bluuebunny/crossref_metadata_2025 huggingface dataset:
The Bloch space and Besov spaces of analytic functions
Authors: Stroethoff Karel
Published: April 2009

We shall give an elementary proof of a characterisation for the Bloch space due to Holland and Walsh, and obtain analogous characterisations for the little Bloch space and Besov spaces of analytic functions on the unit disk in the complex plane.
On almost additive functions
Authors: Brzdȩk Janusz
Published: April 2009

Let (S, +) be a semigroup and (H, +) be a group (neither necessarily commutative). Suppose thatJ⊂ 2sis a proper ideal inSsuch that

and Ω(J) = {M⊂S2: there existsU(M)∈JwithM[x] ∈Jfor x ∈S/U(M)}, whereM[x] = {y∈S: (y, x) ∈M}. We show that iff:S→His a function satisfying

then there exists exactly one additive functionF : S→HwithF(x) =f(x)J-almost everywhere inS.

We also prove some results concerning regularity of the functionF.
On the genus of some modular curves of level N
Authors: Kim Chang Heon , Koo Ja Kyung
Published: April 2009

We estimate the genus of the modular curves X1(N).
Dimensions of spaces of Siegel modular forms of low weight in degree four
Authors: Poor Cris , Yuen David S.
Published: April 2009

We calculate the dimensions of using Erokhin's work on Niemeier lattices and geometric methods involving the hyperelliptic locus.
Approximate methods for modelling cavitation bubbles near boundaries
Authors: Kucera A. , Blake J.R.
Published: April 2009

Approximate methods are developed for modelling the growth and collapse of clouds of cavitation bubbles near an infinite and semi-infinite rigid boundary, a cylinder, between two flat plates and in corners and near edges formed by planar boundaries. Where appropriate, comparisons are made between this approximate method and the more accurate boundary integral methods used in earlier calculations. It is found that the influence of nearby bubbles can be more important than the presence of boundaries. In confined geometries, such as a cylinder, or a cloud of bubbles, the effect of the volume change due to growth or collapse of the bubble can be important at much larger distances. The method provides valuable insight into bubble cloud phenomena.
Optimality conditions for systems with insufficient data
Authors: Papageorgiou Nikolaos S.
Published: April 2009

In this paper we use the Dubovitski–Milyutin formalism to establish necessary and sufficient conditions for optimality in a nonlinear, distributed parameter control system, with convex cost criterion and initial condition not given a priori (that is it is not a known function but instead it belongs to a specified set). Our result extends a recent theorem of Lions. Finally a concrete example is worked out in detail.
A unified approach to continuous and certain non-continuous functions II
Authors: Kohli J.K.
Published: April 2009

A unified theory of continuous and certain non-continuous functions, initiated in an earlier paper, is further elaborated. The proposed theory provides a common platform for dealing simultaneously with continuous functions and a host of non-continuous functions including lower (upper) semicontinuous functions, almost continuous functions, weakly continuous functions (encountered in functional analysis), c-continuous functions, δ-continuous functions, semiconnected functions, H-continuous functions s-continuous functions, ε-continuous functions of Klee and several other variants of continuity.
Relatively congruence distributive subquasivarieties of a congruence modular variety
Authors: Kearnes Keith A.
Published: April 2009

We characterise the relatively congruence distributive subquasivarieties of a modular variety using the modular commutator. Our characterisation allows us to extend the results of Dziobiak concerning relatively congruence distributive quasivarieties of nonassociative R-algebras.
On the minimum number of blocks defining a design
Authors: Gray Ken
Published: April 2009

A set of blocks which is a subset of a unique t – (v, k, λt) design is said to be a defining set of that design. We examine the properties of such a set, and show that its automorphism group is related to that of the whole design. Smallest defining sets are found for 2-designs and 3-designs on seven or eight varieties with block size three or four, revealing interesting combinatorial structures.
A Hilbert algebra of Hilbert-Schmidt quadratic operators
Authors: Amson J.C. , Reddy N. Gopal
Published: April 2009

A quadratic operator Q of Hilbert-Schmidt class on a real separable Hilbert space H is shown to be uniquely representable as a sequence of self-adjoint linear operators of Hilbert-Schmidt class on H, such that Q(x) = Σk〈Lkx, x〉uk with respect to a Hilbert basis . It is shown that with the norm | ‖Q‖ | = (Σk ‖Lk‖2)½ and inner-product 〈〈〈Q, P〉〉〉 = Σk 〈〈Lk, Mk〉〉, together with a multiplication defined componentwise through the composition of the linear components, the vector space of all Hilbert-Schmidt quadratic operators Q on H becomes a linear H*-algebra containing an ideal of nuclear (trace class) quadratic operators. In the finite dimensional case, each Q is also shown to have another representation as a block-diagonal matrix of Hilbert-Schmidt class which simplifies the practical computation and manipulation of quadratic operators.
Infinitary harmonic numbers
Authors: Hagis Peter , Cohen Graeme L.
Published: April 2009

The infinitary divisors of a natural number n are the products of its divisors of the , where py is an exact prime-power divisor of n and (where yα = 0 or 1) is the binary representation of y. Infinitary harmonic numbers are those for which the infinitary divisors have integer harmonic mean. One of the results in this paper is that the number of infinitary harmonic numbers not exceeding x is less than 2.2 x1/2 2(1+ε)log x/log log x for any ε > 0 and x > n0(ε). A corollary is that the set of infinitary perfect numbers (numbers n whose proper infinitary divisors sum to n) has density zero.
Maximal arcs and group divisible designs
Authors: Rahilly Alan
Published: April 2009

The existence of maximal arcs of a certain type in symmetric designs is shown to yield semiregular group divisible designs whose duals are also semiregular group divisible. Two infinite families of such group divisible designs are constructed. The group divisible designs in these families are, in general, not symmetric.
Inequalities between the integral means of a function
Authors: Hajela D.
Published: April 2009

For a measurable function f on a probability space a basic inequality is ‖f‖p ≤ ‖f‖q where 1 ≤ p < q < ∞ and ‖f‖p denotes the Lp norm of f. The above inequality becomes an equality provided |f| is a constant almost everywhere. We obtain an improvement of the above inequality in all cases that |f| is not a constant almost everywhere.
Hereditary and strict domains for radical classes of associative rings
Authors: McConnell N.R.
Published: April 2009

We generalise some existing results on strict radical classes, and introduce some new notions of hereditariness of radical classes. This is achieved by considering the classes of rings for which a radical class is hereditary and/or strict (in the general sense).
On Nunokawa's conjecture for multivalent functions
Authors: Owa Shigeyoshi
Published: April 2009

The object of this paper is to prove a conjecture given recently by Nunokawa that if f(z) ∈ Α(p) satisfies Re{1 + zf″(z)/f′(z)} < p + 1/2 in the unit disk U, then f(z) is p-valently starlike in U.
The other law of the iterated logarithm for martingales
Authors: Huggins R. M.
Published: April 2009

A Skorokhod embedding approach is used to give the other law of the iterated logarithm for square integrable martingales.
Multiple discrete semigroups of operations
Authors: Frishling Volf
Published: April 2009

For each t ∈ {0,1,2,…}, let Tt be a set of operators in a Banach space. Tt is called a multiple semigroup of operators with respect to some operation ⊗ between sets of operators, if Tt satisfies the semigroup property Tt+s = Tt⊗Ts. Two operations, (∘) and (·), between sets of operators are defined and properties of Tt are studied. Applications to the theory of Controlled Markov Processes are considered.
Internal completeness and injectivity of Boolean algebras in the topos of M-sets
Authors: Ebrahimi M. Mehdi
Published: April 2009

In this paper we study internal completeness, injectivity and some related notions in the category MBoo of Boolean algebras in the topos MEns of M-sets, for a monoid M.
Entire functions that share finite values with their derivatives
Authors: Lian-Zhong Yang
Published: April 2009

It is shown that if a nonconstant entire function f(z) and its derivative f(k)(z), share two finite values (counting multiplicities), then f(z) = f(k)(z), where k is a positive integer.
Formal complexity of inverse semigroup rings
Authors: Shehadah Adel A.
Published: April 2009

A ring (R, *) with involution * is called formally complex if implies that all Ai are 0. Let (R, *) be a formally complex ring and let S be an inverse semigroup. Let (R[S], *) be the semigroup ring with involution * defined by . We show that (R[S], *) is a formally complex ring. Let (S, *) be a semigroup with proper involution *(aa* = ab* = bb* ⇒ a = b) and let (R, *′) be a formally complex ring. We give a sufficient condition for (R[S], *′) to be a formally complex ring and this condition is weaker than * being the inverse involution on S. We illustrate this by an example.
On periodic solutions to autonomous retarded functional differential equations
Authors: Hou Zhanyuan
Published: April 2009

Under the assumption that Ca = C([−r, 0], Sn−1(a)) is positively invariant for a > 0, two necessary and sufficient conditions are obtained for an autonomous retarded functional differential equation to have a non-trivial periodic solution in Ca. Moreover, a feasible sufficient condition is given, which is better for n = 2 than that given by Dos Reis and Baroni.
On Dankwerts' transformation for two variable coupled systems
Authors: Hill James M. , McNabb Alex
Published: April 2009

The problem of obtaining explicit solutions to coupled linear reaction-diffusion partial differential equations is generally recognised as technically very difficult. Frequently it is possible to deduce seemingly simple expressions for Laplace or Fourier transforms of the solution but such transforms tend not to be amenable to simple inversion and usually involve, for example, square roots within a square root. Fortunately however, a general uncoupling procedure has previously been established which provides explicit integral expressions in terms of classical heat functions. Such expressions are especially useful for problems with zero boundary data but non-zero initial data. The purpose of this paper is to provide the formal details necessary to deduce corresponding uncoupling transformations for two dependent variables, which preserve zero initial data and constant boundary data. For the case of one dependent variable such a transformation is known as Dankwerts' transformation. For coupled systems the existence of a Dankwerts' transformation means that together with the existing uncoupling transformation, solutions of boundary value problems involving constant boundary data, can be decomposed, just as for the single heat equation, into a contribution from the initial condition and zero boundary data and a contribution from non-zero boundary data and zero initial condition. The problem considered is highly non-trivial and the final expressions obtained are correspondingly complicated. Nevertheless the end results are explicit and together with standard integration routines constitute a powerful solution procedure.
Continuity characterisations of differentiability of locally Lipschitz functions
Authors: Giles J.R. , Sciffer Scott
Published: April 2009

Recently David Preiss contributed a remarkable theorem about the differentiability of locally Lipschitz functions on Banach spaces which have an equivalent norm differentiable away from the origin. Using his result in conjunction with Frank Clarke's non-smooth analysis for locally Lipschitz functions, continuity characterisations of differentiability can be obtained which generalise those for convex functions on Banach spaces. This result gives added information about differentiability properties of distance functions.
On constrained stochastic optimal parameter selection problems
Authors: Goh C.J. , Teo K.L.
Published: April 2009

This paper considers a special class of stochastic optimal parameter selection problem subject to probability constraints on the state. The system dynamics are governed by a linear Ito stochastic differential equation with controllable parameters appearing nonlinearly in the dynamics. The problem seeks to optimise a cost functional which is quadratic in the state with weighting matrices being time invariant but depending nonlinearly on the parameters. Although the inclusion of the probability state constraints renders the problem insolvable by the conventional LQG theory, we show that the problem can in fact be transformed into an equivalent deterministic optimal parameter selection problem solvable by an existing software MISER. Numerical examples are presented to demonstrate the feasibility and efficiency of the proposed approach.
On the mean value of the enumeration function for multiplicative partitions
Authors: Hui-Zong Cao , Tung-Hsin Ku
Published: April 2009

Let g(n) denote the number of multiplicative partitions of the natural number n. We prove that
Free abelian topological groups on countable CW-complexes
Authors: Katz Eli , Morris Sidney A.
Published: April 2009

Let n be a positive integer, Bn the closed unit ball in Euclidean n-space, and X any countable CW-complex of dimension at most n. It is shown that the free Abelian topological group on Bn, F(Bn), has F(X) as a closed subgroup. It is also shown that for every differentiable manifold Y of dimension at most n, F(Y) is a closed subgroup of F(Bn).
An application of differential subordinations and some criteria for univalency
Authors: Owa Shigeyoshi , Obradović Milutin
Published: April 2009

By using the method of differential subordinations, we derive, among other results, some criteria for univalency in the unit disc.
On the drop and weak drop properties for a Banach space
Authors: Giles J.R. , Sims Brailey , Yorke A.C.
Published: April 2009

Rolewicz' drop property is a modification of a concept underlying Daneš' drop theorem. We characterise the drop property by the upper semicontinuity and compact valued property of the duality mapping for the dual. The characterisation suggests that we define a weak drop property which we show characterises the reflexivity of the space.
On topological sequence entropy of piecewise monotonic mappings
Authors: Cánovas Jose S.
Published: April 2009

In this paper a full classification of piecewise monotonic maps from the point of view of the topological sequence entropy is established.
Direct sums of indecomposable injective modules
Authors: Lee Sang Cheol , Lee Dong Soo
Published: April 2009

This paper proves that every direct summand N of a direct sum of indecomposable injective submodules of a module is the sum of a direct sum of indecomposable injective submodules and a sum of indecomposable injective submodules of Z2(N).
Proving a group trivial made easy: A case study in coset enumeration
Authors: Havas George , Ramsay Colin
Published: April 2009

Coset enumeration, based on the methods described by Todd and Coxeter, is one of the basic tools for investigating finitely presented groups. The process is not well understood, and various pathological presentations of, for example, the trivial group have been suggested as challenge problems. Here we consider one such family of presentations proposed by B.H. Neumann. We show that the problems are much easier than they first appear, albeit at the expense of considerable preliminary ‘experimentation’. This demonstrates how far the range of applicability of coset enumeration has improved.
Decompositions of modules into projective modules and CS-modules
Authors: Plubtieng Somyot
Published: April 2009

Let M be a right R-module. It is shown that M is a locally Noetherian module if every finitely generated module in σ[M] is a direct sum of a projective module and a CS-module. Moreover, if every module in σ[M] is a direct sum of a projective module and a CS-module, then every module in σ[M] is a direct sum of modules which are either indecomposable projective or uniform Σ-quasi-injective. In particular, if every module in σ[M] is a direct sum of a projective module and a quasi-continuous module, then every module in σ[M] is a direct sum of a projective module and a quasi-injective module.
Space forms from the viewpoint of their geodesic spheres
Authors: Adachi Toshiaki , Maeda Sadahiro
Published: April 2009

In this paper, we focus our attention on the extrinsic shape of geodesics on geodesic spheres in a given Riemannian manifold M. We characterise real and complex space forms in the class of smooth Riemannian manifolds from this point of view.
Best constants for tensor products of Bernstein, Szász and Baskakov operators
Authors: de la Cal Jesús , Valle Ana M.
Published: April 2009

We consider tensor product operators and discuss their best constants in preservation inequalities concerning the usual moduli of continuity. In a previous paper, we obtained lower and upper bounds on such constants, under fairly general assumptions on the operators. Here, we concentrate on the l∞-modulus of continuity and three celebrated families of operators. For the tensor product of k identical copies of the Bernstein operator Bn, we show that the best uniform constant coincides with the dimension k when k ≥ 3, while, in case k = 2, it lies in the interval [2, 5/2] but depends upon n. Similar results also hold when Bn is replaced by a univariate Szász or Baskakov operator. The three proofs follow the same pattern, a crucial ingredient being some special properties of the probability distributions involved in the mentioned operators, namely: the binomial, Poisson, and negative binomial distributions.
Maximal ideals and the structure of contractible and amenable Banach algebras
Authors: Zhang Yong
Published: April 2009

Properties of minimal idempotents in contractible and reflexive amenable Banach algebras are exploited to prove that such a kind of Banach algebra is finite demensional if each maximal ideal is contained in a maximal left or a maximal right ideal that is complemented as a Banach subspace. This result covers several known results on this subject.
The height of the Leech lattice
Authors: Chua Kok Seng
Published: April 2009

We derive explicit formulae for the height of the Leech lattice and give evidence supporting the conjecture that the Leech lattice has minimum height and minimum values of the Epstein zeta function among all 24 dimensional lattices of determinant one.
Equivariance and imprimivity for discrete Hopf C*-coactions
Authors: Kaliszewski S. , Quigg John
Published: April 2009

Let U, V, and W be multiplicative unitaries coming from discrete Kac systems such that W is an amenable normal submultiplicative unitary of V with quotient U. We define notions for right-Hilbert bimodules of coactions of SV and ŜV, their restrictions to SW and ŜU, their dual coactions, and their full and reduced crossed products. If N (A) denotes the imprimitivity bimodule associated to a coaction δ of SV on a C*-algebra A by Ng's imprimitivity theorem, we prove that for a suitably nondegenerate injective right-Hilbert bimodule coaction of SV on AXB, the balanced tensor products and are isomorphic right-Hilbert A×ŜV×rSU − B × ŜW bimodules. This can be interpreted as a natural equivalence between certain crossed-product functors.
Finding common fixed points of nonexpansive mappings by iteration
Authors: Rhoades B. E.
Published: April 2009

In this paper it is shown that a particular iteration scheme converges weakly to a common fixed point of a finite set of nonexpansive mappings. This result is an improvement of two related theorems in the literature.
Covariance factorisation and abstract representation of generalised random fields
Authors: Anh V. V. , Ruiz-Medina M. D. , Angulo J. M.
Published: April 2009

This paper introduces a new concept of duality of generalised random fields using the geometric properties of Sobolev spaces of integer order. Under this duality condition, the covariance operators of a generalised random field and its dual can be factorised. The paper also defines a concept of generalised white noise relative to the geometries of the Sobolev spaces, and via the covariance factorisation, obtains a representation of the generalised random field as a stochastic equation driven by a generalised white noise. This representation is unique except for isometric isomorphisms on the parameter space.
A dual characterisation of the Radon-Nikodym property
Authors: Bachir M. , Daniilidis A.
Published: April 2009

We prove that a Banach space X has the Radon-Nikodym property if, and only if, every weak*-lower semicontinuous convex continuous function f of X* is Gâteaux differentiable at some point of its domain with derivative in the predual space x.
A perturbed algorithm for strongly nonlinear variational-like inclusions
Authors: Lee C.-H. , Ansari Q. H. , Yao J.-C.
Published: April 2009

In this paper, we define the concept of η- subdifferential in a more general setting than the one used by Yang and Craven in 1991. By using η-subdifferentiability, we suggest a perturbed algorithm for finding the approximate solutions of strongly nonlinear variational-like inclusions and prove that these approximate solutions converge to the exact solution. Several special cases are also discussed.
Nilpotent-like fitting formations of finite soluble groups
Authors: Ballester-Bolinches A. , Pérez-Ramos M. D. , Martínez- Pastor A.
Published: April 2009

Dedicated to Professor K. Doerk on his 60th Birthday.

In this paper the subnormal subgroup closed saturated formations of finite soluble groups containing nilpotent groups are fully characterised by means of extensions of well-known properties enjoyed by the formation of all nilpotent groups.
Quadratic forms associated with planar endomorphisms
Authors: Prince G. E.
Published: April 2009

Any linear operator A on 2 is shown to have two real quadratic form on S1 associated with it. They represent the expansion and rotation of the map and the eigenvalues of A can be described in a geometrically intrinsic way in therms of the eigenvalues of these two quadratic forms via the formula
.

A number of theorems concerning these quadṙatic forms are presented.
An inequality for group presentations
Authors: Mann Avionam
Published: April 2009

To Bernhard Neumann on his 90th Birthday

We prove an inequality involving the number of relations and of relations and of generators of any group, and derive some consequences. The proof applies the theory of pro-p groups.
Cauchy-schwarz functionals
Authors: Cho Y. J. , Dragomir S. S. , Kim S. S. , Pearce C. E. M.
Published: April 2009

We treat a class of functionals which satisfy the Cauchy–Schwarz inequality. This appears to be a natural unifying concept and subsumes inter alia isotonic linear functional and sublinear positive isotonic functionals. Striking superadditivity and monotonicity properties are derived.
Galois module structure of holomorphic differentials
Authors: Rzedowski-Calderón Martha , Villa-Salvador Gabriel , Madan Manohar L.
Published: April 2009

For a finite cyclic P–extension L/K of a rational function field K = κ(x) over an algebraically closed field κ of characteristic P > 0 such that every ramified prime divisor is fully ramified, we find a basis of the κ[G]-module structure of ωL(0) in terms of indecomposable modules.
Regular order-preserving transformation semigroups
Authors: Kemprasit Yupaporn , Changphas Thawhat
Published: April 2009

The semigroupOT(X) of all order-preserving total transformations of a finite chainXis known to be regular. We extend this result to subchains ofZ; and we characterise whenOT(X) is regular for an intervalXinR. We also consider the corresponding idea for partial transformations of arbitrary chains and posets.
A counting formula about the symplectic similitude group
Authors: Lee Kwankyu
Published: April 2009

We derive an explicit formula for the number of elements in the symplectic similitude group GSp(2n, q) with given trace and determinant.
Class number of (v, n, M)-extensions
Authors: Alkam Osama , Bilhan Mehpare
Published: April 2009

An analogue of cyclotomic number fields for function fields over the finite field q, was investigated by L. Carlitz in 1935 and has been studied recently by D. Hayes, M. Rosen, S. Galovich and others. For each nonzero polynomial M in q [T], we denote by k (ΛM) the cyclotomic function field associated with M, where k = q(T). Replacing T by 1/T in k and considering the cyclotomic function field Fv that corresponds to (1/T)v+1 gets us an extension of k, denoted by Lv, which is the fixed field of Fv modulo . We define a (v, n, M)-extension to be the composite N = knk (Λm) Lv where kn is the constant field of degree n over k. In this paper we give analytic class number formulas for (v, n, M)-extensions when M has a nonzero constant term.
Permutation polynomials and group permutation polynomials
Authors: Park Young Ho , Lee June Bok
Published: April 2009

Permutation polynomials of the form xτf (x3) over a finite field give rise to group permutation polynomials. We give a group theoretic criterion and some other criteria in terms of symmetric functions and power functions.
On diagonal acts of monoids
Authors: Robertson E. F. , Ruškuc N. , Thomson M. R.
Published: April 2009

It is proved that the monoid RN of all partial recursive functions of one variable is finitely generated, and that RN × RNis a cyclic (left and right) RN-act (under the natural diagonal actions s (a, b) = (sa, sb), (a, b) s = (as, bs)). We also construct a finitely presented monoid S such that S × S is a cyclic left and right S-act, and study further interesting properties of diagonal acts and their relationship with power monoids.
Weighted composition operators on the Bloch space
Authors: Ohno Shûichi , Zhao Ruhan
Published: April 2009

We characterise bounded and compact weighted composition operators on the Bloch space and the little Bloch space. The results generalise the known corresponding results on composition operators and pointwise multipliers on the Bloch space and the little Bloch space.
Analysis of the affine transformations of the time-frequency plane
Authors: De Mari Filippo , Nowak Krzysztof
Published: April 2009

We consider two aspects of the action of the extended metaplectic representation of the groupGof affine, measure and orientation preserving maps of the time-frequency plane onL2functions on the line. On the one hand, we list, up to equivalence, all possible reproducing formulas that arise by restricting the representation to connected Lie subgroups ofG.On the other hand, we describe, in terms of Weyl calculus, the commutative von Neumann algebras generated by restriction to one-parameter subgroups.
Parabolic equations with discontinuous nonlinearities
Authors: Barletta Giuseppina
Published: April 2009

In this paper we deal with the homogeneous Cauchy-Dirichlet problem for a class of parabolic equations with either Carathéodory or discontinuous nonlinear terms. We then present an application and explicitly point out an existence result for a differential inclusion, which can be applied to the classical Stefan problem.
Helgason spheres of compact symmetric spaces and immersions of finite type
Authors: Chen Bang-Yen
Published: April 2009

A unit speed curve γ = γ(s) in a Riemannian manifold N is called a circle if there exists a unit vector field Y(s) along γ and a positive constant k such that ∇sγ′(s) = kY(s), ∇sY(s) = −kγ′(s). A maximal totally geodesic sphere with maximal sectional curvature in a compact irreducible symmetric space M is called a Helgason sphere. A circle which lies in a Helgason sphere of a compact symmetric space is called a Helgason circle. In this article we establish some fundamental relationships between Helgason circles, Helgason spheres of irreducible symmetric spaces of compact type and the theory of immersions of finite type.
The dyadic trace and odd weight computations for Siegel modular cusp forms
Authors: Poor Cris , Yuen David S.
Published: April 2009

We define the concept of a special positive matrix. We use the dyadic trace to prove the result that dim for odd k ≤ 13 and that dim ≤ 4.
On some sum–to–product identities
Authors: Cooper Shaun , Hirschhorn Michael
Published: April 2009

To George Szekeres on his ninetieth birthday

We give new proofs of some sum–to–product identities due to Blecksmith, Brillhart and Gerst, as well as some other such identities found recently by us.
Dynamics of slowly growing entire functions
Authors: Baker I. N.
Published: April 2009

Dedicated to George Szekeres on his 90th birthday

For a transcendental entire function f let M(r) denote the maximum modulus of f(z) for |z| = r. Then A(r) = log M(r)/logr tends to infinity with r. Many properties of transcendental entire functions with sufficiently small A(r) resemble those of polynomials. However the dynamical properties of iterates of such functions may be very different. For instance in the stable set F(f) where the iterates of f form a normal family the components are preperiodic under f in the case of a polynomial; but there are transcendental functions with arbitrarily small A(r) such that F(f) has nonpreperiodic components, so called wandering components, which are bounded rings in which the iterates tend to infinity. One might ask if all small functions are like this.

A striking recent result of Bergweiler and Eremenko shows that there are arbitrarily small transcendental entire functions with empty stable set—a thing impossible for polynomials. By extending the technique of Bergweiler and Eremenko, an arbitrarily small transcendental entire function is constructed such that F is nonempty, every component G of F is bounded, simply-connected and the iterates tend to zero in G. Zero belongs to an invariant component of F, so there are no wandering components. The Julia set which is the complement of F is connected and contains a dense subset of “buried’ points which belong to the boundary of no component of F. This bevaviour is impossible for a polynomial.
More cranks andt-cores
Authors: Garvan F. G.
Published: April 2009

Dedicated to George Szekeres on the occasion of his 90th Birthday

In 1990, new statistics on partitions (calledcransk) were found which combinatorially prove Ramanujan's congruences for the partition function modulo 5, 7, 11 and 25. The methods are extended to find cranks for Ramanujan's partition congruence modulo 49. A more explicit form of the crank is given for the modulo 25 congruence.
Smooth, very smooth and strongly smooth points in Musielak-Orlicz sequence spaces
Authors: Bian Shurong , Hudzik Henryk , Wang Tingfu
Published: April 2009

Criteria for smooth points, very smooth points and strongly smooth points in Musielak-Orlicz sequence spaces equipped with the Luxemburg norm are given.
Diffusion approximation for a Knudsen gas in a thin domain with reflexive chaotic law
Authors: Dogbé Christian
Published: April 2009

This paper treats a rarefied Knudsen gas flow between two infinite plates, with boundary reflexion ruled by a reflexive chaotic law called “Arnold's cat map”. It is shown that the limiting behaviour, when the distance between the plates goes to 0, is described by an (anisotropic) diffusion equation in the norm topology.
Poisson manifolds in generalised Hamiltonian biomechanics
Authors: Ivancevic V. , Pearce C. E. M.
Published: April 2009

In this paper the generalised Hamiltonian approach to the modelling of dynamical systems is developed no via the standard formalism of symplectic geometry but rather via Poisson manifolds and evolution equations. This alternative approach has the merit of being available in a wider context than the former. Application is made to three biomechanical models, one in which the symplectic–geometry approach also applies (the motion of a body segment) and two in which it does not (Schwan's model of blood and lymph circulation and Davydov's molecular model of muscle contraction).
On strict inclusions of weighted dirichlet spaces of monogenic functions
Authors: Gürlebeck K. , Malonek H. R.
Published: April 2009

We consider a scale of weighted spaces a quaternion-valued functions of three real variables. This scale generalises the idea of Qp-spaces in complex function theory. The goal of this paper is to prove that the inclusions of spaces from the scale are strict inclusion. As a tool we prove some properties of special monogenic polynomials which have an importance in their own right independently of their use in the scale of Qp-spaces.
Self-splitting Abelian groups
Authors: Schultz P.
Published: April 2009

G is reduced torsion-free A belian group such that for every direct sum ⊕G of copies of G, Ext(⊕G, ⊕G) = 0 if and only if G is a free module over a rank 1 ring. For every direct product ΠG of copies of G, Ext(ΠG,ΠG) = 0 if and only if G is cotorsion.

This paper began as a Research Report of the Department of Mathematics of the University of Western Australia in 1988, and circulated among members of the Abelian group community. However, it was never submitted for publication. The results have been cited, widely, and since copies of the original research report are no longer available, the paper is presented here in its original form in Sections 1 to 5. In Section 6, I survey the progress that has been made in the topic since 1988.
Radical extensions and crossed homomorphisms
Authors: Barrera-Mora Fernando , Lam-Estrada Pablo
Published: April 2009

If Ω/F is a Galois extension with Galois G and μ(Ω) denotes the group of roots of unity in Ω, we use the group Z1 (G,μ(Ω)) of crossed homomorphisms to study radical extensions inside Ω. Furthermore, we characterise cubic radical extension, and we provide an example to show that this result can not extended for higher degree extensions.
A theorem on power series with applications to classical groups over finite fields
Authors: Spencer Andrew J.
Published: April 2009

For some of the classical groups over finite fields it is possible to express the proportion of eigenvalue-free matrices in terms of generating functions. We prove a theorem on the monotonicity of the coefficients of powers of power series and apply this to the generating functions of the general linear, symplectic and orthogonal groups. This proves a conjecture on the monotonicity of the proportions of eigenvalue-free elements in these groups.
Unique continuation for non-negative solutions of quasilinear elliptic equations
Authors: Zamboni Pietro
Published: April 2009

Dedicated to Filippo Chiarenza

The aim of this note is to prove the unique continuation property for non-negative solutions of the quasilinear elliptic equation

We allow the coefficients to belong to a generalized Kato class.
Pseudoregular radical classes
Authors: McConnell N. R. , Stokes T.
Published: April 2009

We consider radical classes specified by an associating polynomial in two variables which have a similar form to the polynomial defining the class of quasiregular rings. In particular, the relationships of these classes to the classes of semiprime, nil and quasiregular rings are explored.
Integrable extended Hubbard models with boundary Kondo impurities
Authors: Bracken Anthony J. , Ge Xiang-Yu , Gould Mark D. , Zhou Huan-Qiang
Published: April 2009

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z2-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.
On recurrence relations for Bernoulli and Euler numbers
Authors: Chang Ching-Hua , Ha Chung-Wei
Published: April 2009

We obtain a class of recurrence relations for the Bernoulli numbers that includes a recurrence formula proved recently by M. Kaneko. Analogous formulas are also derived for the Euler and Genocchi numbers.
A note on the interpolation of the Diffie-Hellman mapping
Authors: Winterhof Arne
Published: April 2009

We obtain lower bounds on the degrees of polynomials representing the Diffie-Hellman mapping f (γx, γy) = γxy, where γ is a nonzero element of Fq of order d, x runs through a subset of [0,d – 1], and y runs through a set of consecutive integers.
On the injectivity of the Braid group in the Hecke algebra
Authors: Lehrer Gus I. , Xi Nanhua
Published: April 2009

We show that the well known homomorphism from any Artin braid group to the Hecke algebra of the same type is injective for the universal coxeter system and that the Burau representation is faithful for all finite coxeter systems of rank two.
Short Amicable sets and Kharaghani type orthogonal designs
Authors: Koukouvinos Christos , Seberry Jennifer
Published: April 2009

Dedicated to Professor George Szekeres

Short amicable sets were introduced recently and have many applications. The construction of short amicable sets has lead to the construction of many orthogonal designs, weighing matrices and Hadamard matrices. In this paper we give some constructions for short amicable sets as well as some multiplication theorems. We also present a table of the short amicable sets known to exist and we construct some infinite families of short amicable sets and orthogonal designs.
Arc components in locally compact groups are Borel sets
Authors: Hofmann Karl Heinrich
Published: April 2009

Are the arc components in a locally compact group Borel subsets? An affirmative answer is provide for locally compact groups satisfying the First Axiom of Count-ability. For general locally compact groups the question is reduced to compact connected Abelian groups. In certain models of set theory the answer is negative.
Norm of a linear combination of two operators on a Hilbert space
Authors: Nakazi Takahiko , Yamamoto Takanori
Published: April 2009

Let α, β γ, δ be complex numbers such that γδ ≠ 0. If A and B are bounded linear operators on the Hilbert space H such that γA + δB is right invertible then we study the operator norm of (αA + βB)(γA + δB)−1 using the angle φ between two subspaces ran A and ran B or the angle ψ = ψ(A, B) between two operators A and B where
Rigidity of Hilbert metrics
Authors: Colbois Bruno , Verovic Patrick
Published: April 2009

We study the groups of isometries for Hilbert metrics on bounded open convex domains in ℝn and show that if  is such a set with a strictly convex boundary, the Hilbert geometry is asymptotically Riemannian at infinity. As a consequence of this result, we prove there are no Hausdorff quotients of  by isometry subgroups with finite volume except when ∂ is an ellipsoid.
Semi-orthogonal frame wavelets and frame multi-resolution analyses
Authors: Kim Hong Oh , Kim Rae Young , Lim Jae Kun
Published: April 2009

We first characterise semi-orthogonal frame wavelets by generalising the characterisation of orthonormal wavelets. We then characterise those semi-orthogonal frame wavelets that are associated with frame multi-resolution analyses. This is a generalisation of a result of Wang and another result of Papadakis. Finally, we illustrate our results by an example.
CW decompositions of equivariant CW complexes
Authors: Cencelj M. , Kosta N. Mramor
Published: April 2009

we discuss conditions which ensure that a G-CW complex is G-homotopy equivalent to a CW complex with cellular action with respect to some CW decomposition of the compact Lie group G. For G = SU (2), we prove that for every G-CW complex X, there exists a CW complex Y which is G-homotopy equivalent to X, such that the action G × Y → Y is a cellular map.
Total torsion of closed lines of curvature
Authors: Qin Yong-An , Li Shi-Jie
Published: April 2009

In this article we investigate the total torsion of closed lines of curvature on a surface in 3 and obtain the following results.

(1) The total torsion of a closed line of curvature on a surface is kπ where k is an integer. Conversely, if the total torsion of a closed curve is kπ for an integer k, then the curve can appear as a line of curvature on a surface. In particular, if the total torsion of a closed curve is 2kπ, then it can appear as a line of curvature on a closed, oriented surface of genus 1.

(2) The total torsion of a closed line of curvature on an ovaloid is zero.
Another proof of the Browder–Göhde–Kirk theorem via ordering argument
Authors: Jachymski Jacek
Published: April 2009

Using the Zermelo Principle, we establish a common fixed point theorem for two progressive mappings on a partially ordered set. This result yields the Browder–Göhde–Kirk fixed point theorem for nonexpansive mappings.
Interpolating sequence on certain Banach spaces of analytic functions
Authors: Yousefi B.
Published: April 2009

Let G be a finitely connected domain and let X be a reflexive Banach space of functions analytic on G which admits the multiplication Mz as a polynomially bounded operator. We give some conditions that a sequence in G has an interpolating subsequence for X.
Hausdorff dimension of the limit set on a visibility manifold
Authors: Kim Hyun Jung
Published: April 2009

In this paper, for a given Fuchsian group Γ, we prove an upper estimate for the Hausdorff dimension of the radial limit set in the visibility manifold. Further, if Γ is a convex cocompact group, we find the exact Hausdroff dimension of the limit set.
On a class number formula for real quadratic number fields
Authors: Bradley David M. , Özlük Ali E. , Snyder C.
Published: April 2009

For an even Dirichlet character ψ, we obtain a formula for L (1, ψ) in terms of a sum of Dirichlet L-Series evaluated at s = 2 and s = 3 and a rapidly convergent numerical series involving the central binomial coefficients. We then derive a class number formula for real quadratic number fields by taking L (s, ψ) to be the quadratic L-series associated with these fields.
On ℱ-residuals of finite groups
Authors: Guo Wenbin , Shum K. P. , Skiba A. N.
Published: April 2009

We prove that there exists a soluble, saturated and s-closed formation ℱ of groups such that the class (Gℱ | G is a group, Gℱ is the ℱ-residual of G) is not closed under subdirect products. This result a negative answer to an open problems recently proposed by L.A. Shemetkov in 1998.
Transversals in permutation groups and factorisations of complete graphs
Authors: Kaplan Gil , Lev Arieh
Published: April 2009

Let G be a transitive permutation group acting on a finite set of order n. We discuss certain types of transversals for a point stabiliser A in G: free transversals and global transversals. We give sufficient conditions for the existence of such transversals, and show the connection between these transversals and combinatorial problems of decomposing the complete directed graph into edge disjoint cycles. In particular, we classify all the inner-transitive Oberwolfach factorisations of the complete directed graph. We mention also a connection to Frobenius theorem.
Invexity of supremum and infimum functions
Authors: Ha Nguyen Xuan , Van Luu Do
Published: April 2009

Under suitable assumptions we establish the formulas for calculating generalised gradients and generalised directional derivatives in the Clarke sense of the supremum and the infimum of an infinite family of Lipschitz functions. From these results we derive the results ensuring such a supremum or infimum are an invex function when all functions of the invex. Applying these results to a class of mathematical programs, we obtain necessary and sufficient conditions for optimality.
Usco selections of densely defined set-valued mappings
Authors: Moors Warren B. , Somasundaram Sivajah
Published: April 2009

A set-valued mapping Φ : X → 2Y acting between topological spaces X and Y is said to be “lower demicontinuous” if the interior of the closure of the set Φ−1(V): = {x ∈ X : Φ(x) ∩ V ≠ ∅} is dense in the closure of Φ−1(V) for each open set V in Y. Čoban, Kenderov and Revalski (1994) showed that for every densely defined lower demicontinuous mapping Φ acting from a Baire space X into subsets of a monotonely Čech-complete space Y, there exist a dense and Gδ subset X1 ⊆ X and an usco mapping G: X1 → 2Y such that G (x) ⊆ Φ*(x), for every x ∈ X1, where the mapping Φ*: X → 2Y is the extension of Φ defined by,
W is a neighbourhood of x}.

In this paper we present a proof of the above result with the notion of monotone Čcech-completeness replaced by the weaker notion of partition completeness. In addition, we observe that if the range space also lies is Stegall's class then we may assume that the mapping G is single-valued on X1.
Free surface waves over a depression
Authors: Choi J. W.
Published: April 2009

Steady waves at the free surface of an incompressible fluid passing over a depression are considered. By studying a KdV equation with negative forcing term, new types of solutions are discovered numerically and a new cut-off value of the Froude number, above which unsymmetric solitary-wave-like wave solutions exist, is also found.
Maximal independent system of units in function fields
Authors: Jung Hwanyup , Ahn Jaehyun
Published: April 2009

In this paper, we construct a new maximal independent system of units in cyclotomic function fields and their subfields. We also calculate its index in the full units group and show that it is smaller than the index of Feng-Yin's system.
Permutational labelling of constant weight Gray codes
Authors: Levi Inessa , Seif Steve
Published: April 2009

We prove that for positive integers n and r satisfying 1 < r < n, with the single exception of n = 4 and r = 2, there exists a constant weight Gray code of r-sets of Xn = {1, 2, …, n} that admits an orthogonal labelling by distinct partitions, with each subsequent partition obtained from the previous one by an application of a permutation of the underlying set. Specifically, an r-set A and a partition π of Xn are said to be orthogonal if every class of π meets A in exactly one element. We prove that for all n and r as stated, and taken modulo , there exists a list of the distinct r-sets of Xn with |Ai ∩ Ai+1| = r − 1 and a list of distinct partitions such that πi is orthogonal to both Ai and Ai+1, and πi+1 = πiλi for a suitable permutation λi of Xn.
Two questions on semigroup laws
Authors: Macedońska O.
Published: April 2009

B.H. Neumann recently proved some implications for semigroup laws in groups. This may help in the solution of a problem posed by G.M. Bergman in 1981.
A generalisation of Kramer's theorem and its applications
Authors: Wang Yanming , Wei Huaquan , Li Yangming
Published: April 2009

The main purpose of this paper is to generalise a supersolvability theorem of O. U. Kramer to a saturated formation containing the class of supersolvable groups. As applications, we generalise some results recently obtained by some scholars.
A remark on Littlewood–Paley g-function
Authors: Yan Lixin
Published: April 2009

We prove Lp -estimates for the Littlewood–Paley g-function associated with a complex elliptic operator L = − div A∇ with bounded measurable coefficients in ℝn.
A Beurling algebra is semisimple: an elementary proof
Authors: Bhatt S. J. , Dedania H. V.
Published: April 2009

The Beurling algebra L1(G,ω)on a locally compact Abelian group G with a measurable weight ω is shown to be semisimple. This gives an elementary proof of a result that is implicit in the work of M.C. White (1991), where the arguments are based on amenable (not necessarily Abelian) groups.
Descent on Picard groups using functions on curves
Authors: Siksek Samir
Published: April 2009

Let k be a perfect field, X a smooth curve over k, and denote by Xc the subset of closed points of X. We show that for any non-constant element f of the function field k (X) there exists a natural homomorphism

Where

We explain how this generalises the usual results on descents on Jacobians and Picard groups of curves.
k-gon partitions
Authors: Hirschhorn Michael D.
Published: April 2009

The object of this note is to present a brief derivation of the main result of Andrews, Paule and Riese (2001).