; b)' means that the expression immediately preceding is to be repeated with b written in place of a and a written in place of b.
The interaction of alpha-particles and the binding energy of 8Be
Authors: Edwards S. F.
Published: November 2008

A calculation of the binding energy of 8Be is given, based upon the separation of the eight nucleons into two groups of four, using Gaussian functions and a Yukawa central force. The calculation is considerably simplified by the use of an integral identity between the Gaussian potential and the Yukawa potential. The energy is calculated with a Gaussian potential, and the identity used to convert the result to that which would have been obtained by direct use of the Yukawa potential. The results of the variational calculation show that unless the saturation conditions usually adopted in the theory of heavy nuclei are abandoned, there can be no binding, confirming an earlier result of Margenau, obtained with a Gaussian potential. The results do not depend essentially on the range of the force, nor on the central two-body type of force adopted. When the old saturation conditions are abandoned, quite reasonable results are obtained. The magnitude of the energies due to the exchange of single particles and pairs of particles indicates that the force between alpha-particles is not additive. A discussion of the saturation conditions and of the alpha-particle model in the light of the results is given.
On the second-order correction terms to values of gravity measured at sea
Authors: Worsley Beatrice H.
Published: November 2008

The motion of a pendulum on a periodically accelerated support has been studied by means of an electronic computing machine. The results have been applied to the problem of calculating the second-order correction to measurements of gravity made at sea with the Vening Meinesz three-pendulum apparatus. It is found that the correction for a single horizontal acceleration under typical conditions is likely to be more than twice that found analytically by Browne. His correction for vertical acceleration is valid for a wide range of frequency of the disturbing motion.
Classification of certain 6-manifolds
Authors: Jupp P. E.
Published: November 2008

In (13) Wall classified up to diffeomorphism, PL-homeomorphism, topological homeomorphism, and homotopy equivalence all closed, oriented, 1-connected smooth (or PL) 6-manifolds with torsion-free homology and vanishing second Stiefel-Whitney class. This paper extends these classifications to all closed, oriented, 1-connected topological 6-manifolds with torsion-free homology. The method differs from that of (13) but uses two special cases of Wall's classification.
Products of flows
Authors: Arrowsmith D. K.
Published: November 2008

The aim of the paper is to exhibit the structure of products of flows that are suspensions of diffeomorphisms and show their relationship with suspensions of product diffeomorphisms.

The problem is important for applications of the following type. Suppose we have two dynamical systems each with a stable attractor. If the systems are brought into contact, as, for example, in the way a forced oscillation is imposed upon a natural oscillation in synchronization theory, then this is represented by taking the product flow to find the resulting behaviour of the joint system. However, the product of two stable attractors is no longer stable in general, and therefore it is important to analyse why, in order to understand what new stable attractors can arise from perturbations.
On summability domains
Authors: Kalton N. J.
Published: November 2008

We denote by ω the space of all complex sequences with the topology given by the semi-norms

where δn(x) = xn. An FK-space, E, is a subspace of ω on which there exists a complete metrizable locally convex topology τ, such that the inclusion (E, τ) ⊂ ω is continuous; if τ is given by a single norm then E is a BK-space.
Capillary-gravity waves over a sloping beach
Authors: Allwood D. A.
Published: November 2008

It is shown how the solution for the velocity potential may be determined when the effect of surface tension is included in the linearized theory of surface waves over a sloping beach. In particular, two independent standing wave solutions are found, both of which have finite amplitude at the shoreline. The results agree with those of previous writers when the surface tension force tends to zero.
A Note on the Surface Temperature of Sliding Metals
Authors: Bowden F. P. , Ridler K. E. W.
Published: November 2008

If a simple calculation is made of the amount of heat liberated when one body is slid over another, and of the possible rate of escape of the heat by conduction and emission, it shows that the temperature of the surface may reach a high value.
Two-Dimensional Potential Problems
Authors: Morris Rosa M.
Published: November 2008

The solution of problems in two-dimensional potential theory depends, generally speaking, on the discovery of a conformal transformation suitable for the particular region involved, and the degree of success in the applicability of the method seems to be seriously limited by the complexity of the transformation. Only one serious attempt seems to have been made, by W. G. Bickley*, to formulate a general theory coordinating the different types of boundary value problem for general and inclusive classes of curves, but Bickley's analysis is somewhat involved and not very suitable for certain types of problem. In a re-examination of the subject on the basis of certain suggestions made to me by Prof. Livens, I have discovered what appears to be a much simpler and equally general method of formulating directly the solution for a comprehensive class of problem dealing with simple closed cylinders with curved or rectilinear boundaries, and including all those cases for which solutions are known. In its theoretical aspects the method seems to be perfectly general, but to put it into practice it is necessary to determine explicitly the particular form for the conformal transformation of the space outside the cross-section of the cylinder to the space outside a circle with the points at infinity coinciding.
A partial evaluator for the untyped lambda-calculus
Authors: Gomard Carsten K. , Jones Neil D.
Published: November 2008

This article describes theoretical and practical aspects of an implemented self-applicable partial evaluator for the untyped lambda-calculus with constants and a fixed point operator. To the best of our knowledge, it is the first partial evaluator that is simultaneously higher-order, non-trivial, and self-applicable.

Partial evaluation produces aresidual programfrom a source program and some of its input data. When given the remaining input data the residual program yields the same result that the source program would when given all its input data. Our partial evaluator produces a residual lambda-expression given a source lambda-expression and the values of some of its free variables. By self-application, the partial evaluator can be used to compile and to generate stand-alone compilers from a denotational or interpretive specification of a programming language.

An essential component in our self-applicable partial evaluator is the use of explicitbinding time information.We use this to annotate the source program, marking asresidualthe parts for which residual code is to be generated and marking aseliminablethe parts that can be evaluated using only the data that is known during partial evaluation. We give a simple criterion,well-annotatedness,that can be used to check that the partial evaluator can handle the annotated higher-order programs without committing errors.

Our partial evaluator is simple, is implemented in a side-effect free subset of Scheme, and has been used to compile and to generate compilers and a compiler generator. In this article we examine two machine-generated compilers and find that their structures are surprisingly natural.
Fixed points and frontiers: a new perspective
Authors: Hunt Sebastian , Hankin Chris
Published: November 2008

Abstract interpretation is the collective name for a family of semantics-based techniques for compile-time analysis of programs. One of the most costly operations in automating such analyses is the computation of fixed points. The frontiers algorithm is an elegant method, invented by Chris Clack and Simon Peyton Jones, which addresses this issue.

In this article we present a new approach to the frontiers algorithm based on the insight that frontiers represent upper and lower subsets of a function's argument domain. This insight leads to a new formulation of the frontiers algorithm for higher-order functions, which is considerably more concise than previous versions.

We go on to argue that for many functions, especially in the higher-order case, finding fixed points is an intractable problem unless the sizes of the abstract domains are reduced. We show how the semantic machinery of abstract interpretation allows us to place upper and lower bounds on the values of fixed points in large lattices by working within smaller ones.
Equivalence in functional languages with effects
Authors: Mason Ian , Talcott Carolyn
Published: November 2008

Traditionally the view has been that direct expression of control and store mechanisms and clear mathematical semantics are incompatible requirements. This paper shows that adding objects with memory to the call-by-value lambda calculus results in a language with a rich equational theory, satisfying many of the usual laws. Combined with other recent work, this provides evidence that expressive, mathematically clean programming languages are indeed possible.
Theoretical PearlsEnumerators of lambda terms are reducing
Authors: Barendregt Henk
Published: November 2008

A closed λ-termEis called anenumeratorif

Here ⋀0is the set of closed λ-terms,. is the set of natural numbers and the ⌜n⌝ are the Church's numerals λfx.fnx. Such anEis calledreducingif, moreover

An ingenious recursion theoretic proof by Statman will be presented, showing that every enumerator is reducing. I do not know any direct proof.
A domain-theoretic approach to functional and logic programming
Authors: Silbermann Frank S. K. , Jayaraman Bharat
Published: November 2008

The integration of functional and logic programming languages has been a topic of great interest in the last decade. Many proposals have been made, yet none is completely satisfactory especially in the context of higher order functions and lazy evaluation. This paper addresses these shortcomings via a new approach: domain theory as a common basis for functional and logic programming. Our integrated language remains essentially within the functional paradigm. The logic programming capability is provided by set abstraction (via Zermelo-Frankel set notation), using the Herbrand universe as a set abstraction generator, but for efficiency reasons our proposed evaluation procedure treats this generator's enumeration parameter as a logical variable. The language is defined in terms of (computable) domain-theoretic constructions and primitives, using the lower (or angelic) powerdomain to model the set abstraction facility. The result is a simple, elegant and purely declarative language that successfully combines the most important features of both pure functional programming and pure Horn logic programming. Referential transparency with respect to the underlying mathematical model is maintained throughout. An implicitly correct operational semantics is obtained by direct execution of the denotational semantic definition, modified suitably to permit logical variables whenever the Herbrand universe is being generated within a set abstraction. Completeness of the operational semantics requires a form of parallel evaluation, rather than the more familiar left-most rule.
Functional Pearls A symmetric set of efficient list operations
Authors: Hoogerwoord Rob R.
Published: November 2008

In this paper we show that it is possible to implement a symmetric set of finite-list operations efficiently; the set is symmetric in the sense that lists can be manipulated at either end. We derive the definitions of these operations from their specifications by calculation. The operations have O(1) time complexity, provided that we content ourselves with, so-called, amortized efficiency, instead of worst-case efficiency
Teaching functional programming to first-year students
Authors: Joosten Stef , Van Den Berg Klaas , Van Der Hoeven Gerrit
Published: November 2008

In the period 1986–1991, experiments have been carried out with an introductory course in computer programming, based on functional programming. Due to thorough educational design and evaluation, a successful course has been developed. This has led to a revision of the computer programming education in the first year of the computer science curriculum at the University of Twente.

This article describes the approach, the aim of the computer programming course, the outline and subject matter of the course, and the evaluation. Educational research has been done to assess the quality of the course.
Heap profiling of lazy functional programs
Authors: Runciman Colin , Wakeling David
Published: November 2008

We describe the design, implementation and use of a new kind of profiling tool that yields valuable information about the memory use of lazy functional programs. The tool has two parts: a modified functional language implementation which generates profiling information during the execution of programs, and a separate program which converts this information to graphical form. With the aid of profile graphs, one can make alterations to a functional program which dramatically reduce its space consumption. We demonstrate this in the case of a genuine example - the first to which the tool was applied - for which the results are strikingly successful.
Deciding type isomorphisms in a type-assignment framework
Authors: Di Cosmo Roberto
Published: November 2008

This paper provides a formal treatment of isomorphic types for languages equipped with an ML style polymorphic type inference mechanism. The results obtained make less justified the commonplace feeling that (the core of) ML is a subset of second order λ-calculus: we can provide an isomorphism of types that holds in the core ML language, but not in second order λ-calculus. This new isomorphism allows to provide a complete (and decidable) axiomatization of all the types isomorphic in ML style languages, a relevant issue for thetype as specificationsparadigm in library searches. This work is a very extended version of Di Cosmo (1992): we provide both a thorough theoretical treatment of the topic and describe a practical implementation of a library search system so that the paper can be used as a reference both by those interested in the formal theory of ML style languages, and by those simply concerned with implementation issues. The new isomorphism can also be used to extend the usual ML type-inference algorithm, as suggested by Di Cosmo (1992). Building on that proposal, we introduce a better type-inference algorithm that behaves well in the presence of non-functional primitives like references and exceptions. The algorithm described here has been implemented easily as a variation to the Caml-Light 0.4 system.
On the equivalence between CMC and TIM
Authors: Lins Rafael D. , Thompson Simon J. , Jones Simon Peyton
Published: November 2008

In this paper we present an equivalence between TIM, a machine developed to implement non-strict functional programming languages, and the set of Categorical Multi-Combinators, a rewriting system developed with similar aims. These two models of computation at first appear to be quite different, but we show a direct equivalence between them, thereby adding some new structure to the ‘design-space’ of abstract machines for non-strict languages.
Total unfolding: theory and applications
Authors: Lisper Björn
Published: November 2008

Unfolding is a common technique in program transformations. Here, we present a computation model where unfolding is a simple generalisation of the usual concept of evaluation. The model is a variant of the well-known full substitution evaluation rule for recursive programs. The evaluation mechanism involved is symbolic substitution of function definitions followed by simplification. Simplification is expressed as a confluent rewrite strategy which uses three kinds of reductions: β-reduction, non-erasing reduction, and erasing reduction. Non-erasing reductions include simplification of constant subexpressions. Erasing reductions formalize the behaviour of nonstrict operations. In this computation model, we prove a termination theorem of symbolic unfolding relative to more instantiated calls. A possible application of the model is a technique called total unfolding, where a partially instantiated function call is unfolded until no more calls exist. Under certain conditions the result will be a first order term: such terms correspond to basic blocks in imperative programs and can be efficiently implemented by scheduling techniques. Possible applications are hardware synthesis, and code generation for parallel machines.
Generic functional programming with types and relations
Authors: Bird Richard , De Moor Oege , Hoogendijk Paul
Published: November 2008

Agenericfunctional program is one which is parameterised by datatype. By installing specific choices, for example lists or trees, different programs are obtained that are, nevertheless, abstractly the same. The purpose of this paper is to explore the possibility of deriving generic programs. Part of the theory of lists that deals with segments is recast as a theory about ‘segments’ in a wide class of datatypes, and then used to pose and solve a generic version of a well-known problem.
Sparse matrix representations in a functional language
Authors: Grant P. W. , Sharp J. A. , Webster M. F. , Zhang X.
Published: November 2008

This paper investigates several sparse matrix representation schemes and associated algorithms in Haskell for solving linear systems of equations arising from solving realistic computational fluid dynamics problems using a finite element algorithm. This work complements that of Wainwright and Sexton (1992) in that a Choleski direct solver (with an emphasis on its forward/backward substitution steps) is examined. Experimental evidence comparing time and space efficiency of these matrix representation schemes is reported, together with associated forward/backward substitution implementations. Our results are in general agreement with Wainwright and Sexton's.
Functional Pearl
Authors: Hutton Graham , Meijer Erik
Published: November 2008

A representation changer is a function that converts a concrete representation of an abstract value into a different concrete representation of that value. Many useful functions can be recognised as representation changers; examples include compilers and arithmetic functions such as addition and multiplication. Functions that can be specified as the right inverse of other functions are special cases of representation changers. In recent years, a number of authors have used a relational calculus to derive representation changers from their specifications. In this paper, we show that the generality of relations is not essential, and representation changers can be derived within the more basic setting of functional programming. We illustrate our point by deriving a carry-save adder and a base-converter, two functions which have previously been derived relationally.
Symplectic integrators for Hamiltonian problems: an overview
Authors: Sanz-Serna J. M.
Published: November 2008

In the sciences, situations where dissipation is not significant may invariably be modelled by Hamiltonian systems of ordinary, or partial, differential equations. Symplectic integrators are numerical methods specifically aimed at advancing in time the solution of Hamiltonian systems. Roughly speaking, ‘symplecticness’ is a characteristic property possessed by the solutions of Hamiltonian problems. A numerical method is called symplectic if, when applied to Hamiltonian problems, it generates numerical solutions which inherit the property of symplecticness.
Entwicklung des phonologischen Arbeitsgedächtnisses
Authors: Grube Dietmar , Lingen Michael , Hasselhorn Marcus
Published: November 2008

Zusammenfassung. Die vorliegende Untersuchung zur Entwicklung des Effekts der phonologischen Ähnlichkeit gibt Aufschluss über die Abhängigkeit des Ähnlichkeitseffekts von Rehearsal und Lexikalität. Fünf- und neunjährige Kinder reproduzierten Serien von klangähnlichen und klangunähnlichen Wörtern bzw. Kunstwörtern unter Standardbedingungen und unter der Bedingung artikulatorischer Unterdrückung. Der Ähnlichkeitseffekt auf die Gedächtnisspanne zeigte sich in beiden Altersgruppen gleichermaßen ausgeprägt und reduzierte sich nicht unter der Bedingung artikulatorischer Unterdrückung. Der Ähnlichkeitseffekt fiel für Kunstwörter größer aus als für Wörter. Die Befunde deuten darauf hin, dass der phonologische Ähnlichkeitseffekt nicht auf die Nutzung von Rehearsal, sondern auf Verwechslungen bei der Rekonstruktion zerfallender Spuren im Arbeitsgedächtnis zurückgeht.
Characterization of traverse slippage experienced by Spirit rover on Husband Hill at Gusev crater
Authors: Li Rongxing , Wu Bo , Di Kaichang , Angelova Anelia , Arvidson Raymond E. , Lee I‐Chieh , Maimone Mark , Matthies Larry H. , Richer Lutz , Sullivan Robert , Sims Michael H. , Greenberger Rebecca , Squyres Steven W.
Published: November 2008

Spirit rover experienced significant slips traversing Husband Hill. This paper analyzes the slippage Spirit experienced from Sol 154 to Sol 737. Slippage with respect to terrain type and slope is computed using data downlinked from the rover, rover position, and orientation estimations from visual odometry (VO) and photogrammetry based bundle adjustment (BA) method. Accumulated slippage reached a maximum of 83.86 m on Sol 648. However, as Spirit descended into the Inner Basin, the direction of slippage reversed, and accumulated slippage approached zero by the end of the entire traverse. Eight local regions with significant slips and nineteen traverse segments have been analyzed. Slippage was found to be highly correlated to slope direction and magnitude; the reverse of slope directions in the ascending and descending portions of the traverse proves to be the main contributor to the observed cancellation of slippage. While the horizontal component of the slippage almost canceled out, the difference in elevation continually accumulated, mainly during the ascent. In general, long traverse segments created more slips than short ones. This is reflected in both the accumulated and individual slippages. In considering the four major Mars terrain types, Spirit performed best on bedrock, managing to drive on slopes close to 30°. Fine‐grain surfaces were the most challenging; though progress was made on slopes up to 15°, slippages of over 100% (more slippage than distance traveled) occurred for short segments. The results of this work can be incorporate into a traverse planning framework in which rover slippage is minimized. Results can be employed in landed planetary missions for precision navigation to avoid potentially dangerous regions by considering expected slippage.
Ultraschallgezielte perkutane Punktion und Drainage eines Milzabszesses durch Salmonella heidelberg bei einem Kind
Authors: Handrick W. , Brettschneider D. , Hörmann D. , Scholbach Th.
Published: November 2008

Bei einem 9 11/12 Jahre alten Knaben traten im Anschluß an eine Salmonella-Enteritis Schmerzen im linken Oberbauch auf. Mittels Sonographie wurde die Diagnose Milzabszeß gestellt. Nach ultraschallgezielter Punktion und Drainage sowie entsprechender Chemotherapie kam es zu einer deutlichen Besserung des klinischen Bildes und schließlich zur komplikationslosen Heilung. An Hand einer Literaturübersicht wird auf die Problematik von Milzabszessen und auf die Möglichkeit einer perkutanen Punktionsbehandlung hingewiesen. Bei jeder Erkrankung, die mit Fieber und unklaren Bauchschmerzen einhergeht, sollte man auch an den Milzabszeß denken!
Anomalous transport in a one-dimensional Lorentz gas model
Authors: Eule S. , Friedrich R. , Jenko F.
Published: November 2008

Employing the generalized master equation proposed in [R. Friedrich et al., Phys. Rev. Lett. 96, 230601 (2006)], we derive a kinetic equation for a random kick model. For a particular choice of the time evolution kernel, a fractional master equation is obtained, which can be related to a Lévy walk. In one dimension, we use this model to describe a stochastic Lorentz gas with an annealed disorder. Exact moment relations are obtained in Laplace space, and the long-time behavior of the moments is discussed. The results are compared to those of related models.
The polarization anisotropy of vibrational quantum beats in resonant pump-probe experiments: Diagrammatic calculations for square symmetric molecules
Authors: Farrow Darcie A. , Smith Eric R. , Qian Wei , Jonas David M.
Published: November 2008

By analogy to the Raman depolarization ratio, vibrational quantum beats in pump-probe experiments depend on the relative pump and probe laser beam polarizations in a way that reflects vibrational symmetry. The polarization signatures differ from those in spontaneous Raman scattering because the order of field-matter interactions is different. Since pump-probe experiments are sensitive to vibrations on excited electronic states, the polarization anisotropy of vibrational quantum beats can also reflect electronic relaxation processes. Diagrammatic treatments, which expand use of the symmetry of the two-photon tensor to treat signal pathways with vibrational and vibronic coherences, are applied to find the polarization anisotropy of vibrational and vibronic quantum beats in pump-probe experiments for different stages of electronic relaxation in square symmetric molecules. Asymmetric vibrational quantum beats can be distinguished from asymmetric vibronic quantum beats by a π phase jump near the center of the electronic spectrum and their disappearance in the impulsive limit. Beyond identification of vibrational symmetry, the vibrational quantum beat anisotropy can be used to determine if components of a doubly degenerate electronic state are unrelaxed, dephased, population exchanged, or completely equilibrated.
The study of surface segregation of Re3Pt polycrystalline alloy with photoelectron spectroscopy
Authors: Mun Bongjin S. , Rossi Massimiliano , Ross Philip N.
Published: November 2008

The surface segregation and electronic structure of Re3Pt polycrystalline alloy were investigated via x-ray photoelectron spectroscopy (XPS). The results from angle-resolved core-level XPS show the enrichment of Pt at the top surface layer upon annealing at T=1200K. The experimental results show excellent agreement with a theoretical model calculation, providing the element-specific depth profiles upon the high temperature annealing process. The presence of strong electron hybridization between Re and Pt is evident in the valence-band density-of-states ultraviolet photoemission spectra.
Classification of irreducible weight modules over W-algebra W(2,2)
Authors: Liu Dong , Gao Shoulan , Zhu Linsheng
Published: November 2008

In this paper, we show that the support of an irreducible weight module over the W-algebra W(2,2), which has an infinite dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the W-algebra W(2,2), having a nontrivial finite dimensional weight space, is a Harish–Chandra module (and hence is either an irreducible highest or a lowest weight module or an irreducible module of the intermediate series).
Doppler spectroscopy of hydrogen Balmer lines in a hollow cathode glow discharge in ammonia and argon-ammonia mixture
Authors: Šišović N. M. , Konjević N.
Published: November 2008

The results of Doppler spectroscopy of hydrogen Balmer lines from a stainless steel (SS) and copper (Cu) hollow cathode (HC) glow discharge in ammonia and argon-ammonia mixture are reported. The experimental profiles in ammonia discharge are fitted well by superposing three Gaussian profiles. The half widths, in energy units, of narrow and medium Gaussians are in the ranges 0.3–0.4eV and 3–4eV, respectively, for both hollow cathodes what is expected on the basis of earlier electron beam→NH3 experiments. The half widths of the largest Gaussian in ammonia are 46 and 55eV for SS and Cu HC, respectively. In argon-ammonia discharge, three Gaussians are also required to fit experimental profiles. While half widths of narrow and medium Gaussians are similar to those in ammonia, the half widths of the largest Gaussians are 35 and 42eV for SS and Cu HC, respectively. The half widths of the largest Gaussians in ammonia and in argon-ammonia mixture indicate the presence of excessive Doppler broadening.
Nonmagnetic high pressure cell for magnetic remanence measurements up to 1.5 GPa in a superconducting quantum interference device magnetometer
Authors: Sadykov Ravil A. , Bezaeva Natalia S. , Kharkovskiy Alexander I. , Rochette Pierre , Gattacceca Jérôme , Trukhin Vladimir I.
Published: November 2008

We describe here a compact nonmagnetic composite high pressure cell of piston-cylinder type with inner diameter of 6 mm equipped with manganin pressure sensor. This cell was developed for room temperature measurements of magnetic remanence of relatively large rock samples (up to 5.8 mm in diameter and 15 mm long cylinders) under hydrostatic pressure up to 1.5 GPa (the operating pressure limit) in the 2G Enterprises superconducting quantum interference device magnetometer. Its design was focused on minimizing the remanent magnetic moment mr of the cell (mr=3×10−8 A m2) that allowed direct measurements of remanent magnetic moment Mr under pressure for weakly magnetic materials-rock samples (Mr∊[5×10−7,10−4] A m2). The inner part of this composite cell is made of hard “Russian alloy” (Ni57Cr40Al3) whereas the envelope of the cell corps is made of less magnetic titanium alloy. This design solution permitted to reduce the total remanent magnetic moment of the whole cell and represents the main device feature. We describe here the choice of materials for pressure cell based on their magnetic and mechanical properties, the choice of the pressure transmitting medium (polyethilsiloxane liquid) providing perfectly hydrostatic conditions for the sample as well as the cell geometry. The cell performance is illustrated by results of pressure demagnetization experiments on rocks and minerals.
Observation of molecular hyperfine structure in the extreme ultraviolet: The HF C-X spectrum
Authors: Philippson Jeffrey N. , Shiell Ralph C. , Reinhold Elmar , Ubachs Wim
Published: November 2008

Clearly resolved hyperfine structure has been observed in the extreme ultraviolet (XUV) spectra of the C Π1, v=0−X Σ1+, v=0 transition of HF19 obtained through 1 XUV+1 UV resonance enhanced multiphoton ionization spectroscopy. The hyperfine splitting within the R-branch lines shows significant perturbations, which we attribute to mixing with the rotational levels of the nearby v=29 level of the B Σ1+ ion-pair state. A deperturbation analysis quantitatively explains the apparent variation of the fluorine magnetic hyperfine parameter aF, for which a value of 4034(83) MHz was obtained by averaging over the values derived from the R(0)–R(4) lines, after correcting for the effects of the perturbations.
On states of perfect correlation
Authors: Huang Siendong
Published: November 2008

For finite-dimensional systems, states satisfying perfect correlation are just maximally entangled states that play an essential role in quantum information theory. Thus perfect correlation may be a key to entanglement phenomena. For general systems, Einstein–Podolsky–Rosen type states are characterized by perfect correlation and their properties are discussed. Conditions equivalent to perfect correlation are found. As an application of perfect correlation, all Einstein–Podolsky–Rosen type states on a two-particle system are given. Unlike in finite-dimensional systems, they are generally not quasiequivalent.