bluuebunny/crossref_metadata_2025 huggingface dataset:
Properties (V) and (w V) on C(Ω X)
Authors: Bator Elizabeth M. , Lewis Paul W.
Published: November 2008

A formal series Σxn in a Banach space X is said to be weakly unconditionally converging, or alternatively weakly unconditionally Cauchy (wuc) if Σ|x*(xn)| < ∞ for every continuous linear functional x* ∈ X*. A subset K of X* is called a V-subset of X* if

for each wuc series Σxn in X. Further, the Banach space X is said to have property (V) if the V-subsets of X* coincide with the relatively weakly compact subsets of X*. In a fundamental paper in 1962, Pelczynski [10] showed that the Banach space X has property (V) if and only if every unconditionally converging operator with domain X is weakly compact. In this same paper, Pelczynski also showed that all C(Ω) spaces have property (V), and asked if the abstract continuous function space C(Ω, X) has property (F) whenever X has property (F).
Applications of the Birkhoff–Hopf theorem to the spectral theory of positive linear operators
Authors: Eveson Simon P. , Nussbaum Roger D.
Published: November 2008

This paper may be regarded as a sequel to our earlier paper [19], where we give an elementary and self-contained proof of a very general form of the Hopf theorem on order-preserving linear operators in partially ordered vector spaces (reproduced here as Theorem 1·1).

Versions of this theorem and related ideas have been used by various authors to study both linear and nonlinear integral equations (Thompson [41], Bushell [9, 11], Potter [38, 39], Eveson [16, 17], Bushell and Okrasiriski [12, 13]); the convergence properties of nonlinear maps (Nussbaum [32, 33]); so-called DAD theorems (Borwein, Lewis and Nussbaum [8]) and in the proof of weak ergodic theorems (Fujimoto and Krause [20], Nussbaum [34]).
Equivariant homology
Authors: Austin David M. , Braam Peter J.
Published: November 2008

This paper studies the homology of the homotopy quotient of a G-manifold. We start by formulating a complex based on differential forms to compute this homology. This leads to a topological version of integration formulas over fibred products of G-manifolds. In particular the TQFT formulas studied by Witten and Atiyah–Jeffrey now appear as a pairing of homology and cohomology classes. We compare our construction with both the double complex of Axelrod and Witten and with the distributional complex of Duflo and Vergne.
A rigidity theorem for Haken manifolds
Authors: Soma Teruhiko
Published: November 2008

A compact, orientable 3-manifoldMis calledhyperbolicif intMadmits a complete hyperbolic structure (Riemannian metric of constant curvature − 1) of finite volume. Any hyperbolic 3-manifoldMis irreducible, and each component of∂Mis an incompressible torus. Letf:M→Nbe a proper, continuous map between hyperbolic 3-manifolds. By Mostow's Rigidity Theorem [8], iffis π1-isomorphic thenfis properly homotopic to a diffeomorphismg:M→Nsuch thatg| intM: intM→ intNis isometric. In particular, the topological type of intMdetermines uniquely the hyperbolic structure on intMup to isometry, so the volume vol (intM) of intMis well-defined. This Rigidity Theorem is generalized by Thurston[11, theorem 6·4] so that any proper, continuous mapf:M→Nbetween hyperbolic 3-manifolds with vol(intM) = deg(f) vol(intN) is properly homotopic to a deg(f)-fold coveringg:M→Nsuch thatg| intM: intM→ intNis locally isometric.
Algebraic elements in matrix ring over division algebras
Authors: Lichtman A. I.
Published: November 2008

Let K be an arbitrary field, G a polycyclic-by-finite group and A a prime ideal of the group ring KG. It is well known that the quotient ring (KG)/A is a Goldie ring; we denote by R its ring of fractions. Let U be a subgroup of units of the matrix ring Rn×n let K[U] be the linear envelope of U and let rad (K[U]) be the nilpotent radical of K [U].
The universal multiplicity theory for analytic operator-valued functions
Authors: Arason Jón , Magnus Robert
Published: November 2008

An analytic operator-valued function A is an analytic map A: D → L(E, E), where D = D(A) is an open subset of the complex plane C and E = E(A) is a complex Banach space. For such a function A the singular set σ(A) of A is defined as the set of points z ∈ D such that A(z) is not invertible. It is a relatively closed subset of D.
Lines, circles, focal and symmetry sets
Authors: Bruce J. W.
Published: November 2008

Let X be a surface in Euclidean 3-space, hereafter denoted by ℝ3. In the paper [13] Montaldi considered the contact of the surface X with circles, and obtained some very attractive results. In this piece of work we want to address some more detailed questions concerning such contact. In keeping with a general theme within singularity theory we shall bundle the circles up into fibres of certain maps and consider the restriction of these mappings to our surface X. In other words we shall be interested in the simultaneous contact of the surface X with special families of circles. The particular families we shall consider are parameterized by the set K of all lines in ℝ3; associated to such a line we have the family of all circles lying in planes orthogonal to the line, and centred on the line. The line will be referred to as the axis of the circle. Suppose, for example, the line in question is given by x1 = x2 = 0. We can consider the map ℝ3 → ℝ2 given by . The fibres of this mapping are clearly the set of circles with the properties described above together, of course, with single points on the line itself. So the family of oriented lines parameterizes a family of mappings ℝ3 → ℝ2, and by restriction a family of mappings X → ℝ2. It is of interest to relate the singularities of this mapping to the differential geometry of X. The key geometric invariant of any smooth family is its bifurcation set, that is the set of parameter values for which the corresponding map fails to be stable. We shall see that for the family of circle maps the bifurcation set is of some interest.
Vassiliev invariants and the Hopf algebra of chord diagrams
Authors: Willerton Simon
Published: November 2008

This paper is closely related to Bar-Natan's work, and fills in some of the gaps in [1]. Following his analogy of the extension of knot invariants to knots with double points to the notion of multivariate calculus on polynomials, we introduce a new notation which facilitates the formulation of a Leibniz type formula for the product of two Vassiliev invariants. This leads us to see how Bar-Natan's co-product of chord diagrams corresponds to multiplication of Vassiliev invariants. We also include a proof that the multiplication in is a consequence of Bar-Natan's 4T relation.

The last part of this paper consists of a proof that the space of weight systems is a sub-Hopf algebra of the space *, by means of the canonical projection.
Differential invariants of ℝ*-structures
Authors: Valdés Antonio
Published: November 2008

A differential invariant of a G-structure is a function which depends on the r-jet of the G-structure and such that it is invariant under the natural action of the pseudogroup of diffeomorphisms of the base manifold. The importance of these objects is clear, since they seem to be the natural obstructions for the equivalence of G-structures. Hopefully, if all the differential invariants coincide over two r–jets of G-structure then they are equivalent under the action of the pseudogroup. If all the differential invariants coincide for every r it is hoped that the G-structures are formally equivalent, and so equivalent in the analytic case. This is the equivalence problem of E. Cartan. In this paper we deal with the problem of finding differential invariants on the bundles of ℝ*-structures, following the program pointed out in [3]. There are several reasons that justify the study of this type of G-structures. The first one is that it is a non-complicated example that helps to understand the G-structures with the property for the group G of having a vanishing first prolongation (i.e. of type 1). The simplicity comes from the fact that the algebraic invariants of ℝ* are very simple. The differential geometry of this type of structure, however, has much in common with general G-structures of type 1. Also, ℝ*-structures are objects of geometrical interest. They can be interpreted as ‘projective parallelisms’ of the base manifold and they can also be interpreted as a generalization of Blaschke's notion of a web.
On ground states for CCR algebras and Bogoliubov automorphism groups
Authors: Ogi Hidekazu
Published: November 2008

Let ACCR(L) be the CCR algebra over a Hubert space L, and let {σt}t∈R be a Bogoliubov automorphism group of ACCR(L) induced by a strongly continuous one-parameter unitary group on L. In this paper, we introduce some continuity for linear functionals on ACCR(L) and, under this continuity, we study existence, uniqueness, and non-uniqueness of ground states for {ACCR(L), {σt}t∈R}.
The geometry of open continuous mappings having two valences between Riemann surfaces
Authors: Lyzzaik Abdallah
Published: November 2008

An open continuous function from an open Riemann surface with finite genus and finite number of boundary components into a closed Riemann surface is termed a (p, q)-map, 0 < q < p, if it has a finite number of branch points and assumes every point in the image surface either p or q times, counting multiplicity, with possibly a finite number of exceptions.

The object of this paper is to prove that the geometry of any (p, q)-map resembles that of a (p, q)-map whose q-set (the set of image points of f that are taken on exactly q times, counting multiplicity), constitutes a finite set of Jordan arcs or curves (loops). This leads to interesting geometrie results regarding (p, q)-maps without exceptional points. Further, it yields that every (p, q)-map is homotopic to a simplicial (p, q)-map having the same covering properties.
m-full ideals II
Authors: Watanabe Junzo
Published: November 2008

In his paper 10 the author investigated the structure ofm-full ideals by analysing their syzygies and, as one special case, showed how the Betti numbers of Borel stable ideals over polynomial rings can be computed. The same result, among other things, was also obtained by Eliahou and Kervaire1 by a different method.
Involutory *-antiautomorphisms on On
Authors: Stacey P. J.
Published: November 2008

Let n ℕ{1} and let S1, , Sn be isometries on an infinite-dimensional Hilbert space such that for each i and . It was shown in 1 that the C*-algebra On generated by S1, , Sn is an infinite simple C*-algebra which is, up to isomorphism, independent of the choice of isometries satisfying the given relations. If is a unital *-endomorphism of On then, as shown in 2, is a unitary determining by the equations (Si) = w*Si and each unitary arises in this way.
Complemented copies of l1, in Lp(μ;E)
Authors: Mendoza José
Published: November 2008

Let E be a Banach space, let (Ω, Σ, μ) a finite measure space, let 1 < p < ∞ and let Lp(μ;E) the Banach space of all E-valued p-Bochner μ-integrable functions with its usual norm. In this note it is shown that E contains a complemented subspace isomorphic to l1 if (and only if) Lp(μ; E) does. An extension of this result is also given.
The ideal structure of some Banach algebras
Authors: Filali M.
Published: November 2008

Let G be a locally compact group and let Ĝ be its character group. Among other results, the minimal left ideals of L∞(G)* and LUC(G)* are all found when G is abelian. The main tool used for this study is the set of (topological) χ-invariant functionals (χ∈Ĝ), defined in this paper.
Spectral representation and scattering theory for the wave equation with two unbounded media
Authors: Roach G. F. , Zhang Bo
Published: November 2008

In this paper, we establish the generalized eigenfunction expansions for wave propagation in inhomogeneous, penetrable media in ℝn(n ≥ 2) with an unbounded interface. We then use them together with the method of stationary phase to prove the existence of the wave operators and to obtain the representations of the wave operators in terms of the generalized Fourier transforms.
Julia sets of rational functions are uniformly perfect
Authors: Hinkkanen A.
Published: November 2008

Letfbe a rational function of degree at least two. We shall prove that the Julia setJ(f) offis uniformly perfect. This means that there is a constantc∈(0, 1) depending onfonly such that wheneverz∈J(f) and 0 <r< diamJ(f) thenJ(f) intersects the annulus.
Safe numerical bounds for the Titchmarsh–Weyl m(λ)-function
Authors: Brown B. M. , Kirby V. G. , Evans W. D. , Plum M.
Published: November 2008

Recent efforts have been focused on using numerical methods to estimate the Titchmarsh–Weyl m-coefficient. In this paper we look at interval analytic methods to provide provable bounds for these values.
Real and virtual processes in quantum electrodynamics
Authors: Hamilton J.
Published: November 2008

The S-matrix formulation of quantum electrodynamics, as developed by Feynman (3) and Dyson (1), expresses the matrix element for any process as a power series in the coupling constant, the coefficients of the series being, in general, rather complicated multiple integrals. These integrals contain singularities in their integrands, and in certain circumstances the coincidence of such singularities gives the S-matrix a non-analytic behaviour as a function of, for example, the total energy. The threshold behaviour of the S-matrix in the neighbourhood of energy values at which this phenomenon occurs has been investigated by Eden (2), who shows that the non-analytic behaviour is connected with the possible commencement of new physical processes, such as the creation of a particle.
Maximum zero-dimensional compactifications
Authors: McCartney J. R.
Published: November 2008

All spaces considered in this paper are Hausdorff. θX is a compactification of a completely regular space X means that X is identified with a dense subspace of θX. We shall thus always regard X to be contained in θX. A compactification θX of X is zero-dimension (countable) if its ‘outgrowth” θX ~ X is zero-dimensional (countable).
A partition of non-synthesis for a quotient algebra of A(Z)
Authors: Salinger D. L.
Published: November 2008

Let A(Z) be the Banach algebra of Fourier-Lebesgue coefficients: a function f is an element of A(Z) if it is the Fourier transform

of some function fεL1(T), where T, as usual, denotes the circle group. We write
An application of distribution theory to Martin's method in potential scattering
Authors: Whipp A. T.
Published: November 2008

In order to study the convergence of a series arising from the use of Martin's method in potential scattering a framework consisting of a modifidation to Schwartz's formulation of distribution theory is set up. This modification makes essential use of norms on the spaces of test functions and linear functionals. By making the norm on the space of test functions satisfy extra axioms a bound is obtained on the norm of a generalized convolution of two linear functionals, and this bound is used to prove the convergence of the series. The proof of convergence is generalized to cover the multi-channel problem. The method used may also be applied to many other physical problems.
Stable homotopy types of stunted complex projective spaces
Authors: Feder S. , Gitler S.
Published: November 2008

Let CPn denote the complex projective space of complex dimension n. If k < n, CPk−1 is embedded as the (2k –1)-skeleton of CPn and we denote by , the stunted projective space, the quotient of CPn. by CPk−1.
Lefschetz formulae for modest vector bundles
Authors: Mayer K. H. , Schwarzenberger R. L. E.
Published: November 2008

A number of results are known which relate the characteristic numbers on a differentiable manifold X to the differentiable actions of the circle group S1on X. Many of these results are consequences of the Atiyah–Singer index theorem (2). In particular, an idea due to Hirzebruch sometimes permits one to deduce that certain characters which occur in the index theorem are in fact constant. Examples of this procedure can be found on page 594 of(2), on page 46 of(4), and on pages 21–22 of(1). Our aim in this paper is to make a systematic investigation of such results, and it is this aim which led us naturally to the concept of a modest vector bundle.
Bohr-Sommerfeld orbits and quantizable symplectic manifolds
Authors: Simms D. J.
Published: November 2008

The phase space of a finite dimensional classical Hamiltonian system is a C∞ differentiable manifold M which carries a C∞ differential 2-form ω which is closed, dω = 0, and non-singular in the sense that there is a bijective map α→ Xα from covariant vector fields to contravariant vector fields satisfying the identity

Such a pair (M, μ) is called a symplectic manifold.
On the elliptic ball stability criterion for ordinary differential equations
Authors: Smith Russell A.
Published: November 2008

It is proved that the elliptic ball criterion is a necessary condition on the matrix M(t) for the linear feedback control equation f(D)x + BM(t)g(D)x = 0 to have a special kind of quadratic Lyapunov function. That it is also a sufficient condition has already been proved elsewhere. These two facts lead to a comparison theorem which enables the existence of a quadratic Lyapunov function for one equation to be deduced from that for another equation.
An evaluation of a link polynomial
Authors: Lipson A. S.
Published: November 2008

There exists for each oriented link L in the 3-sphere a unique 2-variable Laurent polynomial defined uniquely by the following:

(i) PU = 1 for the unknot U

(ii) ,

where L+, L− and L0 are identical outside a ball and inside are as shown in Figure 1. See [1] and [2].
The Shot Effect for Showers
Authors: Whittaker J. M.
Published: November 2008

1. A well-known theorem on probability may be stated as follows. Let λdt be the chance that a certain event will happen in time dt, so that λT is the average number of occurrences of the event in an interval T. If we take a large number of repetitions of the interval T the actual numbers of occurrences will fluctuate about the mean λT, being say λT + x′, λT + x″,…. Then the theorem states that

The ejection of an α-particle by a radioactive substance is an event of the type contemplated and the theorem was applied to this physical problem by von Schweidler in 1905. Much similar work, both theoretical and experimental, has been done at intervals since then*.
Implementing the evaluation transformer model of reduction on parallel machines
Authors: Burn G. L.
Published: November 2008

The evaluation transformer model of reduction generalizes lazy evaluation in two ways: it can start the evaluation of expressions before their first use, and it can evaluate expressions further than weak head normal form. Moreover, the amount of evaluation required of an argument to a function may depend on the amount of evaluation required of the function application. It is a suitable candidate model for implementing lazy functional languages on parallel machines.

In this paper we explore the implementation of lazy functional languages on parallel machines, both shared and distributed memory architectures, using the evaluation transformer model of reduction. We will see that the same code can be produced for both styles of architecture, and the definition of the instruction set is virtually the same for each style. The essential difference is that a distributed memory architecture has one extra node type for non-local pointers, and instructions which involve the value of such nodes need their definitions extended to cover this new type of node.

To make our presentation accessible, we base our description on a variant of the well-known G-machine, an abstract machine for executing lazy functional programs.
Explicit substitutions
Authors: Abadi M. , Cardelli L. , Curien P.-L. , Lévy J.-J.
Published: November 2008

The λσ-calculus is a refinement of the λ-calculus where substitutions are manipulated explicitly. The λσ-calculus provides a setting for studying the theory of substitutions, with pleasant mathematical properties. It is also a useful bridge between the classical λ-calculus and concrete implementations.
Using transformations in the implementation of higher-order functions
Authors: Nielson Hanne Riis , Nielson Flemming
Published: November 2008

Traditional functional languages do not have an explicit distinction between binding times. It arises implicitly, however, as one typically instantiates a higher-order function with the arguments that are known, whereas the unknown arguments remain to be taken as parameters. The distinction between ‘known’ and ‘unknown’ is closely related to the distinction between binding times like ‘compile-time’ and ‘run-time’. This leads to the use of a combination of polymorphic type inference and binding time analysis for obtaining the required information about which arguments are known.

Following the current trend in the implementation of functional languages we then transform the run-time level of the program (not the compile-time level) into categorical combinators. At this stage we have a natural distinction between two kinds of program transformations: partial evaluation, which involves the compile-time level of our notation, and algebraic transformations (i.e., the application of algebraic laws), which involves the run-time level of our notation.

By reinterpreting the combinators in suitable ways we obtain specifications of abstract interpretations (or data flow analyses). In particular, the use of combinators makes it possible to use a general framework for specifying both forward and backward analyses. The results of these analyses will be used to enable program transformations that are not applicable under all circumstances.

Finally, the combinators can also be reinterpreted to specify code generation for various (abstract) machines. To improve the efficiency of the code generated, one may apply abstract interpretations to collect extra information for guiding the code generation. Peephole optimizations may be used to improve the code at the lowest level.
A categorical understanding of environment machines
Authors: Asperti Andrea
Published: November 2008

In the last two decades, category theory has become one of the main tools for the denotational investigation of programming languages. Taking advantage of the algebraic nature of the categorical semantics, and of the rewriting systems it suggests, it is possible to use these denotational descriptions as a base for research into more operational aspects of programming languages.

This approach proves to be particularly interesting in the study and the definition of environment machines for functional languages. The reason is that category theory offers a simple and uniform language for handling terms and environments (substitutions), and for studying their interaction (through application).

Several examples of known machines are discussed, among which the Categorical Abstract Machine of Cousineau et al. (1987) and Krivine's machine. Moreover, as an example of the power and fruitfulness of this approach, we define two original categorical machines. The first one is a variant of the CAM implementing a λ-calculus with both call-by-value and call-by-name as parameters passing modes. The second one is a variant of Krivine's machine performing complete reduction of λ-terms.
Distributed random number generation
Authors: Burton F. Warren , Page Rex L.
Published: November 2008

In a functional program, a simple random number generator may generate a lazy list of random numbers. This is fine when the random numbers are consumed sequentially at a single point in the program. However, things are more complicated in a program where random numbers are used at many locations, such as in a large simulation. The programmer should not need to worry about providing separate generators with a unique seed at each point where random numbers are used. At the same time, the programmer should not need to coordinate the use of a single stream of random numbers in many parts of the program, which can be particularly difficult with lazy evaluation or parallel processing.

We discuss several techniques for distributing random numbers to various parts of a program, and some methods of allowing different program components to evaluate random numbers locally. We then propose a new approach in which a random number sequence can be split at a random point to produce a pair of random number sequences that can be used independently at different points in the computation.

The approach can also be used in distributed procedural programs, where it is desirable to avoid dealing with a single source of random numbers. The approach has the added advantage of producing repeatable results, as might be needed in debugging, for example.
On the specialization of online program specializers
Authors: Ruf Erik , Weise Daniel
Published: November 2008

A common technique for improving the speed of program specialization is to specialize the program specializer itself on the program to be specialized, creating a custom program generator. Much research has been devoted to the problem of generating efficient program generators, which do not perform reductions at program generation time which could instead have been performed when the program generator was constructed. The conventional wisdom holds that only program specializers using binding-time approximations can be specialized into such efficient program generators. This paper argues that this is not the case, and demonstrates that the specialization of a nontrivial online program specializer similar to the original ‘naive MIX’ can indeed yield an efficient program generator. The key to our argument is that, while the use of binding-time information at program generator generation time is necessary for the construction of an efficient custom specializer, the use of explicit binding-time approximation techniques is not. This allows us to distinguish the problem at hand (i.e. the use of binding-time information during program generator generation) from particular solutions to that problem (i.e. offline specialization). We show that, given a careful choice of specializer data structures, and sufficiently powerful specialization techniques, binding-time information can be inferred and utilized without explicit approximations. This allows the construction of efficient, optimizing program generators from online program specializers.
Typing first-class continuations in ML
Authors: Harper Robert , Duba Bruce F. , Macqueen David
Published: November 2008

An extension of ML with continuation primitives similar to those found in Scheme is considered. A number of alternative type systems are discussed, and several programming examples are given. A continuation-based operational semantics is defined for a small, purely functional language, and the soundness of the Damas–Milner polymorphic type assignment system with respect to this semantics is proved. The full Damas–Milner type system is shown to be unsound in the presence of first-class continuations. Restrictions on polymorphism similar to those introduced in connection with reference types are shown to suffice for soundness.
An overview of the Flagship system
Authors: Keane John A.
Published: November 2008

The Flagship Project1 was a research collaboration between the University of Manchester, Imperial College London and International Computers Ltd. The project was unusual in that it aimed to produce a complete computing system based on a declarative programming style. Three areas of a declarative system were addressed: (1) programming languages and programming environments; (2) the machine architecture and computational models; and (3) the software environment. This overview paper discusses each of these areas, the intention being to present the project as a coherent whole.
How powerful are folding/unfolding transformations?
Authors: Zhu Hong
Published: November 2008

This paper discusses the transformation power of Burstall and Darlington's folding/unfolding system, i.e. what kind of programs can be derived from a given one. A necessary condition of derivability is proved. The notion of inherent complexity of recursive functions in introduced. A bound on efficiency gain by folding/unfolding transformations is obtained for all reasonable computation models. The well-known partial correctness and incompleteness of the system are corollaries of the result. Examples of underivability are given, e.g. binary searching cannot be derived from linear searching, merge sorting cannot be derived from insert sorting.
Simple type-theoretic foundations for object-oriented programming
Authors: Pierce Benjamin C. , Turner David N.
Published: November 2008

We develop a formal, type-theoretic account of the basic mechanisms of object-oriented programming: encapsulation, message passing, subtyping and inheritance. By modelling object encapsulation in terms of existential types instead of the recursive records used in other recent studies, we obtain a substantial simplification both in the model of objects and in the underlying typed λ-calculus.
Baby Modula-3 and a theory of objects
Authors: Abadi Martin
Published: November 2008

Baby Modula-3 is a small, functional, object-oriented programming language. It is intended as a vehicle for explaining the core of Modula-3 from a biased perspective: Baby Modula-3 includes the main features of Modula-3 related to objects, but not much else. To the theoretician, Baby Modula-3 provides a tractable, concrete example of an object-oriented language, and we use it to study the formal semantics of objects. Baby Modula-3 is defined with a structured operational semantics and with a set of static type rules. A denotational semantics guarantees the soundness of this definition.
Defining data structures via Böhm-out
Authors: Tronci Enrico
Published: November 2008

We show that any recursively enumerable subset of a data structure can be regarded as the solution set to a Böhm-out problem.
Strong normalisation for the linear term calculus
Authors: Benton P. N.
Published: November 2008

We prove a strong normalisation result for the linear term calculus of Benton, Bierman, Hyland and de Paiva. Rather than prove the result from first principles, we give a translation of linear terms into terms in the second-order polymorphic lambda calculus (λ2) which allows the result to be proved by appealing to the well-known strong normalisation property of λ2. An interesting feature of the translation is that it makes use of the λ2 coding of a coinductive datatype as the translation of the !-types (exponentials) of the linear calculus.
On-line and off-line partial evaluation: semantic specifications and correctness proofs
Authors: Consel Charles , Khoo Siau Cheng
Published: November 2008

This paper presents semantic specifications and correctness proofs for both on-line and offline partial evaluation of strict first-order functional programs. To do so, our strategy consists of defining acore semanticsas a basis for the specification of three non-standard evaluations: instrumented evaluation, on-line and off-line partial evaluation. We then use the technique oflogical relationsto prove the correctness of both on-line and off-line partial evaluation semantics.

The contributions of this work are as follows:

1. We provide auniform frameworkto defining and proving correct both on-line and off-line partial evaluation.

2. This work required a formal specification of on-line partial evaluation with polyvariant specialization. We define criteria for its correctness with respect to an instrumented standard semantics. As a by-product, on-line partial evaluation appears to be based on a fixpoint iteration process, just like binding-time analysis.

3. We show that binding-time analysis, the preprocessing phase of off-line partial evaluation, is anabstractionof on-line partial evaluation. Therefore, its correctness can be proved with respect to on-line partial evaluation, instead of with respect to the standard semantics, as is customarily done.

4. Based on the binding-time analysis, we formallyderivethe specialization semantics for off-line partial evaluation. This strategy ensures the correctness of the resulting semantics.
Communication lifting: fixed point computation for parallelism
Authors: Vree Willem G. , Hartel Pieter H.
Published: November 2008

Communication lifting is a program transformation that can be applied to a synchronous process network to restructure the network. This restructuring in theory improves sequential and parallel performance. The transformation has been formally specified and proved correct and it has been implemented as an automatic program transformation tool. This tool has been applied to a small set of programs consisting of synchronous process networks. For these networks communication lifting generates parallel programs that do not require locking. Measurements indicate performance gains in practice both with sequential and parallel evaluation. Communication lifting is a worthwhile optimization to be included in a compiler for a lazy functional language.
Refining reduction in the lambda calculus
Authors: Kamareddine Fairouz , Nederpelt Rob
Published: November 2008

We introduce a λ-calculus notation which enables us to detect in a term, more β-redexes than in the usual notation. On this basis, we define an extended β-reduction which is yet a subrelation of conversion. The Church Rosser property holds for this extended reduction. Moreover, we show that we can transform generalised redexes into usual ones by a process called ‘term reshuffling’.
Functional Pearls
Authors: Gibbons Jeremy
Published: November 2008

Thetree-drawing problemis to produce a ‘tidy’ mapping from elements of a tree to points in the plane. In this paper, we derive an efficient algorithm for producing tidy drawings of trees. The specification, the starting point for the derivations, consists of a collection of intuitively appealingcriteriasatisfied by tidy drawings. The derivation shows constructively that these criteria completely determine the drawing. Indeed, the criteria completely determine a simple but inefficient algorithm for drawing a tree, which can be transformed into an efficient algorithm using just standard techniques and a small number of inventive steps.

The algorithm consists of anupwards accumulationfollowed by adownwards accumulationon the tree, and is further evidence of the utility of these two higher-order tree operations.
A syntactic theory of type generativity and sharing
Authors: Leroy Xavier
Published: November 2008

This paper presents a purely syntactic account of type generativity and sharing – two key mechanisms in the SML module system – and shows its equivalence with the traditional stamp-based description of these mechanisms. This syntactic description recasts the SML module system in a more abstract, type-theoretic framework.
A positive supercompiler
Authors: Sørensen M. H. , Glück R. , Jones N. D.
Published: November 2008

We introduce apositive supercompiler, a version of Turchin's supercompiler maintaining only positive information during transformation, and using folding without generalization. The positive supercompiler can also be regarded as a variant of Wadler's deforestation maintaining an increased amount of information. We compare our algorithm to deforestation and, in less detail, to partial evaluation, Turchin's supercompiler, Generalized Partial Computation (GPC), and partial deduction by classifying these transformers by the amount of information they maintain during transformation. This factor is significant, as a differentiating example reveals: positive supercompilation, Turchin's supercompiler, GPC and partial deduction can specialize a general pattern matcher with respect to a fixed pattern to obtain an efficient matcher very similar to the Knuth–Morris–Pratt algorithm. Deforestation and traditional partial evaluation achieve this effect only after a non-trivial hand rewriting of the general matcher.
Theory of algorithms for unconstrained optimization
Authors: Nocedal Jorge
Published: November 2008

A few months ago, while preparing a lecture to an audience that included engineers and numerical analysts, I asked myself the question: from the point of view of a user of nonlinear optimization routines, how interesting and practical is the body of theoretical analysis developed in this field? To make the question a bit more precise, I decided to select the best optimization methods known to date – those methods that deserve to be in a subroutine library – and for each method ask: what do we know about the behaviour of this method, as implemented in practice? To make my task more tractable, I decided to consider only algorithms for unconstrained optimization.
Sequential Quadratic Programming
Authors: Boggs Paul T. , Tolle Jon W.
Published: November 2008

Since its popularization in the late 1970s, Sequential Quadratic Programming (SQP) has arguably become the most successful method for solving nonlinearly constrained optimization problems. As with most optimization methods, SQP is not a single algorithm, but rather a conceptual method from which numerous specific algorithms have evolved. Backed by a solid theoretical and computational foundation, both commercial and public-domain SQP algorithms have been developed and used to solve a remarkably large set of important practical problems. Recently large-scale versions have been devised and tested with promising results.
Constructing cubature formulae: the science behind the art
Authors: Cools Ronald
Published: November 2008

In this paper we present a general, theoretical foundation for the construction of cubature formulae to approximate multivariate integrals. The focus is on cubature formulae that are exact for certain vector spaces of polynomials. Our main quality criteria are the algebraic and trigonometric degrees. The constructions using ideal theory and invariant theory are outlined. The known lower bounds for the number of points are surveyed and characterizations of minimal cubature formulae are given. We include references to all known minimal cubature formulae. Finally, some methods to construct cubature formulae illustrate the previously introduced concepts and theorems.
Numerical solution of multivariate polynomial systems by homotopy continuation methods
Authors: Li T. Y.
Published: November 2008

LetP(x) = 0 be a system ofnpolynomial equations innunknowns. DenotingP= (p1,…,pn), we want to find all isolated solutions of

forx= (x1,…,xn). This problem is very common in many fields of science and engineering, such as formula construction, geometric intersection problems, inverse kinematics, power flow problems with PQ-specified bases, computation of equilibrium states,etc.Elimination theory-based methods, most notably the Buchberger algorithm (Buchberger 1985) for constructing Gröbner bases, are the classical approach to solving (1.1), but their reliance on symbolic manipulation makes those methods seem somewhat unsuitable for all but small problems.
Approximation theory of the MLP model in neural networks
Authors: Pinkus Allan
Published: November 2008

In this survey we discuss various approximation-theoretic problems that arise in the multilayer feedforward perceptron (MLP) model in neural networks. The MLP model is one of the more popular and practical of the many neural network models. Mathematically it is also one of the simpler models. Nonetheless the mathematics of this model is not well understood, and many of these problems are approximation-theoretic in character. Most of the research we will discuss is of very recent vintage. We will report on what has been done and on various unanswered questions. We will not be presenting practical (algorithmic) methods. We will, however, be exploring the capabilities and limitations of this model.
Psychological Assessment with the Rorschach and the MMPI-2 in a Forensic Psychiatric Hospital
Authors: Hildebrand Martin , de Ruiter Corine
Published: November 2008

In this article, the possibilities of forensic psychological assessment by means of several diagnostic methods (i.e., the MMPI-2 and the Rorschach Inkblot Method) are reviewed. A case example illustrates the serious personality pathology that is often present in forensic psychiatric patients. The basic premise of this case example is that the psychologist’s armamentarium of assessment techniques can be strengthened by using the MMPI-2 and the Rorschach together in a complimentary fashion, and these can be of value in evaluating progress (i.e., change in psychopathology) during long-term forensic psychiatric treatment. It is concluded that only the objective measurement of such change, using reliable and valid psychological tests, can increase our knowledge of the effectiveness of forensic psychiatric treatment
Clinical Use of New Video-Endoscopes (EVIS 100 and 200)
Authors: Niwa H. , Kawaguchi A. , Miyahara T. , Koyama H.
Published: November 2008

The authors report on their clinical experience with two new videoendoscopes developed in cooperation with Olympus Co. One of them is an instantaneous image method videoendoscope (EVIS 100), the other produces sequential images (EVIS 200). EVIS 100 is as compact as a fiberscope; EVIS 200 has the special advantages of electronic magification, the use of infrared rays and image display of hemoglobin concentration in the tissue. In clinical application in 245 patients examined with EVIS 100 and 30 cases with EVIS 200, both instruments were found to be satisfactory in terms of daily use; EVIS 200 could be applied in further endoscopic research. In our opinion videoendoscopes will replace conventional fiberscopes in the future.
Therapeutische, perkutane Punktion und Drainage postoperativer Raumforderungen unter permanenter Ultraschall- und Röntgensicht
Authors: Gerstner G. J. , Schramek P.
Published: November 2008

Im Gegensatz zur diagnostischen, ultraschallgezielten Aspirations-Feinnadelbiopsie, welche eine endgültige histologische oder zytologische Diagnose auch kleiner Raumforderungen gut- oder bösartiger Natur erlaubt, erfordert die therapeutische Punktion und Drainage postoperativer Raumforderungen im Abdomen oder Retroperitoneum (Hämatome, Serome, Lymphozelen oder Abszesse), 1.) das Aufdilatieren des Punktionskanales und 2.) die Möglichkeit einer Dauerabsaugung über mehrere Tage oder Wochen. Wir berichten über drei therapeutische Punktionen bei zwei Patientinnen mit retroperitonealen Lymphzysten nach Wertheimschen Radikaloperationen mit Lymphonodektomie und einem Patienten mit einem Abszeß in der Nephrektomie-Loge, bei welchen eine Technik zur Anwendung kam, wie sie bei der perkutanen Nephrostomie verwendet wird. Dabei wird in Lokalanästhesie unter ständiger sonographischer Kontrolle mit einer 1,3 mm starken, dreiteiligen Punktionsnadel (Fa. Angiomed) gezielt punktiert und nach Aspiration von Sekret ein 0,9-mm-Führungsdraht mit gebogener, weicher Spitze durch die Punktionsnadel in die Raumforderung plaziert und unter Kontrolle der Röntgendurchleuchtung bis auf Charr. 16 bzw. 20 mit einem teflonbeschichteten Fasziendilatator (Fa. Cook) aufbougiert. Sodann wird entweder ein Polyvinylkatheter mit 2 seitlichen Öffnungen (Fa. Cook) durch ein Nephrostomie-Wechselbesteck oder ein doppelläufiges Shirley-Drain gelegt und mit einer Hautnaht fixiert. Die Ableitung erfolgt in einem geschlossenen System. Die Drains fördern über ein bis zwei Wochen zwischen 50 und 200 ml Sekret/ Tag in abnehmender Menge. Die Patienten fieberten ab und waren damit geheilt. Der Vorteil unserer Methode besteht in der Vermeidung gefährlicher und schwieriger Zweitoperationen.
Familiärer partieller Pyruvatdehydrogenase-Mangel
Authors: Kohns U. , Havers W. , Andler W. , Fischer E. , Berger R.
Published: November 2008

In einer türkischen Familie wurde bei 2 lebenden Kindern ein Pyruvatdehydrogenasemangel und bei einem verstorbenen Kind eine Laktatazidose nachgewiesen. 2 weitere Kinder verstarben unter dem Bild einer therapieresistenten metabolischen Azidose ohne erkennbare Ursachen. Die Voraussetzungen zur Entstehung einer Laktatazidose werden am Beispiel des Pyruvatdehydrogenasemangel dargestellt. Das Ausmaß der verbliebenen Aktivität bei einem Pyruvatdehydrogenasemangel bestimmt die klinische Symptomatik und den Krankheitsverlauf, der durch zusätzliche Komplikationen und verschiedene Therapieversuche unterschiedlich beeinflußt werden kann.
Quantum dynamics of NH(aΔ1)+H reactions on the NH2 Ã A21 surface
Authors: Akpinar Sinan , Defazio Paolo , Gamallo Pablo , Petrongolo Carlo
Published: November 2008

We present the Born–Oppenheimer dynamics of the depletion reaction NH(aΔ1)+H′→N(D2)+H2 and of the exchange one NH(aΔ1)+H′→NH′(aΔ1)+H, using the real wavepacket and flux methods and an accurate NH2(Ã A21) surface. We report coupled-channel reaction probabilities, cross sections, and rate constants, taking into account Coriolis couplings. Because the surface is barrierless and strongly bound, probabilities have small centrifugal thresholds and present sharp and large resonances, associated with long-lived collision complexes. Large J’s enhance the high-energy reactivity and favor the exchange reaction, owing to the negative Coriolis couplings, and to K that inhibits depletion but not exchange. Coriolis couplings are important in the collision complexes, and the centrifugal sudden approximation thus gives large errors. Cross sections are large at the threshold and minimal at intermediate collision energies and increase moderately at larger energies. Exchange is preferred, and both reactions are inhibited by the NH rotational excitation. Finally, the present rate constants are in good agreement with previous experimental and semiclassical results.
Synchronization-based scalability of complex clustered networks
Authors: Ma Xiaojuan , Huang Liang , Lai Ying-Cheng , Wang Yan , Zheng Zhigang
Published: November 2008

Complex clustered networks arise in biological, social, physical, and technological systems, and the synchronous dynamics on such networks have attracted recent interests. Here we investigate system-size dependence of the synchronizability of these networks. Theoretical analysis and numerical computations reveal that, for a typical clustered network, as its size is increased, the synchronizability can be maintained or even enhanced but at the expense of deterioration of the clustered characteristics in the topology that distinguish this type of networks from other types of complex networks. An implication is that, for a large network in a realistic situation, if synchronization is important for its function, then most likely it will not have a clustered topology.
The rotation of ripple pattern and the shape of the collision cascade in ion sputtered thin metal films
Authors: Mishra P. , Ghose D.
Published: November 2008

The sputter ripple formation in polycrystalline metal thin films of Al, Co, Cu, and Ag has been studied by 16.7 keV Ar+ and O2+ ion bombardment as a function of angle of ion incidence. The experimental results show the existence of a critical angle of ion incidence (θc) beyond which the ripples of wave vectors perpendicular to the projected ion beam direction appear. Monte Carlo simulation (SRIM) is carried out to calculate the depth, longitudinal and lateral straggling widths of energy deposition as these values are crucial in determining the critical angle θc. It is found that the radial energy distribution of the damage cascade has the maximum slightly away from the ion path in contradiction to the Gaussian distribution and the distribution is better characterized by an exponential function. The lower values of lateral straggling widths as those extracted from the measured critical angles using the Bradley and Harper theory indicate a highly anisotropic deposited-energy distribution.