bluuebunny/crossref_metadata_2025_split huggingface dataset:
Length theorems for the general linear group of a module over a local ring
Authors: Ellers Erich W. , Lausch Huberta 
Published: April 2009

AbstractLet R be a not necessarily commutative local ring, M a free R-module, and π ∈ GL(M) such that B(π) = im(π –1)is a subspace of M. Then π = σ1…σtρ, where σi are simple mappings of given types, ρ is a simple mapping, B(sgr;i) and B(ρ) are subspaces and t ≤ dim B(π).
More on finite groups with few defining relations
Authors: Mennicke J. L. , Neumann B. H. 
Published: April 2009

AbstractCertain central products of the binary polyhedral groups with finite cyclic groups are here shown to have presentations with two generators and two defining relations; this disproves a conjecture of the second author, stated in J. Austral. Math. Soc. Ser. A 38 (1985), 230–240.
An infinite alleles version of the Markov branching process
Authors: Pakes Anthony G. 
Published: April 2009

AbstractIndividuals in a population which grows according to the rules defining the Markov branching process can mutate into novel allelic forms. We obtain some results about the time of the last mutation and the limiting frequency spectrum. In the present context these results refine certain results obtained in the discrete time case and they answer some conjectures still unresolved for the discrete time case.
Balanced tournament designs with almost orthogonal resolutions
Authors: Lamken E. R. , Vanstone S. A. 
Published: April 2009

AbstractA balanced tournament design, BTD(n), defined on a 2n—set V is an arrangement of the () distinct unordered pairs of the elements of V into an n × 2n − 1 array such that (1) every element of V is contained in precisely one cell of each column, and (2) every element of V is contained in at most two cells of each row. In this paper, we investigate the existence of balanced tournament designs with a pair of almost orthogonal resolutions. These designs can be used to construct doubly resolvable (ν, 3, 2)- BIBD s and, in our smallest applications, have been used to construct previously unknown doubly resolvable (ν, 3, 2)- B I B D s.
A character-theory-free characterization of the Mathieu group M12
Authors: Held Dieter , de Angelis Jörg Hrabě 
Published: April 2009

AbstractThe known characterization of the Mathieu group M12 by the structure of the centralizer of a 2-central involution is based on the application of the theory of exceptional characters and uses in addition a block theoretic result which asserts that a simple group of order |M12| is isomorphic to M12. The details of the proof of the latter result had never been published. We show here that M12 can be handled in a completely elementary and group theoretical way.
On countably compact quasi-pseudometrizable spaces
Authors: Salbany Sergio , Romaguera Salvador 
Published: April 2009

AbstractWe prove the following results: (1) A quasi-metrizable space is compact if and only if every compatible quasi-metric has a quasi-metric left d—sequential completion. (2) A quasipseudometrizable space is countably compact if and only if every compatible quasi-pseudometric is pointwise bounded. (3) A quasi-pseudometrizable space is compact if and only if every compatible quasi-pseudometric is precompact.
Riesz sets and the Radon-Nikodym property
Authors: Dowling Patrick N. 
Published: April 2009

AbstractLet X be a complex Banach space, G a compact abelian group and Λ a subset of Ĝ, the dual group pf G. Then LΛ1(G, X) has the Radon-Nikodym property if and only if X has the Radon-Nikodym property and Λ is Riesz set. In particular, H1 (T, X) has the Radon-Nikodym property if and only if X has the Radon-Nikodym property. This solves a problem of Hensgen.
The factorable core of polynomials over finite fields
Authors: Cohen S. D. 
Published: April 2009

AbstractFor a polynomial f(x) over a finite field Fq, denote the polynomial f(y)−f(x) by ϕf(x, y). The polynomial ϕf has frequently been used in questions on the values of f. The existence is proved here of a polynomial F over Fq of the form F = Lr, where L is an affine linearized polynomial over Fq, such that f = g(F) for some polynomial g and the part of ϕf which splits completely into linear factors over the algebraic closure of Fq is exactly φF. This illuminates an aspect of work of D. R. Hayes and Daqing Wan on the existence of permutation polynomials of even degree. Related results on value sets, including the exhibition of a class of permutation polynomials, are also mentioned.
An elementary proof of Weyl's limit-classification
Authors: Das J. 
Published: April 2009

AbstractIt is known [Herman Weyl, 1910] that every linear second-order differential expression L (with real coefficients) is such that Ly = λy (im λ ≠ 0) has at least one solution belonging to the class L2 = L2[0, ∞) of functions, the squares of whose moduli are Lebesgue-integrable on [0, ∞). This celebrated result was later proved by E. C. Titchmarsh (1940–1944), using sophisticated analysis of bilinear transformation. The aim of the present note is to prove the same result once again, but using only elementary analysis and school geometry. The power of this method will be appreciated further when one realises the amount of simplifications that can be acheived by this expressions. This part of the note course will be taken up in a subsequent paper.
On certain pairs of automorphisms of C*-algebras
Authors: Batty C. J. K. 
Published: April 2009

AbstractLet α and β be *-automorphisms of a C*-algebra A such that α + α β + β-1. There exist invariant ideals I1I2 and I3 of A, with II ∩ I2 ∩ I3 = {O}, containing, respectively, the range ofβ − α, the range of β − α-1, and the union of the ranges of β2 − α2 and β2 − α-2. The induced actions on the quotient algebras give a decomposition of the system (A, α, β) into systems where β = α, β = α-2 and α2 = α-2.If α and β are one-parameter groups of *-automorphisms such that α + α-1 = β + β−1, then the corresponding result is valid, and may be strengthened to assert that I1 ∩ I2 = {0}.These results are analogues and extensions of similar results of A. B. Thaheem et al. for von Neumann algebras and commuting automorphisms.
QF-3 rings and torsion theories
Authors: Pardo José L. Gómez , González Nieves Rodríguez 
Published: April 2009

AbstractIn this paper, the rings which have a torsion theory τ with associated torsion radical τ such that R/t(R) has a minimal τ-torsionfree cogenerator are studied. When τ is the trivial torsion theory these are precisely the left QF-3 rings. For τ = τL, the Lambek torsion theory, this class of rings is wider but, with an additional hypothesis on τL it is shown that if R has this property with respect to the Lambek torsion theory on both sides, then R is a (left and right) QF-3 ring. The results obtained are applied to get new characterizations of QF-3 rings with the ascending chain condition on left annihilators.
Odd order groups with an automorphism cubing many elements
Authors: Deaconescu Marian , MacHale Desmond 
Published: April 2009

AbstractWe determine the structure of a nonabelian group G of odd order such that some automorphism of G sends exactly (1/p)|G| elements to their cubes, where p is the smallest prime dividing |G|. These groups are close to being abelian in the sense that they either have nilpotency class 2 or have an abelian subgroup of index p.
On an equivalent class of norms for BMO
Authors: Chen Yong-Zhuo , Lau Ka-Sing 
Published: April 2009

AbstractThe BMO norm of f is equivalent to where Pt is the Poisson kernel. In this note, we show that Pt can be replaced by a nonnegative radial function h, which is positive in a neighbourhood of 0, with and , where h is the least decreasing radial majorant of h.
On the error estimates for the Rayleigh-Schrödinger series and the Kato-Rellich perturbation series
Authors: Kulkarni Rekha P. , Limaye Balmohan V. 
Published: April 2009

AbstractLet λ be a simple eigenvalue of a bounded linear operator T on a Banach space X, and let (Tn) be a resolvent operator approximation of T. For large n, let Sn denote the reduced resolvent associated with Tn and λn, the simple eigenvalue of Tn near λ. It is shown that under the assumption that all the spectral points of T which are nearest to λ belong to the discrete spectrum of T. This is used to find error estimates for the Rayleigh-Schrödinger series for λ and ϕ with initial terms λn and ϕn, where P (respectively, ϕn) is an eigenvector of T (respectively, Tn) corresponding to λ (respectively, λn), and for the Kato-Rellich perturbation series for PPn, where P (respectively, Pn) is the spectral projection for T (respectively, Tn) associated with λ (respectively, λn).
Composition operators on weighted spaces of continuous functions
Authors: Singh R. K. , Summers W. H. 
Published: April 2009

AbstractWe give algebraic criteria for distinguishing composition operators among all continuous linear operators on spaces of continuous functions with topologies generated by seminorms that are weighted analogues of the supremum norm. In another direction, we also characterize those self maps of the underlying topological space which induce composition operators on such weighted spaces, as well as determine conditions on these self maps which correspond to various basic properties of the induced composition operator. Our results are applied to a question concerning translation invariance which arises in the context of topological dynamics.
Group congruences on eventually regular semigroups
Authors: Rao S. Hanumantha , Lakshmi P. 
Published: April 2009

AbstractA characterization of group congruences on an eventually regular semigroup S is provided. It is shown that a group congruence is dually right modular in the lattice of congruences on S. Also for any group congruence ℸ and any congruence p on S, ℸ Vp and kernel ℸ Vp are described.
Classical groups and generalized simple groups of Lie type
Authors: Hu Cheng Chon 
Published: April 2009

AbstractIn this note, for any given simple group obtained from an orthogonal or unitary group of non-zero index, by a procedure similar to the construction of Chevalley groups and twisted groups, we construct a simple group which is identified with the given simple classical group. The simple groups constructed in this note can be interpreted as generalized simple groups of Lie type. Thus all simple groups of Lie type of types An, Bn, Cn and Dn and all generalized simple groups of Lie type constructed in this note exhaust all simple classical groups with non-zero indices.
Positive semigroups of operators on Banach spaces
Authors: Ng K. F. 
Published: April 2009

AbstractWe prove a version of the Feller-Miyadera-Phillips theorem characterizing the infinitesimal generators of positive C0-semigroups on ordered Banach spaces with normal cones. This is done in terms of N(A) as well as the canonical half-norms of Arendt Chernoff and Kato defined by N(a) = inf{‖b‖ |b ≥ a}, where N(A) = sup{N(Aa) |N(a) ≶ 1} for operator A. A corresponding result on –semigroups is also given.
Some embeddings related to C*-embeddings
Authors: Aull C. E. 
Published: April 2009

AbstractA space S is R*-embedded (G*-embedded) in a space X if two disjoint regular closed sets (closure disjoint open sets) of S are contained in disjoint regular closed sets (extended to closure disjoint open sets) of X. A space S is R-extendable to a space X if any regular closed set of S can be extended to a regular closed set of X. It is shown that R*-embedding and G*-embedding are identical with C*-embedding for certain fairly general classes of Tychonoff spaces. Under certain conditions it is shown that R-extendability is related to z-embedding. Spaces in which the regular open sets are C and C*-embedded are also investigated.
Joins of topologies homeomorphic to the rationals
Authors: Jayanthan A. J. , Kannan V. 
Published: April 2009

AbstractLet Q be the space of all rational numbers and (X, τ) be a topological space where X is countably infinite. Here we prove that (1) τ is the join of two topologies on X both homeomorphic to Q if and only if τ is non-compact and metrizable, and (2) τ is the join of topologies on X each homeomorphic to Q if and only if τ is Tychonoff and noncompact.
The non-emptiness of joint spectral subsets of euclidean n-space
Authors: Ricker W. J. , Schep A. R. 
Published: April 2009

AbstractA.McIntosh and A. Pryde introduced and gave some applications of notion of “spectral set”, γ(T), associated with each finite, commuting family of continuous linear operators T in a Banach space. Unlike most concepts of joint spectrum, the set γ(T) is part of real Euclidean space. It is shown that γ(T) is always non-empty whenver there are at least two operators in T.
On the Pták homomorphism theorem
Authors: Rodrigues B. 
Published: April 2009

AbstractIn this note, a brief and accessible proof is given of an extension of the Pták homomorphism theorem to a larger class of spaces—spaces that are not necessarily assumed to be locally convex. This is done by first proving a counterpart of the Bourbaki-Grothendieck homomophism theorem for the non-locally-convex case. Our presentation utilizes the simplifying properties of seminorms.
BMO and singular integrals over local fields
Authors: Daly James E. , Kurtz Douglas S. 
Published: April 2009

AbstractThis paper is concerned with the behavior of certain principal-value, singular integral operators on L∞ and BMO defined over a local field. It is shown that unless the definition of these operators is changed appropriately, they may not be defined for some function in these spaces. Direct, constructive proofs of the existence and boundedness of the altered operators under certain smoothness conditions on the kernel are given.
The spectral theorem for well-bounded operators
Authors: Doust Ian , Bozhou Qiu 
Published: April 2009

AbstractWell-bounded operators are those which possess a bounded functional calculus for the absolutely continuous functions on some compact interval. Depending on the weak compactness of this functional calculus, one obtains one of two types of spectral theorem for these operators. A method is given which enables one to obtain both spectral theorems by simply changing the topology used. Even for the case of well-bounded operators of type (B), the proof given is more elementary than that previously in the literature.
Incompressible surfaces and the topology of 3-dimensional manifolds
Authors: Aitchison Iain R. , Rubinstein J. Hyam 
Published: April 2009

AbstractExistence and properties of incompressible surfaces in 3-dimensional manifolds are surveyed. Some conjectures of Waldhausen and Thurston concerning such surfaces are stated. An outline is given of the proof that such surfaces can be pulled back by non-zero degree maps between 3-manifolds. The effect of surgery on immersed, incompressible surfaces and on hierarchies is discussed. A characterisation is given of the immersed, incompressible surfaces previously studied by Hass and Scott, which arise naturally with cubings of non-positive curvature.
Generation of generators of holomorphic semigroups
Authors: Berg Christian , Boyadzhiev Khristo , Delaubenfels Ralph 
Published: April 2009

AbstractWe construct a functional calculus,g→g(A), for functions,g, that are the sum of a Stieltjes function and a nonnegative operator monotone function, and unbounded linear operators,A, whose resolvent set contains (−∞, 0), with {‖r(r+A)−1‖ ¦r> 0} bounded. For such functionsg, we show that –g(A) generates a bounded holomorphic strongly continuous semigroup of angle θ, whenever –A does.We show that, for any Bernstein functionf, −f(A) generates a bounded holomorphic strongly continuous semigroup of angle π/2, whenever −Adoes.We also prove some new results about the Bochner-Phillips functional calculus. We discuss the relationship between fractional powers and our construction.
On Dirichlet's boundary value problem for some formally hypoelliptic differntial operators
Authors: Jacob Niels 
Published: April 2009

AbstractFor a class of formally hypoelliptic differential operators in divergence form we prove a generalized Gårding inequality. Using this inequality and further properties of the sesquilinear form generated by the differential operator a generalized homogeneous Dirichlet problem is treated in a suitable Hilbert space. In particular Fredholm's alternative theorem is proved to be valid.
Central lacunary sets for Lie groups
Authors: Dooley A. H. 
Published: April 2009

AbstractIf G is a compact connected Lie group every infinite subset of Ĝ contains an infinite central Λ(p) set, for p < 2 + 2 rank G/(dim G - rank G). A subset R of Ĝ is of type central Λ(2) if and only if the associated set of characters on the maximal torus is of type Λ(2). The dual of a compact connected semisimple Lie group contains infinite sets which are central p-Sidon for all p > 1. Every infinite subset of the dual of Su(2) contains such a set.
Smoothness conditions and integrability theorems on bounded Vilenkin groups
Authors: Bloom Walter R. , Fournier John J. F. 
Published: April 2009

AbstractVarious criteria, in terms of forward differences and related operations on coefficients, are shown to imply that certain series on bounded Vilenkin groups represent integrable functions. These results include analogues of known integrability theorems for trigonometric series. The method of proof is to pass from the given series to a derived series, and to deduce the integrability of the original series from smoothness properties of the latter.
Centralizing properties in simple locally finite groups and large finite classical groups
Authors: Hartley Brian 
Published: April 2009

AbstractThe following question is discussed and evidence for and against it is advanced: is it true that if F is an arbitrary finite subgroup of an arbitrary non-linear simple locally finite group G, then CG(F) is infinite? The following points to an affirmative answer.Theorem A. Let F be an arbitrary finite subgroup of a non-linear simple locally finite group G. Then there exist subgroups D ◃ C ≤ G such that F centralizes C/D, F∩C ≤ D, and C/D is a direct product of finite alternating groups of unbounded orders. In particular, F centralizes an infinite section of G.Theorem A is deduced from a “local” version, namelyTheorem B. There exists an integer valued function f(n, r) with the following properties. Let H be a finite group of order at most n, and suppose that H ≤ S, where S is either an alternating group of degree at least f = f(n, r) or a finite simple classical group whose natural projective representation has degree at least f. Then there exist subgroups D ◃ C ≤ S such that (i) [H, C] ≤ D, (ii) H ∩ C ≤ D, (iii) C/D ≅ Alt(r), (iv) D = 1 if S is alternating, and D is a p-group of class at most 2 and exponent dividing p2 if S is a classical group over a field of characteristic p.The natural “local version” of our main question is however definitely false.Proposition C. Let p be a given prime. Then there exists a finite group H that can be embedded in infinitely many groups PSL(n, p) as a subgroup with trivial centralizer.
Structural inference on the generalized gamma distribution based on type-II progressively censored sample
Authors: Maswadah M. S. 
Published: April 2009

AbstractThis paper is concerned with the three-parameter generalized gamma distribution (g.g.d.) which is widely employed as a model in life testing. The structural probability distributions of the parameters and a number of structural prediction densities for specific future measurements have been derived based on type-Il progressively censored sample.
Statistical expansions and locally uniform Fréchet differentiability
Authors: Bednarski T. , Clarke B. R. , Kolkiewicz W. 
Published: April 2009

AbstractEstimators which have locally uniform expansions are shown in this paper to be asymptotically equivalent to M-estimators. The M-functionals corresponding to these M-estimators are seen to be locally uniformly Fréchet differentiable. Other conditions for M-functionals to be locally uniformly Fréchet differentiable are given. An example of a commonly used estimator which is robust against outliers is given to illustrate that the locally uniform expansion need not be valid.
Abelian groups with small cotorsion images
Authors: Göbel Rüdiger 
Published: April 2009

AbstractEpimorphic images of compact (algebraically compact) abelian groups are called cotorsion groups after Harrison. In a recent paper, Ph. Schultz raised the question whether “cotorsion” is a property which can be recognized by its small cotorsion epimorphic images: If G is a torsion-free group such that every torsion-free reduced homomorphic image of cardinality is cotorsion, is G necessarily cortorsion? In this note we will give some counterexamples to this problem. In fact, there is no cardinal k which is large enough to test cotorsion.
On the structure of tame near-rings
Authors: Heatherly H. , Pilz G. 
Published: April 2009

AbstractTame near-rings form an important class of near-rings. They have the common feature that all N-subgroups in a faithful N-group are ideals. Tame near-rings can be very close to and very far from rings. Most of the important classes of distributively generated near-rings and all 2-semisimple near-rings are examples of tame near-rings.
On congruence lattices of m-complete lattices
Authors: Grätzer G. , Lakser H. 
Published: April 2009

AbstractThe lattice of all complete congruence relations of a complete lattice is itself a complete lattice. In an earlier paper, we characterize this lattice as a complete lattice. Let m be an uncountable regular cardinal. The latticeLof all m-complete congruence relations of an m-complete latticeKis an m-algebraic lattice; ifKis bounded, then the unit element ofLis m-compact. Our main result is the converse statement: For an m-algebraic latticeLwith an m-compact unit element, we construct a bounded m-complete latticeKsuch thatLis isomorphic to the lattice of m-complete congruence relations ofK. In addition, ifLhas more than one element, then we show how to constructKso that it will also have a prescribed automorphism group. On the way to the main result, we prove a technical theorem, the One Point Extension Theorem, which is also used to provide a new proof of the earlier result.
Extremal problems in Hp
Authors: Nakazi Takahiko 
Published: April 2009

AbstractLet 1≤p <∞ and 1/p+1/q = 1. If φ ∈ Lq, we denote by Tφ the functional defined on the Hardy space Hp by . A function f in Hp, which satisfies Tpφ(f) = ‖Tpφ‖ and ‖f‖p ≤ 1, is called an extremal function. Also, φ is called an extremal kernel when ‖φ‖q =‖Tpφ‖. In this paper, using the results in the case of p = 1, we study extremal kernel and extremal functions for p > 1.
The dual lattice of an extreme six-dimensional lattice
Authors: Coulson David 
Published: April 2009

AbstractThe best lattice quantizers seem to be duals of extreme lattices. The quantizing constant associated with the dual lattice of Barnes's senary form φ6 is found, together with a new type of quantizing technique. The quantizing constant is better than expected in the sense that it is better than D*6 even though D6 provides a denser packing. This is the smallest dimension for which this occurs.
Some trigonometric extremal problems and duality
Authors: Révész Szilárd GY. 
Published: April 2009

AbstractIn this paper we present a minimax theorem of infinite dimension. The result contains several earlier duality results for various trigonometrical extremal problems including a problem of Fejér. Also the present duality theorem plays a crucial role in the determination of the exact number of zeros of certain Beurling zeta functions, and hence leads to a considerable generalization of the classical Beurling's Prime Number Theorem. The proof used functional analysis.
On the consecutive eigenvalues of the Laplacian of a compact minimal submanifold in a sphere
Authors: Leung Pui-Fai 
Published: April 2009

AbstractLet 0 = λ0 < λ1 ≤ λ2 ≤ λ3 ≤ … denote the sequence of eigenvalues of the Laplacian of a compact minimal submanifold in a unit sphere. Yang and Yau obtained an upper bound on λn+1 in terms of λn and the sum λ1 + … + λn. In this note we shall prove an improved version of this upper bound by using the method of Hile and Protter.