bluuebunny/crossref_metadata_2025 huggingface dataset:
Regular polygons and a propellor problem for convex sets in the plane
Authors: Scott P.R.
Published: April 2009

We find the convex planar set of maximal area which is partitioned into subsets of equal area by a given propellor. The argument depends on the characterisation of an n-sided polygon which is circumscribed about a regula n-gon Pn, and inscribed in a regula n-gon Qn, where Pn and Qn are homothetic about their common centre.
A characterisation of weak compactness in Banach spaces
Authors: Moors Warren B.
Published: April 2009

In this short note we give a new characterisation of weak compactness.
The mod 2 homology of Sp (n) instantons and the classifying space of the gauge group
Authors: Choi Younggi
Published: April 2009

We study the mod 2 homology of the moduli space of instantons associated with the prinicpal Sp (n) bundle over the four-sphere and the classifying space of the gauge group using the Serre spectral sequence and the homology operations.
Regular geodesic normal forms in virtually Abelian groups
Authors: Shapiro Michael , Neumann Walter D.
Published: April 2009

We describe a virtually Abelian group G generated by a finite set X such that there is no regular language of geodesic X-words that surjects to G by evaluation.
Approach regions for the square root of the Poisson kernel and bounded functions
Authors: Sjögren P.
Published: April 2009

If the Poisson kernel of the unit disc is replaced by its square root, it is known that normalised Poisson integrals of Lp boundary functions converge almost everywhere at the boundary, along approach regions wider than the ordinary non-tangential cones. The sharp approach region, defined by means of a monotone function, increases with p. We make this picture complete by determining along which approach regions one has almost everywhere convergence for L∞ boundary functions.
Dissections of quotients of theta-functions
Authors: Chan Song Heng
Published: April 2009

We prove a general theorem on dissections of quotients of theta-functions. As corollaries, we establish six q-series identities that were conjectured by M.D. Hirschhorn:
On rings whose modules of finite length are all cyclic
Authors: Hirano Yasuyuki
Published: April 2009

We give some characterisations of rings R whose modules with composition series are all cyclic. In particular, we prove that all left R-modules of finite length are cyclic if and only if R has no nonzero Artinian factor rings.
Finite p-groups with normal normalisers
Authors: Ormerod Elizabeth A. , Parmeggiani Gemma
Published: April 2009

We consider the class N of groups in which the normaliser of every subgroup is normal, and the class C of groups in which the commutator subgroup normalises every subgroup. It is clear that C ⊆ N, and it is known that groups in the class N are nilpotent of class at most 3. We show that every finite p-group in N is also in C, provided that p ≥ 5, and we give an example showing that this is not true for p = 2.
Direct products and properly 3-realisable groups
Authors: Cárdenas Manuel , Lasheras Francisco F. , Roy Ranja
Published: April 2009

In this paper, we show that the direct of infinite finitely presented groups is always properly 3-realisable. We also show that classical hyperbolic groups are properly 3-realisable. We recall that a finitely presented group G is said to be properly 3-realisable if there exists a compact 2-polyhedron K with π1 (K) ≅ G and whose universal cover K̃ has the proper homotopy type of a (p.1.) 3-manifold with boundary. The question whether or not every finitely presented is properly 3-realisable remains open.
A proof of Higgins's conjecture
Authors: Braun Gábor
Published: April 2009

Let be a group homomorphism between free products of groups such that GλΘ = Bλ for all λ ∈ Λ. Let H ⊆ G be a subgroup such that HΘ = B. Then such that HλΘ = Bλ and where Fλ is free.
Riemannian manifolds whose curvature operator R(X, Y) has constant eigenvalues
Authors: Nikolayevsky Y.
Published: April 2009

A Riemannian manifold Mn is called IP, if, at every point x ∈ Mn, the eigenvalues of its skew-symmetric curvature operator R(X, Y) are the same, for every pair of orthonormal vectors X, Y ∈ TxMn. In [5, 6, 12] it was shown that for all n ≥ 4, except n = 7, an IP manifold either has constant curvature, or is a warped product, with some specific function, of an interval and a space of constant curvature. We prove that the same result is still valid in the last remaining case n = 7, and also study 3-dimensional IP manifolds.
Prediction of fractional Brownian motion with Hurst index less than 1/2
Authors: Anh V. V. , Inoue A.
Published: April 2009

We give a proof based on an integral equation for an explicit prediction formula for fractional Brownian motion with Hurst index less than 1/2.
Witt kernels of bi-quadratic extensions in characteristic 2: Addendum
Authors: Ahmad Hamza
Published: April 2009

In a recent referee's report reviewing [2], it was pointed out to me that Theorem 2.2 in [1] was already known in the literature, and is (originally) due to Mammone and Moresi in [3]. Also in [3], the authors establish the excellence of inseparable quadratic extensions in a shorter way than I presented in [1]. As the paper [3] was unknown to me at the time of submitting [1], I hope by this note to acknowledge and credit [3] for the result(s).
Pointed Blaschke manifolds and geodesic normal sections
Authors: Kim Dong-Soo , Kim Young Ho , Lee Eun Kyoung
Published: April 2009

We study complete submanifolds of Euclidean space where every geodesic passing through a fixed point is the normal section along it. We prove that all such geodesics are independent of the direction at the point and such submanifolds are pointed Blaschke manifolds or diffeomorphic to a Euclidean space.
On the orders of generators of capablep-groups
Authors: Magidin Arturo
Published: April 2009

A group is called capable it if is a central factor group. For each primepand positive integerc, we prove the existence of a capablep-group of classcminimally generated by an element of orderpand an element of orderp1+⌊c−1/p−1⌋. This is best possible.
Polynomial near-rings in k indeterminates
Authors: Lee Enoch K.S. , Groenewald Nico J.
Published: April 2009

Polynomial near-rings in k-commuting indeterminates are our object of study. We illustrate out work for k = 2, that is, N[x, y] as an extension to N[x], while the case for arbitrarily k follows easily. Our approach is different from the recursive definition N[x][y]. However, it can be shown that N[x, y] is isomorphic to N[x][y]. Several important tools such as the degree, the least degree, et cetera are defined with respect to N[x, y]. We also clarify some notations involved in defining polynomial near-rings.
Quadratic reverses of the triangle inequality for Bochner integral in Hilbert spaces
Authors: Dragomir Sever S.
Published: April 2009

Some quadratic reverses of the continuous triangle inequality for the Bochner integral of vector-valued functions in Hilbert spaces are given. Applications of complex-valued functions are provided as well.
A note on Lagrange interpolation for |x|λ at equidistant nodes
Authors: Ganzburg Michael I. , Revers Michael
Published: April 2009

In this note, we discuss the exceptional set E ⊆ [−1, 1] of points x0 satisfying the inequality

where λ > 0, λ ≠ 2, 4, … and Ln(fλ,.) is the Lagrange interpolation polynomial of degree at most n to fλ(x):= |x|λ on the interval [−1, 1] associated with the equidistant nodes. It is known that E has Lebesgue measure zero. Here we show that E contains infinite families of rational and irrational numbers.
Abelian groups as inner mapping groups of loops
Authors: Ali Asif , Cossey John
Published: April 2009

The question of which Abelian groups can be the inner mapping group of a loop has been considered by Niemenmaa, Kepka and others. We give a construction which shows that many finite Abelian groups can be the inner mapping group of a loop.
A note on a continued fraction of Ramanujan
Authors: Adiga C. , Anitha N.
Published: April 2009

Ramanujan recorded many beautiful continued fractions in his notebooks. In this paper, we derive several indentities involving the Ramanujan continued fraction c(q), including relations between c(q) and c(qn). We also obtain explicit evaluations of for various positive integers n.
Properly embedded and immersed minimal surfaces in the Heisenberg group
Authors: Cheng Jih-Hsin , Hwang Jenn-Fang
Published: April 2009

We study properly embedded and immersed p(pseudohermitian)-minimal surfaces in the 3-dimensional Heisenberg group. From the recent work of Cheng, Hwang, Malchiodi, and Yang, we learn that such surfaces must be ruled surfaces. There are two types of such surfaces: band type and annulus type according to their topology. We givn an explicit expression for these surfaces. Among band types there is a class of properly embedded p-minimal surfaces of so called helicoid type. We classify all the helicoid type p-minimal surfaces. This class of p-minimal surfaces includes all the entire p-minimal graphs (except contact planes) over any plane. Moreover, we give a necessary and sufficient condition for such a p-minimal surface to have no singular points. For general complete immersed p-minimal surfaces, we prove a half space theorem and give a criterion for the properness.
Div-curl type theorems on Lipschitz domains
Authors: Lou Zengjian
Published: April 2009

For Lipschitz domains of ℝn we prove div-curl type theorems, which are extensions to domains of the Div-Curl Theorem on ℝn by Coifman, Lions, Meyer and Semmes. Applying the div-curl type theorems we give decompositions of Hardy spaces on domains.
A nonlinear map for midpoint locally uniformly rotund renorming
Authors: Lajara S. , Pallars A.J.
Published: April 2009

We provide a criterion for midpoint locally uniformly rotund renormability of normed spaces involving the class of σ-slicely continuous maps, recently introduced by Moltó, Orihuela, Troyanski and Valdiva in 2003. As a consequence of this result, we obtain a theorem of G. Alexandrov concerning the three space problem for midpoint locally uniformly rotund renormings of Banach spaces.
A remarkable continued fraction
Authors: Angell David , Hirschhorn Michael D.
Published: April 2009

We study a particular oscillating continued fraction, and find its two limit points.
Finite presentability of some metabelian Hopf algebras
Authors: Kochloukova Dessislava H.
Published: April 2009

We classify the Hopf algebras U (L)#kQ of homological type FP2 where L is a Lie algebra and Q an Abelian group such that L has an Abelian ideal A invariant under the Q-action via conjugation and U (L/A)#kQ is commutative. This generalises the classification of finitely presented metabelian Lie algebras given by J. Groves and R. Bryant.
On the monotonicity properties of additive representation functions
Authors: Chen Yong-Gao , Sárközy András , Sós Vera T. , Tang Min
Published: April 2009

If A is a set of positive integers, let R1 (n) be the number of solutions of a + a′ = n, a. a′ ∈ A, and let R2(n) and R3(n) denote the number of solutions with the additional restrictions a < a′, and a ≤ a′ respectively. The monotonicity properties of the three functions R1(n), R2(n), and R3(n) are studied and compared.
Subalgebras of free restricted Lie algebras
Authors: Bryant R.M. , Kovács L.G. , Stöhr Ralph
Published: April 2009

A theorem independently due to A.I. Shirshov and E. Witt asserts that every subalgebra of a free Lie algebra (over a field) is free. The main step in Shirshov's proof is a little known but rather remarkable result: if a set of homogeneous elements in a free Lie algebra has the property that no element of it is contained in the subalgebra generated by the other elements, then this subset is a free generating set for the subalgebra it generates. Witt also proved that every subalgebra of a free restricted Lie algebra is free. Later G.P. Kukin gave a proof of this theorem in which he adapted Shirshov's argument. The main step is similar, but it has come to light that its proof contains substantial gaps. Here we give a corrected proof of this main step in order to justify its applications elsewhere.
Implicit vector equilibrium problems via nonlinear scalarisation
Authors: Li Jun , Huang Nan-Jing
Published: April 2009

The purpose of this paper is to introduce a nonlinear scalarisation function for solving a class of implicit vector equilibrium problems. We prove a scalarisation lemma to show the relation between the implicit vector equilibrium problem and the nonlinear scalarisation function. Then we derive some new existence theorems for solutions of implicit vector equilibrium problems, using the scalarisation lemma and the FKKM theorem.
Ascending HNN-extensions and properly 3-realisable groups
Authors: Lasheras Francisco F.
Published: April 2009

In this paper, we show that any ascending HNN-extension of a finitely presented group is properly 3-realisable. We recall that a finitely presented group G is said to be properly 3-realisable if there exists a compact 2-polyhedron K with π1(K) ≅ G and whose universal cover K̃ has the proper homotopy type of a (PL) 3-manifold (with boundary).
Abstract theory of semiorderings
Authors: Craven Thomas C. , Smith Tara L.
Published: April 2009

Marshall's abstract theory of spaces of orderings is a powerful tool in the algebraic theory of quadratic forms. We develop an abstract theory for semiorderings, developing a notion of a space of semiorderings which is a prespace of orderings. It is shown how to construct all finitely generated spaces of semiorderings. The morphisms between such spaces are studied, generalising the extension of valuations for fields into this context. An important invariant for studying Witt rings is the covering number of a preordering. Covering numbers are defined for abstract preorderings and related to other invariants of the Witt ring.
Characterisation of the isometric composition operators on the Bloch space
Authors: Colonna Flavia
Published: April 2009

In this paper, we characterise the analytic functions ϕ mapping the open unit disk ▵ into itself whose induced composition operator Cϕ: f ↦ f ∘ ϕ is an isometry on the Bloch space. We show that such functions are either rotations of the identity function or have a factorisation ϕ = gB where g is a non-vanishing analytic function from Δ into the closure of ▵, and B is an infinite Blaschke product whose zeros form a sequence{zn} containing 0 and a subsequence satisfying the conditions , and
Examples and classification of Riemannian submersions satisfying a basic equality
Authors: Chen Bang-Yen
Published: April 2009

In an earlier article we obtain a sharp inequality for an arbitrary isometric immersion from a Riemannian manifold admitting a Riemannian submersion with totally geodesic fibres into a unit sphere. In this article we investigate the immersions which satisfy the equality case of the inequality. As a by-product, we discover a new characterisation of Cartan hypersurface in S4.
On coatoms of the lattice of matric-extensible radicals
Authors: France-Jackson Halina
Published: April 2009

A radical α in the universal class of all associative rings is called matric-extensible if for all natural numbers n and all rings A, A ∈ α if and only if Mn(A) ∈ α, where Mn(A) denotes the n × n matrix ring with entries from A. We show that there are no coatoms, that is, maximal elements in the lattice of all matric-extensible radicals of associative rings.
Rendezvous numbers in normed spaces
Authors: Farkas Bálint , Révész Szilárd György
Published: April 2009

In previous papers, we used abstract potential theory, as developed by Fuglede and Ohtsuka, to a systematic treatment of rendezvous numbers. We considered Chebyshev constants and energies as two variable set functions, and introduced a modified notion of rendezvous intervals which proved to be rather nicely behaved even for only lower semicontinuous kernels or for not necessarily compact metric spaces.

Here we study the rendezvous and average numbers of possibly infinite dimensional normed spaces. It turns out that very general existence and uniqueness results hold for the modified rendezvous numbers in all Banach spaces. We also observe the connections of these magical numbers to Chebyshev constants, Chebyshev radius and entropy. Applying the developed notions with the available methods we calculate the rendezvous numbers or rendezvous intervals of certain concrete Banach spaces. In particular, a satisfactory description of the case of Lp spaces is obtained for all p > 0.
The Hutchinson-Barnsley theory for infinite iterated function systems
Authors: Gwóźdź-Lukawska Gertruda , Jachymski Jacek
Published: April 2009

We show that some results of the Hutchinson-Barnsley theory for finite iterated function systems can be carried over to the infinite case. Namely, if {Fi:i∈ ℕ} is a family of Matkowski's contractions on a complete metric space (X, d) such that (Fix0)i∈Nis bounded for somex0∈X, then there exists a non-empty bounded and separable setKwhich is invariant with respect to this family, that is,. Moreover, given σ ∈ ℕℕandx∈X, the limit exists and does not depend onx. We also study separately the case in which (X, d) is Menger convex or compact. Finally, we answer a question posed by Máté concerning a finite iterated function system {F1,…,FN} with the property that each ofFihas a contractive fixed point.
A functional inequality for the polygamma functions
Authors: Alzer Horst
Published: April 2009

Let

where ψ denotes the logarithmic derivative of Euler's gamma function. We prove that the functional inequality

holds if and only if 0 < r ≤ 1. And, we show that the converse is valid if and only if r < 0 or r ≥ n + 1.
Linear structure of weighted holomorphic non-extendibility
Authors: Bernal-González L.
Published: April 2009

In this paper, it is proved that, for any domain G of the complex plane, there exists an infinite-dimensional closed linear submanifold M1 and a dense linear submanifold M2 with maximal algebraic dimension in the space H(G) of holomorphic functions on G such that G is the domain of holomorphy of every nonzero member f of M1 or M2 and, in addition, the growth of f near each boundary point is as fast as prescribed.
Existence of Torus bundles associated to cocycles
Authors: Lee Min Ho
Published: April 2009

A Kuga fibre variety is a fibre bundle over a locally symmetric space whose fibre is a polarized Abelian variety. We describe a complex torus bundle associated to a 2-cocycle of a discrete group, which may be regarded as a generalized Kuga fibre variety, and prove the existence of such a bundle.
On the lengths of pairs of complex matrices of size at most five
Authors: Longstaff W. E. , Niemeyer A. C. , Panaia Oreste
Published: April 2009

The length of every pair {A, B} of n×n complex matrices is at most 2n − 2, if n ≤ 5. That is, for n ≤ 5, the (possibly empty) words in A, B of length at most 2n − 2 span the unital algebra  generated by A, B. For every positive integer m there exist m×m complex matrices C, D such that the length of the pair {C, D} is 2m – 2.
The Γ-opial property
Authors: Budzyńska Monika , Kuczumow Tadeusz , Michalska Małgorzata
Published: April 2009

In this short paper we show that if (X, ∥ · ∥) is a Banach space, Γ a norming set for X and C is a nonempty, bounded and Γ sequentially compact subset of X, then in C the Γ-Opial condition for nets is equivalent to the Γ-Opial condition.
Parallel metrics and reducibility of the holonomy group
Authors: Atkins Richard
Published: April 2009

In this paper we investigate the relationship between the existence of parallel semi-Riemannian metrics of a connection and the reducibility of the associated holonomy group. The question as to whether the holonomy group necessarily reduces in the presence of a specified number of independent parallel semi-Riemannian metrics is completely determined by the the signature of the metrics and the dimension d of the manifold, when d ≠ 4. In particular, the existence of two independent, parallel semi-Riemannian metrics, one of which having signature (p,q) with p ≠ q, implies the holonomy group is reducible. The (p,p) cases, however, may allow for more than one parallel metric and yet an irreducible holonomy group: for n = 2m, m ≥ 3, there exist connections on Rn with irreducible infinitesimal holonomy and which have two independent, parallel metrics of signature (m,m). The case of four-dimensional manifolds, however, depends on the topology of the manifold in question: the presence of three parallel metrics always implies reducibility but reducibility in the case of two metrics of signature (2,2) is guaranteed only for simply connected manifolds. The main theorem in the paper is the construction of a topologically non-trivial four-dimensional manifold with a connection that admits two independent metrics of signature (2,2) and yet has irreducible holonomy. We provide a complete solution to the general problem.
On Kähler nilmanifolds with top homology in codimension two
Authors: Gilligan Bruce
Published: April 2009

SupposeGis a connected, complex, nilpotent Lie group and Γ is a discrete subgroup ofGsuch thatG/Γ is Kähler and the top nonvanishing homology group ofG/Γ (with coefficients in ℤ2) is in codimension two or less. We show thatGis then Abelian. We also note that an example from [12] shows that this fails if the top nonvanishing homology is in codimension three.
A Riemannian invariant and its applications to Einstein manifolds
Authors: Chen Bang-Yen
Published: April 2009

We introduce a Riemannian invariant and establish general optimal inequalities involving the invariants and the squared mean curvature for Einstein manifolds isometrically immersed in real space forms. We show that these inequalities do not hold for arbitrary submanifolds in real space forms in general. We also provide some immediate applications of the inequalities.
Twisted Alexander polynomial for the Lawrence-Krammer representation
Authors: Suzuki Masaaki
Published: April 2009

In this paper, we prove that the twisted Alexander polynomial for the Lawrence-Krammer representation of the braid group B4 is trivial. This gives an answer to the problem of whether the twisted Alexander polynomial for given faithful representations is always non-trivial.
On involutive Lie algebras having a Cartan decomposition
Authors: Martín A. J. Calderón
Published: April 2009

We introduce the concept of Cartan decomposition relative to a Cartan subalgebraHin the sense of Y. Billig and A. Pianzola for involutive complex Lie algebrasLof arbitrary dimension. IfLhas such a decomposition and is infinite dimensional and simple, we show it is *-isomorphic to a direct limit of classical finite dimensional simple involutive Lie algebras of the same typeA,B,C, orD.
Finite dimensional characteristics related to superreflexivity of Banach spaces
Authors: Ostrovskii M. I.
Published: April 2009

One of the important problems of the local theory of Banach Spaces can be stated in the following way. We consider a condition on finite sets in normed spaces that makes sense for a finite set any cardinality. Suppose that the condition is such that to each set satisfying it there corresponds a constant describing “how well” the set satisfies the condition.

The problem is:Suppose that a normed space X has a set of large cardinality satisfying the condition with “poor” constant. Does there exist in X a set of smaller cardinality satisfying the condition with a better constant?

In the paper this problem is studied for conditions associated with one of R.C. James's characterisations of superreflexivity.
On the n-parameter abstract Cauchy problem
Authors: Janfada M. , Niknam A.
Published: April 2009

Let Hi(i = 1, 2, …, n), be closed operators in a Banach space X. The generalised initialvalue problem

of the abstract Cauchy problem is studied. We show that the uniqueness of solution u: [0, T1] × [0, T2] × … × [0, Tn] → X of this n-abstract Cauchy problem is closely related to C0-n-parameter semigroups of bounded linear operators on X. Also as another application of C0-n-parameter semigroups, we prove that many n-parameter initial value problems cannot have a unique solution for some initial values.
A fast algorithm for curve singularities
Authors: Ma Sheng-Ming
Published: April 2009

We demonstrate fast algorithm to resolve local singularities of algebraic curves. The algorithm is based on the monomial transform and is independent of any other coordinate change. Two new invariants are introduced to gauge the singularities and sharply control the number of algorithmic steps. Our algorithm is applicable to both real and complex domains.
The day norm and Gruenhage compacta
Authors: Fabian M. , Montesinos V. , Zizler V.
Published: April 2009

A close connection between the strict convexity of the Day norm to the concept of the Gruenhage compacta is shown. As a byproduct we give an elementary characterisation of Gul'ko compacta in the sigma-product of lines and a more elementary proof of Mercourakis' renorming result for Vašák spaces.
Reverses of the Cauchy–Bunyakovsky–Schwarz inequality for n-tuples of complex numbers
Authors: Dragomir S.S.
Published: April 2009

Some new reverses of the Cauchy–Bunyakovsky–Schwarz inequality for n-tuples of real and complex numbers related to Cassels and Shisha–Mond results are given.
Operator ideals and tensor norms defined by a sequence space
Authors: Molina J.A. López , Rivera M.J.
Published: April 2009

We study the tensor norm defined by a sequence space λ and its minimal and maximal operator ideals associated in the sense of Defant and Floret. Our results extend the classical theory related to the tensor norms of Saphar [16]. They show the key role played by the finite dimensional structure of the ultrapowers of λ in this kind of problems.
The ideal structure of nilpotent-generated transformation semigroups
Authors: Marques-Smith M. Paula O. , Sullivan R.P.
Published: April 2009

In 1987 Sullivan determined the elements of the semigroup N(X) generated by all nilpotent partial transformations of an infinite set X; and later in 1997 he studied subsemigroups of N(X) defined by restricting the index of the nilpotents and the cardinality of the set. Here, we describe the ideals and Green's relations on such semigroups, like Reynolds and Sullivan did in 1985 for the semigroup generated by all idempotent total transformations of X. We then use this information to describe the congruences on certain Rees factor semigroups and to construct families of congruence-free semigroups with interesting algebraic properties. We also study analogous questions for X finite and for one-to-one partial transformations.
A complete classification of finite homogeneous groups
Authors: Li Cai Heng
Published: April 2009

In this short note, we obtain a complete classification of finite homogeneous groups.
Nonlinear hemivariational inequalities at resonance
Authors: Gasiński Leszek , Papageorgiou Nikolaos S.
Published: April 2009

In this paper we consider nonlinear hemivariational inequalities involving the p-Laplacian at resonance. We prove the existence of a nontrivial solution. Our approach is variational based on the critical point theory for nonsmooth, locally Lipschitz functionals due to Chang.
On cohomological deformations of bicrossed product Hopf algebras
Authors: Hong Jeong Hee , Szymański Wojciech
Published: April 2009

We construct and describe two classes of examples of twisted bicrossed product Hopf algebras corresponding to matched pairs of finite groups.
Periodic solutions of some differential delay equations created by Hamiltonian systems
Authors: Li Jibin , Liu Zhengrong , He Xuezhong
Published: April 2009

This paper is concerned with finding periodic solutions of differential delay systems

and

whereri(i= 1, 2,…,n− 1) are positive constants. By using the theory of Hamiltonian systems, we obtain some sufficient conditions under which these systems have many periodic solutions with known periods.
Sur la p-différente du corps des points de p-torsion des courbes elliptiques
Authors: Kraus Alain
Published: April 2009

Let p be a prime number, K be a finite non-ramified extension of ℚp and E be an elliptic curve defined over K. Let K(Ep) be the field of the p-division points of E. In this paper we determine the valuation of the different of the extension K(Ep)/K.
The Ostrowski integral inequality for mappings of bounded variation
Authors: Dragomir S.S.
Published: April 2009

A generalisation of the Ostrowski integral inequality for mappings of bounded variation and applications for general quadrature formulae are given.
A note on subnormality
Authors: Peng T.A.
Published: April 2009

Let H be a subgroup of a finite group G and let S be a set of generators of H. We prove that if G is soluble, then H is subnormal in G if and only if there exists an integer n such that for each g in G and a in S the commutator lies in H. This criterion for subnormality is also valid for soluble groups satisfying the maximal or the minimal condition on subgroups.
A classification of groups with a centralizer condition
Authors: Arad Zvi , Herzog Marcel
Published: April 2009

Let G be a finite group. A nontrivial subgroup M of G is called a CC-subgroup if M contains the centralizer in G of each of its nonidentity elements. The purpose of this paper is to classify groups with a CC-subgroup of order divisible by 3. Simple groups satisfying that condition are completely determined.
On the theory of soluble factorizable groups
Authors: Kramer Otto-Uwe
Published: April 2009

Suppose that a finite soluble group G is the product AB of subgroups A and B. Our question is the following: what conclusions can be made about G if A and B are suitably restricted? First we shall prove that the p–length of G is restricted by the derived lengths of the Sylow p–subgroups of A and B, if A and B are p–closed and p′-closed. Moreover, if in such a group the Sylow p–subgroups of A and B are modular, the p–length of G is at most 1. Next we obtain a general estimate for the derived length of the group G = AB of odd order in terms of the derived lengths of A and B. Furthermore it will be possible to bound the nilpotent length of G and also the p–length of G in terms of other invariants of special subgroups of G.
On an application of the complex nonlinear complementarity problem
Authors: Parida J. , Sahoo B.
Published: April 2009

A theorem on the existence of a solution under feasibility assumptions to a convex minimization problem over polyhedral cones in complex space is given by using the fact that the problem of solving a convex minimization program naturally leads to the consideration of the following nonlinear complementarity problem: given g: Cn → Cn, find z such that g(z) ∈ S*, z ∈ S, and Re〈g(z), z〉 = 0, where S is a polyhedral cone and S* its polar.
Structurally stable flows
Authors: Chi Dong Pyo , Choi Sung Kyu , Park Jong Suh
Published: April 2009

We show that a C1-flow on a compact Riemannian manifold is structurally stable and topologically stable if and only if it satisfies Axiom A and the strong transversality condition. This improves Smale's conjecture for flows.
On a conjecture of Z. Jianzhong
Authors: Matsugu Yasuo
Published: April 2009

Let ϕ be a nonnegative, nondecreasing and nonconstant function defined on [0, ∞) such that Φ(t) = ϕ(et) is a convex function on (-∞, ∞). The Hardy-Orlicz space H (ϕ) is defined to be the class of all those functions f holomorphic in the open unit disc of the complex plane C satisfying The subclass H(ϕ)+ of H(ϕ) is defined to be the class of all those functions f ∈ H(ϕ) satisfying for almost all points eit of the unit circle. In 1990, Z. Jianzhong conjectured that H(ϕ)+ = H(ψ)+ if and only if H(ϕ) = H(ψ). In the present paper we prove that it is true not only on the unit disc of C but also on the unit ball of Cn.
One-sided estimates for quasimonotone increasing functions
Authors: Herzog Gerd , Lemmert Roland
Published: April 2009

Let E be a Banach space ordered by a solid and normal cone K, and normed by the Minkowski functional of an order interval [–p, p], p ∈ K∘. We derive global one-sided estimates for quasimonotone increasing functions f : [0, T) × E → E with respect to the norm, and the distance to the line generated by p, under conditions of f; in direction p.
S-strictly quasi-concave vector maximisation
Authors: Dong Hong-Bin , Gong Xun-Hua , Wang Shou-Yang , Coladas Luis
Published: April 2009

In this paper, we discuss the relationship among the concepts of an S-strictly quasiconcave vector-valued function introduced by Benson and Sun, a C-strongly quasiconcave vector-valued function and a C-strictly quasiconcave vector-valued function in a topological vector space with a lattice ordering. We generalize a main result obtained by Benson and Sun about the closedness of an efficient solution set in multiple objective programming. We prove that an efficient solution set is closed and connected when the objective function is a continuous S-strictly quasiconcave vector-valued function, the objective space is a topological vector lattice and the ordering cone has a nonempty interior.
A note on the least quadratic non-residue of the integer-sequences
Authors: Garaev M. Z.
Published: April 2009

In this paper we consider the problem of an upper bound estimate for the least quadratic non-residue modulo prime number on special arithmetic sequences such as f(n) = [αn] and f(n) = [nc].
Sur un type particulier de valeur propre des solvariétés d'Einstein
Authors: Fanaï Hamid-Reza
Published: April 2009

On montre que la partie nilpotente d'une solveriété d'Einstein standard, dont le type de valeur propre est égal à (1 < 2; d1, d2), est nécessairement indécomposable si d1 et d2 sont premiers entre eux.
Polynomial remainders and plane automorphisms
Authors: Sakkalis Takis
Published: April 2009

This note relates polynomial remainders with polynomial automorphisms of the plane. It also formulates a conjecture, equivalent to the famous Jacobian Conjecture. The latter provides an algorithm for checking when a polynomial map is an automorphism. In addition, a criterion is presented for a real polynomial map to be bijective.
A multiplier rule in set-valued optimisation
Authors: Khan Akhtar A. , Raciti Fabio
Published: April 2009

A multiplier rule is given as a necessary optimality condition for proper minimality in set-valued optimisation. We use derivatives in the sense of the lower Dini derivative for the objective set-valued map and the set-valued maps defining the constraints.
Sums of three integral squares in cyclotomic fields
Authors: Ji Chun-Gang
Published: April 2009

Let m be an odd positive integer greater than 2 and f the smallest positive integer such that 2f ≡ 1 (mod m). It is proved that every algebraic integer in the cyclotomic field ℚ(ζm) can be expressed as a sum of three integral squares if and only if f is even.
On the fitting core of a formation
Authors: Beidleman J. C. , Heineken H.
Published: April 2009

Dedicated to the memory of Bernhard H. Neumann

Not often is a formation also a Fitting class. In this article groups are exhibited that are contained in a given saturated formation and that do not lead out of this formation by forming normal products with other groups of it. This generalises a result of Cossey on T-groups and supersolvable groups.
Approximation and fixed point theorems for countable condensing composite maps
Authors: O'Regan Donal , Shahzad Naseer
Published: April 2009

This paper Presents a multivalued version of an approximation result of Ky Fan (Math. Z.112 (1969)) for maps.
Some results on principal eigenvalues for periodic parabolic problems with weight
Authors: Kaufmann U.
Published: April 2009

Let Ω ⊂ ℝN be a bounded domain. We study existence and uniqueness of principal eigenvalues for the Dirichlet periodic parabolic problem with weight Lu = λmu in Ω × ℝ when the independent coefficient of the differential operator L is not necessarily positive.
Hyperconvex spaces revisited
Authors: Borkowski Marcin , Bugajewski Dariusz , Przybycień Hubert
Published: April 2009

In this paper we describe a construction of a large class of hyperconvex metric spaces. In particular, this construction contains well-known examples of hyperconvex spaces such as ℝ2with the “river” metric or with the radial one.

Further, we investigate linear hyperconvex spaces with extremal points of their unit balls. We prove that only in the case of a plane (and obviously a line) is there a strict connection between the number of extremal points of the unit ball and the hyperconvexity of the space.

Some additional properties concerning the notion of hyperconvexity are also investigated.
Open Engel manifolds admitting compact characteristic leaves
Authors: Inaba Takashi
Published: April 2009

We give an example of an Engel structure on the 4-dimensional Euclidean space which admits a compact characteristic leaf. We also show that every Engel structure on an open 4-manifold can be modified so that the resulting structure has a compact characteristic leaf.
Linear maps leaving invariant subsets of nonnegative symmetric matrices
Authors: Chiang Hanley , Li Chi-Kwong
Published: April 2009

Let  be a certain set of nonnegative symmetric matrices, such as the set of symmetric doubly stochastic matrices or the set, of symmetric permutation matrices. It is proven that a linear transformation mapping  onto  must be of the form X ↦ PtX P for some permutation matrix P except for several low dimensional cases.
Contact and quasiconformal mappings on real model filiform groups
Authors: Warhurst Ben
Published: April 2009

We prove that Carnot groups with real model filiform Lie algebras are not rigid. Consequently non-trivial smooth contact and quasiconformal mappings exist in abundance.
Real hypersurfaces in complex two-plane Grassmannians with commuting shape operator
Authors: Suh Young Jin
Published: April 2009

In this paper we give a non-existence property of real hypersurfaces in complex two-plane Grassmannians G2(ℂm+2) which have a shape operator A commuting with the structure tensors {φ1, φ2, φ3}. From this view point we give a characterisation of real hypersurfaces of type B in G2(ℂm+2).
Elementary operators on 𝒥-subspace lattice algebras
Authors: Li Pengtong , Lu Fangyan
Published: April 2009

The abstract concept of an elementary operator was recently introduced and studied by other authors. In this paper, we describe the general form of elementary operators between standard subalgebras of 𝒥-subspace lattice algebras. The result can apply to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.
On strengthened weighted Carleman's inequality
Authors: Čižmešija Aleksandra , Pecarić Josip , Persson Lars–Erik
Published: April 2009

In this paper we prove a new refinement of the weighted arithmetic-geometric mean inequality and apply this result in obtaining a sharpened version of the weighted Carleman's inequality.
Equicontinuity of a graph map
Authors: Sun Taixiang , Zhang Yongping , Zhang Xiaoyan
Published: April 2009

LetGbe a graph, andf:G→Gbe a continuous map with periodic points. In this paper we show that the following five statements are equivalent.

(1)fis equicontinuous.

(2) There exists some positive integerNsuch thatfNis uniformly convergent.

(3)fisS-equicontinuous for some positive integer sequenceS= {n1<n2< …}.

(4) Ω(x, f) =ω(x, f)for everyx∈G.

(5)is a periodic map.
Worst-case errors in a Sobolev space setting for cubature over the sphereS2
Authors: Hesse Kerstin , Sloan Ian H.
Published: April 2009

This paper studies the problem of numerical integration over the unit sphereS2⊆ ℝ3for functions in the Sobolev spaceH3/2(S2). We consider sequencesQm(n),n∈ ℕ, of cubature (or numerical integration) rules, whereQm(n)is assumed to integrate exactly all (spherical) polynomials of degree ≤n, and to usem = m(n)values off. The cubature weights of all rulesQm(n)are assumed to be positive, or alternatively the sequenceQm(n),n∈ ℕ, is assumed to have a certain local regularity property which involves the weights and the points of the rulesQm(n),n∈ ℕ. Under these conditions it is shown that the worst-case (cubature) error, denoted byE3/2(Qm(n)), for all functions in the unit ball of the Hilbert spaceH3/2(S2) satisfies the estimateE3/2(Qm(n)) ≤c n−3/2, where the constantcis a universal constant for all sequences of positive weight cubature rules. For a sequenceQm(n),n∈ ℕ, of cubature rules that satisfies the alternative local regularity property the constantcmay depend on the sequenceQm(n),n∈ ℕ. Examples of cubature rules that satisfy the assumptions are discussed.
Harmonic sets and the harmonic prime number theorem
Authors: Broughan Kevin A. , Casey Rory J.
Published: April 2009

We restrict primes and prime powers to sets . Let . Then the error in θH(x) has, unconditionally, the expected order of magnitude . However, if then ψH (x) = x log 2 + O (log x). Some reasons for and consequences of these sharp results are explored. A proof is given of the “harmonic prime number theorem”, πH (x)/π (x) → log 2.
An interior point method for linear programming based on a class of Kernel functions
Authors: Amini K. , Peyghami M. R.
Published: April 2009

Interior point methods are not only the most effective methods for solving optimisation problems in practice but they also have polynomial time complexity. However, there is still a gap between the practical behavior of the interior point method algorithms and their theoretical complexity results. In this paper, by focusing on linear programming problems, we introduce a new family of kernel functions that have some simple and easy to check properties. We present a simplified analysis to obtain the complexity of generic interior point methods based on the proximity functions induced by these kernel functions. Finally, we prove that this family of kernel functions leads to improved iteration bounds of the large-update interior point methods.
On the Edgeworth expansion for elementary polynomials based on trimmed samples
Authors: Borovskikh Yuri V. , Weber N. C.
Published: April 2009

This paper develops a one term Edgeworth expansion under minimal conditions for elementary symmetric polynomials of any degree based on trimmed samples. These statistics are special cases of trimmed U-statistics and natural extensions of the trimmed mean.
On the adjoint homology of 2-step nilpotent Lie algebras
Authors: Cagliero Leandro , Tirao Paulo
Published: April 2009

We give a lower bound and an upper bound for the dimension of the homology of 2-step nilpotent Lie algebras with adjoint coefficients. We conjecture, that the upper bound and the actual dimension are asymptotically equivalent.
Inverse semigroups generated by linear transformations
Authors: Mendes-Gonçalves Suzana , Sullivan R. P.
Published: April 2009

Suppose X is a set with |X| = p ≥ q ≥ ℵ0 and let B = BL(p, q) denote the Baer-Levi semigroup defined on X. In 1984, Howie and Marques-Smith showed that, if p = q, then BB−1 = I(X), the symmetric inverse semigroup on X, and they described the subsemigroup of I(X) generated by B−1B. In 1994, Lima extended that work to ‘independence algebras’, and thus also to vector spaces. In this paper, we answer the natural question: what happens when p > q? We also show that, in this case, the analogues BB−1 for sets and GG−1 for vector spaces are never isomorphic, despite their apparent similarities.
Proximal proper efficiency for minimisation with respect to normal cones
Authors: Lalitha C. S. , Arora Ruchi
Published: April 2009

This paper is devoted to the study of a new kind of proper efficiency in terms of proximal normal cones for vector minimisation. This new notion called proximal proper efficiency is used to obtain a scalar characterisation when a set related to the criterion set is a nonconvex set. Proximal proper efficiency is related with the well known notions of Benson and Borwein proper efficiency which are defined in the literature in terms of tangent cones. The study is further extended to characterise Benson and Borwein proper efficiency in terms of normal cones assuming convexity of a related set.
Waring problem with factorials
Authors: Garaev Moubariz Z. , Luca Florian , Shparlinski Igor E.
Published: April 2009

We show that any residue class λ modulopcan be represented in the formn1! +…+nℓ! ≡ λ (modp) with ℓ =O((logp)3log logp).
Uniformity for weak order convergence of Riesz space-valued measures
Authors: Kawabe Jun
Published: April 2009

The purpose of the paper is to show that weak order convergence of a net of Dedekind complete Riesz space-valued σ-measures is uniform over uniformly bounded, uniformly equicontinuous classes of functions. The paper ends with generalizing Ulam's theorem for tightness of positive, finite Borel measures to Riesz space-valued σ-measures.
Existence conditions in general quasimonotone variational inequalities
Authors: Aussel D. , Luc D. T.
Published: April 2009

In this paper we study a general variational inequality model with set-valued quasimonotone operators, a model which includes several variational inequalities and equilibrium problems. We establish unifying conditions for existence of solutions in a topological vector space setting. Applications to parametric equilibrium models and to a contact problem are given.
Shilnikov type solutions under strong non-autonomous perturbation
Authors: Tuma Elías
Published: April 2009

We study the behaviour of solutions in a neighbourhood of the origin for a certain type of non-autonomous system of partial differential equations whose linear approximation is non autonomous.
Generic Lie colour algebras
Authors: Price Kenneth L.
Published: April 2009

We describe a type of Lie colour algebra, which we call generic, whose universal enveloping algebra is a domain with finite global dimension. Moreover, it is an iterated Ore extension. We provide an application and show Gröbner basis methods can be used to study universal enveloping algebras of factors of generic Lie colour algebras.
A simple proof of an expansion of an eta-quotient as a Lambert series
Authors: Cooper Shaun
Published: April 2009

We give a simple proof of the identity

The proof uses only a few well-known properties of the cubic theta functions a(q), b(q) and c(q). We show this identity implies the interesting definite integral
.
The dynamics of an Action of Sp(2n, Z)
Authors: Nielsen Anthony
Published: April 2009

S.G. Dani and S. Raghavan showed the linear action of Sp(2n,ℤ) on the space of symplectic p-frames for p ≤ n is topologically transitive. We give an alternative proof, from the prime number theorem and the congruence subgroup theorem, and show the action of every finite index subgroup of Sp(2n, ℤ) is topologically transitive.
On the nonlinearity of the sequence of signs of Kloosterman sums
Authors: Shparlinski Igor E.
Published: April 2009

It is known that Kloosterman sums with prime denominator p take real values, so one can define a sequence of signs of such sums. Several pseudorandom properties of this sequence have recently been studied by Fouvry, Michel, Rivat and Sárközy. Here we use one of their results to estimate a certain important characteristic of this sequence which is also of cryptographic interest.
Searching for simultaneous arithmetic progressions on elliptic curves
Authors: García-Selfa Irene , Tornero José M.
Published: April 2009

We look for elliptic curves featuring rational points whose coordinates form two arithmetic progressions, one for each coordinate. A constructive method for creating such curves is shown, for lengths up to 5.
Some properties of the projective tensor product UX derived from those of U and X
Authors: Dowling Patrick N.
Published: April 2009

Let X be a real or complex Banach space and let U be a Banach space with an unconditional basis. We show that the projective tensor product of U and X, UX, has the complete continuity property (respectively, the analytic complete continuity property) whenever U and X have the complete continuity property (respectively, the analytic complete continuity property). More general versions of these results are also obtained. Moreover, the techniques applied here to the projective tensor product, can also be used to establish some Banach space properties of the Fremlin projective tensor product.
On generalised Möbius inversion formulas
Authors: He Tian-Xiao , Hsu Leetsch C. , Shiue Peter J.S.
Published: April 2009

We provide a wide class of Möbius inversion formulas in terms of the generalised Möbius functions and their application to the setting of the Selberg multiplicative functions.