bluuebunny/crossref_metadata_2025 huggingface dataset:
Enlarging the Munn representation of inverse semigroups
Authors: Reilly N. R.
Published: April 2009

The inverse semigroup TE of isomorphisms of principal ideals of E onto principal ideals of E, where E is a semilattice, has been introduced and studied by Munn (1966, 1970). He showed that, for any inverse semigroup S with semilattice E, there is a representation of S by an inverse subsemigroup of TE. The Munn representation, however, is not always faithful. In this paper, the possibility is considered of enlarging the carrier set E of the Munn representation in order to obtain a faithful representation of S as an inverse subsemigroup of a structure resembling TE in many ways. A structure X is obtained by replacing each element of E by a set. Then X = ∪{Xe: e ∈ E}, where Xe, denotes some set, has a natural pre-order relation ≤ (where x ≤ y if and only if x ∈ Xe, y ∈ Xf and e ≦ f ) inherited from E such that if T = {(x, y)∈X × X;x ≤ y and y ≤ x} then X/T is isomorphic to E. Such a set X is referred to as a pre-semilattice with semilattice E. If Tx denotes the set of all isomorphisms of principal ideals of X onto principal ideals of X then Tx is an inverse semigroup. Basic properties of Tx are considered. It is shown that when X is locally uniform, that is, when |Xe| = |Xf|, for all e, f ∈ E, Tx may be described as a wreath product of a permutation group with TE.

The set s itself is a presemilattice with semilattice E with respect to the pre-order ≤ defined by a ≤ b if and only if a−1a ≦ b−1b. It is then shown that the Vagner-Preston representation embeds S as a full inverse subsemigroup of Ts. As an application of these concepts the following result is established. Let R and S be inverse semigroups and let θ1(θ2) be an isomorphism of a semilattice E onto the semilattice of R(S). Then there exists a locally uniform presemilattice W and embeddings ϕ1, ϕ2 of R and S, respectively, as full inverse subsemigroups of Tw such that (1) θ1ϕ1 = θ2ϕ2 and (2) (eθ1ϕ1, eθ2ϕ2) ∈ if and only if Ee is isomorphic to Ef.
Two semigroups of continuous relations
Authors: Bednarek A. R. , Norris Eugene M.
Published: April 2009

Synopsis

In this paper we define two semigroups of continuous relations on topological spaces and determine a large class of spaces for which Banach-Stone type theorems hold, i.e. spaces for which isomorphism of the semigroups implies homeomorphism of the spaces. This class includes all 0-dimensional Hausdorff spaces and all those completely regular Hausdorff spaces which contain an arc; indeed all of K. D. Magill's S*-spaces are included. Some of the algebraic structure of the semigroup of all continuous relations is elucidated and a method for producing examples of topological semigroups of relations is discussed.
Decomposable involution centralizers involving exceptional lie type simple groups
Authors: Curran M. J.
Published: April 2009

There have been investigations (Janko (1966), Janko and Thompson (1966), Yamaki (1972)) of finite groups G which contain a central involution t whose centralizer (in G) has the form C(t) = 〈t〉 × F, where F is isomorphic to a non-abelian simple group. Here it is shown such a group cannot be simple when F is isomorphic to an exceptional Lie type simple group of odd characteristic. Specifically the following theorem is proved.
Homeomorphisms of Quaternion space and projective planes in four space
Authors: Price T. M.
Published: April 2009

It is known that all locally flat projective planes in S4 have homeomorphic normal disk bundles. In this paper we investigate the homeomorphisms of Q3 (= boundary of the normal disk bundle) on to itself. We show that a homeomorphisms of Q3 onto itself is determined, up to isotopy, by the outerautomorphism of π1(Q3) that it induces. Since Q3 is an irreducible, not sufficiently large 3-manifold with finite fundamental group this characterization is interesting in its own right. The characterization of homeomorphisms is then used to study certain questions about embeddings of the projective plane in S4. One result is that there are at most two distinct projective planes in S4 with a given complement.
Variations on a theorem of Cowling and Price with applications to nilpotent Lie groups
Authors: Parui S. , Thangavelu S.
Published: April 2009

In this paper we prove a new version of the Cowling-Price theorem for Fourier transforms on Rn. Using this we formulate and prove an uncertainty principle for operators. This leads to an analogue of the Cowling-Price theorem for nilpotent Lie groups. We also prove an exact analogue of the Cowling-Price theorem for the Heisenberg group.
On parabolic submonoids of a class of singular Artin monoids
Authors: Antony Noelle
Published: April 2009

This paper concerns parabolic submonoids of a class of monoids known as singular Artin monoids. The latter class includes the singular braid monoid— a geometric extension of the braid group, which was created for the sole purpose of studying Vassiliev invariants in knot theory. However, those monoids may also be construed (and indeed, are defined) as a formal extension of Artin groups which, in turn, naturally generalise braid groups. It is the case, by van der Lek and Paris, that standard parabolic subgroups of Artin groups are canonically isomorphic to Artin groups. This naturally invites us to consider whether the same holds for parabolic submonoids of singular Artin monoids. We show that it is in fact true when the corresponding Coxeter matrix is of ‘type FC’ hence generalising Corran's result in the ‘finite type’ case.
Recurrence rates for loosely Markov dynamical systems
Authors: Urbański Mariusz
Published: April 2009

The concept of loosely Markov dynamical systems is introduced. We show that for these systems the recurrence rates and pointwise dimensions coincide. The systems generated by hyperbolic exponential maps, arbitrary rational functions of the Riemann sphere, and measurable dynamical systems generated by infinite conformal iterated function systems are all checked to be loosely Markov.
Spaces of vector functions that are integrable with respect to vector measures
Authors: Rodríguez José
Published: April 2009

We study the normed spaces of (equivalence classes of) Banach space-valued functions that are Dobrakov,S* or McShane integrable with respect to a Banach space-valued measure, where the norm is the natural one given by the total semivariation of the indefinite integral. We show that simple functions are dense in these spaces. As a consequence we characterize when the corresponding indefinite integrals have norm relatively compact range. On the other hand, we also determine when these spaces are ultrabornological. Our results apply to conclude, for instance, that the spaces of Birkhoff (respectively McShane) integrable functions defined on a complete (respectively quasi-Radon) probability space, endowed with the Pettis norm, are ultrabornological.
Semicontinuous functions and convex sets inC(K)spaces
Authors: Moreno J. P.
Published: April 2009

The stability properties of the family ℳ of all intersections of closed balls are investigated in spacesC(K), whereKis an arbitrary Hausdorff compact space. We prove that ℳ is stable under Minkowski addition if and only ifKis extremally disconnected. In contrast to this, we show that ℳ is always ball stable in these spaces. Finally, we present a Banach space (indeed a subspace ofC[0, 1]) which fails to be ball stable, answering an open question. Our results rest on the study of semicontinuous functions in Hausdorff compact spaces.
on the value set of the Carmichael λ-function
Authors: Friedlander John B. , Luca Florian
Published: April 2009

In this paper we study the size of the value set of the Carmichael λ-functions.
On values taken by the largest prime factor of shifted primes
Authors: Banks William D. , Shparlinski Igor E.
Published: April 2009

Let P denote the set of prime numbers, and let P(n) denote the largest prime factor of an integer n > 1. We show that, for every real number , there exists a constant c(η) > 1 such that for every integer a ≠ 0, the set has relative asymptotic density one in the set of all prime numbers. Moreover, in the range , one can take c(η) = 1+ε for any fixed ε > 0. In particular, our results imply that for every real number 0.486 ≤ b.thetav; ≤ 0.531, the relation P(q − a) ≍ qθ holds for infinitely many primes q. We use this result to derive a lower bound on the number of distinct prime divisor of the value of the Carmichael function taken on a product of shifted primes. Finally, we study iterates of the map q ↦ P(q - a) for a > 0, and show that for infinitely many primes q, this map can be iterated at least (log logq)1+o(1) times before it terminates.
Twills on a given number of harnesses
Authors: Hoskins W. D. , Street Anne Penfold
Published: April 2009

The simple twills on n harnesses can be classified according to the number of breaks that they possess. An algorithm is detailed for determining these twills and some sample listings given. A formula is derived which evaluates the total number of n-harness twills with a specified number of breaks, and hence also the total possible number of twills on n harnesses. Also the balanced twills on n harnesses are enumerated.
Order-bounded convergence structures on spaces of continuous functions: Corrigendum
Authors: Schroder M.
Published: April 2009

I am greatly in debt to K. Kutzler of Berlin and H.-P. Butzmann of Mannheim for pointing out some errors in the paper named above, Schroder (1979), and to the latter for providing the relevant examples.
Latin squares with highly transitive automorphism groups
Authors: Bailey R. A.
Published: April 2009

A Latin square is considered to be a set ofn2cells with three block systems. An automorphisni is a permutation of the cells which preserves each block system. The automorphism group of a Latin Square necessarily has at least 4 orbits on unordered pairs of cells ifn< 2. It is shown that there are exactly 4 orbits if and only if the square is the composition table of an elementary abelian 2-group or the cclic group of order 3.
Injective and projective Boolean-like rings
Authors: Swaminathan V.
Published: April 2009

A Boolean-like ringRis a commutative ring with unity in which 2x= 0 andxy(1 +x)(1 +y) = 0 hold for all elementsx, yof the ringR. It is shown in this paper that in the category of Boolean-like rings,Ris injective if and only ifRis a complete Boolean ring andRis projective if and only ifR= {0, 1}.
Monotone and 1–1 sets
Authors: Madan D. B. , Robinson R. W.
Published: April 2009

An infinite subset of ω is monotone (1–1) if every recursive function is eventually monotone on it (eventually constant on it or eventually 1–1 on it). A recursively enumerable set is co-monotone (co-1–1) just if its complement is monotone (1–1). It is shown that no implications hold among the properties of being cohesive, monotone, or 1–1, though each implies r-cohesiveness and dense immunity. However it is also shown that co-monotone and co-1–1 are equivalent, that they are properly stronger than the conjunction of r-maximality and dense simplicity, and that they do not imply maximality.
A construction of supernilpotent radical classes
Authors: Olson Dwight M.
Published: April 2009

In a recent paper van Leeuwen and Heyman constructed a supernilpotent radical class using the class of almost nilpotent rings. Using a similar construction, for any class C satisfying the following four properties we obtain a superrnlpotent radical class containing C.

(N1) C contains the class Z of all zero rings.

(N2) C is hereditary.

(N3) C is homomorphically closed.

(N4) If A and A/I are elements of C for some ideal I of a ring A, then A ∈ C.

Every supernilpotent radical class P clearly satisfies these conditions. For any such radical class we define the class of almost radical rings and use these to construct a new radical class P2 which contains the given one. Also, we give a characterization for dual supernilpotent radicals.
The existence of locally fine simplicial subdivisions
Authors: Pfeffer W. F.
Published: April 2009

Given a simplexSand a positive function δ onS, we show that there is asimplicialsubdivision ofSsuch that the diameter of each subdividing simplex is smaller that δ evaluated at some of its vertices.
A coherence theorem on Schützenberger groups
Authors: Grillet Pierre Antoine
Published: April 2009

It is well-known that, in any semigroup S, all the left and right Schützenberger groups of the ℋ-class contained in a fixed D class D of S are isomorphic to one group. We prove a sharper result: that, up to actionpreserving isomorphisms, all these Schützenberger groups and their classical isomorphisms are but one group and its identity isomorphism; thus, one group is essentially sufficient to describe not only all the Schützenberger groups of ℋ-classes in D, but their action on these ℋ-classes and classical isomorphisms as well.
A criterion for the existence of biharmonic Green's functions
Authors: Sario Leo
Published: April 2009

The biharmonic Green's function of a simply supported plate is generalized to Riemannian manifolds and shown to exist if and only if the harmonic measure of the ideal boundary is square integrable.
Finite sublattices of three-generated lattices
Authors: Davey Brian A. , Rival Ivan
Published: April 2009

Every lattice generated by three unordered elements contains a finite sublattice generated by three unordered elements. A list ℒ of twelve finite lattices, each generated by a three-element unordered set, is given. It is proved that every lattice generated by a three-element unordered set contains a sublattice isomorphic to onė of the lattices in ℒ moreover, ℒ is the smallest such list.
Adders for the patterned starter in nonabelian groups
Authors: Gross Kenneth B. , Leonard Philip A.
Published: April 2009

Starters with adders, in abelian groups of odd order, have been used widely in recent combinatorial constructions, most notably in the study of Room squares. In this paper, constructions of adders for the so-called “patterned starter” are described, for a large class of nonabelian groups of odd order.
Round subsets of Wallman-type compactifications
Authors: Su Li Pu
Published: April 2009

Let ℒ be a normal base of a Tychonoff spaceXand ωℒ denote the Wallman-type (real-) compactification ofXgenerated by ℒ. This Wallman-type compactification is known to associate with a unique proximity δ. A ℒ-filter ℒ is round if for eachF∈ ℒ there is anFo∈ ℒ there is anFo∈ ℒ such thatFo(X-F). A subsetAof ω(£) is called a round subset of ω (£) iff for eachZ∈ ℒ, ifC1w(x)Zcontains A, then it is a neighborhood ofA. Properties of round ℒ-filters and round sets of ω(ℒ) are introduced. We also prove that the intersection of all the free ℒ-ultrafilters is ℒ= {Z∈ ℒ: C1x(X-Z) is compact} iff ω(ℒ) –Xis a round subset of ω(ℒ) if ℒ is a separating nest generated intersection ring with property (α) then ω(ℒ) -v(ℒ) is a round subset of ω(ℒ).
Tensor products of l2-valued measures
Authors: Swartz Charles
Published: April 2009

Duchon (1967, 1969) and Duchon and Kluvánek (1967) considered the problems of the existence of countably additive tensor products for vector measures. Duchon and Kluvánek (1967) showed that a countably additive product with respect to the inductive tensor topology always exists while Kluvánek (1970) presented an example which showed that this was not the case for the projective tensor topology. Kluvánek considered yet another tensor product topology which is stronger than the inductive topology but weaker than the projective tensor topology and showed that a countably additive product for two vector measures always exists for this particular tensor topology, see Kluvánek (1973). He has conjectured that this topology is the strongest tensor topology (given by a cross norm) which always admits products for any two arbitrary vector measures. In this note we use an example of Kluvánek (1974) to show that this conjecture is indeed true when one of the factors in the tensor product is l2 and the other factor is metrizable. The construction used also clarifies a conjecture made by Swartz (to appear) concerning products of Hilbert space valued measures.
Group properties of Hadamard matrices
Authors: Hall Marshall
Published: April 2009

An Hadamard matrix H is a square matrix of order n all of whose entries are ± 1 such thatThere are matrices of order 1 and 2and for all other Hadamard matrices the order n is a multiple of 4, n = 4m. It is a reasonable conjecture that Hadamard matrices exist for every order which is a multiple of 4 and the lowest order in doubt is 268. With every Hadamard matrix H4m a symmetric design D exists with
Characterization of optimality for the abstract convex program with finite dimensional range
Authors: Borwein Jon M.
Published: April 2009

This paper presents characterizations of optimality for the abstract convex program

when S is an arbitrary convex cone in a finite dimensional space, Ω is a convex set and p and g are respectively convex and S-convex (on Ω). These characterizations, which include a Lagrange multiplier theorem and do not presume any a priori constraint qualification, subsume those presently in the literature.
Permutation representation of groups with Boolean orthogonalities
Authors: Davis Gary
Published: April 2009

Reduced rings and lattice-ordered groups are examples of groups with Boolean orthogonalities. In this note we show that any group with a Boolean orthogonality satisfying a finiteness condition introduced by Stewart is isomorphic with a group of homeomorphisms of a topological space, in which two homeomorphisms are orthogonal if and only if they have disjoint supports.
Harmonic analysis on the Fourier algebras A1, p(G)
Authors: Lai Hang-Chin , Chen Ing-Sheun
Published: April 2009

Let G be a locally compact group G (which may be non-abelian) and Ap(G) the p-Fourier algebra of Herz (1971). This paper is concerned with the Fourier algebra Al, p(G) = Ap(G) ∩ L1(G) and various relations that exist between Al, p(G), Ap(G) and G.
The laws of some metabelian varieties
Authors: Levingston Richard
Published: April 2009

It is shown that if m, n are relatively prime positive integers, then the variety consisting of those soluble groups of exponent mn in which any subgroup of exponent m or n is abelian has a basis of two-variable laws.
Primitive spaces of matrices of bounded rank
Authors: Atkinson M. D. , Lloyd S.
Published: April 2009

A weak canonical form is derived for vector spaces of m × n matrices all of rank at most r. This shows that the structure of such spaces is controlled by the structure of an associated ‘primitive’ space. In the case of primitive spaces it is shown that m and n are bounded by functions of r and that these bounds are tight.
The iteration of polynomials and transcendental entire functions
Authors: Baker I. N.
Published: April 2009

The iterative behaviour of polynomials is contrasted with that of small transcendental functions as regards the existence of unbounded domains of normality for the sequence of iterates.
Semiconvex geometry
Authors: Flood Joe
Published: April 2009

Semiconvex sets are objects in the algebraic variety generated by convex subsets of real linear spaces. It is shown that the fundamental notions of convex geometry may be derived from an entirely algebraic approach, and that conceptual advantages result from applying notions derived from algebra, such as ideals, to convex sets. Some structural decomposition results for semiconvex sets are obtained. An algebraic proof of the algebraic Hahn-Banach theorem is presented.
A family of groups with nice word problems
Authors: Dyson Verena Huber
Published: April 2009

This paper is an outgrowth of my old battle with the open sentence problem for the theory of finite groups. The unsolvability of the word problem for groups (cf. [1] and [4]) entails the undecidability of the open sentence problem for the elementary theory of groups and thus strengthens the original undecidability result for this theory (cf. [7]). The fact that the elementary theory of finite groups is also undecidable (cf. [2] and [6]) therefore justifies my interest in the open sentence problem for that theory. This paper contains a construction of groups that might lead to a negative solution.
Local systems in groups
Authors: Hulse J. A.
Published: April 2009

Throughout this paper we will assume that all groups are contained in some fixed but arbitrary universe. Thus the class of all groups becomes a set. If is a class of groups then we assume that 1 ∈ and if H ≅ G ∈ then H ∈ . German capitals will be used to denote classes of groups.
A converse to the log-log law for Martingales
Authors: Steiger W. L.
Published: April 2009

For sums of independent and identically distributed random variables xn, the HartmanWintner law of the iterated logarithm is equivalent to xn ∈ L2. We show that this is also true when the xn, form a stationary, ergodic martingale difference sequence. This is accomplished by extending a theorem of Volker Strassen to the present context.
Inaccessible varieties of groups
Authors: Kovács L. G.
Published: April 2009

A weak but still unsolved version of the first half of Problem 7 in Hanna Neumann's book [5] asks whether the product of a nontrivial join-irreducible variety and an arbitrary variety is necessarily also join-irreducible. One of the results of this paper is a positive answer provided either is abelian or the infiniterank free groups of have no nontrivial abelian verbal subgroups. For a general discussion, see [4]; all unexplained notation is as in [5].
Some cancellation theorems with applications to nilpotent groups
Authors: Hirshon R.
Published: April 2009

If C is a group which satisfies the maximal condition for normal subgroups, then C may be cancelled from a group A in direct products if and only if the infinite cyclic group can be cancelled from A. Finitely generated torsion free nilpotent groups of class 2 satisfy a Remak Krull Schmidt condition.
Characterizations of semisimple classes
Authors: van Leeuwen L. C. A. , Roos C. , Wiegandt R.
Published: April 2009

Two characterizations of semisimple classes of associative and alternative rings (and semigroups with 0) are given:

(i) A class is a semisimple class if and only if it is hereditary, closed under extensions and subdirect sums;

(ii) A class is a semisimple class if and only if it is hereditary, closed under extensions, and has the co-inductive property.

The first characterization sharpens Armendariz's (1968) result proved for associative rings, the second one is categorically dual to a characterization of radical classes due to Amitsur (1954).
Bounded Baer-levi semigroups
Authors: Lindsey Diana , Madison Bernard
Published: April 2009

Letpandqbe infinite cardinal numbers, p ≧ q,Xa set of cardinalityp, andBL(X, p, q)the Baer-Levi semigroup of type(p, q)onX. Subsemigroups ofBL(X, p, q)are defined and called bounded Baer-Levi semigroups. These semigroups are right simple and are universal in the embedding sense for the class of idempotent-free, right cancellative semigroupsSso that any two elements ofShave a common right identity inS. Further properties of bounded Baer-Levi semigroups are given and the structure of their lattices of congruences is discussed.
Isomorphisms between inverse semigroups of injective transformations
Authors: Baird Bridget Bos
Published: April 2009

We introduce a class of inverse semigroups of injective transformations and our main result concerns isomorphisms between two such semigroups. This result is then applied to semigroups of homeomorphisms between closed subsets of a T1 topological space, semigroups of homeomorphisms between compact subsets of k-spaces and semigroups of isomorphisms between subsemilattices of semilattices. In the first two cases it is shown that the two inverse semigroups under consideration are isomorphic if and only if the corresponding topological spaces are homeomorphic. In the latter case, the two inverse semigroups are isomorphic if and only if the semilattices are either isomorphic or are dual isomorphic infinite chains.
Varieties of topological algebras
Authors: Taylor Walter
Published: April 2009

By a variety of topological algebras we mean a class V of topological algebras of a fixed type closed under the formation of subalgebras, products and quotients (i.e. images under continuous homomorphisms yielding the quotient topology). In symbols, V = SV = PV = QV. if V is also closed under the formation of arbitrary continuous homomorphic images, then V is a wide variety. variety. As an example we have the full variety V = Modr (Σ), the class of all topological algebras of a fixed type τ obeying a fixed set Σ of algebraic identities. But not every wide variety is full, e.g. the class of all indiscrete topological algebras of a fixed type; in fact, as Morris observed (1970b), there exists a proper class of varieties of topological groups.
A note on isometric immersions
Authors: Baikoussis C. , Brickell F.
Published: April 2009

Let N be a complete connected Riemannian manifold with sectional curvatures bounded from below. Let M be a complete simply connected Riemannian manifold with sectional curvatures KM(σ)≤ −a2 (a ≥ 0) and with dimension < 2 dim N. Suppose that N is isometrically immersed in M and that its image lies in a closed ball of radius ρ. Then sup(KN(σ) − KM(σ)) ≥ μ2(aρ)/ρ2 where the function μ is defined by μ(x) = x coth x for x > 0, μ(0) = 1 and the supremum is taken over all sections tangent to N.
Simultaneous approximation of et and ℘(t)
Authors: Saradha K.
Published: April 2009

Let t be any complex number different from the poles of a Weierstrass elliptic function ℘(z), having algebraic invariants. Then we estimate from below the sum where α and β are algebraic numbers. The estimate is given in terms of the heights of α and β and the degree of the field Q(α, β), where Q is the field of rationals.
Weyl functions and the Ap condition on compact lie groups
Authors: Travaglini Giancarlo
Published: April 2009

Let G be a compact, simple, simply connected Lie group. The Lp-norm of a central trigonometric polynomial reduces naturally to a weighted Lp-norm of a trigonometric polynomial on a maximal torus T. The weight is | Δ |2-p, where Δ is the usual Weyl function. If p ≥ 2, we prove that | Δ |2-p satisfies Muckenhoupt's Ap condition if and only if the Lp-norms of the irreducible characters of G are uniformly bounded.
A simple test for nuclearity of integral operators on L2(Rn)
Authors: O'Brien D. M.
Published: April 2009

This note shows how the rate of decay of the singular values can be easily estimated for a wide class of integral operators on L2(Rn).
Initial and relative limiting behaviour of temperatures on a strip
Authors: Watson N. A.
Published: April 2009

Let u be a solution of the heat equation which can be written as the difference of two non-negative solutions, and let v be a non-negative solution. A study is made of the behaviour of u(x, t)/v(x, t) as t → 0+. The methods are based on the Gauss-Weierstrass integral representation of solutions on Rn × ]0, a[ and results on the relative differentiation of measures, which are employed in a novel way to obtain several domination, non-negativity, uniqueness and representation theorems.
A central limit theorem for empirical processes
Authors: Pollard David
Published: April 2009

The empirical measure Pn for independent sampling on a distribution P is formed by placing mass n−1 at each of the first n sample points. In this paper, n½(Pn − P) is regarded as a stochastic process indexed by a family of square integrable functions. A functional central limit theorem is proved for this process. The statement of this theorem involves a new form of combinatorial entropy, definable for classes of square integrable functions.
Some results concerning quasiperfect numbers
Authors: Hagis Peter , Cohen Graeme L.
Published: April 2009

New methods are introduced here to show that if n is a quasiperfect number and ω(n) the number of its distinct prime factors, then ω(n) ≥ 7 and n > 1035, and if further 3 ∤ n then ω(n) ≥ 9 and n > 1040.
Toeplitz operators on certain weakly pseudoconvex domains
Authors: Crocker David , Raeburn Iain
Published: April 2009

Let Ω be the weakly pseudoconvex domain

and let ∂Ω be its boundary. If ϕ ∈ L∞ (∂Ω), we denote by Tϕ, the Toephtz operator with symbol ϕ acting on the Hardy space H2(∂Ω), and by J(∂Ω) the C*-subalgebra of B(H2(∂Ω)) generated by the Toeplitz operators with continuous symbol. Our main theorem asserts that J(∂Ω) contains the ideal K of all compact operators on H2(∂Ω), and that the symbol map ϕ→Tϕ induces an isomorphism of C(∂Ω) onto the quotient C*-algebra ℑ(∂Ω)/K. Similar results have been established before for other domains, and in particular when Ω is strongly pseudoconvex. The main interest of our results lies in their proofs: ours are elementary, whereas those used in the strongly pseudoconvex case depend heavily on the theory of the tangential Cauchy-Riemann operator.
The proximally continuous integrals
Authors: Sarkhel D. N. , De A. K.
Published: April 2009

This paper introduces certain generalization of the notions of approximate limit, continuity and derivative and of absolute continuity, of real functions, leading to generalized integrals of Perron and Denjoy types comprising the AP-integral of Burkill (1931) and Sonouchi and Utagawa (1949) and the AD-integral of Kubota (1963), respectiely. The generalizations are all substantiated by appropriate examples.
Subordinate semigroups and order properties
Authors: Kishimoto Akitaka , Robinson Derek W.
Published: April 2009

LetSt= exp{−tH},Tt= exp{−tK}, beC0-semigroups on a Banach space. For appropriatefone can define subordinate semigroupsSft= exp{−tf(H)},Ttf= exp{−tf(K)}, onand examine order properties of the pairsS, T, andSf,Tf. If, =Lp(X;dv)we defineSt≽Tt≽ 0 ifSt−TtandTtmap non-negative functions into non-negative functions. Then forpfixed in the range 1 >p> ∞ we characterize the functions for whichSt≽Tt≽ 0 impliesSft≽Tft≽ 0 for eachLp(X;dv)and the converse is true for allLp(X;dv). Further we give irreducibility criteria for the strict ordering of holomorphic semigroups. This extends earlier results forL2-spaces.
The lateral completion of a completely distributive lattice-ordered group (revisited)
Authors: Davis Gary , McCleary Stephen H.
Published: April 2009

The lateral completion of a completely distributive lattice-ordered permutation group is investigated via various completions, obtained by adjoining permutations which match some elements of the given group in various ways. This makes known results on the lateral completion of a completely distributive lattice-ordered group both transparent and easy.
Six classes of theories
Authors: Keisler H. Jerome
Published: April 2009

A theory T is said to κ-stable if, given a pair of models U ⊂ B of T with U of power κ, there are only κ types of elements of B over U (types are defined below). This notion was introduced by Morley (1965) who gave a powerful analysis of ω-stable theories. Shelah (1971) showed that there are only four possibilities for the set of κ in which a countable theory is stable. This partition of all theories into four classes (ω-stable, superstable, stable, and unstable theories) has proved to be of great value. However, most familiar examples of theories are unstable.
Locally trivial homotopy functors and their domain of representation
Authors: Alder Michael D.
Published: April 2009

The well known theorem of E. H. Brown on the representation of Homotopy Functors is extended to a larger domain category. This is accomplished by requiring the functor to satisfy a further condition, that of being locally trivial: the condition is both necessary and sufficient for the extension and is satisfied by functors arising from locally trivial fibre bundles such as K-theory.
Compatible tight Riesz orders on ordered permutation groups
Authors: Davis G. , Loci E.
Published: April 2009

The pointwise order makes the group A(Ω) of order-preserving permutations of a totally-ordered set Ω a lattice-ordered group. We give some criteria for determining the compatible tight Riesz orders on A(Ω) in the case of Ω being a totally-ordered field, and then obtain various adjunctionshellip one between tight Riesz orders on A(Ω) and certain ideals of the fixed point lattice Φ(Ω), and a second between maximal tangents and certain filters of Φ(Ω). We also establish a correspondence between tight Riesz orders and first-order properties. Finally, we make use of our results to say what we can in the case of the automorphisms of the real field, and to pose several open problems.
Characterizations of maximal topologies
Authors: Joseph James E.
Published: April 2009

New characterizations of maximal topologies are given for a class of topologies including the compact, Lindelöf and m-compact topologies.
On the Stone-Weierstrass theorem
Authors: Ng Kung-Fu
Published: April 2009

Let M be a vector subspace of the Banach space C(Ω) of all real-valued continuous functions on a compact space Ω, and suppose that M contains a subset L and the constant functions. Then in order that L be dense in M it is necessary and sufficient that L, M satisfy a filtering property and that each m in M can be approximated on every two points of Ω by functions in L.
On the commutativity of some class of rings
Authors: Harmanci Abdullah
Published: April 2009

Throughout, R will denote an associative ring with center Z. For elements x, y of R and k a positive integer, we define inductively [x, y]0 = x, [x, y] = [x, y]1 = xy − yx, [x, y, y, hellip, y]k = [[x, y, y, hellip, y]k−1, y]. A ring R is said to satisfy the k-th Engel condition if [x, y, y, hellip, y]k = 0. By an integral domain we mean a nonzero ring without nontrivial zero divisors.
On the compatibility of algebraic equations with extensions
Authors: Hule Harald , Müller Winfried B.
Published: April 2009

In this paper we investigate the following problem proposed by Lausch and Nöbauer: Let be a variety of universal algebras, B an algebra of and A a subalgebra of B. If a system of algebraic equations over A is solvable in , is it then solvable over B? We show that the answer is affirmative in certain varieties but negative in the general case.
Rings with dual continuous right ideals
Authors: Mohamed Saad
Published: April 2009

In this paper the structure of rings with dual continuous right ideals is discussed. The main result is the following: If R is a ring with (Jacobson) radical nil, and all of its finitely generated right ideals are dual continuous, then where S is a finite direct sum of local rings each of which has its radical square zero, or is a right valuation ring, T is semiprimary right semihereditary ring, and M is an (S, T)-bimodule such that all of its finitely generated T-submodules are projective. A partial converse of this result is obtained: any matrix ring of the above type with M = 0 has all of its finitely generated right ideals dual continuous.
Abelian 2-subgroups of finite symplectic groups in characteristic 2
Authors: Barry M. J. J. , Wong W. J.
Published: April 2009

If Sp(V) is the symplectic group of a vector space V over a finite field of characteristic p, and r is a positive integer, the abelian p-subgroups of largest order in Sp(V) whose fixed subspaces in V have dimension at least r were determined in the preceding paper, in the case p ≠ 2. Here we deal with the case p = 2. Our results also complete earlier work on the orthogonal groups.
On Modular Representation Algebras and a Class of Matrix Algebras
Authors: Renaud J-C.
Published: April 2009

Let G be a cyclic group of prime order p and K a field of characteristic p. The set of classes of isomorphic indecomposable (K, G)-modules forms a basis over the complex field for an algebra p (Green, 1962) with addition and multiplication being derived from direct sum and tensor product operations.

Algebras n with similar properties can be defined for all n ≥ 2. Each such algebra is isomorphic to a matrix algebra Mn of n × n matrices with complex entries and standard operations. The characters of elements of n are the eigenvalues of the corresponding matrices in Mn.
The degree of approximation by positive operators on compact connected abelian groups
Authors: Bloom Walter R. , Sussich Joseph F.
Published: April 2009

In 1953 P. P. Korovkin proved that if (Tn) is a sequence of positive linear operators defined on the space C of continuous real 2 π-periodic functions and lim Tnf = f uniformly for f = 1, cos and sin, then lim Tnf = f uniformly for all f ∈ C. Quantitative versions of this result have been given, where the rate of convergence is given in terms of that of the test functions 1, cos and sin, and the modulus of continuity of f. We extend this result by giving a quantitative version of Korovkin's theorem for compact connected abelian groups.
On a problem of mahler for transcendency of function values
Authors: Nishioka Kumiko
Published: April 2009

A transcendence theorem is proved for functions satisfying functional equations of the shape P(z, f(z), f(zp)) = 0, where P is a polynomial and p ≥ 2 is an integer.
Attainable bounds for expectations
Authors: Seneta E. , Weber N. C.
Published: April 2009

A simple technique for obtaining bounds in terms of means and variances for the expectations of certain functions of random variables in a given class is examined. The bounds given are sharp in the sense that they are attainable by at least one random variable in the class. This technique is applied to obtain bounds for moment generating functions, the coefficient of skewness and parameters associated with branching processes. In particular an improved lower bound for the Malthusian parameter in an age-dependent branching process is derived.
Omega-Polish spaces and measurable selections
Authors: Tu Le Van
Published: April 2009

In this paper, the author introduces the notion of Ω-Polish spaces (which includes the Polish spaces and a large class of Banach spaces) and extends Castaing's selection theorem (1966) for closed-valued measurable thin multifunctions from a measurable space into an Ω-Polish space. He also extends Robertson's theorem (1974) in the same way.
Combinatorial solution of certain systems of linear equations involving (0,1) matrices
Authors: Longstaff W. E.
Published: April 2009

If m and n are natural numbers satisfying 1 ≦ m < n let denote the least integer k such that the statement: ‘Every (0,1) matrix with n columns, with constant row-sum m, and with at least k distinct rows, has rank n’ is true. Then = +1 for m ≧ 2, n ≧ m2 + 2. Further, for 1 ≦ m < n.
Note on monoidal monads
Authors: Day B. J.
Published: April 2009

The representation theory of categories is used to embed each promonoidal monad in a monoidal biclosed monad. The existence of a promonoidal structure on the ordinary Eilenberg- Moore category generated by a promonoidal monad is examined. Several results by previous authors (notably A. Kock and F. E. J. Linton) are reproved and extended.
Construction of balanced incomplete block designs
Authors: Morgan Elizabeth J.
Published: April 2009

Given a symmetric balanced incomplete block design or a finite plane, we recursively construct balanced incomplete block designs by taking unions of certain blocks and points of the original design to be the blocks of the new design.
The bichromaticity of a lattice-graph
Authors: Harary Frank , Hsu Derbiau , Miller Zevi
Published: April 2009

The bichromaticity β(B) of a bipartite graph B has been defined as the maximum order of a complete bipartite graph onto which B is homomorphic. This number was previously determined for trees and even cycles. It is now shown that for a lattice-graph Pm × Pm the cartesian product of two paths, the bichromaticity is 2 + {mn/2}.
On transposes of nilpotent matrices over arbitrary rings
Authors: Kezlan Thomas P.
Published: April 2009

It is shown that if every nilpotent 2 × 2 matrix over a ring has nilpotent transpose, then the commutator ideal must be contained in the Jacobson radical, thus generalizing a result of R. S. Gupta, who considered the division ring case. Moreover, if the nilpotent elements form an ideal or if the ring satisfies a polynomial identity, then the above property of the transpose implies that in fact the commutator ideal must be nil.
A discrete analogue of the Paley-Wiener theorem for bounded analytic functions in a half plane
Authors: Zeilberger Doron
Published: April 2009

In this note we prove a discrete analogue to the following Paley–Weiner theorem: Let f be the restriction to the line of a bounded analytic function in the upper half plane; then the spectrum of f is contained in ([0, ∈). The discrete analogue of complex analysis is the theory of discrete analytic functions invented by Lelong-Ferrand (1944) and developed by Duffin (1956) and others.
The Artin radical of a Noetherian ring
Authors: Chatters A. W. , Hajarnarvis C. R. , Norton N. C.
Published: April 2009

In this note we define the Artin radical of a Noetherian ring and describe some of its applications.
Identities in the universal envelopes of Lie algelras
Authors: Bachturin Yu. A.
Published: April 2009

It is well known (see Latyšev [1] for finite dimensional case) that the universal envelope of Lie Alaebra g over a commutative field ť of characteristic 0 is a PI-alaebra (i.e. possesses a nontrivial identity) if and only if this Lie algebra is abelian. On the other hand the recent results due to Passman [2] describe the conditions under which the group algebra of a group over an arbitrary commutative field is a PI-algebra. A. L. Šmel'kin suggested that I should find necessary and sufficient conditions for a Lie algebra g over a field of nonzero characteristic under which its universal envelope Ug should be a PI-algebra. These conditions are given in the following theorem.
Intersection theorems for systems of sets (III)
Authors: Erdös P. , Milner E. C. , Rado R.
Published: April 2009

A system or family (Aγ: γ∈ N) of sets Aγ, indexed by the elements of a set N, is called an (a, b)-system if ¦N¦ = a and ¦Aγ¦ = b for γ ∈ N. Expressions such as “(a, <b)-system” are self-explanatory. The system (Aγ: γ∈N) is called a δ-system [1] if Aμ∩Aγ = Ap ∩ Aσ whenever μ, γ, ρ, σ ∈ N; μ≠ γ; ρ ≠ σ. If we want to indicate the cardinality ¦N¦ of the index set N then we speak of a δ(¦N¦) system. In [1] conditions on cardinals a, b, c were obtained which imply that every (a, b)-system contains a δ(c)-subsystem. In [2], for every choice of cardinals b, c such that the least cardinal a = fδ(b, c) was determined which has the property that every (a, < b)-system contains a δ(c)-subsystem.
Some finite groups with zero deficiency
Authors: Wamsley J. W.
Published: April 2009

We introduce further finite groups which can be presented with an equal number of generators and relations.
Finite groups with short nonnormal chains
Authors: Spencer Armond E.
Published: April 2009

This note is a continuation of the author's work [6], describing the structure of a finite group given some information about the distribution of the subnormal subgroups in the lattice of all subgoups.

DEFINITION. An upper chain of length n in the finite group G is a sequence of subgroups of G; G = Go > G1 > … > Gn, such that for each i, Gi is a maximal subgroup of Gi-1. Let h(G) = n if every upper chain in G of length n contains a proper ( ≠ G) subnormal entry, and there is at least one upper chain in G of length (n – 1) which contains no proper subnormal entry.
The effect of smoothness on variation
Authors: Howlett P. G.
Published: April 2009

Let R be the set of real numbers, and let S1 denote the class of all real valued functions f on R which are smooth to the first order (i.e. the derivative ƒ(1) exists and is continuous) and have compact support. The first order variation off on an open set U is given by and in the case where U = R we have the total first order variation of f, usually denoted by I1(f).
George Szekeres
Authors: Giles J. R. , Wallis Jennifer Seberry
Published: April 2009

George Szekeres was born in Budapest on 29th May, 1911 the second of three sons to wealthy Jewish parents. As a youth he was shy and retiring, but early it become clear that his gifts lay in the direction of science and mathematics. At high school George was greatly influenced by his teacher in mathematics and physics, K. (Charles) Novobátzky, who worked actively in the theory of relativity and was in 1945 to become a professor of theoretical physics at the University of Budapest. Small wonder that George's first great mathematical interest was relativity. The other major formative influence at high school was the journal ‘Koözeépiskolai Matematikai és Fizikai Lapok’. The names of problem solver were published with each solution and with the completion of the year's volume, photographs of the main contributors were reproduced.
Uniformly weak differentiability of the norm and a condition of Vlasov
Authors: Giles J. R.
Published: April 2009

In determining geometrical conditions on a Banach space under which a Chebychev set is convex, Vlasov (1967) introduced a smoothness condition of some interest in itself. Equivalent forms of this condition are derived and it is related to uniformly weak differentiability of the norm and rotundity of the dual norm.
Signed sums of reciprocals I
Authors: Worley R. T.
Published: April 2009

The author investigates M(n)= min¦Σηkk−1¦ where the minimum is over all sets of signs η1 = ±1 and shows M(n) < n½−(1−e)log2n.
On the fixed points of Sylow subgroups of transitive permutation groups
Authors: Herzog Marcel , Praeger Cheryl E.
Published: April 2009

Let G be a transitive permutation group on a set Ω of n points, and let P be a Sylow p-subgroup of G for some prime p dividing ∣G∣. If P has t long orbits and f fixed points in Ω, then it is shown that f ≦ tp − ip(n), where ip(n) = p – rp(n), rp(n) denoting the residue of n modulo p. In addition, groups for which f attains the upper bound are classified.
Stability of line graphs
Authors: Grant Douglas D.
Published: April 2009

We present in this paper a discussion on some stability properties of line graphs. After relating the semi-stability properties of the line graph of a graph to a concept of Sheehan, we proceed to deduce that, with fully characterised lists of exceptions, the line graphs of trees and unicyclic graphs are semi-stable. We then discuss the problem of deciding which line graphs are stable. Via a discovery of the finite number of graphs G such that both G and its complement have stable line graphs, we show that P4 is the only self-complementary graph whose line graph is stable.
A problem of Paul Erdös on groups
Authors: Neumann B. H.
Published: April 2009

Let G be a group, and associate with G a graph 1 γ = Γ (G) as follows: the vertices of Γ are the elements of G, and two vertices g, h of Γ are joined by an undirected edge if, and only if, g and h do not commute as elements of G, that is [g, h] ≠ 1 [where [g, h] is the commutator g−1h−1gh, and 1 is the unit element of the groups that occur as well as the integer, according to context].We are interested in complete subgraphs of Γ, or equivalently in sets of elements of G no two of which commute.
The chromatic number of the sphere
Authors: Simmons Gustavus J.
Published: April 2009

Erdös, Harary and Tutte have defined the chromatic number of the plane to be the least number of sets partitioning the plane such that no set contains two points at unit distance apart. By analogy, the chromatic number χ(S1), of the sphere, Sr of radius r is defined to be the least number of sets partitioning the surface of Sr such that no set contains two points at unit chordal distance apart. In this paper it is proven that and that this bound is best possible since .
On the boundedness of multiplicative and positive functionals
Authors: Husain Taqdir , Ng Shu-Bun
Published: April 2009

Let A be a complex sequentially complete, locally convex (not necessarily commutative) topological algebra with the defining family {pα}α∈D of seminorms in which (*): for each sequence xn → 0 there exists xm ∈ {xn} such that xmk → 0 as k → ∞. Then each multiplicative linear functional on a Fréchet algebra satisfying the above condition (*) is Continuous.

These results answer open questions (1) and (2) (Mem. Amer. Math. Soc. 11, 1953) in the affirmative for Fréchet algebras in which (*) holds. It is also shown that a positive linear functional on such algebras with identity and continuous involution is continuous, thus partially generalizing Shah's result (1959).