bluuebunny/crossref_metadata_2025 huggingface dataset:
On the connectification of a space by a countable point set
Authors: Miller Gary , Pearson B. J.
Published: April 2009

In this note we define a rather pathological connectedness property of Hausdorff spaces which is stronger than ordinary connectedness. We obtain a few basic properties of such spaces and derive a method for constructing them. It turns out that countable Hausdorff spaces having the connectedness property are as easily constructed as uncountable ones. Hence we have still another method for constructing countable connected Hausdorff spaces.
Permutation characters
Authors: Ross Fiona M.
Published: April 2009

We suppose throughout that G is a finite group with a faithful matrix representation X over the complex field. We suppose that X affords a character π of degree r whose values are rational (hence rational integers). If the matrices in some representation of G affording a character π0 are all permutation matrices, then π0 is called a permutation character. Permutation characters have non-negative integral values. In the general case, we consider what properties of permutation characters are true of π, and in particular, under what circumstances π is a permutation character. Note that assuming X to b faithful is equivalent to considering the image group X(G) instead of G.
Multivariate semi-markov matrices
Authors: Neuts Marcel F. , Purdue Peter
Published: April 2009

Finite matrices with entries pij Fij (x1,…, xk), where {pij} is stochastic and Fij(.) is a k-variate probability distribution are discussed. It is shown that the matrix of k-variate Laplace-Stieltjes transforms of the Pij Fij(x1, …, xk) has a Perron-Frobenius eigenvalue which is a convex function in k variables in a suitably defined region. The values of the partial derivatives near the origin of this maximal eigenvalue are exhibited. They are quantities of interest in a variety of applications in Probability theory.
On the radical of the group algebra of a p-nilpotent group
Authors: Clarke R. J.
Published: April 2009

In this note we give a basis for the radical of the group algebra of a p-nilpotent group over a field of characteristic p in terms of the ordinary representation theory of the group. We use our result to calculate the exponent of the radical for such a group.
A note on commutative Baer rings
Authors: Speed T. P.
Published: April 2009

In this note we study commutative Baer rings, uniting the abstract algebraic approach with the approach of [3] using minimal prime ideals. Some new characterisations of this class of rings are obtained, relations between the minimal prime ideals of a commutative Baer ring B and its algebra EB of idempotents are considered, and some results concerning the direct decomposition of commutative Baer rings are given. We then study Baer ideals, and finally state without proof a new construction of the Baer extension of a commutative semiprime ring.
A note on Pt-ideals
Authors: Spirason G. T. , Strzelecki E.
Published: April 2009

Let E be a vector lattice in the sense of [2]. Two elements a, b in E are said to be disjoint (written a⊥b) if ′a′^′b′ = 0. For any subset A of E, A⊥ is the set If A is a one point set {a}, then we shall use a⊥ for {a}⊥. A⊥⊥ is denned by A⊥⊥ = {A⊥}⊥. A subset B of E is said to be a polar if it is of the form A⊥ for some subset A of E. It is well known [1] that the set of all polars of E ordered by inclusion forms a Boolean algebra. We shall denote this algebra by B, and M will mean the set of all maximal ideals of B. The following properties of polars will be used in the paper.
On the semigroup of Hadamard differentiable mappings
Authors: Yamamuro Sadayuki
Published: April 2009

The main purpose of this paper is to prove that every automorphism of the semigroup of all Hadamard-differentiable mappings of a separable real Banach space into itself is inner. This generalizes the results of [7] which is a generalization of a result proved by Magill, Jr. [5].
Computation of the transformation semigroups on three letters
Authors: Wilde Carroll , Raney Sharon
Published: April 2009

Let H denote a set with three elements, and T3 the full transformation semigroup on X, i.e. T3 consists of the twenty-seven self maps of X under functional composition. A transformation semigroup (briefly a τ-semigroup) on three letters is an ordered pair (X, S), where S is any subsemigroup of T3.
Two finiteness theorems in the Minkowski theory of reduction
Authors: Aitchison P. W.
Published: April 2009

Minkowski proved two important finiteness theorems concerning the reduction theory of positive definite quadratic forms (see [6], p. 285 or [7], §8 and §10). A positive definite quadratic form in n variables may be considered as an ellipsoid in n-dimensional Euclidean space, Rn, and then the two results can be investigated more generally by replacing the ellipsoid by any symmetric convex body in Rn. We show here that when n≧3 the two finiteness theorems hold only in the case of the ellipsoid. This is equivalent to showing that Minkowski's results do not hold in a general Minkowski space, namely in a euclidean space where the unit ball is a general symmetric convex body instead of the sphere or ellipsoid.
Conjugates of differentiable flows
Authors: Johnson Gordon G.
Published: April 2009

The work in this paper is directed at the question: What differentiable flows on [0, 1] [1] are conjugates of linear fractional flows on [0, 1]?
A characterization of the orders of regressive ω-groups
Authors: Hassett Matthew J.
Published: April 2009

Let IE, ∧ and ∧R denote the collections of all non-negative integers, isols and regressive isols respectively. An ω-group is a pair (α, p) where (1) α ⊆ E, (2) p(x, y) is a partial recursive group multiplication for α and (3) the function which maps each element of α to its inverse under p has a partial recursive extension. If G = (α, p) is an ω-group, we call the recursive equivalence type of a the RET or order of G (written o(G)). Let GR = {T∈∧R′T = o(G) for some ω-group G}. It follows from the version of the Lagrange Theorem given in [4] that ∧R − GR is non-empty and has cardinality c. In this paper we characterise the isols in GR as follows: A regressive isol T belongs to GR if and only if T∈E or T is infinite and there exist a regressive isol U ≦ T and a function an from E into E − {0} such that U ≦*an and T = ΠUan. (The “≦*” is denned in [2]). In presenting the proof of this result, we shall assume that the reader is familiar with either [3] or [4]. The proof that, given an and U ≦*an, a group of order ΠUan exists is based on the natural trick—one constructs a direct product of disjoint cyclic groups of order a0, a1,… indexed by elements of a set of RET U. The proof that any regressive group G has order of the form ΠUan is trivial for finite groups; the proof for infinite regressive groups is based upon the construction of an ascending chain of finite subgroups Gi of G such that and .
Addendum to “Changing the order of integration”
Authors: Love E. R.
Published: April 2009

Dr. Roy O. Davies, of the University of Leicester, has sent me a neat proof of Theorem 3, p. 430, of my paper “Changing the Order of Integration” [1]. Perhaps other readers would appreciate this improvement, as I do; I therefore present it below, with his agreement, together with a consequent improved proof of Theorem 2. The counter-example, which is the main part of that paper, is unaffected.
Loomis-Sikorski theorem for monotone σ-complete effect algebras
Authors: Dvurečenskij Anatolij
Published: April 2009

We show that monotone σ -complete effect algebras under some conditions are σ - homomorphic images of effect-tribes (as monotone σ -complete effect algebras), which are nonempty systems of fuzzy sets closed under complements, sums of fuzzy sets less than 1, and containing all pointwise limits of nondecreasing fuzzy sets. Because effect-tribes are generalizations of Boolean σ -algebras of subsets, we present a generlization of the Loomis-Sikorski theorem for such effect algebras. We show that we can choose an effect-tribe to be a system of affin fuzzy sets. In addition, we present a new version of the Loomis-Sikorski theorem for σ-complete MV-algebras.
Pseudo-elliptic integrals, units, and torsion
Authors: Pappalardi Francesco , Van Der Poorten Alfred J.
Published: April 2009

We remark on pseudo-elliptic integrals and on exceptional function fields, namely function fields defined over an infinite base field but nonetheless containing non-trivial units. Our emphasis is on some elementary criteria that must be satisfied by a squarefree polynomialD(x)whose square root generates a quadratic function field with non-trivial unit. We detail the genus I case.
Two index laws for fractional integrals and derivatives
Authors: Love E. R.
Published: April 2009

The first index law, or addition theorem, is well known. The second is much less well known; but both have been found to be of importance in recent studies of hypergeometric integral equations. The first law has usually been considered only in the simple case of orders of integration which have positive real part, or in the context of generalized functions. Arising out of the need to manipulate expressions involving several fractional integrals and derivatives, our aim here is to establish both laws for all combinations of complex orders of integration and differentiation, and for nearly all functions for which the fractional derivatives involved exist as locally integrable functions.
Geometric realizations for free quotients
Authors: Jaco William
Published: April 2009

In [7] Lyndon introduced the concept of inner rank for groups. He defined the inner rank of an arbitrary groupGto be the upper bound of the ranks of free homomorphic images ofG. Both Lyndon and Jaco have shown that the inner rank of the fundamental group of a closed 2-manifold with Euler characteristic 2 − p, p ≧ 0, is [p/2] where [p/2] is the greatest integer ≦p/2. The proof given by lyndon [8] uses algebraic techniques; whereas, the proof by Jaco [4] is geometrical.
Lower radicals in nonassociative rings
Authors: Tangeman R. , Kreiling D.
Published: April 2009

Let W be a universal class of (not necessarily associative) rings and let A ⊆ W. Kurosh has given in [6] a construction for LA, the lower radical class determined by A in W. Using this construction, Leavitt and Hoffmann have proved in [4] that if A is a hereditary class (if K ∈ A and I is an ideal of K, then I ∈ A), then LA is also hereditary. In this paper an alternate lower radical construction is given. As applications, a simple proof is given of the theorem of Leavitt and Hoffmann and a result of Yu-Lee Lee for alternative rings is extended to not necessarily associative rings.
The descending chain condition in modular lattices
Authors: Newman Thomas G.
Published: April 2009

In a recent paper Kovács [1] studied join-continuous modular lattices which satisfy the following conditions: (i) every element is a join of finitely many join-irredicibles, and, (ii) the set of join-irreducibles satisfies the descending chain condition. He was able to prove that such a lattice must itself satisfy the descending chain condition. Interest was expressed in whether or not one could obtain the same result without the assumption of modularity and/or of join-continuity. In this paper we give an elementary proof of this result without the assumption of join- continuity (which of course must then follow as a consequence of the descending chain condition). In addition we give a suitable example to show that modularity may not be omitted in general.
On fundamental operations in groups
Authors: Fajtlowicz S.
Published: April 2009

By anoperationin equationally definable class of group we mean here the element of a free group in this class generated by set {x, y}.

An operation ω(x, y) is calledfundamentalin a class of groupsKif for every groupGωKthe operationxy−1can be expressed in terms of ω.

Higman and Neumann raised in [1] the problem: Is there any binary operation other thanxy-1,x-1y,yx-1,y-1xfundamental in the class of all groups?*
N-compact spaces as limits of inverse systems of discrete spaces
Authors: Chew Kim-Peu
Published: April 2009

LetNdenote the discrete space of all natural numbers. A spaceXisN-compact if it is homeomorphic with some closed subspace of a product of copies ofN. In this paper,N-compact spaces are characterized as homeomorphs of inverse limit space of inverse systems of copies of subsets ofN. Also, it is shown that a spaceXisN-compact if and only if the space(X) of all non-empty compact subsets ofXwith the finite topology isN-compact.
The absolute Euler summability of Fourier series
Authors: Kwee B.
Published: April 2009

The series is said to be summable |Eα| (0 < α < 1) if where Sv = a0 + a1 … + av, and . Since (see [2]), (1) is equivalent to .
On non-Cross varieties of A-groups
Authors: Cossey John
Published: April 2009

The purpose of this paper is to provide a proof for a result announced in [3]. The result arose from a search for just-non-Cross varieties (recall that a Cross variety is one which can be generated by a finite group, and a just-non-Cross variety is a non-Cross variety every proper subvariety of which is Cross). For the motivation for this search, we refer the reader to [12]: for related results, see [1], [12], [13].
A note on countably compact semigroups
Authors: Mukherjea A. , Tserpes N. A.
Published: April 2009

It is well known that every compact topological semigroup has an idempotent and every compact bicancellative semigroup is a topological group. Also every locally compact semigroup which is algebraically a group, is a topological group. In this note we extend these results to the case of countably compact semigroups satisfying the Ist axiom of countability. Some of our results are valid under the weaker condition of sequential compactness.
A remark on Latin squares and block designs
Authors: Wallis W. D.
Published: April 2009

Throughout this paper any matrix is square and of orderqunless otherwise specified.IandJwill represent an identity matrix and a square matrix with every element + 1 respectively; if necessary, the size will be indicated by a subscript. The Kronecker product of matricesA= (aij) andBis the block matrix whose (i, j)-th block isaijB, and is writtenA x B.
Zeta functions of twisted modular curves
Authors: Virdol Cristian
Published: April 2009

In this paper we compute and continue meromorphically to the whole complex plane the zeta function for twisted modular curves. The twist of the modular curve is done by a modprepresentation of the absolute Galois group.
A note on the characterization of CM-fields
Authors: Blanksby P. E. , Loxton J. H.
Published: April 2009

This note deals with some properties of algebraic number fields generated by numbers having all their conjugates on a circle. In particular, it is shown that an algebraic number field is a CM-field if and only if it is generated over the rationals by an element (not equal to ±1) whose conjugate all lie on the unit circle.

Subject classification(Amer. Math. Soc.(MOS)1970): 12 A 15, 12 A 40, 14 K 22.
Algebraic independence properties of the Fredholm series
Authors: Loxton J. H. , van der Poorten A. J.
Published: April 2009

We consider algebraic independence properties of series such as We show that the functions fr(z) are algebraically independent over the rational functions Further, if αrs (r = 2, 3, 4, hellip; s = 1, 2, 3, hellip) are algebraic numbers with 0 < |αrs|, we obtain an explicit necessary and sufficient condition for the algebraic independence of the numbers fr(αrs) over the rationals.
On localizing orderable modules
Authors: Fox Colin D.
Published: April 2009

If A is a T-orderable R-module and S is a multiplicative subsemigroup of R, each s∈S acting as a monomorphism of A, then it is possible sometimes A in a T-orderable R-module on which each s∈S as an automorphism. We show that such an embedding does not always exist and, by generalizing a theorem of Kokorin and Kopytov, provide a partial answer to the question “when is such an embedding possible?”

Subject classification (Amer. Math. Soc. (MOS) 1970): 06 A 70, 16 A 08, 16 A 64.
A uniqueness set for all Hp(Bn) with p>0
Authors: Chee P. S.
Published: April 2009

For n≥2, a hypersurface in the open unit ball Bn in is constructed which satisfies the generalized Blaschke condition and is a uniqueness set for all Hp(Bn) with p>0. If n≥3, the hypersurface can be chosen to have finite area.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 32 A 10.
Normal partitions of idempotents of regular semigroups
Authors: Trotter P. G.
Published: April 2009

A characterization is provided here for any normal partition of the set of idempotents of a regular semigroup S. As a by-product of the method used, a new characterization of the greatest congruence on S corresponding to a given normal partition of its idempotents is obtained.

Subject classification (Amer. Math. Soc. (MOS) 1970): 20 M 10.
Integrability of Fourier transforms under an ergodic hypothesis
Authors: Brown Gavin
Published: April 2009

The object is to unify and complement some recent theorems of Hewitt and Ritter on the integrability of Fourier transforms, but the underlying theme is the ancient one that Plancherel's theorem is the “only” integrability constraint on Fourier transforms. The distinguishing feature of the results is that we restrict attention to positive measures (or functions) which satisfy an ergodic condition and whose transforms are positive. (In fact we employ sums of discrete random variables, a technique which seems to have been largely ignored in context.) The general setting is that of locally compact abelian groups but we are chiefly interested in the line or the circle, and it appears that the theorems are new for these classical groups.
On Ky Fan's minimax principle
Authors: Tarafdar E. , Thompson H. B.
Published: April 2009

A generalized version of the Knaster-Kuratowski-Mazurkiewicz theorem is obtained and used to generalize Ky Fan's minimax principle. This result is applied to a variational inequality.
Characterization of pseudocompactness by the topology of uniform convergence on function spaces
Authors: McCoy R. A.
Published: April 2009

It is shown that a Tychonoff space X is pseudocompact if and only if for every metrizable space Y, all uniformities on Y induce the same topology on the space of continuous functions from X into Y. Also for certain pairs of spaces X and Y, a necessary and sufficient condition is established in order that all uniformities on Y induce the same topology on the space of continuous functions from X into Y.
On the Lie-Kolchin-Mal'cev theorem
Authors: Wehrfritz B. A. F.
Published: April 2009

We discuss generalizations of the Lie-Kolchin-Mal'cev theorem. For example we show that if G is a soluble linear group of degree n, then G contains a triangularizable subgroup T whose index in G is bounded by function of n only and such that T is normalized by every automorphism of G normalizing G0, the Zariski connected component of G containing the identity. We also prove that in certain situations at least the index of G0 in G can be bounded in terms of the degree and the ground field.
Positive points in polar lattices
Authors: Hossain F. , Worley R. T.
Published: April 2009

The authors investigate max min μF(x) F(y)for two standard distance functions F in R2, where μ denotes the area of {x ∈ R2; F(x)≤ 1}, the maximum is over all (geometric) lattices Λ in R2 and the minimum is over all positive points x ∈ Λ and y ∈ Λ* (the polar lattice of Λ). An application is given to a problem on fractional parts.
Varieties that make one Cross
Authors: MacDonald Sheila Oates , Vaughan-Lee M. R.
Published: April 2009

An example is constructed of a locally finite variety of non-associative algebras which satisfies the maximal condition on subvarieties but not the minimal condition. Based on this, counterexamples to various conjectures concerning varieties generated by finite algebras are constructed. The possibility of finding a locally finite variety of algebras which satisfies the minimal condition on subvarieties but not the maximal is also investigated.
The characters and structure of a class of modular representation algebras of cyclic p-groups
Authors: Renaud J. C.
Published: April 2009

Let p,m be the modular representation algebra of the cyclic group of order pm over the prime field Zp. The characters of p, m are derived. For p = 2, this provides an alternative proof of a result due to Carlson (1975), tha 2,m is a local ring. It is shown that for p>2, p, m is a direct sum of 2m local rings. Their dimensions and primitive idempotents are derived.

Subject classification (Amer. Math. Soc. (MOS) 1970): 20 C 20, 12 C 05, 12 C 30, 33 A 65.
Completion of lattices of semi-continuous functions
Authors: August John , Byrne Charles
Published: April 2009

If U and V are toplogies on an abstract set x, then the triple (X, U, V) is a bitopologica space. Using the theorem of Priestley on the representation of distributive lattices, results of Dilworth concerning the normal completion of the lattice of bounded, continuous, realvalued functions on a topological space are extended to include the lattice of bounded, semi-continuous, real-valued functions on certain bitopological spaces. The distributivity of certain lattices is investigated, and the theorem of Funayama on distributive normal completions is generalized.
A new definition of the density of an integer sequence
Authors: Hall R. R.
Published: April 2009

The divisor density of an integer sequence is defined: this measures the tendency of divisors of (almost all) integers to belong to the sequence. A proof of a conjecture of Erdös is given and this is linked to some previous conjectures of the author's concerning distribution (mod 1) of functions of the divisors.
Necessary and sufficient conditions for the existence of a generalized Stieltjes integral
Authors: Russell A. M.
Published: April 2009

In Russell (1973) a Riemann-type necessary and sufficient condition was given for the existence of (defined also in Russell (1975)) when f was bounded and g was k-convex in [a′, b′]. In this paper we present necessary and sufficient conditions for the existence of a particular Stieltjes-type integral without imposing a convexity condition upon g. These conditions are used to obtain an additivity result for the integral over adjoining intervals without any additional restrictions being imposed upon the functions involved.
Optimality conditions for a cone-convex programming problem
Authors: Massam Hélène M.
Published: April 2009

Optimality conditions without constraint qualifications are given for the convex programming problem: Maximize f(x) such that g(x) ∈ B, where f maps X into R and is concave, g maps X into Rm and is B-concave, X is a locally convex topological vector space and B is a closed convex cone containing no line. In the case when B is the nonnegative orthant, the results reduce to some of those obtained recently by Ben-Israel, Ben-Tal and Zlobec.
Representation of pseudo-lattice ordered vector spaces
Authors: Metzler Richard C.
Published: April 2009

Ordered vector spaces more general than vector lattices are represented as function spaces with ‘almost’ the pointwise order. The ‘pseudo-lattice’ property which is necessary (and sufficient in the finite-dimensional case) for the representation is also studied in relation to the lattice property.
Vanishing coefficients in infinite product expansions
Authors: Andrews George E. , Bressoud David M.
Published: April 2009

Richmond and Szekeres (1977) have conjecturned that certain of the coefficients in the power series expansions of certain infinite products vanish. In this paper, we prove a general family of results of this nature which includes the above conjectures.
On the existence of Nash equilibrium points
Authors: Tarafdar E. , Husain T.
Published: April 2009

The existence of Nash equilibrium points of game between n players has been established under the conditions dual to known ones.
A lambda calculus with naive substitution
Authors: Staples John
Published: April 2009

An alternative approach is proposed to the basic definitions of the lassical lambda calculus. A proof is sketched of the equivalence of the approach with the classical case. The new formulation simplifies some aspects of the syntactic theory of the lambda calculus. In particular it provides a justification for omitting in syntactic theory discussion of changes of bound variable.
Direct decompositions of groups with finitely generated commutator quotient group
Authors: Hirshon Ronald
Published: April 2009

Let G/G' be finitely generated and let G = B1 x A1 = B2 x A2 = … = Bi x Ai = … with each Bi isomorphic to a fixed group B which obeys the maximal condition for normal subgroups. Then the Ai represent only finitely many isomorphism classes. We give an example with B infinite cyclic, G/G' free abelian of infinite (countable) rank and such that G is decomposed as above with no two Ai isomorphic.
Measurability of cross section measure of a product Borel set
Authors: Johnson Roy A.
Published: April 2009

Suppose μ and ν are Borel measures on locally compact spaces X and Y, respectively. A product measure λ can be defined on the Borel sets of X x Y by the formula λ(M) = ∫ν(Mx) dμ, provided that vertical cross section measure ν(Mx) is a measurable function in x. Conditions are summarized for ν(Mx) to be measurable as a function in x, and examples are given in which the function ν(Mx) is not measurable. It is shown that a dense, countably compact set fails to be a Borel set if it contains no nonempty zero set.
Decompositions of complete symmetric digraphs into the oriented pentagons
Authors: Alspach Brian , Heinrich Katherine , Varma Badri N.
Published: April 2009

We show that the complete symmetric digraph DKn, n≧5, can be decomposed into each of the four oriented pentagons if and only if n ≡ 0 or 1 (mod 5).
On the relationship between a summability matrix and its transpose
Authors: Swetits J.
Published: April 2009

Let E, F be sequence spaces and A an infinite matrix that maps E to F. Sufficient conditions are given so that the transposed matrix maps Fβ to Eβ.
Radical properties defined locally by polynomial identities II
Authors: Gardner B. J.
Published: April 2009

A radical class R of rings (not necessarily associtative) is called an n-radical class if it has the property that a ring is in R if and only if every subring generated by ≤n elements is in R. A transfer theorem is proved, relating n-radical classes in two universal varieties which share the same ≤n-generator rings. Partially through the use of this result, we obtain information about extension closed subvarieties of various universal varieties of power-associative rings.
Decompositions of modules over a discrete valuation ring
Authors: Stanton Robert O.
Published: April 2009

Let N be a direct summand of a module which is a direct sum of modules of torsion-free rank one over a discrete valuation ring. Then there is a torsion module T such that N⊕T is also a direct sum of modules of torsion-free rank one.
Some problems in partitio numerorum
Authors: Erdös P. , Loxton J. H.
Published: April 2009

We consider some unconventional partition problems in which the parts of the partition are restricted by divisibility conditions, for example, partitions n = a1+…+ak into positive integers a1, …, ak such that a1 ∣ a2 ∣ … ∣ ak. Some rather weak estimates for the various partition functions are obtained.
Locally uniformly rotund norms and Markuschevich bases
Authors: Yorke A. C.
Published: April 2009

If a Banach space E admits a Markuschevich basis, then E can be renormed to be locally uniformly rotund. When the coefficient space of the basis is 1-norming, and this norm is very smooth, E is weakly compactly generated.
Permutation characters of finite groups of Lie type
Authors: Surowski David B.
Published: April 2009

Let g be a connected reductive linear algebraic group, and let G = gσ be the finite subgroup of fixed points, where σ is the generalized Frobenius endomorphism of g. Let x be a regular semisimple element of G and let w be a corresponding element of the Weyl group W. In this paper we give a formula for the number of right cosets of a parabolic subgroup of G left fixed by x, in terms of the corresponding action of w in W. In case G is untwisted, it turns out thta x fixes exactly as many cosets as does W in the corresponding permutation representation.
The 𝒥-classes of an inverse semigroup
Authors: Ash C. J.
Published: April 2009

It is shown, using the author's construction for ‘labelled semilattices’, that every partially ordered set, in which every two elements have a common lower bound, is isomorphic to the partiallyordered set of 𝒥-classes of some completely semi-simple inverse semigroup.

1980 Mathematics subject classification (Amer. Math. Soc): primary 20 M 10, secondary 04 A 05, 08 A 05.
Resolvable (r, λ)-designs and the Fisher inequality
Authors: Vanstone S. A.
Published: April 2009

It is well known that in any (v, b, r, k, λ) resolvable balanced incomplete block design that b≧ ν + r − l with equality if and only if the design is affine resolvable. In this paper, we show that a similar inequality holds for resolvable regular pairwise balanced designs ((ρ, λ)-designs) and we characterize those designs for which equality holds. From this characterization, we deduce certain results about block intersections in (ρ, λ)-designs.
Balanced binary arrays iii: the hexagonal grid
Authors: Oates-Williams Sheila , Street Anne Penfold
Published: April 2009

We consider the following problem arising in agricultural statistics. Suppose that a large number of plants are set out on a regular grid, which may be triangular, square or hexagonal, and that among these plants, half are to be given one and half the other of two possible treatments. For the sake of statistical balance, we require also that, if one plant in every k plants has i of its immediate neighbours receiving the same treatment as itself, then k is constant over all possible values of i. For square and triangular grids, there exist balanced arrays of finite period in each direction, but for the hexagonal grid, we show that no such balanced array can exist. Several related questions are discussed.
Homomorphisms having a given H-class as a single class
Authors: Hunter R. P. , Anderson L. W.
Published: April 2009

In [1] it was shown if S is a stable semigroup and H an ℋ-class of S then there is a congruence (H) on S in which H is a single class. After considering some consequences of this result for abstract semigroups, we consider some analogous questions for compact semigroups.
A note on commutative Baer rings III
Authors: Speed T. P.
Published: April 2009

If R is a commutative semiprime ring with identity Kist [4], [5] has shown that R can be embedded into a commutative Baer ring B(R), and has given some properties of this embedding. More recently Mewborn [7] has given a construction which embeds R into a commutative Baer ring with the stronger property that every annihilator is generated by an idempotent. Both of these constructions involve a representation of R as a ring of global sections of a sheaf over a Boolean space.
On the product of vector measures
Authors: Kluvánek Igor
Published: April 2009

Let μ and ν be measures defined on some σ-algebrs with values in locally convex topological vector spaces X and Y, repectively. It is possible [1] to construct their product λ = μ × ν as a measure on a σ-algebra if λ is allowed to take its values in X ⊗ε Y, the completion of X ⊗ Y in the topology of bi-equicontinuous convergence. The reason is, roughly speaking, that the topology of biequicontinuous convergence on X ⊗ Y is coarse enough to make λ σ-additive and the completion X ⊗ε Y is big enough to accommodate all values of λ. Here we are going to improve the result by introducing a finer topology on X ⊗ Y in which λ will be σ-additive and such that all values of λ will belong to the completion of X ⊗ Y under that topology. The topology in question is obtained by a slight modification from a topology considered for the first time in the work [3] of Jacobs. Curiously enough, the proof of the improved result is simpler than that of [1] and reduces almost to a direct observation avoiding duality arguments.
Random walks on random trees
Authors: Moon J. W.
Published: April 2009

Let T denote one of the nn−2 trees with n labelled nodes that is rooted at a given node x (see [6] or [8] as a general reference on trees). If i and j are any two nodes of T, we write i ∼ j if they are joined by an edge in T. We want to consider random walks on T; we assume that when we are at a node i of degree d the probability that we proceed to node j at the next step is di–1 if i ∼ j and zero otherwise. Our object here is to determine the first two moments of the first return and first passage times for random walks on T when T is a specific tree and when T is chosen at random from the set of all labelled trees with certain properties.
The endomorphism ring of the additive group of a ring
Authors: Schultz P.
Published: April 2009

One of the still unsolved problems posed by Fuchs in his well-known book “Abelian Groups” [2] is Problem 45: characterize the rings R for which . I present here a partial solution.
Denominator Sequences of continued fractions I
Authors: Worley R. T.
Published: April 2009

Let α be an irrational number with simple continued fraction α = (a0, a1, a2,…). The problem studied is that of whether the sequence (qn) of denominators of the convergents pn/qn to α has a subsequence (Bn) = (qin} which is the sequence of denominators of convergents An/Bn to a different number α′. In other words, does there exist a subsequence {qin} which satisfies qio= 1 and For example, the sequence of denominators of convergents to ½(3 − e) is a subsequence of the sequence of denominators of convergents to ε.
Gauge invariance of the Dirac equation
Authors: Smrz P.
Published: April 2009

The Dirac equation in its most usual form can be derived by the minimum action principle from the Lagrangian density where γk (k =1,2,3,4) are the Dirac 4 × 4 matrices satisfying relations; ψ(x) is a column matrix with 4 complex elements being functions of x1, x2, x3, x4, coordinates of the pseudo-Euclidean space with metric gik.(
Double ideals in compact semirings
Authors: Bertman Martha , Selden John
Published: April 2009

By a topological semiring we mean a Hausdorff space S together with two continuous associative operations on S such that one (called multiplication) distributes across the other (called addition). That is, we insist that for all x, y and z in S. Note that, in contrast to the purely algebraic situation [1,2], we do not postulate the existence of an additive identity which is a multiplicative zero.
On the semigroup of bounded C1-mappings
Authors: Yamamuro Sadayuki
Published: April 2009

Let E be a real Banach space. If f: E→E is (Fréchet-) differentiable at every point of E, the derivative of f at x is denoted by f'(x), which is an element of the Banach algebra ℒ=ℒ(E) of all linear continuous mappings of E into itself with the usual upper bound norm, and, if we put , we have .
The recursive equivalence type of a decomposition of an ω-group: The RET of a decomposition
Authors: Applebaum C. H.
Published: April 2009

Let ε, Λ, Λ*, ΛR stand for the set of non-negative integers, isols, isolic integers and regressive isols respectively, and let P(τ) be the ω-group of Gödel numbers of permutations of the set τ ε ε which move only finitely many elements of τ. The concept of an ω-group was studied by Hassett [5]. He proved in P12 of [5] that for an isolated set τ, the decomposition of P(τ) into conjugacy sets is a gc-decomposition if and only if τ is regressive. For the finite symmetric group on n elements, Sn it is known that the order of the conjugacy class is p(n), where p(n) is the partition function. The author shows in this paper, using a result of Barback [1], that if pΛ(T) is Nerode's canonical extension of p(n) to Λ and Req (τ) = T, then pΛ(T) = Req Cτ, where Cτ is the decomposition of P(τ) into conjugacy sets. The reader is assumed to be familiar with the contents of [2], [4] and [5].
A remark on “Uniform O– estimates of certain error functions connected with k-free integers”
Authors: Suryanarayana D.
Published: April 2009

In this note I follow the same notation adopted in [2]. Let Qk(x, n) denote the number of k-free integers ≦x which are prime to n. In [2], I proved the following: For o≦s>1/k uniformly, where σ*−s(n) is the sum of the reciprocals of the sth powers of the square-free divisor of n.
Application of Baecklund transformations to the Stokes-Beltrami equations
Authors: Rogers C. , Kingston J. G.
Published: April 2009

The Stokes-Beltrami equations, being applicable to many classes of physical problems, have for a long time received a great deal of attention from authors investigating their various aspects. One may cite, for example, Weinstein [1] and more recently Ranger [2] as just two of many research papers into this topic. Baecklund transformations have, in previous work, been applied to hodograph-type equations (Loowrner ], Power, Rogers and Onborn [4], Rogers [5, 6]) and reduction to appropriate canonical forms in elliptic, parabolic, and hyprebolic regimes has been achieved.
Tauberian theorems for [J, f(x)] transformations
Authors: Jakimovski A. , Livne A.
Published: April 2009

Let Σ∞n=0 an(sn=a0+…+an, n≧0) be a series of real or complex numbers. Denote by and two linear transforms T1 and T2 of {sn}. Estimates of the form for sequences {sn} satisfying where {dn} is a certain fixed linear transform of the sequence and depend on the transforms T1, T2 and {dn}, were considered for the first time by Hadwiger [2]. The smallest value of C satisfying (1.2) for all sequences {sn} satisfying (1.3) is known as the Tauberian constant associated with the pair of transforms T1, T2 and {dn}.
Group algebras with an Engel group of units
Authors: Bovdi A.
Published: April 2009

Let F be a field of characteristic p and G a group containing at least one element of order p. It is proved that the group of units of the group algebra FG is a bounded Engel group if and only if FG is a bounded Engel algebra, and that this is the case if and only if G is nilpotent and has a normal subgroup H such that both the factor group G/H and the commutator subgroup H′ are finite p–groups.
Some new Besov and Triebel-Lizorkin spaces associated with para-accretive functions on spaces of homogeneous type
Authors: Deng Dongguo , Yang Dachun
Published: April 2009

Let (X, ρ, μ)d, θbe a space of homogeneous type withd< 0 and θ ∈ (0, 1],bbe a para-accretive function, ε ∈ (0, θ], ∣s∣ > ∈ and a0∈ (0, 1) be some constant depending ond, ∈ ands. The authors introduce the Besov spacebBspq(X) with a0> p ≧ ∞, and the Triebel-Lizorkin spacebFspq(X) with a0>p> ∞ and a0> q ≧∞ by first establishing a Plancherel-Pôlya-type inequality. Moreover, the authors establish the frame and the Littlewood-Paley function characterizations of these spaces. Furthermore, the authors introduce the new Besov spaceb−1Bs(X) and the Triebel-Lizorkin spaceb−1Fspq(X). The relations among these spaces and the known Hardy-type spaces are presented. As applications, the authors also establish some real interpolation theorems, embedding theorems,T btheorems, and the lifting property by introducing some new Riesz operators of these spaces.
Almost sure convergence of quadratic forms in random variables
Authors: Rohatgi V. K.
Published: April 2009

Let X1, X2, … be a sequence of random variables and let {ajk}, j,k = 1, 2, …, be a matrix of real numbers. Write We establish the following result.
Centre-by-metabelian Lie algebras
Authors: Vaughan-Lee M. R.
Published: April 2009

If V is a variety of metabelian Lie algebras then V has a finite basis for its laws [3]. The proof of this result is similar to Cohen's proof that varieties of metabelian groups have the finite basis property [1]. However there are centre-by-metabelian Lie algebras of characteristic 2 which do not have a finite basis for their laws [4] this contrasts with McKay's recent result that varieties of centre-by-metabelian groups do have the finite basis property [2]. The rollowing theorem shows that once again “2” is the odd man out.
A relation between the permanental and determinantal adjoints
Authors: Marcus Marvin , Merris Russell
Published: April 2009

Let Hn denote the set of complex n-square positive semidefinite hermtian matrices. We partially order Hn: If A, B, A–B єHn, write A > B. For A єHn, Write P(A) for the permanental adjoint of A, i.e., P(A) is the n-suare matrix whose i, j entry is per A(j/i), where A(j/i) is the submatrix of A obtained by deleting row j and column i. Now, P(A) is a principal submatrix of t he (n–1)st induced power matrix of AT. Hence, P(A) ∈Hn. Also D(A), the classical adjoing, is in Hn.
Homotopy classification of filtered complexes
Authors: Street Ross
Published: April 2009

The homology functor from the category of free abelian chain complexes and homotopy classes of maps to that of graded abelian groups is full and replete (surjective on objects up to isomorphism) and reflects isomorphisms. Thus such a complex is determined to within homotopy equivalence (although not a unique homotopy equivalence) by its homology. The homotopy classes of maps between two such complexes should therefore be expressible in terms of the homology groups, and such an expression is in fact provided by the Künneth formula for Hom, sometimes called ‘the homotopy classification theorem’.
Quasicompactness and functionally Hausdorff spaces
Authors: D'Aristotle A. J.
Published: April 2009

In [1] Van Est and Freudenthal introduced and studied several new separation axioms for a topological space. One of these was thepτsq axiom: Given distinct pointspandqofX, there exists a real continuous functionfonXwithf(p) ≠f(q). They observed that thepτsqaxiom lies strictly between the Hausdorff and completely regular axioms, and that it neither implies nor is implied by theT3axiom.
Elementary proofs of Peano's existence theorem
Authors: Dow M. A. , Výborný R.
Published: April 2009

An “elementary” proof of Peano's existence theorem is given that, in addition to avoiding the Ascoli lemma, relies neither on Dini's theorem, nor on uniform continuity of the right hand side of φ' = f(t,φ). It is based on superfunctions. Also, another standard proof of that theorem, based on approximation of the right hand side, is made elementary.
Embedding the complement of two lines in a finite projective plane
Authors: Totten Jim
Published: April 2009

In this paper we use a result from graph theory on the characterization of the line graphs of the complete bigraphs to show that if n is any integer ≥ 2 then any finite linear space having p = n2 − n or p = n2 − n + 1 points, of which at least n2 − n have degree n + 1, and q ≤ n2 + n − 1 lines is embeddable in an FPP of order n unless n = 4. If n = 4 there is only one possible exception for each of the two values of p, and for p = n2 − n, this exception can be embedded in the FPP of order 5.
Using cyclotomy to construct orthogonal designs
Authors: Cooper Joan , Wallis Jennifer Seberry
Published: April 2009

An orthogonal design of order n and type (s1, s2) on the commuting variables x1, x2 is a matrix of order n with entries from {0, ± x1, ± x2} whose row vectors are formally orthogonal.

This note uses cyclotomy to construct orthogonal designs and finds several infinite families of new designs.
Dual functors and the Radon-Nikodym property in the category of Banach spaces
Authors: Pelletier John Wick
Published: April 2009

The notion of duality of functors is used to study and characterize spaces satisfying the Radon-Nikodym property. A theorem of equivalences concerning the Radon-Nikodym property is proved by categorical means; the classical Dunford-Pettis theorem is then deduced using an adjointness argument. The functorial properties of integral operators, compact operators, and weakly compact operators are discussed. It is shown that as an instance of Kan extension the weakly compact operators can be expressed as a certain direct limit of ordinary hom functors. Characterizations of spaces satisfying the Radon-Nikodym property are then given in terms of the agreement of dual functors of the functors mentioned above.
The type set of a torsion-free abelian group of rank two
Authors: Jackett David R.
Published: April 2009

In this paper we generalize a recent result of Freedman (1973) concerning the cardinality of the type set of a rank two torsion-free abelian group. We show that ifAis such a group andAsupports a non-trivial associative ring then the type set ofAcontains at most three elements.
Operator-valued multiplier theorems characterizing Hilbert spaces
Authors: Arendt Wolfgang , Bu Shangquan
Published: April 2009

We show that the operator-valued Marcinkiewicz and Mikhlin Fourier multiplier theorem are valid if and only if the underlying Banach space is isomorphic to a Hilbert space.
Optimal natural dualities: the role of endomorphisms
Authors: Saramago M. J.
Published: April 2009

The optimality of dualities on a quasivariety , generated by a finite algebra , has been introduced by Davey and Priestley in the 1990s. Since every optimal duality is determined by a transversal of a certain family of subsets of Ω, where Ω is a given set of relations yielding a duality on , an understanding of the structures of these subsets—known as globally minimal failsets—was required. A complete description of globally minimal failsets which do not contain partial endomorphisms has recently been given by the author and H. A. Priestley. Here we are concerned with globally minimal failsets containing endomorphisms. We aim to explain what seems to be a pattern in the way endomorphisms belong to these failsets. This paper also gives a complete description of globally minimal failsets whose minimal elements are automorphisms, when is a subdirectly irreducible lattice-structured algebra.
An example involving a non-regular -class in a semigroup
Authors: Hall T. E.
Published: April 2009

We answer in the negative (by considering an example) the problem posed in exercise 6 of § 2.3, page 62 [1], namely: If aD-classDof a semigroupSis a subsemigroup of S, then is D necessarily bisimple? For any semigroupT, we letLT,RT,HT,DTandJTdenote Green's relations onT.
Congruences on orthodox semigroups II
Authors: Meakin John
Published: April 2009

If ρ is a congruence on a regular semigroup S, then the kernel of ρ is defined to be the set of ρ-classes which contain idempotents of S. Preston [7] has proved that two congruences on a regular semigroup coincide if and only if they have the same kernel: this naturally poses the problem of characterizing the kernel of a congruence on a regular semigroup and reconstructing the congruence from its kernel. In some sense this problem has been resolved by the author in [5]. Using the well-known theorem of M. Teissier (see for example, A. H. Clifford and G. B. Preston [1], Vol. II, Theorem 10.6), it is possible to characterize the kernel of a congruence on a regular semigroup S as a set A = {Ai: i ∈ I} of subsets of S which satisfy the Teissier-Vagner-Preston conditions:
Approximation of functions by a new class of linear operators
Authors: Jain G. C.
Published: April 2009

Various extensions and generalizations of Bernstein polynomials have been considered among others by Szasz [13], Meyer-Konig and Zeller [8], Cheney and Sharma [1], Jakimovski and Leviatan [4], Stancu [12], Pethe and Jain [11]. Bernstein polynomials are based on binomial and negative binomial distributions. Szasz and Mirakyan [9] have defined another operator with the help of the Poisson distribution. The operator has approximation properties similar to those of Bernstein operators. Meir and Sharma [7] and Jam and Pethe [3] deal with generalizations of Szasz-Mirakyan operator. As another generalization, we define in this paper a new operator with the help of a Poisson type distribution, consider its convergence properties and give its degree of approximation. The results for the Szasz-Mirakyan operator can easily be obtained from our operator as a particular case.