bluuebunny/crossref_metadata_2025_split huggingface dataset:
The sheaf of relative differentials of a fibred surface
Authors: Serrano Fernando 
Published: November 2008

AbstractLet Φ: S → C denote a fibration from a smooth projective surface onto a smooth curve, with fibres of genus ≥2. The double dual of the sheaf of relative differentials has been studied by F. Serrano [14]. There, it was proved that dim grows asymptotically as the square of n in case Φ is not isotrivial (i.e. fibres vary in modulus), and the converse holds true in most cases, in a way that can be made precise. In the non-isotrivial case, the present paper provides further information about by analysing the linear systems for large n. If P denotes the positive part of in its Zariski decomposition, then it is shown that |rP| is eventually base-point free for some r > 0. Furthermore, Proj is a normal projective surface, fibred over C, birational to S, and with only rational singularities.
Ordered orbits of the shift, square roots, and the devil's staircase
Authors: Bullett Shaun , Sentenac Pierrette 
Published: November 2008

AbstractAn orbit of the shift σ: t ↦ 2t on the circle = ℝ/ℤ is ordered if and only if it is contained in a semi-circle Cμ = [μ, μ+½]. We investigate the ‘devil's staircase’ associating to each μ ε the rotation number ν of the unique minimal closed σ-invariant set contained in Cμ; we present algorithms for μ in terms of ν, and we prove (after Douady) that if ν is irrational then μ is transcendental. We apply some of this analysis to questions concerning the square root map, and mode-locking for families of circle maps, we generalize our algorithms to orbits of the shift having ‘sequences of rotation numbers’, and we conclude with a characterization of all orders of points around realizable by orbits of σ.
Static solutions of the spherically symmetric Vlasov–Einstein system
Authors: Rein Gerhard 
Published: November 2008

AbstractWe consider the Vlasov—Einstein system in a spherically symmetric setting and prove the existence of static solutions which are asymptotically flat and have finite total mass and finite extension of the matter. Among these there are smooth, singularity-free solutions, which have a regular centre and have isotropic or anisotropic pressure, and solutions which have a Schwarzschild-singularity at the centre.
The even master system and generalized Kummer surfaces
Authors: Bertin Jose , Vanhaecke Pol 
Published: November 2008

AbstractIn this paper we study a generalized Kummer surface associated to the Jacobian of those complex algebraic curves of genus two which admit an automorphism of order three. Such a curve can always be written as y2 = x6 + 2kx3 + 1 and k2 ╪ 1 is the modular parameter. The automorphism extends linearly to an automorphism of the Jacobian and we show that this extension has a 94 invariant configuration, i.e. it has 9 fixed points and 9 invariant theta curves, each of these curves contains 4 fixed points and 4 invariant curves pass through each fixed point. The quotient of the Jacobian by this automorphism has 9 singular points of type A2 and the 94 configuration descends to a 94 configuration of points and lines, reminiscent to the well-known 166 configuration on the Kummer surface. Our ‘generalized Kummer surface’ embeds in ℙ4 and is a complete intersection of a quadric and a cubic hypersurface. Equations for these hypersurfaces are computed and take a very symmetric form in well-chosen coordinates. This computation is done by using an integrable system, the ‘even master system’.
Chaos map for the universal enveloping algebra ofU(N)
Authors: Hudson R. L. , Parthasarathy K. R. 
Published: November 2008

AbstractIt is shown that the family of representations {jt,t∈ ℝ+} of the universal enveloping algebra U of theN-dimensional unitary group which is generated by theN-dimensional number process of quantum stochastic calculus can be expressed in the formwhere ψ is a bijective linear map from U onto the space S of symmetric tensors over the Lie algebra, andItis the iterated (chaotic) integral on S. The chaotic product * is defined by the formulaand satisfiesThis work generalizes and completes earlier results on the centre of U.
Moduli spaces of compact complex submanifolds of complex fibered manifolds
Authors: Merkulov Sergey A. 
Published: November 2008

In 1962 Kodaira[11] proved that ifX ↪ Y is a compact complex submanifold with normal bundle N such that H1(X, N) = 0, then X belongs to a locally complete family {Xt: t ∈ M} of complex submanifolds Xt of Y with the moduli space M being a (dimcH0(X, N))-dimensional complex manifold, and there exists a canonical isomorphismbetween the tangent space of M at a point t ∈ M and the space of all global sections of the normal bundle Nt of the embedding Xt ↪ Y.
A uniform Kadec-Klee property for symmetric operator spaces
Authors: Dodds P. G. , Dodds T. K. , Dowling P. N. , Lennard C. J. , Sukochev F. A. 
Published: November 2008

AbstractWe show that if a rearrangement invariant Banach function space E on the positive semi-axis satisfies a non-trivial lower q-estimate with constant 1 then the corresponding space E(M) of τ-measurable operators, affiliated with an arbitrary semi-finite von Neumann algebra M equipped with a distinguished faithful, normal, semi-finite trace τ, has the uniform Kadec-Klee property for the topology of local convergence in measure. In particular, the Lorentz function spaces Lq, p and the Lorentz-Schatten classes Cg, p have the UKK property for convergence locally in measure and for the weak-operator topology, respectively. As a partial converse, we show that if E has the UKK property with respect to local convergence in measure then E must satisfy some non-trivial lower q-estimate. We also prove a uniform Kadec-Klee result for local convergence in any Banach lattice satisfying a lower q-estimate.
On 2-dimensional aspherical complexes and a problem of J. H. C. Whitehead
Authors: Luft E. 
Published: November 2008

In [W] J. H. C. Whitehead posed the following question: ‘Is every subcomplex K of a 2-dimensional aspherical complex L itself aspherical ?’This problem is usually referred to as the ‘Whitehead Conjecture’ though it was only stated in the form of a question. For convenience we treat it also as a conjecture.The Whitehead Conjecture has been proved in special cases: if the subcomplex K has only one 2-cell, and also in the case where π1(K) is either finite, abelian, of free [C] For more partial results see, for example, the introduction of [H1].
The packing dimension of projections and sections of measures
Authors: Falconer Kenneth J. , Mattila Pertti 
Published: November 2008

AbstractWe show that for a probability measure μ on ℝnfor almost all m–dimensional subspaces V, provided dimH μ≤m. Here projv denotes orthogonal projection onto V, and dimH and dimp denote the Hausdorff and packing dimension of a measure. In the case dimH μ > m we show that at μ-almost all points x the slices of μ by almost all (n − m)-planes Vx through x satisfyWe give examples to show that these inequalities are sharp.
Lagrangian submanifolds satisfying a basic equality
Authors: Chen Bang-Yen , Vrancken Luc 
Published: November 2008

AbstractIn [3], B. Y. Chen proved that, for any Lagrangian submanifold M in a complex space-form Mn(4c) (c = ± 1), the squared mean curvature and the scalar curvature of M satisfy the following inequality:He then introduced three families of Riemannian n-manifolds and two exceptional n-spaces Fn, Ln and proved the existence of a Lagrangian isometric immersion pa from into ℂPn(4) and the existence of Lagrangian isometric immersions f, l, ca, da from Fn, Ln, , into ℂHn(− 4), respectively, which satisfy the equality case of the inequality. He also proved that, beside the totally geodesie ones, these are the only Lagrangian submanifolds in ℂPn(4) and in ℂHn(− 4) which satisfy this basic equality. In this article, we obtain the explicit expressions of these Lagrangian immersions. As an application, we obtain new Lagrangian immersions of the topological n-sphere into ℂPn(4) and ℂHn(−4).
Ramanujan's formula for the logarithmic derivative of the gamma function
Authors: Bradley David 
Published: November 2008

AbstractWe prove a remarkable formula of Ramanujan for the logarithmic derivative of the gamma function, which converges more rapidly than classical expansions, and which is stated without proof in the notebooks [5]. The formula has a number of very interesting consequences which we derive, including an elegant hyperbolic summation, Ramanujan's formula for the Riemann zeta function evaluated at the odd positive integers, and new formulae for Euler's constant γ.
A generalization of the Whitney rank generating function
Authors: Farr G. E. 
Published: November 2008

AbstractThe Whitney quasi-rank generating function, which generalizes the Whitney rank generating function (or Tutte polynomial) of a graph, is introduced. It is found to include as special cases the weight enumerator of a (not necessarily linear) code, the percolation probability of an arbitrary clutter and a natural generalization of the chromatic polynomial. The crucial construction, essentially equivalent to one of Kung, is a means of associating, to any function, a rank-like function with suitable properties. Some of these properties, including connections with the Hadamard transform, are discussed.
Simultaneous rational approximations and related diophantine equations
Authors: Rickert John H. 
Published: November 2008

AbstractIn this paper we shall consider simultaneous approximations to algebraic numbers of the form for rational t1, …, tm, v. If t1, …, tm, are sufficiently close to 1 with respect to a common denominator we shall derive an effective inequality of the form max {|θ1 – p1 / q|, …, |θm – pm / q|} > cq–1–λ for all integers p1, …, pm, q with q > 0. The technique is used to derive the inequalityWe use this to show that the only solution to the simultaneous equationsare the trivial ones.
On the decimal representation of integers
Authors: Drazin M. P. , Griffith J. Stanley 
Published: November 2008

Let r be any fixed integer with, r≥ 2; then, given any positive integer n, we can find* integers αk(r, n) (k = 0, 1, 2, …) such thatwhere, subject to the conditionsthe integers αk(r, n) are uniquely determined, and, in fact, clearlyαk(r, n) = [n/rk] − r[n/rk+1](square brackets denoting integral parts, according to the usual convention).
Tauberian theory for the asymptotic forms of statistical frequency functions
Authors: Hammersley J. M. 
Published: November 2008

An Abelian theorem is a theorem stating that a given behaviour on the part of each of several quantities entails similar behaviour for their average. A Tauberian theorem is a converse to an Abelian theorem. As a rule, a given behaviour of an average will not entail similar behaviour of the individual quantities themselves unless there is some condition imposed to secure reasonably uniform behaviour amongst the individuals. Such a condition, known as a Tauberian condition, is usually sufficient but not necessary, and it enters into the premises of the Tauberian theorem. We interpret ‘average’ in a wide sense to include any kind of smoothing process; for example, the integral of a functionf(t) is an average of the values off(t) corresponding to individual values oft;and we may seek a sufficient Tauberian condition such that a limit-behaviour of an integral-averageentails the corresponding limit-behaviourfor individual values oft.
Statistical mechanics and the partition of numbers II. The form of crystal surfaces
Authors: Temperley H. N. V. 
Published: November 2008

AbstractThe classical theory of partition of numbers is applied to the problem of determining the equilibrium profile of a simple cubic crystal. It is concluded that it may be thermo-dynamically profitable for the surface to be ‘saw-toothed’ rather than flat, the extra entropy associated with such an arrangement compensating for the additional surface energy. For both a two- and a three-dimensional ‘saw-tooth’ the extra entropy varies, to a first approximation, in the same way as the surface energy, i.e. is proportional to or respectively, where N is the number of molecules in a ‘tooth’. For the simple cubic lattice, the entropy associated with the formation of a tooth containing N atoms is estimated to be 3.3 It is also possible to estimate the variation of the ‘equilibrium roughness’ of a crystal with temperature, if its surface energy is known.
Removal of an inconsistency in the theory of diffraction
Authors: Jones D. S. 
Published: November 2008

AbstractIt is indicated by means of a particular example how an inconsistency arises in one formulation of diffraction problems. It is shown that the inconsistency is removed if different boundary conditions are imposed during the formulation. In the proof it is necessary to determine the contributions to the field from parts of a sphere of radius R at an interior point when the field on the sphere is a plane wave. It is found that, as R → ∞, the part of the sphere near the source which subtends a solid angle of order at the centre contributes the plane wave and that the remainder of the sphere provides a contribution which vanishes in the limit. The demonstration involves the use of the principle of stationary phase for an integral of two variables.In the final section special boundary conditions are given for an exceptional three-dimensional problem.
A quantum theory of Wheeler–Feynman electrodynamics
Authors: Davies P. C. W. 
Published: November 2008

AbstractA quantum mechanical theory of the action-at-a-distance electrodynamics of Wheeler and Feynman is given using an S-matrix approach. The response of the universe is introduced, and a perturbation expansion leads to the usual expression for the spontaneous transition rate between atomic energy levels, an effect normally attributed to quantized field oscillators. The Feynman propagator is then recovered, leading to the familiar self-energy formulae. Finally, a comparison of the formal structure of the new theory with the conventional is shown to establish a complete mathematical equivalence to all orders in the expansion.
Circular inclusion in an infinite elastic medium with a circular hole
Authors: Bhargava R. D. , Kapoor O. P. 
Published: November 2008

AbstractThis paper deals with the two-dimensional problem of a circular inclusion undergoing spontaneous dimensional changes in an infinite elastic medium with a circular hole. This provides a more realistic model for some physical phenomena where inclusions have found applications. The effect of a concentrated force acting at an arbitrary point of an infinite medium with a circular hole has been found as an auxiliary result. After the evaluation of the effect of a concentrated force, Eshelby's. point force approach (1) has been used to get an exact solution to the inclusion problem.
Higher-order functions for parsing
Authors: Hutton Graham 
Published: November 2008

AbstractIn combinator parsing, the text of parsers resembles BNF notation. We present the basic method, and a number of extensions. We address the special problems presented by white-space, and parsers with separate lexical and syntactic phases. In particular, a combining form for handling the ‘offside rule’ is given. Other extensions to the basic method include an ‘into’ combining form with many useful applications, and a simple means by which combinator parsers can produce more informative error messages.
The complexity of type inference for higher-order typed lambda calculi
Authors: Henglein Fritz , Mairson Harry G. 
Published: November 2008

AbstractWe analyse the computational complexity of type inference for untyped λ-terms in the second-order polymorphic typed λ-calculus (F2) invented by Girard and Reynolds, as well as higher-order extensionsF3,F4, …,Fωproposed by Girard. We prove that recognising theF2-typable terms requires exponential time, and forFωthe problem is non-elementary. We show as well a sequence of lower bounds on recognising theFk-typable terms, where the bound forFk+1is exponentially larger than that forFk.The lower bounds are based on generic simulation of Turing Machines, where computation is simulated at the expression and type level simultaneously. Non-accepting computations are mapped to non-normalising reduction sequences, and hence non-typable terms. The accepting computations are mapped to typable terms, where higher-order types encode reduction sequences, and first-order types encode the entire computation as a circuit, based on a unification simulation of Boolean logic. A primary technical tool in this reduction is the composition of polymorphic functions having different domains and ranges.These results are the first nontrivial lower bounds on type inference for the Girard/Reynolds system as well as its higher-order extensions. We hope that the analysis provides important combinatorial insights which will prove useful in the ultimate resolution of the complexity of the type inference problem.
Safe fusion of functional expressions II: Further improvements
Authors: Chin Wei-Ngan 
Published: November 2008

AbstractLarge functional programs are often constructed by decomposing each big task into smaller tasks which can be performed by simpler functions. This hierarchical style of developing programs has been found to improve programmers' productivity because smaller functions are easier to construct and reuse. However, programs written in this way tend to be less efficient. Unnecessary intermediate data structures may be created. More function invocations may be required.To reduce such performance penalties, Phil Wadler proposed a transformation algorithm, called deforestation, which could automatically fuse certain composed expressions together to eliminate intermediate tree-like data structures. However, his technique is currently safe (terminates with no loss of efficiency) for only a subset of first-order expressions.This paper will generalise the deforestation technique to make it safe for all first-order and higher-order functional programs. Our generalisation is explained using a model for safe fusion which views each function as a producer and its parameters as consumers. Through this model, syntactic program properties are proposed to classify producers and consumers as either safe or unsafe. This classification is used to identify sub-terms that can be safely fused/eliminated. We present the generalised transformation algorithm, illustrate it with examples and provide a termination proof for the transformation algorithm of first-order programs. This paper also contains a suite of additional techniques to further improve the basic safe fusion method. These improvements could be viewed as enhancements to compensate for some inadequacies of the syntactic analyses used.
A unifying type-theoretic framework for objects
Authors: Hofmann Martin , Pierce Benjamin 
Published: November 2008

AbstractWe give a direct type-theoretic characterization of the basic mechanisms of object-oriented programming, including objects, methods, message passing, and subtyping, by introducing an explicit constructor for object types and suitable introduction, elimination, and equality rules. The resulting abstract framework provides a basis for justifying and comparing previous encodings of objects based on recursive record types (Cardelli, 1984; Cardelli, 1992; Bruce, 1994; Cooket al., 1990; Mitchell, 1990a) and encodings based on existential types (Pierce & Turner, 1994).
Operational interpretations of an extension of Fω with control operators
Authors: Harper Robert , Lillibridge Mark 
Published: November 2008

AbstractWe study the operational semantics of an extension of Girard's System Fω with two control operators: an abort operation that abandons the current control context, and a callcc operation that captures the current control context. Two classes of operational semantics are considered, each with a call-by-value and a call-by-name variant, differing in their treatment of polymorphic abstraction and instantiation. Under the standard semantics, polymorphic abstractions are values and polymorphic instantiation is a significant computation step; under the ML-like semantics evaluation proceeds beneath polymorphic abstractions and polymorphic instantiation is computationally insignificant. Compositional, type-preserving continuation-passing style (cps) transformation algorithms are given for the standard semantics, resulting in terms on which all four evaluation strategies coincide. This has as a corollary the soundness and termination of well-typed programs under the standard evaluation strategies. In contrast, such results are obtained for the call-by-value ML-like strategy only for a restricted sub-language in which constructor abstractions are limited to values. The ML-like call-by-name semantics is indistinguishable from the standard call-by-name semantics when attention is limited to complete programs.
Relative perturbation results for matrix eigenvalues and singular values
Authors: Ipsen Ilse C. F. 
Published: November 2008

It used to be good enough to bound absolute of matrix eigenvalues and singular values. Not any more. Now it is fashionable to bound relative errors. We present a collection of relative perturbation results which have emerged during the past ten years.No need to throw away all those absolute error bound, though. Deep down, the derivation of many relative bounds can be based on absolute bounds. This means that relative bounds are not always better. They may just be better sometimes – and exactly when depends on the perturbation.
Anthropogenic impacts to large lakes in China: the Tai Hu example
Authors: Dokulil M. , Chen W. , Cai Q. 
Published: November 2008

Abstract
The objective of this study is to summarise limnological effects of cultural eutrophication in some Chinese lakes. Detailed data are shown for Lake Tai Hu as an example for a very large shallow lake affected by anthropogenic impacts. Urban and industrial waste water discharged to the lake result in high nutrient concentrations, large algal blooms dominated by cyanobacteria, mainly species of Microcystis and strong horizontal gradients. Algal growth in this lake is mainly ligh and/or phosphorus limited. This situation is typical for most of the lakes included in this review although some of the large deep lakes seem to be nitrogen deficient. In some cases toxicological effects may be the reason for observed discrepancies. Lakes are of vital importance for populations in China as drinking water and nutritional resources. To prevent water shortage because of conflicting usage, anticipation, control and management of water pollution is urgently needed. Moreover, efforts must be taken to rehabilitate deteriorated freshwater ecosystems.
Application of exergy and specific exergy as ecological indicators of coastal areas
Authors: Jørgensen S.E. 
Published: November 2008

Abstract
Exergy and specific exergy have been found together with nine other ecological attributes for 12 coastal ecosystems. The correlation of the 11 attributes was examined, and the extent to which exergy and specific exergy can be applied as indicators to assess ecosystem health was discussed. The two concepts cover a range of important properties of ecosystems, but other indicators are also required to provide a sufficiently comprehensive assessment of ecosystem health.