bluuebunny/crossref_metadata_2025 huggingface dataset:
Averaging distances in certain Banach spaces
Authors: Wolf Reinhard
Published: April 2009

Let E be a Banach space. The averaging interval AI(E) is defined as the set of positive real numbers α, with the following property: For each n ∈ ℕ and for all (not necessarily distinct) x1, x2, … xn ∈ E with ∥x1∥ = ∥x2∥ = … = ∥xn∥ = 1, there is an x ∈ E, ∥x∥ = 1, such that

It follows immediately, that AI(E) is a (perhaps empty) interval included in the closed interval [1,2]. For example in this paper it is shown that AI(E) = {α} for some 1 < α < 2, if E has finite dimension. Furthermore a complete discussion of AI(C(X)) is given, where C(X) denotes the Banach space of real valued continuous functions on a compact Hausdorff space X. Also a Banach space E is found, such that AI(E) = [1,2].
Conditions for oscillation of first order neutral delay differential equations
Authors: Jiang Ziwen
Published: April 2009

In this paper, some new sufficient conditions for oscillation of first order neutral delay differential equations with several variable coefficients are obtained. These sufficient conditions include and are in many cases weaker than those known.
Symmetric spectral factorisation of self-adjoint rational matrix functions
Authors: Groenewald G.J. , Petersen M.A.
Published: April 2009

For a self-adjoint rational matrix function, not necessarily analytic at infinity, the existence of a right (symmetric) spectral factorisation is described in terms of a given left spectral factorisation. The formula for the right spectral factor is given in terms of the formula for the given left spectral factor. All formulas are based on a special realisation of a rational matrix function, which is different from ones that have been used before.
A one dimensional analogue of the vorticity equation
Authors: Sriskandarajah K.
Published: April 2009

We study the qualitative properties of the one dimensional analogue of the Helmholtz vorticity advection equation. The second order hyperbolic equation has the unusual characteristic of disturbances propagating at infinite speed. The global solution for Goursat data is given in closed form. We also obtain qualitative results on the nodal curve where the solution is zero. A related perturbation problem is considered and solutions for small data are obtained. The forced vorticity equation admits a class of soliton solutions.
On the implicit Darboux problem in Banach spaces
Authors: Wójtowicz Daria
Published: April 2009

In this paper we prove the existence theorem for the implicit Darboux problem on the quarterplane x ≥ 0, y ≥ 0. Moreover, we study the topological structure of the solution set of this problem.
Finite element methods for compressible Stokes equations with inflow boundary condition
Authors: Kweon Jae Ryong
Published: April 2009

A finite element method for solving the compressible viscous Stokes equation with an inflow boundary condition is presented. The unique existence of the solution of the discrete problem is established, and an error analysis is given. It is shown that the error in pressure is dominated by the one in velocity and an error at the inflow portion of the boundary.
Hypersurfaces with special quadric representations
Authors: Jitan Lu
Published: April 2009

Let x: Mn → Em be an isometric immersion of an n-dimensional Riemannian manifold into the m-dimensional Euclidean space. Then the map (where t denotes transpose) is called the quadric representation of Mn. In this paper, we study and classify hypersurfaces in the Euclidean space Em which satisfy , where B and C are two constant matrices, and Δ is the Laplacian operator of Mn. Some classification results are obtained.
On finite groups with the Cayley invariant property
Authors: Li Cai Heng
Published: April 2009

A finite group G is said to have the m-CI property if, for any two Cayley graphs Cay(G, S) and Cay(G, T) of valency m, Cay(G, S) ≅ Cay(G, T) implies Sσ = T for some automorphism σ of G. In this paper, we investigate finite groups with the m-CI property. We first construct groups with the 3-CI property but not with the 2-CI property, and then prove that a nonabelian simple group has the 3-CI property if and only if it is A5. Finally, for infinitely many values of m, we construct Frobenius groups with the m-CI property but not with the nontrivial k-CI property for any k < m.
Comparable differentiability characterisations of two classes of Banach spaces
Authors: Giles J.R.
Published: April 2009

We characterise Banach spaces not containing l1 by a differentiability property of each equivalent norm and show that a slightly stronger differentiability property characterises Asplund spaces.
Uniformities and uniformly continuous functions on locally connected groups
Authors: Megrelishvili (Levy) Michael , Nickolas Peter , Pestov Vladimir
Published: April 2009

We show that the left and the right uniformities on a locally connected topological group G coincide if and only if every left uniformly continuous real-valued function on G is right uniformly continuous.
Convexité holomorphe intermédiaire des revetements d'un domaine pseudoconvexe
Authors: Asserda S.
Published: April 2009

Let M be a complex manifold and L → M be a positive holomorphic line bundle over M equipped with a Hermitian metric h of class C2. If D ⊂⊂ M is a pseudoconvex domain which is relatively compact in M then there exists an integer r0 such that for every r ≥ r0 and for every connected holomorphic covering π: the covering is holomorphically convex with respect to holomorphic sections of .
Seiberg-Witten invariants of generalised rational blow-downs
Authors: Park Jongil
Published: April 2009

One of the main problems in Seiberg-Witten theory is to find (SW)-basic classes and their invariants for a given smooth 4-manifold. The rational blow-down procedure introduced by Fintushel and Stern is one way to compute these invariants for some smooth 4-manifolds. In this paper, we extend their results to the general case. That is, we find (SW)-basic classes and Seiberg-Witten invariants for generalised rational blow-down 4-manifolds by using index computations.
Primeness of the enveloping algebra of Hamiltonian superalgebras
Authors: Wilson Mark C.
Published: April 2009

In 1990 Allen Bell presented a sufficient condition for the primeness of the universal enveloping algebra of a Lie superalgebra. Let Q be a nonsingular bilinear form on a finite-dimensional vector space over a field of characteristic zero. In this paper we show that Bell's criterion applies to the Hamiltonian Cartan type superalgebras determined by Q, and hence that their enveloping algebras are semiprimitive.
Solution behaviour in a class of difference–differential equations
Authors: Fedorenko A.D. , Fedorenko V.V. , Ivanov A.F. , Sharkovsky A.N.
Published: April 2009

Difference equations with piecewise continuous nonlinearities and their singular perturbations, first order neutral type delay differential equations with small parameters, are considered. Solutions of the difference equations are shown to be asymptotically periodic with period-adding bifurcations and bifurcations determined by Farey's rule taking place for periods and types of solutions. Solutions of the singularly perturbed delay differential equations are considered and compared with solutions of the difference equations within finite time intervals. The comparison is based on a continuous dependence of solutions on the singular parameter.
A new proof of the Banach-stone theorem
Authors: Cutland N.J. , Zimmer G.B.
Published: April 2009

Banach's original proof of the Banach-Stone theorem for compact metric spaces uses peak functions, that is, continuous functions which assume their norm in just one point. We show by using nonstandard methods that the peak point approach also works for compact Hausdorff spaces. The peak functions are replaced by internal functions whose standard part is supported in one monad.
Products of two idempotent transformations over arbitrary sets and vector spaces
Authors: Thomas Rachel
Published: April 2009

In this paper we consider the characterisation of those elements of a transformation semigroup S which are a product of two proper idempotents. We give a characterisation where S is the endomorphism monoid of a strong independence algebra A, and apply this to the cases where A is an arbitrary set and where A is an arbitrary vector space. The results emphasise the analogy between the idempotent generated subsemigroups of the full transformation semigroup of a set and of the semigroup of linear transformations from a vector space to itself.
Optimal presentations for solvable 2-knot groups
Authors: Hillman Jonathan A.
Published: April 2009

We find presentations for the groups of Cappell-Shaneson 2-knots and other solvable 2-knot groups which are optimal in terms of deficiency and number of generators.
Lifting unconditionally converging series and semigroups of operators
Authors: González Manuel , Martínez-Abejón Antonio
Published: April 2009

We introduce and study two semigroups of operators u+ and u_, defined in terms of unconditionally converging series. We prove a lifting result for unconditionally converging series that allows us to show examples of operators in u+. We obtain perturbative characterisations for these semigroups and, as a consequence, we derive characterisations for some classes of Banach spaces in terms of the semigroups. If u+(X, Y) is non-empty and every copy of c0 in Y is complemented, then the same is true in X. We solve the perturbation class problem for the semigroup u_, and we show that a Banach space X contains no copies of ℓ∞ if and only if for every equivalent norm |·| on X, the semiembeddings of (X, |·|) belong to u+.
On the critical points of a polynomial
Authors: Aziz Abdul , Zargar B.A.
Published: April 2009

Let p be a complex polynomial, of the form , where |zk| ≥ 1 when 1 ≤ k ≤ n − 1. Then p′(z) ≠ 0 if |z| /n.

Let B(z, r) denote the open ball in with centre z and radius r, and denote its closure. The Gauss-Lucas theorem states that every critical point of a complex polynomial p of degree at least 2 lies in the convex hull of its zeros. This theorem has been further investigated and developed. B. Sendov conjectured that, if all the zeros of p lie in then, for any zero ζ of p, the disc contains at least one zero of p′; see [3, Problem 4.1]. This conjecture has attracted much attention-see, for example, [1], and the papers cited there. In connection with this conjecture, Brown [2] posed the following problem.
Isomorphisms of Cayley digraphs of Abelian groups
Authors: Li Cai Heng
Published: April 2009

For a finite group G and a subset S of G with 1 ∉ S, the Cayley graph Cay(G, S) is the digraph with vertex set G such that (x, y) is an arc if and only if yx−1 ∈ S. The Cayley graph Cay(G, S) is called a CI-graph if, for any T ⊂ G, whenever Cay (G, S) ≅ Cay(G, T) there is an element a σ ∈ Aut(G) such that Sσ = T. For a positive integer m, G is called an m-DCI-group if all Cayley graphs of G of valency at most m are CI-graphs; G is called a connected m-DCI-group if all connected Cayley graphs of G of valency at most m are CI-graphs. The problem of determining Abelian m-DCI-groups is a long-standing open problem. It is known from previous work that all Abelian m-DCI-groups lie in an explicitly determined class of Abelian groups. First we reduce the problem of determining Abelian m-DCI-groups to the problem of determining whether every subgroup of a member of is a connected m-DCI-group. Then (for a finite group G, letting p be the least prime divisor of |G|,) we completely classify Abelian connected (p + 1)-DCI-groups G, and as a corollary, we completely classify Abelian m-DCI-groups G for m ≤ p + 1. This gives many earlier results when p = 2.
Permutation polynomials with exponents in an arithmetic progression
Authors: Park Young Ho , Lee June Bok
Published: April 2009

We examine the permutation properties of the polynomials of the type hk, r, s(x) = xr (1 + xs + … + xsk) over the finite field , of characteristic p. We give sufficient and necessary conditions in terms of k and r for hk, r, l(x) to be a permutation polynomial over , for q = p or p2. We also prove that if hk, r, s(x) is a permutation polynomial over , then (k + 1)s = ±1.
Sharp gradient estimates for eigenfunctions on Riemannian manifolds
Authors: Borbély Albert
Published: April 2009

Sharp gradient estimates are derived for positive eigenfunctions on complete Riemannian manifolds with Ricci curvature bounded below.
An isodiametric problem with lattice-point constraints
Authors: Cifre M. A. Hernández , Scott P.R.
Published: April 2009

The isodiametric problem in the Euclidean plane is solved for bounded convex sets, which are symmetric about the origin, and which contain no interior non-zero point of an arbitrary lattice L.
The Weyl calculus and Clifford analysis
Authors: Jefferies Brian , McIntosh Alan
Published: April 2009

The connection between Clifford analysis and the Weyl functional calculus for an n-tuple of bounded selfadjoint operators is noted. The operators do not necessarily commute with each other.
Quasi-convex functions and Hadamard's inequality
Authors: Dragomir S.S. , Pearce C.E.M.
Published: April 2009

Some extensions of quasi-convexity appearing in the literature are explored and relations found between them. Hadamard's inequality is connected tenaciously with convexity and versions of it are shown to hold in our setting. Our theorems extend and unify a number of known results. In particular, we derive a generalised Kenyon-Klee theorem.
Finite-dimensional simple modules over quantised Weyl algebras
Authors: Fukuda Nobuyuki
Published: April 2009

We classify finite-dimensional simple modules over quantised n-th Weyl algebras. over an algebraically closed field under a certain condition on the parameters.
The predual of the space of convolutors on a locally compact group
Authors: Cowling Michael
Published: April 2009

Let Cvp(G) be the space of convolution operators on the Lebesgue space LP(G), for an arbitrary locally compact group G. We describe Cvp(G) as a dual space, whose predual, is a Banach algebra of functions on G, under pointwise operations, with maximal ideal space G. This involves a variation of Herz's definition of AP(G); the benefit of this new definition is that all of Cvp(G) is obtained as the dual in the nonamenable setting. We also discuss further developments of this idea.
An oscillation estimate to a variational inequality
Authors: Bae Hyeong-Ohk , Choe Hi Jun
Published: April 2009

We prove that solutions for elliptic equations and variational inequalities are continuous pointwisely if the obstacle is continuous pointwisely. The continuity of weakly monotone functions in a high Sobolev space is crucial. Also a comparison principle is useful in estimating oscillations of solutions.
On a theorem of Bryce and Cossey
Authors: Ballester-Bolinches A. , Ezquerro L.M.
Published: April 2009

In this paper we characterise the subgroup–closed Fitting formations of finite groups which are saturated. This is an extension of the Bryce and Cossey result proving the saturation of all subgroup-closed Fitting formations of finite soluble groups.
The reduced group C*-algebra of a triangle building
Authors: Mantero A.M. , Zappa Z.
Published: April 2009

Let Δ be an affine building of type Ã2 and let Γ be a discrete group of type-rotating automorphisms acting simply transitively on the vertices of δ. We prove that the reduced group C*-algebra is simple. To prove this result we use the sufficient condition for the simplicity of given in a recent paper by M. Bekka, M. Cowling and P. de la Harpe.
Multiple closed orbits for N-body-type problems
Authors: Zhang Shiqing
Published: April 2009

Using the equivariant Ljusternik-Schnirelmann theory and the estimate of the upper bound of the critical value and lower bound for the collision solutions, we obtain some new results in the large concerning multiple geometrically distinct periodic solutions of fixed energy for a class of planar N-body type problems.
Fixed point theorems and equilibrium points in abstract economies
Authors: O'Regan Donal
Published: April 2009

New fixed point theorems are given which have applications in the theory of abstract economies.
Primitive ideals in the coordinate ring of quantum Euclidean space
Authors: Oh Sei-Qwon , Park Chun-Gil
Published: April 2009

A twisted group algebra kσP on a free Abelian group P with finite rank and a Poisson structure on kP are studied. As an application, the primitive spectrum of , the coordinate ring of quantum Euclidean space, is described and a Poisson algebra A is constructed so that there is a bijection between the primitive spectrum of and the symplectic spectrum of R.
Monochromatic sequences whose gaps belong to {d, 2d, …, md}
Authors: Landman Bruce M.
Published: April 2009

For m and k positive integers, define a k-term hm-progression to be a sequence of positive integers {x1,…,xk} such that for some positive integer d, xi + 1 − xi ∈ {d, 2d,…, md} for i = 1,…, k - 1. Let hm(k) denote the least positive integer n such that for every 2-colouring of {1, 2, …, n} there is a monochromatic hm-progression of length k. Thus, h1(k) = w(k), the classical van der Waerden number. We show that, for 1 ≤ r ≤ m, hm(m + r) ≤ 2c(m + r − 1) + 1, where c = ⌈m/(m − r)⌉. We also give a lower bound for hm(k) that has order of magnitude 2k2/m. A precise formula for hm(k) is obtained for all m and k such that k ≤ 3m/2.
Projective schur algebras over a field of positive characteristic
Authors: Choi Eunmi , Lee Heisook
Published: April 2009

If the characteristic of a field K is not zero then the Schur group S(K) = 0. In this paper we ask a similar question for the projective Schur group PS(K) and prove that the subgroup of PS(K) consisting of radical algebras is trivial. This disproves the conjecture that every projective Schur algebra is similar to a radical algebra.
Some p-groups of Weilandt length three
Authors: Ormerod Elizabeth A.
Published: April 2009

Finite p-groups of Wielandt length 1 are groups in which every subgroup is normal and are Dedekind groups. When the prime is odd therefore a finite p-group of Wielandt length 1 is Abelian. For an odd prime, a finite p-group of Wielandt length 2 has nilpotency class at most 3 and for such a goup to have class 3 there must be a 2-generator subgroup of this class. In this paper it is shown that for any prime p > 3 a finite p-group of Wielandt length 3 has nilpotency class at most 4, and for such a group to have class 4 there must be a 2-generator subgroup with this class. Two families of p-groups of Wielandt length 3 are described. One is a family of 3-generator groups with the property that each group modulo its Wielandt subgroup has class 2, the other is a family of 2-generator groups with the property that each group modulo its Wielandt subgroup has class 3.
On isomorphisms of connected Cayley graphs, III
Authors: Li Cai Heng
Published: April 2009

For a finite group G and a subset S of G which does not contain the identity of G, we use Cay(G, S) to denote the Cayley graph of G with respect to S. For a positive integer m, the group G is called a (connected) m-DCI-group if for any (connected) Cayley graphs Cay(G, S) and Cay(G, T) of out-valency at most m, Sσ = T for some σ ∈ Aut(G) whenever Cay(G, S) ≅ Cay(G, T). Let p(G) be the smallest prime divisor of |G|. It was previously shown that each finite group G is a connected m-DCI-group for m ≤ p(G) − 1 but this is not necessarily true for m = p(G). This leads to a natural question: which groups G are connected p(G)-DCI-groups? Here we conjecture that the answer of this question is positive for finite simple groups, that is, finite simple groups are all connected 2-DCI-groups. We verify this conjecture for the linear groups PSL(2, q). Then we prove that a nonabelian simple group G is a 2-DCI-group if and only if G = A5.
The heat flows and harmonic maps from complete manifolds into regular balls
Authors: Li Jiayu , Wang Silei
Published: April 2009

We generalise the existence result for harmonic maps obtained by Hildebrandt-Kaul-Widman to the case where the domain manifold is complete noncompact.
G-Fonctions et cohomologie des hypersurfaces singuliéres II
Authors: Bertolin Cristiana
Published: April 2009

Following Dwork's indications, in this work we give a further elaboration and a list of corrections for the article “G-fonctions et cohomologie des hypersurfaces singulières”. Moreover we extend the contents of that work to quasi-homogeneous polynomials.
Abstract reflexive sublattices and completely distributive collapsibility
Authors: Longstaff W. E. , Nation J. B. , Panaia Oreste
Published: April 2009

There is a natural Galois connection between subspace lattices and operator algebras on a Banach space which arises from the notion of invariance. If a subspace lattice ℒ is completely distributive, then ℒ is reflexive. In this paper we study the more general situation of complete lattices for which the least complete congruence δ on ℒ such that ℒ/δ is completely distributive is well-behaved. Our results are purely lattice theoretic, but the motivation comes from operator theory.
Discrete quadratic estimates and holomorphic functional calculi in Banach spaces
Authors: Franks Edwin , McIntosh Alan
Published: April 2009

We develop a discrete version of the weak quadratic estimates for operators of type w explained by Cowling, Doust, McIntosh and Yagi, and show that analogous theorems hold. The method is direct and can be generalised to the case of finding necessary and sufficient conditions for an operator T to have a bounded functional calculus on a domain which touches σ(T) nontangentially at several points. For operators on Lp, 1 < p < ∞, it follows that T has a bounded functional calculus if and only if T satisfies discrete quadratic estimates. Using this, one easily obtains Albrecht's extension to a joint functional calculus for several commuting operators. In Hilbert space the methods show that an operator with a bounded functional calculus has a uniformly bounded matricial functional calculus.

The basic idea is to take a dyadic decomposition of the boundary of a sector Sv. Then on the kth ingerval consider an orthonormal sequence of polynomials . For h ∈ H∞(Sν), estimates for the uniform norm of h on a smaller sector Sμ are obtained from the coefficients akj = (h, ek, j). These estimates are then used to prove the theorems.
Remarks on the pure critical exponent problem
Authors: Dancer E.N.
Published: April 2009

In this paper, we use geometric and analytic methods to study the existence of positive solutions of the pure critical exponent problem with Dirichlet boundary conditions. In particular we prove that there is no solution for domains which are nearly star-shaped and we show that being conformal to a star-shaped domain does not characterise the domains for which the problem has no solution. We also answer some questions of Rodriguez et al.
Generalisation of Euler's identity
Authors: Sofo A. , Cerone P.
Published: April 2009

An investigation of representation of Abel type infinite sums in closed form will be presented in this paper. An arbitrary order forced differential-difference equation will be analysed from which sums will be generated. Identities of resulting infinite sums will be proved.
Remarks on the topology of spatial polygon spaces
Authors: Kamiyama Yasuhiko
Published: April 2009

Let Mn be the “polygon space” introduced by Kirwan and Klyachko. In this paper, we give new results on the topology of Mn for odd n. We determine πq(Mn) (q ≤ n − 3). Then we describe Mn in the oriented cobordism ring . We also give new and elementary proofs of the result on the ring structure of H*(Mn/Sn; Q), where Sn denotes the symmetric group acting naturally on Mn.
Edgeworth expansion on n-spheres and Jacobi hypergroups
Authors: Pap Gyula , Voit Michael
Published: April 2009

Suitable normalisation of time-homogeneous rotation-invariant random walks on unit spheres Sd ⊂ ℝd+1 for d ≥ 2 leads to a central limit theorem with a Gaussian limit measure. This paper is devoted to an associated Edgeworth expansion with respect to the total variation norm. This strong type of convergence is different from the classical case. The proof is performed in the more general setting of Jacobi-type hypergroups on an interval.
On algebraic numbers close to 1
Authors: Dubickas Artūras
Published: April 2009

We prove that there exists a polynomial of small height with a root close to 1. This implies that there are algebraic numbers close to 1 with relatively small Mahler measure. We also give an explicit construction of such numbers with small Weil height.
Fixed points of upper semicontinuous mappings in locally G-convex spaces
Authors: Yuan George Xian-Zhi
Published: April 2009

In this paper a new fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values is established in the setting of an abstract convex structure – called a locally G-convex space, which generalises usual convexity such as locally convex H-spaces, locally convex spaces (locally H-convex spaces), hyperconvex metric spaces and locally convex topological spaces. Our fixed point theorem includes corresponding Fan-Glicksberg type fixed point theorems in locally convex H-spaces, locally convex spaces, hyperconvex metric space and locally convex spaces in the existing literature as special cases.
On the approximation of certain functions by interpolating polynomials
Authors: Revers Michael
Published: April 2009

In the present paper we consider the approximation of |x|α on [−1, 1] by interpolating polynomials and we establish upper bounds for the approximation error. It turns out that these bounds, apart from the constants, are of the best possible order. We compare our results with estimates for the best approximation, established by Bernstein.
Properties of the Berezin transform of bounded functions
Authors: Lee Jaesung
Published: April 2009

We find the spectrum of the Berezin operator T on L∞(Bn), then we show that if f ∈ L∞(Bn) satisfies Sf = rf for some r in the unit circle, where S is any convex combination of the iterations of T, then f is M-harmonic.

Finally we decompose the subspace of L∞(Bn) where lim Tkf exists into the direct sum of two subspaces of L∞(Bn).
Generalised variational-like inequalities and a gap function
Authors: Ansari Q.H. , Yao J.C.
Published: April 2009

In this paper, we study the existence of solutions of generalised variational-like inequality problems by using a generalised form of the Fan-KKM-Theorem. We also introduce a gap function for generalised variational-like inequalities.
Hankel operators from the space of bounded analytic functions to the Bloch space
Authors: Zhao Ruhan
Published: April 2009

Boundedness and compactness of little Hankel operators from H∞ to the Bloch space and the little Bloch space are characterised.
Circular colouring and graph homomorphism
Authors: zhu Xuding
Published: April 2009

For any pair of integers p, q such that (p, q) = 1 and p ≥ 2q, the graph has vertices {0, 1, …, p − 1} and edges {ij: q ≤ |i − j| ≤ p − q}. These graphs play the same role in the study of circular chromatic number as that played by the complete graphs in the study of chromatic number. The graphs share many properties of the complete graphs. However, there are also striking differences between the graphs and the complete graphs. We shall prove in this paper that for many pairs of integers p, q, one may delete most of the edges of so that the resulting graph still has circular chromatic number p/q. To be precise, we shall prove that for any number r < 2, there exists a rational number p/q (where (p, q) = 1) which is less than r but arbitrarily close to r, such that contains a subgraph H with and . This is in sharp contrast to the fact that the complete graphs are edge critical, that is, the deletion of any edge will decrease its chromatic number and its circular chromatic number.
Wandering domains in the dynamics of certain meromorphic functions
Authors: Wang Yuefei
Published: April 2009

It is shown that meromorphic solutions of certain first-order nonlinear differential equations do not have wandering domains.
Extension of localised approximation by neural networks
Authors: Hahm Nahmwoo , Hong Bum Il
Published: April 2009

We prove generalised results for localised approximation by generalised translation networks. We also show the relationship between the minimum number of neurons in the generalised translation networks with one hidden layer and the desired accuracy where the target functions are in a subset V1, p ([−1, 1]s) of the Sobolev space W1, p([−1, 1]s).
Conjugate radius and isometry group of a manifold with negative Ricci curvature
Authors: Paeng Seong-Hun
Published: April 2009

It is known that the order of the isometry group on a compact Riemannian manifold with negative Ricci curvature is finite. We show by local nilpotent structures that a bound on the orders of the isometry groups exists depending only on the Ricci curvature, the conjugate radius and the diameter.
Bipartite graph bundles with connected fibres
Authors: Hong Sungpyo , Kwak Jin Ho , Lee Jaeun
Published: April 2009

Let G be a finite connected simple graph. The isomorphism classes of graph bundles and graph coverings over G have been enumerated by Kwak and Lee. Recently, Archdeacon and others characterised bipartite coverings of G and enumerated the isomorphism classes of regular 2p-fold bipartite coverings of G, when G is nonbipartite. In this paper, we characterise bipartite graph bundles over G and derive some enumeration formulas of the isomorphism classes of them when the fibre is a connected bipartite graph. As an application, we compute the exact numbers of the isomorphism classes of bipartite graph bundles over G when the fibre is the path Pn or the cycle Cn.
Inradius and circumradius for planar convex bodies containing no lattice points
Authors: Scott P.R. , Awyong P.W.
Published: April 2009

Let K be a planar convex body containing no points of the integer lattice. We give a new inequality relating the inradius and circumradius of K.
Symmetric geodesics on conformal compactifications of Euclidean Jordan algebras
Authors: Lee Sang Youl , Lim Yongdo , Park Chan-Young
Published: April 2009

In this article we define symmetric geodesies on conformal compactifications of Euclidean Jordan algebras and classify symmetric geodesics for the Euclidean Jordan algebra of alln×nsymmetric real matrices. Furthermore, we show that the closed geodesics for the Euclidean Jordan algebra of all 2 × 2 symmetric real matrices are realised as the torus knots in the Shilov boundary of a Lie ball.
Some results on defining sets of t-designs
Authors: Gray Brenton D. , Ramsay Colin
Published: April 2009

We investigate how varying the parameters of t-(ν, κ, λ) designs affects the sizes of smallest defining sets. In particular, we consider the effect of varying each of the parameters t, ν and λ. We establish a number of new bounds for the sizes of smallest defining sets and find the size of smallest defining sets for an infinite family of designs. We also show how one of our results can be applied to the problem of finding critical sets of Latin squares.
Restricted Lie algebras of maximal class
Authors: Riley D.M.
Published: April 2009

Let L be a possibly infinite-dimensional Lie algebra of maximal class. We show that if L admits the structure of a Lie p-algebra then the dimension of L can be at most p + 1. Furthermore, this bound is best possible.
Fatou-Julia theory on transcendental semigroups II
Authors: Poon Kin-Keung
Published: April 2009

In this paper, we extend our theories on the dynamics of transcendental semigroups. Several properties of Fatou and Julia sets of transcendental semigroups will be explored.
The distribution of zeros of solutions of first order functional differential equations
Authors: Zhou Yong
Published: April 2009

In this paper, we establish some estimates for the distance between adjacent zeros of the solutions of the first order delay differential equation

and the first order advanced differential equation

whereP∈C([t0, ∞), [0, ∞)) and τ ∈R+. Our results improve recent results in the literature.
A generalisation of the summation formula of Plana
Authors: Frappier Clément
Published: April 2009

An extension of the classical summation formula of Plana is obtained. The extension is obtained by using the zeros of a Bessel function of the first kind.
Quelques remarques sur des questions d'approximation diophantienne
Authors: Philippon Patrice
Published: April 2009

Hoping for a hand-shake between methods from diophantine approximation theory and transcendance theory, we show how zeros estimates from transcendance theory imply Roth's type lemmas (including the product theorem). We also formulate some strong conjectures on lower bounds for linear forms in logarithms of rational numbers with rational coefficients, inspired by the subspace theorem and which would imply, for example, the abc conjecture.
An uncertainty principle for the Dunkl transform
Authors: Rösler Margit
Published: April 2009

This note presents an analogue of the classical Heisenberg-Weyl uncertainty principle for the Dunkl transform on ℝN. Its proof is based on expansions with respect to generalised Hermite functions.
Two-transitive actions on conjugacy classes
Authors: Barry Michael J.J. , Ward Michael B.
Published: April 2009

Every group acts transitively by conjugation on each of its conjugacy classes of elements. It is natural to wonder when this action becomes multiply transitive. In this paper, we determine all finite groups which act faithfully and 2-transitively on a conjugacy class of elements. We also give some consequences including a solvability criterion based on what fraction of elements belong to conjugacy classes upon which the group acts faithfully and 2–transitively.
A note on the equation λ * ρ * μ = ρ
Authors: Raja C. Robinson Edward
Published: April 2009

Let G be a Hausdorff topological group and μ and λ be probability measures on G. We prove necessary and sufficient conditions for the existence of a probability measure ρ such that λ * ρ * μ = ρ under certain conditions. We prove a similar result for probability measures on semigroups.
A fixed point theorem and its applications to a system of variational inequalities
Authors: Ansari Qamrul Hasan , Yao Jen-Chih
Published: April 2009

In this paper, we first prove a fixed point theorem for a family of multivalued maps defined on product spaces. We then apply our result to prove an equilibrium existence theorem for an abstract economy. We also consider a system of variational inequalities and prove the existence of its solutions by using our fixed point theorem.
Weak convergence of tensor products of vector measures with values in nuclear spaces
Authors: Kawabe Jun
Published: April 2009

We study weak convergence of tensor products of vector measures with values in nuclear spaces, such as the space of all rapidly decreasing, infinitely differentiable functions, the space of all test functions, and the strong duals of those spaces. It is shown that the weak convergence of a net of tensor products of vector measures follows from that of the corresponding net of real product measures.
A KKM type theorem and its applications
Authors: Lin Lai-Jiu
Published: April 2009

In this paper we establish a generalised KKM theorem from which many well-known KKM theorems and a fixed point theorem of Tarafdar are extended.
The second variation formula for exponentially harmonic maps
Authors: Cheung Leung-Fu , Leung Pui-Fai
Published: April 2009

We derive the formula in the title and deduce some consequences. For example we show that the identity map from any compact manifold to itself is always stable as an exponentially harmonic map. This is in sharp contrast to the harmonic or p-harmonic cases where many such identity maps are unstable. We also prove that an isometric and totally geodesic immersion of Sm into Sn is an unstable exponentially harmonic map if m ≠ n and is a stable exponentially harmonic map if m = n.
Regular multilinear operators onC(K)spaces
Authors: Bombal Fernando , Villanueva Ignacio
Published: April 2009

The purpose of this paper is to characterise the class ofregularcontinuous multilinear operators on a product ofC(K)spaces, with values in an arbitrary Banach space. This class has been considered recently by several authors in connection with problems of factorisation of polynomials and holomorphic mappings. We also obtain several characterisations of a compact dispersed spaceKin terms of polynomials and multilinear forms defined onC(K).
Hyperbolic manifolds with the strongly shadowing property
Authors: Lee Keon-Hee , Kim Jong-Myung
Published: April 2009

Let f be a C1 diffeomorphism of a compact smooth manifold M and λ ⊂ M a C1 compact invariant submanifold with a hyperbolic structure as a subset of M. We show that the diffeomorphism | λ is Anosov if and only if λ has the strongly shadowing property, and find hyperbolic sets which have the strongly shadowing property.
Hirschhorn's identities
Authors: Hammond Paul , Lewis Richard , Liu Zhi-Guo
Published: April 2009

We prove a general identity between power series and use this identity to give proofs of a number of identities proposed by M.D. Hirschhorn. We also use the identity to give proofs of a well-known result of Jacobi, the quintuple-product identity and Winquist's identity.
Quasi-concave functions and convex convergence to infinity
Authors: Beer Gerald
Published: April 2009

By a convex mode of convergence to infinity 〈Ck〉, we mean a sequence of nonempty closed convex subsets of a normed linear space X such that for each k, Ck+1 ⊆ int Ck and and a sequence 〈xn〉 is X is declared convergent to infinity with respect to 〈Ck〉 provided each Ck contains xn eventually. Positive convergence to infinity with respect to a pointed cone with nonempty interior as well as convergence to infinity in a fixed direction fit within this framework. In this paper we study the representation of convex modes of convergence to infinity by quasi-concave functions and associated remetrizations of the space.
Oscillation criteria for certain second order nonlinear difference equations
Authors: Grace S.R. , El-Morshedy H.A.
Published: April 2009

This paper is concerned with nonlinear difference equations of the form

where δ is the forward difference operator defined by δun−1 =un−un−1 δ2un−1= δ(δun-1) and {an} is a real sequence which is not assumed to be nonnegative. The functionfis such thatuf(u) < 0 for allu≠ 0 andf(u) −f(v) =g(u, v)(u − v), for allu, v≠ 0, and for some nonnegative functiong. Our results are not only new but also improve and generalise some recent oscillation criteria. Examples illustrating the importance of our main results are also given.
Smooth variational principles in Radon-Nikodým spaces
Authors: Deville Robert , Maaden Abdelhakim
Published: April 2009

We prove that if f is a real valued lower semicontinuous function on a Banach space X, for which there exist a > 0 and b ∈ ℝ such that f(x) ≥ 2a∥x∥ + b, x ∈ X, and if X has the Radon-Nikody´m property, then for every Ε > 0 there exists a real function φ X such that φ is Fréchet differentiable, ∥φ∥∞ < Ε, ∥φ′∥∞ < Ε, φ′ is weakly continuous and f + φ attains a minimum on X. In addition, if we assume that the norm in X is β-smooth, we can take the function φ = g1 + g2 where g1 is radial and β-smooth, g2 is Fréchet differentiable, ∥g1∥∞ < Ε, ∥g2∥∞ < Ε, ∥g′1∥∞ < Ε, ∥g′1∥∞ < Ε, g′2 is weakly continuous and f + g1 + g2 attains a minimum on X.
Bifurcation of nonsymmetric solutions for some duffing equations
Authors: Nakajima Fumio
Published: April 2009

For some symmetric Duffing equation, the existence of bifurcation of nonsymmetric, periodic solutions from symmetric periodic solutions is proved by using the change of index of symmetric, periodic solutions for variation of parameters.
Topologically simple Banach algebras with derivation
Authors: Illoussamen El Hossein , Runde Volker
Published: April 2009

It is not known if a commutative, topologically simple, radical Banach algebra exists. If, however, every derivation on such an algebra is continuous, this yields the automatic continuity of all derivations on commutative, semiprime Banach algebras. Utilising techniques used by Thomas in his proof of the Singer-Wermer conjecture, we show that, if A is a commutative, topologically simple Banach algebra with a non-zero derivation on it, then a quotient of a certain localisation of A has a power series structure. A pivotal role is played by what we call ample sets of denominators.
Stronger maximal monotonicity properties of linear operators
Authors: Bauschke H.H. , Simons S.
Published: April 2009

The subdifferential mapping associated with a proper, convex lower semicontinuous function on a real Banach space is always a special kind of maximal monotone operator. Specifically, it is always “strongly maximal monotone” and of “type (ANA)”. In an attempt to find maximal monotone operators that do not satisfy these properties, we investigate (possibly discontinuous) maximal monotone linear operators from a subspace of a (possibly nonreflexive) real Banach space into its dual. Such a linear mapping is always “strongly maximal monotone”, but we are only able to prove that is of “type (ANA)” when it is continuous or surjective — the situation in general is unclear. In fact, every surjective linear maximal monotone operator is of “type (NA)”, a more restrictive condition than “type (ANA)”, while the zero operator, which is both continuous and linear and also a subdifferential, is never of “type (NA)” if the underlying space is not reflexive. We examine some examples based on the properties of derivatives.
Commutators of BMO functions and singular integral operators with non-smooth kernels
Authors: Duong Xuan Thinh , Yan Lixin
Published: April 2009

Let χ be a space of homogeneous type of infinite measure. Let T be a singular integral operator which is bounded on Lp (χ) for some p, 1 < p < ∞. We give a sufficient condition on the kernel of T so that when a function b ∈ BMO(χ), the commutator [b, T](f) = T (bf) – bT (f) is bounded on Lp spaces for all p, 1 < p > ∞. Our condition is weaker than the usual Hörmander condition. Applications include Lp-boundedness of the commutators of BMO functions and holomorphic functional calculi of Schrödinger operators, and divergence form operators on irregular domains.
The wielandt series of metabelian groups
Authors: Wetherell C.J.T.
Published: April 2009

The Wielandt subgroup of a group is the intersection of the normalisers of its subnormal subgroups. It is non-trivial in any finite group and thus gives rise to a series whose length provides a measure of the complexity of the group's subnormal structure. In this paper results of Ormerod concerning the interplay between the Wielandt series and upper central series of metabelian p-groups, p odd, are extended to the class of all odd order metabelian groups. These extensions are formulated in terms of a natural generalization of the upper central series which arises from Casolo's strong Wielandt subgroup, the intersection of the centralisers of a group's nilpotent subnormal sections.
Semiorderings and Witt rings
Authors: Craven Thomas C. , Smith Tara L.
Published: April 2009

For a pythagorean fieldFwith semiorderingQand associated preorderingT, it is shown that the Witt ringWT(F) is isomorphic to the Witt ringW(K) whreKis a closure ofFwith respect toQ. For an arbitrary preorderingT, it is shown how the covering number ofTrelates to the construction ofWT(F).
Hardy Martingales and Jensen's inequality
Authors: Asmar Nakhlé H. , Montgomery-Smith Stephen J.
Published: April 2009

Hardy martingales were introduced by Garling and used to study analytic functions on the N-dimensional torus 𝕋N, where analyticity is defined using a lexicographic order on the dual group ℤN. We show how, by using basic properties of orders on ℤN, we can apply Garling's method in the study of analytic functions on an arbitrary compact Abelian group with an arbitrary order on its dual group. We illustrate our approach by giving a new and simple proof of a famous generalised Jensen's Inequality due to Helson and Lowdenslager[5].
A Korovkin type theorem for weighted spaces of continuous functions
Authors: Roth Walter
Published: April 2009

We prove a Korovkin type approximation theorem for positive linear operators on weighted spaces of continuous real-valued functions on a compact Hausdorff space X. These spaces comprise a variety of subspaces of C (X) with suitable locally convex topologies and were introduced by Nachbin 1967 and Prolla 1977. Some early Korovkin type results on the weighted approximation of real-valued functions in one and several variables with a single weight function are due to Gadzhiev 1976 and 1980.
The algebraic closure in function fields of quadratic forms in characteristic 2
Authors: Ahmad Hamza
Published: April 2009

For a fieldkof characteristic not two, it is known thatkis algebraically closed in the function field of any (non-degenerate) quadratic form in three or more variables. In this note we consider fields of characteristic two and decide whenkis algebraically closed in a function field of a quadratick-form. For quadratic forms in three variables this has recently been done by Ohm.
G-fonctions et cohomologie des hypersurfaces singulières
Authors: Bertolin Cristiana
Published: April 2009

Our object of study is the arithmetic of the differential modules (l)(l∈ ℕ – {0}), associated by Dwork's theory to a homogeneous polynomialf(λ,X) with coefficients in a number field. Our main result is that (1)is a differential module of typeG, c'est-à-dire, a module those solutions areG-functions. For the proof we distinguish two cases: the regular one and the non regular one.

Our method gives usan effective upper bound for the global radius of(l),which doesn't depend on “l”but only on the polynomialf(λ,X). This upper bound is interesting because it gives an explicit estimate for the coefficients of the solutions of (l).

In the regular case we know there is an isomorphism of differential modules between (1)and a certain De Rham cohomology group, endowed with the Gauss-Manin connection, c'est-à-dire, our module “comes from geometry”. Therefore our main result is a particular case of André's theorem which assert thatat least in the regular case, all modules coming from geometry are of type G.
The Helgason Fourier transform on a class of nonsymmetric harmonic spaces
Authors: Astengo Francesca , Camporesi Roberto , Blasio Bianca Di
Published: April 2009

Given a group N of Heisenberg type, we consider a one-dimensional solvable extension NA of N, equipped with the natural left-invariant Riemannian metric, which makes NA a harmonic (not necessarily symmetric) manifold. We define a Fourier transform for compactly supported smooth functions on NA, which, when NA is a symmetric space of rank one, reduces to the Helgason Fourier transform. The corresponding inversion formula and Plancherel Theorem are obtained. For radial functions, the Fourier transform reduces to the spherical transform considered by E. Damek and F. Ricci.
Nilpotents in semigroups of partial transformations
Authors: Sullivan R. P.
Published: April 2009

In 1987, Sullivan determined when a partial transformation α of an infinite set X can be written as a product of nilpotent transformations of the same set: he showed that when this is possible and the cardinal of X is regular then α is a product of 3 or fewer nilpotents with index at most 3. Here, we show that 3 is best possible on both counts, consider the corresponding question when the cardinal of X is singular, and investigate the role of nilpotents with index 2. We also prove that the nilpotent-generated semigroup is idempotent-generated but not conversely.
Additive groups of rings whose subrings are ideals
Authors: Feigelstock Shalom
Published: April 2009

An Abelian group G is called an SI-group if for every ring R with additive group R+ = G, every subring S of R is an ideal in R. A complete description is given of the torsion SI-groups, and the completely decomposable torsion free SI-groups. Results are obtained in other cases as well.