bluuebunny/crossref_metadata_2025_split huggingface dataset:
Weighted shifts and commuting normal extension
Authors: Lubin Arthur 
Published: April 2009

AbstractThe main result of this paper shows that the existence of commuting normal extension (c.n.e.) for an arbitrary family of commuting subnormal operators can be determined by considering appropriate families of multivariable weighted shifts. In proving this some known criteria for c.n.e. are generalized. It is also shown that a family of jointly quasi-normal operators has c.n.e.
Algebras stably equivalent to Nakayama algebras of Loewy length at most 4
Authors: Reiten Idun 
Published: April 2009

AbstractTwo artin algebras Λ and Λ′ are said to be stably equivalent if their categories of finitely generated modules modulo projectives are equivalent. In this paper a characterization is given of the artin algebras stably equivalent to Nakayama algebras of Loewy length (at most) four. The proof is an illustration of the technique of using irreducible maps to study problems about stable equivlence.
Large abelian subgroups of Chevalley groups
Authors: Barry Michael J. J. 
Published: April 2009

AbstractFor any group S let Ab(S) = {A∣A is an abelian subgroup of S of maximal order}. Let G be a Chevalley group of type An, Bn, Cn, or Dn over a finite field of characteristic p and let. In this paper Ab(U) is determined for all such groups.
The Gaussian law and lacunary sets of characters
Authors: Dudley E. , Hall P. 
Published: April 2009

AbstractSalem and Zygmund (1947, 1948), Baker (1972) and Dudley (1975) have shown that certain lacunary sets P of characters of a compact abelian group have sequences of the form where фk∈P converge to the normal distribution if suitably normalized. In this paper, a theorem of probability due to McLeish (1974) is applied to clarify and extend the previous results.
The funnel boundary of multivalued dynamical systems
Authors: Kloeden P. E. 
Published: April 2009

AbstractProperties of the funnel boundary are investigated for multivalued dynamical systems defined axiomatically in terms of attainability set mappings on complete, locally compact metric state spaces. The set of regular boundary events is shown to be dense in the funnel boundary and theorems of Fukuhara and Zaremba on peripheral attainability are generalized to the systems considered here.
Direct products and the Hopf property
Authors: Jones J. M. Tyrer 
Published: April 2009

In [1] Neumann and Dey prove that the free product of two finitely generated Hopf groups is Hopf and ask whether a similar result holds for direct products. It is the purpose of this paper to show that this is not the case. We proveTHEOREM A. There exists a finitely generated group G satisfying the following conditions:(i) G is isomorphic to a proper direct factor of itself;(ii) G is the direct product of two Hopf groups.
Free products of hopfian lattices
Authors: Grätzer G. , Sichler J. 
Published: April 2009

In this paper we are going to prove the following results:Theorem 1. There exist two bounded hopfian lattices such that their {0,1}- free product is not hopfian.Theorem 2. There exist two hopfian lattices such that their free product is not hopfian.In Theorem 2 free product (coproduct, sum) has its usual meaning (see, for instance, [4]); in Theorem 1 we use the usual definition but all lattices are assumed to be bounded (that is, having a least element 0 and largest element 1) and all homomorphisms are assumed to be {0, l}-homomorphisms (that is, homomorphisms preserving 0 and 1).
A functional calculus for sesquihermitian operators on quaternionic Hilbert space
Authors: Powers N. C. 
Published: April 2009

AbstractA continuous real-linear operator A = A0 + i1A1 + i2A2 + i3A3 on a quaternionic Hilbert space is called sesquihermitian if the linear operators Av are Hermitian; this condition is independent of the choice of quaternion basis (i1,i2,i3). The joint spectral distribution of the Av provides a functional calculus for sesquihermitian operators and real-valued C∞-functions on . This calculus is independent of the quaternion basis and extends naturally to quaternion-valued functions to give a continuous quaternion-linear mapping from the algebra of these functions to that of sesquihermitian operators. The mapping is not, in general, multiplicative unless the Av commute, in which case it agrees with that for several commuting operators on complex Hilbert space.
A characterization of finite p-soluble groups of p-length one by commutator identities
Authors: Brandl Rolf 
Published: April 2009

AbstractA classical result of M. Zorn states that a finite group is nilpotent if and only if it satisfies an Engel condition. If this is the case, it satisfies almost all Engel conditions. We shall give a similar description of the class of p-soluble groups of p-length one by a sequence of commutator identities.
Facial reduction for a cone-convex programming problem
Authors: Borwein Jon M. , Wolkowicz Henry 
Published: April 2009

AbstractIn this paper we study the abstract convex programwhere 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 (on Ω). We use the concept of a minimal cone for (P) to correct and strengthen a previous characterization of optimality for (P), see Theorem 3.2. The results presented here are used in a sequel to provide a Lagrange multiplier theorem for (P) which holds without any constraint qualification.
On arithmetic functions and divisors of higher order
Authors: Alladi Krishnaswami 
Published: April 2009

AbstractWe discuss properties of arithmetic functions of higher order defined through the introduction of a new concept of divisor of higher order. We shall construct an infinite sequence of Euler-like functions and the well known Euler function will be the first member of this sequence. Asymptotic estimates of such functions are given and a study of error functions associated with the Euler-like sequence is made. We would like to mention that the familiar number theoretic functions become only the first members of an infinite sequence of functions of similar behaviour.
Enlarging the Munn representation of inverse semigroups
Authors: Reilly N. R. 
Published: April 2009

AbstractThe 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

SynopsisIn 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.
Homeomorphisms of Quaternion space and projective planes in four space
Authors: Price T. M. 
Published: April 2009

AbstractIt 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

AbstractIn 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

AbstractThis 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

AbstractThe 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

AbstractWe 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

AbstractThe 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 values taken by the largest prime factor of shifted primes
Authors: Banks William D. , Shparlinski Igor E. 
Published: April 2009

AbstractLet 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

AbstractThe 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.
Latin squares with highly transitive automorphism groups
Authors: Bailey R. A. 
Published: April 2009

AbstractA 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

AbstractA 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

AbstractAn 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

AbstractIn 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.
Finite sublattices of three-generated lattices
Authors: Davey Brian A. , Rival Ivan 
Published: April 2009

AbstractEvery 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

AbstractStarters 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.
Characterization of optimality for the abstract convex program with finite dimensional range
Authors: Borwein Jon M. 
Published: April 2009

AbstractThis paper presents characterizations of optimality for the abstract convex programwhen 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

AbstractReduced 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

AbstractLet 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.
Primitive spaces of matrices of bounded rank
Authors: Atkinson M. D. , Lloyd S. 
Published: April 2009

AbstractA 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.
Semiconvex geometry
Authors: Flood Joe 
Published: April 2009

AbstractSemiconvex 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.
Some cancellation theorems with applications to nilpotent groups
Authors: Hirshon R. 
Published: April 2009

AbstractIf 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

AbstractTwo 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

AbstractLetpandqbe 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

AbstractWe 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.
A note on isometric immersions
Authors: Baikoussis C. , Brickell F. 
Published: April 2009

AbstractLet 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

AbstractLet 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.