bluuebunny/crossref_metadata_2025 huggingface dataset:
Continuity of solutions of Schrödinger equations
Authors: Nakai Mitsuru
Published: November 2008

We denote by N(x, y) the Newtonian kernel on the d-dimensional Euclidean space (where d ≥ 2) so that N(x, y) = log|x–y|-1 for d = 2 and N(x, y) = |x−y|2−d for d ≥ 3. A signed Radon measure μ on an open subset Ω in d is said to be of Kato class if

for every y in Ω. where |μ| is the total variation measure of μ.
Torsion and periods in some groups of homeomorphisms of the circle
Authors: Greenberg P.
Published: November 2008

If g is an element of torsion of a group G, its order o(g) is the least positive integer such that go(g) = e. Let OG = {o(g);g ∈ G}. If G is a group of homeomorphisms of a space X, and if g ∈ G, x ∈ X let q(g, x) denote the cardinality of the g-orbit {gnx}n∈Z of x.
Generalized Eilenberg–Moore spectral sequences for elementary abelian groups and tori
Authors: Greenlees J. P. C.
Published: November 2008

In this note we prove universal coefficient theorems for Borel cohomology and related theories. Whatever other merit this may have the comment of Borel [5] applies ‘ …elle a au moms l'utilité de bien mettre en évidence le rôle fondamental joué dans cette question par la cohomologie des groupes’.

Indeed the purpose of the enterprise is to use homological properties of the group cohomology ring H*(BG+) to study properties of G-spaces. Because of the relative simplicity of ordinary cohomology much attention in the proofs and applications is concentrated on change of groups, and on changes in the way the group action is exploited. Nonetheless we are able to adapt the non-equivariant approach of Adams ([1, 2]; see also [3]). Thus the existence of universal coefficient theorems automatically gives Kiinneth theorems as special cases.
Discriminants of Casson–Gordon invariants
Authors: Gilmer Patrick , Livingston Charles
Published: November 2008

Casson–Gordon invariants were first used to prove that certain algebraically slice knots in S3 are not slice knots [2, 3]. Since then they have been applied to a wide range of problems, including embedding problems and questions relating to boundary links [2, 10, 21, 25]. The most general Casson–Gordon invariant takes its value in L0(ℚ(ζd)(t)) ⊗ ℚ; here ζd denotes a primitive dth root of unity. Litherland [20] observed that one could usually tensor with ℤ(2) instead of ℚ, and in this way preserve the 2-torsion in the Witt group. He then constructed new examples of non-slice genus two knots which were detected with torsion classes in L0(ℚ(ζd)) ⊗ ℤ(2) modulo the image of L0(ℚ(ζd)) ⊗ ℤ(2).
The limiting-amplitude principle for the wave propagation problem with two unbounded media
Authors: Roach G. F. , Zhang Bo
Published: November 2008

In this paper, we consider the diffraction problem for wave propagation in inhomogeneous, penetrable media with an unbounded interface. The low frequency behaviour of the resolvent for the reduced wave operator is studied, and the validity of the limiting-amplitude principle for such an operator is proved.
Properly algebraic and spectrum-finite ideals in Jordan systems
Authors: Loos Ottmar
Published: November 2008

The two main results of this paper are:

(i) The set of properly algebraic elements of a Jordan system (algebra, triple system or pair) over an uncountable field is an ideal.

(ii) For a semiprimitive Banach Jordan system, the socle, the largest properly algebraic ideal, the largest properly spectrum-finite ideal and the largest von Neumann regular ideal all coincide.
Minimal primal ideals in Banach algebras
Authors: Somerset Douglas W. B.
Published: November 2008

An ideal I in a ring R is primal if whenever J1, …, Jn is a finite set of ideals of R with J1 … Jn = {0} then Ji ⊆ I for at least one i ∈ {1, …, n}. If the ring is commutative then is is easily shown that each primal ideal contains a prime ideal. In this paper it is shown that in a separable semi-simple Banach algebra each primal ideal contains a prime ideal, and that the space of minimal prime ideals is compact and extremally disconnected in the hull-kernel topology. An example is given of an inseparable C-algebra with a primal ideal which does not contain a prime ideal.
Covering groups of non-connected topological groups revisited
Authors: Brown Ronald , Mucuk Osman
Published: November 2008

All spaces are assumed to be locally path connected and semi-locally 1-connected. Let X be a connected topological group with identity e, and let be the universal cover of the underlying space of X. It follows easily from classical properties of lifting maps to covering spaces that for any point ẽ in with pẽ = e there is a unique structure of topological group on such that ẽ is the identity and is a morphism of groups. We say that the structure of topological group on X lifts to .
The weak Banach-Saks property on Lp(μ, E)
Authors: Cembranos Pilar
Published: November 2008

A Banach space E is said to have the Banach-Saks property (BS) if every bounded sequence (xn) in E has a subsequence (x′n) with norm convergent Cesaro means; that is, there is x in E such that

If this occurs for every weakly convergent sequence in E it is said that E has the Weak Banach-Saks property (WBS) (also called Banach-Saks-Rosenthal property).
Kähler–Einstein metrics with SU(2) action
Authors: Dancer Andrew S. , Strachan Ian A. B.
Published: November 2008

The aim of this paper is to analyse Riemannian Kähler–Einstein metrics g in real dimension four admitting an isometric action of SU(2) with generically three-dimensional orbits. The Kähler condition means that there is a complex structure I, with respect to which the metric is hermitian, such that the two-form Ωdefined by

is closed. It is well-known that if this condition holds then Ω is in fact covariant constant.
Compactifications of locally compact groups and quotients
Authors: Lau A. T. , Milnes P. , Pym J. S.
Published: November 2008

LetNbe a compact normal subgroup of a locally compact groupG. One of our goals here is to determine when and how a given compactificationYofG/Ncan be realized as a quotient of the analogous compactification (ψ,X) ofGbyNψ= ψ(N) ⊂X; this is achieved in a number of cases for which we can establish that μNψ⊂Nψμ for all μ ∈XA question arises naturally, ‘Can the latter containment be proper?’ With an example, we give a positive answer to this question.

The groupGis an extension ofNbyGNand can be identified algebraically withNx GNwhen this product is given the Schreier multiplication, and for our further results we assume that we can also identify G topologically withN x GN. WhenGNis discrete andXis the compactification ofGcoming from the left uniformly continuous functions, we are able to show thatXis an extension ofNby(GN)(X≅N x (G/N))even when G is not a semidirect product. Examples are given to illustrate the theory, and also to show its limitations.
On contractions with spectrum contained in the Cantor set
Authors: Esterle J. , Zarrabi M. , Rajoelina M.
Published: November 2008

For ξ ε (0, ½) let Eξ be the perfect symmetric set of constant ratio ξ and set

It was shown by the first author that if T is a contraction on the Hilbert space H with spectrum contained in Eξ, and if log ∥T−n∥ = O(nα) as n → ∞ for some α < b(ξ), then T is unitary. In the other direction, we show here that there exists a (non-unitary) contraction T on H such that SpT = Eξ, log ∥T-n∥ = O(nb(ξ)) as n → ∞, and lim supn → ∞ ∥T−n∥ = ∞.
Differential spaces of finite type
Authors: Gonzalez Juan A. Navarro
Published: November 2008

This paper shows that the localization theory for algebras of smooth functions and Fréchet modules provides a basis for a theory of differential spaces of finite type, as well as the usual localization theory for commutative rings and modules grounds the theory of schemes. Moreover, most of the elementary results and proofs in the theory of schemes remain valid for differential spaces.
Spectral characterization of the socle in Jordan–Banach algebras
Authors: Aupetit Bernard
Published: November 2008

If A is a complex Banach algebra the socle, denoted by Soc A, is by definition the sum of all minimal left (resp. right) ideals of A. Equivalently the socle is the sum of all left ideals (resp. right ideals) of the form Ap (resp. pA) where p is a minimal idempotent, that is p2 = p and pAp = ℂp. If A is finite-dimensional then A coincides with its socle. If A = B(X), the algebra of bounded operators on a Banach space X, the socle of A consists of finite-rank operators. For more details about the socle see [1], pp. 78–87 and [3], pp. 110–113.
A note on the Julia set of a rational function
Authors: Letherman S. D. , Wood R. M. W.
Published: November 2008

The purpose of this note is to present a few facts about the Julia set of a rational function that are well known to the experts in the subject of complex dynamics but whose documented exposition in the literature seems to need a little clarification. For example, under conditions set out in Theorem 1, the Julia set of a rational function can be expressed as the limit of a sequence of finite sets. In particular, for certain choices of a point α, the Julia set is the limit as n increases of the inverse image sets R−n(α). This formulation is widely exploited in the backwards iteration algorithm to produce computer illustrations of Julia sets (see for example Section 5·4 of [14]).
Fermionic Gaussians
Authors: Robinson P. L.
Published: November 2008

The notion of a Gaussian as the exponential of a quadratic is rather familiar. Such functions are of considerable importance in a number of contexts, for example within quantum theory. Thus, in the Schrödinger representation of the canonical commutation relations they alone minimize uncertainty and they appear as ground states for harmonic oscillators. Also in the complex-wave representation of a free boson field they arise as transforms of the Fock vacuum under certain Bogoliubov automorphisms.
The Askey–Wilson polynomials and q-Sturm–Liouville problems
Authors: Brown B. Malcolm , Evans W. Desmond , Ismail Mourad E. H.
Published: November 2008

We find the adjoint of the Askey–Wilson divided difference operator with respect to the inner product on L2(–1, 1, (1– x2)½dx) defined as a Cauchy principal value and show that the Askey-Wilson polynomials are solutions of a q-Sturm–Liouville problem. From these facts we deduce various properties of the polynomials in a simple and straightforward way. We also provide an operator theoretic description of the Askey-Wilson operator.
Examples of tunnel number one knots which have the property ‘1 + 1 = 3’
Authors: Morimoto Kanji , Sakuma Makoto , Yokota Yoshiyuki
Published: November 2008

Let K be a knot in the 3-sphere S3, N(K) the regular neighbourhood of K and E(K) = cl(S3−N(K)) the exterior of K. The tunnel number t(K) is the minimum number of mutually disjoint arcs properly embedded in E(K) such that the complementary space of a regular neighbourhood of the arcs is a handlebody. We call the family of arcs satisfying this condition an unknotting tunnel system for K. In particular, we call it an unknotting tunnel if the system consists of a single arc.
Marked homeomorphisms and the realization problem
Authors: Greenberg Peter
Published: November 2008

The role played by the classical braid groups in the interplay between geometry, algebra and topology (see [Ca]) derives, in part, from their definition as the fundamental groups of configuration spaces of points in the plane. Seeking to generalize these groups and to understand them better, one is led to ask: are there other discrete groups whose topological invariants arise from configuration spaces?

The groups of marked homeomorphisms (1·1) provide a positive response which is in some sense banal; the realization problem (1·5) is to find non-banal examples.
Localization of modular lattices, Krull dimension, and the Hopkins-Levitzki theorem (I)
Authors: Albu Toma , Smith Patrick F.
Published: November 2008

The Hopkins–Levitzki Theorem, discovered independently in 1939 by C. Hopkins and J. Levitzki states that a right Artinian ring with identity is right Noetherian. In the 1970s and 1980s it has been generalized to modules over non-unital rings by Shock[10], to modules satisfying the descending chain condition relative to a heriditary torsion theory by Miller-Teply[7], to Grothendieck categories by Năstăsescu [8], and to upper continuous modular lattices by Albu [1]. The importance of the relative Hopkins-Levitzki Theorem in investigating the structure of some relevant classes of modules, including injectives as well as projectives is revealed in [3] and [6], where the main body of both these monographs deals with this topic. A discussion on the various forms of the Hopkins–Levitzki Theorem for modules and Grothendieck categories and the connection between them may be found in [3].
Limits of commutative triangular systems on real and p-adic groups
Authors: Shah Riddhi
Published: November 2008

A fundamental theorem of Khinchin says that every limit of an infinitesimal triangular system of probability measures on R is infinitely divisible. This was generalized to all divisible locally compact second countable abelian groups by Parthasarathy et al. (cf. [PRV]). Recently, Ruzsa eliminated the second countability condition and also proved the theorem for all Banach spaces (cf. [R2]). A similar theorem was also proved by Gangolli for certain symmetric spaces (cf. [G]). A result of Carnal shows that infinite divisibility of limits holds for commutative infinitesimal triangular systems on compact groups (cf. [C]). The same was recently proved by Neuenschwander for simply connected step-2 nilpotent Lie groups, provided the system is symmetric or supported on a discrete subgroup (cf. [N]).
Entanglement complexity of graphs in Z3
Authors: Soteros C. E. , Sumners D. W. , Whittington S. G.
Published: November 2008

In this paper we are concerned with questions about the knottedness of a closed curve of given length embedded in Z3. What is the probability that such a randomly chosen embedding is knotted? What is the probability that the embedding contains a particular knot? What is the expected complexity of the knot? To what extent can these questions also be answered for a graph of a given homeomorphism type?

We use a pattern theorem due to Kesten 12 to prove that almost all embeddings in Z3 of a sufficiently long closed curve contain any given knot. We introduce the idea of a good measure of knot complexity. This is a function F which maps the set of equivalence classes of embeddings into 0, ). The F measure of the unknot is zero, and, generally speaking, the more complex the prime knot decomposition of a given knot type, the greater its F measure. We prove that the average value of F diverges to infinity as the length (n) of the embedding goes to infinity, at least linearly in n. One example of a good measure of knot complexity is crossing number.

Finally we consider similar questions for embeddings of graphs. We show that for a fixed homeomorphism type, as the number of edges n goes to infinity, almost all embeddings are knotted if the homeomorphism type does not contain a cut edge. We prove a weaker result in the case that the homeomorphism type contains at least one cut edge and at least one cycle.
Minimal immersions of S2 and ℝP2 into ℂPn with few higher order singularities
Authors: Bolton J. , Woodward L. M. , Vrancken L.
Published: November 2008

In this paper we extend ideas developed in 2, 4 to study certain minimal immersions of S2 and ℝP2 into ℂPn. Here S2 denotes the unit sphere in ℝ3 with its standard conformal structure and ℝP2 is S2 factored out by the antipodal map, while ℂPn denotes complex projective n-space equipped with the FubiniStudy metric of constant holomorphic sectional curvature 4. Since ℝPn with its standard metric of constant curvature 1 is included in ℂPn as a totally geodesic submanifold, this includes the case of minimal immersions into the unit sphere Sn(1) with its standard metric.
Zeros of random polynomials over finite fields
Authors: Odoni R. W. K.
Published: November 2008

Let be the finite field with q elements (q a prime power), let r 1 and let X1, , Xr be independent indeterminates over . We choose an arbitrary and a d 1 and consider
Power series methods and almost sure convergence
Authors: Kiesel Rüdiger
Published: November 2008

Let (Ω, Σ,P) be a probability space and suppose that all random variables are defined on this space.
Oblique reflexion of electromagnetic waves from isotropic media with limiting Epstein-type stratifications
Authors: Westcott B. S.
Published: November 2008

Analytical reflexion coefficients are obtained for horizontally and vertically polarized electromagnetic waves respectively, obliquely incident from below two recently devised models of horizontally stratified isotropic media. It is shown that both models are totally reflecting and the phases of the reflexion coefficients may be expressed in terms of arg Γ(z).
On an eigenfunction expansion associated with a condition of radiation. II
Authors: Naylor D. , Choo F. C. , Barclay D. W.
Published: November 2008

In this paper the authors consider a problem, frequently encountered in diffraction theory, of expanding a given function f(r) in terms of a set of orthogonal functions which is not complete. The expansion in question can be written as

where r < a and
Encapsulating non-determinacy in an abstract data type with determinate semantics
Authors: Burton F. Warren
Published: November 2008

A parallel program may be indeterminate so that it can adapt its behavior to the number of processors available.

Indeterminate programs are hard to write, understand, modify or verify. They are impossible to debug, since they may not behave the same from one run to the next.

We propose a new construct, a polymorphic abstract data type called an improving value, with operations that have indeterminate behavior but simple determinate semantics. These operations allow the type of indeterminate behavior required by many parallel algorithms.

We define improving values in the context of a functional programming language, but the technique can be used in procedural programs as well.
Tail recursion without space leaks
Authors: Jones Richard
Published: November 2008

The G-machine (Johnsson, 1987; Peyton Jones, 1987) is a compiled graph reduction machine for lazy functional languages. The G-machine compiler contains many optimizations to improve performance. One set of such optimizations is designed to improve the performance of tail recursive functions. Unfortunately, the abstract machine is subject to a space leak—objects are unnecessarily preserved by the garbage collector. This paper analyses why a particular form of space leak occurs in the G-machine, and presents some ideas for fixing this problem. This phenomena in other abstract machines is also examined briefly.
Computing with lattices: An application of type classes
Authors: Jones Mark P.
Published: November 2008

This paper presents a simple framework for performing calculations with the elements of (finite) lattices. A particular feature of this work is the use of type classes to enable the use of overloaded function symbols within a strongly typed language. Previous applications of type classes have been in areas that are of most interest to language implementors. This paper suggests that type classes might also be useful as a general tool in the development of clear and modular programs.
Partially strict non-recursive data types
Authors: Nöcker Eric , Smetsers Sjaak
Published: November 2008

Values belonging to lazy data types have the advantage that sub-components can be accessed without evaluating the values as a whole: unneeded components remain unevaluated. A disadvantage is that often a large amount of space and time is required to handle lazy data types properly. Many special constructor cells are needed to ‘glue’ the individual parts of a composite object together and to store it in the heap. We present a way of representing data in functional languages which makes these special constructor cells superfluous. In some cases, no heap at all is needed to store this data. To make this possible, we introduce a new kind of data type: (partially) strict non-recursive data types. The main advantage of these types is that an efficient call-by-value mechanism can be used to pass arguments. A restrictive subclass of (partially) strict non-recursive data types, partially strict tuples, is treated more comprehensively. We also give examples of important classes of applications. In particular, we show how partially strict tuples can be used to define very efficient input and output primitives. Measurements of applications written in Concurrent Clean which exploit partially strict tuples have shown that speedups of 2 to 3 times are reasonable. Moreover, much less heap space is required when partially strict tuples are used.
Program transformation with metasystem transitions
Authors: Turchin Valentin F.
Published: November 2008

A new program transformation method is presented. It is a further refinement of supercompilation where the supercompiler is not applied directly to the function to be transformed, but to a metafunction, namely an interpreter which computes this function using its definition and an abstract (i.e. including variables) input. It is shown that with this method such tranformations become possible which the direct application of the supercompiler cannot perform. Examples include the merging of iterative loops, function inversion, and transformation of deterministic into non-deterministic algorithms, and vice-versa.
Efficient analyses for realistic off-line partial evaluation
Authors: Bondorf Anders , Jørgensen Jesper
Published: November 2008

Based on Henglein's efficient binding-time analysis for the lambda calculus (with constants and ‘fix’) (Henglein, 1991), we develop three efficient analyses for use in the preprocessing phase of Similix, a self-applicable partial evaluator for a higher-order subset of Scheme. The analyses developed in this paper are almost-linear in the size of the analysed program. (1) A flow analysis determines possible value flow between lambda-abstractions and function applications and between constructor applications and selector/predicate applications. The flow analysis is not particularly biased towards partial evaluation; the analysis corresponds to the closure analysis of Bondorf (1991b). (2) A (monovariant) binding-time analysis distinguishes static from dynamic values; the analysis treats both higher-order functions and partially static data structures. (3) A new is-used analysis, not present in Bondorf (1991b), finds a non-minimal binding-time annotation which is ‘safe’ in a certain way: a first-order value may only become static if its result is ‘needed’ during specialization; this ‘poor man's generalization’ (Holst, 1988) increases termination of specialization. The three analyses are performed sequentially in the above mentioned order since each depends on results from the previous analyses. The input to all three analyses are constraint sets generated from the program being analysed. The constraints are solved efficiently by a normalizing union/find-based algorithm in almost-linear time. Whenever possible, the constraint sets are partitioned into subsets which are solved in a specific order; this simplifies constraint normalization. The framework elegantly allows expressing both forwards and backwards components of analyses. In particular, the new is-used analysis is of backwards nature. The three constraint normalization algorithms are proved correct (soundness, completeness, termination, existence of a best solution). The analyses have been implemented and integrated in the Similix system. The new analyses are indeed much more efficient than those of Bondorf (1991b); the almost-linear complexity of the new analyses is confirmed by the implementation.
Specifying the correctness of binding-time analysis
Authors: Wand Mitchell
Published: November 2008

Mogensen has exhibited a very compact partial evaluator for the pure lambda calculus, using binding-time analysis followed by specialization. We give a correctness criterion for this partial evaluator and prove its correctness relative to this specification. We show that the conventional properties of partial evaluators, such as the Futamura projections, are consequences of this specification. By considering both a flow analysis and the transformation it justifies together, this proof suggests a framework for incorporating flow analyses into verified compilers.
A-translation and looping combinators in pure type systems
Authors: Coquand Thierry , Herbelin Hugo
Published: November 2008

We present here a generalization of A-translation to a class of pure type systems. We apply this translation to give a direct proof of the existence of a looping combinator in a large class of inconsistent type systems, a class which includes type systems with a type of all types. This is the first non-automated solution to this problem.
Lilac: a functional programming language based on linear logic
Authors: Mackie Ian
Published: November 2008

We take Abramsky's term assignment for Intuitionistic Linear Logic (the linear term calculus) as the basis of a functional programming language. This is a language where the programmer must embed explicitly the resource and control information of an algorithm. We give a type reconstruction algorithm for our language in the style of Milner's W algorithm, together with a description of the implementation and examples of use.
Lexical profiling: theory and practice
Authors: Clack Chris , Clayman Stuart , Parrott David
Published: November 2008

This paper addresses the issue of analysing the run-time behaviour of lazy, higher-order functional programs. We examine the difference between the way that functional programmers and functional language implementors view program behaviour. Existing profiling techniques are discussed and a new technique is proposed which produces results that are straightforward for programmers to assimilate. The new technique, which we call lexical profiling, collects information about the run-time behaviour of functional programs, and reports the results with respect to the original source code rather than simply listing the actions performed at run-time. Lexical profiling complements implementation-specific profiling and is important because it provides a view of program activity which is largely independent of the underlying evaluation mechanism. Using the lexical profiler, programmers may easily relate results back to the source program. We give a full implementation of the lexical profiling technique for a sequential, interpretive graph reduction engine, and extensions for compiled and parallel graph reduction are discussed.
Weak polymorphism can be sound
Authors: Greiner John
Published: November 2008

The weak polymorphic type system of Standard ML of New Jersey (SML/NJ) (MacQueen, 1992) has only been presented as part of the implementation of the SML/NJ compiler, not as a formal type system. As a result, it is not well understood. And while numerous versions of the implementation have been shown unsound, the concept has not been proved sound or unsound. We present an explanation of weak polymorphism and show that a formalization of this is sound. We also relate this to the SML/NJ implementation of weak polymorphism through a series of type systems that incorporate elements of the SML/NJ type inference algorithm.
Canonical typing and ∏-conversion in the Barendregt Cube
Authors: Kamareddine Fairouz , Nederpelt Rob
Published: November 2008

In this article, we extend the Barendregt Cube with ∏-conversion (which is the analogue of β-conversion, on product type level) and study its properties. We use this extension to separate the problem of whether a term is typable from the problem of what is the type of a term.
Benchmarking implementations of functional languages with ‘Pseudoknot’, a float-intensive benchmark
Authors: Hartel Pieter H. , Feeley Marc , Alt Martin , Augustsson Lennart , Baumann Peter , Beemster Marcel , Chailloux Emmanuel , Flood Christine H. , Grieskamp Wolfgang , Van Groningen John H. G. , Hammond Kevin , Hausman Bogumil , Ivory Melody Y. , Jones Richard E. , Kamperman Jasper , Lee Peter , Leroy Xavier , Lins Rafael D. , Loosemore Sandra , Röjemo Niklas , Serrano Manuel , Talpin Jean-Pierre , Thackray Jon , Thomas Stephen , Walters Pum , Weis Pierre , Wentworth Peter
Published: November 2008

Over 25 implementations of different functional languages are benchmarked using the same program, a floating-point intensive application taken from molecular biology. The principal aspects studied are compile time and execution time for the various implementations that were benchmarked. An important consideration is how the program can be modified and tuned to obtain maximal performance on each language implementation. With few exceptions, the compilers take a significant amount of time to compile this program, though most compilers were faster than the then current GNU C compiler (GCC version 2.5.8). Compilers that generate C or Lisp are often slower than those that generate native code directly: the cost of compiling the intermediate form is normally a large fraction of the total compilation time. There is no clear distinction between the runtime performance of eager and lazy implementations when appropriate annotations are used: lazy implementations have clearly come of age when it comes to implementing largely strict applications, such as the Pseudoknot program. The speed of C can be approached by some implementations, but to achieve this performance, special measures such as strictness annotations are required by non-strict implementations. The benchmark results have to be interpreted with care. Firstly, a benchmark based on a single program cannot cover a wide spectrum of ‘typical’ applications. Secondly, the compilers vary in the kind and level of optimisations offered, so the effort required to obtain an optimal version of the program is similarly varied.
Old and new convergence proofs for multigrid methods
Authors: Yserentant Harry
Published: November 2008

Multigrid methods are the fastest known methods for the solution of the large systems of equations arising from the discretization of partial differential equations. For self-adjoint and coercive linear elliptic boundary value problems (with Laplace's equation and the equations of linear elasticity as two typical examples), the convergence theory reached a mature, if not its final state. The present article reviews old and new developments for this type of equation and describes the recent advances.
Introduction to Adaptive Methods for Differential Equations
Authors: Eriksson Kenneth , Estep Don , Hansbo Peter , Johnson Claes
Published: November 2008

Knowing thus the Algorithm of this calculus, which I call Differential Calculus, all differential equations can be solved by a common method (Gottfried Wilhelm von Leibniz, 1646–1719).

When, several years ago, I saw for the first time an instrument which, when carried, automatically records the number of steps taken by a pedestrian, it occurred to me at once that the entire arithmetic could be subjected to a similar kind of machinery so that not only addition and subtraction, but also multiplication and division, could be accomplished by a suitably arranged machine easily, promptly and with sure results…. For it is unworthy of excellent men to lose hours like slaves in the labour of calculations, which could safely be left to anyone else if the machine was used…. And now that we may give final praise to the machine, we may say that it will be desirable to all who are engaged in computations which, as is well known, are the managers of financial affairs, the administrators of others estates, merchants, surveyors, navigators, astronomers, and those connected with any of the crafts that use mathematics (Leibniz).
Numerical Solutions to Free Boundary Problems
Authors: Hou Thomas Y.
Published: November 2008

Many physically interesting problems involve propagation of free surfaces. Vortex-sheet roll-up in hydrodynamic instability, wave interactions on the ocean's free surface, the solidification problem for crystal growth and Hele-Shaw cells for pattern formation are some of the significant examples. These problems present a great challenge to physicists and applied mathematicians because the underlying problem is very singular. The physical solution is sensitive to small perturbations. Naïve discretisations may lead to numerical instabilities. Other numerical difficulties include singularity formation and possible change of topology in the moving free surfaces, and the severe time-stepping stability constraint due to the stiffness of high-order regularisation effects, such as surface tension.

This paper reviews some of the recent advances in developing stable and efficient numerical algorithms for solving free boundary-value problems arising from fluid dynamics and materials science. In particular, we will consider boundary integral methods and the level-set approach for water waves, general multi-fluid interfaces, Hele–Shaw cells, crystal growth and solidification. We will also consider the stabilising effect of surface tension and curvature regularisation. The issue of numerical stability and convergence will be discussed, and the related theoretical results for the continuum equations will be addressed. This paper is not intended to be a detailed survey and the discussion is limited by both the taste and expertise of the author.
Theory, algorithms, and applications of level set methods for propagating interfaces
Authors: Sethian James A.
Published: November 2008

We review recent work on level set methods for following the evolution of complex interfaces. These techniques are based on solving initial value partial differential equations for level set functions, using techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting. The methodology results in robust, accurate, and efficient numerical algorithms for propagating interfaces in highly complex settings. We review the basic theory and approximations, describe a hierarchy of fast methods, including an extremely fast marching level set scheme for monotonically advancing fronts, based on a stationary formulation of the problem, and discuss extensions to multiple interfaces and triple points. Finally, we demonstrate the technique applied to a series of examples from geometry, material science and computer vision, including mean curvature flow, minimal surfaces, grid generation, fluid mechanics, combustion, image processing, computer vision, and etching, deposition and lithography in the microfabrication of electronic components.
A new version of the Fast Multipole Method for the Laplace equation in three dimensions
Authors: Greengard Leslie , Rokhlin Vladimir
Published: November 2008

We introduce a new version of the Fast Multipole Method for the evaluation of potential fields in three dimensions. It is based on a new diagonal form for translation operators and yields high accuracy at a reasonable cost.
HOWWAS RACE CONSTRUCTED IN THE NEW SOUTH?
Authors: Steedman Marek D.
Published: November 2008

This article focuses on the construction and reconfiguration of race in the U.S. South during the late nineteenth and early twentieth centuries. Much literature on race is designed to show that race is socially constructed, with the inference that race ismerelya social construction. Thus, talk about race, which is not demonstrably grounded in human biology, must be akin to talk about unicorns. But so what? Does race being a social construction make any difference to the historical accounts we give of how racial practices work? This article suggests that it can if we focus on the process of construction itself, in a particular time and place, and askhowrace was socially constructed. I trace how race was made, unmade, and remade in the years between 1865 and 1920. During the postemancipation era, Southern White elites constructed race as and through naturalized relations of dependence and independence. This construction was held in place and then undermined by the prevailing social order. I offer an account of the sharp increase in racist practices at the turn of the century, focused on the notion ofmobility. I show how, in the decades since the war, mobility undermined race as it had been socially constructed.
Ionospheric measurement with GPS: Receiver techniques and methods
Authors: Dyrud Lars , Jovancevic Aleksandar , Brown Andrew , Wilson Derek , Ganguly Suman
Published: November 2008

Accurate characterization of ionospheric parameters such as total electron content (TEC) and scintillation (signal fluctuation due to ionospheric irregularities) is critical to all users of GPS, whether the ultimate goal is measurement in navigation, geodesy, ionospheric, or atmospheric studies. Improved absolute TEC measurement accuracy is demanded by many global ionospheric characterization schemes, where small errors can be magnified in 3‐D tomographic profile reconstructions. We present research showing that there are three errors, or biases that typically result from characterizing TEC with GPS receiver data. These biases are (1) estimation, instead of measurement of receiver differential code bias (DCB); (2) ionospheric divergence of pseudorange‐code‐derived TEC resulting from code smoothing; and (3) delay of pseudorange TEC as a result of code smoothing. We present results of ionospheric data collected with a receiver that mitigates these biases to demonstrate the utility of improved accuracy, particularly for ingestion into tomographic reconstructions, but also for conversion from slant to vertical TEC.
Micrometeorites: A possible bias on the sedimentary magnetic record
Authors: Suavet C. , Rochette P. , Gattacceca J. , Folco L.
Published: November 2008

Micrometeorites are strongly magnetic and continuously accumulate at the Earth's surface. On the basis of previously acquired magnetic data, we investigated at which conditions micrometeorites can bias the sedimentary palaeomagnetic and rock magnetic record. We calculated the probabilities for a sediment sample (discrete samples or U‐channel samples) to have its detrital remanent magnetization deviated by the presence of a micrometeorite. Our model shows that direction anomalies >5° caused by micrometeorites may be rather frequent (more than 1% of measured samples), even for sediments with typical values of sedimentation rate (up to 10 cm/kyr) and remanent magnetization (up to 5 × 10−3 A/m). Excursions >30° caused by micrometeorites have probabilities >1% in sediments with remanent magnetization <10−3 A/m and sedimentation rate <10 cm/ka. Reversals caused by micrometeorites have probabilities >1% for sediments with remanent magnetization <2 × 10−4 A/m and sedimentation rate <1 cm/ka. On the other hand, only sediments with magnetic susceptibilities <10−5 SI and sedimentation rates <1 cm/ka can be significantly affected by the presence of micrometeorites.
Sonographischer Nachweis eines vom Hüftgelenk ausgehenden zystischen Tumors (Bursitis iliopectinea)
Authors: Wilhelm E.
Published: November 2008

Bei Weichteiltumoren der Hüftgegend kann die Sonographie mit dem 5-MHz-Schallkopf zur Klärung der Diagnose entscheidend beitragen. Im vorliegenden Fall konnte die Fehldiagnose einer Schenkelhernie korrigiert werden und die Diagnose eines zystischen Tumors mit Verbindung zum Hüftgelenk gestellt werden (Bursitis iliopectinea). Die Diagnose wurde operativ und histologisch bestätigt.
Verletzungen der Augenhöhle durch Fremdkörper
Authors: Vlková E. , Šlapák I.
Published: November 2008

Es werden vier Fälle von Orbitaverletzungen mit Fremdkörpern größeren Ausmaßes ohne Verletzung des Augapfels beschrieben. Die Fremdkörper wurden entfernt, die Heilung verlief ohne Komplikationen. Zwei Fremdkörper drangen ins Schädelinnere ein und in einem Fall war ein ausgedehnterer chirurgischer Eingriff nötig. In beiden Fällen des Eindringens der Fremdkörper in das Gehirn kam es zu einer Sehnervenverletzung mit nachfolgender Erblindung.
Augenbeteiligung bei AIDS
Authors: Fabricius E.-M. , Jäger H. , Lander Th. , Prantl F. , Högel B. , Greite J.-H.
Published: November 2008

Von 1984 bis 1987 (Zeitraum 2œ Jahre) wurden 30 stationär behandelte Patienten mit HIV-Infektionen verschiedener Schweregrade konsiliarisch augenärztlich untersucht. Bei 17 Patienten waren die Augen beteiligt (etwa 57%). 16 dieser 17 Patienten mit pathologischen Augenbefunden wiesen bereits das Vollbild der AIDS-Erkrankung auf (etwa 94%). Augenbeteiligung ist somit ein prognostisch ungünstiges Zeichen. 14 Patienten hatten ein Mikroangiopathiesyndrom der Netzhaut, 4 Patienten eine infektiöse (Chorio-)Retinitis, Erreger: Cytomegalievirus (3 Fälle), Cryptococcus neoformans (1 Fall). Weitere Befunde waren: Sicca-Syndrom mit Keratitis punctata superficialis (2 Fälle), Keratitis bei ausgedehnter mucokutaner Candidiasis (1 Fall), Kaposi-Sarkom der Lidhaut (2 Fälle), Kaposi-Sarkom der Bindehaut (1 Fall), Papillenödem bei Cryptococcen-Meningitis (1 Fall), atypisches Hordeolum (1 Fall). Morphologische und pathogenetische Gesichtspunkte der Augenbefunde, ihr Stellenwert und Verlauf im Rahmen der AIDS-Erkrankung sowie Probleme der Therapie werden diskutiert.
Nouvelle méthode de mesure de l'acuité visuelle. (Méthode des limites)
Authors: Paliaga G. P.
Published: November 2008

Die Methode benutzt eine neue Optotypentafel mit einem besonderen Prüfungsverfahren. Die Tafel enthält E-Zeichen in 4 randomisierten Orientierungen und in 13 Visusstufen. Die Größenabstufung der Optotypen ist logarithmisch; die Zwischenräume von einem E-Zeichen zum nächsten betragen 5.5 Bogenminuten. Die E-Zeichen werden in einer absteigenden Reihenfolge gezeigt, 10 Reihen entlang, bis zum ersten Fehler. Die Sehschärfe ergibt sich aus dem arithmetischen Mittel von 10 Werten. Die Standardabweichung erlaubt es, die Konfidenzgrenzen für die Sehschärfe und für den Unterschied zweier Sehschärfe zu schätzen.
Glaukombehandlung mit dem gepulsten Argonlaser*
Authors: Stiegler G.
Published: November 2008

Es wird über laserchirurgische Eingriffe zur Prophylaxe und Therapie des Glaukoms mit dem gepulsten Argonlaser berichtet. Standardisierte Technik und Ergebnisse werden besprochen.
Quantitative Evaluation of the Effects of Gravity and Dependency on Microvascular Tissue Transfer to the Lower Limb, with Clinical Applications
Authors: Isenberg Jeffrey Scott , Siegal Ann , Sherman Randolph
Published: November 2008

Accepted for publication June 15 1996

The authors have attempted quantitatively to evaluate the effects of gravity and dependency on free-tissue transfers to the lower limb, particularly in the immediate postoperative period, using the diagnostic modalities of Doppler ultrasonography and interstitial compartment pressure measurements. Results of these quantitative evaluations promoted a change in postoperative management among patients undergoing lower-limb tissue transfer. The experience in two patient cohorts is presented.
Temporäre, belastungsabhängige Parästhesien bei Agenesie der Vena cava inferior
Authors: Boecken G.
Published: November 2008

Im Vordergrund einer Agenesie der Vena cava inferior mit sogenannter Azygoskontinuation bei einem 23jährigen Patienten standen progrediente, temporäre, belastungsabhängige Parästhesien der unteren Extremitäten nach zunehmender sportlicher Aktivierung als Soldat. Erkennbar wurde diese Anomalie an der Vergrößerung des Azygos-Schattens im Thorax-Röntgenbild sowie im Computertomogramm durch retro- und paraaortale Raumforderungen, die den erweiterten Kollateralen für den Abfluß des Blutes aus der unteren Körperhälfte entsprachen. Therapeutische Möglichkeiten bei dieser äußerst seltenen Fehlbildung sind bisher nicht bekannt, so daß der Prophylaxe von Komplikationen, wie Thrombosen im distalen Zuflußgebiet, die größte Bedeutung zukommt.
Engendering ‘Race’ in Calls for Diasporic Community in Sweden
Authors: Sawyer Lena
Published: November 2008

This article argues that theorists of black/African diasporas should interrogate the specific ways in which ‘race’ is used to engage people in diasporic projects, and that such projects are intimately intertwined with specifically gendered, sexualized, and generational class relations and positionalities in specific national contexts and spaces. Attention to these intersections can help us better understand hierarchies of power between and among diasporic individuals and communities. This article focuses on historically specific Swedish meanings of racialized femininities and the different forms of agency women use to negotiate the gendered processes of racialization they encounter in a variety of settings and sources. It draws on interviews and fieldnotes conducted between 1994 and 2007, together with analysis of popular culture (music and radio programmes) and ethnographic material collected by Swedish ethnologist Viveca Motsieloa, and maps out some of the complexities utilized by different generations of Swedish women of African heritage in a changing Swedish landscape of racial formations. Their negotiations show how tensions and differences between ‘second-generation’ migrants and those of the ‘first generation’ are expressed through gender, sexuality, and differing understandings of ‘race’ (and the place of ‘racial mixture’).
‘I like Your Colour!’ Skin Bleaching and Geographies of Race in Urban Ghana
Authors: Pierre Jemima
Published: November 2008

This article explores chemical skin bleaching practices in urban Ghana to demonstrate the ways that particular racialized understandings of meaning are deployed in a contemporary postcolonial African society. I argue that the processes of racialization indexed by skin bleaching in Ghana must be contextualized within global racial formations; specifically, they can only be understood by examining the interlinked local and global ideologies and practices of race. In elaborating this argument, the essay also engages with contemporary African diaspora theorization that tends to foreground diasporic identity and experience at the expense of contemporary continental processes. By bringing a postcolonial African society into a dialogue about race, processes of racialization, and the interlinked transnational construction of black identities, this essay offers one way out of the ambivalent relationship that I believe diaspora theorization has with Africa.
High resolution electron paramagnetic resonance spectroscopy of septet pyridyl-2,4,6-trinitrene in solid argon: Fine-structure parameters of six electron-spin cluster
Authors: Misochko E. Ya. , Akimov A. V. , Chapyshev S. V.
Published: November 2008

The high resolution 9GHz electron paramagnetic resonance (EPR) spectrum of septet pyridyl-2,4,6-trinitrene was recorded after the photolysis of 2,4,6-triazido-3,5-dichloropyridine in solid argon matrix at 15K. Owing to the high resolution of the experimental EPR spectrum, the zero-field splitting parameters of the septet trinitrene were determined with a high accuracy: Ds=−0.1019±0.0004cm−1 and Es=0.00325±0.00015cm−1. All EPR transitions of the septet trinitrene were, for the first, unambiguously assigned based on the eigenfield calculations of the Zeeman energy levels. The spectrum of the septet trinitrene represents a new type of EPR spectra of septet spin states with nonzero zero-field splitting parameter Es. The nonvanishing parameter Es of the septet trinitrene arises due to magnetic nonequivalence of three triplet centers in the molecule and is manifested in the appearance in the spectrum of separate x and y transitions. The septet spin states of this type display at very low magnetic fields two intense z transitions since the ∣3Ds∣ energy gap between zero-field energy levels W±1 and W±2 fits the quantum of microwave irradiation of a 9GHz EPR spectrometer. Analysis of the magnetic parameters shows that semiempirical description of the fine-structure tensor for six electron-spin cluster in the septet trinitrene is appropriate for precise estimations of the parameter Ds but it is too crude to estimate small value of the parameter Es.