bluuebunny/crossref_metadata_2025 huggingface dataset:
A right continuous right weakly si-ring is semisimple
Authors: Van Huynh Dinh , Van Sanh Nguyen
Published: April 2009

It is shown that a projective CS right module M over a ring R is a direct sum of uniform modules of composition lengths at most 2 if (i) every finitely generated direct summand of M is continuous and (ii) every non-zero M-singular right R-module contains a non-zero M-injective submodule. In particular, a right continuous ring R is semisimple if R is right weakly SI, that is, if every non-zero singular right R-module contains a non-zero injective submodule.
Implicit parabolic differential equations
Authors: Bonafede Salvatore , Marano Salvatore A.
Published: April 2009

Let QT = ω x (0, T), where ω is a bounded domain in ℝn (n ≥ 3) having the cone property and T is a positive real number; let Y be a nonempty, closed connected and locally connected subset of ℝh; let f be a real-valued function defined in QT × ℝh × ℝnh × Y; let ℒ be a linear, second order, parabolic operator. In this paper we establish the existence of strong solutions (n + 2 ≤ p < + ∞) to the implicit parabolic differential equation

with the homogeneus Cauchy-Dirichlet conditions where u = (u1, u2, …, uh), Dxu = (Dxu1, Dxu2, …, Dxuh), Lu = (ℒu1, ℒu2, … ℒuh).
The fit and flat components of barrelled spaces
Authors: Saxon Stephen A. , Tweddle Ian
Published: April 2009

The Splitting Theorem says that any given Hamel basis for a (Hausdorff) barrelled space E determines topologically complementary subspaces Ec and ED, and that Ec is flat, that is, contains no proper dense subspace. By use of this device it was shown that if E is non-flat it must contain a dense subspace of codimension at least ℵ0; here we maximally increase the estimate to ℵ1 under the assumption that the dominating cardinal ∂ equals ℵ1 [strictly weaker than the Continuum Hypothesis (CH)]. A related assumption strictly weaker than the Generalised CH allows us to prove that ED is fit, that is, contains a dense subspace whose codimension in ED is dim (ED), the largest imaginable. Thus the two components are extreme opposites, and E itself is fit if and only if dim (ED) ≥ dim (Ec), in which case there is a choice of basis for which ED = E. Morover, E is non-flat (if and) only if the codimension of E′ is at least in E*. These results ensure latitude in the search for certain subspaces of E* transverse to E′, as in the barrelled countable enlargement (BCE) problem, and show that every non-flat GM-space has a BCE.
Rank one Drinfeld modules on hyperelliptic curves
Authors: Bae Sunghan , Kang Pyung-Lyun
Published: April 2009

We extend the recent work of Dummit and Hayes on rank one Drinfeld modules on elliptic curves and hyperelliptic curves in the case that the infinite place is ramified to the case that the infinite place is inert.
Rings characterised by semiprimitive modules
Authors: Hirano Yasuyuki , Van Huynh Dinh , Park Jae Keol
Published: April 2009

A module M is called a CS-module if every submodule of M is essential in a direct summand of M. It is shown that a ring R is semilocal if and only if every semiprimitive right R-module is CS. Furthermore, it is also shown that the following statements are equivalent for a ring R: (i) R is semiprimary and every right (or left) R-module is injective; (ii) every countably generated semiprimitive right R-module is a direct sum of a projective module and an injective module.
Groups 2-Transitive on a set of their Sylow subgroups
Authors: Brewster Ben , Ward Michael B.
Published: April 2009

We classify, modulo the kernel of the action, finite groupsGthat act 2-transitively onSylr(G) for some primerdividing |G|. We furthermore prove that any finite group that acts 2-transitively onSylr(G) for each prime r is solvable and of nilpotent length at most 3.
On the maximal circumradius of a planar convex set containing one lattice point
Authors: Awyong Poh W. , Scott Paul R.
Published: April 2009

We obtain a result about the maximal circumradius of a planar compact convex set having circumcentre O and containing no non-zero lattice points in its interior. In addition, we show that under certain conditions, the set with maximal circumradius is a triangle with an edge containing two lattice points.
Weighted normal numbers
Authors: Choe Geon H.
Published: April 2009

We show that if {ak}k is bounded then for almost every 0 < x < 1 where is the dyadic expansion of x. It is also shown that almost everywhere where p > 1 is any fixed integer.
Soluble and linear repetitive groups
Authors: Kelarev A.V. , Shumyatsky P.V.
Published: April 2009

Our main theorem describes FC-soluble and linear repetitive groups. As a corollary, we characterise algebraic linear repetitive semigroups.
Partial clones containing all permutations
Authors: Haddad Lucien , Rosenberg Ivo G.
Published: April 2009

For every nonsingleton finite set A, we construct three families of partial clones on A that contain all permutations of A and are of continuum cardinality.
Discrete product systems with twisted units
Authors: Laca Marcelo
Published: April 2009

The spectral C*-algebra of the discrete product systems of H.T. Dinh is shown to be a twisted semigroup crossed product whenever the product system has a twisted unit. The covariant representations of the corresponding dynamical system are always faithful, implying the simplicity of these crossed products; an application of a recent theorem of G.J. Murphy gives their nuclearity. Furthermore, a semigroup of endomorphisms of B(H) having an intertwining projective semigroup of isometries can be extended to a group of automorphisms of a larger Type I factor.
The Stone-Čech compactification of Prim A
Authors: Nilsen May
Published: April 2009

For a C*-algebra A, we give simple proofs of the following: Cb (Prim A) is isomorphic to the centre ZM(A) of the multiplier algebra, Cb (Prim A) is isomorphic to C (Prim M(A)) and Prim ZM(A) is the Stone-Čech compactification of Prim A.
Notes on weakly-semisimple rings
Authors: Zhou Yiqiang
Published: April 2009

Responding to a question on right weakly semisimple rings due to Jain, Lopez-Permouth and Singh, we report the existence of a non-right-Noetherian ringRfor which every uniform cyclic right it-module is weakly-injective and every uniform finitely generated rightR-module is compressible. We show that a ringRis a right Noetherian ring for which every cyclic rightR-module is weaklyR-injective if and only ifRis a right Noetherian ring for which every uniform cyclic rightR-module is compressible if and only if every cyclic rightR-module is compressible. Finally, we characterise those modulesMfor which every finitely generated (respectively, cyclic) module in σ[M] is compressible.
Admissible limits of bloch functions on bounded strongly pseudoconvex domains
Authors: Zhangjian Hu
Published: April 2009

Let be a bounded strongly pseudoconvex domain with C2 boundary . In this paper we prove that for a Bloch function in the existance of radial limits at almost all implies the existence of admissible limits almost everywhere on .
On a conjecture of Higgins
Authors: Heath Philip R. , Nickolas Peter
Published: April 2009

In his work on a proof of Grushko's theorem by groupoid methods, Philip Higgins proved the following subgroup theorem.

Theorem. Suppose that θ:G → B is a surjective map of groups, where G and B are free products and , and where θ(Gλ) = Bλ for each λ. Let H be a subgroup of G with the property that the restriction of θ to H is surjective. Then there is a free decomposition of H with θ(Hλ) = Bλ for each λ.

As Higgins has noted, there is a common strategy in the proff of this theorem and in the groupoid proofs of Kurosh and Neilsen-Schreier subgroup theorems. Higgins conjectured the existence of a common generalisation of his theorem and the Kurosh theorem, proposed a plausible statement for such a result, and hinted that the common strategy of these proofs might be extended to give a proof of the conjecture. Examined at more detailed level, however, the common strategy used in the proofs of the Kurosh theorem and Higgin's theorem is seen to diverge into two strads. In this paper, it is shown that the construction entailed in these divergent approaches are in genera; incompatible. Thus any proof of Higgin's conjecture must require substantially different techniques. In particular, the proof of a theorem by Ordman that purports to affirm the conjecture is incorrect, and the approach used in his argument cannot yield a valid proof.
Time-discretised Galerkin approximations of parabolic stochastic PDE's
Authors: Grecksch W. , Kloeden P.E.
Published: April 2009

The global discretisation error is estimated for strong time discretisations of finite dimensional Ito stochastic differential equations (SDEs) which are Galerkin approximations of a class of parabolic stochastic partial differential equation (SPDE) with a strongly monotone linear operator with eigenvalues λ1 ≤ λ2 ≤ … in its drift term. If an order γ strong Taylor scheme with time-step δ is applied to the N dimensional Ito-Galerkin SDE, the discretisation error is bounded above by

where [x] is the integer part of the real number x and the constant K depends on the initial value, bounds on the other coefficients in the SPDE and the length of the time interval under consideration.
The convex function determined by a multifunction
Authors: Coodey M. , Simons S.
Published: April 2009

We shall show how each multifunction on a Banach space determines a convex function that gives a considerable amount of information about the structure of the multifunction. Using standard results on convex functions and a standard minimax theorem, we strengthen known results on the local boundedness of a monotone operator, and the convexity of the interior and closure of the domain of a maximal monotone operator. In addition, we prove that any point surrounded by (in a sense made precise) the convex hull of the domain of a maximal monotone operator is automatically in the interior of the domain, thus settling an open problem.
On weak Hadamard differentiability of convex functions on Banach spaces
Authors: Giles J.R. , Sciffer Scott
Published: April 2009

We study two variants of weak Hadamard differentiability of continuous convex functions on a Banach space, uniform weak Hadamard differentiability and weak Hadamard directional differentiability, and determine their special properties on Banach spaces which do not contain a subspace topologically isomorphic to l1.
Quantum double construction for graded Hopf algebras
Authors: Gould M.D. , Zhang R.B. , Bracken A.J.
Published: April 2009

A detailed proof of the quantum double construction is given for Z2 -graded Hopf algebras, and an explicit formula for the graded universal R−matrix is obtained in a general fashion.
Structure des cones normaux contenus dans un espace de Banach ou son dual II
Authors: Becker Richard
Published: April 2009

Let B be a Banach space and X ⊂ B a normal cone such that the norm is monotone on X for the order determinated by X.

We study the sup, denoted by i(X), of the q ≥ 1 such that, for each E> 0 and each n, there are x1, …, xn in X such that:

for all a1, …, an ≥ 0, where ‖ ‖q is the norm in lq.

We prove that i(X) is the inf of the p for which we have:

The proof use a similar theorem of Kirvine, concerning Banach Riesz spaces. Here conical measures are a useful tool. We establish a link with a preceding work in which we adapt the Maurey theory factorisation of operators with values in a LP space, to the case of normal cones, contained in a Banach space.
The approximate subdifferential of composite functions
Authors: Jourani A. , Thibault L.
Published: April 2009

This paper deals with the approximate subdifferential chain rule in a Banach space. It establishes specific results when the real-valued function is locally Lipschitzian and the mapping is strongly compactly Lipschitzian.
A decision problem for varieties of commutative semigroups
Authors: Cao W.L.
Published: April 2009

For a first order formula P: ∀x1, …, ∀xn, ∃y1, …, ∃ym (u(x1, …, xn, y1, …, ym) ≡ v(x1, …, xn, y1, …, ym)) where u and v are two words on the alphabet {x1, …, xn, y1, …, ym}, and a finite set E of semigroup identities with xy ≡ yx in it, we prove that it is decidable whether P follows from E, that is whether all the semigroups in the variety defined by E satisfy P.
A minimax inequality with applications to existence of equilibrium points
Authors: Tan Kok-Keong , Yuan Zian-Zhi
Published: April 2009

A new minimax inequality is first proved. As a consequence, five equivalent fixed point theorems are formulated. Next a theorem concerning the existence of maximal elements for an Lc-majorised correspondence is obtained. By the maximal element theorem, existence theorems of equilibrium points for a non-compact one-person game and for a non-compact qualitative game with Lc-majorised correspondences are given. Using the latter result and employing an “approximation” technique used by Tulcea, we deduce equilibrium existence theorems for a non-compact generalised game with LC correspondences in topological vector spaces and in locally convex topological vector spaces. Our results generalise the corresponding results due to Border, Borglin-Keiding, Chang, Ding-Kim-Tan, Ding-Tan, Shafer-Sonnenschein, Shih-Tan, Toussaint, Tulcea and Yannelis-Prabhakar.
The implications for differentiability of a weak index of non-compactness
Authors: Giles John R. , Moors Warren B.
Published: April 2009

In a recent paper the authors showed that certain set-valued mappings from a Baire space into subsets of a Banach space which have a continuity property defined in terms of Kuratowski's index of non-compactness have inherent single-valued properties. Here we generalise the continuity property to one defined in terms of a weak index of non-compactness and we show that this wider class of set-valued mappings also has significant implications for the differentiability of convex functions on Banach spaces.
Invexity at a point: generalisations and classification
Authors: Mititelu S. , Stancu-Minasian I.M.
Published: April 2009

This paper uses Clarke’s generalised directional derivative to describe several types of invexity, pseudoinvexity and quasiinvexity at a point of a nonlinear function. Direct implications of the relations existing between the various types of invexity and generalised invexity are presented, as well as a block diagram of these implications. In particular, similar results in the class of quasiconvex functions are obtained.
Periodic solutions and Galerkin approximations to the autonomous reaction-diffusion equations
Authors: Dikansky Arnold
Published: April 2009

The assumption that a Galerkin equation of the reaction-diffusion system of high order has an asymptotically orbitally stable time-periodic solution implies that the full reaction-diffusion system has a nearby asymptotically orbitally stable time-periodic solution with asymptotic phase.
On SC-modules
Authors: Van Sank Nguyen
Published: April 2009

Let R be a ring. A right R-module M is called an SC-module if every M-singular right R-module is continuous. The purpose of this note is to give some characterisations of SC-modules.
Remarks concerning the 2-Hilbert class field of imaginary quadratic number fields
Authors: Benjamin Elliot
Published: April 2009

Letkbe an imaginary quadratic number field and letk1be the 2-Hilbert class field ofk. IfCk,2, the 2-Sylow subgroup of the ideal class group ofk, is elementary and |Ck,2|≥ 8, we show thatCk1,2is not cyclic. IfCk,2is isomorphic toZ/2Z×Z/4ZandCk1,2is elementary we show thatkhas finite 2-class field tower of length at most 2.
Multipliers for weighted Hardy spaces on locally compact Vilenkin groups
Authors: Kitada Toshiyuki
Published: April 2009

Let G be a locally compact Vilenkin group. We study multipliers which satisfy a generalised Hörmander condition from power-weighted Hardy space (G) to (G) with 0 < p ≤ q < ∞, 0 < p ≤ 1, −1 < β, β′.
New generalisations of an H-KKM type theorem and their applications
Authors: Ding Xie Ping
Published: April 2009

In this note, we establish some new generalisations of an H-KKM type theorem which unify and generalise the corresponding results of Horvath, Bardaro-Ceppitelli, Tarafdar, Shioji, Park and others. As applications of our H-KKM type principle, we obtain some new generalisations of the Ky Fan type geometric properties of.H-spaces, minimax inequalities and coincidence theorems in Horvath's abstract setting.
On the orders of primitive linear P'-groups
Authors: Weigel A. Gambini , Weigel T.S.
Published: April 2009

A group G ≤ GLK(V) is called K-primitive if there exists no non-trivial decomposition of V into a sum of K-spaces which is stabilised by G. We show that if V is a finite vector space and G a K-primitive subgroup of GLK(V) whose order is coprime to |V|, we can bound the order of G by |V|log2(|V|) apart from one exception. Later we use this result to obtain some lower bounds on the number of p–singular elements in terms of the group order and the minimal representation degree.
Two counter-examples in nonseparable Banach spaces
Authors: Alexandrov G.A. , Kadec M.I.
Published: April 2009

It is shown that the well-known theorem of Kadec for the HГ renorming of separable Banach spaces, when Г is a norming subspace in the dual, cannot be extended to the class of nonseparable Banach spaces.
A note on prime essential rings
Authors: Zand Hossein
Published: April 2009

It is proved that the upper radical determined by the class of prime essential rings is an N-radical.
Primitive ideals of the quantised enveloping algebra of a complex lie algebra
Authors: Oh Sei-Qwon
Published: April 2009

In this paper, we characterise all primitive ideals of the quantised enveloping algebra Uq[sl(2, ℂ)] of the complex Lie algebra sl(2, ℂ) and show how they are similar to those of U[sl(2, ℂ)], the enveloping algebra of sl(2, ℂ).
On distinguishing spaces not homotopy-equivalent
Authors: Eggar M.H.
Published: April 2009

A non-pathological example is given of two topological spaces which have isomorphic homotopy groups, homology groups and cohomology ring and which cannot be distinguished from each other by the Whitehead product structure. A family of examples can be constructed likewise.
On generalised convex nonsmooth functions
Authors: Luc Dinh The
Published: April 2009

Some characterisations of generalised convex functions are established by means of Clarke's subdifferential and directional derivatives.
Symmetries of the self-dual Yang-Mills equations
Authors: Halburd Rod
Published: April 2009

It has been conjectured by R. S. Ward that the self-dual Yang-Mills Equations (SDYMEs) form a “master system” in the sense that most known integrable ordinary and partial differential equations are obtainable as reductions. We systematically construct the group of symmetries of the SDYMEs on R4 with semisimple gauge group of finite dimension and show that this yields only the well known gauge and conformal symmetries.
Algebras of cancellative semigroups
Authors: Okninski Jan
Published: April 2009

The Jacobson radical J(K[S]) of the semigroup ring K[S] of a cancellative semigroup S over a field K is studied. We show that, if J(K[S]) ≠ 0, then either S is a reversive semigroup or K[S] has many nilpotents and J(K[P]) ≠ 0 for a reversive subsemigroup P of S. This is used to prove that J(K[S]) = 0 for every unique product. semigroup S.
Anisotropic principal series and generators of a free group
Authors: Pensavalle Carlo
Published: April 2009

In this paper we prove that the equivalence of anisotropic principal series of a free group Г related to different generator sets induces a Г-isomorphism between the related Cayley-graphs. As a consequence we obtain that a nontrivial change of generators for Г leads to inequivalent anisotropic principal series.
The strict topology on spaces of bounded holomorphic functions
Authors: Ferrera Juan , Prieto Angeles
Published: April 2009

We introduce in this paper the space of bounded holomorphic functions on the open unit ball of a Banach space endowed with the strict topology. Some good properties of this topology are obtained. As applications, we prove some results on approximation by polynomials and a description of the continuous homomorphisms.
The sextic period polynomial
Authors: Lazarus Andrew J.
Published: April 2009

In this paper we show that the method of calculating the Gaussian period polynomial which originated with Gauss can be replaced by a more general method based on formulas for Lagrange resolvants. The period polynomial of cyclic sextic fields of arbitrary conductor is determined by way of example.
Strong unicity versus modulus of convexity
Authors: Huotari Robert , Sahab Salem
Published: April 2009

We show that a Banach space has modulus of convexity of power type p if and only if best approximants to points from straight lines are uniformly strongly unique of order p. Assuming that the space is smooth, we derive a characterisation of the best simultaneous approximant to two elements, and use the characterisation to prove that p–type modulus of convexity implies order p strong unicity of the simultaneous approximant.
Local homeo- and diffeomorphisms: invertibility and convex image
Authors: Zampieri Gaetano , Gorni Gianluca
Published: April 2009

We prove a necessary and sufficient condition for a local homeomorphism defined on an open, connected subset of a Euclidean space to be globally one-to-one and, at the same time, for the image to be convex. Among the applications we give a practical sufficiency test for invertibility for twice differentiable local diffeomorphisms defined on a ball.
On the Hölder semi-norm of the remainder in polynomial approximation
Authors: Elliott David
Published: April 2009

Suppose the qth derivative of a function f is Hölder continuous of index α, where 0 < α ≤ 1, on the interval [-1,1]. Suppose further that pn is any polynomial of degree at most n such that |τn(x)| = |f(x) - pn(x)| ≤ c {max ((1 - x2)½/n, 1/n2) } q+a [-1,1]. If

then it is shown that

‖τn‖β ≤ cn−q−α+β, 0 < β ≤ 1.
Uniform density and M−density for subrings of C(X)
Authors: Garrido M.I. , Montalvo F.
Published: April 2009

This paper deals with the equivalence between u−density and m−density for the subrings of C(X). It was proved by Kurzweil that such equivalence holds for those subrings that are closed under bounded inversion. Here an example is given in C(N) of a u−dense subring that is not m−dense. It is deduced that the two types of density coincide only in the trivial case where these topologies are the same, that is, if and only if X is a pseudocompact space.
Some convolution identities based upon Ramanujan's bilateral sum
Authors: Srivastava H.M.
Published: April 2009

Recently, Bhargava, Adiga and Somashekara made use of Ramanujan's 1Ψ1 summation formula to prove a convolution identity for certain coefficients generated by the quotient of two infinite products. As special cases of this identity, they deduced several results (connected especially with the generalised Frobenius partition functions) including, for example, the convolution identities given earlier by Kung-Wei Yang. In this sequel to the aforementioned works, we provide a complete answer to an interesting question raised by Bhargava, Adiga and Somashekara in connection with one class of their convolution identities.
A multiple linking minimax principle
Authors: Motreanu Dumitru
Published: April 2009

The aim of this paper is three-fold: to fill the gap between different deformation lemmas, to obtain a unifying minimax result where multiple linking situations can occur, and to locate the critical points as solutions of minimisation problems.
Critical algebras and the Frattini congruence, II
Authors: Kearnes Keith A.
Published: April 2009

We prove that any finite subdirectly irreducible algbra in a congruence modular variety with trivial Frattini congruence is critical. We also show that if A and B are critical algebras which generate the same congruence modular variety, then the variety generated by the proper sections of A equals the variety generated by the proper sections of B.
On the self-length of two-dimensional Banach spaces
Authors: Chalmers B. , Franchetti C. , Giaquinta M.
Published: April 2009

The aim of this paper is to prove the following result: if X is a 2-dimensional symmetric real Banach space, then its self-length is greater than or equal to 2π. Moreover, the minimum value 2π is uniquely attained (up to isometries) by euclidean space.
On rings with invariant radicals
Authors: Kelarev A. V. , Plant A.
Published: April 2009

We give necessary and sufficient conditions on the semigroup S for the Jacobson radical to be S-invariant.
A continuous analogue and an extension of Radó's formulæ
Authors: Pearce C.E.M. , pečarić J.
Published: April 2009

A continuous analogue is derived for Radó's comparison formulæ. The analogue is then employed to provide a result which continues Radó's result and interpolates an inequality of Pittenger.
Diophantine equations of Erdös-Moser type
Authors: Moree Pieter
Published: April 2009

Using an old result of Von Staudt on sums of consecutive integer powers, we shall show by an elementary method that the Diophantine equation 1k + 2k + … + (x − l)k = axk has no solutions (a, x, k) with k > 1, . For a = 1 this equation reduces to the Erdös-Moser equation and the result to a result of Moser. Our method can also be used to deal with variants of the equation of the title, and two examples will be given. For one of them there are no integer solutions with
A note on frame starters
Authors: Wang Cheng-De
Published: April 2009

We construct frame starters in Z2n − {0, n}, for n ≡ 0, 1 mod 4, where Z2n denotes the cyclic group of order 2n. We also construct left frame starters in Q2n − {e, αn}, where Q2n is the dicyclic group of order 4n and αn is the unique element of order 2 in Q2n.
Global attractivity and stability in some monotone discrete dynamical systems
Authors: Zhao Xiao-Qiang
Published: April 2009

The existence of globally attractive order intervals for some strongly monotone discrete dynamical systems in ordered Banach spaces is first proved under some appropriate conditions. With the strict sublinearity assumption, threshold results on global asymptotic stability are then obtained. As applications, the global asymptotic behaviours of nonnegative solutions for time-periodic parabolic equations and cooperative systems of ordinary differential equations are discussed and some biological interpretations and concrete application examples are also given.
A vanishing theorem for hyperplane cohomology
Authors: Lehrer G.I.
Published: April 2009

Let A be a hyperplane arrangement in an arbitrary finite dimensional vector space V and let G ≤ GL(V) be an automorphism group of A. If λ is a complex representation of G such that (λ,1)GH=0 for all pointwise isotropy groups GH (H ∈ A), then we prove the “local-global” result that λ does not appear in the representation of G on the Orlik-Solomon algebra of A. The result is applied to complex reflection groups and to finite orthogonal groups. It may also be viewed as a combinatorial result concerning the homology of the lattice of intersections of A. A more general version of the main result is also discussed.
For the minimal surface equation, the set of solvable boundary values need not be convex
Authors: Morgan Frank
Published: April 2009

One might think that if the minimal surface equation had a solution on a smooth domain D ⊂ Rn with boundary values φ, it would have a solution with boundary values tφ for all 0 ≤ t ≤ 1. We give a counterexample in R2.
Commensurability and elementary equivalence of polycyclic groups
Authors: Raphael Deborah
Published: April 2009

It is shown that two polycyclic-by-finite groups G and H, satisfying the same sentences with one alternation of quantifiers, are commensurable. In fact we show something stronger: given n > 1 there is a subgroup Hn of H and a subgroup Gn of G such that Hn≃G, Gn≃H and the indices [G: Gn] and [H: Hn] are finite and prime to n.
A property of series of holomorphic homogeneous polynomials with Hadamard gaps
Authors: Choa Jun Soo
Published: April 2009

Recently J. Miao proved that if is a holomorphic function with Hadamard gaps on the open unit disc D then f ∈ Xp if and only if f ∈ Bp if and only if if and if only if where Xp, Bp and denote respectively the class of holomorphic functions on D which satisfy |f′(z)|p(1 − |z|2)p − 1dxdy is a finite measure, a Carleson measure and a little Carleson measure on D. In this paper we give a higher-dimensional version of Miao's result.
On the cancellation problem of Zariski
Authors: Byeon Dongho , Kim Hyun Kwang
Published: April 2009

Let K1 and K2 be extension fields over a field K with char K = p > 0. Assume L = K1(x1) = K2(x2) ⊃ K where xi is transcendental over Ki, for i = 1, 2. In this paper we prove that if K1 is a perfect field, then K1 = K2.
Almost complex structures on the orthogonal twistor bundle
Authors: Yang Kichoon
Published: April 2009

We give a construction of 2s, s = n(n – 1)/2, many natural almost complex structures on the orthogonal twistor bundle over a 2n-dimensional Riemannian manifold. The usual almost complex structures are then characterised by the condition that they correspond to integrable invariant complex structures on the standard fibre which is identified with the hermitian symmetric space SO(2n)/U(n).
Asymptotic behaviour of solutions to neutral functional differential equations
Authors: Chen Shaozhu , Huang Qingguang
Published: April 2009

Sufficient or necessary conditions are established so that the neutral functional differential equation [x(t) − G(t, xt)]″ + F(t, xt) = 0 has a solution which is asymptotic to a given solution of the related difference equation x(t) = G(t, xt) + a + bt, where a and b are constants.
On a problem of Szász
Authors: Hirano Yasuyuki
Published: April 2009

Let R be a ring with centre Z. In this note, we prove the following: If the additive group Z+ of Z has finite group-theoretic index in R+, then R has an ideal I contained in Z such that R/I is a finite ring. This is a solution of a problem posed by F.A. Szász.
Covers and complements in the subalgebra lattice of a Boolean algebra
Authors: Düntsch Ivo
Published: April 2009

Section 1 addresses the problem of covers in Sub D, the lattice of subalgebras of a Boolean algebra; we describe those BA's in whose subalgebra lattice every element has a cover, and show that every small and separable subalgebra of P(ω) has 2ω covers in SubP(ω). Section 2 is concerned with complements and quasicomplements. As a general result it is shown that Sub D is relatively complemented if and only if D is a finite– cofinite BA. Turning to Sub P(ω), we show that no small and separable D ≤ P(ω) can be a quasicomplement. In the final section, generalisations of packed algebras are discussed, and some properties of these classes are exhibited.
Stationary subspaces in ordered spaces
Authors: Kemoto Nobuyuki
Published: April 2009

In this paper, we shall characterise the B(k)-property in generalised ordered (GO) spaces as follows.

For every uncountable regular cardinal K, every GO space has the B(K)-property if and only if it has no closed subspace which is homeomorphic to a stationary set in K (with the subspace topology in K).
Another generalisation of smith's determinant
Authors: Beslin Scott , Ligh Steve
Published: April 2009

Let S = {x1, x2, …, xn} be a set of distinct positive integers. The n × n matrix [S] = (Sij), where Sij, = (xi, xj), the greatest common divisor of xi, and xj, is called the greatest common divisor (GCD) matrix on S. H.J.S. Smith showed that the determinant of the matrix [E(n)], E(n) = { 1,2, …, n}, is ø(1)ø(2) … ø(n), where ø(x) is Euler's totient function. We extend Smith's result by considering sets S = {x1, x2, … xn} with the property that for all i and j, (xi, xj) is in S.
On approximation by trigonometric Lagrange interpolating polynomials
Authors: Xie T.F. , Zhou S.P.
Published: April 2009

It is well-known that the approximation to f(x) ∈ C2π, by nth trigonometric Lagrange interpolating polynomials with equally spaced nodes in C2π, has an upper bound In(n)En(f), where En(f) is the nth best approximation of f(x). For various natural reasons, one can ask what might happen in Lp space? The present paper indicates that the result about the trigonometric Lagrange interoplating approximation in Lp space for 1 < p < ∞ may be “bad” to an arbitrary degree.
Plücker formulae for the orthogonal group
Authors: Yang Kichoon
Published: April 2009

Plücker formulae for horizontal curves in SO(m)-flag manifolds are derived. These formulae are seen to generalise the usual Plücker formulae for projective space curves. They also have applications in the theory of minimal surfaces in Euclidean sphere and the complex hyperquadric.
On denseness of certain norms in Banach spaces
Authors: Sevilla M. Jiménez , Moreno J.P.
Published: April 2009

We give several results dealing with denseness of certain classes of norms with many vertex points. We prove that, in Banach spaces with the Mazur or the weak* Mazur intersection property, every ball (convex body) can be uniformly approximated by balls (convex bodies) being the closed convex hull of their strongly vertex points. We also prove that given a countable set F, every norm can be uniformly approximated by norms which are locally linear at each point of F.
Harmonicity of a foliation and of an associated map
Authors: Tondeur Philippe , Vanhecke Lieven
Published: April 2009

A foliation on a Riemannian manifold (M, g) is harmonic if all the leaves are minimal submanifolds. We give a new characterisation of the harmonicity of a foliation on (M, g) by the harmonicity of an associated bundle map of (T M, gC), where gC is the complete lift metric of g to the tangent bundle as introduced by Yano and Ishihara.
Diagonal Cauchy spaces
Authors: Kent D.C. , Richardson G.D.
Published: April 2009

A diagonal condition is defined which internally characterises those Cauchy spaces which have topological completions. The T2 diagonal Cauchy spaces allow both a finest and a coarsest T2 diagonal completion. The former is a completion functor, while the latter preserves uniformisability and has an extension property relative to θ-continuous maps.
Full subrings of E-rings
Authors: Feigelstock Shalom
Published: April 2009

A ring R is said to be an E-ring if the map R → of E (R)+ into the ring of endomorphisms of its additive group via a ↪ al = left multiplication by a, is an isomorphism. In this note torsion free rings R for which the group Rl, of left multiplication maps by elements of R, is a full subgroup of E(R)+ will be considered. These rings are called TE-rings. It will be shown that TE-rings satisfy many properties of E-rings, and that unital TE-rings are E-rings. If R is a TE-ring, then E(R+) is an E-ring, and E(R+)+ / is bounded. Some results concerning additive groups of TE-rings will be obtained.
Some existence theorems for differential inclusions in Hilbert spaces
Authors: Chang Shih-Sen , Chen Yu-Qing , Lee Byung Soo
Published: April 2009

Some existence theorem for solutions of two kinds of differential inclusions with monotone type mappings in Hilbert spaces are given.
Continuous and numerical analysis of a boundary shock problem
Authors: Vulanović Relja
Published: April 2009

A quasilinear singularly perturbed boundary value problem whose solution has a shock layer is investigated. Estimates of the derivatives of the solution are derived. Based on these estimates, a new independent variable is introduced. Then the transformed problem is solved numerically using finite - difference schemes. The transformation corresponds to solving the original problem on a mesh which is dense in the layer. The linear convergence uniform in the perturbation parameter is proved in the discrete L1 norm. Numerical results show uniform pointwise convergence too.
Note on the extensions of Butler groups
Authors: Fuchs L. , Viljoen G.
Published: April 2009

In terms of a new notion, called prebalancedness, those extensions of a Butler group by a Butler group which are again Butler groups are characterised. It is shown that the prebalanced extensions of torsion-free abelian groups form a divisible subgroup in the group of extensions.
Slant immersions
Authors: Chen Bang-Yen
Published: April 2009

A slant immersion is defined as an isometric immersion from a Riemannnian manifold into an almost Hermitian manifold with constant Wirtinger angle. In this article we give some fundamental results concerning slant immersions. Several results on slant surfaces in ℂ2 are also proved.
Mordell's equation in characteristic three
Authors: Voloch J.F.
Published: April 2009

Let K be a function field in one variable over a finite field of characteristic three. If a ∈ K is not a cube, we show that the equation y2 = x3 + a has only finitely many solutions x, y ∈ K.
Expected number of excursions above curved boundarie by a random walk
Authors: Klebaner Fima C.
Published: April 2009

An asymptotic relation for the expected number of excursions above a boundary g(n) by a random walk Sn, n = 1,2, ‥, N is given in terms of an integral involving g. An integral test is given to determine whether the total excursion time has finite expectation. If some moment assumptions hold then the expectation of the total excursions is finite if and only if .
Contributions to computational analysis
Authors: Dobner H-J.
Published: April 2009

In this paper some new results concerning computational analysis are established. The fundamental concepts of interval analysis and fixed point theorems suitable for computational purposes are developed and applied to concrete examples illustrating this new method of proving mathematical statements.
Norms in polynomial rings
Authors: Myerson G.
Published: April 2009

We give a formula for the norm on a polynomial ring modulo an ideal in terms of the zero-set of the ideal. We hint at the relation to resultants.
The coincidence problem for compositions of set-valued maps
Authors: Ben-El-Mechaiekh H.
Published: April 2009

The main purpose of this work is to give a general and elementary treatment of the fixed point and the coincidence problems for compositions of set-valued maps with not necessarily locally convex domains and to display, once more, the central rôle played by the selection property.
Area and length maxima for univalent functions
Authors: Yamashita Shinji
Published: April 2009

Let S be the family of functions f(z) = z + a2z2 + … which are analytic and univalent in |z| < 1. We find the value

as a function of r 0 < r < 1. The known lower estimate of

is improved. Relations with the growth theorem are considered and the radius of univalence of f(z)/z is discussed.
A new minimax inequality on H-spaces with applications
Authors: Ding Xie Ping , Kim Won Kyu , Tan Kok-Keong
Published: April 2009

A new minimax inequality on H-spaces is obtained together with six equivalent formulations. As applications, some results on fixed point theorems and system of inequalities are proved. Our results generalise the corresponding results on (1) minimax inequalities due to Fan, Yen, Tan, Shih-Tan and Ding-Tan, (2) fixed point theorems due to Browder, Tarafdar, Shih-Tan and Ding-Tan, (3) convex inequalities due to Fan, (4) systems of inequalities due to Granas-Liu and (5) a minimax theorem due to Kneser.
Applications of a minimax inequality on H-spaces
Authors: Ding Xie Ping , Kim Won Kyu , Tan Kok-Keong
Published: April 2009

By applying a minimax inequality on H-spaces from our earlier work, new generalisations of well-known intersection theorems concerning sets with convex sections and minimax inequalities of von Neumann type are obtained. Our results generalise the corresponding results of Ben-El-Mechaiekh, Deguire and Granas, Fan, Liu, Shih-Tan, Sion and Tarafdar.
Limits of unbounded sequences of continued fractions
Authors: Tong Jingcheng
Published: April 2009

Let X = {xk}k≥1 be a sequence of positive integers. Let Qk = [O;xk,xk−1,…,x1] be the finite continued fraction with partial quotients xi(1 ≤ i ≤ k). Denote the set of the limit points of the sequence {Qk}k≥1 by Λ(X). In this note a necessary and sufficient condition is given for Λ(X) to contain no rational numbers other than zero.
On adelic automorphic forms with respect to a quadratic extension
Authors: Dou Ze-Li
Published: April 2009

Let E/F be a totally real quadratic extension of a totally real algebraic number field. The author has in an earlier paper considered automorphic forms defined with respect to a quaternion algebra BE over E and a theta lift from such quaternionic forms to Hilbert modular forms over F. In this paper we construct adelic forms in the same setting, and derive explicit formulas concerning the action of Hecke operators. These formulas give an algebraic foundation for further investigations, in explicit form, of the arithmetic properties of the adelic forms and of the associated zeta and L-functions.
Common fixed point theorems for two mappings satisfying some conditions
Authors: Ume Jeong Sheok , Kim Jong Kyu
Published: April 2009

In this paper, using the concept of w-distance, we first prove common fixed point theorems in a complete metric space. Then these theorems are used to improve Kannan's fixed point theorem, Ćirić's fixed point theorem, Kada, Suzuki and Takahashi's fixed point theorem and Ume's fixed point theorem.
On totally umbilical QR-submanifolds of quaternion Kaehlerian manifolds
Authors: Bejancu Aurel , Farran Hani Reda
Published: April 2009

We introduce the notion of generalised 3-Sasakian structure on a manifold and show that a totally umbilical, but not totally geodesic, proper QR-submanifold of a quaternion Kaehlerian manifold is an extrinsic sphere and inherits such a structure.
The average distance property of classical Banach spaces
Authors: Hinrichs Aicke
Published: April 2009

A Banach space X has the average distance property (ADP) if there exists a unique real number r such that for each positive integer n and all x1,…,xn in the unit sphere of X there is some x in the unit sphere of X such that
.

It is known that l2 and l∞ have the ADP, whereas lp fails to have the ADP if 1 ≤ p < 2. We show that lp also fails to have the ADP for 3 ≤ p ≤ ∞. Our method seems to be able to decide also the case 2 < p < 3, but the computational difficulties increase as p comes closer to 2.
Some Engel conditions on infinite subsets of certain groups
Authors: Abdollahi Alireza
Published: April 2009

Let k be a positive integer. We denote by ɛk(∞) the class of all groups in which every infinite subset contains two distinct elements x, y such that [x,k y] = 1. We say that a group G is an -group provided that whenever X, Y are infinite subsets of G, there exists x ∈ X, y ∈ Y such that [x,k y] = 1. Here we prove that:

(1) If G is a finitely generated soluble group, then G ∈ ɛ3(∞) if and only if G is finite by a nilpotent group in which every two generator subgroup is nilpotent of class at most 3.

(2) If G is a finitely generated metabelian group, then G ∈ ɛk(∞) if and only if G/Zk (G) is finite, where Zk (G) is the (k + 1)-th term of the upper central series of G.

(3) If G is a finitely generated soluble ɛk(∞)-group, then there exists a positive integer t depending only on k such that G/Zt (G) is finite.

(4) If G is an infinite -group in which every non-trivial finitely generated subgroup has a non-trivial finite quotient, then G is k-Engel. In particular, G is locally nilpotent.
Complementation in the group of units of a ring
Authors: Coleman Clare , Easdown David
Published: April 2009

By adding 1 to elements of the nilradical and Jacobson radical of a ring with identity, normal subgroups of the group of units are obtained. In this paper we record observations about complementation of these subgroups in the group of units of a ring, identifying large classes where complementation takes place and some examples where it fails.
Toeplitz operators on the Bergman space of the unit ball
Authors: Raimondo Roberto
Published: April 2009

We prove that if an operator A is a finite sum of finite products of Toeplitz operators on the Bergman space of the unit ball Bn, then A is compact if and only if its Berezin transform vanishes at the boundary. For n = 1 the result was obtained by Axler and Zheng in 1997.
The linearisations of cyclic permutation have rational zeta functions
Authors: Du Bau-Sen
Published: April 2009

Letn≥ 2 be an integer. LetPbe the set of all integers in [1,n+ 1] and let σ be a cyclic permutation onP. Assume thatfis the linearisation of σ onP. Then we show thatfhas rational Artin-Mazur zeta function which is closely related to the characteristic polynomial of somen×nmatrix with entries either zero or one. Some examples of non-conjugate maps with the same Artin-Mazur zeta function are also given.
Families of elliptic curves with trivial Mordell-Weil group
Authors: Dabrowski Andrzej , Wieczorek Małgorzata
Published: April 2009

Fix and elliptic curve y2 = x3 + Ax + B, satisfying A, B ∈ ℤ A ≥ |B| > 0. We prove that the associated quadratic family contains infinitely many elliptic curves with trivial Mordell-Weil group.
On minimal faithful permutation representations of finite groups
Authors: Kovács L. G. , Praeger Cheryl E.
Published: April 2009

The minimal faithful permutation degree μ(G) of a finite group G is the least positive integer n such that G is isomorphic to a subgroup of the symmetric group Sn. Let N be a normal subgroup of a finite group G. We prove that μ(G/N) ≤ μ(G) if G/N has no nontrivial Abelian normal subgroup. There is an as yet unproved conjecture that the same conclusion holds if G/N is Abelian. We investigate the structure of a (hypothetical) minimal counterexample to this conjecture.
Minimally irreducible groups of prime degree
Authors: Volta F. Dalla , Martino L. Di
Published: April 2009

We determine the irreducible subgroups G of GL (r,ℂ), where r is prime and all proper subgroups of G are reducible.
Virtual surface Bundle groups
Authors: Hillman J. A.
Published: April 2009

We show that all torsion free groups which are virtual surface bundle groups of type I in Johnson's trichotomy may be realised by aspherical closed smooth 4-manifolds. (This was already known for type II.)
Edwards-Walsh resolutions of complexes and Abelian groups
Authors: Yokoi Katsuya
Published: April 2009

We give a necessary and sufficient condition for the existence of an Edwards-Walsh resolution of a complex. Our theorem is an extension of Dydak-Walsh's theorem to all simplicial complexes of dimension ≥ n + 2. We also determine the structure of an Abelian group with the Edwards-Walsh condition, (which was introduced by Koyama and the author).
Asymptotic behaviour of small solutions of singularly perturbed problems
Authors: Guo Zongming
Published: April 2009

We consider the singular limit of small solutions of some singularly perturbed problems where the nonlinearity changes sign.
Syntactic semigroups and graph algebras
Authors: Kelarev A. V. , Sokratova O. V.
Published: April 2009

We describe all directed graphs with graph algebras isomorphic to syntactic semigroups of languages.
An (n + 1)– fold Marcinkiewicz multiplier theorem on the Heisenberg group
Authors: Fraser A. J.
Published: April 2009

We prove a Marcinkiewicz-type multiplier theorem on the Heisenberg group: for 1 < p < ∞, we establish the boundedness on Lp (ℍn) of spectral multipliers m (ℒ1,…,ℒn, iT) of the n partial sub-Laplacians ℒ1,…,ℒn and iT, where m satisfies an (n + l)-fold Marcinkiewicz-type condition. We also establish regularity and cancellation conditions which the convolution kernels of these Marcinkiewicz multipliers m (ℒ1,…,ℒn,iT) satisfy.
An analogue for semigroups of a group problem of P. Erdös and B. H. Neumann
Authors: Kappe Luise-Charlotte , Lennox John C. , Wiegold James
Published: April 2009

In response to a question posed by P. Erdös, B. H. Neumann showed that in a group with every subset of pairwise noncommuting elements finite there is a bound on the size of these sets. Recently, H. E. Bell, A. A. Klein and the first author showed that a similar result holds for rings. However in the case of semigroups, finiteness of subsets of pairwise noncommuting elements does not assure the existence of a bound for their size. The largest class of semigroups in which we found Neumann's result valid are cancellative semigroups.