bluuebunny/crossref_metadata_2025 huggingface dataset:
Finite generation of equivariant cohomology for a p-compact group G
Authors: Lee Hyang-Sook
Published: April 2009

For a p-compact group G and G-space X, we prove the finite generation of the equivariant cohomology and give the form of the Poincaré series of .
Fatou-Julia theory on transcendental semigroups
Authors: Poon Kin-Keung
Published: April 2009

In this paper, we shall study the dynamics on transcendental semigroups. Several properties of Fatou and Julia sets of transcendental semigroups will be explored. Moreover, we shall investigate some properties of Abelian transcendental semigroups and wandering domains of transcendental semigroups.
Heron triangles and elliptic curves
Authors: Buchholz Ralph H. , Rathbun Randall L.
Published: April 2009

In this paper we present a proof that there exist infinitely many rational sided triangles with two rational medians and rational area. These triangles correspond to rational points on an elliptic curve of rank one. We also display three triangles (one previously unpublished) which do not belong to any of the known infinite families.
Coordinates of the representation space in the semisimple Lie group of rank one
Authors: Kim Inkang
Published: April 2009

In this paper we show that the space of irreducible representations from a finitely presented group into the group of isometries of a rank one symmetric space of non-compact type, embeds into ℝn for some n, where the coordinates are the translation lengths of isometries in the representation. The ingredients of the proof consist of the two facts that the representation is determined by its marked length spectrum and that the nested sequence of algebraic subvarieties is stabilised at a finite step by the Noetherian property of the polynomial ring. As a minor application, we use this fact to simplify McMullen's proof about the exponential algebraic convergence of Thurston's double limit to the geometrically infinite manifold in the space of discrete faithful representations of π1(S) in Iso+.
Annular Dehn functions of groups
Authors: Brick Stephen G. , Corson Jon M.
Published: April 2009

For a finite presentation of a group, or more generally, a two-complex, we define a function analogous to the Dehn function that we call the annular Dehn function. This function measures the combinatorial area of maps of annuli into the complex as a function of the lengths of the boundary curves. A finitely presented group has solvable conjugacy problem if and only if its annular Dehn function is recursive.

As with standard Dehn functions, the annular Dehn function may change with change of presentation. We prove that the type of function obtained is preserved by change of presentation. Further we obtain upper bounds for the annular Dehn functions of free products and, more generally, amalgamations or HNN extensions over finite subgroups.
Proofs of some hyperelliptic function identities
Authors: Hirschhorn Michael D.
Published: April 2009

We give simple direct proofs of some hyperelliptic function identities conjectured by R.J. Baxter which arose in his study of the chiral Potts model.
On the Schur multiplier of a quotient of a direct product of groups
Authors: Ellis Graham
Published: April 2009

We use a nonabelian exterior product to strengthen two old and basic results on the Schur multiplier of a (central) quotient of a direct product of groups.
Nontrivial rational polynomials in two variables have reducible fibres
Authors: Neumann Walter D. , Norbury Paul
Published: April 2009

We show that every f: ℂ2 → ℂ which is a rational polynomial map with irreducible fibres is a coordinate.
Dynamics of homeomorphisms on minimal sets generated by triangular mappings
Authors: Forti Gian Luigi , Paganoni Luigi , Smítal Jaroslav
Published: April 2009

The main goal of the paper is the construction of a triangular mapping F of the square with zero topological entropy, possessing a minimal set M such that F|M is a strongly chaotic homeomorphism, as well as other properties that are impossible for continuous maps on an interval.

To do this we define a parametric class of triangular maps on Q × I, where Q is an infinite minimal set on the interval, which are extendable to continuous triangular maps F: I2 → I2. This class can be used to create other examples.
Shin's formulas for Eigenpairs of symmetric tridiagonal 2-Toeplitz matrices
Authors: Ikramov Khakim D.
Published: April 2009

A relationship is pointed out between the results in a recent paper of Shin's and those in a previously published paper by M.J.C. Gover.
Twisted Hilbert spaces
Authors: Sánchez Félix Cabello
Published: April 2009

A Banach space X is called a twisted sum of the Banach spaces Y and Z if it has a subspace isomorphic to Y such that the corresponding quotient is isomorphic to Z. A twisted Hilbert space is a twisted sum of Hilbert spaces. We prove the following tongue-twister: there exists a twisted sum of two subspaces of a twisted Hilbert space that is not isomorphic to a subspace of a twisted Hilbert space. In other words, being a subspace of a twisted Hilbert space is not a three-space property.
Heron quadrilaterals with sides in arithmetic or geometric progression
Authors: Buchholz R.H. , MacDougall J.A.
Published: April 2009

We study triangles and cyclic quadrilaterals which have rational area and whose sides form geometric or arithmetic progressions. A complete characterisation is given for the infinite family of triangles with sides in arithmetic progression. We show that there are no triangles with sides in geometric progression. We also show that apart from the square there are no cyclic quadrilaterals whose sides form either a geometric or an arithmetic progression. The solution of both quadrilateral cases involves searching for rational points on certain elliptic curves.
Coincidences and fixed points in locally G-convex spaces
Authors: Watson P.J.
Published: April 2009

A new coincidence point theorem is proved for a pair of multivalued mappings operating between G-convex spaces. From this theorem, a generalisation of the classical Fan-Glicksberg fixed point theorem is established.
Linear isometries between spaces of functions of bounded variation
Authors: Araujo Jesuś
Published: April 2009

Given two subsets X and Y of ℝ each with at least two points, we describe the surjective linear isometries between the spaces of functions of bounded variation BV(X) and BV(Y): namely, if T : BV(X) → BV(Y) is such an isometry, then there exist α ∈ ℂ, |α| = 1, and a monotonic bijective map h : Y → X such that (Tf)(y) = αf(h(y)) for every f ∈ BV(X) and every y ∈ Y.
Lipschitz continuity of spectral measures
Authors: Ricker Werner J.
Published: April 2009

A characterisation is given of all (finitely additive) spectral measures in a Banach space (and defined on an algebra of sets) which satisfy a Lipschitz condition. This also corrects (slightly) an analogous result in the more specialised setting of resolutions of the identity of scalar-type spectral operators (due to C.A. McCarthy).
Optimal weighted estimates for the Cauchy-Riemann equation on analytic polyhedra
Authors: Cho Hong Rae , Lee Jinkee
Published: April 2009

Andersson obtained weighted Lp estimates for on analytic polyhedra. We provide an example to show why they cannot be improved.
A note on Jeśmanowicz' conjecture concerning Pythagorean triples
Authors: Le Maohua
Published: April 2009

Let n be a positive integer, and let (a, b, c) be a primitive Pythagorean triple. In this paper we give certain conditions for the equation (an)x + (bn)y = (cn)z to have positive integer solutions (x, y, z) with (x, y, z) ≠ (2, 2, 2). In particular, we show that x, y and z must be distinct.
An Euler-type volume identity
Authors: Callahan Kevin , Hann Kathy
Published: April 2009

In this paper we present an elementary proof of a congruence by subtraction relation. In order to prove congruence by subtraction, we produce a dissection relating equal sub-polytopes. An immediate consequence of this relation is an Euler-type volume identity in ℝ3 which appeared in the Unsolved Problems section of the December 1996 MAA Monthly.

This Euler-type volume identity relates the volumes of subsets of a polytope called wedges that correspond to its faces, edges, and vertices. A wedge consists of the inward normal chords of the polytope emanating from a face, vertex, or edge. This identity is stated in the theorem below.

Euler Volume Theorem. For any three dimensional convex polytope P

This identity follows immediately from
A note on cohomology over non algebraically closed fields
Authors: Gamboa J.M.
Published: April 2009

We characterise algebraically closed fields as those for which the first cohomology group H1(kn, On) of the sheaf On of regular functions over kn vanishes for all positive intergers n.
Quasi-projectivity over domains
Authors: Alexeev Dmitri
Published: April 2009

Let R be an integral domain with quotient field Q. We investigate quasi- and Q-projective ideals, and properties of domains all ideals of which are quasi-projective. It is shown that the so-called l½-generated ideals are quasi-projective, moreover, projective. A module M is quasi-projective if and only if, for a projective ideal P of R, the tensor product M ⊗RP is quasi-projective. Domains whose all ideals are quasi-projective are characterised as almost maximal Prüfer domains. Q is quasi-projective if and only if every proper submodule of Q is complete in its R-topology.
Irreducible decomposition of the Magnus representation of the Torelli group
Authors: Suzuki Masaaki
Published: April 2009

In this paper we describe the irreducible decomposition of the Magnus representation of the Torelli group.
Continuous inverse shadowing and hyperbolicity
Authors: Lee Keonhee
Published: April 2009

We study the concepts of continuous shadowing and continuous inverse shadowing with respect to various classes of admissible pseudo orbits, and characterize hyperbolicity and structural stability using the notion of continuous inverse shadowing.
C-totally real submanifolds in (κ,μ)-contact space forms
Authors: Tripathi Mukut Mani , Kim Jeong-Sik
Published: April 2009

We obtain a basic B,-Y. Chen's inequality for a C-totally real submanifold in a (κ,μ)-contact space form involving intrinsic invariants, namely the scalar curvature and the sectional curvatures of the submanifold on left hand side and the main extrinsic invariant, namely the squared mean curvature on the right hand side. Inequalities between the squared mean curvature and Ricci curvature and between the squared mean curvature and κ-Ricci curvature are also obtained. These results are applied to get corresponding results for C-totally real submanifolds in a Sasakian space form.
Geodesic uniqueness and derivatives of Bers projection
Authors: Guo Hui
Published: April 2009

In this paper, we discover a sufficient and necessary condition under which two geodesic segments joining the base point and another point in an infinite-dimensional Teichmüller space are the same.
On the normaliser problem for G-adapted group rings of torsion groups
Authors: Li Yuanlin
Published: April 2009

In this note, we prove that if a torsion group G has an Abelian subgroup B such that G/B is Abelian and R is a G-adapted ring with the property that R (G/B) has only trivial units then G has the normaliser property in RG.
The effect of the dual on a Banach space and the weak fixed point propery
Authors: Dalby Tim
Published: April 2009

A number of Banach space properties have been shown to imply the weak fixed point property. If the dual of a Banach space were to possess some of these properties then the original space can been shown to satisfy related conditions.
Gaussian bounds for complex subelliptic operators on Lie groups of polynomial growth
Authors: Ter Elst A. F. M. , Robinson Derek W.
Published: April 2009

We prove large time Gaussian bounds for the semigroup kernels associated with complex, second-order, subelliptic operators on Lie groups of polynomial growth.
Generalised Jordan-von Neumann constants and uniform normal structure
Authors: Dhompongsa S. , Piraisangjun P. , Saejung S.
Published: April 2009

We introduce a new geometric coefficient related to the Jordan-von Neumann constant. This leads to improved versions of known results and yields new ones on super-normal structure for Banach spaces.
Sharp bounds of Čebyšev functional for Stieltjes integrals and applications
Authors: Dragomir S. S.
Published: April 2009

Sharp bounds of the Čebyšev functional for the Stieltjes integrals similar to the Grüss one and applications for quadrature rules are given.
Boolean algebras of projections in (DF)-and (LF)-spaces
Authors: Bonet J. , Ricker W. J.
Published: April 2009

Conditions are presented which ensure that an abstractly σ-complete Boolean algebra of projections on a (DF)-space or on an (LF)-space is necessarily equicontinuous and/or the range of a spectral measure. This is an extension, to a large and important class of locally convex spaces, of similar and well known results due to W. Bade (respectively, B. Walsh) in the setting of normed (respectively metrisable) spaces.
On metric regularity in metric spaces
Authors: Gautier Serge , Pichard Karine
Published: April 2009

We prove metric regularity results for both single-valued maps and set-valued maps defined between metric spaces.
Some geometric properties of a sequence space related to ℓp
Authors: Mursaleen
Published: April 2009

The sequence space m (ø), introduced and studied by W.L.C. Sargent in 1960, is closely related to the space ℓp. In this paper we obtain an explicit formula for the Hausdorff measure of noncompactness of any bounded subset in m (ø). We also show that m (ø)enjoys the weak Banach-Saks property, while C (m (ø)) = 2. This shows that the condition C (X) < 2, known to be sufficient for the space X to have the weak Banach-Saks property, is not a necessary one.
A formula for Eigenpairs of certain symmetric tridiagonal matrices
Authors: Shin Byeong Chun
Published: April 2009

A closed form expression is given for the eigenvalues and eigenvectors of a symmetric tridiagonal matrix of odd order whose diagonal elements are all equal and whoes superdiagonal elements alternate between the values c and d. An implicit formula is given for the even order case.
On classical Krull dimension of group-graded rings
Authors: Kelarev A. V.
Published: April 2009

For any ring R graded by a finite group, we give a bound on the classical Krull dimension of R in terms of the dimension of the initial component Re. It follows that if Re has finite classical Krull dimension, then the same is true of the whole ring R, too.
A 3-manifold with a non-subgroup-separable fundamental group
Authors: Matsumoto Saburo
Published: April 2009

We examine a 3-manifold Γ whose fundamental group is known to be non-subgroup-separable (non-LERF). We show that this manifold Γ is a graph manifold and that the subgroup known to be non-separable is not geometric. On the other hand, there are incompressible surfaces immersed in the manifold which do not lift to embeddings in any finite-degree covering space. We then prove that thesebadincompressible surfaces must have non-empty boundary.
Automatic continuity of perturbations of casual operators
Authors: Harrison K. J. , Eaton L-J. , Ward J. A.
Published: April 2009

We obtain automatic continuity results for finite-rank perturbations of causal sequence space operators, and provide examples to illustrate cases where automatic continuity does not hold.
On some mappings associated with geometric and arithmetic means
Authors: Dragomir S. S. , Comănescu D. , Pearce C. E. M.
Published: April 2009

In this paper we introduce some new mappings associated with the weighted geometric mean. These are used to derive structural results linking weighted geometric and arithmetic means.
Homological properties of SF rings
Authors: Shamsuddin Ahmad
Published: April 2009

A ring R is said to left SF if all simple left R-modules are flat. We study some homological properties of such rings and find situations in which these become von Neumann regular.
High order divergence-form elliptic operators on Lie groups
Authors: ter Elst A. F. M. , Robinson Derek W.
Published: April 2009

We give a straightforward proof that divergence-form elliptic operators of ordermon ad-dimensional Lie group withm≥dhave Hölder continuous kernels satisfying Gaussian bounds.
Groups with a Cayley graph isomorphic to a hypercube
Authors: Dixon John D.
Published: April 2009

A process is described for enumerating the Cayley graphs isomorphic to a binary d-cube for small values of d. There are 4 Cayley graphs isomorphic to the 3-cube, 14 isomorphic to the 4-cube, 45 isomorphic to the 5-cube and 238 isomorphic to the 6-cube. A similar method may be used for any graph with a prime power number of vertices.
On the common right factors of meromorphic functions
Authors: Ng Tuen-Wai , Yang Chung-Chun
Published: April 2009

In this paper, common right factors (in the sense of composition) of p1 + p2F and p3 + p4F are investigated. Here, F is a transcendental meromorphic function and pi's are non-zero polynomials. Moreover, we also prove that the quotient (p1 + p2F)/(p3 + p4F) is pseudo-prime under some restrictions on F and the pi's. As an application of our results, we have proved that R (z) H (z)is pseudo-prime for any nonconstant rational function R (z) and finite order periodic entire function H (z).
An isoperimetric inequality for the thread problem
Authors: Morgan Frank
Published: April 2009

Given a fixed curve C0 in Rn of length L0 and a variable curve C of fixed length L ≤ L0, the thread problem seeks a least-area surface bounded by C0 + C. We show that an extreme case is a circular arc and its chord. We provide some counterexamples and generalisations to higher dimensions.
A Schwarz lemma for complete Riemannian manifolds
Authors: Cheung Leung-Fu , Leung Pui-Fai
Published: April 2009

We prove a Schwarz Lemma for conformal mappings between two complete Riemannian manifolds when the domain manifold has Ricci curvature bounded below in terms of its distance function. This gives a partial result to a conjecture of Chua.
Saturated formations and Sylow normalisers
Authors: D'Aniello A. , De Vivo C. , Giordano G.
Published: April 2009

Sufficient conditions are provided in order that some classes of finite soluble groups, defined by properties of the Sylow normalisers, are saturated formations.
Pointwise chain recurrent maps of the tree
Authors: Gengrong Zhang , Fanping Zeng
Published: April 2009

Let T be a tree, f: T → T be a continuous map. We show that if f is pointwise chain recurrent (that is, every point of T is chain recurrent under f), then either fan is identity or fan is turbulent if Fix(f) ∩ End(T) = ∅ or else fan−1 is identity or fan−1 is turbulent if Fix(f) ∩ End(T) ≠  . Here n denotes the number of endpoints of T and, an denotes the minimal common multiple of 2,3,…,n.
On biorthogonal systems and Maxur's intersection property
Authors: Rychtář Jan
Published: April 2009

We give a characterisation of Banach spaces X containing a subspace with a shrinking Markushevich basis {xγ, fγ}γ∈Γ. This gives a sufficient condition for X to have a renorming with Mazur's intersection property.
Almost all normal sets are strictly normal
Authors: Zaslavski Alexander J.
Published: April 2009

We consider the space Sn of all nonempty bounded closed normal subsets of the cone where is the set of all vectors x ∈ Rn with nonnegative coordinates. We equip the space Sn with the Hausdorff metric and show that most elements of Sn are, in fact, strictly normal. More precisely, we show that the complement of the collection of all stricly normal elements of Sn is a σ-porous subset of Sn.
On tensor factorisation for representations of finite groups
Authors: Pacifici Emanuele
Published: April 2009

We prove that, given a quasi-primitive complex representation D for a finite group G, the possible ways of decomposing D as an inner tensor product of two projective representations of G are parametrised in terms of the group structure of G. More explicitly, we construct a bijection between the set of such decompositions and a particular interval in the lattice of normal subgroups of G.
Complementation in the group of units of matrix rings
Authors: Wilcox Stewart
Published: April 2009

Let R be a ring with 1 and (R) its Jacobson radical. Then 1 + (R) is a normal subgroup of the group of units, G(R). The existence of a complement to this subgroup was explored in a paper by Coleman and Easdown; in particular the ring R = Matn(ℤpk) was considered. We prove the remaining cases to determine for which n, P and k a complement exists in this ring.
Rolling of a body on a plane or a sphere: a geometric point of view
Authors: Moghadasi S. Reza
Published: April 2009

A pair of bodies rolling on each other is an interesting example of nonholonomic systems in control theory. Here the controllability of rolling bodies is investigated with a global approach. By using simple geometric facts, this problem has been completely solved in the special case where one of them is a plane or a sphere.
Blocks of consecutive integers in sumsets (A + B)t
Authors: Guo Shu-Guang , Chen Yong-Gao
Published: April 2009

Let A, B ⊆ {1, …, n}. For m ∈ Z, let rA,B(m) be the cardinality of the set of ordered pairs (a, b) ∈ A × B such that a + b = m. For t ≥ 1, denote by (A + B)t the set of the elements m for which rA, B(m) ≥ t. In this paper we prove that for any subsets A, B ⊆ {1, …, n} such that |A| + |B| ≥ (4n + 4t − 3)/3, the sumset (A + B)t contains a block of consecutive integers with the length at least |A| + |B| − 2t + 1, and that (a) for any two subsets A and B of {1, …, n} such that |A| + |B| ≥ (4n)/3, there exists an arithmetic progression of length n in A + B; (b) for any 2 ≤ r ≤ (4n − 1)/3, there exist two subsets A and B of {1, …, n} with |A| + |B| = r such that any arithmetic progression in A + B has the length at most (2n − 1)/3 + 1.
On finite G-locally primitive graphs and the Weiss conjecture
Authors: Iranmanesh Mohammad A.
Published: April 2009

A graph Γ is said to be a G-locally primitive graph, for G ≥ Aut Γ, if for every vertex, α, the stabiliser Gα induces a primitive permutation group on Γ (α) the set of vertices adjacent to α. In 1978 Richard Weiss conjectured that there exists a function f: ℕ →ℕ such that for any finite connected vertex-transitive G-locally primitive graph of valency d and a vertex α of the graph, |Gα| ≥ f(d). The purpose of this paper is to prove that, in the case Soc(G) = Sz(q), the conjecture is true.
On the injectivity of the Vassiliev homomorphism of singular Artin monoids
Authors: Antony Noelle
Published: April 2009

I prove general combinatorial properties which apply to singular Artin monoids and examine their relationship with the Vassiliev homomorphism ≠. I show that ≠ preserves the Intermediate Property, discovered by Corran, which holds in positive singular Artin monoids of finite type. From this it follows that ≠ is injective for a class of monoids which include singular Artin monoids of type I2(p), generalising a result of East.
Two necessary and sufficient conditions for Möbius subgroups to be g-discontinuous
Authors: Long Zheng-Wu , Wang Xian-Tao
Published: April 2009

In this paper, two necessary and sufficient conditions of Möbius subgroups to be g-discontinuous are obtained. These are generalisations of Lehner's and Larcher's corresponding results.
Hardy-type inequalities for means
Authors: Páles Zsolt , Persson Lars-Erik
Published: April 2009

In this paper we consider inequalities of the form, WhereMis a mean. The main results of the paper offer sufficient conditions onMso that the above inequality holds with a finite constantC. The results obtained extend Hardy's and Carleman's classical inequalities together with their various generalisations in a new dirction.
A note on the lattice of density preserving maps
Authors: Shah Sejal , Das T.K.
Published: April 2009

We study here the poset DP (X) of density preserving continuous maps defined on a Hausdorff sapce X and show that it is a complete lattice for a compact Hausdorff space without isolated points. We further show that for countably compact T3 spaces X and Y without isolated points, DP (X) and DP (Y) are order isomorphic if and only if X and Y are homeomorphic. Finally, Magill's result on the remainder of a locally compact Hausdorff space is deduced from the relation of DP (X) with posets IP (X) of covering maps and EK (X) of compactifications respectively.
Linear geometries on the Moebius strip: A theorem of Skornyakov type
Authors: Löwen Rainer , Polster Burkard
Published: April 2009

We show that the continuity properties of a stable plane are automatically satisfied if we have a linear space with point set a Moebius strip, provided that the lines are closed subsets homeomorphic to the real line or to the circle. In other words, existence of a unique line joining two distinct points implies continuity of join and intersection. For linear spaces with an open disk as point set, the same result was proved by Skornyakov.
Boundary unique continuation theorems under zero Neumann boundary conditions
Authors: Tao Xiangxing , Zhang Songyan
Published: April 2009

Let u be a solution to a second order elliptic equation with singular potentials belonging to the Kato-Fefferman-Phong's class in Lipschitz domains. We prove the boundary unique continuation theorems and the doubling properties for u2 near the boundary under the zero Neumann boundary condition.
Generation of diagonal acts of some semigroups of transformations and relations
Authors: Gallagher Peter , Ruškuc Nik
Published: April 2009

The diagonal right (respectively, left) act of a semigroup S is the set S × S on which S acts via (x, y) s = (xs, ys) (respectively, s (x, y) = (sx, sy)); the same set with both actions is the diagonal bi-act. The diagonal right (respectively, left, bi-) act is said to be finitely generated if there is a finite set A ⊆ S × S such that S × S = AS1 (respectively, S × S = S1A, S × S = SlASl).

In this paper we consider the question of finite generation for diagonal acts of certain infinite semigroups of transformations and relations. We show that the semi-groups of full transformations, partial transformations and binary relations on an infinite set each have cyclic diagonal right and left acts. The semigroup of full finite-to-one transformations on an infinite set has a cyclic diagonal right act but its diagonal left act is not finitely generated. The semigroup of partial injections on an infinite set has neither finitely generated diagonal right nor left act, but has a cyclic diagonal bi-act. The semigroup of bijections (symmetric group) on an infinite set does not have any finitely generated diagonal acts.
A multiple character sum evaluation
Authors: Kim Dae San
Published: April 2009

We evaluate in a simple and direct manner a multiple character sum. a special case of which can also be derived from the Möbius inversion and a result of Hanlon.
OnC*-algebras with the approximaten-th root property
Authors: Chigogidze A. , Karasev A. , Kawamura K. , Valov V.
Published: April 2009

We say that aC*-algebraXhas the approximaten-th root property (n≥2) if for everya∈Xwith ∥a∥ ≤ 1 and every ɛ > 0 there exitsb∈Xsuch that ∥b∥ ≤ 1 and ∥a − bn∥ < ɛ. Some properties of commutative and non-commutativeC*-algebras having the approximaten-th root property are investigated. In particular, it is shown that there exists a non-commutative (respectively, commutative) separable unitalC*-algebraXsuch that any other (commutative) separable unitalC*-algebra is a quotient ofX. Also we illustrate a commutativeC*-algebra, each element of which has a square root such that its maximal ideal space has infinitely generated first Čech cohomology.
Flat Laguerre planes of Kleinewillinghöfer type E obtained by cut and paste
Authors: Steinke Günter F.
Published: April 2009

We provide examples of flat Laguerre planes of Kleinewillinghöfer type E, thus completing the classification of flat Laguerre planes with respect to Laguerre translations in B. Polster and G.F. Steinke, Results Maths. (2004). These planes are obtained by a method for constructing a new flat Laguerre plane from three given Laguerre planes devised in B. Polster and G. Steinke, Canad. Math. Bull. (1995) but no examples were given there.
Finding the group structure of elliptic curves over finite fields
Authors: Friedlander John B. , Pomerance Carl , Shparlinski Igor E.
Published: April 2009

We show that an algorithm of V. Miller to compute the group structure of an elliptic curve over a prime finite field runs in probabilistic polynomial time for almost all curves over the field. Important to our proof are estimates for some divisor sums.
Complementation of the Jacobson group in a matrix ring
Authors: Dolžan David
Published: April 2009

The Jacobson group of a ring R (denoted by  = (R)) is the normal subgroup of the group of units of R (denoted by G(R)) obtained by adding 1 to the Jacobson radical of R (J(R)). Coleman and Easdown in 2000 showed that the Jacobson group is complemented in the group of units of any finite commutative ring and also in the group of units a n × n matrix ring over integers modulo ps, when n = 2 and p = 2, 3, but it is not complemented when p ≥ 5. In 2004 Wilcox showed that the answer is positive also for n = 3 and p = 2, and negative in all the remaining cases. In this paper we offer a different proof for Wilcox's results and also generalise the results to a matrix ring over an arbitrary finite commutative ring. We show this by studying the generators and relations that define a matrix ring over a field. We then proceed to examine the complementation of the Jacobson group in the matrix rings over graded rings and prove that complementation depends only on the 0-th grade.
Bifurcation of positive entire solutions for a semilinear elliptic equation
Authors: Hsu Tsing-San , Lin Huei-Li
Published: April 2009

In this paper, we consider the nonhomogeneous semilinear elliptic equation

,

where λ ≥ 0, 1 < p < (N + 2)/(N − 2), if N ≥ 3, 1 < p < ∞, if N = 2, h(x) ∈ H−l(ℝN), 0 ≢ h(x) ≥ 0 in ℝN, K(x) is a positive, bounded and continuous function on ℝN. We prove that if K(x) ≥ K∞ > 0 in ℝN, and lim∣x∣⃗∞K(x) = K∞, then there exists a positive constant λ✶ such that (✶)λ has at least two solutions if λ ∈ (0, λ✶) and no solution if λ > λ✶. Furthermore, (✶)λ has a unique solution for λ = λ✶ provided that h(x) satisfies some suitable conditions. We also obtain some further properties and bifurcation results of the solutions of (1.1)λ at λ = λ✶.
A strong convergence theorem for contraction semigroups in Banach spaces
Authors: Xu Hong-Kun
Published: April 2009

We establish a Banach space version of a theorem of Suzuki [8]. More precisely we prove that if X is a uniformly convex Banach space with a weakly continuous duality map (for example, lp for 1 < p < ∞), if C is a closed convex subset of X, and if F = {T (t): t ≥ 0} is a contraction semigroup on C such that Fix(F) ≠ ∅, then under certain appropriate assumptions made on the sequences {αn} and {tn} of the parameters, we show that the sequence {xn} implicitly defined by

for all n ≥ 1 converges strongly to a member of Fix(F).
A characteristic subgroup and kernels of Brauer characters
Authors: Isaacs I. M. , Navarro Gabriel
Published: April 2009

If G is finite group and P is a Sylow p-subgroup of G, we prove that there is a unique largest normal subgroup L of G such that L ⋂ P = L ⋂ NG (P). If G is p-solvable, then L is the intersection of the kernels of the irreducible Brauer characters of G of degree not divisible by p.
Note on the Schwarz triangle functions
Authors: Harmer Mark
Published: April 2009

We shown the rationality of the Taylor coefficients of the inverse of the Schwarz triangle functions for a triangle group about any vertex of the fundamental domain.
Approximate solutions for the Couette viscometry equation
Authors: de Hoog F. R. , Anderssen R. S.
Published: April 2009

The recovery of flow curves for non-Newtonian fluids from Couette rheometry measurements involves the solution of a quite simple first kind Volterra integral equation with a discontinuous kernel for which the solution, as a summation of an infinite series, has been known since 1953. Various methods, including an Euler-Maclaurin sum formula, have been proposed for the estimation of the value of the summation. They all involve the numerical differentiation of the observational data. In this paper, the properties of Bernoulli polynomials, in conjunctions with the special structure of the integral equation, are exploited to derive a parametric family of representations for its solution. They yield formulas similar to, but more general than, the previously published Euler-Maclaurin sum formula representations. The parameterisation is then utilised to derive two new classes of approximations. The first yields a family of finite difference approximations, which avoids the direct numerical differentiation of the observational data, while the second generates a framework for the construction of improved power law approximations.
On 3-Class groups of certain pure cubic fields
Authors: Gerth Frank
Published: April 2009

Recently Calegari and Emerton made a conjecture about the 3-class groups of certain pure cubic fields and their normal closures. This paper proves their conjecture and provides additional insight into the structure of the 3-class groups of pure cubic fields and their normal closures.
There are no n-point Fσ sets in Rm
Authors: Fearnley David L. , Fearnley L. , Lamoreaux J. W.
Published: April 2009

We show that, for any positive integers n and m, if a set S ⊂ Rm intersects every m − 1 dimensional affine hyperplane in Rm in exactly n points, then S is not an Fσ set. This gives a natural extension to results of Khalid Bouhjar, Jan J. Dijkstra, and R. Daniel Mauldin, who have proven this result for the case when m = 2, and also Jan J. Dijkstra and Jan van Mill, who have shown this result for the case when n = m.
Equivalent conditions of a tree map with zero topological entropy
Authors: Sun Taixiang , Xie Mingde , Zhao Jinfeng
Published: April 2009

Let f: T → T be a tree map with n end-points, SAP(f) the set of strongly almost periodic points of f and CR(f) the set of chain recurrent points of f. Write E(f,T) = {x: there exists a sequence {ki} with 2 ≤ ki ≤ n such that and g = f\CR(f). In this paper, we show that the following three statements are equivalent:

(1) f has zero topological entropy.

(2) SAP(f) ⊂ E(f,T).

(3) Map ωg: x → ω(x,g) is continuous at p for every periodic point p of f.
Relative Abelian kernels of some classes of transformation monoids
Authors: Cordeiro E. , Delgado M. , Fernandes V.H.
Published: April 2009

We consider the symmetric inverse monoid ℐnof ann-element chain and its inverse submonoids ℐn, ℐn, ℐnand ℘ℐnof all order-preserving, order-preserving or order-reversing, orientation-preserving and orientation-preserving or orientation-reversing transformations, respectively, and give descriptions of their Abelian kernels relative to decidable pseudovarieties of Abelian groups.
Universality of methods approximating the derivative
Authors: Herzog Gerd , Lemmert Roland
Published: April 2009

We prove the existence of universal functions for mappings Tn: C([0,1]) → Lp([0,1]), 0 < p < 1, with Tn(f) → f′ (n → ∞) on certain subsets of C1([0,1]). As an application we conclude that there are continuous functions f ∈ C([0,1]), such that the derivatives of the Bernstein polynomials form a dense subset of Lp([0,1]) for each 0 < p < 1.
The Helgason Fourier transform for semisimple Lie groups I: The Case of SL2(ℝ)
Authors: Sarkar Rudra P. , Sitaram Alladi
Published: April 2009

We consider a Helgason-type Fourier transform on SL2(ℝ) and prove various results on L1-harmonic analysis on the full group analogous to those on symmetric spaces.
Non-residues and primitive roots in Beatty sequences
Authors: Banks William D. , Shparlinski Igor E.
Published: April 2009

We study multiplicative character sums taken on the values of a non-homogeneous Beatty sequence where α,β ∈ ℝ, and α is irrational. In particular, our bounds imply that for every fixed ε > 0, if p is sufficiently large and p½+ε ≤ N ≤ p, then among the first N elements of ℬα,β, there are N/2+o(N) quadratic non-residues modulo p. When more information is available about the Diophantine properties of α, then the error term o(N) admits a sharper estimate.
The structure of reversing symmetry groups
Authors: Baake Michael , Roberts John A.G.
Published: April 2009

We present some of the group theoretic properties of reversing symmetry groups, and classify their structure in simple cases that occur frequently in several well-known groups of dynamical systems.
Graphs with constant ratio of mean curvatures and spherical caps
Authors: Koh Sung-Eun
Published: April 2009

Let f be a smooth nonconstant function defined on an n dimensional ball and zero on the boundary n − 1 dimensional sphere. It is shown that the graph of f is a spherical cap (1) if f is positive and if the ratio Hk/Hr is a nonzero constant for 1 ≤ k < r ≤ n on the graph of f or (2) if the ratio Hn/Hk is a nonzero constant on the graph of f.
Necessary and sufficient conditions for precompact sets to be metrisable
Authors: Ferrando J.C. , Kasakol J. , Pellicer M. López
Published: April 2009

This self-contained paper characterises those locally convex spaces whose (weakly) precompact (respectively, compact) subsets are metrisable. Applications and examples are provided. Our approach also applies to get Cascales-Orihuela's, Valdivia's and Robertson's metrisation theorems for (pre)compact sets.
ℒ-Injective Hulls of Modules
Authors: Mao Lixin , Ding Nanqing
Published: April 2009

Let R be a ring and ℒ a class of R-modules. An R-module N is called ℒ-injective if for all L ∈ ℒ. An ℒ-injective hull of an R-module M is defined to be a homomorphism φ: M → F with F ℒ-injective such that for any monomorphism f: M → F′ with F′ ℒ-injective, there is a monomorphism g: F → F′ satisfying gφ = f. The aim of this paper is to study ℒ-injective hulls and their relations with ℒ-injective envelopes in Enochs' sense.
An active set sequential quadratic programming algorithm for nonlinear optimisation
Authors: Hu Qing-Jie , Xiao Yun-Hai , Chen Y.
Published: April 2009

In this paper, we have proposed an active set feasible sequential quadratic programming algorithm for nonlinear inequality constraints optimization problems. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving a reduced quadratic programming subproblem. To overcome the Maratos effect, a higher-order correction direction is obtained by solving a reduced least square problem. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without strict complementarity.
Elliptic problems in variable exponent spaces
Authors: Mihailescu Mihai
Published: April 2009

In this paper we study a nonlinear elliptic equation involving p(x)-growth conditions on a bounded domain having cylindrical symmetry. We establish existence and multiplicity results using as main tools the mountain pass theorem of Ambosetti and Rabinowitz and Ekeland's variational principle.
Ensuring a finite group is supersoluble
Authors: Bryce R. A.
Published: April 2009

A special case of the main result is the following. LetGbe a finite, non-supersoluble group in which from arbitrary subsetsX,Yof cardinalitynwe can always findx∈Xandy∈Ygenerating a supersoluble subgroup. Then the order ofGis bounded by a function ofn. This result is a finite version of one line of development of B.H. Neumann's well-known and much generalised result of 1976 on infinite groups.
Constant mean curvature surfaces in homogeneously regular 3-manifolds
Authors: Rosenberg Harold
Published: April 2009

We establish several theorems concerning properly embedded constant mean curvature surfaces (cmc-surfaces) in homogeneously regular 3-manifolds, when the mean curvature H is large.
On the boundary spectrum in banach algebras
Authors: Mouton S.
Published: April 2009

We investigate some properties of the set S∂(a) = {λ ∈ ℂ: λ – a ∈ ∂S} (which we call the boundary spectrum of a) where ∂S denotes the topological boundary of the set S of all non-invertible elements of a Banach algebra A, and where a is an element of A.
Linear relations on hereditarily indecomposable normed spaces
Authors: Álvarez Teresa
Published: April 2009

We introduce the notion of hereditarily indecomposable normed space and we prove that this class of normed spaces may be characterised by means of F+ and strictly singular linear relations. We also show that if X is a complex hereditarily indecomposable normed space then every partially continuous linear relation in X with dense domain can be written as λI + S, where λ ∈ ℂ and S is a strictly singular linear relation.
A new system of variational inclusions with (H, η)-monotone operators
Authors: Peng Jianwen , Huang Jianrong
Published: April 2009

In this paper, We introduce and study a new system of variational inclusions involving(H, η)-monotone operators in Hilbert spaces. By using the resolvent operator method associated with (H, η)-monotone operators, we prove the existence and uniqueness of solutions and the convergence of some new three-step iterative algorithms for this system of variational inclusions and its special cases. The results in this paper extends and improves some results in the literature.
Annihilator graphs and semigroups of matrices
Authors: Quinn S. J.
Published: April 2009

Matrices provide essential tools in many branches of mathematics and matrix semigroups have applications in various areas. In this paper we give a complete description of all infinite matrix semigroups satisfying a certain combinatorial property defined in terms of annihilator graphs.
The curvature and topological properties of hypersurfaces with constant scalar curvature
Authors: Shichang Shu , Sanyang Liu
Published: April 2009

In this paper, we consider n (n ≥ 3)-dimensional compact oriented connected hypersurfaces with constant scalar curvature n(n − 1)r in the unit sphere Sn+1(1). We prove that, if r ≥ (n − 2)/(n − 1) and S ≤ (n − 1)(n(r − 1) + 2)/(n − 2) + (n − 2)/(n(r − 1) + 2), then either M is diffeomorphic to a spherical space form if n = 3; or M is homeomorphic to a sphere if n ≥ 4; or M is isometric to the Riemannian product , where c2 = (n − 2)/(nr) and S is the squared norm of the second fundamental form of M.
Topological entropy for the canonical completely positive maps on graph C*-Algebras
Authors: Jeong Ja A. , Park Gi Hyun
Published: April 2009

Let C*(E) = C*(se, pv) be the graph C*-algebra of a directed graph E = (E0, E1) with the vertices E0 and the edges E1. We prove that if E is a finite graph (possibly with sinks) and φE: C*(E) → C*(E) is the canonical completely positive map defined by

then Voiculescu's topological entropy ht(φE) of φE is log r(AE), where r(AE) is the spectral radius of the edge matrix AE of E. This extends the same result known for finite graphs with no sinks. We also consider the map φE when E is a locally finite irreducible infinite graph and prove that , where the supremum is taken over the set of all finite subgraphs of E.
Trace of Frobenius endomorphism of an elliptic curve with complex multiplication
Authors: Ishii Noburo
Published: April 2009

Let E be an elliptic curve with complex multiplication by R, where R is an order of discriminant D < −4 of an imaginary quadratic field K. If a prime number p is decomposed completely in the ring class field associated with R, then E has good reduction at a prime ideal p of K dividing p and there exist positive integers u and υ such that 4p = u2 – Du;2. It is well known that the absolute value of the trace ap of the Frobenius endomorphism of the reduction of E modulo p is equal to u. We determine whether ap = u or ap = −u in the case where the class number of R is 2 or 3 and D is divisible by 3, 4 or 5.
Classification theorems for theC*-Algebras of graphs with sinks
Authors: Raeburn Iain , Tomforde Mark , Williams Dana P.
Published: April 2009

We consider graphsEwhich have been obtained by adding one or more sinks to a fixed directed graphG. We classify theC*-algebra ofEup to a very strong equivalence relation, which insists, loosely speaking, thatC*(G) is kept fixed. The main invariants are vectorsWE:G0→ ℕ which describe how the sinks are attached toG; more precisely, the invariants are the classes of theWEin the cokernel of the mapA – I, whereAis the adjacency matrix of the graphG.
On τ-completely decomposable modules
Authors: Crivei Septimiu
Published: April 2009

For a hereditary torsion theory τ, a moduleAis called τ-completedly decomposable if it is a direct sum of modules that are the τ-injective hull of each of their non-zero submodules. We give a positive answer in several cases to the following generalised Matlis' problem: Is every direct summand of a τ-completely decomposable module still τ-completely decomposable? Secondly, for a commutative Noetherian ringRthat is not a domain, we determine those torsion theories with the property that every τ-injective module is an essential extension of a (τ-injective) τ-completely decomposable module.
A note on the Doob-Meyer-decomposition of Lp-valued submartingales
Authors: Burgstaller Bernhard
Published: April 2009

Let p > 1 real. We Doob-Meyer-decompose Lp(ℙ)-valued positive submartingales such that the martingale and predictable parts are also in Lp(ℙ). We give two variants of such a decomposition. The first one handles also not necessarily right continuous submartingales, since its proof is as discrete in its nature as Doob's archaically decomposition. The second decomposition acts in Lp (ℝ × Ω ℬ ⊗ ℱ, μ ⊗ ℙ) for some finite measure μ on ℝ.
Etude des interruptions dans l'algorithme de Jacobi–Perron
Authors: Dubois Eugène , Farhane Ahmed , Paysant-Le Roux Roger
Published: April 2009

It is well known that in general the Jacobi–Perron algorithm (a multi-dimensional analogue of the continued fraction algorithm) may or might not acknowledge the dependence over ℚ of its arguments 1, α1,…, αn by truncating itself down to fewer arguments from some step onwards (if so, the algorithm is said to display an ‘interruption’). We show here that if n = 2 then 1, α1, α2 are linearly dependent over ℚ of and only if the Jacobi–Perron Algorithm displays an interruption. We give examples showing this is not so for any n ≥ 3.
Nontrivial solutions of a semilinear elliptic problem via variational methods
Authors: Han Zhi-Qing
Published: April 2009

Using variational methods, we investigate the existence of nontrivial solutions of a nonlinear elliptic boundary value problem at resonance under generalised Ahmad-Lazer-Paul conditions. Some new results are obtained and some results in the literature are improved.
Finitistic dimensions and good filtration dimensions of stratified algegras
Authors: Wang Shugui , Zhu Bin
Published: April 2009

Δ–finitistic dimensions of standardly stratified algebras are defined similarly to properly stratified algebras. It is proved that the finitistic dimension for any standardly stratified algebra is bounded by the sum of the Δ–finitistic dimension and the ∇ good filtration dimension. Finally, the ∇–good filtration dimension of standardly stratified algebras is equal to the Δ–good filtration dimension of their Ringel duals.
Corrigendum: Irreducible decompositon of the Magnus representation of the Torelli group
Authors: Suzuki Masaaki
Published: April 2009

Due to a printing error, a significant graph on page 12 was omitted from the paper [1].
A note on Cohn's universal localisation at a semiprime ideal
Authors: Beachy John A.
Published: April 2009

The universal localisation RΓ(s) at a semiprime ideal S of a left Noetherian ring R was defined and studied by P. M. Cohn. In this note we investigate the interaction between the universal localisation RΓ(s), the Ore localisation at S, and the torsion-theoretic localisation at the injective envelope E(R/S) of the module R(R/S).
A note on the roots of trinomials over a finite field
Authors: Coulter Robert , Henderson Marie
Published: April 2009

For non-negative integers n we determine the roots of the trinmial , with a ≠ 0, over a finite field of characteristic p.