bluuebunny/crossref_metadata_2025 huggingface dataset:
Polyhedral decompositions of cubic graphs
Authors: Szekeres G.
Published: April 2009

A polyhedral decomposition of a finite trivalent graphGis defined as a set of circuits= {C1, C2, …Cm} with the property that every edge ofGoccurs exactly twice as an edge of someCk. The decomposition is called even if everyCkis a simple circuit of even length. IfGhas a Tait colouring by three coloursa, b, cthen the (a, b), (b, c) and (c, a) circuits obviously form an even polyhedral decomposition. It is shown that the converse is also true: ifGhas an even polyhedral decomposition then it also has a Tait colouring. This permits an equivalent formulation of the four colour conjecture (and a much stronger conjecture of Branko Grünbaum) in terms of polyhedral decompositions alone.
Small sets with large power sets
Authors: Monro G.P.
Published: April 2009

One problem in set theory without the axiom of choice is to find a reasonable way of estimating the size of a non-well-orderable set; in this paper we present evidence which suggests that this may be very hard. Given an arbitrary fixed aleph κ we construct a model of set theory which contains a set X such that if Y ⊆ X then either Y or X - Y is finite, but such that κ can be mapped into S(S(S(X))). So in one sense X is large and in another X is one of the smallest possible infinite sets. (Here S(X) is the power set of X.)
Solid convergence spaces
Authors: Schroder M.
Published: April 2009

The category of solid convergence spaces is introduced, and shown to lie strictly between the category of all convergence spaces and that of pseudo-topological spaces. A wide class of convergence spaces, including the c-embedded spaces of Binz, is then characterized in terms of this concept. Finally, several illustrative examples are given.
A remark on a mean value theorem of Alexander Weinstein in Generalized Axially Symmetric Potential Theory
Authors: Diaz J.B. , Leschen John G.
Published: April 2009

Cordially dedicated to Professor Alexander Weinstein, on the occasion of his Seventyseventh birthday, January 21, 1974.

This note contains the proof of an extension of Alexander Weinstein's mean value theorem for Generalized Axially Symmetric Potential Theory.
Conditions for a plane projective metric to be a norm
Authors: Phadke B.B.
Published: April 2009

Let R be a metrization with distance xy of an open convex set D in the 2-dimensional real affine plane such that xy + yz = xz whenever x, y, z lie on an affine line with y between x and z and such that all the balls px ≤ ρ are compact. The study of such metrics, called open plane projective metrics falls under the topic of Hilbert's Problem IV of his famous mathematical problems. In this paper it is proved that if in R the sets of points equidistant from lines lie again on lines then D must be the entire affine plane and the distance must in fact be a norm. The paper contributes to and gives extensions of similar results proved earlier. The novel features of the present result are that in the space collinearity of points x, y, z is taken only as a sufficient condition for the equality xy + yz = xz. Consequently the solution encompasses all normed linear planes, that is, norms whose unit circles are not necessarily strictly convex are also admitted.
On categorical semigroups
Authors: Monzo R.A.R.
Published: April 2009

A semigroup S is called categorical if every ideal I of S has the property that abc є I (a, b, c є S) implies ab є I or be bc є I Necessary and sufficient conditions for an orthodox semigroup to be categorical are found and then used to characterize those bands which appear as an isomorphic copy of the band of idempotents of some orthodox categorical semigroup and to simplify the proof of a theorem of Mario Petrich. The structure of commutative categorical semigroups is found modulo the structure of abelian groups and categorical semilattices.
Invariant metrics on free topological groups
Authors: Morris Sidney A. , Thompson H.B.
Published: April 2009

For a completely regular space X, G(X) denotes the free topological group on X in the sense of Graev. Graev proves the existence of G(X) by showing that every pseudo-metric on X can be extended to a two-sided invariant pseudo-metric on the abstract group G(X). It is natural to ask if the topology given by these two-sided invariant pseudo-metrics on G(X) is precisely the free topological group topology on G(X). If X has the discrete topology the answer is clearly in the affirmative. It is shown here that if X is not totally disconnected then the answer is always in the negative.
Uniqueness of invariant means on certain introverted spaces
Authors: Grossman Marvin W.
Published: April 2009

Let S be a topological semigroup with separately continuous multiplication and H a uniformly closed invariant subspace of LUC(S) (the space of left uniformly continuous bounded functions on S ) that contains the constants. It is shown that if H is left introverted and H admits a tight two-sided invariant mean m, then for each h ∈ H, m(h) is the unique constant function in the norm closed convex hull of the left orbit of h; consequently, H has a unique left invariant mean. (In fact, it is enough for H to admit a tight right invariant mean and a left invariant mean. ) For certain S, a similar result is obtained when H is a left compact-open introverted subspace of LCC(S) (the space of left compact-open continuous functions on S ).
Minimal generating sets for some wreath products of groups
Authors: Chye Yeo Kok
Published: April 2009

Let d(G) denote the minimum of the cardinalities of the generating sets of the group G. Call a generating set of cardinality d(G) a minimal generating set for G. If A is a finitely generated nilpotent group, B a non-trivial finitely generated abelian group and A wr B is their (restricted, standard) wreath product, then it is proved (by explicitly constructing a minimal generating set for A wr B ) that d(AwrB) = max{l+d(A), d(A×B)} where A × B is their direct product.
Matchings in graphs
Authors: McCarthy P.J.
Published: April 2009

Results of Tutte and of Anderson giving conditions for a simple graph G to have a perfect matching are generalized to give conditions for G to have a matching of defect d. A corollary to one of these results is a theorem of Berge on the size of a maximum matching in G.
Relative annihilators in semilattices
Authors: Varlet J.C.
Published: April 2009

An α-distributive (respectively α-implicative) semilattice S is a lower semilattice (with greatest lower bound denoted by juxtaposition) in which the annihilator 〈x, a〉, that is {y ∈ S: xy ≤ α}, is an ideal (respectively a principal ideal) for the fixed element α and any x of S. These semilattices appear as natural links between general and distributive semi-lattices on the one hand, and between pseudo-complemented and implicative semilattices on the other hand. Prime and dense elements, as well as maximal and prime filters, are essential. Mandelker's result, a lattice L is distributive if and only if 〈x, y〉 is an ideal for any x, y ∈ L is extended to semi-lattices.
Helgason's number and lacunarity constants
Authors: Edwards R.E. , Ross Kenneth A.
Published: April 2009

This paper studies the connection between the best possible value of a constant in the compact abelian case of a known inequality due to Helgason and the Λ2-constants of sets of characters. Various estimates of and expressions for the best possible value are given.
Connected expansions of topologies
Authors: Guthrie J.A. , Reynolds D.F. , Stone H.E.
Published: April 2009

This note presents a characterization of connected simple expansions of topologies in terms of conditions on subspaces, and gives corollaries improving and unifying known sufficient conditions. These results are applied to obtain information about maximally connected spaces, and it is shown that maximal connectedness is inherited by connected subspaces.
Uniform convergence and everywhere convergence of Fourier series. II
Authors: Izumi Masako , Izumi Shin-ichi
Published: April 2009

The first theorem shows that the subspaces of the space of functions with everywhere convergent Fourier series, defined in our previous paper, is a good subspace. The second theorem shows that convergence criterion in the previous paper is the proper generalization of Lebesgue's Convergence Criterion.
Transient development of capillary-gravity waves in a running stream
Authors: Bagchi Kalyan Kumar , Debnath Lokenath
Published: April 2009

An initial value investigation is made of the propagation of capillary-gravity waves generated by an oscillating pressure distribution acting at the free surface of a running stream of finite, infinite, and shallow depth. The solution for the free surface elevation is obtained explicitly by using the generalized Fourier transform and its asymptotic expansion. It is found that the solution consists of both the steady state and the transient components. The latter decays asymptotically as t → ∞ and the ultimate steady state is attained. It is shown that the steady state consists of two or four progressive capillary-gravity waves travelling both upstream and downstream according as the basic stream velocity is less or greater than the critical speed. Special attention is given to the existence of the critical values associated with the running stream of finite, infinite, and shallow depth. A comparison is made between the unsteady wave motions in an inviscid fluid with or without surface tension.
A family of supplementary difference sets
Authors: Lehmer Emma
Published: April 2009

This note exhibits a family of m – (ν, k, λ) supplementary difference sets with parameters ν = 2mf + 1, where ν = p is a prime and f is odd, k = mf and λ = m(mf−1)/2. These sets are composed of a union of cosets of 2m-th power residues of p.
The numerical ranges of unbounded operators
Authors: Giles J.R. , Joseph G.
Published: April 2009

On a Banach space the numerical range of an unbounded operator has a certain density property in the scalar field. Consequently all hermitian and dissipative operators are bounded. For a smooth or separable or reflexive Banach space the numerical range of an unbounded operator is dense in the scalar field.
Defining relations for the Held-Higman-Thompson simple group
Authors: Cannon John J. , Havas George
Published: April 2009

A set of defining relations for the Held-Higman-Thompson simple group of order 4 030 387 200 is given.
Polar analogues of two theorems by Minkowski
Authors: Mahler Kurt
Published: April 2009

Since Minkowski's time, much progress has been made in the geometry of numbers, even as far as the geometry of numbers of convex bodies is concerned. But, surprisingly, one rather obvious interpretation of classical theorems in this theory has so far escaped notice.

Minkowski's basic theorem establishes an upper estimate for the smallest positive value of a convex distance function F(x) on the lattice of all points x with integral coordinates. By contrast, we shall establish a lower estimate for F(x) at all the real points X on a suitable hyperplane

with integral coefficients u1, …, un not all zero. We arrive at this estimate by means of applying to Minkowski's Theorem the classical concept of polarity relative to the unit hypersphere

This concept of polarity allows generally to associate with known theorems on point lattices analogous theorems on what we call hyperplane lattices. These new theorems, although implicit in the old ones, seem to have some interest and perhaps further work on hyperplane lattices may lead to useful results.

In the first sections of this note a number of notations and results from the classical theory will be collected. The later sections deal then with the consequences of polarity.
Solution branches for mappings in cones, and applications
Authors: Dancer E.N.
Published: April 2009

We prove the existence of global solution branches for positive mappings. This improves an earlier result of the author. We also prove a related result for mappings in wedges. We then use these two results to prove the existence of solutions for boundary-value problems for systems of ordinary differential equations.
On varieties closed under the construction of power algebras
Authors: Shafaat A.
Published: April 2009

It is shown that if a variety V of (universal) algebras, defined by a set Σ of identities, is closed under the construction of power algebras then V can be defined by the subset Σ′ of Σ consisting of those identities ν = w of Σ such that every variable in ν = w occurs exactly once on both sides.
Preregular maps between Banach lattices
Authors: Birnbaum David A.
Published: April 2009

A continuous linear map from a Banach lattice E into a Banach lattice F is preregular if it is the difference of positive continuous linear maps from E into the bidual F″ of F. This paper characterizes Banach lattices B with either of the following properties:

(1) for any Banach lattice E, each map in L(E, B) is preregular;

(2) for any Banach lattice F, each map in L(B, F) is preregular.

It is shown that B satisfies (1) (repectively (2)) if and only if B′ satisfies (2) (respectively (1)). Several order properties of a Banach lattice satisfying (2) are discussed and it is shown that if B satisfies (2) and if B is also an atomic vector lattice then B is isomorphic as a Banach lattice to 11(Γ) for some index set Γ.
Waves on a shear flow
Authors: Puri K.K.
Published: April 2009

The propogation of disturbance when a shear flow with a free surface, in a channel of infinite horizontal extent and finite depth, is disturbed by the application of time-oscillatory pressure, is studied. The initial value problem is solved by using transform techniques and the steady state solution is obtained therefrom in the limit t → ∞. The effect of the initial shear on the development of the wave system is investigated.
Verifications of a formal technique for viscoelastodynamics
Authors: Barclay D.W. , Moodie T. Bryant
Published: April 2009

Presented in this paper are justifications for the formal Karal-Keller technique as it applies to propagation, reflection, and transmission of one-dimensional impact waves in nonhomogeneous viscoelastic solids.
A note on limbless trees
Authors: McAvaney K.L.
Published: April 2009

It is shown by enumeration that for any two non-isomorphic limbs with the same number of points the number of trees with p points that contain one limb equals the number of trees with p points that contain the other.
The distribution of prime ideals of a Dedekind domain
Authors: Grams Anne P.
Published: April 2009

Let G be an abelian group, and let S be a subset of G. Necessary and sufficient conditions on G and S are given in order that there should exist a Dedekind domain D with class group G with the property that S is the set of classes that contain maximal ideals of D. If G is a torsion group, then S is the set of classes containing the maximal ideals of D if and only if S generates G. These results are used to determine necessary and sufficient conditions on a family {Hλ} of subgroups of G in order that there should exist a Dedekind domain D with class group G such that {G/Hλ} is the family of class groups of the set of overrings of D. Several applications are given.
An inequality for characteristic functions
Authors: Heathcote C.R. , Pitman J.W.
Published: April 2009

The paper is concerned with an extension of the inequality 1 - u(2nt) ≤ 4n[1-u(t)] for u(t) the real part of a characteristic function. The main result is that the inequality in fact holds for all positive integer n and not only powers of 2. Certain consequences are deduced and a brief discussion is given of the circumstances under which equality holds.
Relations between boundaries of a riemannian manifold
Authors: Schiff J.L.
Published: April 2009

For a noncompact riemannian manifold R, let MP (R) be the P-algebra, and R*P the P-compactification, with the assumption that ∫RPdV = ∞. If s is the P-singular point of the P-harmonic boundary ΔP, and Δ is the harmonic boundary of Royden's compactification R*, we construct a continuous mapping π: R* → R*P such that π(Δ) = Δp or π(Δ) = ΔP – s.
Soluble linear groups
Authors: Frick M. , Newman M.F.
Published: April 2009

The least upper bound for the nilpotent lengths of soluble linear groups of degreenis calculated. For eachnit is, wherer(n) = [log3(2n–1)/4] and [x] is the integral part ofx.
Laminar forced convection at low Péclet number
Authors: Jones A.S.
Published: April 2009

This work is concerned with the forced convection of heat in a circular tube. The fluid flow is assumed to be laminar Poiseuille flow, and the physical parameters; viscosity, density, conductivity; are assumed to be independent of temperature changes. Viscous dissipation terms are also ignored, and there are no heat sources in the fluid. The problem is treated for the case of a step change in the wall temperature, and the eigenvalues have been obtained as an expansion in powers of the Péclet number for the smaller values, and in an asymptotic form for the larger values. The temperature distribution in the fluid in the neighbourhood of the temperature jump has been calculated for two values of the Péclet number, as have the Nusselt numbers.
On theorems of Thornton
Authors: Lalithambal R.
Published: April 2009

The topology of a topological group in which the intersection of open sets is open is uniquely determined by a normal subgroup, and the group is uniquely an extension of an indiscrete group by a discrete group. This was proved by M.C. Thornton under the additional hypothesis that the group is a torsion group. The proofs here given make the more general facts almost trivial.
Inductive and projective limits of smooth topological vector spaces
Authors: Lloyd John W. , Yamamuro S.
Published: April 2009

In J. Math. Mech. 15 (1966), 877–898, Bonic and Frampton have laid the foundation for a general theory of smoothness of Banach spaces. In this paper, we shall study one aspect of the smoothness of topological vector spaces, namely, the relationship between smoothness and inductive and protective limits of topological vector spaces. As a consequence, we obtain smoothness results for nuclear spaces and some Montei spaces.
Extreme point properties of fixed-point sets
Authors: Nillsen Rodney
Published: April 2009

We consider a semigroup S acting as affine continuous maps on a compact convex set X. F denotes the corresponding set of fixed points. Let exX and exF denote the corresponding sets of extreme points. If X is a simplex, conditions are given which ensure that when x ε F, the maximal measure representing x invariant under S. We also prove exF = F ∩ exX under conditions involving extreme amenability of S. Topological properties of exF are also studied.
Extension of multipliers by periodicity
Authors: Cowling Michael G.
Published: April 2009

A theorem proved by de Leeuw for Γ = Rn and later generalized by Lohoué and Saeki states that if Γ is an LCA group, Γ0 a closed subgroup thereof, π the canonical mapping from Γ onto Γ/Γ0 and Φ a Fourier multiplier of type (p, p) on Γ/Γ0, then Φ ० π is a Fourier multiplier of type (p, p) on Γ. We show here that if 1 ≤ p < q ≤ ∞, Γ and Φ is a Fourier multiplier of type (p, q) on Γ/Γ, then Φ ० π is a Fourier multiplier of type (p, q) on Γ and if Γ0 is a non-compact subgroup of Γ and Φ ० π is a Fourier multiplier of type (p, q) on Γ for some p and q satisfying 1 ≤ p ≤ q ≤ ∞, then Φ is zero. We prove also that if Φ is a Fourier multiplier of type (p, q) and Γ/Γ0, whee 1 ≤ q < p ≤ ∞ and Γ is discrete, then Φ ० π is a Fourier multiplier of type (p, q) on Γ.
On a problem of K. A. Bush concerning Hadamard matrices
Authors: Wallis W.D.
Published: April 2009

K.A. Bush has asked whether there is a symmetric Hadamard matrix of order m2, m even, which can be partitioned into an m × m array of m × m blocks, such that:

(i) each diagonal block has every entry 1;

(ii) each non-diagonal block has every row-sum zero?

We give two ways of constructing such matrices.
A note on the countable chain condition and sigma-finiteness of measures
Authors: Bhaskara Rao K.P.S. , Rao M. Bhaskara
Published: April 2009

The objectives of this paper are the following:

(1) to show that a theorem of Ficker is incorrect;

(2) to show that a stronger version of Ficker's Theorem is valid for a certain class of measures;

(3) characterize all σ-algebras on which every measure is a countable sum of finite measures.
A remark on a theorem of Caradus
Authors: Johnson J.A.
Published: April 2009

It is shown how a result of S.R. Caradus on the approximation problem can be obtained from known theorems.

Terms used here are standard (see [1] or [3]).

Let X denote a Banach space, S its unit ball in the weak topology, and X* the dual of X. In [1], the following theorem is proved:
(I) If X is reflexive and X* (considered as a subspaoe of the continuous scalar-valued functions C(S) in the canonical way) is complemented in C(S), then X has the approximation property.

It is our purpose to point out that (I) is a corollary to some known theorems that yield the stronger conclusion (II) below.
The skeleton of a variety of groups
Authors: Bryant R.M. , Kovács L.G.
Published: April 2009

The skeleton of a variety of groups is defined to be the intersection of the section closed classes of groups which generate . If m is an integer, m > 1, is the variety of all abelian groups of exponent dividing m, and , is any locally finite variety, it is shown that the skeleton of the product variety is the section closure of the class of finite monolithic groups in . In particular, S) generates . The elements of S are described more explicitly and as a consequence it is shown that S consists of all finite groups in if and only if m is a power of some prime p and the centre of the countably infinite relatively free group of , is a p–group.
Properties of the solution set of a generalized differential equation
Authors: Davy J.L.
Published: April 2009

We prove that the solution set of a generalized differential equation is connected and that points on the boundary of the solution funnel are peripherally attainable. This is done without the additional assumption of continuity in the state variable required in previous results. The result on upper semicontinuity of the solution set with respect to initial conditions is extended to include variations of initial time.
An index of P. Hall for varieties of groups
Authors: Harris L.F.
Published: April 2009

P. Hall defined the k–index of a variety , of groups to be the least cardinal number r such that if a group G is generated by a set S and every subset of S of cardinality at most r generates a group in then G ∈ . We show that the only variety which has finite k–index and contains a product of two non-trivial varieties is the variety of all groups. As a consequence of this and P. Hall's result that nilpotent varieties have finite k–index we show that a soluble variety or a variety generated by a finite group has finite k–index if and only if it is nilpotent.
A characterization of the Hall planes of odd order
Authors: Kirkpatrick P.B.
Published: April 2009

The Hall projective planes of odd order are characterized in terms of their translations, collineations which fix all the points of a Baer subplane, and involutory homologies.
Elementary abelian operator groups
Authors: Gross Fletcher
Published: April 2009

Suppose G is a finite solvable p′-group admitting the elementary abelian p–group A as an operator group. if n = max{nilpotent length of CG(X)| X ∈ A#} and |A| ≥ pn+2, then the nilpotent length of G is n.
A note on planes of characteristic three
Authors: Kallaher Michael J.
Published: April 2009

A projective plane has characteristic three if in every ternary ring coordinatizing it all elements ≠ 0 of the additive loop have order 3. We show that if a finite plane of characteristic three is coordinatized by a near-field, then the plane is desarguesian.
Pseudo-fields and doubly transitive groups
Authors: Wilke F.W.
Published: April 2009

A sharply doubly transitive group which acts on a set of at least two elements is isomorphic to the group of affine transformations on a system S. This statement is true if S is replaced by either strong pseudo-field or pseudo-field. The additive system of a strong pseudo-field is a loop while the additive system of a pseudo-field need not be a loop. We show that any pseudo-field is either a strong pseudo-field or can be obtained from a strong pseudo-field in a nice way. Every near-field is a strong pseudo-field. The converse is an open question.
Classical groups over division rings of characteristic two
Authors: Pender William M. , Wall G.E.
Published: April 2009

The notion of quadratic form over a field of characteristic two is extended to an arbitrary division ring of characteristic two with an involution of the first kind. The resulting isometry groups are shown to have a simple normal subgroup and the structure of the factor group is calculated. It is indicated how one may define and analyse all the classical groups in a unified manner by means of quadratic forms.
Simple proofs of Steck's determinantal expressions for probabilities in the Kolmogorov and Smirnov tests
Authors: Pitman E.J.G.
Published: April 2009

This paper gives simple proofs of two theorems of Steck concerning the distribution of sample distribution functions.
A construction for Hadamard arrays
Authors: Cooper Joan , Wallis Jennifer
Published: April 2009

We give a construction for Hadamard arrays and exhibit the arrays of orders 4t, t ∈ {1, 3, 5, 7, …, 19}. This gives seventeen new Hadamard matrices of order less than 4000.
Isomorphisms of some convolution algebras and their multiplier algebras
Authors: Tewari U.B. , Gaudry G.I.
Published: April 2009

Let G1 and G2 be two locally compact abelian groups and let 1 ≤ p ∞. We prove that G1 and G2 are isomorphic as topological groups provid∈d there exists a bipositive or isometric algebra isomorphism of M(Ap (G1)) onto M(Ap (G2)). As a consequence of this, we prove that G1 and G2 are isomorphic as topological groups provided there exists a bipositive or isometric algebra isomorphism of Ap (G1) onto Ap (G2). Similar results about the algebras L1 ∩ Lp and L1 ∩ C0 are also established.
Remainders of metric completions
Authors: Knight C.J.
Published: April 2009

Certain topological spaces X may bear various uniform structures compatible with the topology of X; to each uniform structure there corresponds a completion of X, that is, a complete space Z containing X as a dense subspace. For compact completions, there has been extensive study of the relationship between X and the possible remainders Z\X. This paper begins a study of the more general, and apparently easier, problem of the relationship between X and its not necessarily compact remainders. We find that for spaces X admitting a complete metric, every space Y which satisfies certain conditions obviously necessary for Y to be the remainder of a completion of X in fact occurs as such a completion.
On the relation of a distributive lattice to its lattice of ideals
Authors: Gaskill Herbert S.
Published: April 2009

In this note we examine the relationship of a distributive lattice to its lattice of ideals. Our main result is that a distributive lattice and its lattice of ideals share exactly the same collection of finite sublattices. In addition we give a related result characterizing those finite distributive lattices L which can be embedded in a lattice L′ whenever they can be embedded in its lattice of ideals T(L′).
A note on flabby sheaves
Authors: Levaro Richard A.
Published: April 2009

It is shown that any sheaf of R˜-modules, all of whose stalks are injective, is necessarily a flabby sheaf. This generalizes the result or Grothendieck that the sheaf M˜ determined by an injective module M over a commutative noetherian ring with 1 is flabby.
Free generators in free inverse semigroups
Authors: Reilly N.R.
Published: April 2009

Using the characterization of the free inverse semigroup F on a set X, given by Scheiblich, a necessary and sufficient condition is found for a subset K of an inverse semigroup S to be a set of free generators for the inverse sub semigroup of S generated by K. It is then shown that any non-idempotent element of F generates the free inverse semigroup on one generator and that if |X| > 2 then F contains the free inverse semigroup on a countable number of generators. In addition, it is shown that if |X| = 1 then F does not contain the free inverse semigroup on two generators.
Aspects of topoi: Corrigenda and acknowledgements
Authors: Freyd Peter
Published: April 2009

“Aspects of Topoi” [1] appeared in July 1972 through the Herculean efforts of Bernard Neumann with the able assistance of Tim Brook and Max Kelly. The original manuscript was written in haste during the last two weeks of the author's visit to Australia. Somehow just five months later it appeared in print. Among the difficulties surmounted was a set of page proofs which having been sent via slow steamer by the U. of Penn. administration arrived after the paper was in press.
Some dynamic properties of a prestressed incompressible hyperelastic material
Authors: Belward J.A.
Published: April 2009

The work continues some earlier investigations into dynamic properties of prestressed incompressible elastic materials. Whereas the material was previously assumed to be a Mooney material, it is here allowed to have any strain energy function. Plane wave propagation and the motions caused by an impulsive line of traction are examined. The results obtained are compared with the earlier work.
A necessary and sufficient condition for exponentially bounded existence and uniqueness
Authors: Lovelady David Lowell
Published: April 2009

A condition which was previously found to be sufficient for global existence and uniqueness of solutions of an ordinary differential equation is shown herein to be necessary, if it is also required that solutions are exponentially bounded.
The multiplicator of finite nilpotent groups
Authors: Wamsley J. W.
Published: April 2009

Let G be a group and M a G-module; then d(G) denotes the minimal number of generators of G and dG(M) the minimal number of generators over ZG of M. For G a finite nilpotent group let G = F/R, F free, be a presentation for G; then it is shown that
d(R/[F, R]) = dG(R/[R, R]),
that is
d(G) + d(M(G)) = dG(R/R′),
where M(G) denotes the Schur multiplicator of G.
Integro-differential equations of Volterra type
Authors: Mohana Rao M. Rama , Tsokos Chris P.
Published: April 2009

The aim of this paper is concerned with studying the stability properties of an integro-differential system by reducing it into a scalar integro-differential equation. A theorem is stated about the existence of a maximal solution of such systems and a basic result on integro-differential inequalities. Utilizing these results we obtain sufficient conditions for uniform asymptotic stability of the trivial solution of the integro-differential system of the form

where , with , , C(J) denotes the space of continuous functions, A a continuous operator such that A maps C(J) into C(J). The fruitfulness of the results of the paper are illustrated with two applications.
Eigenvalues of partitioned hermitian matrices
Authors: Thompson Robert C. , Freede Linda J.
Published: April 2009

Let C = (Aij)1≤i, j≤t be a hermitian matrix in partitioned form; here Aij, is an ni × nj. block. The purpose of this paper is to obtain inequalities linking the eigenvalues of C to those of the main diagonal blocks A11, …, Att of C.

These inequalities include, as special cases, inequalities due to N. Aronszajn and A. Hoffman.
The identity of certain representation algebra decompositions
Authors: Conlon S. B. , Wallis W. D.
Published: April 2009

Let G be a finite group and F a complete local noetherian commutative ring with residue field of characteristic p # 0. Let A(G) denote the representation algebra of G with respect to F. This is a linear algebra over the complex field whose basis elements are the isomorphism-classes of indecomposable finitely generated FG-representation modules, with addition and multiplication induced by direct sum and tensor product respectively. The two authors have separately found decompositions of A(G) as direct sums of subalgebras. In this note we show that the decompositions in one case have a common refinement given in the other's paper.
On multigraphs with a given partition
Authors: Cadogan C. C.
Published: April 2009

Relationships between the numbers of general graphs and the numbers of multigraphs are set up with a view to enumerating multigraphs with a given partition. In the process of doing so certain structures which we call graph-lattices evolve. The principle of inclusion-exclusion plays an important part in the formulation of theorems and actual numerical results are computed with the aid of S-functions.
An order property of partition cardinals
Authors: Williams N. H.
Published: April 2009

This note studies cardinal numbers κ which have a partition property which amounts to the following. Let ν be a cardinal, η an ordinal limit number and m a positive integer. Let the m-length sequences of finite subsets of κ be partitioned into ν parts. Then there is a sequence H1, … Hm of subsets of κ, each having order type η, such that for each choice of non-zero numbers n1, …, nm there is some class of the partition inside which fall all sequences having in their i-th place (for i = 1, …, m) a subset of Hi which contains exactly ni elements. The case when m = 1 is thus seen to be the well known property κ . The most interesting results obtained relate to the ordering of the least cardinals with the appropriate properties as m and η vary.
A theorem on absolute summability of Fourier series by Riesz means
Authors: Chandra Prem , Izumi S.
Published: April 2009

In 1951 Mohanty established the following theorem.

If Φ(t)log is of bounded variation in (0, π), wherek ≥ πe2and, then is summable, for however large positive Δ. In this present note we have generalised the above theorem by taking a more general type of Riesz means and under the condition, is of bounded variation in (0, π), where c is finite, imposed upon the generating function of Fourier series.
Unicity in the uniform approximation of vector-valued functions
Authors: Johnson Lee W.
Published: April 2009

The problem of unicity in the uniform approximation of vector-valued functions is considered. A recent result of Cheney and Wulbert concerning unicity in the uniform approximation of real-valued functions is extended and some “point-wise” criteria for unicity are given.
Convergence of approximate operator methods for eigenvectors
Authors: Andrew A. L.
Published: April 2009

This paper examines a large class of common numerical methods for computing the eigenvectors of a compact linear operator. Special cases include all projection methods and the Weinstein intermediate problems method. Simple sufficient conditions are established for the sequence of approximate eigenvectors obtained by any of these methods to converge to an exact eigenvector. In the most general case only the convergence of a subsequence was proviously known.
Some product varieties of groups
Authors: Bryce R. A. , Cossey John
Published: April 2009

We consider varietieswithmprime top. We show that the subvariety lattice ofdistributive and has descending chain condition and thatis its only just non-Cross subvariety. Whenmis prime we determine the join-irreducible subvarieties of. The method involves fairly detailed description of the structure of non-nilpotent critical groups in.
A solvability condition for finite groups with nilpotent maximal subgroups
Authors: Randolph John
Published: April 2009

Let G be a finite group with a nilpotent maximal subgroup S and let P denote the 2-Sylow subgroup of S. It is shown that if P ∩ Q is a normal subgroup of P for any 2-Sylow subgroup Q of G, then G is solvable.
On probabilities of large deviations
Authors: Rohatgi Vijay K.
Published: April 2009

Let {Xn} be a sequence of independent identically distributed random variables and let The rate of convergence of probabilities , where 2 > r > 1, is studied.
On regular semigroups whose idempotents form a semigroup: Addenda
Authors: Hall T. E.
Published: April 2009

The results in the first parts of Theorems 2 and 3 of the paper in the title (see [2]) have been previously obtained by B.M. Schein in Theorem 1.12, page 299 [4], and in Proposition 1.13 (combined with the last paragraph of page 300) [4], respectively. To deduce the first part of Theorem 2 [2] from Theorem 1.12 [4] one merely uses the fact that a binary relation R on a set X satisfies RR−1R ⊆ R if if and only if it satisfies: R{x) ∩ R(y) ≠ □ implies R(x) = R(y), for any x, y ∈ X (see Proposition 9, page 132 [3]).
A generalization of Lagrange multipliers
Authors: Craven B. D.
Published: April 2009

The method of Lagrange multipliers for solving a constrained stationary-value problem is generalized to allow the functions to take values in arbitrary Banach spaces (over the real field). The set of Lagrange multipliers in a finite-dimensional problem is shown to be replaced by a continuous linear mapping between the relevant Banach spaces. This theorem is applied to a calculus of variations problem, where the functional whose stationary value is sought and the constraint functional each take values in Banach spaces. Several generalizations of the Euler-Lagrange equation are obtained.
Remarks on triples in enriched categories
Authors: Wiesler H. , Calugareanu G.
Published: April 2009

Let v be a symmetric monoidal closed category with equalizers. The v–triples T, T′, … in the enriched category A, together with suitably defined morphisms form a category v–Trip(A). The v–categories AT, AT′, … and the v–functors R: AT′ → AT which are compatible with the forgetful functors form a category V–Alg(A).

In the subsequent note it is shown that V–Trip(A) is isomorphic to the dual of V–Alg(A) and that the morphisms of V–Alg(A) are inverse limit preserving V–functors.
A note on subdirectly irreducible rings
Authors: Deshpande Madhukar G.
Published: April 2009

It is proved that every subdirectly irreducible ring can be obtained as a proper homomorphic image of another subdirectly irreducible ring. An example of a subdirectly irreducible ring R with heart H is given for which
i) R has a non-subdirectly irreducible homomorphic image,
ii) R/H is an integral domain, and
iii) the commutator ideal C(R) of R coincides with R.
Paths of charges in general relativity as geodesics of Einstein's non-Riemannian geometry
Authors: Burman R. R.
Published: April 2009

The equation of motion of charged incoherent matter, and hence of a test charge, in general relativity can be written as the geodesic equation of an affine connection. Here, the connection is chosen to satisfy a condition which has the form of one of the basic geometrical principles of Einstein's unified field theory. The symmetric part of the fundamental tensor of the geometry is chosen to be the metric tensor of general relativity; equations to be satisfied by the skew part, involving the electromagnetic field, are obtained. An alternative condition on the affinity is also considered.
Hurwitz on Hadamard designs
Authors: Storer T.
Published: April 2009

An n × n–matrix on n signed variables is called Hadamard of Williamson type if each variable occurs exactly once in each row, and the inner product of any pair of distinct rows is zero. We show here that these matrices correspond in a natural way to rational formulas for products of sums of n squares, shown by Hurwitz to exist only for n = 1, 2, 4, and 8. Hurwitz' arguments contain an implicit proof that this correspondence is one-to-one (we show this directly) and hence that Hadamard matrices of Williamson type exist for orders 1, 2, 4 and 8 only.
A characterization of Banach-star-algebras by numerical range
Authors: Sims Brailey
Published: April 2009

It is known that in a B*-algebra every self-adjoint element is hermitian. We give an elementary proof that this condition characterizes B*-algetras among Banach*-algebras.
Convergence criteria for Fourier series
Authors: Gopal Rao V. Venu
Published: April 2009

The following convergence criterion of Fourier series is due to M. Izumi, S. Izumi and the author:

THEOREM. Let Δ ≥ 1. If

(i) , and

(ii) as t → 0

for an a, 0 < a < 1 and for a δ, 0 < δ < π, then the Fourier series of φ(t) is convergent at the origin.

The object of this paper is to generalize the above theorem in the Hardy-Littlewood direction.
On the extension of orders in ordered modules: Corrigenda
Authors: Ribenboim P.
Published: April 2009

The author has noticed a faulty argument in his paper [1]; it occurs on p. 85 and requires the following changes:

At the end of line 9, for (Qi)i=1,2,… read (Qi)i ∈ I; in line 10, the equation should read ; lines 15 to 20 should be replaced by the following: then there exists some n–tuple δ = (δ1, …, δn) such that for every io there exists i ≥ io with εi = δ. Then δ1a1, …, δnan are positively independent over Q; for if rj ∈ PR and then there exists io such that , and for appropriate i ≥ io it follows that rj = 0 for j = 1, …, n.
Chunikhin's existence theorem for subgroups of a finite group
Authors: Cooper C.D.H.
Published: April 2009

We give a simplified proof of a general theorem of Chunikhin on existence of subgroups of a finite group. The proof avoids the technical device of “indexials” which Chunikhin set up for this purpose.
A remark on compact semigroups having certain decomposition spaces embeddable in the plane: Corrigendum
Authors: Hunter R.P. , Anderson L.W.
Published: April 2009

Through an editorial error, the second sentence in the penultimate paragraph of [1] does not make sense. The first line in that paragraph should read:

“It now follows that K/G separates the plane, Where K is, as usual,”.
Character tables of certain finite simple groups
Authors: Hunt David C.
Published: April 2009

M(22) is the sporadic simple group discovered by Fischer in 1969. The character tables of M(22) and the simple groups PSU(5, 2), PSU(6, 2), PSΩ+(6, 3) and PSΩ(7, 3) are presented. Only a brief description of the methods used to determine the tables is given.
Divisibility of binary relations
Authors: Fitz-Gerald D.G. , Preston G.B.
Published: April 2009

In his paper in Mat. Sb. (N.S.) 61 (103) (1963), Zareckiĭ associated with any binary relation α an ordered pair, (Lα Mα), say, of lattices and showed that α is a left [right] divisor of β if and only if We provide an alternative proof of this result by embedding the category of relations in the category of sets. Our approach provides a unified treatment of several hitherto independent results, and gives new results for the category of partial transformations.
A Banach space with support homeomorphism is reflexive
Authors: Giles J.R.
Published: April 2009

For every Banach space X there is a natural non-linear mapping from X into its dual X*. It is shown that if this mapping is a homeomorphism then it is onto X* and X is reflexive.
A skew-Hadamard matrix of order 92
Authors: Wallis Jennifer
Published: April 2009

There is a skew-Hadamard matrix of order 92.

Previously the smallest order for which a skew-Hadamard matrix was not known was 92. We construct such a matrix below. The orders < 200 which are now undecided are 100, 116, 148, 156, 172, 188, 196; see [2], [3]. The existence of any Hadamard matrix of order 92 was unknown until 1962 [1].
Cotorsion radicals and projective modules
Authors: Beachy John A.
Published: April 2009

We study the notion (for categories of modules) dual to that of torsion radical and its connections with projective modules.

Torsion radicals in categories of modules have been studied extensively in connection with quotient categories and rings of quotients. (See [8], [12] and [13].) In this paper we consider the dual notion, which we have called a cotorsion radical. We show that the cotorsion radicals of the category RM correspond to the idempotent ideals of R. Thus they also correspond to TTF classes in the sense of Jans [9].

It is well-known that the trace ideal of a projective module is idempotent. We show that this is in fact a consequence of the natural way in which every projective module determines a cotorsion radical. As an application of these techniques we study a question raised by Endo [7], to characterize rings with the property that every finitely generated, projective and faithful left module is completely faithful. We prove that for a left perfect ring this is equivalent to being an S-ring in the sense of Kasch. This extends the similar result of Morita [15] for artinian rings.
Some definitions of finiteness
Authors: Hickman J. L.
Published: April 2009

Since Paul J. Cohen's 1963 result, it has been possible to investigate the consequences of the axioms of Zermelo-Fraenkel set theory without the Axiom of Choice. In this paper we examine the relative strengths of a number of finiteness criteria against the background of ZF set theory without AC.
Minimal vector lattice covers
Authors: Bleier Roger D.
Published: April 2009

We show that each archimedean lattice-ordered group is contained in a unique (up to isomorphism) minimal archimedean vector lattice. This improves a result of Paul F. Conrad appearing previously in this Bulletin. Moreover, we show that this relationship between archimedean lattice-ordered groups and archimedean vector lattices is functorial.
A problem of Hanna Neumann on closed sets of group words
Authors: Kovács L.G. , Vaughan-Lee M.R.
Published: April 2009

In Problem 1 of her book Varieties of groups, Hanna Neumann asked whether a fully invariant subsemigroup of a free group of infinite rank is necessarily a subgroup. This note presents an example which shows that the answer is negative.
Coretraction-fibrations are retractions
Authors: Chislett E. , Hoo C.S.
Published: April 2009

We prove that if C is an abelian category and M is the class of all coretractions, then the class of M-fibrations is the class of all retractions. As a corollary we prove that the class of all retractions is contained in the class of M-fibrations for any M.
The weak density of the non-invertible elements of a commutative algebra
Authors: Narici L. , Bachman G. , Beckenstein E.
Published: April 2009

Let X be a commutative locally convex Hausdorff topological algebra with identity over a non-trivially valued field F. Let Mc denote the continuous nontrivial homomorphisms of X into F and M the set of all maximal ideals of X. If the spectrum of each element x in X is the set of scalars {f(x) | f ∈ Mc}, it is shown that the singular elements of X are weakly dense in X if and only if M is an infinite set.
Varieties of soluble groups and a dichotomy of P. Hall
Authors: Groves J.R.J.
Published: April 2009

Let denote the variety of all abelian groups and, for each prime p, let p be the variety of all elementary abelian p-groups. Let be a subvariety of a product of (finitely many) varieties each of which is either soluble or Cross.
An elementary existence theorem for entire functions
Authors: Mahler Kurt
Published: April 2009

It is proved that, for any m given distinct real numbers a1, …, am, there exist transcendental entire functions f(z) at most of order m for which all the values

are rational integers.
On Reversible Group Rings
Authors: Li Yuanlin , Bell Howard E. , Phipps Colin
Published: April 2009

Let G be an arbitrary finite group, R be a finite associative ring with identity and RG be the group ring. We show that ℤ2Q8 is the minimal reversible group ring which is not symmetric, and we also characterise the finite rings R for which RQ8 is reversible. The first result extends a result of Gutan and Kisielewicz which shows that ℤ2Q8 is the minimal reversible group algebra over a field which is not symmetric, and it answers a question raised by Marks for the group ring case.