bluuebunny/crossref_metadata_2025 huggingface dataset:
On almost-Hermite-Fejér-interpolation: pointwise estimates
Authors: Gonska Heinz H.
Published: April 2009

We give a brief survey of the results obtained by numerous authors in so-called almost-Hermite-Fejér-interpolation and deal mainly with new quantitative assertions.

These are based upon more general theorems for certain continuous linear operators which yield estimates involving different types of moduli of continuity.

Our paper shows that in the case of almost-Hermite-Fejér-interpolation the underlying general technique can be used to treat three essentially different cases: sequences of positive operators, which converge uniformly for every continuous function on [−1, 1], sequences of non-positive operators doing the same, and sequences of operators which converge on proper subspaces ofC[−1, 1] only.
On vector spaces of certain modular forms of given weights: Addendum
Authors: Aggarwal A.R. , Agrawal M.K.
Published: April 2009

The statement used in proving Theorem 2 of [1] needs explanation. This was pointed out to us by Professor S. Raghwan of Tata Institute of Fundamental Research, Bombay, and we gave the explanation of this in [2]. For the sake of completeness we give here the full proof of the theorem; filling the gap in the proof. We use the same notations and definitions as those of [1]. Also for simplicity of notation we write kmn, gmn and amn to mean km,n, gm,n and a respectively. We need the following lemma.
Conjugacy classes of involutions in Coxeter groups
Authors: Richardson R.W.
Published: April 2009

In this paper we give an elementary method for classifying conjugacy classes of involutions in a Coxeter group (W, S). The classification is in terms of (W-equivalence classes of certain subsets of S).
Boundary behaviour of solutions of the non-parametric least area problem
Authors: Simon Leon
Published: April 2009

Previous work concerning boundary regularity of solutions of the non-parametric least area problem leaves open the question of regularity of solutions at points where the mean curvature of the boundary of the domain vanishes. We here prove that the solutions may be discontinuous at such points, even when the given boundary data is smooth. We also give a sufficient condition which will ensure continuity at such points.
On the structure of a class of equivariant maps
Authors: Field M.J.
Published: April 2009

Let G be a compact Lie group and M be a compact G-manifold. We investigate the class of equivariant diffeomorphisms of M covering the identity map on the orbit space M/G.
Recurrence relations in a modular representation algebra
Authors: Renaud J-C.
Published: April 2009

In 1978 Almkvist and Fossum examined the decomposition of the exterior powers of basis modules in the modular representation algebra of a cyclic group of prime order. In particular they developed an isomorphism between these exterior powers and terms of binomial coefficient type in the algebra.

We derive several recurrence relations for these terms.
Two addenda to the author's ‘Transfinite constructions’
Authors: Kelly G.M.
Published: April 2009

Since the author's article “A unified treatment of transfinite constructions …”, in Volume 22 (198O) of this Bulletin, had an encyclopaedic goal, he now takes the opportunity to answer two further questions raised since that article was submitted. The lesser of these asks whether the only pointed endofunctors for which every action is an isomorphism are the well-pointed ones, at least when the endofunctor is cocontinuous; a counter-example provides a negative answer. The more important question concerns the reflexion from the comma-category T/A into the category of algebras for the pointed endofunctor T of A, and the algebra-reflexion sequence which converges to this reflexion; and asks for simplified descriptions in the special case where T is cocontinuous. We give closed formulas in this case, both for the reflexion and for the sequence which converges to it. The reader may wonder why we care about the approximating sequence when we have a closed formula for the reflexion; the answer is that, in certain applications, we need to separate the roles of finite colimits and filtered ones.
Cyclically separated groups
Authors: Hartley Brian , Lennox John C. , Rhemtulla Akbar H.
Published: April 2009

We call a group G cyclically separated if for any given cyclic subgroup B in G and subgroup A of finite index in B, there exists a normal subgroup N of G of finite index such that N ∩ B = A. This is equivalent to saying that for each element x ∈ G and integer n ≥ 1 dividing the order o(x) of x, there exists a normal subgroup N of G of finite index such that Nx has order n in G/N. As usual, if x has infinite order then all integers n ≥ 1 are considered to divide o(x). Cyclically separated groups, which are termed “potent groups” by some authors, form a natural subclass of residually finite groups and finite cyclically separated groups also form an interesting class whose structure we are able to describe reasonably well. Construction of finite soluble cyclically separated groups is given explicitly. In the discussion of infinite soluble cyclically separated groups we meet the interesting class of Fitting isolated groups, which is considered in some detail. A soluble group G of finite rank is Fitting isolated if, whenever H = K/L (L ⊲ K ≤ G) is a torsion-free section of G and F(H) is the Fitting subgroup of H then H/F(H) is torsion-free abelian. Every torsion-free soluble group of finite rank contains a Fitting isolated subgroup of finite index.
Paranormal operators on Banach spaces
Authors: Chourasia N.N. , Ramanujan P.B.
Published: April 2009

In this note we show that a paranormal operator T on a Banach space satisfies Weyl's theorem. This is accomplished by showing that

(i) every isolated point of its spectrum is an eigenvalue and the corresponding eigenspace has invariant complement,

(ii) for α ≠ 0, Ker(T-α) ⊥ Ker (T-β) (in the sense of Birkhoff) whenever β ≠ α.
Comparison theorems of Hille-Wintner type for third order linear differential equations
Authors: Erbe L.
Published: April 2009

Integral comparison theorems of Hille-Wintner type of second order linear equations are shown to be valid for the third order linear equation y‴ + q(t)y = 0.
Normal Fitting classes and Hall subgroups
Authors: Cusack Elspeth
Published: April 2009

It was shown by Bryce and Cossey that each Hall π-subgroup of a group in the smallest normal Fitting class S* necessarily lies in S*, for each set of primes π. We prove here that for each set of primes π such that |π| ≥ 2 and π′ is not empty, there exists a normal Fitting class without this closure property. A characterisation is obtained of all normal Fitting classes which do have this property.

Let F be a normal Fitting class closed under taking Hall π-subgroups, in the sense of the paragraph above, and let Sπ denote the Fitting class of all finite soluble π-groups, for some set of primes π. The second main theorem is a characterisation of the groups in the smallest Fitting class containing F and Sπ in terms of their Hall π-subgroups.
Infinite series and the derived set of the aggregate of the fractional parts of its partial sums
Authors: Moorthy S. Audinarayana
Published: April 2009

The aim of this paper is to study the relationship between the nature of an infinite series of real terms in which the general term tends to zero and the derived set (set of limit points) of the aggregate of the fractional parts of its partial sums. For all types of series (in which the nth term tends to zero) we determine the derived set.

We denote by F the set of the fractional parts of the partial sums of the series, and by F′ the derived set of F. The principal results of the paper can be stated as follows:

1. the series is convergent if and only if F has at most one limit point in [0, 1] or F′ ⊆ {0, 1};

2. the series, if non-oscillatory, is divergent if and only if F′ = [0, 1];

3. if the series is oscillatory, F′ is a closed sub-interval of [0, 1] or [0, 1] - (a, b), where (a, b) ⊊ (0, 1).
Convergence tensor products and a strict topology
Authors: Müller Bernd
Published: April 2009

We are interested in the strict topology τ on , the set L(E, F) of all continuous linear mappings from E into a Banach space F endowed with the topology of pointwise convergence. The T3-completion of the convergence tensor product E ⊗cLc F is the set of all τ-continuous linear functionals on L(E, F) and τ is the topology of uniform convergence on the compact subsets of . In the case that E is a nuclear Fréchet space, a nuclear (DF)-space or a Banach space with the bounded approximation property the topology τ agrees with the topology of Lco (E, F).
On hereditarily Lindelöf spaces
Authors: Reilly I. L. , Vamanamurthy M. K.
Published: April 2009

This paper considers the question of when a space with the property that each discrete subspace is countable is hereditarily Lindelbölf. The question is answered affirmatively for the class of ROP spaces and for the class of hereditarily meta-Lindelöf spaces. A characterization of hereditarily Lindelöf spaces in terms of countable subspaces is given.
On intersecting families of finite sets
Authors: Frankl Peter
Published: April 2009

Let F be a family of k-element subsets of an n-set, n > n0(k). Suppose any two members of F have non-empty intersection. Let τ(F) denote min|T|, T meets every member of F. Erdös, Ko and Rado proved and that if equality holds then τ(F) = 1. Hilton and Milner determined max|F| for τ(F) = 2. In this paper we solve the problem for τ(F) = 3.

The extremal families look quite complicated which shows the power of the methods used for their determination.
Notes on the inverse mapping theorem in locally convex spaces
Authors: Yamamuro Sadayuki
Published: April 2009

Several problems arising from a functional analytic study on Omori's inverse mapping theorem are considered arriving at an inverse mapping theorem in locally convex spaces.
A remark on a paper of V. K. Srinivasan
Authors: Heinze Joachim
Published: April 2009

An associative locally finite algebra which is also an integral domain over an algebraically closed field is isomorphic to the ground field.
What is the theory of shape?
Authors: Borsuk Karol , Dydak Jerzy
Published: April 2009

This expository article on Shape Theory contains the main concepts of this theory with a formulation of the most important results of this theory and also with some open problems. The proofs are omitted, however the article gives references to the hooks and papers, in which the reader can find the proofs.

For simplicity, we formulate several theorems only in the form which clearly gives their geometric sense, even if there are known more general results with rather complicated formulations. The reader more interested in details, can find them in the original papers quoted in the list of references.
A new definition of variational derivative
Authors: Hamilton Eugene P.
Published: April 2009

It is shown that the functional fails to possess a variational derivative, contrary to what is claimed by Gelfand and Fomin. A modified definition is given with respect to which the functional does possess a variational derivative.
On starlike functions
Authors: Gupta V.P. , Ahmad Iqbal
Published: April 2009

Let S denote the class of functions f analytic and univalent in the open disc {z: |z| < 1} and normalized by f(0) = 0 = f′(0) − 1, and S*(α) denote the set of starlike functions of order α (0 ≤ α ≤ 1) in S. In this paper, the results of William M. Causey and William L. White [J. Math. Anal. Appl. 64 (1978), 458–466] are generalized by the following:

THEOREM 1. Let f, g and h belong to S*(α), S*(λ) and S*(γ) , respectively and let F be defined by

where a, c ∈ N. Then F belongs to S*(β) for |z| less than a suitably chosen number.

THEOREM 2. Let F, g and h belong to S*(α), S*(λ) and S*(γ) , respectively and f be given by **. Then f belongs to S*(β) , for |z| less than a suitably chosen number.
Minimal requirements for Minkowski's theorem in the plane II
Authors: Arkinstall J.R.
Published: April 2009

Let K be a closed convex set in the Euclidean plane, with area A(K), which contains in its interior only one point 0 of the integer lattice. If K has other than one or three chords through 0 of one of the following types, it is shown that A(K) ≤ 4, while if K has three of one type, A(K) ≤ 4.5. The types of chords considered are chords which partition K into two regions of equal area, chords which lie midway between parallel supporting lines of K, and chords such that K is invariant under reflection in them. The results are generalised to any lattice in the plane.
Some commutativity results for rings
Authors: Klein Abraham A. , Nada Itzhak , Bell Howard E.
Published: April 2009

It is proved that certain rings satisfying generalized-commutator constraints of the form [xm, yn, yn, …, yn] = 0 must have nil commutator ideal.
Metric projections and the differentiability of distance functions
Authors: Fitzpatrick Simon
Published: April 2009

Let M be a closed subset of a Banach space E such that the norms of both E and E* are Fréchet differentiable. It is shown that the distance function d(·, M) is Fréchet differentiable at a point x of E ∼ M if and only if the metric projection onto M exists and is continuous at X. If the norm of E is, moreover, uniformly Gateaux differentiable, then the metric projection is continuous at x provided the distance function is Gateaux differentiable with norm-one derivative. As a corollary, the set M is convex provided the distance function is differentiable at each point of E ∼ M. Examples are presented to show that some of our hypotheses are needed.
Metrizable (LF)-spaces, (db)-spaces, and the separable quotient problem
Authors: Saxon Stephen A. , Narayanaswami P.P.
Published: April 2009

The existence of metrizable (LF)-spaces was announced by Stephen A. Saxon (“Metrizable generalized (LF)-spaces”, 701–46–14), in Notices Amer. Math. Soc. 20 (1973), A–143. Elsewhere, the authors have discovered an abundant existence of metrizable and normable (generalized) (LF)-spaces, while observing that an (LF)-space is metrizable if and only if it is Baire-like. Recently, W. Robertson, I. Tweddle and F.E. Yeomans introduced the class of locally convex spaces E having the property

(db) if E is the union of an increasing sequence (En) of vector subspaces, then some En is dense and barrelled.
Degrees giving independent edges in a hypergraph
Authors: Daykin David E. , Häggkvist Roland
Published: April 2009

For r-partite and for r-uniform hypergraphs bounds are given for the minimum degree which ensures d independent edges.
Stability of strongly regular graphs
Authors: Shukla S.K. , Sridharan M.R. , Mohanty S.P.
Published: April 2009

In this note we characterize strongly regular graphs which are stable.
Weak and semi-strong solutions of the Schneider-Tricomi problem in the euclidean space; a uniqueness theorem for the Chaplygin-Frankl problem: Corrigenda
Authors: Rassias John M.S.
Published: April 2009

As they stand, the two papers [1], [2] are vacuous by the virtue of the fact that it is not possible to choose any functions a, k and constant β satisfying all the necessary hypotheses.
Some results for the general bulk service queueing system
Authors: Holman D.F. , Chaudhry M.L. , Ghosal A.
Published: April 2009

This paper deals with a general bulk service queueing system with one server, for which customers arrive in a Poisson stream and the service is in bulk. The maximum number of customers to be served in one lot isB(capacity), but the server does not start service untilA(quorum, less thanB) customers have accumulated; and the service time follows a general probability distribution. Probability generating functions of the distributionsPnand, under equilibrium, have been derived by using the supplementary variable technique. An expression has been derived for the expected value of the queue size and its relation with the expected value of the waiting time of a customer has been explored. A numerical case has been worked out on the assumption that bulk service follows a specified Erlangian distribution.
A remark on an integral inequality
Authors: Raghavendra V.
Published: April 2009

A counter example is constructed to show that an integral inequality established by Sree Hari Rao (Theorem 3.1,J. Math. Anal. Appl. 72(1979), 545–550) is erroneous.
Notions of topos
Authors: Street Ross
Published: April 2009

A Grothendieck topos has the property that its Yoneda embedding has a left-exact left adjoint. A category with the latter property is called lex-total. It is proved here that every lex-total category is equivalent to its category of canonical sheaves. An unpublished proof due to Peter Freyd is extended slightly to yield that a lex-total category, which has a set of objects of cardinality at most that of the universe such that each object in the category is a quotient of an object from that set, is necessarily a Grothendieck topos.
Composition operators and several complex variables
Authors: Singh R.K. , Sharma S.D.
Published: April 2009

Let Un be the open unit polydisc, and let T be a mapping from Un into itself. Then the composition transformation CT is a mapping on the Hardy space H2(Un) into the space of complex functions on Un defined as CTf = f ∘ T for every f ∈ H2(Un). An attempt is made to study some properties of CT in this note. A partial generalization of a result of Schwartz, and a relation between intertwining analytic Toeplitz operators and composition operators are reported.
Automatic continuity of positive functionals on topological involution algebras
Authors: Dixon P.G.
Published: April 2009

This paper surveys the known results on automatic continuity of positive functionals on topological *-algebras and then shows how two theorems on Banach *-algebras extend to complete metrizable topological *-algebras. The two theorems concerned are Loy's theorem on separable Banach *-algebras A with centre Z such that AZ is of countable codimension and Varopoulos' result on Banach *-algebras with bounded approximate identity. Both theorems have the conclusion that all positive functionals on such algebras are continuous. The extension of the second theorem requires the algebra to be locally convex and the approximate identity to be ‘uniformly bounded’. Neither extension requires the algebra to be LMC. This means that the proof of the first theorem is quite different from the corresponding Banach algebra result (which used spectral theory). The proof of the second is closer to the previously known LMC version, but actually neater by being more general. It is also shown that the well-known estimate of |f(a*ba)| for a positive functional f on a Banach *-algebra may be obtained without the usual use of spectral theory. The paper concludes with a list of open questions.
Some translation planes constructed by multiple derivation
Authors: Johnson N. L.
Published: April 2009

It is noted that the translation planes of Rao and Rao may be constructed from a Desarguesian plane by the replacement of a set of disjoint derivable nets. Their plane of order 25 which admits a collineation group splitting the infinite points into orbits of lengths 18 and 8 may be obtained by replacing exactly three disjoint derivable nets and may be viewed as being derived from the Andre nearfield plane of order 25.
Nonlinear hydromagnetic convection in a moderate prandtl number fluid
Authors: Riahi N.
Published: April 2009

Nonlinear hydromagnetic connection is investigated using the modal equations for cellular convection. The boundary layer method is used assuming large Rayleigh number R, moderate Prandtl number σ and for different ranges of the Chandrasekhar number Q. The heat flux F is determined for the value of the horizontal wave number which maximizes F. For a weak field, the inertial force dominates over the Lorentz force. F is independent of Q, but it increases with R and σ. For a moderate field, the Lorentz force is significant. F increases with R and σ and decreases as Q increases. For a strong field, the Lorentz force dominates over the inertial force. F is independent of σ, but it increases with R and decreases as Q increases.
Varieties of groups and of completely simple semigroups
Authors: Petrich Mario , Reilly Norman R.
Published: April 2009

Completely simple semigroups form a variety if we consider them both with the multiplication and the operation of inversion. Denote the lattice of all varieties of completely simple semi-groups by L(CS) and that of varieties of groups by L(G). We prove that the mappings V → V ∩ G and V → V v G are homomorphisms of L(CS) onto L(G) and the interval [G, CS], respectively. The homomorphism V → (V ∩ G, V v G) is an isomorphism of L(CS) onto a subdirect product. We explore different properties of the congruences on L(CS) induced by these homomorphisms.
Degree of approximation of a function by Nörlund means of its Fourier series
Authors: Saxena R. B.
Published: April 2009

Two theorems of T.M. Flett [Quart. J. Math. Oxford Ser. (2) 7 (1956), 81–95] on the degree of approximation to a function by the Cesàro means of its Fourier series are extended to Nörlund means. Their conjugate analogues are also proved.
Not quite inner automorphisms
Authors: Neumann B. H.
Published: April 2009

A question asked by G. Kowol is answered by the construction, to an arbitrarily given natural number n, of groups G with automorphisms that agree with inner automorphisms on each set of fewer than n elements of G, but fail to agree with any inner automorphism on at least one set of n elements.
A note on d-symmetric operators
Authors: Gupta B. C. , Ramanujan P. B.
Published: April 2009

An operator T on a complex Hilbert space is d-symmetric if , where is the uniform closure of the range of the derivation operator δT(X)=TX−XT. It is shown that if the commutator ideal of the inclusion algebra for a d-symmetric operator is the ideal of all compact operators then T has countable spectrum and T is a quasidiagonal operator. It is also shown that if for a d-symmetric operator I(T) is the double commutant of T then T is diagonal.
Isometries of measurable functions
Authors: Cambern Michael
Published: April 2009

Let (X, Σ, μ) be a σ-finite measure space and denote by L∞(X, K) the Banach space of essentially bounded, measurable functions F defined on X and taking values in a separable Hilbert space K. In this article a characterization is given of the linear isometries of L∞(X, K) onto itself. It is shown that if T is such an isometry then T is of the form (T(F))(x) = U(x)(φ(F))(x), where φ is a set isomorphism of Σ onto itself, and U is a measurable operator-valued function such that U(x) is almost everywhere an isometry of K onto itself. It is a consequence of the proof given here that every isometry of L∞(X, K) is the adjoint of an isometry of L1(x, K).
Manifolds of smooth maps II: transversality
Authors: Nghê Truong Công
Published: April 2009

We generalise the standard notion of transversality to maps between manifolds modelled on locally convex spaces and prove that all standard transversal theorems remain valid for this generalised notion.

As first applications, we use our generalised Transversal Density Theorem to prove several simple “generic” results for local smooth maps which parallel the usual ones.
On meromorphic functions of one complex variable having algebraic Laurent coefficients
Authors: Bertrand Daniel , Waldschmidt Michel
Published: April 2009

We study the set of points at which two algebraically independent meromorphic functions have algebraic coefficients in their Laurent expansions. After a survey of the present knowledge in this field, we obtain two general transcendence criteria which sharpen previous results of Straus, Schneider and Lang. As a corollary, we give a new proof, based on Gel'fond's method, of some of Siegel's results on E-functions.
Multipliers between some function spaces on groups
Authors: Gupta A.K. , Tewari U.B.
Published: April 2009

Let G be a nondiscrete locally compact abelian group with dual group Γ. For 1 ≤ p ≤ ∞, denote by Ap(G) the space of integrable functions on G whose Fourier transforms belong to Lp(Γ). We investigate multipliers from Ap(G) to Aq(G). If G is compact and 2 < p1, p2 < ∞, we show that multipliers of and multipliers of are different, provided Pl ≠ P2. For compact G, we also exhibit a relationship between lr (Γ) and the multipliers from Ap(G) to Aq(G). If G is a compact nonabelian group we observe that the spaces Ap(G) behave in the same way as in the abelian case as far as the multiplier problems are concerned.
A new graph product and its spectrum
Authors: Godsil C.D. , McKay B.D.
Published: April 2009

A new graph product is introduced, and the characteristic polynomial of a graph so–formed is given as a function of the characteristic polynomials of the factor graphs. A class of trees produced using this product is shown to be characterized by spectral properties.
Monotone operators and dentability
Authors: Fitzpatrick S.P.
Published: April 2009

P.S. Kenderov has shown that every monotone operator on an Asplund Banach space is continuous on a dense Gδ subset of the interior of its domain. We prove a general result which yields as special cases both Kenderov's Theorem and a theorem of Collier on the Fréchet differentiability of weak* lower semicontinuous convex functions.
On coinduced corepresentations
Authors: Wilson William H.
Published: April 2009

We prove a Frobenius reciprocity type theorem for coinduced comodules.
On characterisation of finitary algebraic categories
Authors: Borceux Francis , Day B.J.
Published: April 2009

The aim of this article is to characterise categories which are V–algebraic (equals V–theoretical) over V where V is a symmetric monoidal closed category satisfying suitable limit-colimit commutativity conditions (basicly axiom π).
Semi-simple classes in a variety satisfying an Andrunakievich Lemma
Authors: Anderson Tim , Gardner B.J.
Published: April 2009

It is shown that in a variety of (not necessarily associative) algebras which satisfies a variant of Andrunakievich's Lemma, a classCcontaining no solvable algebras is the semi-simple class corresponding to some supernilpotent radical class if and only ifCis hereditary and is closed under extensions and sub-direct products. Semi-simple classes in general are not characterized by these properties. If the variety satisfies the further condition that some proper power of every ideal is an ideal, then analogous results hold for the semi-simple classes corresponding to radical classes containing no solvable algebras. In particular, for algebras over a field in the latter situation, all semi-simple classes are characterized by the three closure properties mentioned.
On boundedness of impulsively perturbed systems
Authors: Rao V. Sree Hari
Published: April 2009

A few results on uniform and uniform ultimate boundedness properties of solutions of impulsively perturbed systems are presented in this paper, assuming the corresponding properties of solutions of the unperturbed nonlinear system.
Periodic points and chaotic functions in the unit interval
Authors: Butler G.J. , Pianigiani G.
Published: April 2009

It is shown that the set of chaotic self-maps of the unit interval contains an open dense subset of the space of all continuous self-maps of the unit interval. Other aspects of chaotic behaviour are also considered together with some illustrative examples.
On embedding closed categories
Authors: Day B.J. , Laplaza M.L.
Published: April 2009

This article contains one method of fully embedding a symmetric closed category into a symmetric monoidal closed category. Such an embedding is very useful in the study of coherence problems. Also we give an example of a non-symmetric closed category for which, under the embedding discussed in this article, the resultant monoidal closed structure has associativity not an isomorphism.
A new extension of Minkowski's Theorem
Authors: Scott P.R.
Published: April 2009

Let K be a closed convex set in the plane containing no nonzero point of the integral lattice. We show that if the area A(K) of K is equally distributed amongst the four principal quadrants of the plane, then A(K) < 4.
Further results on an integral representation of functions of generalised variation
Authors: Russell A.M.
Published: April 2009

In this paper we present further properties of the kth variation of a function, and obtain an integral representation for a function having bounded kth variation and an absolutely continuous (k-l)th derivative. The absolute continuity-requirement replaces a previous stronger condition that required the kth derivative of a function to be continuous except on a set of Lebesgue measure zero.
On doubly transitive permutation groups
Authors: Praeger Cheryl E.
Published: April 2009

Suppose that G is a doubly transitive permutation group on a finite set Ω and that for α in ω the stabilizer Gα of αhas a set σ = {B1, …, Bt} of nontrivial blocks of imprimitivity in Ω – {α}. If Gα is 3-transitive on σ it is shown that either G is a collineation group of a desarguesian projective or affine plane or no nonidentity element of Gα fixes B pointwise.
A construction of monogenic near-ring groups, and some applications
Authors: Scott S.D.
Published: April 2009

Let V be a group generated by elements ν1 and ν2 of finite coprime order, and let N be the near-ring generated by the inner automorphism induced by ν1.It is proved that V is a monogenic N-group. Certain consequences of this result are discussed. There exist finite near-rings N with identity generated by a single distributive element μ, such that μ2 = 1 and where the radical J2(N) (see Günter Pilz, Near-rings. The theory and its applications, 1977, p. 136) is non-nilpotent.
Inverse semigroups and their natural order
Authors: Mitsch H.
Published: April 2009

The natural order of an inverse semigroup defined by a ≤ b ⇔ a′b = a′a has turned out to be of great importance in describing the structure of it. In this paper an order-theoretical point of view is adopted to characterise inverse semigroups. A complete description is given according to the type of partial order an arbitrary inverse semigroup S can possibly admit: a least element of (S, ≤) is shown to be the zero of (S, ·); the existence of a greatest element is equivalent to the fact, that (S, ·) is a semilattice; (S, ≤) is directed downwards, if and only if S admits only the trivial group-homomorphic image; (S, ≤) is totally ordered, if and only if for all a, b ∈ S, either ab = ba = a or ab = ba = b; a finite inverse semigroup is a lattice, if and only if it admits a greatest element. Finally formulas concerning the inverse of a supremum or an infimum, if it exists, are derived, and right-distributivity and left-distributivity of multiplication with respect to union and intersection are shown to be equivalent.
Characterizations of invertible, unitary, and normal composition operators
Authors: Singh R.K. , Kumar Ashok
Published: April 2009

Let Cφ be a composition operator on L2(λ), where λ is a σ-finite measure on a set X. Conditions under which Cφ is invertible, unitary, and normal are investigated in this paper.
On the absolute Nörlund summability factors of a Fourier series and its conjugate series at a point
Authors: Kanno Kôsi
Published: April 2009

The object of this paper is to give generalizations of Okuyama's Theorem [Bull. Austral. Math. Soc.12 (1975), 9–21, Tôohoku Math. J. (2) 28 (1976), 563–581] on the absolute Nörlund summability factors of a Fourier series and its conjugate series.

Our theorems imply many results proved by other authors: especially Theorem 1 includes the results of Bhatt and Kishor [Indian J. Math.9 (1967), 259–267 (1968)], Dikshit [Pacific J. Math.63 (1976), 371–379], and Lal [Publ. Inst. Math. (Beograd) 20 (34) (1976), 169–178], and we can easily deduce Lal's result [Indian J. Math.16 (1974), 1–22] from our Corollary 2.
Oscillatory behaviour of first order delay differential equations
Authors: Tomaras Alexander
Published: April 2009

Best possible conditions are given here, under which all solutions of several delay differential equations are oscillatory.
Fibonacci varieties
Authors: Kim Ann Chi
Published: April 2009

This is a report on a family of varieties of algebraic systems that are groups with an additional unary operation satisfying certain laws. The study was inspired by the theory of Fibonacci groups, and the free one-generator algebras of our varieties turn out to have, in fact, the abelianized Fibonnaci groups as their underlying groups.
Residual finiteness of cyclic extensions of certain free products
Authors: Baumslag Benjamin , Gupta Narain , Levin Frank
Published: April 2009

We prove that a cyclic extension of a free product of finitep-groups is residually finite,pa fixed prime. The question of cyclic extensions of free products of arbitrary cyclic groups remains open.
Path decompositions of digraphs
Authors: Abdul-Kader Issam
Published: April 2009

Let G = (X, U) be a digraph of order n. P(G) denotes the minimal cardinal of a path-partition of the arcs of G.

Oystein Ore, Theory of graphs (Amer. Math. Soc, Providence, Rhode Island, 1962) has proved that , where . We say that G satisfies Q if the preceeding inequality is an equality.

We give some properties of the digraphs satisfying Q, and in particular the case where G is strongly connected. Then we prove that P(G) ≤ [n2/4], and that this result is the best possible. Next we exhibit the existence of digraphs with circuits such that P(G) = [n2/4].

Finally we prove that if G is a strongly connected digraph of order n which satisfies Q, then there exists a strongly connected digraph H of order n + 1 having G as a sub-digraph and satisfying Q, too.
Note on duality of Kelleyspace products
Authors: Day B.J.
Published: April 2009

It has been shown by W.F. LaMartin that the Pontryagin dual of a k-space product of Hausdorff abelian k-groups is the coproduct of their duals. Here we offer a different proof, based partly on LaMartin's, that the dual of a product is the coproduct of the duals in a more general setting.
Note on asymptotic equivalence for measure differential equations Corrigendum
Authors: Rao V. Sree Hari
Published: April 2009

The last 3 references in the author's note [1] should read as follows:

[4] V. Sree Hari Rao, “On boundedness of impulsively perturbed systems”, Bull. Austral. Math. Soc. 18 (1978), 237–242.

[5] V. Sree Hari Rao, “Asymptotically self invariant sets and stability of measure differential equations“, Nonlinear Anal., Theory, Methods Appl. 2 (1978), 483–489.

[6] V. Sree Hari Rao, ”Note on conditionally asymptotically invariant sets“, J. Mathematical and Physical Sci. 12 (1978), 469–471.
On the positivity of weak supersolutions of non-uniformly elliptic equations
Authors: Trudinger Neil S.
Published: April 2009

The classical maximum principle for homogeneous, second order, uniformly elliptic equations implies that non-negative, classical supersolutions are either positive or vanish identically in the interior of their domain of definition. This paper is concerned with an extension of this result to weak supersolutions of non-uniformly elliptic equations subject to only mild coefficient restrictions.
On open mappings, closed mappings, and ordinal invariants
Authors: Boone James R.
Published: April 2009

In this brief note new characterizations of open mappings and closed mappings are presented which involve the compact order of the domain. The paper answers some of the questions which resulted from the study of the ordinal monotonicity of pseudo-open mappings and thus constitutes an extension of that work. Another characterization of open mappings is introduced.
On injective profinite algebras
Authors: Day B.J.
Published: April 2009

It is shown that if с is a finitely productive and hereditary class of uniformly pointed finite discrete universal algebras then any injective in с is an injective in Proс.
A translation plane of order 25 and its full collineation group
Authors: Rao M.L. Narayana , Rao K. Kuppuswamy
Published: April 2009

Ostrom proposed classifications of translation planes on the basis of the action of the collineation group of the plane on the ideal points. There are examples of translation planes in which ideal points form a single orbit (flag transitive planes) and also several orbits (Hall, André, Foulser, and so forth, planes). In this paper the authors have constructed a translation plane in which the ideal points are divided into two orbits of lengths 18 and 8 respectively. A few collineatlons are computed together with their actions. The group of collineations G1 which is transitive on the two sets of 18 and 8 lines separately is calculated. All the collineations that fix L0 are also calculated and they form a group of. If G2 is the group of translations then the full collineation group is shown to be 〈G1, G2, G3〉.
On loop near-rings
Authors: Ramakotaiah D. , Santhakumari C.
Published: April 2009

A new class of algebraic systems known as loop near-rings are introduced, which includes near-rings and consequently rings. Different types of radicals are introduced in a loop near-ring N which coincide with the Jacobson radical when N happens to be a ring, and several characterizations of these radicals are obtained.
A complex nonlinear complementarity problem
Authors: Nanda Sribatsa , Nanda Sudarsan
Published: April 2009

In this paper we study the existence and uniqueness of solutions for the following complex nonlinear complementarity problem: find z ∈ S such that g(z) ∈ S* and re(g(z), z) = 0, where S is a closed convex cone in Cn, S* the polar cone, and g is a continuous function from Cn into itself. We show that the existence of a z ∈ S with g(z) ∈ int S* implies the existence of a solution to the nonlinear complementarity problem if g is monotone on S and the solution is unique if g is strictly monotone. We also show that the above problem has a unique solution if the mapping g is strongly monotone on S.
An extension of Pontryagin duality
Authors: Day B.J.
Published: April 2009

Let V denote the symmetric monoidal closed category of limit-space abelian groups and let L denote the full subcategory of locally compact Hausdorff abelian groups. Results of Samuel Kaplan on extension of characters to products of L–groups are used to show that each closed subgroup of a product of L-groups is a limit of L–groups. From this we deduce that the limit closure of L in V is reflective in V and has every group Pontryagin reflexive with respect to the structure of continuous convergence on the character groups. The basic duality L ≃ Lop is then extended.
Groups of exponent eight
Authors: Grunewald Fritz J. , Havas George , Mennicke J.L. , Newman M.F.
Published: April 2009

This paper is a survey of the current state of knowledge on groups of exponent 8. It contains a report on a first stage of an attempt to answer the Burnside questions for these groups.
Indecomposable representations of certain commutative quivers
Authors: Donovan P.W. , Freislich M.-R.
Published: April 2009

This paper gives a detailed classification of the indecomposable representations of one non-trivial “commutative quiver”, gives brief details of certain generalisations, and uses methods likely to be more widely applicable.
Isometric multipliers of Segal algebras
Authors: Parthasarathy K. , Tewari U.B.
Published: April 2009

We prove that for a large class of Segal algebras, the isometric multipliers consist of scalar multiples of translation operators.
Interpolation in triangles
Authors: Nielson G.M. , Thomas D.H. , Wixom J.A.
Published: April 2009

Several new methods of approximation which assume arbitrary values on the boundary of a triangular domain are presented. All of the methods are affine invariant and have optimal algebraic precision. Nine parameter discrete interpolants which result from these methods are also given.
Continuity of Cima and Rung's extension and non normal meromorphic functions
Authors: Campbell Douglas M.
Published: April 2009

A function meromorphic in |z| < 1 is constructed such that on every curve in |z| < 1 which goes to |z| = 1 the set of limit points of the function is the entire complex plane. This example is used to prove the existence of non-normal meromorphic functions in |z| < 1 which have continuous set valued extensions. Cima and Rung had introduced a set valued extension for meromorphic functions and proved that all normal meromorphic functions have a continuous extension while all functions with a continuous extension have the Lindelöf property. For a long time it was thought that this might characterize normal meromorphic functions. This paper proves that it is not possible to determine the normality of a meromorphic function by the continuity of Cima and Rung's set valued extension. The paper closes with the open problem: do there exist non-normal analytic functions for which Cima and Rung's set valued extension is continuous?
Indecomposable 2-groups with all automorphisms central
Authors: Curran M.J.
Published: April 2009

This paper provides examples of indecomposable 2-groups with non-abelian automorphism groups in which every automorphism is central.
A note on arewise connected sets and functions
Authors: Yadav Shri Ram , Mukherjee R.N.
Published: April 2009

We introduce a new class of generalized arcwise connected functions and discuss their basic properties. Our generalization is illustrated by an example and an application is given for a mathematical programming problem involving this new class of functions.
A crossing theorem for distribution functions and their moments
Authors: MacGillivray H.L.
Published: April 2009

It is proved here that for two distribution functions with equal moments up to ordern, the number of crossings is at leastn, and if exactlyn, the remaining odd or even moments (forneven or odd respectively) do not cross again. This both generalises and extends a number of previous results.
On the basis number of some complete bipartite graphs
Authors: McCall J.
Published: April 2009

This note completes the determination of the basis numbers of the complete bipartite graphs.
Groups with no nontrivial linear representations
Authors: Derrick A.J.
Published: April 2009

We study the class of groups having no nontrivial linear representations over certain fields. After showing the class to be closed under perfect extensions with locally soluble kernel, we expand considerably the number of acyclic groups known to be in the class, by application to both binate groups and the acyclic automorphism groups of de la Harpe and McDuff.
On the meromorphic solutions of some functional equations
Authors: Chen Jianhua , Qiao Jianyong , Zhang Wenjun
Published: April 2009

Let f(z) be a meromorphic function, let P(z) and Q(z) be two polynomials. We shall investigate the asymptotic behaviour of the ratio T(r, f(P))/T(r, f(Q)), and discuss the growth of the meromorphic solutions of some functional equations.
Group extensions are quasi-simply-filtrated
Authors: Brick S.G. , Mihalik M.L.
Published: April 2009

A finitely presented group G is quasi-simply-filtrated (abbreviated qsf) if, given a finite complex with fundamental group G, the universal cover of the complex can be “approximated” by simply connected finite complexes. This notion is a generalisation of a concept of Casson's used in the study of three-manifolds.

In this paper we show that any extension of a finitely presented infinite group by a finitely presented infinite group is qsf.
Towards a calculus of algorithms
Authors: Bulmer M. , Fearnley-Sander D. , Stokes T.
Published: April 2009

We develop a generalised polynomial formalism which captures the concept of an algebra of piece-wise denned polynomials. The formalism is based on the Boolean power construction of universal algebra. A generalisation of the theory of substitution homomorphisms is developed. The abstract operation of composition of generalised polynomials in one variable is denned and shown to correspond to function composition.
A simple proof of an identity of Pethe and Horadam
Authors: Chen Kuo-Jye
Published: April 2009

An identity for two generalised Tribonacci sequences is obtained. Earlier identities by Pethe and Horadam follow as special cases.
Convergence of relaxed chaotic parallel iterative methods
Authors: Kloeden Peter E. , Yuan Dong-Jin
Published: April 2009

Sufficient conditions involving uniform multisplittings are established for the convergence of relaxed and AOR versions of asynchronous or chaotic parallel iterative methods for solving a large scale nonsingular system of linear equations Ax = b.
On the properties of an integral operator
Authors: Jakubowski Zbigniew Jerzy
Published: April 2009

The main aim of the paper is to examine the properties of the integral operator, α ∈C, defined on some classes of functionsunivalent and convex in the disc |z| < 1. As special cases we obtain results of Kim and Merkes and of Kumar and Shukla.
Joint Browder spectra and tensor products
Authors: Dash A.T.
Published: April 2009

There exists in the literature several notions of joint spectra which can be generalized to joint Browder spectra. The purpose of this note is to show that various notions of joint Browder spectra coincide for a special class of operators.
The minimal number of periodic orbits of periods guaranteed in Sharkovskii's theorem: Corrigendum
Authors: Du Bau-Sen
Published: April 2009

In Theorem 2 of [1] conclusion (c) should read:

(c) lim(log[Φn(m)/(m])/m=log λn, where λn is the (unique) m→∞ positive (and the largest in absolute value) zero of the x2n+1 − x2n+1 − 1.
Some properties of the lattice of subalgebras of a Boolean algebra
Authors: Düntsch Ivo
Published: April 2009

We investigate the structure of the lattice of subalgebras of an infinite Boolean algebra; in particular, we make a contribution to the question as to when such a lattice is simple.
Blaschke-type maps and harmonic majoration on Riemann surfaces
Authors: Yamashita Shinji
Published: April 2009

An analytic map h of type Bl from a Riemann surface R into another S, both having Greens functions, behaves well near the “boundaryr” of R. Let X stand for a family of holomorphic functions, and let f be holomorphic on S. We shall show, for several X′s, the following:

(i) f ∈ X(S) ⇔ foh ⇔ X(R);

‖foh‖ = ‖f‖.

Use is made of harmonic majoration of subharmonic functions on R and on S.
The kernel of the cup product
Authors: Hillman Jonathan A.
Published: April 2009

We relate the kernel of the cup product of 1-dimensional cohomology classes for a group G acting trivially on a field R to Hom(G2/G3,R), the space of group homomorphisms of the second stage of the lower central series for G into R, by means of explicit computations with cocycles. The precise result depends on whether the characteristic of the field is 0, an odd prime or 2.
A complete classification of dynamical symmetries in classical mechanics
Authors: Prince Geoff
Published: April 2009

This paper deals with the interaction between the invariance group of a second order differential equation and its variational formulation. In particular I construct equivalent Lagrangians from all such group actions, thereby successfully completing an earlier attempt of mine which dealt with some traditionally important classes of actions.
Central automorphisms of finite groups
Authors: Curran M. J. , McCaughan D. J.
Published: April 2009

This paper considers an aspect of the general problem of how the structure of a group influences the structure of its automorphisms group. A recent result of Beisiegel shows that if P is a p-group then the central automorphisms group of P has no normal subgroups of order prime to p. So, roughly speaking, most of the central automorphisms are of p-power order. This generalizes an old result of Hopkins that if Aut P is abelian (so every automorphisms is central), then Aut P is a p-group.

This paper uses a different approach to consider the case when P is a π-group. It is shown that the central automorphism group of P has a normal. π′-subgroup only if P has an abelian direct factor whose automorphism group has such a subgroup.