bluuebunny/crossref_metadata_2025 huggingface dataset:
On the propagation, reflection, and transmission of transient cylindrical shear waves in nonhomogeneous four-parameter viscoelastic media
Authors: Moodie T. Bryant
Published: April 2009

The purpose of this paper is to study the propagation of cylindrical shear waves in nonhomogeneous four-parameter viscoelastic plates of arbitrary thickness. The plates have a transverse cylindrical hole and their material properties are functions of the radial distance from the center of this opening. They are initially unstressed and at rest. A suddenly rising shearing traction is applied uniformly over the boundary of the opening and parallel to the faces of the plates and thereafter steadily maintained; they are otherwise free from loading. We consider both the case of a finite plate with a stress-free cylindrical outer boundary, and an infinite plate composed of two media in welded contact along a cylindrical surface symmetrical with respect to the center of the opening. We find that a reflected pulse is produced at the outer boundary of the finite plate while reflected and transmitted pulses are produced at the interface in the infinite bi-viscoelastic plate. Ray techniques are used throughout, and formal asymptotic wavefront expansions of the solution functions are obtained.
On the units of a modular group ring II
Authors: Pearson K.R.
Published: April 2009

Let R be a ring of nonzero characteristic and let G be a finite group with subgroup H. It is shown that H is a normal subgroup of the group of units of the group ring RG if and only if H is contained in the centre of G or R is the field with 2 elements, G is the symmetric group on 3 letters and H is normal in G.
Trifactorisable groups
Authors: Pennington Elizabeth
Published: April 2009

The group G is called trifactorisable if G has three subgroups, A, B, and C such that G = AB = BC = CA. Obviously the structure of the group G will be restricted by the structure of these subgroups. In this paper it will be shown that a finite group G is π-separable if and only if it satisfies Dπ and has a trifactorisation with two factors π closed and the third, C say, π-separable. In this case we show that the π- and π′-lengths of G can be at most one more than those of C, and so it is this factor which “controls” the structure of G. Similar results are proved for π-solubility and solubility.
When projective covers and injective hulls are isomorphic
Authors: Boyle Ann K.
Published: April 2009

It is shown that rings in which the projective cover and injective hull of cyclic modules are isomorphic are equivalent to uniserial rings. Further, it is shown that rings for which the top and bottom of finitely generated modules are isomorphic also are equivalent to uniserial rings.
Extensions of a semilattice by an inverse semigroup
Authors: Green D.G.
Published: April 2009

The structure of inverse semigroup extensions of one inverse semigroup R by any other is analyzed in the case where R is a semilattice. Both a representation and method of construction are given. A brief preliminary examination is made of a certain class of congruences, on inverse semigroups, which are intimately related to such extensions.
Remark on a theorem of E.H. Brown
Authors: Alder Michael D.
Published: April 2009

The proliferation of classifying spaces in recent years owes much to the theorem of Edgar H. Brown, Jr on the representability of homotopy functors. Since the theorem only gives a representation for functors defined on the category of spaces having the homotopy type of a CW complex, there is some interest in finding conditions under which the domain category may be enlarged. It appears that a version of the theorem holds for any small full subcategory of Htp, the category of topological spaces and homotopy classes of continuous maps, but that the resulting classifying space is generally intractable.
Quasi proximal continuity
Authors: Lambrinos Panayotis Th.
Published: April 2009

Conditions are given, under which a quasi-proximally continuous function is quasi-uniformly continuous, or a continuous function is quasi-proximally continuous. Thus, basic results on uniform and proximal continuity are extended and some new results are obtained. Three results in the literature are shown to be false.
A final remark on extending to strict total orders in modules
Authors: Fleischer Isidore
Published: April 2009

The remark is that the recent work in this Bulletin dealing with the extension of a partial to a total strict order on a module over a partially ordered ring falls under standard order extension results for operator groups once it is noted that the added requirement of strictness just comes to injective operation of the positive scalars. These standard results are in turn generalized to a universal algebra setting.
Differential equations in Banach spaces
Authors: Noussair E.S.
Published: April 2009

Let H be a fixed Hilbert space and B(H, H) be the Banach space of bounded linear operators from H to H with the uniform operator topology. Oscillation criteria are obtained for the operator differential equation

where the coefficients A, C are linear operators from B(H, H) to B(H, H), for each t ≤ 0. A solution Y: R+ → B(H, H) is said to be oscillatory if there exists a sequence of points ti ∈ R+, so that ti → ∞ as i → ∞, and Y(ti) fails to have a bounded inverse. The main theorem states that a solution Y is oscillatory if an associated scalar differential equation is oscillatory.
On a random solution of a nonlinear perturbed stochastic integral equation of the Volterra type
Authors: Milton J. Susan , Tsokos Chris P.
Published: April 2009

The object of this present paper is to study a nonlinear perturbed stochastic integral equation of the form

where ω ∈ Ω, the supporting set of the complete probability measure space (Ω A, μ). We are concerned with the existence and uniqueness of a random solution to the above equation. A random solution, x(t; ω), of the above equation is defined to be a vector random variable which satisfies the equation μ almost everywhere.
On saturated formations whose projectors are complemented
Authors: Makan A.R.
Published: April 2009

It is shown that a saturated formation F has the property that in each group G each F-projector of G is complemented if and only if F is the formation of finite soluble π-groups for some set π of primes.
On the complex complementarity problem
Authors: Mond Bertram
Published: April 2009

The complex linear complementarity problem considered here is the following: Find z such that

where S is a polyhedral convex cone in Cp, S* the polar cone, M ∈ Cp×p and q ∈ Cp.

Generalizing earlier results in real and complex space, it is shown that if M satisfies RezHMz ≥ 0 for all z ∈ Cp and if the set satisfying Mz + q ∈ S*, z ∈ S is not empty, then a solution to the complex linear complementarity problem exists. If RezHMz > 0 unless z = 0, then a solution to this problem always exists.
Finite groups which are the product of two nilpotent subgroups
Authors: Gross Fletcher
Published: April 2009

Suppose G = AB where G is a finite group and A and B are nilpotent subgroups. It is proved that the derived length of G modulo its Frattini subgroup is at most the sum of the classes of A and B. An upper bound for the derived length of G in terms of the derived lengths of A and B also is obtained.
A converse of Bernstein's inequality for locally compact groups
Authors: Bloom Walter R.
Published: April 2009

Let G be a Hausdorff locally compact abelian group, Γ its character group. We shall prove that, if S is a translation-invariant subspace of Lp (G) (p ∈ [1, ∞]),

for each a ∈ G and , then is relatively compact (where Σ(f) denotes the spectrum of f). We also obtain a similar result when G is a Hausdorff compact (not necessarily abelian) group. These results can be considered as a converse of Bernstein's inequality for locally compact groups.
Uniform convergence and everywhere convergence of Fourier series. I
Authors: Izumi Masako , Izumi Shin-ichi
Published: April 2009

Carleson and Hunt proved that the space of functions with almost everywhere convergent Fourier series contains Lp (p > l) as a subspace. We shall give two kinds of subspaces of the spaces of functions with everywhere convergent or uniformly convergent Fourier series.
On groups admitting a noncyclic abelian automorphism group
Authors: Ward J.N.
Published: April 2009

It is shown that a condition of Kurzwell concerning fixed-points of certain operators on a finite group G is sufficient to ensure that G is soluble. The result generalizes those of Martineau on elementary abelian fixed-point-free operator groups.
Nilpotent signalizer functors on finite groups
Authors: Ward J.N.
Published: April 2009

In a recent paper Martineau has shown that the study of groups with a fixed-point-free automorphism group can be applied to help in the investigation of signalizer functors. We prove further results about signalizer functors by this method.
Hermite-Fejer interpolation at the ‘practical’ Chebyshev nodes
Authors: Riess R.D.
Published: April 2009

Berman has raised the question in his work of whether Hermite-Fejér interpolation based on the so-called “practical” Chebyshev points, , 0(1)n, is uniformly convergent for all continuous functions on the interval [−1, 1]. In spite of similar negative results by Berman and Szegö, this paper shows this result is true, which is in accord with the great similarities of Lagrangian interpolation based on these points versus the points , 1(1)n.
Computer results on Burnside groups
Authors: Macdonald I.D.
Published: April 2009

Power and commutator structure tables are obtained for a number of factor groups of Burnside groups.
How a rare species might become a pest
Authors: Diamond Phil
Published: April 2009

A model is proposed for the population growth of a rare species after predation pressure is lifted. A geometric probability argument is used to suggest that, as population density increases, breeding encounters become more frequent and the consequent rate of increase is much steeper than the exponential. This may explain the population explosion of crown-of-thorns starfish recorded recently.
The determination of Fibonacci groups
Authors: Brunner A.M.
Published: April 2009

Fibonacci groups are the groups

where r is a natural number. The groups F(2, 8) and F(2, 10) are shown to he infinite, thus leaving F(2, 9) as the only Fibonacci group whose finiteness or infiniteness has not been determined.
Two fixed point theorems and invariant integrals
Authors: Cooper T.J. , Michael J.H.
Published: April 2009

Two fixed point theorems for a subset C of a normed vector space X are established by using the concept of centre. These results differ from previous fixed point theorems in that X is assumed to have a topology T as well as a norm. The norm is required to be lower semi-continuous with respect to T and C is required to be convex, bounded with respect to the norm and compact with respect to T.
The order completeness of some spaces of vector-valued functions
Authors: Cartwright Donald I.
Published: April 2009

Let E be a Banach lattice. Necessary and sufficient conditions are given for the order completeness of the Banach lattices C(X, E) and L1(μ, E) in terms of the compactness of the order intervals in E. The results have interpretations in terms of spaces of compact and nuclear operators.
Padé approximation and gaussian quadrature
Authors: Allen G.D. , Chui C.K. , Madych W.R. , Narcowich F.J. , Smith P.W.
Published: April 2009

For certain types of formal power series, including the series of Stieltjes, we prove that the [n, n+j], j ≥ −1, Padé approximants coincide with certain gaussian quadrature formulae and hence, convergence of these approximants follows immediately.
Isoclinisms and covering groups
Authors: Jones Michael R. , Wiegold James
Published: April 2009

The article examines the connection between the concepts of isoclinism and covering groups for finite groups. The main result is that all covering groups for a given finite group are mutually isoclinic. The converse is false.
Regular completions of Cauchy spaces via function algebras
Authors: Gazik R.J. , Kent D.C.
Published: April 2009

A regular completion with the universal property is obtained for each member of a certain class of Cauchy spaces by embedding the Cauchy space in a complete function algebra with the continuous convergence structure.
Metabelian groups with the same finite quotients
Authors: Pickel P.F.
Published: April 2009

Let F(G) denote the set of isomorphism classes of finite quotients of the group G. Two groups G and H are said to have the same finite quotients if F(G) = F(H). We construct infinitely many nonisomorphic finitely presented metabelian groups with the same finite quotients, using modules over a suitably chosen ring. These groups also give an example of infinitely many nonisomorphic split extensions of a fixed finitely presented metabelian group by a fixed finite abelian group, all having the same finite quotients.
An integral representation for a generalised variation of a function
Authors: Russell A.M.
Published: April 2009

In this note we present sufficient conditions for the continuity of the total kth variation of a function defined on a closed interval [a, b]. We also give an integral representation for total feth variation, thus obtaining an extension of the classical result
A note on simultaneous polynomial approximation of exponential functions
Authors: Loxton J.H. , van der Poorten A.J.
Published: April 2009

Let α1, …, αmbe distinct complex numbers and τ(1), …, τ(m) be non-negative integers. We obtain conditions under which the functions

form a perfect system, that is, for every set ρ(1), …, ρ(m) of non-negative integers, there are polynomialsa1(z), …,am(z) with respective degrees exactly ρ(1)−1, …, ρ(m)−1, such that the function

has a zero of order at least ρ(1) + … + ρ(m)−1 at the origin. Moreover, subject to the evaluation of certain determinants, we give explicit formulae for the approximating polynomialsa1(z), …,am(z).
A note on regular modules
Authors: Ramamurthi V.S.
Published: April 2009

Kaplansky's observation, namely, a commutative ring R is (von Neumann) regular if and only if each simple R-module is injective, is generalized to projective modules over a commutative ring.
Mercer's Theorem and Fredholm resolvents
Authors: Withers C.S.
Published: April 2009

Multivariate versions of Mercer's Theorem and the usual expansions of the resolvent and Fredholm determinant are shown to hold for an n × n symmetric kernel N(x, y) with arbitrary domain in Rp under weakened continuity conditions. Further, the resolvent and determinant of N(x, y) − a(x)b(y) are given in terms of those of N(x, y).
Multifunctions of Souslin type
Authors: Leese S.J.
Published: April 2009

LetSandXbe any two sets; then a mapping Γ which assigns to each pointtinSa set Γ(t) of points inXis called amultifunctionfromSintoX. Aselectorfor Γ is a functionffromSintoXsuch thatf(t)∈ Γ(t) for eacht. We introduce here a class of multifunctions which is both well-supplied with measurable selectors and yet is comprehensive enough to include those kinds of multifunction which have been most commonly studied before. Hence in order to show that a multifunction with non-empty values, which may arise naturally in an implicit function problem, has a measurable selector, it is sufficient to show that it is of Souslin type.
Regular completions of uniform convergence spaces
Authors: Gazik R.J. , Kent D.C. , Richardson G.D.
Published: April 2009

A regular completion with universal property is obtained for each member of the class ofu–embedded uniform convergence spaces, a class which includes the Hausdorff uniform spaces. This completion is obtained by embedding eachu-embedded uniform convergence space (X,I) into the dual space of a complete function algebra composed of the uniformly continuous functions from (X,I) into the real line.
On equidistant sets in normed linear spaces
Authors: Panda B.B. , Kapoor O.P.
Published: April 2009

In this note some results concerning the equidistant setE(−x, x) and the kernelMθof the metric projectionPM, whereMis a Chebyshev subspace of a normed linear spaceX, have been obtained. In particular, whenX=lp(1 <p< ∞), it has been proved that every equidistant set is closed in thebw-topology of the space. Inc0no equidistant set has this property.
The free topological group on a cell complex
Authors: Hardy J.P.L.
Published: April 2009

It is proved that the free k-group on a CW-complex X is itself a CW-complex containing X as a subcomplex. It follows, as a corollary, that the free topological group on a countable CW-complex is a countable CW-complex.
Non-local rings whose ideals are all quasi-injective
Authors: Ivanov G.
Published: April 2009

A ring is a left Q-ring if all of its left ideals are quasi-injective. For an integer m ≤ 2, a sfield D, and a null D-algebra V whose left and right D-dimensions are both equal to one, let H(m, D, V) be the ring of all m x m matrices whose only non-zero entries are arbitrary elements of D along the diagonal and arbitrary elements of V at the places (2, 1), …, (m, m-l) and (l, m). We show that the only indecomposable non-local left Q-rings are the simple artinian rings and the rings H(m, D, V). An arbitrary left Q-ring is the direct sum of a finite number of indecomposable non-local left Q-rings and a Q-ring whose idempotents are all central.
Sequences defined as minima of two Fibonacci-type relations
Authors: Booth R.S.
Published: April 2009

If {Ln} is a sequence defined by
Ln = min {Ln-a +Ln-b, Ln-c +Ln-d},
with a, b, c, d positive integers, then one can ask if necessarily Ln = Ln-b + Ln-b, for all sufficiently large n.

The answer is yes if a and b are relatively prime, Ln > 0 initially, and λ < μ, where λ-a + λ-b = 1, μ-c + μ-d = 1. The answer is no if instead a and b have greatest common divisor k ≥2, with c ≡ 0 (mod k), d ≢ 0 (mod k).
Laminar forced convection at low Péclet number. II
Authors: Jones A.S.
Published: April 2009

In this paper, the problem of heat transfer to laminar Poiseuille flow in a circular tube is discussed for the case of an insulated tube with a ring source of heat on the boundary. The solution is developed analytically for low values of the Péclet number, and formulae for calculating the eigenvalues and coefficients have been obtained. The temperature distributions in the neighbourhood of the source have been calculated for two values of the Péclet number. The extension to the case of arbitrary wall flux has also been discussed.
A characterization of pre-near-standardness in locally convex linear topological spaces
Authors: Chadwick J.J.M. , Cross R.W.
Published: April 2009

Let X be a locally convex linear topological space. A point z in an ultralimit enlargement of X is pre-near-standard if and only it is finite and for every equicontinuous subset S′ of the dual space X′, a point z′ belongs to *S′ ∩ μσ(X′, X) (0) only if z′ (z) is infinitesimal.
Inequalities connecting the eigenvalues of a hermitian matrix with the eigenvalues of complementary principal submatrices
Authors: Thompson Robert C. , Therianos S.
Published: April 2009

Let be a hermitian matrix in partitioned form. Let the eigenvalues of A, B, C be α1 ≥ … ≥ αa, β1 ≥ … ≥ βb, γ1 ≥ … ≥ γn, respectively. In this paper four classes of inequalities are proved comparing the αi. and βj with the γk. The simplest of these is:

if the subscripts is, js satisfy 1 ≤ i1 < … < im ≤ α, 1 ≤ j1 < … < jm ≤ b.
Diffraction of planetary waves by a semi-infinite plate
Authors: Siew P.P. , Hurley D.G.
Published: April 2009

In this paper the diffraction of a planetary wave by a semi-infinite plate of arbitrary inclination is investigated using a β-plane approximation. The Wiener-Hopf technique is used to obtain an integral representation of the solution and an asymptotic description of the diffracted wave is obtained by the method of steepest descent.
Local analytic structure in certain commutative topological algebras
Authors: Loy R.J.
Published: April 2009

Let B be a topological algebra with Fréchet space topology, A an algebra with locally convex topology and an algebra of formal power series over A in n commuting indeterminates which carries a Fréchet space topology. In a previous paper the author showed, for the case n = 1, that a homomorphism of B into whose range contains polynomials is necessarily continuous provided the coordinate projections of into A satisfy a certain equicontinuity condition. This result is here extended to the case of general n, and also to weaker topological assumptions.
Profinite posets
Authors: Speed T.P.
Published: April 2009

The class of ordered topological spaces which are projective limits of finite partially ordered sets (equipped with the restriction of the product of the discrete topologies) is shown to coincide with the class of compact totally order-disconnected ordered topological spaces. Hence this is another category of spaces equivalent to the category of distributive lattices with zero and unit.
Inequalities related to those of Hausdorff-Young
Authors: Edwards R.E.
Published: April 2009

This note establishes the impossibility of certain inequalities of the form

holding for all trigonometric polynomials f on an infinite compact abelian group G. From this is deduced the impossibility of corresponding inclusion relations of the type

or

where FS denotes the Fourier image of the set S of integrable functions on G.
The Fitting length of a finite soluble group and the number of conjugacy classes of its maximal nilpotent subgroups
Authors: Makan A.R.
Published: April 2009

It is shown that there exists a logarithmic upper bound on the Fitting length h(G) of a finite soluble group G in terms of the number ν(G) of the conjugacy classes of its maximal nilpotent subgroups. For ν(G) = 3, the best possible bound on h(G) is shown to be 4.
On the maximal normal prime-nilpotent subgroup of a prime-solvable group
Authors: Gagen Terence M. , Hale Mark P.
Published: April 2009

A characterization of the maximal normal p-nilpotent subgroup of a finite p-solvable group is obtained for primes p ≠ 2 or 3.
The subnormal structure of metanilpotent groups
Authors: McCaughan D.J. , McDougall D.
Published: April 2009

LetGbe a group with a normal nilpotent subgroupNsuch thatG/Nis periodic and nilpotent. IfG(p)/Nis the Sylowp-subgroup ofG/NandQ(p) is the maximalp-radicable subgroup ofN, it is shown thatGhas a bound on the subnormal indices of its subnormal subgroups if and only if there is a positive integercsuch thatG(p)/Q(p) is nilpotent of class at mostc, for all primesp. It is also shown that ifGis a periodic metanilpotent group andQis its maximal radicable abelian normal subgroup thenGhas a bound on its subnormal indices if and only if there is a positive integercsuch that for all primespthe Sylowp-subgroups ofG/Qare nilpotent of class at mostc.
Functions of asymptotic expansions
Authors: Love E.R.
Published: April 2009

Led on by a paper of Brown and Dancer with the same title, this paper gives two further theorems on asymptotic expansions of composite functions.
Some definitions of finiteness: Corrigenda
Authors: Hickman J.L.
Published: April 2009

The statements of Lemma 3 and Lemma 4 in [1] are incorrect. They should read as follows.

LEMMA 3.

LEMMA 4.
Asymptotic analysis of a linearized trailing edge flow
Authors: Capell K.
Published: April 2009

An Oseén type linearization of the Navier-Stokes equations is made with respect to a uniform shear flow at the trailing edge of a flat plate. Asymptotic expansions are obtained to describe a symmetrical merging flow for distances from the trailing edge that are, in a certain sense, large. Expansions for three regions are found:

(i) a wake region,

(ii) an inviscid region, and

(iii) an upstream lower order boundary layer.

The results are compared with those of Hakkinen and O'Neil (Douglas Aircraft Co. Report, 1967) and Stewartson (Proc. Roy. Soc. Ser. A 306 (1968)). They are further related to the results of Stewartson (Mathematika 16 (1969)) and Messiter (SIAM J. Appl. Math. 18 (1970)).
Maximal sum-free sets in abelian groups of order divisible by three
Authors: Street Anne Penfold
Published: April 2009

A subset S of an additive group G is called a maximal sum-free set in G if (S+S) nS = Φ and |S| ≥ |T| for every sum-free set T in G. In this note, we prove a conjecture of Yap concerning the structure of maximal sum-free sets in finite abelian groups of order divisible by 3 but not divisible by any prime congruent to 2 modulo 3.
On the commutativity of near-rings III
Authors: Ligh Steve
Published: April 2009

Part of the recent work on near-rings has been concerned with sufficient conditions for near-rings to be commutative. Recently Howard E. Bell proved that if a d.g. near-ring R has an identity and for each x, y in R, there exists an n(x, y) > 1, such that (xy−yx)n(x, y) = xy − yx, then R is a commutative ring. In this paper we drop the requirement that R has an identity and show that the other condition is sufficient (and necessary) for R to be commutative. The inspiration for an important lemma, comes from a result of B.H. Neumann.
Aspects of topoi
Authors: Freyd Peter
Published: April 2009

After a review of the work of Lawvere and Tierney, it is shown that every topos may be exactly embedded in a product of topoi each with 1 as a generator, and near-exactly embedded in a power of the category of sets. Several metatheorems are then derived. Natural numbers objects are shown to be characterized by exactness properties, which yield the fact that some topoi can not be exactly embedded in powers of the category of sets, indeed that the “arithmetic” arising from a topos dominates the exactness theory. Finally, several, necessarily non-elementary, conditions are shown to imply exact embedding in powers of the category of sets.
On complemented chief factors of finite soluble groups
Authors: Barnes D.W.
Published: April 2009

Let G = H0 > H1 > … > Hr = 1 and G = K0 > K1 > … > Kr =1 be two chief series of the finite soluble group G. Suppose Mi complements Hi/Hi+1. Then Mi also complements precisely one factor Kj/Kj+1, of the second series, and this Kj/Kj+1 is G-isomorphic to Hi/Hi+1. It is shown that complements Mi can be chosen for the complemented factors Hi/Hi+1 of the first series in such a way that distinct Mi complement distinct factors of the second series, thus establishing a one-to-one correspondence between the complemented factors of the two series. It is also shown that there is a one-to-one correspondence between the factors of the two series (but not in general constructible in the above manner), such that corresponding factors are G-isomorphic and have the same number of complements.
Residual properties of free groups II
Authors: Pride Stephen J.
Published: April 2009

In this paper it is proved that non-abelian free groups are residually (x, y | xm = 1, yn = 1, xk = yh} if and only if min{(m, k), (n, h)} is greater than 1, and not both of (m, k) and (n, h) are 2 (where 0 is taken as greater than any natural number). The proof makes use of a result, possibly of independent interest, concerning the existence of certain automorphisms of the free group of rank two. A useful criterion which enables one to prove that non-abelian free groups are residually G for a large number of groups G is also given.
An algebraic characterization of symmetric graphs with a prime number of vertices
Authors: Berggren J.L.
Published: April 2009

A graph Γ is called symmetric if its automorphism group is transitive on its vertices and edges. Let p be an odd prime, Z(p) the field of integers modulo p, and Z*(p) = (a ∈ Z(p) | a ≠ 0}, the multiplicative subgroup of Z(p). This paper gives a simple proof of the equivalence of two statements:

(1) Γ is a symmetric graph with p vertices, each having degree n ≥ 1;

(2) the integer n is an even divisor of p − 1 and Γ is isomorphic to the graph whose vertices are the elements of Z(p) and whose edges are the pairs {a, a+h} where a ∈ Z(p) and h ∈ H, the unique subgroup of Z*(p) of order n.

In addition, the automorphism group of Γ is determined.
A note on a result of K.D. Magill, Jr
Authors: Warren Eric , Yamamuro S.
Published: April 2009

The result of Magill concerning differentiable maps on the reals; namely, that all automorphisms of this semigroup are inner; is shown to be untrue in the case of analytic maps on the complexes. Also a characterization of the inner automorphisms of the analytic maps is given.
Sufficient conditions for a continuous linear operator to be weakly compact
Authors: Howard Joe , Melendez Kenneth
Published: April 2009

A locally convex topological vector (LCTV) space E is said to have property V (Dieudonné property) if for every complete separated LCTV space F, every unconditionally converging (weakly completely continuous) operator T: E → F is wsakly compact. First, an investigation of the permanence of property V is given. The permanence of the Dieudonné is analogous. Relationships between property V and the Dieudonné property are then given.
Classical groups over division rings of characteristic two: Corrigenda and an acknowledgement
Authors: Pender William M.
Published: April 2009

In my paper [1], part (b) of Lemma 3.4 and the remark following it are incorrect and should be omitted.

The isometry P in page 215, line 2, need not be a generator of T(E, q) as asserted, but can be shown to lie in T(E, q).

I am indebted to Professor Tits for pointing out that extended ideas of quadratic forms have already appeared in his paper [2] and in Wall's paper [3]. Professor Tits also discusses the corresponding groups and Clifford algebras in detail.
Mean-square stability of a class of stochastic integral equations
Authors: Padgett W.J.
Published: April 2009

The object of this paper is to investigate under very general conditions the existence and mean-square stability of a random solution of a class of stochastic integral equations in the form

for t ≥ 0, where a random solution is a second order stochastic process {x(t; w) t ≥ 0} which satisfies the equation almost certainly. A random solution x(t; w) is defined to be stable in mean-square if E[|x(t; w)|2] ≤ p for all t ≥ 0 and some p > 0 or exponentially stable in mean-square if E[|x(t; w)|2] ≤ pe-at, t ≥ 0, for some constants ρ > 0 and α > 0.
Transversals of squares
Authors: Williams N.H.
Published: April 2009

Let κ and λ be cardinal numbers. Take any family A = {Aν; ν ∈ N} where each Aν is a product Aν = Bν x Cν with |Bν = |Cν| = Nα, such that if B x CAμ x Aν (for μ ≠ ν) then |B|, |c| < λ. We investigate under what conditions on α, κ, λ and |N| there will be a set T with 1 ≤ |T∩Aν| < κ for each ν.
Epireflection operators vs perfect morphisms and closed classes of epimorphisms
Authors: Strecker G.E.
Published: April 2009

Operators are defined that yield basic Galois closure operations for almost every category. These give rise to a new and more general approach for characterization of epireflective subcategories, and construction of epireflective hulls. As a by-product, satisfactory characterizations of classes of perfect morphisms and ω-extendable epimorphisms are obtained. Detailed proofs and examples will appear elsewhere.
Maximal perfect spaces
Authors: Baggs Ivan
Published: April 2009

Let (X, T) be a topological space (we assume T1. throughout) where every point is a limit point. The purpose of this note is to present an internal construction of a maximal perfect topology on (X, T). The existence of a maximal connected Hausdorff space has not been demonstrated. However, this construction of a maximal perfect topology is useful in constructing connected Hausdorff spaces which cannot be embedded in a maximal connected Hausdorff space.
Note on monoidal localisation
Authors: Day Brian
Published: April 2009

If a class Z of morphisms in a monoidal category A is closed under tensoring with the objects of A then the category obtained by inverting the morphisms in Z is monoidal. We note the immediate properties of this induced structure. The main application describes monoidal completions in terms of the ordinary category completions introduced by Applegate and Tierney. This application in turn suggests a “change-of-universe” procedure for category theory based on a given monoidal closed category. Several features of this procedure are discussed.
Cancellative medial groupoids and arithmetic means
Authors: Howroyd T.
Published: April 2009

It is shown that a homomorphism from a commutative, idempotent and medial groupoid with a reducible set of generators into another medial groupoid may be characterized by certain simultaneous equations. This result is used to characterize the arithmetic mean without introducing either continuity or order.
The computability of group constructions II
Authors: Gatterdam R.W.
Published: April 2009

Finitely presented groups having word, problem solvable by functions in the relativized Grzegorczyk hierarchy, {En(A)| n ε N, A ⊂ N (N the natural numbers)} are studied. Basically the class E3 consists of the elementary functions of Kalmar and En+1 is obtained from En by unbounded recursion. The relativization En(A) is obtained by adjoining the characteristic function of A to the class En.

It is shown that the Higman construction embedding, a finitely generated group with a recursively enumerable set of relations into a finitely presented group, preserves the computational level of the word problem with respect to the relativized Grzegorczyk hierarchy. As a corollary it is shown that for every n ≥ 4 and A ⊂ N recursively enumerable there exists a finitely presented group with word problem solvable at level En(A) but not En-1(A). In particular, there exist finitely presented groups with word problem solvable at level En but not En-1 for n ≥ 4, answering a question of Cannonito.
Interchange of modal properties in the propagation of harmonic waves in heat-conducting materials
Authors: Chadwick P.
Published: April 2009

A study is made of the secular equation governing the propagation of plane harmonic waves of small amplitude in a continuum which is able to conduct heat. This equation defines an algebraic function, called the modal function, whose regular branches specify the slownesses of the possible modes of harmonic wave propagation as functions of the frequency. At each extreme of the frequency range one mode is diffusive in type and the others wave-like, and we suppose here that there is a single wave-like mode which produces changes of temperature. In this case the mode which is diffusive in type at low frequencies is wave-like or diffusive in the high-frequency limit according as the thermoelastic coupling constant (a dimensionless measure of the strength of thermo-mechanical interaction in the continuum) does or does not exceed unity. This property is shown to have a simple interpretation in terms of a Riemann surface of the modal function. The results obtained are quite general, referring to principal longitudinal waves in a homogeneously deformed isotropic heat-conducting elastic material, to dilatational disturbances of a stress-free configuration of such a material, and to acoustic waves in a heat-conducting inviscid fluid.
Tubular neighbourhoods for submersions of topological manifolds
Authors: Gauld David B.
Published: April 2009

Let φ: M → N be a submersion from a metrizable manifold to any (topological) manifold, let B ⊂ M be compact, y є N and C ⊂ φ−1(y) be a compact neighbourhood (in φ−1(y)) of B ∩ φ−1(y). It is proven that there is a neighbourhood U of y in N and an embedding ε: U × C → M such that φε is projection on the first factor, ε(y, x) = x for each x ε C, and B ∩ φ−1 (U) ⊂ ε(U×C). The main application given is to topological foliations, it being shown that if C is a compact regular leaf of a foliation F on M then every neighbourhood of C contains a saturated neighbourhood which is the union of compact regular leaves of F.
Regular metabelian groups of prime-power order
Authors: Faudree R. J.
Published: April 2009

Let H be a finite metabelian p-group which is nilpotent of class c. In this paper we will prove that for any prime p > 2 there exists a finite metacyclic p-group G which is nilpotent of class c such that H is isomorphic to a section of a finite direct product of G.
Boolean-valued equivalence relations and complete extensions of complete boolean algebras
Authors: Higgs Denis
Published: April 2009

It is remarked that, if A is a complete boolean algebra and δ is an A-valued equivalence relation on a non-empty set I, then the set of δ-extensional functions from I to A can be regarded as a complete boolean algebra extension of A and a characterization is given of the complete extensions which arise in this way.
A prime ideal and its quotient ring
Authors: Atterton T. W.
Published: April 2009

Given arbitrary rings A, B such that A ⊂ B and an arbitrary prime ideal P of A, we show how to construct a quotient ring Ap such that A ⊂ Ap ⊂ B. The ring Ap contains a prime ideal P lying over P and the prime ring A/P may be embedded in Ap/P.
Generating groups of nilpotent varieties
Authors: Vaughan-Lee M. R.
Published: April 2009

If is a variety of groups which are nilpotent of class c then is generated by its free group of rank c. It is proved that under certain general conditions cannot be generated by its free group of rank c - 2, and that under certain other conditions is generated by its free group of rank c - 1. It follows from these results that if is the variety of all groups which are nilpotent of class c, then the least value of k such that the free group of of rank k generates is c - 1. This extends known results of L.G. Kovács, M.F. Newman, P.P. Pentony (1969) and F. Levin (1970).
A remark on primes in arithmetic progressions
Authors: Alter Ronald , Villarino Mark
Published: April 2009

By generalizing a technique of Landau, the authors prove that the excess of the number of primes of the form 10x ± 3 over the number of primes of the form 10x ± 1 is infinite.
Free algebra structure: categorical algebras
Authors: Moore H. G.
Published: April 2009

One of the more important concepts in the study of universal algebras is that of a free algebra. It is our purpose in this communication to describe the structure of the free algebra Kk() of k generators (k a positive integer) determined by a categorical algebra, and to indicate how this information encompasses results in such diverse areas as the study of Post algebras, boolean rings, p-rings, pk-rings, finite commutative rings with unity, etc.

A finite algebra is called categorical if every algebra in its equational class is isomorphic to a sub-direct power of A. If has n elements, permutable identities, no non-identical automorphism and exactly m distinct one-element subalgebras, then .
Absolute Riesz summability of Fourier series and their conjugate series
Authors: Izumi Masako , Izumi Shin-ichi
Published: April 2009

This paper contains two theorems. The first theorem treats the |R, r, l| summability of Fourier series and their associated series of functions of bounded variation. The second concerns the |R, r, l| summability of Fourier series of functions f such that φ(t)m(l/t) is of bounded variation where m(u) increases to infinity as u → ∞. These theorems generalize Mohanty's theorems.
On the classification of just-non-Cross varieties of groups
Authors: Brady J. M.
Published: April 2009

Apart from some (insoluble) subvarieties of , the jnC (just-non-Cross) varieties known so far comprise the following list: , , , , where p, q and r are any three distinct primes. In a recent paper I gave a partial confirmation of the conjecture that the soluble jnC varieties all appear in this list. Here I show that a jnC variety is reducible if and only if it is soluble of finite exponent; this reduces the problem of classifying jnC varieties to finding the irreducibles of finite exponent. I observe that these fall into three distinct classes, and show that the questions of whether or not two of these classes are empty have some bearing on some apparently difficult problems of group theory.
On soluble just-non-Cross varieties of groups
Authors: Brady J. M.
Published: April 2009

We prove a partial confirmation of Kovács and Newman's conjecture that a just-non-Cross variety is soluble if and only if it is in the following list: , , , , where p, q and r are any three distinct primes.
Endomorphism rings of non-abelian groups
Authors: McQuarrie B. C. , Malone J. J.
Published: April 2009

In 1942 F.W. Levi described those groups in which any two inner automorphic images of an arbitrary element commute. Until recently it was not known whether there existed non-abelian groups with the property that any two endomorphic images of an arbitrary element commute. Now, R. Faudree has given examples of finite p–groups having this property. In this paper we give a necessary and sufficient condition that a torsion group which contains no elements of order 2 has this property. The technique of proof involves looking at certain near rings of functions on the group. The inspiration for the theorem comes from the “halving” technique used by B.H. Neumann in 1940.
A note on order topologies on ordered tensor products
Authors: Davis G.
Published: April 2009

If E, F are regularly ordered vector spaces the tensor product E ⊗ F can be ordered by the conic hull Kπ of tensors, x ⊗ y with x ≥ 0 in E and y ≥ 0 in F, or by the cone K⊗ of tensors Φ ∈ E ⊗ F such that Φ(x′, y′) ≥ 0 for positive linear functionals x′, y′ on E, F.

If E, F are locally convex spaces the tensor product can te given the π-topology which is defined by seminorms pα ⊕ qβ where {pα}, {qβ} are classes of seminorms defining the topologies on E, F. The tensor product can also be given the ε-topology which is the topology of uniform convergence on equicontinuous subsets J x H of E′ x F′. The main result of this note is that if the regularly ordered vector spaces E, F carry their order topologies then the order topology on E ⊕ F is the π-topology when E ⊕ F is ordered by kπ, and the ε-topology when E ⊕ F is ordered by K⊕.
On a class of differential equations which model tide-well systems
Authors: Noye B. J.
Published: April 2009

For three possible types of tide-well systems the non-dimensional head response, Y(τ), to a sinusoidal fluctuation of the sea-level is given by the differential equation

Estimates of the non-dimensional well response Z(τ) = sinτ - Y(τ)
are found by considering the steady state solutions of the above equation. With n = 2 the equation is linear and an exact solution can be found; for n ≠ 2 the equation is non-linear and several methods which give approximate solutions are described. The methods used can be extended to cover other values of n; for example, with n = 4 the equation corresponds to one governing oscillations near resonance in open pipes.
Fundamental singularities in the theory of water waves with surface tension: Corrigenda
Authors: Rhodes-Robinson P. F.
Published: April 2009

The Editor regrets that two errors have appeared in [1], through no fault of the author's. On page 325 the result (3.5) and the two lines following it should read:

where

On page 328 the result (4.3) and the two lines following it should read:

where
Uniqueness of the Fréchet space topology on certain topological algebras
Authors: Loy R. J.
Published: April 2009

It is well known that the complete norm topology on a Banach algebra is not unique in general, though semisimplicity is sufficient (but not necessary) for uniqueness. In this note we consider a class of topological algebras of formal power series which have unique Fréchet space topology. The structure of these algebras in the Banach algebra case will be considered in a later paper.
On the definition of saturated formations of groups
Authors: Cossey John , Macdonald Sheila Oates
Published: April 2009

We exhibit a closure operation which serves to define saturated formations of finite soluble groups.
Minimal vector lattice covers
Authors: Conrad Paul F.
Published: April 2009

We show that each abelian l–group G is a large l–subgroup of a minimal vector lattice V and if G is archimedean then V is unique, in fact, V is the l–subspace of (Gd)^ that is generated by G, where Gd is the divisible hull of G and (Gd)^ is the Dedekind-MacNeille completion of Gd. If G is non-archimedean then V need not be unique, even if G is totally ordered.
A note on modules over regular rings
Authors: Rangaswamy K. M. , Vanaja N.
Published: April 2009

It is shown that a von Neumann regular ring R is left seif-injective if and only if every finitely generated torsion-free left R-module is projective. It is further shown that a countable self-injective strongly regular ring is Artin semi-simple.
Two structure theorems for homeomorphism groups
Authors: Vobach A. R.
Published: April 2009

Let H(C) be the group of homeomorphisms of the cantor set, C onto itself. Let p: C → M be a (continuous) map of C onto a compact metric space M, and let G(p, M) be {h ∈ H(C) | ∀x ∈ C, p(x) = ph(x)}. G(p, M) is a group. The map p: C → M is standard, if for each (x, y) ∈ C × C such that p(x) = p(y), there is a sequence and a sequence such that xn → x and hn(xn) → y. Standard maps and their associated groups characterize compact metric spaces in the sense that: Two such spaces, M and N, are homeomorphic if and only if, given p standard from C onto M, there is a standard q from C onto N for which G(p, M) = h−1G(q, N)h, for some h ∈ H(C). That is, two compact metric spaces are homeomorphic if and only if they determine, via standard maps, the same classes of conjugate subgroups of H(C).

The present note exhibits two natural structure theorems relating algebraic and topological properties: First, if M = H ∪ K (H, K ≠ π) , compact metric, and p : C → M are given, then G(p, M) is isomorphic to a subdirect product of G(p, M)/S(p, H\K) and G(p, M)/S(p, K\H) where, generally, S(p, N) is the normal subgroup of homeomorphisms supported on p−1M . Second, given M and N compact metric and p : M → N continuous and onto, let M ≠ M − CID*α ≠ 0 , where {Dα}α ∈ A is the collection of non-degenerate preimages of points in N Then there is a standard p : C → M such that fp : C → N is standard and there is a homomorphism

.
The practical use of the Rayleigh-Ritz method in compressible flow
Authors: Lush P. E. , Stephenson J. W.
Published: April 2009

We show

(i) that the Rayleigh-Ritz method is a practical procedure for obtaining approximations to the velocity potential for compressible flows, and

(ii) how to calculate an estimate of the error in such approximations.
A family of groups with a countable infinity of full orders
Authors: Buttsworth R. N.
Published: April 2009

We construct a family of groups with precisely NO full orders.
A family of non-invertible prime links
Authors: McPherson James M.
Published: April 2009

The purpose of this paper is to show that there exists an infinite family of non-invertible prime 2-component links in S3. It is then noted that the existence of such a family implies the existence of a family of non-invertible wild arcs in S3, which are tame modulo an endpoint.
A remark on compact semigroups having certain decomposition spaces embeddable in the plane
Authors: Hunter R. P. , Anderson L. W.
Published: April 2009

Let S be a compact connected semigroup. If the decomposition space of S, under the action of a compact connected subgroup at the identity, is a plane continuum then this decomposition is a congruence.
Nilpotency and related properties of group extensions
Authors: Shield David , Neumann Hanna
Published: April 2009

Gilbert Baums lag has given sufficient conditions for a group G to be nilpotent in terms of properties of a normal subgroup H and the quotient G/H, and has shown these conditions to be necessary when G is a wreath product and H its base group. His results are extended here to give corresponding conditions for weaker properties ranging from “bounded local nilpotency” to “being an Engel group”. Again we ask whether the sufficient conditions found are necessary when G is non-trivially a wreath product, or is of the form the answer is “yes” for the stronger properties considered, but for the weaker ones the question remains open.