bluuebunny/crossref_metadata_2025 huggingface dataset:
Groups in which every subgroup is modular-by-finite
Authors: De Falco M. , De Giovanni F. , Musella C.
Published: April 2009

A group G is called a BCF-group if there is a positive integer κ such that |X : XG| ≤ κ for each subgroup X of G. The structure of BCF-groups has been studied by Buckley, Lennox, Neumann, Smith and Wiegold; they proved in particular that locally finite groups with the property BCF are Abelian-by-finite. As a group lattice version of this concept, we say that a group G is a BMF-group if there is a positive integer κ such that every subgroup X of G contains a modular subgroup Y of G for which the index |X : Y| is finite and the number of its prime divisors with multiplicity is bounded by κ (it is known that that such number can be characterised by purely lattice-theoretic considerations, and so it is invariant under lattice isomorphisms of groups). It is proved here that any locally finite BMF-group contains a subgroup of finite index with modular subgroup lattice.
An inequality with application to a difference equation
Authors: Chen Jong-Yi , Chow Yunshyong
Published: April 2009

In this paper we shall prove that for any 0 < d ≤ 2,
holds for n ≥ 1.

As an application, we shall then show that the following recursively defined sequence

satisfies

The difference equation above originates from a heat conduction problem studied by Myshkis (J. Difference Equ. Appl. 3(1997), 89–91).
A bound on the Schur multiplier of a prime-power group
Authors: Ellis Graham , Wiegold James
Published: April 2009

The paper improves on an upper bound for the order of the Schur multiplier of a finite p-group given by Wiegold in 1969. The new bound is applied to the problem of classifying p-groups according to the size of their Schur multipliers.
Finitely generated subgroups and the centre of some factor groups of free products
Authors: Gupta C.K. , Romanovski N.
Published: April 2009

For groups of the type F/[R, R], where F is a free product, we prove a generalisation of a theorem of Karrass and Solitar on a finitely generated subgroup of a free product containing a nontrivial subnormal subgroup. We also describe the centre of the group F[/R, R].
Counting cyclic and separable matrices over a finite field
Authors: Wall G.E.
Published: April 2009

A square matrix is called cyclic if its characteristic and minimum polynomials coincide, separable if the characteristic polynomial has no repeated roots. Recent results of P. Neumann and Praeger, and of Lehrer, about the numbers of such matrices over a finite field are sharpened.
Reduction of dimension of approximate intertial manifolds by symmetry
Authors: Rodriguez-Bernal Anibal , Wang Bixiang
Published: April 2009

In this paper, we study approximate inertial manifolds for nonlinear evolution partial differential equations which possess symmetry. The relationship between symmetry and dimensions of approximate inertial manifolds is established. We demonstrate that symmetry can reduce the dimensions of an approximate inertial manifold. Applications for concrete evolution equations are given.
Slice convergence of parametrised sums of convex functions in non-reflexive spaces
Authors: Wenczel Robert , Eberhard Andrew
Published: April 2009

The objectives of this study of slice convergence are two-fold. The first is to derive results regarding the passage of certain semi–convergences through Young–Fenchel conjugation. These semi–convergences arise from the splitting of the usual slice topology in the primal and dual spaces into (non-Hausdorff) topologies: the upper slice topology ; a topology generating a convergence closely resembling the bounded–weak* upper Kuratowski convergence; along with the respective primal and dual lower Kuratowski topologies. This gives rise to topological convergences not reliant on sequentially–based definitions found in many such studies, and associated topological continuity results for conjugation (in normed spaces), in contrast to the usual sequential continuity exhibited by analogues of Mosco convergence. The second objective is to study the passage of slice convergence through addition. Such sum theorems have been derived in other works and we establish previous theorems from a unified framework as well as obtaining a new result.
Identities in algebras with involution
Authors: Rashkova Tsetska Grigorova
Published: April 2009

There is an approach due to Bergman describing ordinary polynomial identities for Mn (K) by means of commutative algebra. In the paper we apply this approach to the matrix algebra of even order M2n (K, *) with symplectic involution *.
Plane curves and p-adic roots of unity
Authors: Voloch José Felipe
Published: April 2009

We prove the following result: Let f(x, y) be a polynomial of degree d in two variables whose coefficents are integers in an unramified extension of Qp. Assume that the reduction of f modulo p is irreducible of degree d and not a binomial. Assume also that p > d2 + 2. Then the number of solutions of the inequality |f(ζ1, ζ2)| < p−1, with ζ1, ζ2 roots of unity in Q̄p or zero, is at most pd2.
On the three-space problem for the Dunford-Pettis property
Authors: Castillo J.M.F. , Simoes M.A.
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 in such a way that the corresponding quotient is isomorphic to Z. In this paper we study twisted sums of Banach spaces with either have the Dunford-Pettis property, are c0-saturated or l1-saturated. Amongst other things, we show that every Banach space is a complemented subspace of a twisted sum of two Banach spaces with the Dunford-Pettis property.
Rigidities of asymptotically Euclidean manifolds
Authors: Paeng Seong-Hun
Published: April 2009

Let M be an n-dimensional compact Riemannian manifold. We study the fundamental group of M when the universal covering space of M, M is close to some Euclidean space ℝs asymptotically.
Groups of automorphisms of linearly ordered sets
Authors: Hickman J.L.
Published: April 2009

I show that a group of order-automorphisms of a linearly ordered set can be expressed as an unrestricted direct product in which each factor is either the infinite cyclic group or else a group of order-automorphisms of a densely ordered set. From this a couple of simple group embedding theorems can be derived. The technique used to obtain the main result of this paper was motivated by the Erdös-Hajnal inductive classification of scattered sets.
Computing the effectively computable bound in Baker's inequality for linear forms in logarithms
Authors: van der Poorten A.J. , Loxton J.H.
Published: April 2009

For certain number theoretical applications, it is useful to actually compute the effectively computable constant which appears in Baker's inequality for linear forms in logarithms. In this note, we carry out such a detailed computation, obtaining bounds which are the best known and, in some respects, the best possible. We show inter alia that if the algebraic numbers α1, …, αn all lie in an algebraic number field of degree D and satisfy a certain independence condition, then for some n0(D) which is explicitly computed, the inequalities (in the standard notation)

have no solution in rational integers b1, …, bn (bn ≠ 0) of absolute value at most B, whenever n ≥ n0(D). The very favourable dependence on n is particularly useful.
Categories whose objects are determined by their rings of endomorphisms
Authors: Călugăreanu Grigore
Published: April 2009

In an additive category A0, objects are said to be determined by their rings of endomorphisms if for each ring-isomorphism F of the rings of endomorphisms of two objects A, B in A0 there is an isomorphism f: A → B in A0 such that F(α) = fαf-1, for every endomorphism α of A. Considering.this problem in the context of closed categories (in Eilenberg and Kelly's sense), the author proves a general theorem which generalises results of Eidelheit (for real Banach spaces) and of Kasahara (for real locally convex spaces).
Families of finite sets satisfying an intersection condition
Authors: Frankl Peter
Published: April 2009

The following theorem is proved.

Let X be a finite set of cardinality n ≥ 2, and let F be a family of subsets of X. Suppose that for F1, F2, F3 ∈ F we have |F1 ∩ F2 ∩ F3| ≥ 2. Then |F| ≤ 2n−2with equality holding if and only if for two different elements x, y of X, F = {F ⊆ X | x ∈ F, y ∈ F}.
Asymptotic centres of filters on uniformly rotund spaces
Authors: Staples John
Published: April 2009

The notion of asymptotic centre of a bounded sequence of points in a uniformly convex Banach space was introduced by Edelstein in order to prove, in a quasi-constructive way, fixed point theorems for nonexpansive and similar maps.

Similar theorems have also been proved by, for example, adding a compactness hypothesis to the restrictions on the domain of the maps. In such proofs, which are generally less constructive, it may be possible to weaken the uniform convexity hypothesis.

In this paper Edelstein's technique is extended by defining a notion of asymptotic centre for an arbitrary set of nonempty bounded subsets of a metric space. It is shown that when the metric space is uniformly rotund and complete, and when the set of bounded subsets is a filter base, this filter base has a unique asymptotic centre. This fact is used to derive, in a uniform way, several fixed point theorems for nonexpansive and similar maps, both single-valued and many-valued.

Though related to known results, each of the fixed point theorems proved is either stronger than the corresponding known result, or has a compactness hypothesis replaced by the assumption of uniform convexity.
The theorem of Marggraff on primitive permutation groups which contain a cycle
Authors: Levingston Richard , Taylor D.E.
Published: April 2009

A short elementary proof is given of the theorem of Marggraff which states that a primitive permutation group which contains a cycle fixing k points is (k+1)-fold transitive. It is then shown that the method of proof actually yields a generalization of Marggraff's theorem.
A smooth, non-reflexive second conjugate space
Authors: Smith M.A.
Published: April 2009

It is shown that a separable, quasi-reflexive Banach space of deficiency one admits an equivalent norm such that its second conjugate space is smooth; this answers a question raised by Ivan Singer [Bull. Austral. Math. Soc. 12 (1975), 407–416.
On the hamiltonian product of graphs: Corrigendum
Authors: Krishnamoorthy V.
Published: April 2009

The author has noticed two small errors in his paper [1]: In Figure 1 on p. 290, the vertices labelled 4n, 4n + 1, 4n + 2 should be labelled 4n − 1, 4n, 4n + 1, respectively. In the 14th line on p. 291, “at a distance greater than 2n − 1” should read “at a distance greater than 2n − 2”.
Abelian Groups that are unions of proper subgroups
Authors: Bhaskara Rao K.P.S. , Reid J.D.
Published: April 2009

The abelian groups that can be written as a union of proper subgroups are characterised, all the ways that this can be done for a given group are indicated, and the minimal number of subgroups necessary for such a decomposition of a given group is determined.
A nonlinear ergodic theorem for asymptotically nonexpansive mappings
Authors: Tan Kok-Keong , Xu Hong-Kun
Published: April 2009

Let X be a real uniformly convex Banach space satisfying the Opial's condition, C a bounded closed convex subset of X, and T: C → C an asymptotically non-expansive mapping. Then we show that for each x in C, the sequence {Tnx} almost converges weakly to a fixed point y of T, that is,

This implies that {Tnx} converges weakly to y if and only if T is weakly asymptotically regular at x, that is, weak- . We also present a weak convergence theorem for asymptotically nonexpansive semigroups.
On the duality of some martingale spaces
Authors: Bassily N.L. , Abdel-Fattah A.M.
Published: April 2009

Fefferman has proved that the dual space of the martingale Hardy space H1 is the BMO1-space. Garsia went further and proved that the dual of Hp is the so-called martingale Kp-space, where p and q are two conjugate numbers and 1 ≤ p < 2.

The martingale Hardy spaces HΦ with general Young function Φ, were investigated by Bassily and Mogyoródi. In this paper we show that the dual of the martingale Hardy space HΦ is the martingale Hardy space HΦ where (Φ, Ψ) is a pair of conjugate Young functions such that both Φ and Ψ have finite power. Moreover, two other remarkable dualities are presented.
Conical inverse mapping theorems
Authors: Frankowska Hélène
Published: April 2009

We prove a high order conical inverse mapping theorem for set-valued maps on complete metric spaces. An application to a control problem is provided.
Some nilpotent Lie algebras of even dimension
Authors: Seeley Craig
Published: April 2009

For each even dimension greater than or equal to 8, an infinite family of 3-step nilpotent Lie algebras over ℂ is constructed. In dimension m, the family contains isomorphism classes parameterised locally by approximately m3/48 essential parameters.

One particular case is studied further to get some global information about the variety of all nilpotent Lie algebras of dimension 8. Using the results obtained here, and some known facts, it is shown that there is a component consisting of algebras not having minimal possible central dimensions.
A property of analytic functions with Hadamard gaps
Authors: Miao Jie
Published: April 2009

In this paper we obtain a sufficient and necessary condition for an analytic function f on D with Hadamard gaps, that is, for satisfying nk+1/nk ≥ λ 1 for all k, to belong to a kind of space consisting of analytic functions on D. The special cases of these spaces are BMOA and VMOA. In view of our result we can answer the open question given recently by Stroethoff.
A note on the radial growth of Bloch functions
Authors: Girela Daniel
Published: April 2009

The radial growth of Bloch functions has been extensively studied. Using integral means estimates and the Hardy Littlewood theorem, Makarov proved the so called law of iterated logarithm for Bloch functions. This result has also been obtained using probabilistic arguments. In this paper we present another method of studying the radial growth of Bloch functions, having the integral means estimates as starting point and using certain results about normal functions.
A note on high degree linear complementarity problems
Authors: Stewart David E.
Published: April 2009

Topological degree theory can be applied to maps defined from Linear Complementarity Problems, as has been done by Howe and Stone, Ha, and Stewart. It is shown here that the definitions of Howe and Stone, and Stewart, are equivalent. Also a new family of matrices is defined whose degrees' magnitudes increase exponentially as 2n/√2πn, whereas Howe and Stone give examples whose degrees go as (22/5)n.
On the Pass-equivalence of links
Authors: Wong Yan-Loi
Published: April 2009

We give a simple geometric proof that the Jones polynomial at the value i of an oriented link is invariant under pass-equivalence.
Cardinalities of locally compact groups and their Stone-Čech compactifications
Authors: Itzkowitz Gerald L. , Morris Sidney A. , Tkachuk Vladimir V.
Published: April 2009

Dedicated to Edwin Hewitt

If G is any Hausdorff topological group and βG is the Stone-Čech compactification then where |G| denotes the cardinalty of G It is known that if G is a discrete group then and if G is the additive group of real numbers with the Euclidean topology, then |βG| = 2|G|. In this paper the cardinality and weight of βG, for a locally compact group G, is calculated in terms of the character and Lindelöf degree of G The results make it possible to give a reasonably complete description of locally compact groups G for which |βG| = 2|G| or even |βG| = |G|.
Derivatives of kernels associated to complex subelliptic operators
Authors: ter Elst A. F. M.
Published: April 2009

We prove large time Gaussian bounds for the derivatives of the semigroups kernel associated with complex, second-order, subelliptic operators on Lie groups of polynomial growth.
Structure of the kernels associated with invariant subspaces of the Bergman shift
Authors: Chailos George
Published: April 2009

In this article we consider index 1 invariant subspaces M of the operator of multiplication by ζ(z) = z, Mζ, on the Bergman space of the unit disc . It turns out that there is a positive sesquianalytic kernel lλ defined on  ×  which determines M uniquely. Here we study the boundary behaviour and some of the basic properties of the kernel lλ. Among other things, we show that if the lower zero set of M, Z̲(M), is nonempty, the kernel lλ for fixed λ ∈  has a meromorphic continuation across \Z̲(M), where  is the unit circle. Furthermore we consider some special type of kernels lλ and by studying their structure we obtain information for the invariant subspaces related to them. Lastly, and after introducing the general for the invariant subspaces related to them. Lastly, and after introducing the general vector valued setting, we discuss some analogous results for the case of , where m is a positive integer.
The uniform law of large numbers for the Kaplan-Meier integral process
Authors: Bae Jongsig , Kim Sungyeun
Published: April 2009

Let be the function-indexed Kaplan-Meier integral process constructed from the random censorship model. We study a uniform version of the law of large numbers of Glivenko-Cantelli type for {Un} under the bracketing entropy condition. The main result is that the almost sure convergence and convergence in the mean of the process Un holds uniformly in ℱ. In proving the result we shall employ the bracketing method which is used in the proof of the uniform law of large numbers for the complete data of the independent and identically distributed model.
The uniform central limit theorem for the Kaplan-Meier integral process
Authors: Bae Jongsig , Kim Sungyeun
Published: April 2009

Letbe the Kaplan-Meier integral process constructed from the random censorship model. We prove a uniform central limit theorem for {Un} under the bracketing entropy condition and mild conditions due to the censoring effects. We also prove a sequential version of the uniform central limit theorem that will give a functional law of the iterated logarithm of Strassen type.
Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator
Authors: Suh Young Jin
Published: April 2009

In this paper we show that there do not exist any real hypersurfaces in a complex two dimensional Grassmannians G2(ℂn+2) with parallel shape operator.
On A Banach space property of Trubnikov
Authors: Reich Simeon , Xu Hong-Kun
Published: April 2009

Turbnikov/s property (U, λ, α, β) is investigated. In particular, it is shown that property (U, λ, α, α, − 1) with α > 1 is equivalent to α-uniform smoothness. It s also shown that property (U, 1, α, 1) with α > 1 is equivalent to the space being a Hilbert space. The dual property (U*, γ α α − 1) is also introduced and it is shown that a Banach space X has (U*, γ α, α − 1) if and only if X is α-uniformly convex.
Erratum: Two hyperbolic Shwarz lemmas
Authors: Bernal-González L. , Calderón-Moreno M. C.
Published: April 2009

In [1] there is an error, as pointed out to us by J.M. Isidro. In that paper we consider the set Rm of all m-rotations, that is, Rm = {czm: |c| = 1}; the set Aut() of the automorphisms of the unit disc  and the set of the m-automorphisms of , Autm () = {ψ ∘ R ∘ ϕ : ψ, ϕ ∈ Aut(), R ∈ Rm}. We asserted that

where ϕa(Z) = (a − z)/(1 − āz). Equality (1) is not true. For instance, it suffices to consider f (z) = ϕ¼ ∘ ∘ z2 ∘ ϕ½. We have that f ∈ Aut2 (), f (0) = (0) and, after calculations, f (z) = (7z2 − 6z)/(6z − 7). Then it is evident that will never hold f (z) = ϕ0 ∘ R ∘ ϕ0 with R ∈ R2, because ϕ0 is equal to identity.
A cubic analogue of the RSA cryptosystem
Authors: Said Mohamad Rushdan Md , Loxton John
Published: April 2009

In this paper, we investigate a public key cryptosystem which is derived from a third order linear recurrence relation and is analogous to the RSA and LUC cryptosystems. The explicit formulation involves a generalisation of the rule for composition of powers and of the calculus of the Euler totient function which underlie the algebra of the RSA cryptosystem. The security of all these systems appears to be comparable and to depend on the intractability of factorization but the systems do not seem to be mathematically equivalent.
Some finite solvable groups with non-trivial lattice endomorphisms
Authors: Stonehewer S. E. , Zacher G.
Published: April 2009

The main purpose of this paper is to exhibit a doubly-infinite family of examples which are extensions of a p-group by a p′-group, with the action satisfying some conditions of Zappa (1951), arising from his study of dual-standard (meet-distributive) subgroups. The examples show that Zappa's conditions do not bound the nilpotency class (or even the derived length) of the p-group. The key to this work is found in closely related conditions of Hartley (published here for the first time). The examples use some exceptional relationships between primes.
Spectrally bounded traces on C*-algebras
Authors: Mathieu Martin
Published: April 2009

A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is called spectrally bounded if there is a constant M ≥ 0 such that r(T x) ≤ Mr(x) for all x ∈ E, where r (·) denotes the spectral radius. We establish the equivalence of the following properties of a unital linear mapping T from a unital C* -algebra A into its centre:

(a) T is spectrally bounded;

(b) T is a spectrally bounded trace;

(c) T is a bounded trace.
Characterisations of Bloch functions in the unit ball of ℂn, I
Authors: Lou Zengjian , Wulan Hasi
Published: April 2009

Weighted Hadamard product characterisations of Bloch functions in the unit ball of ℂn are studied. In particular, we prove that f belongs to the Bloch space ℬ(Bn) if and only if the non-weighted Hadamard products of f and g belong to BMOA(Un) for all f in , a subspace of the Hardy space H1(Bn).
Best approximation by polynomials
Authors: Kim Sung Guen
Published: April 2009

In this paper we show that if E is a separable Banach space, F is a reflexive Banach space, and n, k ∈ ℕ, then every continuous polynomial of degree n from E into F has at least one element of best approximation in the Banach subspace of all continuous k–homogeneous polynomials from E into F.
On 3-dimensional contact slant submanifolds in Sasakian space forms
Authors: Mihai Ion , Tazawa Yoshihiko
Published: April 2009

Recently, B.-Y. Chen obtained an inequality for slant surfaces in complex space forms. Further, B.-Y. Chen and one of the present authors proved the non-minimality of proper slant surfaces in non-flat complex space forms. In the present paper, we investigate 3-dimensional proper contact slant submanifolds in Sasakian space forms. A sharp inequality is obtained between the scalar curvature (intrinsic invariant) and the main extrinsic invariant, namely the squared mean curvature.

It is also shown that a 3-dimensional contact slant submanifold M of a Sasakian space form M̆(c), with c ≠ 1, cannot be minimal.
Group gradings of M2(K)
Authors: Khazal R. , Boboc Crina , Dăscălescu S.
Published: April 2009

We describe all group gradings of the matrix algebra M2(k), where k is an arbitrary field. We prove that any such grading reduces to a grading of type C2, a grading of type C2 × C2, or to a good grading. We give new simple proofs for the description of C2-gradings and C2 × C2-gradings on M2(K).
A presentation for the monoid of uniform block permutations
Authors: FitzGerald D. G.
Published: April 2009

The monoid n of uniform block permutations is the factorisable inverse monoid which arises from the natural action of the symmetric group on the join semilattice of equivalences on an n-set; it has been described in the literature as the factorisable part of the dual symmetric inverse monoid. The present paper gives and proves correct a monoid presentation forn. The methods involved make use of a general criterion for a monoid generated by a group and an idempotent to be inverse, the structure of factorisable inverse monoids, and presentations of the symmetric group and the join semilattice of equivalences on an n-set.
Some necessary and sufficient conditions for p-nilpotence of finite groups
Authors: Wei Huaquan , Wang Yanming , Liu Xiaolei
Published: April 2009

The purpose of this paper is to give some necessary and sufficient conditions for p-nilpotent groups. We extend some results, including the well-known theorems of Burnside and Frobenius as well as some very recent theorems. We also apply our results to determine the structure of some finite groups in terms of formation theory.
n-Prüfer domains
Authors: Lee Sang Bum
Published: April 2009

We introduce n-Prüfer domains which axe generalisations of Prüfer domains and give several characterisations of them in terms of generalisations of purity, flatness and absolute purity.
Stacked submodules of torsion modules over discrete valuation domains
Authors: Astuti Pudji , Wimmer Harald K.
Published: April 2009

A submodule W of a torsion module M over a discrete valuation domain is called stacked in M if there exists a basis ℬ of M such that multiples of elements of ℬ form a basis of W. We characterise those submodules which are stacked in a pure submodule of M.
On properties of semipreinvex functions
Authors: Yang X. M. , Yang X. Q. , Teo K. L.
Published: April 2009

In this paper, we first discuss some basic properties of semipreinvex functions. We then show that the ratio of semipreinvex functions is semipreinvex, which extends earlier results by Khan and Hanson [6] and Craven and Mond [3]. Finally, saddle point optimality criteria are developed for a multiobjective fractional programming problem under semipreinvexity conditions.
System of generalised set-valued quasi-variational-like inequalities
Authors: Peng Jianwen
Published: April 2009

In this paper, we shall introduce a system of generalised set-valued quasi-variational-like inequalities, which generalises and unifies systems of generalised vector variational inequalities, systems of variational inequalities, generalised vector quasi-variational-like inequalities as well as various extensions of the classic variational inequalities in the literature. Some existence results for a solution of a system of generalized set-valued quasi-variational-like inequalities without any monotonity are obtained.
Strictly singular and strictly cosingular linear relations and their conjugates
Authors: Álvarez Teresa
Published: April 2009

In this paper various conditions are given under which the strict singularity (respectively, strict cosingularity) of a linear relation implies the strict singularity (respectively, strict cosingularity) of its conjugate.
Two necessary and sufficient conditions for the extension of Möbius groups
Authors: Wang Xiantao , Xiong Shouyao
Published: April 2009

Let SL(2, Γn) be the n-dimensional Clifford matrix group and G ⊂ SL(2, Γn) be a non-elementary subgroup. We show that G is the extension of a subgroup of SL(2, ℂ) if and only if G is conjugate in SL(2, Γn) to a group G′ which satisfies the following properties:

(1) there exist loxodromic elements g0, h ∈ G′ such that fix(g0) = {0, ∞}, fix(g0) ∩ fix(h) = ∅ and fix(h) ∩ ℂ ≠ ∅;

(2) tr(g) ∈ ℂ for each loxodromic element g ∈ G′.

Further G is the extension of a subgroup of SL(2, ℝ) if and only if G is conjugate in SL(2, Γn) to a group G′ which satisfies the following properties:

(1) there exists a loxodromic element g0 ∈ G′ such that fix(g0) ∩ {0, ∞} ≠ ∅;

(2) tr(g) ∈ ℝ for each loxodromic element g ∈ G′.

The discreteness of subgroups of SL(2, Γn) is also discussed.
On extremality of two connected locally extremal Beltrami coefficients
Authors: Yao Guowu
Published: April 2009

Let Ω1 and Ω2 be two domains in the complex plane with a nonempty intersection. Suppose that μj are locally extremal Beltrami coefficients in Ωj (j = 1, 2) respectively. In 1980, Sheretov posed the problem: Will the coefficient μ defined by the condition μ(z) = μj(z) for z ∈ Ωj, j = 1, 2, be locally extremal in Ω1 ∪ Ω2? We give a counterexample to show that μ may not be locally extremal and not even be extremal.
Solvability of singular second order m-point boundary value problems of Dirichlet type
Authors: Ma Ruyun , Thompson Bevan
Published: April 2009

Let f: [0, 1] × ℝ2 → ℝ be a function satisfying the Carathéodory conditions and t (1 − t) e (t) ∈ L1(0, 1). Let ai ∈ ℝ and ξi ∈ (0, 1) for i = 1, …, m − 2 where 0 < ξ1 < ξ2 < … < ξm−2 < 1. In this paper we study the existence of C[0, 1] solutions for the m-point boundary value problem

The proof of our main result is based on the Leray-Schauder continuation theorem.
The structure of elements in finite full transformation semigroups
Authors: Ayik Gonca , Ayik Hayrullah , Ünlü Yusuf , Howie John M.
Published: April 2009

Theindexandperiodof an elementaof a finite semigroup are the smallest values ofm≥ 1 andr≥ 1 such thatam+r= am. An element with indexmand period 1 is called anm-potentelement. For an element α of a finite full transformation semigroup with indexmand periodr, a unique factorisation α = σβ such that Shift(σ) ∩ Shift(β) = ∅ is obtained, where σ is a permutation of orderrand β is anm-potent. Some applications of this factorisation are given.
A new approach to Jacobi's theorems via Ramanujan's continued fractions
Authors: Adiga Chandrashekar , Han Jung Hun
Published: April 2009

In this paper, we show that Jacobi's two-square and two-triangular number theorems are immediate consequence of Ramanujan's continued fraction identities.
Flat submodules of free modules over commutative Bezout rings
Authors: Samei K.
Published: April 2009

A ring is called Bezout if every finitely generated ideal is principal. We show that every ideal of a commutative Bezout ring R is flat if and only if every submodule of a free R-module is flat. Using this theorem we obtain Neville's theorem.
Conjugaison Géodésique en rang 1
Authors: Fanaï Hamid-Reza
Published: April 2009

Soit (M, g0) une variété riemannienne compacte de courbure sectionnelle négative. Soit g1 une autre métrique riemannienne sur M de rang 1. On montre que l'égalité des spectres marqués des longueurs de g0 et g1 implique que le flot géodésique de g0 est un facteur de celui de g1.
Power integral bases for real cyclotomic fields
Authors: Miller-Sims Laurel , Robertson Leanne
Published: April 2009

We consider the problem of determining all power integral bases for the maximal real subfieldQ(ζ + ζ−1) of thep-th cyclotomic fieldQ(ζ), wherep≥ 5 is prime and ζ is a primitivep-th root of unity. The ring of integers isZ[ζ+ζ−1] so a power integral basis always exists, and there are further non-obvious generators for the ring. Specifically, we prove thatifor one of the Galois conjugates of these five algebraic integers. Up to integer translation and multiplication by −1, there are no additional generators forp≤ 11, and it is plausible that there are no additional generators forp> 13 as well. Forp= 13 there is an additional generator, but we show that it does not generalise to an additional generator for 13 <p< 1000.
On super efficiency in set-valued optimisation in locally convex spaces
Authors: Xu Yihong , Zhu Chuanxi
Published: April 2009

The set-valued optimisation problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of nearly cone-subconvexlikeness, by applying the separation theorem for convex sets, Kuhn-Tucker and Lagrange necessary conditions for the set-valued optimisation problem to attain its super efficient solutions are obtained. Also, Kuhn-Tucker and Lagrange sufficient conditions are derived. Finally two kinds of unconstrained programs equivalent to set-valued optimisation problems are established.
An Alexsandrov type theorem fork-convex functions
Authors: Chaudhuri Nirmalendu , Trudinger Neil S.
Published: April 2009

In this note we show thatk-convex functions on ℝnare twice differentiable almost everywhere for every positive integerk>n/2. This generalises Alexsandrov's classical theorem for convex functions.
Lower and upper bounds for Cohen-Macaulay dimension
Authors: Asadollahi J. , Salarain Sh.
Published: April 2009

Lower and upper bounds for CM-dimension, called CM*-dimension and CM*-dimension, will be defined for any finitely generated module M over a local Noetherian ring R. Both CM* and CM*-dimension reflect the Cohen–Macaulay property of rings. Our results will show that these dimensions have the expected basic properties parallel to those of the homological dimensions. In particular, they satisfy an analog of the Auslander-Buchsbaum formula.
On the dynamics of the linear action of SL(n, Z)
Authors: Cairns Grant , Nielsen Anthony
Published: April 2009

Using Moore's ergodicity theorem, S.G. Dani and S. Raghavan proved that the linear action of SL(n, ℤ) on ℝn is topologically (n − l)-transitive; that is, topologically transitive on the Cartesian product of n − 1 copies of ℝn. In this paper, we give a more direct proof, using the prime number theorem. Further, using the congruence subgroup theorem, we generalise the result to arbitrary finite index subgroups of SL(n, ℤ).
Minimax inequalities inG-convex spaces
Authors: Balaj Mircea
Published: April 2009

In this paper we establish two minimax theorems of Sion-type inG-convex spaces. As applications we obtain generalisations of some theorems concerning compatibility of some systems of inequalities.
Farthest points and the farthest distance map
Authors: Bandyopadhyay Pradipta , Dutta S.
Published: April 2009

In this paper, we consider farthest points and the farthest distance map of a closed bounded set in a Banach space. We show, inter alia, that a strictly convex Banach space has the Mazur intersection property for weakly compact sets if and only if every such set is the closed convex hull of its farthest points, and recapture a classical result of Lau in a broader set-up. We obtain an expression for the subdifferential of the farthest distance map in the spirit of Preiss' Theorem which in turn extends a result of Westphal and Schwartz, showing that the subdifferential of the farthest distance map is the unique maximal monotone extension of a densely defined monotone operator involving the duality map and the farthest point map.
Multiple Hilbert and Hardy-Hilbert inequalities with non-conjugate parameters
Authors: Brnetić Ilko , Krnić Mario , Pečarić Josip
Published: April 2009

The main objective of this paper is a study of some new generalisations of Hilbert and Hardy-Hilbert type inequalities involving non-conjugate parameters. We prove general forms of multiple Hilbert-type inequalities, and we also introduce multiple inequalities of Hardy-Hilbert type with non-conjugate parameters.
Permutation representations and rational irreducibility
Authors: Dixon John D.
Published: April 2009

The natural character π of a finite transitive permutation group G has the form 1G + θ where θ is a character which affords a rational representation of G. We call G a QI-group if this representation is irreducible over ℚ. Every 2-transitive group is a QI-group, but the latter class of groups is larger. It is shown that every QI-group is ¾-transitive and primitive, and that it is either almost simple or of affine type. QI-groups of affine type are completely determined relative to the 2-transitive affine groups, and partial information is obtained about the socles of simply transitive almost simple QI-groups. The only known simply transitive almost simple QI-groups are of degree 2k−1(2k − 1) with 2k − 1 prime and socle isomorphic to PSL(2, 2k).
The group of Poisson automorphisms of the Poisson symplectic space
Authors: Oh Sei-Qwon , Cho Eun-Hee
Published: April 2009

The group of Poisson automorphisms of the coordinate ring of Poisson symplectic 2n-space is isomorphic to the algebraic torus (κ✶)n+1 and it confirms that the algebra constructed by K.L. Horton (2003) is a quantisation of the coordinate ring of Poisson symplectic 2n-space.
Generating functions related to the Okamoto polynomials for the Painlevé IV equation
Authors: Goto Hiromichi , Kajiwara Kenji
Published: April 2009

We construct generating functions for the entries of Hankel determinant formula for the Okamoto polynomials which characterise a class of rational solutions to the Painlevé IV equation. Generating functions are characterised as asymptotic expansions of log derivative of Ai and Bi, which are solutions of the Airy equation.
A rigidity theorem for discrete groups
Authors: Chen Wen-Haw , Wu Jyh-Yang
Published: April 2009

This work considers the discrete subgroups of group of isometries of an Alexandrov space with a lower curvature bound. By developing the notion of Hausdorff distance in these groups, a rigidity theorem for the close discrete groups was proved.
Complete spacelike hypersurfaces in a de Sitter space
Authors: Shichang Shu
Published: April 2009

In this paper, we characterise the n-dimensional (n ≥ 3) complete spacelike hypersurfaces Mn in a de Sitter space with constant scalar curvature and with two distinct principal curvatures. We show that if the multiplicities of such principal curvatures are greater than 1, then Mn is isometric to Hk (sinh r) × Sn−k (cosh r), 1 < k < n − 1. In particular, when Mn is the complete spacelike hypersurfaces in with the scalar curvature and the mean curvature being linearly related, we also obtain a characteristic Theorem of such hypersurfaces.
On stallings' unique factorisation groups
Authors: Cartwright Donald I. , Krön Bernhard
Published: April 2009

Let Γ be a group and Σ a symmetric generating set for Γ. In 1966, Stallings called Γ a unique factorisation group if each group element may be written in a unique way as a product a1…am, where ai ∈ Σ for each i and aiai+1 ∉ Σ ∪ {1} for each i < m. In this paper we give a complete combinatorial proof of a theorem, not explicitly stated by Stallings in 1966, characterising all such pairs (Γ, Σ). We also characterise the unique factorisation pairs by a certain tree-like property of their Cayley graphs.
A class of finite commutative rings constructed from Witt rings
Authors: Craven Thomas , Vo Monika
Published: April 2009

Motivated by constructions of Witt rings in the algebraic theory of quadratic forms, the authors construct new classes of finite commutative rings and explore some of their properties. These rings are constructed as quotient rings of a special class of integral group rings for which the group is an elementary 2-group. The new constructions are compared to other rings in the literature.
Reverses of the Schwarz inequality generalising a Klamkin–McLenaghan result
Authors: Dragomir Sever S.
Published: April 2009

New reverses of the Schwarz inequality in inner product spaces that incorporate the classical Klamkin-McLenaghan result for the case of positive n-tuples are given. Applications for Lebesgue integrals are also provided.
Generalised monotone line search algorithm for degenerate nonlinear minimax problems
Authors: Jian Jin-Bao , Quan Ran , Zhang Xue-Lu
Published: April 2009

In this paper, nonlinear minimax problems are discussed. Using Sequential Quadratic Programming and the generalised monotone line search technique, we propose a new algorithm for solving degenerate minimax problems. At each iteration of the proposed algorithm, a search direction is obtained by solving a new Quadratic Programming problem which always has a solution. Global convergence can be obtained without the regularity condition of linear independence. Finally, some numerical experiments are reported.
Remarks on the uniqueness problem for the logistic equation on the entire space
Authors: Du Yihong , Liu Lishan
Published: April 2009

We consider the logistic equation −Δu=a(x)u−b(x)uqon all ofRNwitha(x)/|x|γandb(x)/|x|τbounded away from 0 and infinity for all large |x|, where γ > −2, τ ∈ (−∞, ∞). We show that this problem has a unique positive solution. This considerably improves some earlier results. The main new technique here is a Safonov type iteration argument. The result can also be proved by a technique introduced by Marcus and Veron, and the two different techniques are compared.
Cyclic Tarski algebras
Authors: Zander Marta A.
Published: April 2009

The variety of cyclic Boolean algebras is a particular subvariety of the variety of tense algebras. The objective of this paper is to study the variety  of {→,g, h}-subreducts of cyclic Boolean algebras, which we call cyclic Tarski algebras. We prove that  is generated by its finite members and we characterise the locally finite subvarieties of . We prove that there are no splitting varieties in the lattice Λ() of subvarieties of . Finally, we prove that the subquasivarieties and the subvarieties of a locally finite subvariety of  coincide.
Multiplicity of positive periodic solutions to second order differential equations
Authors: Chu Jifeng , Lin Xiaoning , Jiang Daqing , O'Regan Donal , Agarwal R. P.
Published: April 2009

In this paper, we study the existence of positive periodic solutions to the equation x″ = f (t, x). It is proved that such a equation has more than one positive periodic solution when the nonlinearity changes sign. The proof relies on a fixed point theorem in cones.
Construction of elliptic curves with cyclic groups over prime fields
Authors: Nakazawa Naoya
Published: April 2009

The purpose of this article is to construct families of elliptic curves E over finite fields F so that the groups of F-rational points of E are cyclic, by using a representation of the modular invariant function by a generator of a modular function field associated with the modular group Γ0(N), where N = 5, 7 or 13.
Namioka spaces and topological games
Authors: Mykhaylyuk V. V.
Published: April 2009

We introduce a class of β − v-unfavourable spaces, which contains some known classes of β-unfavourable spaces for topological games of Choquet type. It is proved that every β − v-unfavourable space X is a Namioka space, that is for any compact space Y and any separately continuous function f : x × Y → ℝ there exists a dense in XGδ-set A ⊆ X such that f is jointly continuous at each point of A × Y.
On representations of variants of semigroups
Authors: Kudryavtseva Ganna , Maltcev Victor
Published: April 2009

We construct a family of representations of an arbitrary variantSaof a semigroupS, induced by a given representation ofS, and investigate properties of such representations and their kernels.
A note on a theorem of F. Wang and G. Tang
Authors: Takahashi Ryo
Published: April 2009

In this paper, we refine a theorem of F. Wang and G. Tang concerning freeness of reflexive modules over coherent GCD-domains.
The generalised f-projection operator with an application
Authors: Wu Ke-Qing , Huang Nan-Jing
Published: April 2009

In this paper, we introduce a new concept of generalised f-projection operator which extends the generalised projection operator πK : B* → K, where B is a reflexive Banach space with dual space B* and K is a nonempty, closed and convex subset of B. Some properties of the generalised f-projection operator are given. As an application, we study the existence of solution for a class of variational inequalities in Banach spaces.
Inverse limits as limits with respect to the Hausdorff metric
Authors: Banič Iztok
Published: April 2009

We show that the inverse limit of any inverse sequence of compact metric spaces and surjective bonding maps is in fact the limit of a sequence of homeomorphic copies of the same spaces with respect to the Hausdorff metric.
Problèmes D'effectivité sur les Quartiques de Fermat
Authors: Cali Élie , Kraus Alain
Published: April 2009

Let K be a number field. An element b ∈ K* being given, let Cb be the curve defined over K by the equation x4 + y4 = bz4. Let Cb(K) be the set of the K-rational points of Cb. This paper uses Dem'janenko and Manin type methods to obtain effective criteria for Cb(K) to be empty.
The Hahn-Schur Theorem on effect algebras
Authors: Aizpuru A. , Nicasio-Llach M. , Tamayo M.
Published: April 2009

In this paper we obtain new results on the uniform convergence on matrices and a new version of the matrix theorem of the Hahn-Schur summation theorem in effect algebras.
Nearly extremal Cohen–Macaulay and Gorenstein algebras
Authors: Kumar Chanchal , Singh Pavinder , Kumar Ashok
Published: April 2009

This paper study nearly extremal Cohen–Macaulay and Gorenstein algebras and characterise them in terms of their minimal free resolutions. Explicit bounds on their graded Betti numbers and their multiplicities are obtained.
On the distribution of angles of the Salié sums
Authors: Shparlinski Igor E.
Published: April 2009

For a primepand integersaandb, we consider Salié sums

where χ2(x) is a quadratic character and x¯ is the modular inversion ofx, that is,xx¯≡ 1 (modp). One can naturally associate withSp(a, b) a certain angle θp(a, b) ∈ [0, π]. We show that, for any fixed ε > 0, these angles are uniformly distributed in [0, π] whenaandbrun over arbitrary sets , ℬ ⊆ {0, 1, …,p− 1} such that there are at leastp1+εquadratic residues modulopamong the productsab, where (a, b) ∈  × ℬ.
Some invariants of Pretzel links
Authors: Kim Dongseok , Lee Jaeun
Published: April 2009

We show that nontrivial classical pretzel knots L (p, q, r) are hyperbolic with eight exceptions which are torus knots. We find Conway polynomials of n-pretzel links using a new computation tree. As applications, we compute the genera of n-pretzel links using these polynomials and find the basket number of pretzel links by showing that the genus and the canonical genus of a pretzel link are the same.
Composition operators on weighted Bergman-Orlicz spaces
Authors: Sharma Ajay K. , Sharma S. D.
Published: April 2009

In this paper, composition operators acting on Bergman-Orlicz spaces

are studied, where ψ is a non-constant, non-decreasing convex function defined on (-∞, ∞) which satisfies the growth condition . In fact, under a mild condition on ∞, we show that every holomorphic-self map ∞ of induces a bounded composition operator on and C∞ is compact on if and only if it is compact on .
A class of iteration methods for the matrix equation A×B = C
Authors: Guo Konghua , Hu Xiyan , Zhang Lei
Published: April 2009

An iteration method for the matrix equation A×B = C is constructed. By this iteration method, the least-norm solution for the matrix equation can be obtained when the matrix equation is consistent and the least-norm least-squares solutions can be obtained when the matrix equation is not consistent. The related optimal approximation solution is obtained by this iteration method. A preconditioned method for improving the iteration rate is put forward. Finally, some numerical examples are given.
Two Ostrowski type inequalities for the Stieltjes integral of monotonic functions
Authors: Cheung W.-S. , Dragomir S. S.
Published: April 2009

Two integral inequalities of Ostrowski type for the Stieltjes integral are given. The first is for monotonic integrators and Hölder continuous integrands while the second considers the dual case, that is, for monotonic integrands and Hölder continuous integrators. Applications for the mid-point inequality that are useful in the numerical analysis of Stieltjes integrals are exhibited. Some connections with the generalised trapezoidal rule are also presented.
Unique extremality, local extremality and extremal non-decreasable dilatations
Authors: Yao Guowu
Published: April 2009

Given a quasi-symmetric self-homeomorphism h of the unit circle Sl, let Q(h) be the set of all quasiconformal mappings with the boundary correspondence h. In this paper, it is shown that there exists certain quasi-symmetric homeomorphism h, such that Q(h) satisfies either of the conditions,

(1) Q(h) admits a quasiconformal mapping that is both uniquely locally-extremal and uniquely extremal-non-decreasable instead of being uniquely extremal;

(2) Q(h) contains infinitely many quasiconformal mappings each of which has an extremal non-decreasable dilatation.

An infinitesimal version of this result is also obtained.