bluuebunny/crossref_metadata_2025 huggingface dataset:
Sharply transitive posets with free abelian automorphism group
Authors: Behrendt Gerhard
Published: November 2008

Let (X,≤) be a partially ordered set (in short, a poset). The automorphism group Aut (X,≤) is the group of all permutations g of X such that x ≤ y if and only if xg ≤ yg for all x,y∈X. We say that (X,≤) is sharply transitive if Aut(X,≤) is sharply transitive on X, that is, for x,y∈X there exists a unique g∈Aut(X,≤) with y = xg. Sharply transitive totally ordered sets have been studied by Ohkuma[4, 5], Glass, Gurevich, Holland and Shelah [3] (see also [2] and [6]). Whereas the only countable sharply transitive totally ordered set is the set of integers, there are a great variety of countable sharply transitive posets. Amongst other results, in [1] the author showed that there are countably many non-isomorphic sharply transitive posets whose automorphism group is infinite cyclic (and also gave a full description of those), whereas there are 2N0 non-isomorphic sharply transitive posets whose automorphism group is isomorphic to the additive group of the rational numbers. This suggests also that one should consider the analogous problem for free abelian groups. The purpose of this note is to show that whenever G is a countable free abelian group then there exists a sharply transitive poset whose automorphism group is isomorphic to G, and that there are already 2N0 non-isomorphic sharply transitive posets whose automorphism group is the free abelian group of rank 2.
Convolution estimates related to surfaces of half the ambient dimension
Authors: Drury S. W. , Guo Kanghui
Published: November 2008

Let ƒ be a smooth function of compact support defined in the plane and consider the integral

The estimate

is well-known, see for instance the work of Littman[4]. The operator T amounts to convolution with the measure σ carried by the parabola t → (t, ½t2) and given by dσ = dt. Usually one proves (1) by embedding σ in an analytic family of distributions σz in ℝ2 given by
Groups of Wielandt length two
Authors: Ormerod Elizabeth A.
Published: November 2008

The Wielandt subgroup ω(G) of a group G is the subgroup of elements that normalize every subnormal subgroup of G. This subgroup, now named for Wielandt, was introduced by him in 1958 [15]. For a finite non-trivial group the Wielandt subgroup is always a non-trivial, characteristic subgroup. Thus it is possible to define the ascending Wielandt series for a finite group G which terminates at the group. Write ω0(G) = 1, and for i ≥ 1, ωi(G)/ωi–1(G) = ω(G/ωi–1(G)). The smallest n such that ωn(G) = G is called the Wielandt length of G, and the class of groups of Wielandt length at most n is denoted by . From the definition it follows that is closed under homomorphic images and taking normal subgroups. Nilpotent groups in are also closed under taking subgroups.
Products of idempotent integer matrices
Authors: Fountain John
Published: November 2008

Let E denote the set of non-identity idempotent matrices in the full matrix ring Mn(R) over a principal ideal domain R. A necessary and sufficient condition is found for the subsemigroup generated by E to be the set of all matrices in Mn(R) of rank less than n. The condition is satisfied when R is a discrete valuation ring and when R is the ring of integers. Thus every n × n matrix of rank less than n is a product of idempotent integer matrices.
Twisting formulae of the Jones polynomial
Authors: Yokota Yoshiyuki
Published: November 2008

Let be an oriented knot in S3 and a solid torus endowed with a preferred framing which contains in its interior. By ρ and λ we denote the wrapping and winding numbers of in respectively. That is, they are the geometric and algebraic intersection numbers of and a meridian disk of . For an integer μ, let τμ be an orientation-preserving homeomorphism of satisfying τμ(m) = m and τμ(l) = l + μm in H1(∂), where (m, l) is a meridian-longitude pair of . We call τμ(), denoted by μ, the knot obtained from by μ-twisting along .
Strictly singular and strictly cosingular operators on spaces of continuous functions
Authors: Abbott Catherine , Bator Elizabeth , Lewis Paul
Published: November 2008

In this paper we will be concerned with studying operatorsT:C(K, X) →Ydefined on Banach spaces of continuous functions. We will be particularly interested in studying the classes of strictly singular and strictly cosingular operators. In the process, we obtain answers to certain questions recently raised by Bombal and Porras in [5]. Specifically, we study Banach spaceXandYfor which an operatorT:C(K, X) →Ywith representing measuremis strictly singular (strictly cosingular) whenevermis strongly bounded andm(A) is strictly singular (strictly cosingular) for each Borel subsetAofK. Along the way we establish several results dealing with non-compact operators on continuous function spaces, and we consolidate numerous results concerning extension theorems for operators defined on these same spaces. Also, we join Saab and Saab [25] in demonstrating that if l1does not embed inX* then the adjointT* of a strongly bounded map must be weakly precompact, thereby presenting an alternative solution to a question raised in [2].
Polynomial expansions of positive harmonic functions in the unit ball
Authors: Armitage D. H.
Published: November 2008

It is well known that if h is harmonic in the open unit ball B of the Euclidean space N (where N ≥ 2), then there exist homogeneous harmonic polynomials Hn of degree n in N such that converges absolutely and locally uniformly to h in B (see e.g. Brelot[2], appendice). Further, it is easy to show that this series is unique and that each polynomial Hn is the sum of all the monomial terms of degree n in the multiple Taylor series of h about the origin 0. We call the polynomial expansion of h. Our aim is to obtain sharp upper and lower bounds for the individual terms Hn and for the partial sums of this expansion in the case where h > 0 in B.
Pseudo-Anosov homeomorphisms on a sphere with four punctures have all periods
Authors: Llibre Jaume , Mackay Robert S.
Published: November 2008

It is proved that if ƒ is a homeomorphism of the two-sphere with an invariant set V of cardinality N = 4, then either ƒ has periodic orbits of all periods or it belongs to one of a small number of algebraically finite isotopy classes relative to V. For N ≤ 4, the second case always holds. On the other hand, for each N ≥ 7 we give examples of pseudo-Anosov homeomorphisms of the sphere, relative to a set of N points, for which not all periods occur.
The connection between the universal enveloping C*-algebra and the universal enveloping von Neumann algebra of a JW-algebra
Authors: Jamjoom Fatmah B.
Published: November 2008

This article aims to study the relationship between the universal enveloping C*-algebra C*(M) and the universal enveloping von Neumann algebra W*(M), when M is a JW-algebra. In our main result (Theorem 2·7) we show that C*(M) can be realized as the C*-subalgebra of W*(M) generated by M.
Spectral inequalities for compact integral operators on Banach function spaces
Authors: Drnovšek Roman
Published: November 2008

This article generalizes some spectral inequalities for non-negative matrices (see [2] and [3]) to compact integral operators with non-negative kernels defined on Banach function spaces. The spectral radius of a sum of such operators is estimated under certain conditions and a generalization of this inequality is given. An inequality for the spectral radius of a compact integral operator with the kernel equal to a weighted geometric mean of non-negative kernels is also proved.
Jacobian in genus 2
Authors: Cassels J. W. S.
Published: November 2008

In [2] the author proposed the study of the geometry and arithmetic of the general curve

of genus 2 over a general groundfield such as the rationals in order to attack Diophantine problems. He gave the form of the Jacobian, and Flynn[4, 5] determined the group law on it. This paper is preparatory to a planned study of heights under duality. It extends to a general groundfield the description of the Jacobian as the variety of lines on the intersection of two quadric surfaces in P5 given over the complexes in the last chapter of the textbook [7] of Griffiths and Harris. This description is a generalization of that of a curve of genus 1 as the intersection of two quadric surfaces in P3 and is a special case of a more general result [3]: its first appearances seem to be in [12] and [13].
On 3-dimensional Poincaré duality complexes and 2-knot groups
Authors: Hillman Jonathan A.
Published: November 2008

We show that a PD3-complex P such that π = π1(P) is infinite and has a non-trivial finite normal subgroup must be homotopy equivalent to RP2 × S1. Hence if A is an abelian normal subgroup of a 2-knot group πK which is not contained in the commutator subgroup πK′ and πK′ is infinite then A is torsion free.
Products of idempotent endomorphisms of an independence algebra of infinite rank
Authors: Fountain John , Lewin Andrew
Published: November 2008

In 1966, J. M. Howie characterized the self-maps of a set which can be written as a product (under composition) of idempotent self-maps of the same set. In 1967, J. A. Erdos considered the analogous question for linear maps of a finite dimensional vector space and in 1985, Reynolds and Sullivan solved the problem for linear maps of an infinite dimensional vector space. Using the concept of independence algebra, the authors gave a common generalization of the results of Howie and Erdos for the cases of finite sets and finite dimensional vector spaces. In the present paper we introduce strong independence algebras and provide a common generalization of the results of Howie and Reynolds and Sullivan for the cases of infinite sets and infinite dimensional vector spaces.
Height one prime ideals of certain iterated skew polynomial rings
Authors: Jordan David A.
Published: November 2008

(1·1) Introduction. This paper is concerned with the prime and primitive ideals of certain iterated skew polynomial rings in two variables. These rings include those constructed in [7] but an extra parameter, ρ, has been introduced to the construction. This leads to greater variety in the behaviour of the height one prime ideals.
Limiting properties of Inverse Beta and generalized Bleimann–Butzer–Hahn operators
Authors: Adell José A. , De La Cal Jesús
Published: November 2008

In this paper, we consider limiting properties concerning linear operators of probabilistic type. Specifically, we show that gamma operators are limits of inverse Beta operators and that Bleimann–Butzer–Hahn, Szász and Baskakov operators are limits of generalized Bleimann–Butzer–Hahn operators. By duality, these results are closely related to the convergence in the total variation distance of the probability measures involved. In each case, rates of convergence are given.
Subsemigroups of Stone-Čech compactifications
Authors: Budak Talin , Işik Nilgün , Pym John
Published: November 2008

The Stone–Čech compactification βℕ of the discrete space ℕ of positive integer is a very large topological space; for example, any countable discrete subspace of the growth ℕ* = βℕ/ℕ has a closure which is homeomorphic to βℕ itself ([23], §3·5] Now ℕ, while hardly inspiring as a discrete topological space, has a rich algebrai structure. That βℕ also has a semigroup structure which extends that of (ℕ, +) and in which multiplication is continuous in one variable has been apparent for about 30 years. (Civin and Yood [3] showed that βGwas a semigroup for each discrete groupG, and any mathematician could then have spotted that βℕ was a subsemigroup of βℕ.) The question which now appears natural was explicitly raised by van Douwen[6] in 1978 (in spite of the recent publication date of his paper), namely, does ℕ* contain subspaces simultaneously algebraically isomorphic and homeomorphic to βℕ? Progress on this question was slight until Strauss [22] solved it in a spectacular fashion: the image of any continuous homomorphism from βℕ into ℕ* must be finite, and so the homomorphism cannot be injective. This dramatic advance is not the end of the story. It is still not known whether that image can contain more than one point. Indeed, what appears to be one of the most difficult questions about the algebraic structure of βℕ is whether it contains any non-trivial finite subgroups
On the Friedrichs extension of semi-bounded difference operators
Authors: Benammar M. , Evans W. D.
Published: November 2008

In [5] Kalf obtained a characterization of the Friedrichs extension TF of a general semi-bounded Sturm–Liouville operator T, the only assumptions made on the coefficients being those necessary for T to be defined. The domain D(TF) of TF was described in terms of ‘weighted’ Dirichiet integrals involving the principal and non-principal solutions of an associated non-oscillatory Sturm–Liouville equation. Conditions which ensure that members of D(TF) have a finite Dirichlet integral were subsequently given by Rosenberger in [7].
Stable splittings of classifying spaces of metacyclic 2-groups
Authors: Dietz Jill
Published: November 2008

We determine the stable decompositions of the classifying spaces of metacyclic 2-groups into wedges of indecomposable spectra. The stable decompositions of classifying spaces of finite groups with metacyclic 2-Sylow subgroups are also determined.
Full and reduced C*-coactions
Authors: Quigg John C.
Published: November 2008

Full and reduced C*-coactions are shown to be essentially equivalent as far as the representations and cocrossed products are concerned, at least in the presence of non-degeneracy. This is shown to be particularly true for a special class of full coactions which are given the name normal.
Extending finite group actions on surfaces to hyperbolic 3-manifolds
Authors: Gradolato Monique , Zimmermann Bruno
Published: November 2008

Let G be a finite group of orientation preserving isometrics of a closed orientable hyperbolic 2-manifold Fg of genus g > 1 (or equivalently, a finite group of conformal automorphisms of a closed Riemann surface). We say that the G-action on Fgbounds a hyperbolic 3-manifold M if M is a compact orientable hyperbolic 3-manifold with totally geodesic boundary Fg (as the only boundary component) such that the G-action on Fg extends to a G-action on M by isometrics. Symmetrically we will also say that the 3-manifold M bounds the given G-action. We are especially interested in Hurwitz actions, i.e. finite group actions on surfaces of maximal possible order 84(g — 1); the corresponding finite groups are called Hurwitz groups. First examples of bounding and non-bounding Hurwitz actions were given in [16].
Invariant domains and singularities
Authors: Bergweiler Walter
Published: November 2008

Let U be an invariant component of the Fatou set of an entire transcendental function f such that the iterates of f tend to ∞ in U. Let P(f) be the closure of the set of the forward orbits of all critical and asymptotic values of f. We show that there exists a sequence pn∈P(f) such that dist(pn, U) = o(|pn|), where dist(·, ·) denotes Euclidean distance. On the other hand, we give an example where dist (P(f), U) > 0. In this example, U is bounded by a Jordan curve.
Closed model categories for the n-type of spaces and simplicial sets
Authors: Elvira-Donazar Carmen , Hernandez-Paricio Luis-Javier
Published: November 2008

For each integer n ≥ 0, we give a distinct closed model category structure to the categories of spaces and of simplicial sets. Recall that a non-empty map is said to be a weak equivalence if it induces isomorphisms on the homotopy groups for any choice of base point. Putting the condition on dimensions ≥ n, we have the notion of a weak n-equivalence which is at the base of the nth closed model category structure given here.
Locally compact groups with closed subgroups open and p-adic
Authors: Hofmann Karl H. , Morris Sidney A. , Oates-Williams Sheila , Obraztsov V. N.
Published: November 2008

An open subgroup U of a topological group G is always closed, since U is the complement of the open set . An arbitrary closed subgroup C of G is almost never open, unless G belongs to a small family of exceptional groups. In fact, if G is a locally compact abelian group in which every non-trivial subgroup is open, then G is the additive group δp of p-adic integers or the additive group Ωp of p-adic rationale (cf. Robertson and Schreiber[5[, proposition 7). The fact that δp has interesting properties as a topological group has many roots. One is that its character group is the Prüfer group ℤp∞, which makes it unique inside the category of compact abelian groups. But even within the bigger class of not necessarily abelian compact groups the p-adic group δp is distinguished: it is the only one all of whose non-trivial subgroups are isomorphic (cf. Morris and Oates-Williams[2[), and it is also the only one all of whose non-trivial closed subgroups have finite index (cf. Morris, Oates-Williams and Thompson [3[).
Large deviations and overflow probabilities for the general single-server queue, with applications
Authors: Duffield N. G. , O'connell Neil
Published: November 2008

We consider queueing systems where the workload process is assumed to have an associated large deviation principle with arbitrary scaling: there exist increasing scaling functions (at, vt, t∈R+) and a rate function I such that if (Wt, t∈R+) denotes the workload process, then

on the continuity set of I. In the case that at = vt = t it has been argued heuristically, and recently proved in a fairly general context (for discrete time models) by Glynn and Whitt[8], that the queue-length distribution (that is, the distribution of supremum of the workload process Q = supt≥0Wt) decays exponentially:

and the decay rate δ is directly related to the rate function I. We establish conditions for a more general result to hold, where the scaling functions are not necessarily linear in t: we find that the queue-length distribution has an exponential tail only if limt→∞at/vt is finite and strictly positive; otherwise, provided our conditions are satisfied, the tail probabilities decay like
Extension of Jauch–Piron states on Jordan algebras
Authors: Bunce L. J. , Hamhalter J.
Published: November 2008

A state ρ on a JW-algebra or von Neumann algebra M is said to be a Jauch–Piron state if whenever e and f are projections in M with ρ(e) = ρ(f) = 0 then ρ(e ∨ f) = 0.
Traced monoidal categories
Authors: Joyal André , Street Ross , Verity Dominic
Published: November 2008

Traced monoidal categories are introduced, a structure theorem is proved for them, and an example is provided where the structure theorem has application.
A natural invariant algebra for the Harada-Norton group
Authors: Ryba A. J. E.
Published: November 2008

The Harada-Norton group is one of the twenty-six sporadic simple groups. It has order 273, 030, 912, 000, 000 = 214.36.56.7.11.19. In this paper our main objective is:

Theorem 1. The Harada-Norton group acts as a group of linear automorphisms of a 133-dimensional commutative, non-associative algebra defined over F5.
Representation of an element in SL(2, ,) as a short word in two generators
Authors: Bender Andreas
Published: November 2008

It is one of the first theorems proved in the theory of modular forms [1, p. 78] that every element in SL (2, ℤ), and hence in SL(2, ), can be written as a product of the two generators

While this is quite an easy result, it required more advanced tools such as spectral analysis on Riemann surfaces [2] to show that there is in fact always such a product of length O(log p). This result is not constructive and therefore immediately [2, p. 102] raises the following:

Problem. Is there an algorithm polynomial in log p for constructing a monomial in S and T, of degree O(log p), whose value is

In this note, we construct such an algorithm. We will carry out all the details only for the particular element

but it will become obvious that our method works for all elements in SL(2, ).
Invariant theory and Steenrod operations – maps between rings of invariants
Authors: Mahmud Zafer , Smith Larry
Published: November 2008

Let G ′, G ″ be finite groups and p ′: G ↪ GL(n ′,ℚ), p ″: G ″ ↪ GL(n ″, ℚ) faithful rational representations. If T: V′ = ℚn′ → ℚn″ = V ″ is a linear transformation and Ξ: G ′ → G ″ a function such that

then there are induced algebra homomorphisms ℚ[V ″] → ℚ[V ] and ℚ[V ″]G ″ → ℚ[V ′]G ′ making the diagram

commute. In this note we isolate the invariant theory portion of [1] and extend it to provide a necessary and sufficient condition that an algebra homomorphism between rings of invariants ℚ[V ″]G ″ → ℚ[V ′]G ′ arises in this way.
On braid monodromies of non-simple braided surfaces
Authors: Kamada Seiichi
Published: November 2008

A braided surface of degree m is a compact oriented surface S embedded in a bidisk such that is a branched covering map of degree m and , where is the projection. It was defined L. Rudolph [14, 16] with some applications to knot theory, cf. [13, 14, 15, 16, 17, 18]. A similar notion was defined O. Ya. Viro: A (closed) 2-dimensional braid in R4 is a closed oriented surface F embedded in R4 such that and pr2 │F: F → S2 is a branched covering map, where is the tubular neighbourhood of a standard 2-sphere in R4. It is related to 2-knot theory, cf. [8, 9, 10]. Braided surfaces and 2-dimensional braids are called simple if their associated branched covering maps are simple. Simple braided surfaces and simple 2-dimensional braids are investigated in some articles, [5, 8, 9, 14, 16], etc. This paper treats of non-simple braided surfaces in the piecewise linear category. For braided surfaces a natural weak equivalence relation, called braid ambient isotopy, appears essentially although it is not important for classical dimensionai braids Artin's argument [1].
On block Behrend sequences
Authors: Tenenbaum G.
Published: November 2008

Let A be a strictly increasing sequence of integers exceeding 1 and let

denote its set of multiples. We say that A is a Behrend sequence if M(A) has asymptotic density 1. The theory of sets of multiples was first developed in the late thirties, under the influence of Erdős, Besicovitch, and others. An account of the classical notions is presented in the book of Halberstam and Roth (1966), and recent progress in the area may be found in Hall and Tenenbaum [7], Erdős and Tenenbaum [4], Ruzsa and Tenenbaum [9]. As underlined by Erdős in [3], one of the central problems in the field is that of finding general criteria to decide whether a given sequence A is Behrend.
Artinian modules over commutative rings
Authors: Sharp R. Y.
Published: November 2008

In 5, I provided a method whereby the study of an Artinian module A over a commutative ring R (throughout the paper, R will denote a commutative ring with identity) can, for some purposes at least, be reduced to the study of an Artinian module A' over a complete (Noetherian) local ring; in the latter situation, Matlis' duality 1 (alternatively, see 6, ch. 5) is available, and this means that the investigation can often be converted into a dual one about a finitely generated module over a complete (Noetherian) local ring.
The dimension of self-affine fractals II
Authors: Falconer K. J.
Published: November 2008

A family {S1, ,Sk} of contracting affine transformations on Rn defines a unique non-empty compact set F satisfying . We obtain estimates for the Hausdorff and box-counting dimensions of such sets, and in particular derive an exact expression for the box-counting dimension in certain cases. These estimates are given in terms of the singular value functions of affine transformations associated with the Si. This paper is a sequel to 4, which presented a formula for the dimensions that was valid in almost all cases.
On the braid index of links with nested diagrams
Authors: Chalcraft D. A.
Published: November 2008

The number of Seifert circuits in a diagram of a link is well known 9 to be an upper bound for the braid index of the link. The -breadth of the so-called P-polynomial 3 of the link is known 5, 2 to give a lower bound. In this paper we consider a large class of links diagrams, including all diagrams where the interior of every Seifert circuit is empty. We show that either these bounds coincide, or else the upper bound is not sharp, and we obtain a very simple criterion for distinguishing these cases.
Local uniform and uniform convexity of non-commutative symmetric spaces of measurable operators
Authors: Chilin Vladimir I. , Krygin Andrei V. , Sukochev Pheodor A.
Published: November 2008

Let E be a separable symmetric sequence space, and let CE be the unitary matrix space associated with E, i.e. the Banach space of all compact operators x on l2 so that s(x) E, with the norm , where are the s-numbers of x. One of the interesting subjects in the theory of the unitary matrix spaces is the clarification of correlation between the geometric properties of the spaces E and CE. A series of results in this direction related with the notions of type, cotype and uniform convexity of the spaces CE has been already obtained (see 13).
Restriction implies Bochner–Riesz for paraboloids
Authors: Carbery Anthony
Published: November 2008

Let Σ ⊆ ℝn be a (compact) hypersurface with non-vanishing Gaussian curvature, with suitable parameterizations, also called Σ: U → ℝn (U open patches in ℝn−1). The restriction problem for Σ is the question of the a priori estimate (for f ∈ S(ℝ))

(^denoting the Fourier transform). The Bochner-Riesz problem for Σ is the question of whether the functions

define Lp-bounded Fourier multiplier operators on ℝn in the range

.
Kadec–Klee properties of vector-valued Hardy spaces
Authors: Dowling P. N. , Lennard C. J.
Published: November 2008

In 1930, S. Warschawski [19] showed that H1(D), where D is the open unit disc in ℂ, has the following property: Let be a sequence of functions in H1(D) converging uniformly on compact subsets of D to a function f∈H1(D) and suppose that ‖fn‖1 = |f‖1 = 1 for all n∈ℕ. Then converges to zero. From a Banach space standpoint, this result says that H1(D) has the Kadec–Klee property with respect to uniform convergence on compact subsets of D. Warschawski's result was proved independently by Newman [16] in 1963 (see also [13] for another proof) and extended to more general domains by Hoffman [12], Goldstein and Swaminathan [8] and Godefroy [7]. A uniform version of Warschawski's result and its subsequent extensions was recently obtained by Besbes, Dilworth, Dowling and Lennard [2] (see also [1]). We mention here that these results for H1 spaces also hold for the Hp-spaces for 1 < p < ∞ because these spaces are uniformly convex.
Transmutation theory and rank for quantum braided groups
Authors: Majid Shahn
Published: November 2008

Let f: H1 → H2be any pair of quasitriangular Hopf algebras over k with a Hopf algebra map f between them. We construct in this situation a quasitriangular Hopf algebra B(H1, f, H2) in the braided monoidal category of H1-modules. It consists in the same algebra as H2 with a modified comultiplication and has a quasitriangular structure given by the ratio of those of H1 and H2. This transmutation procedure trades a non-cocommutative Hopf algebra in the category of k-modules for a more cocommutative object in a more non-commutative category. As an application, every Hopf algebra containing the group algebra of ℤ2 becomes transmuted to a super-Hopf algebra.
On the cohomology of the sporadic simple group J4
Authors: Green David John
Published: November 2008

In this paper we calculate part of the integral cohomology ring of the sporadic simple group J4; this group has order 221.33.5.7. 113.23.29.31.37.43. More precisely, we obtain all of the cohomology ring except for the 2-primary part. As the cohomology has already been written down [9] at the primes which divide the group order only once, we concentrate here on the primes 3 and 11. In both of these cases the Sylow p-subgroups are extraspecial of order p3 and exponent p. We use the method which identifies the p-primary cohomology with the ring of stable classes in the cohomology of a Sylow p-subgroup. The stable classes are all invariant under the action of the Sylow p-normalizer; and some time is spent finding invariant classes in the cohomology ring of , the extraspecial group. Section 2 studies the prime 11: the invariant classes are the stable classes, because the Sylow 11-subgroups have the Trivial Intersection (T.I.) property. In Section 3 we study the prime 3, and see that all conditions for invariant classes to be stable reduce to one condition.
Combinatorial results for semigroups of order-preserving mappings
Authors: Higgins Peter M.
Published: November 2008

Consider the finite setXn= {1,2, …,n} ordered in the standard way. LetTndenote the full transformation semigroup onXn, that is, the semigroup of all mappings α:Xn→Xnunder composition. We shall call α order-preserving ifi≤jimpliesiα ≤jα fori,j∈Xn, and α is decreasing ifiα ≤ifor alli∈Xn. This paper investigates combinatorial properties of the semigroup O of all order-preserving mappings onXn, and of its subsemigroup C which consists of all decreasing and order-preserving mappings.
Simple singularities of space curves
Authors: Gibson C. G. , Hobbs C. A.
Published: November 2008

The genesis of this paper lies in theoretical questions in kinematics where a central role is played by naturally occurring families of rigid motions of 3-space. The resulting trajectories are parametrized families of space curves, and it is important to understand the generic singularities they can exhibit. For practical purposes one seeks to classify germs of space curves of fairly small Ae-codimension. It is however little harder to list the A-simple germs, which includes all germs of Ae-codimension ≤11: that then is the principal objective of this paper.
On free actions on Λ-trees
Authors: Urbański Mariusz , Zamboni Luca
Published: November 2008

In this paper we show that if a group generated by two elements acts freely and without phantom inversions on a Λ-tree, then it is either free or free abelian.
On epimorphisms of non-commutative rings
Authors: Knight J. T.
Published: November 2008

From a commutative ring A, Lazard(8) has made a flat injective epimorphism: A → B of commutative rings, such that if A → C is another flat injective epimorphism of commutative rings, then there is one and only one ring morphism: B → C such that the diagram

commutes; and he shows too that B → C is a flat injective epimorphism. The main aim of the present paper is to make a similar object for not necessarily commutative rings: this is achieved thanks to the notion of an A-prering, intermediate between that of an A-bimodule and that of an A-ring. In passing, prerings are also used to construct a kind of non-commutative ring of fractions.
On the relation of connective K-theory to homology
Authors: Smith Larry
Published: November 2008

Let us denote by k*( ) the homology theory determined by the connective BU spectrum, bu, that is, in the notations of (1) and (9), bu2n = BU(2n,…,∞), bu2n+1 = U(2n + 1,…, ∞) with the spectral maps induced via Bott periodicity. The resulting spectrum, bu, is a ring spectrum. Recall that k*(point) ≅ Z[t], degree t = 2. There is a natural transformation of ring spectra

inducing a morphism

of homology functors. It is the objective of this note to establish: Theorem. Let X be a finite complex. Then there is a natural exact sequence

where Z is viewed as a Z[t] module via the augmentation

and, is induced by η*in the natural way.
An elementary proof of the invertible powers theorem
Authors: Singer Michael
Published: November 2008

In this note we give a new, easy proof of the results on invertible powers of ideals that we established in (3). The deduction of the Dade–Taussky–Zassenhaus theorems (1) may be carried out as we did before in (3).
On the periods of the exponential and elliptic functions
Authors: Masser D. W.
Published: November 2008

Let ℘ be a Weierstrass elliptic function satisfying the differential equation

and let ζ(z) be the associated Weierstrass ζ-function satisfying (z) = −℘(z). Corresponding to a pair of fundamental periods ω1, ω2 of ℘(z), there is a pair of quasi-periods η1, η2 of ζ(z) defined by

and we have ηi = 2ζ(ωi/2) for i = 1, 2.
Averages of holomorphic mappings
Authors: Nestoridis V.
Published: November 2008

In this paper we present two versions in several variables of the following result:

Theorem 1([2, 3]). Let f be a function in the disc algebra (more generally in H1). Then for every point z0 in the open unit disc, there is an interval I on the unit circle T such that f(z0) = 1/|I| ∫Ifdσ, where 0 < |I| ≤ 2π denotes the length of I and σ the Lebesgue measure on T.
Disturbance produced in an elastic half-space by impulsive normal pressure
Authors: Mitra M.
Published: November 2008

1. Introduction. The disturbance produced in an elastic half-space by different types of buried sources have been studied by various authors. However, the only exact solutions of problems for the half-space in which the disturbance is produced by impulsive surface tractions are due to Pekeris (9) and Chao (4), though for the half-plane such problems have been studied by de Hoop (5), Ang (1) and Mitra (8). Pekeris (9) evaluated the surface displacement produced by a normal point load on the surface using a method of inversion of the operational solution developed earlier (Bateman & Pekeris (2)). A finite pressure-area, however, represents physical situations better than a point load. In this paper, the displacement produced in the half-space by uniform impulsive pressure acting over a circular portion of the surface has been obtained in terms of definite integrals. On the surface, the displacement has been split up into a number of terms some of which represent the P-wave contribution, while others give the Rayleigh-wave contribution to the displacement. The method of solution involves the use of integral transforms and Cagniard's (3) method; Pekeris's method is not applicable in this case since the appropriate transformation of an integral along the real axis to one along the imaginary axis cannot be carried out.
Note on the Invariants of the Canonical System of an Algebraic Variety
Authors: Todd J. A. , Maxwell E. A.
Published: November 2008

This note is concerned with the relations between the invariants Ωi (i = 0,1,…, d – 1) of the canonical system on an algebraic Vd. Here Ω0 is the grade of the canonical system, and Ωi is the virtual arithmetic genus of the Vi of intersection of d – i canonical Vd–1's.
Superconductors in Alternating Magnetic Fields
Authors: Shoenberg D.
Published: November 2008

A method of studying magnetic properties in alternating fields and its application to the intermediate state of a superconducting sphere are described. It is shown that the behaviour of the sphere in alternating fields of frequencies between 10 and 100 is different from that in very slowly varying fields, the difference becoming less for lower frequencies and for smaller radius. When the specimen is in the intermediate state, energy losses are produced in it by the alternating field, showing that the induced currents are out of phase with the alternating field. The induced currents do not, however, flow in the same way as in a homogeneous isotropic conductor, and this is probably on account of an anisotropic structure of the specimen when in the intermediate state. This structure depends strongly on the amplitude of the alternating field in such a way that the effective average conductivity is increased with decreasing amplitude, and this amplitude effect depends on the size of the specimen. Evidence is given for a time lag in the magnetocaloric effect, and this time lag decreases with decrease of the size of the specimen, being of order sec. for a sphere of about 1 cm. diameter.

In conclusion I wish to thank Prof. Lord Rutherford and Dr Cockcroft for their interest in this work; Dr Peierls for suggesting the experiment and for much valuable advice and assistance; Mr Shire for advice on some technical points; and various members of the staff of the Royal Society Mond Laboratory for help in the measurements.
Functional Pearls Two greedy algorithms
Authors: Bird R.S.
Published: November 2008

At the recent TC2 working conference on constructing programs from specifications (Moeller, 1991), I presented the derivation of a functional program for solving a problem posed by Knuth (1990). Slightly simplified, the problem was to construct a shortest decimal fraction representing a given integer multiple of 1/216. Later in the conference – and in a different context – Robert Dewar described a second problem that he had recently set as an examination question. In brief, the problem was to replace sequences of blanks in a file by tab characters wherever possible. Although Knuth's and Dewar's problems appear to have little in common, I suspected that both had the same ‘deep structure’ and were instances of a single general result about greedy algorithms. The purpose of this note is to bring the genral result to light and to unify the treatment of the two problems. We begin by describing the problems more precisely.
Theoretical Pearls:Representing ‘undefined’ in lambda calculus
Authors: Barendregt Henk
Published: November 2008

Let ψ be a partial recursive function (of one argument) with λ-defining termF∈Λ°. This meansThere are several proposals for whatF⌜n⌝ should be in case ψ(n) is undefined: (1) a term without a normal form (Church); (2) an unsolvable term (Barendregt); (3) an easy term (Visser); (4) a term of order 0 (Statman).

These four possibilities will be covered by one ‘master’ result of Statman which is based on the ‘Anti Diagonal Normalization Theorem’ of Visser (1980). That ingenious theorem about precomplete numerations of Ershov is a powerful tool with applications in recursion theory, metamathematics of arithmetic and lambda calculus.
Abstract interpretation by dynamic partitioning
Authors: Bourdoncle François
Published: November 2008

The essential part of abstract interpretation is to build a machine-representable abstract domain expressing interesting properties about the possible states reached by a program at runtime. Many techniques have been developed which assume that one knows in advance the class of properties that are of interest. There are cases however when there are no a priori indications about the 'best' abstract properties to use. We introduce a new framework that enables non-unique representations of abstract program properties to be used, and expose a method, called dynamic partitioning, that allows the dynamic determination of interesting abstract domains using data structures built over simpler domains. Finally, we show how dynamic partitioning can be used to compute non-trivial approximations of functions over infinite domains and give an application to the computation of minimal function graphs.
Using Miranda as a first programming language
Authors: Lambert Tim , Lindsay Peter , Robinson Ken
Published: November 2008

The functional programming language Miranda has been used as a first programming language at the University of NSW since the beginning of 1989, when a new computer engineering course and a revised computer science course were introduced. This paper explains the reasons for choosing the language, and describes the subject in which Miranda is introduced. Examples of the presentation of the material, and of exercises and assignment used in the course, are given. Finally, an assessment of the experience is given.
The virtues of eta-expansion
Authors: Jay C. Barry , Ghani Neil
Published: November 2008

Interpreting η-conversion as an expansion rule in the simply-typed λ-calculus maintains the confluence of reduction in a richer type structure. This use of expansions is supported by categorical models of reduction, where β-contraction, as the local counit, and η-expansion, as the local unit, are linked by local triangle laws. The latter form reduction loops, but strong normalization (to the long βη-normal forms) can be recovered by ‘cutting’ the loops.
The resource constrained shortest path problem implemented in a lazy functional language
Authors: Hartel Pieter H. , Glaser Hugh
Published: November 2008

The resource constrained shortest path problem is an NP-hard problem for which many ingenious algorithms have been developed. These algorithms are usually implemented in Fortran or another imperative programming language. We have implemented some of the simpler algorithms in a lazy functional language. Benefits accrue in the software engineering of the implementations. Our implementations have been applied to a standard benchmark of data files, which is available from the Operational Research Library of Imperial College, London. The performance of the lazy functional implementations, even with the comparatively simple algorithms that we have used, is competitive with a reference Fortran implementation.
Predictive parser combinators need four values to report errors
Authors: Partridge Andrew , Wright David
Published: November 2008

A combinator-based parser is a parser constructed directly from a BNF grammar, using higher-order functions (combinators) to model the alternative and sequencing operations of BNF. This paper describes a method for constructing parser combinators that can be used to build efficient predictive parsers which accurately report the cause of parsing errors. The method uses parsers that return values (parse trees or error indications) decorated with one of four tags.
A review of pseudospectral methods for solving partial differential equations
Authors: Fornberg Bengt , Sloan David M.
Published: November 2008

Finite Difference (FD) methods approximate derivatives of a function bylocalarguments (such as du(x) / dx≈ (u(x+h) −u(x−h))/2h, wherehis a small grid spacing) – these methods are typically designed to be exact for polynomials of low orders. This approach is very reasonable: since the derivative is a local property of a function, it makes little sense (and is costly) to invoke many function values far away from the point of interest.
Exact and approximate controllability for distributed parameter systems
Authors: Glowinski R. , Lions J.L.
Published: November 2008

We consider a system whose state is given by the solution y to a Partial Differential Equation (PDE) of evolution, and which contains control functions, denoted by v.
Particle Methods for the Boltzmann Equation
Authors: Neunzert Helmut , Struckmeier Jens
Published: November 2008

In the following chapters we will discuss particle methods for the numerical simulation of rarefied gas flows.

We will mainly treat a billiard game, that is, our particles will be hard spheres. But we will also touch upon cases where particles have internal energies due to rotation or vibration, which they exchange in a collision, and we will talk about chemical reactions happening during a collision.

Due to the limited size of this paper, we are only able to mention the principles of these real-gas effects. On the other hand, the general concepts of particle methods to be presented may be used for other kinds of kinetic equations, such as the semiconductor device simulation. We leave this part of the research to subsequent papers.
Monte Carlo and quasi-Monte Carlo methods
Authors: Caflisch Russel E.
Published: November 2008

Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N−1/2), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Carlo quadrature is attained using quasi-random (also called low-discrepancy) sequences, which are a deterministic alternative to random or pseudo-random sequences. The points in a quasi-random sequence are correlated to provide greater uniformity. The resulting quadrature method, called quasi-Monte Carlo, has a convergence rate of approximately O((logN)kN−1). For quasi-Monte Carlo, both theoretical error estimates and practical limitations are presented. Although the emphasis in this article is on integration, Monte Carlo simulation of rarefied gas dynamics is also discussed. In the limit of small mean free path (that is, the fluid dynamic limit), Monte Carlo loses its effectiveness because the collisional distance is much less than the fluid dynamic length scale. Computational examples are presented throughout the text to illustrate the theory. A number of open problems are described.
Numerical relativity: challenges for computational science
Authors: Cook Gregory B. , Teukolsky Saul A.
Published: November 2008

We describe the burgeoning field of numerical relativity, which aims to solve Einstein's equations of general relativity numerically. The field presents many questions that may interest numerical analysts, especially problems related to nonlinear partial differential equations: elliptic systems, hyperbolic systems, and mixed systems. There are many novel features, such as dealing with boundaries when black holes are excised from the computational domain, or how even to pose the problem computationally when the coordinates must be determined during the evolution from initial data. The most important unsolved problem is that there is no known general 3-dimensional algorithm that can evolve Einstein's equations with black holes that is stable. This review is meant to be an introduction that will enable numerical analysts and other computational scientists to enter the field. No previous knowledge of special or general relativity is assumed.
THE RACIAL VECTORS OF EMPIRE
Authors: Baldoz Rick
Published: November 2008

This paper examines the role of racial ideology in shaping U.S. colonial policy in the Philippines during the early years of American rule in the islands c. 1898–1905. The first section of the essay focuses on congressional debates between pro- and anti-imperialist lawmakers regarding the annexation and governance of the Philippines. The imperialist lobby advocated a paternalistic racial ideology to advance their case for American annexation, citing “the White man's burden” to civilize Filipinos as their rationale for colonizing the islands. The anti-imperialists, on the other hand, employed an ideology of aversive racism to oppose the incorporation of the Philippines, suggesting that annexation would unleash a flood of Filipino immigrants into the United States, thus creating a “race problem” for White citizens. Frequent unfavorable comparisons with Blacks, Chinese, and “Indians” were employed to produce racial knowledge about Filipinos who were unfamiliar to most Americans. This knowledge served as the basis for excluding Filipinos from American citizenship on racial grounds. The second section of the article traces the implementation of an institutionalized racial order in the Philippines, examining a series of population surveys conducted by colonial officials during the first years of American rule. These surveys employed American-style racial classifications that ranked and evaluated the various races and “tribes” that were identified in the islands. This project culminated in the first official census of the islands in 1905, which formally institutionalized racial categories as an organizing principle of Philippine society.