bluuebunny/crossref_metadata_2025 huggingface dataset:
Univalent functions with univalent Gelfond-Leontev derivatives
Authors: Juneja O.P. , Shah S.M.
Published: April 2009

Let be a nondecreasing sequence of positive numbers. We consider Gelfond-Leontev derivative Df(z), of a function , defined by for univalence and growth properties, and extend some results of Shah and Trimble. Set en = {d1d2 … dn), n≥l, e0 = 1, . Let r be the radius of convergence of p(z). We state parts of Theorem 1 and Corollaries. Let f and all Dkf, k = 1, 2,…, be analytic and univalent in the unit disk U. Then

(iii) if p is entire and of growth (ρ, T) then f must be entire and of growth not exceeding (ρ, 2d2T),

(iv) if D corresponds to the shift operator (dn ≡ l), then .

Another class of functions is defined by a condition of the form |an+1/an| ≤ bn+1/dn+1, where is a sequence of positive numbers satisfying and inequality, and it is shown that all functions in this class along with all their Gelfond–Leontev successive derivatives are regular and univalent in U. An extension of the definition of a linear invariant family is given and results analogous to (i) and (ii) are stated.
Graphs with Eulerian chains
Authors: Eggleton Roger B. , Skilton Donald K.
Published: April 2009

An eulerian chain in a graph is a continuous route which traces every edge exactly once. It may be finite or infinite, and may have 0,1 or 2 end vertices. For each kind of eulerian chain, there is a characterization of the graphs which admit such a tracing. This paper derives a uniform characterization of graphs with an eulerian chain, regardless of the kind of chain. Relationships between the edge complements of various kinds of finite subgraphs are also investigated, and hence a sharpened version of the eulerian chain characterization is derived.
Boundary value problems for systems of differential equations
Authors: Thompson H.B.
Published: April 2009

We give sufficient conditions for systems of the form y′ = f(x, y), x in [0, 1] and y″ = f(x, y, y′), x in [0, 1] to have solutions y with (x, y) in Ω ⊆ [0, 1] x Rn. We use degree theory and allow the shape of Ω to depend on x.
On the weakly strongly exposed property and some smoothness properties of Orlicz spaces
Authors: Cui Yunan , Hudzik Henry K. , Zhu Hongwei
Published: April 2009

The notion of a weakly strongly exposed Banach space is introduced and it is shown that this property is the dual property of very smoothness. Criteria for this property in Orlicz function spaces equipped with the Orlicz norm are presented. Criteria for strong smoothness and very smoothness of their subspaces of order continuous elements in the case of the Luxemburg norm are also given.
Characterisation of multipliers for the double Henstock integrals
Authors: Tuo-Yeong Lee , Tuan-Seng Chew , Peng-Yee Lee
Published: April 2009

In this paper, we prove thatfgis Henstock integrable on an interval in the Euclidean space for each Henstock integrable functionfif and only ifgis a function of essentially strongly bounded variation.
Characterisation of nilpotent-by-finite groups
Authors: Trabelsi Nadir
Published: April 2009

LetGbe a finitely generated soluble group. The main result of this note is to prove thatGis nilpotent-by-finite if, and only if, for every pairX,Yof infinite subsets ofG, there exist anxinX,yinYand two positive integersm=m(x,y),n=n(x,y) satisfying [x,nym] = 1. We prove also that ifGis infinite and ifmis a positive integer, thenGis nilpotent-by-(finite of exponent dividingm) if, and only if, for every pairX,Yof infinite subsets ofG, there exist anxinX,yinYand a positive integern=n(x,y) satisfying [x,nym] = 1.
A family of 2-dimensional Laguerre planes of generalised shear type
Authors: Polster B. , Steinke G. F.
Published: April 2009

We construct a family of 2-dimensional Laguerre planes that generalises ovoidal Laguerre planes and the Laguerre planes of shear type, as described by Löwen and Pfüller, by gluing together circle sets from up to eight different ovoidal Laguerre planes. Each plane in this family admits all maps (x, y) ↦ (x, ry) for r > 0 as central automorphisms at the circle y = 0.
On convex vector optimisation
Authors: Dutta Joydeep
Published: April 2009

In this article we present a simple method to deduce necessary conditions for weak minimisation of a convex vector program in a Banach space. Our main tool here will be the generalised Jabcobian of Ralph.
A maximal Gross-Stadje number in the Euclidean plane
Authors: Pillichshammer F.
Published: April 2009

Let X be a compact, connected Hausdorff space and f a real valued, symmetric, continuous function on X × X. Then the Gross-Stadje number r (X, f) is the unique real number with the property that for each positive integer n and for all (not necessarily distinct) x1,…,xn in X, there exists some x in X such that . This paper solves the following open question in distance geometry: What is the least upper bound g2(R2) of r (X, d2), where X ranges over all compact, connected subsets of the Euclidean plane with diameter one and where d2 denotes the squared, Euclidean distance. We show: .
Thurston distance on the Teichmüller space of hyperbolic 3-manifolds
Authors: Kim Inkang
Published: April 2009

In this paper we show that the Thurston distance together with the critical exponent on the Teichmüller space of a convex cocompact hyperbolic 3-manifold distinguishes the different points.
On an inequality of Kolmogorov and Stein
Authors: Bang Ha Huy , Le Hoang Mai
Published: April 2009

A.N. Kolmogorov showed that, if f, f′, …, f (n) are bounded continuous functions on ℝ, then when 0 < k < n. This result was extended by E.M. Stein to Lebesgue Lp-spaces and by H.H. Bang to Orlicz spaces. In this paper, the inequality is extended to more general function spaces.
On some difference problems
Authors: Jankowski Tadeusz
Published: April 2009

In this paper we discuss in some detail the difference equations arising in the discretization of some second-order differential equations. We also show how such difference problems can be solved exactly.
On the arc index of an adequate link
Authors: Park Chan-Young , Seo Myoungsoo
Published: April 2009

In 1996, Cromwell and Nutt conjectured that α(L) − c (L) = 2 for a link L if and only if L is alternating. In this paper we calculate that α(L) = c (L) for some non-alternating pretzel links L, define a new invariant ρ(L) of adequate links L and show that for each non-negative integer n, there is a prime adequate knot K such that α(K) − c (K) = −2n. We conjecture that α(L) − c (L) = 2ρ(L) for any adequate link L.
Subdifferentials of convex functions and sigma-cyclic monotonicity
Authors: Daniilidis Aris
Published: April 2009

The property of σcyclic monotonicity is proposed here to describe subdifferentials of lsc convex functions that are continuous in their domains. It is shown that all monotone operators in R and all densely defined cyclically monotome operators in Rn share this property. Examples of a densely defined maximal cyclically monotone operator in a Hilbert space and of a subdifferential of a convex lsc function in R2 which are not σ-cyclically monotone operators are given.
On the volume of lattice manifolds
Authors: Kołodziejczyk Krzysztof
Published: April 2009

The volume of a general lattice polyhedron P in ℝN can be determined in terms of numbers of lattice points from N − 1 different lattices in P Ehrhart gave a formula for the volume of “polyèdre entier” in even-dimensional spaces involving only N/2 lattices. The aim of this note is to comment on Ehrhart's formula and provide a similar volume formula applicable to lattice polyhedra that are N-dimensional manifolds in ℝN.
Arithmetic on certain families of elliptic curves
Authors: Dabrowski Andrzej , Wieczorek Małgorzata
Published: April 2009

Consider a family of elliptic curves (A, A0, d0 fixed integers). We prove that, under certain conditions on A0 and d0, the rational torsion subgroup of E(B) is either cyclic of order ≤ 3 or non-cyclic of order 4. Also, assuming standard conjectures, we establish estimates for the order of the Tate-Shafarevich groups as B varies.
Naturality and induced representations
Authors: Echterhoff Siegfried , Kaliszewski S. , Quigg John , Raeburn Iain
Published: April 2009

We show that induction of covariant representations for C*-dynamical systems is natural in the sense that it gives a natural transformation between certain crossed-product functors. This involves setting up suitable categories of C*-algebras and dynamical systems, and extending the usual constructions of crossed products to define the appropriate functors. From this point of view, Green's Imprimitivity Theorem identifies the functors for which induction is a natural equivalence. Various special cases of these results have previously been obtained on an ad hoc basis.
Two-block configuration formulae for BTD's with parameters (V,B,R, 3, Λ)
Authors: Francel M. A.
Published: April 2009

In this paper, we count two-block configurations in a general setting. In particular, no restriction is put on the pair repetition factor (that is, the parameter Λ) of the block designs being considered. Besides giving formulae for the counts of the two-block BTD (V, B, R, 3, Λ) configuration classes, a basis for the formulae is given and shown to have size four. Details of the special cases where Λ equals two and three are also presented, along with 2-block BIBD (v, b, r, 3, λ) configuration results.
Global smoothness preservation by multivariate singular integrals
Authors: Anastassiou George A. , Gal Sorin G.
Published: April 2009

By using various kinds of moduli of smoothness, it is established that the multivariate variants of the well-known singular integrals of Picard, Poisson-Cauchy, Gauss-Weierstrass and their Jackson-type generalisations satisfy the “global smoothness preservation” property. The results are extensions of those proved by the authors for the univariate case.
On the Riemann zeta-function I
Authors: Izumi Masako , Izumi Shin-ichi
Published: April 2009

We prove an approximation formula for the Riemann zeta function. We show that a classical theorem:

uniformly in the domain ½ ≤ σ < 1, is an immediate consequence of our approximation formula. Our method is real and free from complex analysis.
The regularity series of a convergence space II
Authors: Kent D.C. , Richardson G.D.
Published: April 2009

This study is a continuation of an earlier paper on the regularity series of a convergence space. The notions of aR-Hausdorff series and theT3-modification of a convergence space are introduced, and their relationship with the regularity series is studied. The concept of a symmetric space is shown to be useful in studyingT3-compactifications. Several examples are given; one being a Hausdorff convergence space with an arbitrarily large regularity series.
Ascent and descent of going-down rings for integral extensions
Authors: Dobbs David E.
Published: April 2009

The author and Ira J. Papick have termed an integral domainRa going-down ring ifR⊂Tsatisfies going-down for each domainTcontainingR. The present paper investigates conditions which, for an integral extensionA⊂Bof domains, imply thatA(respectivelyB) is going-down wheneverB(respectivelyA) is going-down. This explains the “descent” (respectively “ascent”) in the title. Two typical results (the first about descent, the second about ascent) are given next.
Separability axioms and metric-like functions
Authors: Anton Howard
Published: April 2009

We call a topological space completely regular if points and closed sets can be separated by continuous real-valued functions, and we call a topological space Tychonoff or T3α if it is T1 and completely regular. It is well known that the Tychonoff spaces are precisely the gauge spaces, that is the topological spaces whose topologies are induced by separating families of pseudometrics. V.G. Boltjanskiĭ has given analogous characterizations for T0, T1, T2, regular, and regular-T1 spaces in terms of families of “metric-like” functions. The purpose of this note is to fill in a case missing in Boltjanskiĭ's paper, the completely regular spaces, and to relate Boltjanskiĭ's work to results on quasi-uniformization by William J. Pervin and results about semi-gauge spaces by J.V. Michalowicz.
Nilpotent groups acting fixed point freely on solvable groups
Authors: Bailey Beverly J.
Published: April 2009

All groups considered are finite. We enlarge the class of groups for which the conjecture below is known to hold, to include all nilpotent groups A such that every proper subgroup of A is Zp ˜ Zp free for all primes p.
A property of finitely generated residually finite groups
Authors: Pickel P.F.
Published: April 2009

Let F(G) denote the set of isomorphism classes of finite quotients of the group G. We say that groups G and H have isomorphic finite quotients (IFQ) if F(G) = F(H). In this note, we show that a finitely generated residually finite group G cannot have the same finite quotients as a proper homomorphic image (G is IFQ hopfian). We then obtain some results on groups with the same finite quotients as a relatively free group.
Cogeneration of algebras in regular categories
Authors: Adámek Jiří
Published: April 2009

A quotient algebra of a given algebra is said to be cogenerated by a quotient object if it is contained in the quotient object and is the biggest with this property. Triples T over a regular category are characterized which have the property that every quotient object of a T-algebra cogenerates some quotient algebra: these are precisely the right exact triples, preserving colimits of quotient chains. This improves a result of Michael Barr (J. Pure Appl. Algebra 4 (1974), 1–8) that every right exact, finitary triple has the investigated property. This result is related to categorical automata, since a triple has the above property iff triple machines admit a minimal realization of every behavior.
Chaotic difference equations are dense
Authors: Kloeden Peter E.
Published: April 2009

A continuous function mapping a compact interval of the real line into itself is called chaotic if the difference equation defined in terms of it behaves chaotically in the sense of Li and Yorke. The set of all such chaotic functions is shown to toe a dense subset of the space of continuous mappings of that interval into itself with the max norm. This result indicates the structural instability of nonchaotic difference equations with respect to chaotic behaviour.
An adjoint-functor theorem over topoi
Authors: Day B.J.
Published: April 2009

The usual statements of the classical adjoint-functor theorems contain the hypothesis that the codomain category should admit arbitrary intersections of families of monomorphisms with a common codomain. The aim of this article is to formulate an adjoint-functor theorem which refers, in a similar manner, to arbitrary internal intersections of “families of monomorphisms” in the case where the categories under consideration are suitably defined relative to a fixed elementary base topos (in the usual sense of Lawvere and Tierney).
A nonoscillation theorem for a second order sublinear retarded differential equation
Authors: Kusano Takaŝi , Onose Hiroshi
Published: April 2009

Sufficient conditions are obtained for all solutions of a class of second order nonlinear functional differential equations to be nonoscillatory.
Indecomposable representations in characteristic two of the simple groups of order not divisible by eight
Authors: Donovan P.W. , Freislich M-R.
Published: April 2009

The indecomposable representations in characteristic two of the groups PSL(2, q) where q is congruent to 3 or 5 modulo 8 are classified. For q = 3 or 5 the classification is obtained by explicit construction of modules, using the Green correspondence to prove completeness. For larger q, the classification is obtained using equivalences between appropriate categories of modules.
Left and right zero divisors in group algebras
Authors: Handelman D. , Lawrence J.
Published: April 2009

We prove that most group algebras of free products have left zero divisors that are not right zero divisors.
Coproducts of De Morgan algebras
Authors: Cornish William H. , Fowler Peter R.
Published: April 2009

The dual of the category of De Morgan algebras is described in terms of compact totally ordered-disconnected ordered topological spaces which possess an involutorial homeomorphism that is also a dual order-isomorphism. This description is used to study the coproduct of an arbitrary collection of De Morgan algebras and also to represent the coproduct of two De Morgan algebras in terms of the continuous order-preserving functions from the Priestley space of one algebra to the other algebra, endowed with the discrete topology. In addition, it is proved that the coproduct of a family of Kleene algebras in the category of De Morgan algebras is the same as the coproduct in the subcategory of Kleene algebras if and only if at most one of the algebras is not boolean.
Pseudo-autonomous linear systems
Authors: Coppel W.A.
Published: April 2009

Pseudo-autonomous linear differential equations are defined. A linear differential equation with bounded coefficient matrix is pseudo-autonomous if and only if it is almost reducible. A linear differential equation with recurrent coefficient matrix is pseudo-autonomous if and only if it has pure point spectrum.
Remarks on superlinear boundary value problems
Authors: Fučík Svatopluk
Published: April 2009

Necessary and sufficient conditions for the weak solvability of the Dirichlet problem for nonlinear differential equations of the second order are proved. The differential operators considered are in the form of a sum of a linear noninvertible operator, with the null-space generated by a positive function, and a monotone nonlinear perturbation, the growth of which is more than linear.
On a conjecture of T. Lewis
Authors: Shanbhag D.N.
Published: April 2009

In this note, Conjecture Cl of Toby Lewis (1976), concerning a reciprocal pair of characteristic variables, is shown to be false.
Stratifications of equivariant varieties
Authors: Field M.J.
Published: April 2009

Let G be a compact Lie group and V and W be linear G spaces. A study is made of the canonical stratification of some algebraic varieties that arise naturally in the theory of C∞ equivariant maps from V to W. The main corollary of our results is the equivalence of Bierstone's concept of “equivariant general position” with our own of “G transversal”. The paper concludes with a description of Bierstone's higher order conditions for equivariant maps in the framework of equisingularity sequences.
High dimensional knot groups which are not two-knot groups
Authors: Hillman Jonathan A.
Published: April 2009

This paper presents three arguments, one involving orientability, and the others Milnor duality and, respectively, the injectivity of cup product into H2 for an abelian group and free finite group actions on homotopy 3-spheres to show that there are high dimensional knot groups which are not the groups of knotted 2-spheres in S4, thus answering a question of Fox (“Some problems in knot theory”, Topology of 3-manifolds and related topics”, 168–176 (Proceedings of the University of Georgia Institute, 1961. Prentice-Hall, Englewood Cliffs, New Jersey, 1962).
On the absolute Nörlund summability factors of Fourier series
Authors: Okuyama Yasuo
Published: April 2009

The object of this paper is to give a general theorem which implies Izumi's Theorem and Kanno's Theorem on the absolute Nörlund summability factors of Fourier series and deduce to several known and new results from the theorem.
The numerical ranges of unbounded linear operators
Authors: Bollobás Béla , Eldridge Stephan E.
Published: April 2009

Giles and Joseph (Bull. Austral. Math. Soc. 11 (1974), 31–36), proved that the numerical range of an unbounded operator on a Banach space has a certain density property. They showed, in particular, that the numerical range of an unbounded operator on certain Banach spaces is dense in the scalar field. We prove that the numerical range of an unbounded operator on a Banach space is always dense in the scalar field.
A note on the edge reconstruction conjecture
Authors: Schmeichel E.F.
Published: April 2009

Let G be a graph with vertex degree sequence d1 ≤ d2 ≤ … ≤ dp It is shown that if di + dp–i+1 ≥ p for some i, then G is uniquely reconstructable from its collection of maximal (edge deleted) subgraphs. This generalizes considerably a result of Lovász. As a corollary, it is shown that Chvátal's existence condition for hamiltonian cycles implies edge reconstructability as well.
On largest Hausdorff compactification for convergence spaces
Authors: Rao C.J.M.
Published: April 2009

In this note we obtain a characterization of the class of convergence spaces for which Richardson's compactification is the largest Hausdorff compactification and a characterization of the class of convergence spaces which possess largest Hausdorff compactifications.
A characterization of boolean spaces
Authors: Dickerson C.E. , Moore M.E.
Published: April 2009

A boolean space is a compact Hausdorff space which is zero-dimensional. In this paper, a boolean space X is characterized in terms of its ring of real-valued functions C(X). The result is sharpened for the case when X is an F-space (every finitely generated ideal of C(X) is principal).
Automorphic compactifications and the fixed point lattice of a totally-ordered set
Authors: Davis Gary
Published: April 2009

When a totally-ordered set Ω has no points fixed by all automorphisms ve equip Ω with the support topology which has fixed-sets of automorphisms as basic closed sets. There is a mapping from Ω into the set of prime dual ideals of the lattice Φ(Ω) of basic closed sets and this allows us to classify the points of Ω as excellent, isolated, static, or extraordinary. There is an action of the group of automorphisms of Ω on the lattice Φ(Ω) and this allows us to see that automorphisms of Ω preserve the prime dual ideal classification of points of Ω. When the empty set is a basic closed subset of Ω the dual spectrum of Φ(Ω) is a compact T0 space (Hausdorff when all points of Ω are excellent) containing Ω as a dense subspace and allowing an extension of each automorphism of Ω ťo a homeomorphism of the dual spectrum.
Fixed point theorems for condensing multivalued mappings on a locally convex topological space
Authors: Tarafdar E. , Výborný R.
Published: April 2009

A general definition for a measure of nonprecompactness for bounded subsets of a locally convex linear topological space is given. Fixed point theorems for condensing multivalued mappings have been proved. These fixed point theorems are further generalizations of Kakutani's fixed point theorems.
A note on divisible and codivisible dimension
Authors: Bland Paul E.
Published: April 2009

In this paper the right global divisible dimension and the right global codivisible dimension of a ring R are studied relative to a torsion theory of modR. The main result shows that if (A, B) is a central splitting torsion theory on modR. then the right global divisible dimension of R with respect to (B, A) is equal to the right global codivisible dimension of R with respect to (A, B).
A differentiation in locally convex spaces
Authors: Yamamuro Sadayuki
Published: April 2009

The theory of F-finite linear operators developed by Robert T. Moore is used to construct a differential calculus in locally convex spaces. This note contains the fundamental theory up to the implicit function theorem.
On the construction of soluble groups satisfying the minimal condition for normal subgroups
Authors: Silcock Howard L.
Published: April 2009

A general method is described for constructing examples of soluble groups whose normal subgroups form a well-ordered chain under the ordering of inclusion. This method is a variant of one introduced in a recent paper by Heineken and Wilson. Each of the resulting groups is obtained by an embedding procedure from a pair of iterated wreath products A1 wr A2 wr … wr An, B1 wr B2 wr … wr Bn, where the constituent groups Ai., Bi are each either cyclic of prime power order or quasicyclic. Here n may be chosen arbitrarily, and the choice of constituent groups is subject only to a condition on the sequences of prime numbers that may occur as orders of elements in the groups

respectively. The construction is applied to give certain examples which illustrate the limitations of results on particular classes of soluble groups satisfying the minimal condition for normal subgroups obtained in recent papers by Hartley, McDougall, and the present author.
The hulls of semiprime rings
Authors: Conrad Paul F.
Published: April 2009

Each semiprime ring admits a unique projectable, strongly projectable, laterally complete and orthocomplete hull. Almost all of the theory for X–hulls of lattice-ordered groups in Paul Conrad, “The hulls of representable l-groups and f-rings”, J. Austral. Math. Soc. 16 (1973), 385–415, has a counterpart for semiprime rings. The proofs of these results will appear elsewhere. They come in a large part directly from the corresponding theory for lattice-ordered groups. There is also a feedback from the rings to the groups.
Approximative compactness and continuity of metric projections: Corrigendum
Authors: Panda B.B. , Kapoor O.P.
Published: April 2009

There is a small error in the proof of Lemma 1 [1], namely, that there may not be a subsequence of the sequence {Φn} converging to Φ in the weak*-topology. Thus equation (5) should read: In view of continuity of Pk we have

The same error occurs in the proof of Theorem 1 and Lemma 2 also. Therefore, equation (7) should read

and this leads to lim . Similarly, equation (8) should read

which implies that Ψn (x) → ‖x‖. Then there is no need of taking a subsequence.

All the same the results are not affected by the above error.
Nonlinear fractional programming
Authors: Mond B. , Craven B.D.
Published: April 2009

If an optimal solution exists for a nonlinear fractional programming problem, then this solution is shown to be obtainable by solving two associated programming problems whose objective functions are no longer fractional. A certain restriction is assumed on the constraint sets of the latter problems. This result includes various known theorems as special cases.
Oscillations of an equation relevant to an industrial problem
Authors: Tomaras Alexander
Published: April 2009

The oscillatory behaviour of the solutions of a functional differential equation, of more general form than an equation arising from in industrial problem, is examined. The question of whether one can maintain the oscillatory properties of this equation by adding a forcing term is also answered. The results obtained extend already known results on the subject and complete the relevant literature.
On Berman's phenomenon in interpolation theory
Authors: Cook W. Lyle , Mills T.M.
Published: April 2009

In 1965, D.L. Berman established an interesting divergence theorem concerning Hermite-Fejér interpolation on the extended Chebyshev nodes. In this paper it is shown that this phenomenon is not an isolated incident. A similar divergence theorem is proved for a higher order interpolation process. The paper closes with a list of several related open problems.
Nonlinear eigenvalue problems
Authors: Fradkin L.Ju. , Wake G.C.
Published: April 2009

The object of this paper is to prove two new results on the nature of the spectrum of a class of nonlinear elliptic eigenvalue problems. In the first case, sufficient conditions are given for which the spectrum is bounded and, in the second case, conditions are given for which the spectrum is open.
Free products of topological groups: Corrigendum
Authors: Morris Sidney A.
Published: April 2009

Professor Edward T. Ordman has pointed out to the author that the proof of Theorem 2.2 in [2] is incorrect. The theorem is, in fact, correct and was proved by Graev [1] The incorrect proof presented in my paper has been modified by Ordman [3] to provide a much simpler proof than Graev's in a special case.
Presentations of some classical groups
Authors: Wicks M.J.
Published: April 2009

The groups considered are Λ = GL(2, Z), π = SL(2, Z) and Θ = PSL(2, Z). A presentation of Λ is obtained for which the word problem can be solved by a simple intrinsic algorithm. The presentation is modified to display other features of Λ, and to obtain related presentations of Λ and Θ. There is an algorithm which solves the conjugacy problem of Λ.
The regularity series of a convergence space
Authors: Richardson G.D. , Kent D.C.
Published: April 2009

The regularity series, or brieflyR-series, of a convergence space is an ordinal sequence of spaces leading to the regular modification of the space. The behavior of this series is studied relative to such basic constructs as products, subspaces, and various quotient maps. Upper bounds on the length of theR-series are obtained for several classes of spaces. This series can be employed to construct regular completions and compactifications.
Martingale central limit theorems without uniform asymptotic negligibility
Authors: Adler R.J. , Scott D.J.
Published: April 2009

Central limit theorems are obtained for martingale arrays without the requirement of uniform asymptotic negligibility. The results obtained generalise the sufficiency part of Zolotarev's extension of the classical Lindeberg-Feller central limit theorem [V.M. Zolotarev, Theor. Probability Appl. 12 (1967), 608–618] and also the main martingale central limit theorem (not functional central limit theorem however) of D.L. McLeish [Ann. Probability 2 (1974), 620–628.
Projective metabelian nonfree groups
Authors: Artamonov V.A.
Published: April 2009

This paper is concerned with projective metabelian -groups. where is the variety of all abelian groups, - of all abelian groups of exponent n. Let P be a projective -group. Since the group P/P′ is a free abelian group. Define rank P = rank P/P′. It is shown that for all numbers r, n > 1, except r = n = 2, there exists a protective nonfree -group of rank r with r + 1 generators.
Fluid flow in fields of resistance
Authors: Blake J.R.
Published: April 2009

The velocity profiles in volumes of either passive resistance or active transport are calculated for both linear and non-linear resistive models. These include fluid flows containing particles in a channel or pipe subject to either a steady or oscillatory pressure gradient, cilia induced transport, and laminar flow in a non-linear resistive shear layer. Resistive elements tend to substantially reduce the inertial phase lag component in oscillatory flows. Only small concentrations of particles are needed to reduce the flow field to the Darcy approximation. An ‘active porous media’ model for a cilia sublayer predicts accurate voleoity profiles for dense concentrations of cilia (for example, on Opaline, and in the lung).
The freeness of some projective metabelian groups
Authors: McIsaac A.J.
Published: April 2009

The question whether there exist non-free projective groups of rank r in the variety has been answered in the affirmative for n ≥ 2, r ≥ 2, except for n = r = 2, by V.A. Artamonov. This paper consists in a proof that a projective group G of rank 2 in is free. If x and y are any two elements which generate G modulo , then the group F generated by x and y is free in , and the index of F in G is finite and not divisible by 2. One wishes to replace x by xu and y by yν, where u and vν lie in , so that 〈xu, yν〉 is the whole of G. This can be done: first, on general grounds, it is sufficient that 〈xu, yν〉 contain every C(a), where C(a) is the centralizer in the G/-module of an element a in (and moreover choices of u and ν for each C(a) can be combined to give a single choice good for all C(a)); second, for the particular small numbers involved, the structure of C(a) is sufficiently simple for one to pick suitable u and ν without trouble.
On a family of contractive maps
Authors: Tasković Milan R.
Published: April 2009

The object of this paper is to study common fixed points of mappings of a complete metric space into itself. The results obtained are generalizations of theorems of Iséki and Ray. An example is given to show that our results are indeed extensions of the theorem of Iséki.
Geometric properties of the norm and basic sequences in Banach spaces
Authors: Singer Ivan
Published: April 2009

We introduce some generalizations of Kadec'-Klee norms and use them to study characteristics of subspaces of conjugate spaces and smoothness. We give some connections between such characteristics and basic sequences, which yield, in particular, sharpenings and simpler proofs of some known characterizations of reflexivity.
Maximal sum-free sets in finite abelian groups, V
Authors: Yap H.P.
Published: April 2009

Let λ(G) be the cardinality of a maximal sum-free set in a group G. Diananda and Yap conjectured that if G is abelian and if every prime divisor of |G| is congruent to 1 modulo 3, then λ(G) = |G|(n−1)/3n where n is the exponent of G. This conjecture has been proved to be true for elementary abelian p−groups by Rhemtulla and Street ana for groups by Yap. We now prove this conjecture for groups G = Zpq ⊕ Zp where p and q are distinct primes.
On semi-simple radical classes
Authors: Gardner B.J. , Stewart Patrick N.
Published: April 2009

It has been incorrectly asserted that each non-trivial semi-simple radical class of associative rings is a variety defined by an equation of the form xn = x. In this paper we give, for each non-trivial semi-simple radical class of associative rings, a set of equations which does define that class as a variety.
Relatively flat modules
Authors: Bland Paul E.
Published: April 2009

If (A′, B′), (B′, C′) and (A, B), (B, C) are torsion-torsion free theories on RM and MR respectively which are generated by an idempotent ideal I of R, then M ∈ RM is said to be relatively flat if (·) ⊗ RM preserves short exact sequences 0 → L → X → N → 0 in MR with N ∈ B. Several characterizations of relatively flat modules are given and it is shown that any module M ∈ RM which is codivisible with respect to (A′, B′) is relatively flat. In addition, when (A′, B′) is hereditary, it is proven that M ∈ RM is relatively flat if and only if M/IM is a flat R/I-module. Finally, a relatively flat dimension for M ∈ RM and a left global relatively flat dimension for R are defined and it is shown, again when (A′, B′) is hereditary, that the left global relatively flat dimension of R coincides with the left global flat dimension of R/I.
On the existence and uniqueness of solutions of parabolic equations
Authors: Teo K.L.
Published: April 2009

Recently, Eklund (Proc. Amer. Math. Soc. 47 (1975), 137–142) has shown that to each continuous function F on ∂pQ −⊲ {∂Ω × [0, T]} ∪ {Ω × (0)} there is a unique solution to the boundary value problem

where L is a linear second order parabolic operator in divergence form, Ω ⊂ Rn is a bounded domain with compact closure and ∂Ω denotes its boundary. In this note, it is shown that the existence theorem of Eklund remains valid for the following boundary problem
On the orbit-sizes of permutation groups containing elements separating finite subsets
Authors: Birch B.J. , Burns R.G. , Macdonald Sheila Oates , Neumann Peter M.
Published: April 2009

It is proved that ifGis a permutation group on a set Ω every orbit of which contains more thanmnelements, then any pair of subsets of Ω containingmandnelements respectively can be separated by an element ofG.
The ideals of the hurwitzean polynomial ring
Authors: Morton Margaret J.
Published: April 2009

In 1919, Adolf Hurwitz formed the quaternion ring R composed of elements whose coordinates were either all integers or halves of odd integers. The objective of this paper is to examine the (two-sided) ideal structure in the hurwitzean polynomial ring R[x], formed by taking all polynomials with coefficients in R. The maximal and prime ideals of R[x] will be characterized with results surprisingly analogous to those in Z[x]. In addition, a canonical basis, of the type developed by G. Szekeres, 1952, for polynomial domains, will be developed for the ideals of R[x].
On the complex nonlinear complementary problem
Authors: Parida J. , Sahoo B.
Published: April 2009

The complex nonlinear complementarity problem considered here is the following: find z such that

where S is a polyhedral cone in Cn, S* the polar cone, and g is a mapping from Cn into itself. We study the extent to which the existence of a z ∈ S with g(z) ∈ S* (feasible point) implies the existence of a solution to the nonlinear complementarity problem, and extend, to nonlinear mappings, known results in the linear complementarity problem on positive semi-definite matrices.
An embedding theorem for fields
Authors: Cassels J.W.S.
Published: April 2009

It is shown that every finitely generated field K of characteristic 0 may be embedded in infinitely many p-adic fields in such a way that the images of any given finite set C of non-zero elements of K are p-adic units. The result is suggested by Lech's proof of his generalization of Mahler's theorem on recurrent sequences. It also provides a simple proof of Selberg's theorem about torsion-free normal subgroups of matrix groups.
Two fixed point theorems in topological and metric spaces
Authors: Daneš Josef
Published: April 2009

Some fixed point results are derived for mappings of contractive type in metric and topological spaces.
A functional calculus for continuous affine operators
Authors: Koliha J.J.
Published: April 2009

In the Appendix to a recent paper by J.J. Koliha and A.P. Leung (Math. Ann.216 (1975), 273–284), a functional calculus for continuous affine operators was constructed on the basis of the Taylor-Dunford calculus. This calculus applied only to functions defined and analytic in an open set containing the spectrum of an operator and the point λ = 1. In the present paper I examine the affine resolvent, and develop independently a more general calculus applicable to functions which are analytic in any open neighbourhood of the spectrum of an affine operator.
A computer aided study of a group defined by fourth powers
Authors: Newman M.F.
Published: April 2009

There is a group defined by fourth powers which did not yield to attempts to determine its order by coset enumerations. This group has now been shown to be infinite with the aid of a computer. An outline of the method is given as well as a simple direct proof inspired by the results of further computer calculations.
Oscillation criteria for second order nonlinear delay inequalities
Authors: Nababan S. , Noussair E.S.
Published: April 2009

Oscillation criteria are obtained, for the nonlinear delay differential inequality u(u″+f(t, u(t), u(g(t)))) ≤ 0. The main theorems give sufficient conditions (and in some cases sufficient and. necessary conditions) for all solutions u(t) to have arbitrary large zeros. Generalizations to more general cases are discussed.
A comparison theorem for functional differential equations
Authors: Kartsatos Athanassios G. , Onose Hiroshi
Published: April 2009

In this paper, we study the oscillation of nth-order differential equations. Recently, Atkinson and the present authors studied (separately) the comparison properties of differential inequalities. Kartsatos treated the nth-order ordinary case and proposed several open problems.

The purpose of this paper is to answer one of them in the affirmative concerning more general functional differential equations. The result is that if under several conditions, the equation

is oscillatory for n even or a solution x(t) of (1) is oscillatory or for n odd, then this is also the case for the equation
Equations of motion in Poincaré-Četaev variables with constraint multipliers
Authors: Ghori Q.K.
Published: April 2009

Suslev's constraint multipliers are used to derive the equations of motion of dynamical systems (holonomic or nonholonomic) in the form of Poincaré-Četaev equations and in the canonical form. For holonomic systems defined by redundant variables, the constraint multipliers occuring in the canonical equations are determined and a modification of the Hamilton-Jacobi Theorem for integrating the canonical equations is presented.
On conjugacy classes in certain isogenous groups
Authors: Ketter T.A. , Lehrer G.I.
Published: April 2009

We give some results on the number of G-orbits (G = GL(n, q)) on groups isogenous (in the algebraic-geometric sense) to SL(n, q). The conjectured isogeny invariance of this number is contradicted by computer calculations.
A theorem of Thompson on isomorphisms induced by automorphisms
Authors: Vermani L.R.
Published: April 2009

Using homological methods (and in particular the 5-term sequence of Hochschild-Serre in the homology of groups) a generalization of the theorem of John G. Thompson (J. Austral. Math. Soc. 16 (1973), 16–17) referred to in the title is proved.
Transformations on tensor products and the torsionless property in abelian groups
Authors: Webb Cary
Published: April 2009

Suppose T is the natural transformation

where the variables are abelian groups. We find conditions on A, B, and C that guarantee that T is injective.
An addition to a note of mine
Authors: Mahler Kurt
Published: April 2009

A recent improvement by H. Guggenheimer of the lower bound for the product of the volumes of a pair of polar reciprocal convex bodies is used to replace one of the results of Kurt Mahler, “Polar analogues of two theorems by Minkowski”, Bull. Austral. Math. Soc. 11 (1974), 121–129 by a best possible one. A similar improvement can be made for the other theorems in my note.
On a unified approach to the law of the iterated logarithm for martingales
Authors: Hall P.G. , Heyde C.C.
Published: April 2009

There are two distinct approaches in the literature to framing a version of the law of the iterated logarithm for martingales. One involves norming by constants, using the martingale variance and the other involves norming by random variables, using the sums of conditional variances of the increments, given their past. In this paper a portmanteau approach is provided, still based on the Skorokhod representation of the martingale, but involving normalization by more general random variables. This extends the functional forms of all the previously existing results.
On the algebraic Riccati equation
Authors: Wimmer Harald K.
Published: April 2009

In this note the matrix equation A + WB + BTW + WCW = 0 is considered. A monotoneity result and an inertia theorem on the location of the eigenvalues of W and B + CW are proved.
A theorem on diophantine approximations
Authors: Mahler Kurt
Published: April 2009

If S is a set of positive integers which contains 1, 2, …, n–1, but not n or any multiple of n, where n ≥ 2, then

Here R is the field of real numbers, and ∥α∥ denotes the distance of α from the nearest integer.
An embedding theorem for fields: Addendum
Authors: Cassels J.W.S.
Published: April 2009

The proof of Lemma 2 in [1] invoked elementary analytic number-theory. I have just realized that there is a proof which is entirely elementary. It is doubtless “well-known” (in the usual technical sense that it appears somewhere in the literature) and it is certainly “well-knowable” in Conway's terminology. However, as it renders the entire argument of my paper elementary, I give it here.
Hitting times of Markov chains, with application to state-dependent queues
Authors: Tweedie R.L.
Published: April 2009

We present in this note a useful extension of the criteria given in a recent paper [Advances in Appl. Probability8 (1976), 737–771] for the finiteness of hitting times and mean hitting times of a Markov chain on sets in its (general) state space. We illustrate our results by giving conditions for the finiteness of the mean number of customers in the busy period of a queue in which both the service-times and the arrival process may depend on the waiting time in the queue. Such conditions also suffice for the embedded waiting time chain to have a unique stationary distribution.
A classification of groups with a centralizer condition II: Corrigendum and addendum
Authors: Arad Zvi , Herzog Marcel
Published: April 2009

The aim of this note is to prove a theorem, which extends the results of the authors' earlier paper, Bull. Austral. Math. Soc. 16 (1977), 55–60. As one of the corollaries we prove Theorem 2 of that paper, the proof of which was incomplete.
Analytic contractive vector fields in Fréchet spaces
Authors: Duc Duong Minh
Published: April 2009

Using degree theory we establish the inverse mapping theorem and a Sard-Smale theorem for analytic contractive vector fields in Fréchet spaces. Applying these theorems we obtain Cronin's theorem relating topological degree to the number of zeros of analytic contractive vector fields.
Complete hypersurface of non-positive Ricci curvature
Authors: Leung Pui-Fai
Published: April 2009

We conjecture that a complete hypersurface of non-positive Ricci curvature in the Euclidean space must be unbounded. We prove this under the additional assumption that all sectional curvatures of the hypersurface are bounded away from negative infinity.
Atomic measure spaces and essentially normal composition operators
Authors: Singh R.K. , Veluchamy T.
Published: April 2009

The adjoint of a composition operator CT on the L2-space of an atomic measure is computed and a characterization for an operator to be a composition operator is given in this short note. The dimensions of kernel and co-kernel of CT are calculated in order to characterise Fredholm composition operators. Finally, essentially normal composition operators are studied on l2.
A characterization of real and complex Hilbert spaces among all normed spaces
Authors: Vukman J.
Published: April 2009

Let X be a real or complex normed space and L(X) the algebra of all bounded linear operators on X. Suppose there exists a *-algebra B(X) ⊂ L(X) which contains the identity operator I and all bounded linear operators with finite-dimensional range. The main result is: if each operator U ∈ B(X) with the property U*U = UU* = I has norm one then X is a Hilbert space.
On the existence of optimal controls in Banach spaces
Authors: Joshi Mohan
Published: April 2009

We prove the existence of an optimal control in Banach spaces for a system characterized by Hammerstein operator equations.
An inequality for the derivative of self-inversive polynomials
Authors: Dewan K.K. , Govil N.K.
Published: April 2009

In this paper it is shown that if p(z) is a polynomial of degree n satisfying then

The result is best possible.
On the embedding of processes in Brownian motion and the law of the iterated logarithm for reverse martingales
Authors: Scott D.J. , Huggins R.M.
Published: April 2009

Techniques from martingale theory are used to obtain the Skorokhod embedding of reverse martingales in Brownian motion. This result is then used to obtain a functional law of the iterated logarithm for reverse martingales.
A characterization of recurrent motions
Authors: Knight Ronald A.
Published: April 2009

Necessary and sufficient conditions for a Poisson stable flow to be recurrent are given.
Are chaotic functions really chaotic
Authors: Du Bau-Sen
Published: April 2009

We give a classCof continuous functions from [0, 1] onto itself which are chaotic in the sense of Li and Yorke, but with the property that almost all (in the sense of Lebesgue) points of [0, 1] are eventually fixed. For some continuous functions from [0, 1] onto itself which are not inC, We also show that their non-wandering sets are all equal to the interval [0, 1].
On groups with small Engel depth
Authors: Brandl Rolf
Published: April 2009

Every finite group G satisfies a law [x, ry] = [x, sy] for some positive integers r < s. The minimal value of r is called the depth of G. It is well known that groups of depth 1 are abelian. In this paper we prove the following. Let G be a finite group of depth 2. Then G/F(G) is supersoluble, metabelian and has abelian Sylow p-subgroups for all odd primes p. Moreover, lp(G) ≤ 1 for p odd and l2(G2) ≤ 1.
Free k-tuples in linear groups
Authors: Mandel Arnaldo , Gonçalves Jairo Z.
Published: April 2009

Let PGL(P) be the group of projective linear transformations of the n-dimensional projective space P over a field F. A topology is given on F, and it is assumed that F is locally-compact; PGL(P) is endowed with the quotient topology from the canonical projection map GL(n, F) → PGL(P), where

.

For any given k, it is shown that the set of k–tuples (g1, g2, … gk) ɛ PGL(P)k which freely generate a free sub-group of PGL(P) and has a nonvoid interior.