bluuebunny/crossref_metadata_2025 huggingface dataset:
On Λ-Ω-extendable distributions
Authors: Dierolf Peter
Published: November 2008

Let Λ ⊂ Ω ⊂ ℝnbe open subsets. We construct a natural space of test functions on Λ such that the dual consists exactly of those distributions on Λ which can be extended to distributions on Ω. As an application of this representation we calculate the space of multiplication operators on as well as the space of absolutely regular extendable distributions.
On convergence and quasiconformality of complex planar spline interpolants
Authors: Dikshit H. P. , Ojha A.
Published: November 2008

There appear to be two main approaches for developing complex splines. One of these, which has been in use for quite some time, consists in defining splines on the boundary of a given region which are then extended into the interior by Cauchy's integral formula (see e.g. [1]). The other approach, which is of a more recent origin, is motivated in spirit by the theory of finite elements (see e.g. [10], p. 320) and is contained in [8] and [9]. Observing that the foregoing extension into the interior is not easy to execute numerically, certain continuous piecewise non-holomorphic functions, called complex planar splines have been studied in [8] and [9]. The choice of non-holomorphic functions is justified, since if we take the pieces to be holomorphic functions like polynomials, then by the well known identity theorem ([5], p. 132, theorem 60) the continuity of such a piecewise function implies that all the pieces represent just one holomorphic function. Thus, we shall consider polynomials in z and its conjugate z¯ of the form

which are generally non-holomorphic functions. The number

will be called the degree of q. For simplicity we also write q(z) for q(z, z¯).
On square values of quadratics
Authors: Allison D.
Published: November 2008

Let N be a positive integer. We enquire whether there is a quadratic f(t)=at2 + bt + c, not identically square, which takes square values for N consecutive integers t. In [1] it was shown that this was possible, in what we shall call the symmetric case, if N = 8. A better treatment of this case appears here, together with a discussion of the nonsymmetric case, where we may take N = 7. There is no evidence that these are the best possible results.
On some Cauchy-separable integral equations
Authors: Porter D.
Published: November 2008

In a recent paper, Porter [9] devised two generalized Volterra operators which convert integral equations with the Hankel function kernel into Cauchy singular equations. The transformations were exploited in [9], and in a subsequent paper (Porter and Chu [10]), in relation to certain wave diffraction problems.
Quotients of groupoids by an action of a group
Authors: Taylor John
Published: November 2008

For any category A and group G there is a category AG of A-objects with G-action. An object of AG is an A-object A together with a group morphism, θA:G → Isom (A, A), of G into the group of invertible A-morphisms A → A. A morphism of AG is an A-morphism f: A → B which commutes with the G-action; that is, for each g∈G, the following diagram commutes.
Cayley graphs and group presentations
Authors: Thomas Richard M.
Published: November 2008

The aim of this paper is to prove the following result:

Theorem. Let G be the group defined by the presentation

where each ui is a word in the xj and , and suppose that there is a homomorphism σ such that the orders of the elements respectively. Let If G is finite, then α−d + 1 > 0 and .
Mal'cev H*-algebras
Authors: Cabrera-Garcia M. , Martinez-Moreno J. , Rodriguez-Palacios A.
Published: November 2008

The only finite-dimensional simple non-Lie Mal'cev complex algebra is given the structure of an H*-algebra and it is proved that this is the only topologically simple non-Lie Mal'cev H*-algebra.
Far field patterns and the inverse scattering problem for electromagnetic waves in an inhomogeneous medium
Authors: Colton David , Päivärinta Lassi
Published: November 2008

We consider the scattering of time harmonic electromagnetic waves by an inhomogeneous medium of compact support. It is first shown that the set of far field patterns of the electric fields corresponding to incident plane waves propagating in arbitrary directions is complete in the space of square-integrable tangential vector fields defined on the unit sphere. We then show that under certain conditions the electric far field patterns satisfy an integral identity involving the unique solution of a new class of boundary value problems for Maxwell's equations called the interior transmission problem for electromagnetic waves. Finally, it is indicated how this integral identity can be used to formulate an optimization scheme yielding an optimal solution of the inverse scattering problem for electromagnetic waves.
Partitioning projective planes into arcs
Authors: Kestenband Barbu C.
Published: November 2008

We show how to partition certain classes of finite projective planes into equicardinal arcs. Several partitions of this kind are to be found in the recent literature and they have aroused a certain amount of interest on two counts, as we shall shortly see.
Generalized pointwise symmetric Riemannian spaces: a classification
Authors: Marinosci R. A.
Published: November 2008

The theory of generalized symmetric spaces was begun by P. J. Graham and A. J. Ledger in 1967 in their paper [1]. Other authors who contributed to this topic were, e.g. F. Brickel, A. Deicke, A. S. Fedenko, A. Gray, V. G. Kac, M. Obata, B. Pettit, K. Sekigawa and J. Wolf; more recently also J. A. Jiménez, A. R. Razawi, C. Sánchez, M. Sekizawa, M. Toomanian, G. Tsagas and L. Vanhecke. A systematic exposition is given in the book by O. Kowalski[3, 4]. The author classifies all generalized symmetric Riemannian spaces in dimension n ≤ 5, using a systematic method.
Limit points for infinitely generated Fuchsian groups
Authors: Morosawa Shunsuke
Published: November 2008

Let D be the unit disc in the complex plane ℂ with centre 0 and let ∂D be its boundary. By Möb (D) we denote the group of all Möbius transformations which leave D invariant. A Fuchsian group G acting on D is a discrete subgroup of Möb (D). The limit set of G is in ∂D. We decompose ∂D into the following three disjoint sets:
Intersection properties of functions on cardinals
Authors: Gibbon Greg
Published: November 2008

A family of sets is said to possess property B if there is a set T such that A ∪ T ╪ ø and yet A ⊈ T for all sets A in . These two requirements may be restated in terms of the characteristic functions of the sets in as follows:
Star multigraphs with three vertices of maximum degree
Authors: Chetwynd A. G. , Hilton A. J. W.
Published: November 2008

The graphs we consider here are either simple graphs, that is they have no loops or multiple edges, or are multigraphs, that is they may have more than one edge joining a pair of vertices, but again have no loops. In particular we shall consider a special kind of multigraph, called a star-multigraph: this is a multigraph which contains a vertex v*, called the star-centre, which is incident with each non-simple edge. An edge-colouring of a multigraph G is a map ø: E(G)→, where is a set of colours and E(G) is the set of edges of G, such that no two edges receiving the same colour have a vertex in common. The chromatic index, or edge-chromatic numberχ′(G) of G is the least value of || for which an edge-colouring of G exists. Generalizing a well-known theorem of Vizing [14], we showed in [6] that, for a star-multigraph G,

where Δ(G) denotes the maximum degree (that is, the maximum number of edges incident with a vertex) of G. Star-multigraphs for which χ′(G) = Δ(G) are said to be Class 1, and otherwise they are Class 2.
Multiple points of singular maps
Authors: Szücs András
Published: November 2008

In 1979 at the Siegen Topology conference Peter Eccles in his lecture asked and in most cases answered the following

Question. For which values of n does an immersion of a closed n-dimensional manifold into Rn+1 exist with a single (n + 1)-tuple point?

The answer (see [3–5, 8]) implies the following:

Proposition (Eccles). No immersion of an even dimensional orientable manifold Mn into Rn+1 has a single (n + l)-tuple point.
On boundary-link cobordism
Authors: Mio Washington
Published: November 2008

An n-dimensional m-component link is an oriented smooth submanifold Σn of Sn+2, where is the ordered disjoint union of m submanifolds of Sn+2, each homeomorphic to Sn. Σ is a boundary link if there is an oriented smooth submanifold Vn+1 of Sn+1, the disjoint union of the submanifolds , such that ∂Vi = Σi (i = 1,…, m). A pair (Σ, V), where Σ is a boundary link and V as above, with each Vi connected (i = 1,…, m), is called an n-dimensional special Seifert pair. In this paper, we define a notion of cobordism of special Seifert pairs and give an algebraic description of the set (group) of cobordism classes.
Asymptotic estimates of the eigenvalues of certain positive Fredholm operators. II
Authors: Little G.
Published: November 2008

In a previous paper [1] we gave examples of positive integral operators on L2( − 1, 1) and estimates of their eigenvalues. In theorem 1 we treated operators with kernels of the form Σan sn tn, where (an) is a sequence of non-negative real numbers satisfying an ≃ α2n and 0 < α < 1 (here and throughout the notation an ≃ bn shall mean that an = O(bn) and bn = O(an)). In this paper we prove the more comprehensive Theorem 1 a below; theorem 1 of [1] is just the case b = 0. The term q(2α/(1 + α2)) will be explained immediately after the statement of the result.
Partitioning Euclidean space
Authors: Kunen Kenneth
Published: November 2008

R denotes the set of real numbers. For any finite n, Rn denotes n-dimensional space with the usual (Hilbert space) metric, d.
Cyclic homology and path algebra resolutions
Authors: Benson Dave
Published: November 2008

It follows from a theorem of Loday and Quillen (proposition 5·4 of [6]) that one may calculate the cyclic homology of an algebra in characteristic zero by taking a semisimplicial resolution by free algebras, quotienting out commutators and then taking homology of the resulting complex. In this paper we explain how this is a special case of a more general method based on resolutions by path algebras of directed graphs. The Loday–Quillen result may be seen as the case where the graph has only one vertex.
A note on Morita context functors
Authors: Zhou Borong
Published: November 2008

It is claimed in [3], proposition 4 that if a Morita context (R, V, W, S) is such that WVW = W and S/WV is flat as a right S-module, then Vω = 0, ω ∈ W, implies ω = 0. The proof given for this uses proposition 5 of Azumaya[l] in which rings have unity and so is only applicable when the ring S has a unity. Thus proposition 4 in [3] should be amended so that the additional hypothesis that S has a unity is imposed for statement (4) to be equivalent to the first three statements. It is the purpose of this note to give an example to show that the claim in [3] is false in general.
A note on stochastic integrators
Authors: Edwards D. A.
Published: November 2008

The object of this paper is to show that some important classes of stochastic processes can be proved to be stochastic integrators, in the sense of Bichteler[1], by entirely elementary methods. Let us recall what this means.
The t3, moves conjecture for oriented links with matched diagrams
Authors: Przytycki Józef H.
Published: November 2008

The local change in an oriented link diagram which replaces by k positive half-twists is called a tk move. For k even, the local change replacing by is called a tk move. For an unoriented diagram define a k-move, replacing by for any k. The following conjecture was stated in [14] and [10].
A Markov chain identity and monotonicity of the diffusion constants for a random walk in a heterogeneous environment
Authors: Roerdink J. B. T. M.
Published: November 2008

We consider a 2-dimensional square lattice which is partitioned into a periodic array of rectangular cells, on which a nearest neighbour random walk with symmetric increments is defined whose transition probabilities only depend on the relative position within a cell. On the basis of a determinantal identity proved in this paper, we obtain a result for finite Markov chains which shows that the diffusion constants for the random walk are monotonic functions of the individual transition probabilities. We point out the similarity of this monotonicity property to Rayleigh's Monotonicity Law for electric networks or, equivalently, reversible random walks.
A generalization of a theorem of Sharp on big Cohen-Macaulay modules
Authors: Zarzuela Santiago
Published: November 2008

Let (A, m) be a (commutative, Noetherian) local ring, and a1, …, an a system of parameters for A. Let M be an A-module. We say that M is a big Cohen-Macaulay module with respect to a1, …, an if a1, …, an, is an M-sequence. In this case we call M balanced if any system of parameters for A is an M-sequence.
Periodic orbits and fixed points of a C1 orientation-preserving embedding of D2
Authors: Gambaudo J. M.
Published: November 2008

We prove that any periodic orbit O of a C1 orientation-preserving embedding f of the 2-disc D2 is linked with a fixed point P in the sense that the corresponding periodic orbits {Φt(O)}t ≥ 0 and {Φt(P)}t ≥ 0 of any torus flow Φt suspending f are linked as knots in S3.
Selectionable distributions for a random set
Authors: Ross David
Published: November 2008

Artstein has given a characterization of the distributions induced by selections of a random compact subset of a complete separable metric space. In this paper, Artstein's results are extended to spaces which may be neither metric nor separable.
One-relator surface groups
Authors: Hempel John
Published: November 2008

For X a subset of a group G, the smallest normal subgroup of G which contains X is called the normal closure of X and is denoted by ngp (X; G) or simply by ngp (X) if there is no possibility of ambiguity. By a surface group we mean the fundamental group of a compact surface. We are interested in determining when a normal subgroup of a surface group contains a simple loop – the homotopy class of an embedding of S1 in the surface, or more generally, a power of a simple loop. This is significant to the study of 3-manifolds since a Heegaard splitting of a 3-manifold is reducible (cf. [2]) if and only if the kernel of the corresponding splitting homomorphism contains a simple loop. We give an answer in the case that the normal subgroup is the normal closure ngp (α) of a single element α: if ngp (α) contains a (power of a) simple loop β then α is homotopic to a (power of a) simple loop and β±1 is homotopic either to (a power of) α or to the commutator [α, γ] of a with some simple loop γ meeting a transversely in a single point. This implies that if a is not homotopic to a power of a simple loop, then the quotient map π1(S) → π1(S)/ngp (α) does not factor through a group with more than one end. In the process we show that π1(S)/ngp (α) is locally indicable if and only if α is not a proper power and that α always lifts to a simple loop in the covering space Sα of S corresponding to ngp (α). We also obtain some estimates on the minimal number of double points in certain homotopy classes of loops.
Characteristic classes of Galois representations
Authors: Kozlowski A.
Published: November 2008

Let K be a field with char if K≠2 and let Ks denote the separable closure of K and GK the Galois group of the extension Ks/K. If K⊂L is a finite extension and ρ:GL↦Or(R) a (continuous) real representation of GL we have a map ρ:BGL→BO which is used to define Stiefel–Whitney classes wi(ρ) = ρ*(wi). In general if f is any element of H*(BO; ℤ/2) we denote by f(ρ) the characteristic class ρ*(f). Now let

be a genus (see e.g. [9]), for example the total Stiefel–Whitney class w = 1+w1+w2 + … Let K⊂L and ρ be as above and let denote the multiplicative transfer (see e.g. [3, 5, 2, 14, 15]). Our principal result is a generalization of theorem 1 of [3]
A geometric characterization concerning compact, convex sets
Authors: Mulvey Christopher J. , Pelletier Joan Wick
Published: November 2008

In this paper, we are concerned with establishing a characterization of any compact, convex set K in a normed space A in an arbitrary topos with natural number object. The characterization is geometric, not in the sense of categorical logic, but in the intuitive one, of describing any compact, convex set K in terms of simpler sets in the normed space A. It is a characterization of the compact, convex set in the sense that it provides a necessary and sufficient condition for an element of the normed space to lie within it. Having said this, we should immediately qualify our statement by stressing that this is the intuitive content of what is proved; the formal statement of the characterization is required to be in terms appropriate to the constructive context of the techniques used.
A geometric proof that alternating knots are non-trivial
Authors: Menasco William , Thistlethwaite Morwen
Published: November 2008

There are many proofs in the literature of the non-triviality of alternating, classical links in the 3-sphere, but almost all use a combinatorial argument involving some algebraic invariant, namely the determinant [1], the Alexander polynomial [3], the Jones polynomial [5], and, in [6], the Q-polynomial of Brandt–Lickorish–Millett. Indeed, alternating links behave remarkably well with respect to these and other invariants, but this fact has not led to any significant geometric understanding of alternating link types. Therefore it is natural to seek purely geometric proofs of geometric properties of these links. Gabai has given in [4] a striking geometric proof of a related result, also proved earlier by algebraic means in [3], namely that the Seifert surface obtained from a reduced alternating link diagram by Seifert's algorithm has minimal genus for that link. Here, we give an elementary geometric proof of non-triviality of alternating knots, using a slight variation of the techniques set forth in [7, 8]. Note that if L is a link of more than one component and some component of L is spanned by a disk whose interior lies in the complement of L, then L is a split link, i.e. it is separated by a 2-sphere in S3\L; thus we do not consider alternating links of more than one component here, as it is proved in [7] that a connected alternating diagram cannot represent a split link.
On the asymptotic normality of self-normalized sums
Authors: Griffin Philip S. , Mason David M.
Published: November 2008

Let X1, …, Xn be a sequence of non-degenerate, symmetric, independent identically distributed random variables, and let Sn(rn) denote their sum when the rn largest in modulus have been removed. We obtain necessary and sufficient conditions for asymptotic normality of the studentized version of Sn(rn), and compare this to the condition for asymptotic normality of the scalar normalized version. In particular, when rn = r these conditions are the same, but when rn → ∞the former holds more generally.
Discontinuous homomorphisms from C*-algebras
Authors: Somerset D. W. B.
Published: November 2008

A necessary and sufficient condition is given for a unital C*-algebra A to admit a discontinuous homomorphism into a Banach algebra which is continuous on its centre. The condition is that A must have a Glimm ideal G such that the C*-algebra A/G admits a discontinuous homomorphism into a Banach algebra.
The representation of analytic multivalued functions by compact operators
Authors: White M. C.
Published: November 2008

In this paper we consider the problem of characterizing the variation of the spectrum of a holomorphic family of compact operators ƒ:G → KB(X), where G is an open subset of ℂ and X is a Banach space. The natural conjecture, which the author first heard in a lecture by Professor B. Aupetit, is that these spectra are characterized as those analytic multivalued functions which have as values null sequences. This is obviously a necessary condition, and we prove that this is also sufficient. It will be convenient to use the notation K(ℂ) for the set of compact non-empty subsets of the plane and K0(ℂ) for the subset of K(ℂ) consisting of null sequences.
Submersive second order ordinary differential equations
Authors: Kossowski Marek , Thompson Gerard
Published: November 2008

The objectives of this paper are to define and to characterize submersive second order ordinary differential equations (ODE) and to examine several situations in which such ODE occur. This definition and characterization is in terms of tangent bundle geometry as developed in [4, 6, 7, 10, 11, 14]. From this viewpoint second order ODE are identified with a special vector field on the tangent bundle. The ODE are said to be submersive when this vector field and the canonical vertical endomorphism [14] define a foliation, relative to which the vector field passes to the local quotient.
Lines, surfaces and duality
Authors: Bruce J. W.
Published: November 2008

In the paper [12] Shcherbak studied some duality properties of projective curves and applied them to obtain information concerning central projections of surfaces in projective three space. He also states some interesting results relating the contact of a generic surface with lines and the contact of its dual with lines in the dual space. In this paper we extend this duality to cover non-generic surfaces. Our proof is geometric, and uses deformation theory. The basic idea is the following. Given a surface X in projective 3-space we can consider the lines tangent to X, and measure their contact. The points on the surface with a line yielding at least 4-point contact are classically known as the flecnodal. (The reason is that the tangent plane meets the surface in a nodal curve, one branch of which has an inflexion at the point in question; see Proposition 7 below. The line in question is the inflexional tangent, which is clearly asymptotic.)
Dehn fillings of Klein bottle bundles
Authors: Heil Wolfgang , Raspopović Pedja
Published: November 2008

An important problem in the topology of 3-manifolds is to classify manifolds obtained by Dehn surgeries on a knot in a closed 3-manifold, or equivalently, Dehn fillings of a 3-manifold M with boundary a torus.
On radial basis approximation on periodic grids
Authors: Buhmann Martin D. , Micchelli Charles A.
Published: November 2008

A radial basis function approximation in n variables has the form

where ø:ℝn → ℝ denotes the n-variate, spherically symmetric function associated with a prescribed radial basis function ø+:ℝ+ → ℝ, i.e. ø = ø+(‖ · ‖), the norm being Euclidean. The are real coefficients (often, approximants s above are considered where only finitely many λjs are non-zero), and is a fixed set of points in ℝn (of course, only the xj with non-zero coefficient λj affect s). Thus s is a linear combination of translates of a radially symmetric function which can be of global support, the simplest choice being , where c is a positive parameter. The latter is referred to as the multiquadric function and is usefull in applications.
Isomorphic measures on compact groups
Authors: Grekas S.
Published: November 2008

This paper deals with the problem of point realizations of isomorphisms of measure algebras.
Global bitangency properties of generic closed space curves
Authors: Ballesteros Juan J. Nuño , Romero Fuster M. Carmen
Published: November 2008

We study bitangency properties of space curves in general position from a global viewpoint. As a consequence we obtain some results on their total numbers of bitangent osculating planes and cross tangents, and prove that in the absence of both, the number of zero torsion points of a curve in general position is a multiple 4.
Amenability of Lipschitz algebras
Authors: Gourdeau Frédéric
Published: November 2008

In this article, we study the amenability of Banach algebras in general, and that of Lipschitz algebras in particular. After introducing an alternative definition of amenability, we extend a result of [5], thereby proving a new characterization of amenability for Banach algebras. This characterization relates the amenability of a Banach algebra A to the space of bounded homomorphisms from A into another Banach algebra B (Theorem 4). This result allows us to solve the problem of amenability for virtually all Lipschitz algebras (of complex or Banach algebra valued functions), a class of algebras which has been studied in [2], [4] and [5].
The algebra of differential forms on a full matric bialgebra
Authors: Sudbery A.
Published: November 2008

We construct a non-commutative analogue of the algebra of differential forms on the space of endomorphisms of a vector space, given a non-commutative algebra of functions and differential forms on the vector space. The construction yields a differential bialgebra which is a skew product of an algebra of functions and an algebra of differential forms with constant coefficients. We give necessary and sufficient conditions for such an algebra to exist, show that it is uniquely determined by the differential algebra on the vector space, and show that it is a non-commutative superpolynomial algebra in the matrix elements and their differentials (i.e. that it has the same dimensions of homogeneous components as in the classical case).
The harmonic functions of (At, Bt,)
Authors: Rogers L. C. G.
Published: November 2008

The non-negative harmonic functions of a transient Markov process yield a great deal of information about the ‘behaviour at infinity’ of the process, and can be used to h-transform the process to behave in a certain way at infinity. The traditional analytic way of studying the non-negative harmonic functions is to construct the Martin boundary of the process (see, for example, Meyer [4], Kunita and T. Watanabe[3], and Kemeny, Snell & Knapp[2], Williams [7] for the chain case). However, certain conditions on the process need to be satisfied, one of the most basic of which is that there exists a reference measure η such that Uλ (x, ·) ≪ η for all λ > 0, all x ∈ E, the state space of the Markov process. (Here, (Uλ)λ>0 is the resolvent of the process.)
The class semigroup of orders in number fields
Authors: Zanardo P. , Zannier U.
Published: November 2008

Let R be a commutative domain, and let us denote by (R) the set of non-zero fractional ideals of R, which is a commutative semigroup under multiplication.
Corrigenda
Authors: Teragaito Masakazu
Published: November 2008

K. Motegi has kindly pointed out that the Lemma in Section 4 of the paper is incorrect. (The assertion in Case 1 on p. 95 that the sewing map of E(K) is periodic is false.) Hence Theorem 6 is unproven. However, we have a weaker result.
Subgroups and subrings of profinite rings
Authors: Abercrombie A. G.
Published: November 2008

A profinite topological group is compact and therefore possesses a unique invariant probability measure (Haar measure). We shall see that it is possible to define a fractional dimension on such a group in a canonical way, making use of Haar measure and a natural choice of invariant metric. This fractional dimension is analogous to Hausdorff dimension in ℝ.

It is therefore natural to ask to what extent known results concerning Hausdorff dimension in ℝ carry over to the profinite setting. In this paper, following a line of thought initiated by B. Volkmann in [12], we consider rings of a-adic integers and investigate the possible dimensions of their subgroups and subrings. We will find that for each prime p the ring of p-adic integers possesses subgroups of arbitrary dimension. This should cause little surprise since a similar result is known to hold in ℝ. However, we will also find that there exists a ring of a-adic integers possessing Borel subrings of arbitrary dimension. This is in contrast with the situation in ℝ, where the analogous statement is known to be false.
Minimal representation-infinite artin algebras
Authors: Skowroński Andrzej
Published: November 2008

Let A be an artin algebra over a commutative artin ring R, mod A be the category of finitely generated right A-modules, and rad∞ (modA) be the infinite power of the Jacobson radical rad(modA) of modA. Recall that A is said to be representation-finite if mod A admits only finitely many non-isomorphic indecomposable modules. It is known that A is representation-finite if and only if rad∞ (mod A) = 0. Moreover, from the validity of the First Brauer–Thrall Conjecture [26, 2] we know that A is representation-finite if and only if there is a common bound on the length of indecomposable modules in mod A.
Hyperbolic Weingarten surfaces
Authors: Van-Brunt B. , Grant K.
Published: November 2008

Weingarten surfaces which can be represented locally as solutions to second order hyperbolic partial differential equations are examined in this paper. In particular, the geometry of the families of curves corresponding to characteristics on these surfaces is investigated and the relationships of these curves with other curves on the surface such as asymptotic lines and lines of curvature are explored. It is shown that singularities in the lines of curvature, i.e. umbilic points, correspond to singularities in the families of characteristics, and that lines of curvature are non-characteristic curves. If there is a linear relation between the Gaussian and mean curvatures and real characteristics exist, then the characteristics form a Tchebychef net on the corresponding Weingarten surface.
Graphs with a locally linear group of automorphisms
Authors: Trofimov V. I. , Weiss R. M.
Published: November 2008

Let Γ be an undirected graph, V(Γ) the vertex set of Γ and G a subgroup of aut(Γ). For each vertex x ↦ V(Γ), let Γx denote the set of vertices adjacent to x in Γ and the permutation group induced on Γx. by the stabilizer Gx. For each i ≥ 1, will denote the pointwise stabilizer in Gx of the set of vertices at distance at most i from x in Γ. Let

for each i ≥ 1 and any set of vertices x, y, …, z of Γ. An s-path (or s-arc) is an (s + 1)-tuple (x0, x1, … xs) of vertices such that xi ↦ Γxi–1 for 1 ≤ i ≤ s and xi ╪ xi–2 for 2 ≤ i ≤ s.
Complexity and varieties for infinitely generated modules
Authors: Benson D. J. , Carlson Jon F. , Rickard J.
Published: November 2008

In the past fifteen years the theory of complexity and varieties of modules has become a standard tool in the modular representation theory of finite groups. Moreover the techniques have been used in the study of integral representations [8] and have been extended to the representation theories of objects such as groups of finite virtual cohomological dimension [1], infinitesimal subgroups of algebraic groups and restricted Lie algebras [14, 16]. In all cases some sort of finiteness condition on the module category has been required to make the theory work. Usually this comes in the form of stipulating that all modules under consideration be finitely generated. While the restrictions have been efficient for most applications to date, there are very good reasons for wanting to develop a theory that will accommodate infinitely generated modules. One reason might be the possibility of extending the techniques of representations to other classes of infinite groups. Another reason is that some recent work has revealed a few of the defects of the finiteness requirement. One such problem can be summarized as follows.
An oscillation theorem for self-adjoint differential systems and an index result for corresponding Riccati matrix differential equations
Authors: Kratz Werner
Published: November 2008

The main result of this paper is an oscillation theorem on linear self-adjoint differential systems and a corresponding eigenvalue problem. It establishes a formula between the number of focal points of a so-called conjoined basis of the differential system on a given compact interval and the number of eigenvalues which are less than the given eigenvalue parameter. It extends an earlier result of the author and generalizes an oscillation theorem of M. Morse. Among others the proof of the theorem requires a formula on the index of the difference of symmetric solutions of a corresponding Riccati matrix differential equation. This index formula is the other new result presented.
Global properties of locally spatially homogeneous cosmological models with matter
Authors: Rendall Alan D.
Published: November 2008

The existence and nature of singularities in locally spatially homogeneous solutions of the Einstein equations coupled to various phenoraenological matter models is investigated. It is shown that, under certain reasonable assumptions on the matter, there are no singularities in an expanding phase of the evolution and that unless the spacetime is empty a contracting phase always ends in a singularity where at least one scalar invariant of the curvature diverges uniformly. The class of matter models treated includes perfect fluids, mixtures of non-interacting perfect fluids and collisionless matter.
Projection theorems for box and packing dimensions
Authors: Falconer K. J. , Howroyd J. D.
Published: November 2008

We show that if E is an analytic subset of ℝn then

for almost all m–dimensional subspaces V of ℝn, where projvE is the orthogonal projection of E onto V and dimp denotes packing dimension. The same inequality holds for lower and upper box counting dimensions, and these inequalities are the best possible ones.
Cosmological solutions of the Vlasov-Einstein system with spherical, plane, and hyperbolic symmetry
Authors: Rein Gerhard
Published: November 2008

The Vlasov-Einstein system describes a self-gravitating, collisionless gas within the framework of general relativity. We investigate the initial value problem in a cosmological setting with spherical, plane, or hyperbolic symmetry and prove that for small initial data solutions exist up to a spacetime singularity which is a curvature and a crushing singularity. An important tool in the analysis is a local existence result with a continuation criterion saying that solutions can be extended as long as the momenta in the support of the phase-space distribution of the matter remain bounded.
On the lengths of Koszul homology modules and generalized fractions
Authors: Cuong N. T. , Minh N. D.
Published: November 2008

Throughout this paper, let A be a Noetherian local ring with maximal ideal m and M a finitely generated A-module with d = dimAM ≥ 1. Denote by N the set of all positive integers.

Let x = (x1, …, xd) be a system of parameters (s.o.p) for M and let

We consider the following two problems: (i) When is the length of Koszul homology

a polynomial in n for all k = 0, …, d and n1; …, nd sufficiently large (n ≫ 0)?

(ii) Is the length of the generalized fraction in a polynomial in n for n ≫ 0?
A characterization of generalized Hughes complexes
Authors: Sharp R. Y. , Tousi M.
Published: November 2008

While trying to place the grade-theoretic analogue of the Cousin complex (for a commutative Noetherian ring A) of K. R. Hughes [7], and the complexes of modules of generalized fractions studied by the first author and H. Zakeri[18], and by L. O'Carroll [10, p. 420], on a similar footing, Sharp and M. Yassi[15] introduced the concept of generalized Hughes complex. Such complexes are described as follows.
On the homotopy theory of sheaves of simplicial groupoids
Authors: Joyal André , Tierney Myles
Published: November 2008

The aim of this paper is to contribute to the foundations of homotopy theory for simplicial sheaves, as we believe this is the natural context for the development of non-abelian, as well as extraordinary, sheaf cohomology.

In [11] we began constructing a theory of classifying spaces for sheaves of simplicial groupoids, and that study is continued here. Such a theory is essential for the development of basic tools such as Postnikov systems, Atiyah-Hirzebruch spectral sequences, characteristic classes, and cohomology operations in extraordinary cohomology of sheaves. Thus, in some sense, we are continuing the program initiated by Illusie[7], Brown[2], and Brown and Gersten[3], though our basic homotopy theory of simplicial sheaves is different from theirs. In fact, the homotopy theory we use is the global one of [10]. As a result, there is some similarity between our theory and the theory of Jardine[8], which is also partially based on [10]
A note on iterative arguments in a topos
Authors: Vermeulen J. J. C.
Published: November 2008

Intuitively, transfinite iteration is a repetitive process, which eventually reaches completion, but might need to progress through an infinite chain of steps before finally doing so. But whereas such a chain is always readily at hand in classical set theory in the form of ordinals, iterative arguments involving sets (i.e. objects) in a general topos have to depend on some intrinsic or naturally available inductive structure, say algebraic, which might not be associated with a (well-ordered) chain.
Spaces of functions determined by iterated limits at infinity on an oid
Authors: Aminpour A. M.
Published: November 2008

In recent years many mathematicians have studied the semigroups S, the Stone-ech compactification of the discrete semigroup S, and more particularly ℕ, where ℕ is the usual semigroup of positive integers with addition (see the surveys by Hindman and Pym 6). An important role in this theory is played by sequences in S which have distinct finite sums, for these sequences are closely linked to idempotents in S (see the survey by Hindman 6). Pym 8 introduced the concept of an oid in order to show that the structure of ℕ in 5 could be obtained in a simple way for a large class of semigroups. Papazyan 7 pointed out that the theories of sequences with distinct finite sums and of oids are the same. Thus oids have a central position in the theory of semigroup compactifications.
Invariant states and ergodic dynamical systems on W*-algebras
Authors: uczak Andrzej
Published: November 2008

An amenable semigroup of positive linear unital mappings on a W*-algebra is considered. Two main questions are dealt with: the existence of a normal faithful state invariant with respect to this semigroup and the description of ergodicity conditions. An explicit form of the ergodic projection, useful in treating the ergodicity problems, is also derived.
Strongly torsion generated groups
Authors: Berrick A. J. , Miller C. F.
Published: November 2008

It has long been known that the integral homology of a non-trivial finite group must be non-zero in infinitely many dimensions 17. Recent work on the Sullivan conjecture in homotopy theory has made it possible to extend this result to locally finite groups. For more general groups with torsion it becomes more difficult to make such a strong statement. Nevertheless we prove that when a non-perfect group is generated by torsion elements its integral homology must also be non-zero in infinitely many dimensions. Remarkably, this result is best possible, in that for perfect torsion generated groups all (finite or infinite) sequences of abelian groups are shown below to be attainable as higher homology groups.
On various types of convergence of positive definite functions on foundation semigroups
Authors: Lashkarizadeh-Bami M.
Published: November 2008

As is known, on a locally compact groupG, the mere assumption of pointwise convergence of a sequence (n) of continuous positive definite functions implies uniform convergence of (n) to on compact subsets ofG. This result was first proved in 1947 by Raikov8 (and independently by Yoshizawa9). An interesting discussion of the relationship between such theorems and various Cramr-Lvy theorems of the 1920s and 1930s, concerning the Central Limit Problem of probability, is given by McKennon(7, p. 62).
Roll-spun knots
Authors: Teragaito Masakazu
Published: November 2008

In this paper we will study 2-knots in the 4-sphere S4 which are obtained by roll-spinning 1-knots in the 3-sphere S3. The process of spinning was introduced by Artin[2] and generalized to twist-spinning by Fox [7] and Zeeman [20]. In [7] Fox introduced another variation of the spinning process, called roll-spinning. He only showed that the roll-spun figure-eight knot cannot be obtained by twist-spinning the figure-eight knot. Finally Litherland [14] described the general process of deform-spinning, and he gave a precise definition of roll-spinning. We remark that Fox's roll-spinning is not the same as Litherland's: Fox's roll-spun figure-eight knot is the symmetry-spun figure-eight knot in terms of [14].
Semi-Fredholm perturbations and commutators
Authors: Mbekhta Mostafa
Published: November 2008

The Laffey–West theorem concerning finite rank perturbations of bounded Fredholm operators is extended to closed densely defined operators on Banach Spaces.
Geometric characterization of separable second-order differential equations
Authors: Martínez Eduardo , Cariñena José F. , Sarlet Willy
Published: November 2008

We establish necessary and sufficient conditions for the separability of a system of second-order differential equations into independent one-dimensional second-order equations. The characterization of this property is given in terms of geometrical objects which are directly related to the system and relatively easy to compute. The proof of the main theorem is constructive and thus yields a practical procedure for constructing coordinates in which the system decouples.
h-cobordisms of pairs
Authors: Gordon C. McA.
Published: November 2008

LetMandQbe closed manifolds, and write ℝ+= [0, ∞). Our main result is that, in both the PL and topological categories,M× ℝ+unknots in Q × ℝ+in codimension ≥ 3 (see Theorem 1 for a precise statement). The proof is essentially a generalization of Stallings's topological unknotting of spheres(13), the main tool being engulfing.
A note on Subalgebras of co-dimension 1
Authors: Rennison J. F.
Published: November 2008

Sawon and Warzecha established in (2) the general form of a subalgebra of codimension 1 in a commutative Banach algebra with identity. A short and elegant proof of their result was later given by Detraz in(1). This note is intended to show that an even more elementary proof is possible and which has the advantage that no use is made of the existence of maximal ideals.
An application of the theory of regenerative phenomena
Authors: Kingman J. F. C.
Published: November 2008

One of the classical models of applied probability is that which may be described as the covering of a line with a random collection of intervals of random length. It appears as such in ((9), pp. 23–25), but also as the problem of Type II counters with random dead time (1, 4, 10), as a model for a pedestrian crossing a busy road(5), and as the queue M/G/∞. If an excuse is required for returning to a problem which has been the object of so much research in the past, it is to be found in the fact, noted by Kendall (5), that the model gives rise to the general stable infinitely divisible p-function, and that the theory of the semigroup P of standard p-functions (6) requires deeper information than previous, practically motivated, studies have provided.
An inequality for Mill's ratio for the type III population
Authors: Nath G. Baikunth
Published: November 2008

Mills(7), Gordon(5), Birnbaum(1), and the author(6) have studied the ratio of the area of the standardized normal curve from x to ∞ and the ordinate at x. Des Raj (4) established the monotonic character of, and obtained lower and upper bounds for this ratio for the standardized type III population. This ratio, as shown by Cohen (2) and Des Raj (3), has to be calculated for several values of x when solving approximately the equations involved in the problem of estimating the para-meters of type III populations from truncated samples. When the areas and ordinates are small, either this ratio cannot be obtained from existing tables prepared by Salvosa(8) or that very few significant digits are available for its calculation. The object of this note is to obtain an upper bound which could satisfactorily locate this ratio over the range x > −1.
Comments on Wang's paper
Authors: Shanbhag D. N.
Published: November 2008

Recently Wang (5) has given some results concerning characterizations of Poisson, normal, gamma, binomial and negative binomial distributions. We shall show here that these results are incorrect and also attempt to rectify them.
On the propagation of disturbances in a laminar boundary layer. I
Authors: Brown S. N. , Stewartson K.
Published: November 2008

An analysis is made of the response of a laminar boundary layer to a perturbation, either in the mainstream, or of the boundary conditions at the wall. The disturbance propagates with the mainstream velocity, and the manner in which it decays at large distances downstream is determined by eigensolutions of the boundary-layer equations. The elucidation of the structure of these eigensolutions requires division of the boundary layer into three regions. Comparison of the asymptotic formula obtained for the displacement thickness is made with the numerical results of Ackerberg and Phillips (1).
On the Elastic Stability of a Rectangular Plate, when Subjected to a Variable Edge Thrust
Authors: Leggett D. M. A.
Published: November 2008

The stability of a rectangular plate, subjected to constant thrust over opposite pairs of edges, has been treated with some degree of completeness for various boundary conditions. The more general problem, in which the thrusts are no longer constant, has not yet received any treatment apart from the approximate method developed by E. Schwerin†, which would appear to be capable of only limited extension. The object of this paper is accordingly the detailed consideration of a simple case when the thrust is no longer constant.
Some Properties of Dipole and Quadripole Radiation from Nuclei
Authors: Taylor H. M.
Published: November 2008

1. The purpose of this paper is to examine in detail the types of radiation emitted by a quantum mechanical system (representing a nucleus) when the radiating particle changes its azimuthal quantum number l by two, one, or nought. We assume that the radiating particle is spinless* and that it moves in a field possessing central symmetry, so that the particle may be described by a wave function ψn,l,m which factorizes into radial and angular parts,

We assume secondly that the nucleus has a finite radius aN of the order of 10−12 cm., that is to say that π(r) = 0 for r > aN.
On the Theory of Ionic Recombination: A Correction
Authors: Harper W. R.
Published: November 2008

In previous communications* the author has discussed the recombination of gaseous ions, subsequently extending the theory to include large ions† and also to apply to the coagulation of colloids and of smokes‡. The predictions of the original theory were in excellent agreement with experiment, but discrepancies appeared when it was generalized. The author is now indebted to Dr F. J. W. Whipple for the discovery of a numerical error in the first paper, the correction of which leads on the whole to a much more satisfactory agreement with experiment.
Functional programming for business students
Authors: Molyneux Phil
Published: November 2008

A functional language, Miranda, is being used on an introductory programming course for business students. This paper describes the rationale for such a course and choice of language. An application in the area of operations management, which is used in teaching, is given as an example of the benefits of using a functional language in this area. The reaction of the students and staff to this (for them) new paradigm of programming is described. Some conclusions are drawn for computing education for non-specialists.
Improving intervals
Authors: Jackson W. Ken , Burton F. Warren
Published: November 2008

We show how improving values (Burton, 1991) can be extended to handle both upper and lower bounds. The result is a new data type, called improving intervals. We give a simple implementation of improving intervals that uses a list of successively tighter bounds to represent a value. A program using improving intervals can be evaluated as a parallel program using speculative evaluation. The utility of improving intervals is demonstrated through two programs: parallel alpha-beta and parallel branch-and-bound