bluuebunny/crossref_metadata_2025 huggingface dataset:
Variation of Fixed-Point and Coincidence Sets
Authors: Gauld David
Published: April 2009

Topologise the set of continuous self-mappings of a Hausdorff space by the graph topology. When the set of closed subsets of the space is given the upper semi-finite topology then the function which assigns to a map its fixed-point set is continuous. In many familiar cases this is the largest such topology. Related results also hold for the function which assigns to each pair of maps their coincidence set.
Injective Modules Over Non-Artinian Serial Rings
Authors: Hill David A.
Published: April 2009

A module is uniserial if its lattice of submodules is linearly ordered, and a ring R is left serial if R is a direct sum of uniserial left ideals. The following problem is considered. Suppose the injective hull of each simple left R-module is uniserial. When does this imply that the indecomposable injective left R-modules are uniserial? An affirmative answer is known when R is commutative and when R is Artinian. The following result is proved.

Let R be a left serial ring and suppose that for each primitive idempotent e, eRe has indecomposable injective left modules uniserial. The following conditions are equivalent. (a) The injective hull of each simple left R-module is uniserial. (b) Every indecomposable injective left R-module is univerial. (c) Every finitely generated left R-module is serial.

The rest of the paper is devoted to a study of some non-Artinian serial rings which serve to illustrate this theorem.
LECs, Local Mixers, Topological Groups and Special Products
Authors: Borges Carlos R.
Published: April 2009

We prove that every (locally) contractible topological group is (L)EC and apply these results to homeomorphism groups, free topological groups, reduced products and symmetric products. Our main results are: The free topological group of a θ-contractible space is equiconnected. A paracompact and weakly locally contractible space is locally equiconnected if and only if it has a local mixer. There exist compact metric contractible spaces X whose reduced (symmetric) products are not retracts of the Graev free topological groups F(X) (A(X)) (thus correcting results we published ibidem).
Certain Finitely Generated Compact Zero Dimensional Semigroups
Authors: Hunter R. P.
Published: April 2009

Consider a compact zero dimensional (profinite) monoid. While the group of units must be open, a regular D-class need not be open in the ideal it generates. This is the case if and only if the semigroup contains infinitely many copies of a certain semilattice composed of an increasing sequence of idempotents converging to an upper bound.

Using compactifications of free products, two generator compact monoids with these properties are constructed.
Characterizations of Quasi-Metrizable Bitopological Spaces
Authors: Raghavan T. G. , Reilly I. L.
Published: April 2009

In this paper we prove that a pairwise Hausdorff bitopological space is quasi-metrizable if and only if for each point x ∈ X and for i, j = 1,2, i ≠ j, one can assign nbd bases { S(n, i; x) | n = 1, 2,… } such that (i) y ∉ S (n − 1, i; x) imples S(n, i; x) ∩ S (n, j; y) = φ, (ii) y ∈ S (n, i; x) implies S (n, i; y) ⊂ S(n − 1, i; x). We derive two further results from this.
Vector lattices over subfields of the reals
Authors: Bixler P. , Conrad P. , Powell W. B. , Tsinakis C.
Published: April 2009

In this paper we consider classes of vector lattices over subfields of the real numbers. Among other properties we relate the archimedean condition of such a vector lattice to the uniqueness of scalar multiplication and the linearity ofl-automorphisms. If a vector lattice in the classes considered admits an essential subgroup that is not a minimal prime, then it also admits a non-linearl-automorphism and more than one scalar multiplication. It is also shown that eachl-group contains a largest archimedean convexl-subgroup which admits a unique scalar multiplication.
Groups with many permutable subgroups
Authors: Curzio Mario , Lennox John , Rhemtulla Akbar , Wiegold James
Published: April 2009

We consider the influence on a group G of the condition that every infinite set of cyclic subgroups of G contains a pair that permute and prove (Theorem 1) that finitely generated soluble groups with this condition are centre-by-finite, and (Theorem 2) that torsion free groups satisfying the condition are abelian.
Multipliers on weighted Hardy spaces over locally compact Vilenkin groups, I
Authors: Onneweer C. W. , Quek T. S.
Published: April 2009

Let G denote a locally compact Vilenkin group with dual group Γ. We give sufficient conditions for a function ϕ ∈ L∞ (Γ) to be a multiplier from the power-weighted Hardy space to itself or the corresponding power-weighted Lebesgue space
Subgroups of the Schur multiplier
Authors: Higgs R. J.
Published: April 2009

Two subgroups ME(G) and MI(G) of the Schur multiplier M(G) of a finite group G are introduced: ME(G) contains those cohomology classes [α] of M(G) for which every element of G is α-regular, and MI(G) consists of those cohomology classes of M(G) which contain a G-invariant cocycle. It is then shown that under suitable circumstances, such as when G has odd order, that each element of MI(G) can be expressed as the product of an element of ME(G) and an element of the image of the inflation homomorphism from M(G/G′) into M(G).
A geometric property of convex sets with applications to minimax type inequalities and fixed point theorems
Authors: Shih Mau-Hsiang , Tan Kok-Keong
Published: April 2009

A geometric property of convex sets which is equivalent to a minimax inequality of the Ky Fan type is formulated. This property is used directly to prove minimax inequalities of the von Neumann type, minimax inequalities of the Fan-Kneser type, and fixed point theorems for inward and outward maps.
A filtration of Weyl modules for large weights
Authors: Wong W. J.
Published: April 2009

A filtration is constructed for each dual Weyl module of a connected reductive group in prime characteristic p, and the quotients of the filtration are identified when the highest weight is far enough from the walls of the dominant chamber. The existence of certain composition factors is deduced.
Bounded spherical functions for abstract operators
Authors: Cohen Joel M.
Published: April 2009

The aim of this paper is to study the spherical functions associated to an operator. These functions can be thought of abstractly as being eigenfunctions of the operator which can be expressed in terms of the operator. The meaning of these properties will be made precise as will a notion of boundedness. The results are obtained by studying a specific shift operator on the algebra of functionals on the complex polynomial ring. For the class studied, we obtain ellipses of eigenvalues for which there exist bounded spherical functions. As an application of the results, we study radial functions on discrete groups.
Cartan subalgebras of regular extensions of von Neumann algebras
Authors: Sutherland Colin E.
Published: April 2009

We analyse the structure of a regular extension ℳ ⋊ γ, υQ of a von Neumann algebra ℳ by an action (modulo inner automorphisms) γ of a discrete group Q, and a nonabelian 2-cycle υ for γ, under the assumption that the “action” γ of Q is cocycle conjugate to an “action”, α which leaves globally invariant a cartan subalgebra of ℳ. we show that ℳ ⋊ γ, υQ is isomorphic with the algebra of the left regular projective representation of a certain discrete, non-principal groupoid ℜ V Q determined by the action of Q on the given cartan subalgebrs, where ℜ is the Takesaki relation associated to the pair (ℳ, ) we apply this description to give a decomposition of the regular representation of a group G into irreducibles, where G is a split extension of a type I group K by an abelian group Q, and work out the details of the author's earlier abstract plancherel theorem in the case when K is abelian.
The characterization of elliptic curves over finite fields
Authors: Hirschfeld J. W. P. , Voloch J. F.
Published: April 2009

In a finite Desarguesian plane of odd order, it was shown by Segre thirty years ago that a set of maximum size with at most two points on a line is a conic. Here, in a plane of odd or even order, sufficient conditions are given for a set with at most three points on a line to be a cubic curve. The case of an elliptic curve is of particular interest.
Oscillation criteria for second order differential equations with damping
Authors: Grace S. R.
Published: April 2009

New oscillation criteria are given for second order nonlinear ordinary differential equations with alternating coefficients. The results involve a condition obtained by Kamenev for linear differential equations. The obtained criterion for superlinear differential equations is a complement of the work established by Kwong and Wong, and Philos, for sublinear differential equations and by Yan for linear differential equations.
On transition multimeasures with values in a Banach space
Authors: Papageorgiou Nikolaos S.
Published: April 2009

The theory of multimeasures (set valued measures), has its origins in mathematical economics and in particular in equilibrium theory for exchange economies with production, in which the coalitions and not the individual agents are the basic economic units (see Vind [25] and Hildenbrand [15]). Since then the subject of multimeasures has been developed extensively. Important contributions were made, among others, by Artstein [1], Costé [8], [9], Costé and Pallu de la Barrière [10], Drewnowski [12], Godet-Thobie [13], Hiai [14] and Pallu de la Barrière [17]. Further applications in mathematical economics can be found in Klein and Thompson [16] and Papageorgiou [19].
Sharp function estimates for fractional integrals and related operators
Authors: Kurtz Douglas S.
Published: April 2009

This paper considers analogs of results on integral operators studied by Hörmander. Using the sharp function introduced by Fefferman and Stein, we prove weighted norm inequalities on kernel operators which map an Lp space into an Lq space, with q not equal to p. The techniques recover known results about fractional integral operators and apply to multiplier operators which satisfy a generalization of the Hörmander multiplier condition.
Eigenelements of perturbed operators
Authors: Limaye B. V. , Nair M. T.
Published: April 2009

Let λ0 be a semisimple eigenvalue of an operator T0. Let Γ0 be a circle with centre λs0 containing no other spectral value of T0. Some lower bounds are obtained for the convergence radius of the power series for the spectral projection P(t) and for trace T(t)P(t) associated with linear perturbation family T(t) = T0 + tV0 and the circle Γ0. They are useful when T0 is a member of a sequence (Tn) which approximates an operator T in a collectively compact manner. These bounds result from a modification of Kato's method of majorizing series, based on an idea of Redont. I λ0 is simple, it is shown that the same lower bound are valid for the convergence radius of a power series yielding an eigenvector of T(t).
Fundamental systems and solutions of nonhomogeneous equations for a pair of mixed linear ordinary differential equations
Authors: Venkatesulu M. , Bhaskar T. Gnana
Published: April 2009

Two different ordinary differential operators L1 and L2 (not of the same order) defined on two adjacent intervals I1 and I2, respectively, with certain mixed conditions at the interface are considered. These problems are encountered in the study of ‘acoustic waveguides in ocean’, ‘transverse vibrations in nonhomogeneous strings’, etc. A complete set of physical conditions on the system give rise to three types of (selfadjoint) boundary value problems associated with the pair (L1, L2). In a series of papers, a systematic study of these new classes of problems is being developed. In the present paper, we construct the fundamental systems and exhibit the forms of solutions of nonhomogeneous problems associated with the pair (L1, L2).
A maximum principle related to level surfaces of solutions of parabolic equations
Authors: Pucci Carlo
Published: April 2009

Let u be a solution of a parabolic equation ut = F(u, Du, D2u). Under convenient hypotheses it is proved that the angle between a given direction and the normal to the level surfaces of u(·,t) satisfies a maximum principle.
The maximum distribution of a Gaussian stochastic process indexed by a local field
Authors: Evans Steven N.
Published: April 2009

We consider continuous Gaussian stochastic process indexed by a compact subset of a vector space over a local field. Under suitable conditions we obtain an asymptotic expression for the probability that such a process will exceed a high level. An important component in the proof of these results is a theorem of independent interest concerning the amount of ‘time’ which the process spends at high levels.
The growth of the expected number of real zeros of a random polynomial
Authors: Glendinning Richard
Published: April 2009

Let X0, X1…Xn,… be a stationary Gaussian process. We give sufficient conditions for the expected number of real zeros of the polynomial Qn (z) = Σnj =o X jzj to be (2/ π)log n as n tends to infinity.
Length theorems for the general linear group of a module over a local ring
Authors: Ellers Erich W. , Lausch Huberta
Published: April 2009

Let 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

Certain 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

Individuals 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

A 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

The 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

We 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

Let 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

For 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

It 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

Let 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.
Ideals in the Wiener algebra W+
Authors: Mortini Raymond , von Renteln Michael
Published: April 2009

Let W+ denote the Banach algebra of all absolutely convergent Taylor series in the open unit disc. We characterize the finitely generated closed and prime ideals in W+. Finally, we solve a problem of Rubel and McVoy by showing that W+ is not coherent.
Proper efficiency in linear vector maximum problems with nonlinear constraints
Authors: Gulati T. R. , Islam M. A.
Published: April 2009

A linear vector maximum problem with nonlinear constraints is considered. A condition is derived which is necessary for an efficient solution and sufficient for a properly efficient solution of this problem. This leads to sufficient conditions for an efficient solution to be properly efficient. An example is discussed at the end.
QF-3 rings and torsion theories
Authors: Pardo José L. Gómez , González Nieves Rodríguez
Published: April 2009

In 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

We 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

The 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.
A self-centralizing characteristic subgroup
Authors: Perez-Ramos M. D.
Published: April 2009

In this note we introduce a self-centralizing characteristic subgroup, associated with quasinilpotent injectors, of a finite group.
Complete hypersurfaces in cylinders
Authors: Hasanis Thomas
Published: April 2009

We consider the extent of certain complete hypersurfaces of Euclidean space. We prove that every complete hypersurface in En+1 with sectional curvature bounded below and non-positive scalar curvature has at least (n − 1) unbounded coordinate functions.
Maximal subgroups and the Jordan-Hölder Theorem
Authors: Lafuente Julio
Published: April 2009

In this note we present a general Jordan-Hölder type theorem for modular lattices and apply it to obtain various (old and new) versions of the Jordan-Hölder Theorem for finite groups.
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

Let 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).
The group of formal power series under substitution
Authors: Johnson D. L.
Published: April 2009

This is a study of formal power series under the binary operation of formal composition from a group-theoretical point of view. Various “large” properties are derived.
Composition operators on weighted spaces of continuous functions
Authors: Singh R. K. , Summers W. H.
Published: April 2009

We 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

A 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

In 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

We 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.
A note on real hypersurfaces of a complex projective space
Authors: Kwon Jung-Hwan , Nakagawa Hisao
Published: April 2009

We study real hypersurfaces of a complex projection space and show that there are no such hypersurfaces with harmonic curvature on which the structure vector is principal.
The odd-local subgroups of the Monster
Authors: Wilson Robert A.
Published: April 2009

We determine all conjugacy classes of maximal p-local subgroups of the Monster for p ≠ 2.
Some embeddings related to C*-embeddings
Authors: Aull C. E.
Published: April 2009

A 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.
Non-Complemented Open Sets in Effective Topology
Authors: Hingston Philip
Published: April 2009

Notions of effective complementation in effective topological spaces are considered, and several types of non-complemented sets are constructed. While there are parallels with recursively enumerable sets, some unexpected differences appear. Finally, a pair of splitting theorems is proved.
Hereditarily universal sets
Authors: Ellentuck Erik
Published: April 2009

An immune set is found such that the recursive equivalence type of its infinite subsets are universal in a very strong sense.
Remarks on a class of 2-generator groups of deficiency zero
Authors: Campbell C. M. , Robertson E. F.
Published: April 2009

Let G be a finitely presented group. A finite presentation P of G is said to have defiency m – n if it defines G with m generators and n relations. The deficiency of G is the maximum of the deficiencies of all the finite presentations P of G. If G is finite the deficiency of G is less than or equal to zero. The only finite two generator groups of deficiency zero that are known are certain metacyclic groups given by Wamsley (1970), a class of nilpotent groups given by Macdonald in (1962) and a class of groups given by Wamsley (1972).
A consequence of the axiom of choice
Authors: Ash C. J.
Published: April 2009

Let R, C be the additive groups of the real, complex numbers respectively. Using the Axiom of Choice (A.C.), these groups may be shown to be isomorphic. We show that this cannot be proved in Zermelo-Fraenkel set theory (see e.g. Fraenkel, Bar-Hillel and Levy (1973)) without the additional assumption of A.C. This is one of the most “concrete” used of the Axiom of Choice of which I know. THEOREM 1 (assuming (A.C)). C ≅ R.
A technique for finding minimal paths in subspaces of a metric space
Authors: Milnes Harold Willis , Hildebrand S. K.
Published: April 2009

In this paper the problem of constructing an arc of minimum length joining two fixed points: P1, P2, in an arbitrary subset: S, of a metric space is considered. The approach taken is a departure from the classical methods of the calculus of variations in that it is topological character, making use of the properties of sets rather than differential calculus.
Closure operators
Authors: Collyer P. J. , Sullivan R. P.
Published: April 2009

A mapping κ: P(X) → P(X) is a quasi-closure operator (see Thron (1966) page 44) if (i) □κ = □, and for all A, B ∈ P(X) we have (ii) A ⊆ Aκ, and (iii) (A ⋓ B)κ = Aκ ∪ Bκ one easily deduces that such operators have the further property: (iv) if A ⊆ B ⊆ X, then Aκ if κ also satisfies: (v) Aκ2 ⊆ Aκ for all A ⊆ X, then κ is called a Kuratowski closure operator.
Hypernormalizing groups
Authors: Heineken Hermann
Published: April 2009

All subnormal subgroups of hypernormalizing groups have by definition subnormal normalizers. It is shown that finite soluble HN-groups belong to the class of groups of Fitting length three. Finite HN-groups are considered including those with subnormal quotient isomorphic to SL(2,5).
Driving from degeneracy
Authors: Cameron Neil
Published: April 2009

A method is proposed for driving degenerate feasible solutions to linear programming problems away from essential degeneracy and in particular for identifying essentially degenerate optimal solutions. An essentially degenerate cycling example is also given, so answering a question raised earlier.
On non-isotropic homogeneous Lipschitz spaces
Authors: Meda Stefano
Published: April 2009

We prove that in a non-isotropic Euclidean space, homogeneous Lipschitz spaces of distributions, defined in terms of (generalized) Weierstrass integrals, can be characterized by means of higher order difference operators.
Joins of topologies homeomorphic to the rationals
Authors: Jayanthan A. J. , Kannan V.
Published: April 2009

Let 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

A.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

In 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

This 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

Well-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.
The vector lattice cover of certain partially ordered groups
Authors: Buskes G. , Van Rooij A.
Published: April 2009

In this paper we introduce the notion of Riesz homomorphism on Archimedean directed partially ordered groups and use it to study the vector lattice cover of such groups.
Incompressible surfaces and the topology of 3-dimensional manifolds
Authors: Aitchison Iain R. , Rubinstein J. Hyam
Published: April 2009

Existence 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.
On spines of 3-manifolds with boundary
Authors: Gordon C. McA.
Published: April 2009

We give a simple necessary and sufficient condition for the inclusion map of a subpolyhedron into a compact 3-manifold with non-empty boundary to be a homotopy equivalence.
Generation of generators of holomorphic semigroups
Authors: Berg Christian , Boyadzhiev Khristo , Delaubenfels Ralph
Published: April 2009

We 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

For 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

If 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

Various 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.
Finitely sorting Lie algebras
Authors: Barnes Donald W.
Published: April 2009

Lie algebras whose finite-dimensional modules decompose into direct sums of modules involving only one type of irreducible are investigated. Some vanishing theorems for the cohomology of some infinite-dimensional Lie algebras are thereby obtained.
Centralizing properties in simple locally finite groups and large finite classical groups
Authors: Hartley Brian
Published: April 2009

The 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, namely

Theorem 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.
Groups with Černikov conjugacy classes
Authors: Franciosi S. , De Giovanni F. , Tomkinson M. J.
Published: April 2009

The aim of this paper is to prove some embedding theorems for groups with Černikov conjugacy classes. Moreover a characterization of periodic central-by-Černikov groups is given.
Structural inference on the generalized gamma distribution based on type-II progressively censored sample
Authors: Maswadah M. S.
Published: April 2009

This 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

Estimators 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

Epimorphic 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

Tame 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

The 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

Let 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.
A note on right equivalence of module presentations
Authors: Canfell M. J.
Published: April 2009

If R has 1 in the stable range, then any two presentations f, g: p→ M of an R-module M by a finitely generated projective p are right equivalent, that is, f = gh for some automorphism h of P. The convers is also true.
The dual lattice of an extreme six-dimensional lattice
Authors: Coulson David
Published: April 2009

The 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

In 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

Let 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.
Geometry of Neumann subgroups
Authors: Kulkarni Ravi S.
Published: April 2009

A Neumann subgroup of the classical modular group is by definition a complement of a maximal parabolic subgroup. Recently Neumann subgroups have been studied in a series of papers by Brenner and Lyndon. There is a natural extension of the notion of a Neumann subgroup in the context of any finitely generated Fuchsian group Γ acting on the hyperbolic plane H such that Γ/H is homeomorphic to an open disk. Using a new geometric method we extend the work of Brenner and Lyndon in this more general context.
Inverse semigroups with isomorphic partial automorphism semigroups
Authors: Goberstein Simon M.
Published: April 2009

It is shown that a so-called shortly connected combinatorial inverse semigroup is strongly lattice-determined “modulo semilattices”. One of the consequences of this theorem is the known fact that a simple inverse semigroup with modular lattice of full inverse subsemigroups is strongly lattice-determined [7]. The partial automorphism semigroup of an inverse semigroup S consists of all isomorphisms between inverse subsemigroups of S. It is proved that if S is a shortly connected combinatorial inverse semigroup, T an inverse semigroup and the partial automorphism semigroups of S and T are isomorphic, then either S and T are isomorphic or they are dually isomorphic chains (with respect to the natural partial order); moreover, any isomorphism between the partial automorphism semigroups of S and T is induced either by an isomorphism or, if S and T are dually isomorphic chains, by a dual isomorphism between S and T. Counter-examples are constructed to demonstrate that the assumptions about S being shortly connected and combinatorial are essential.
Symplectic complex bundles over real algebraic four-folds
Authors: Kucharz Wojciech
Published: April 2009

LetXbe a compact affine real algebraic variety of dimension 4. We compute the Witt group of symplectic bilinear forms over the ring of regular functions fromXto C. The Witt group is expressed in terms of some subgroups of the cohomology groups.
Total chromatic number of graphs of high degree
Authors: Yap H. P. , Jian-Fang Wang , Zhongfu Zhang
Published: April 2009

Using a new proof technique of the first author (by adding a new vertex to a graph and creating a total colouring of the old graph from an edge colouring of the new graph), we prove that the TCC (Total Colouring Conjecture) is true for any graph G of order n having maximum degree at least n - 4. These results together with some earlier results of M. Rosenfeld and N. Vijayaditya (who proved that the TCC is true for graphs having maximum degree at most 3), and A. V. Kostochka (who proved that the TCC is true for graphs having maximum degree 4) confirm that the TCC is true for graphs whose maximum degree is either very small or very big.
The cohomology ring of a combinatorially aspherical group
Authors: Horadam K. J.
Published: April 2009

A presentation is given for the cohomology ring of a finitely presented combinatorially aspherical group with trivial coefficients in an integral domain. Cohomological periodicity is characterized in terms of the cup product.
The characteristic ring and the “best” way to adjoin a one
Authors: Burgess W. D. , Stewart P. N.
Published: April 2009

For any ring S we define and describe its characteristic ring, k(S). It plays the rôle of the usual characteristic even in rings whose additive structure, (S, +), is complicated. The ring k(S) is an invariant of (S, +) and also reflects certain non-additive properties of S. If R is a left faithful ring without identity element, we show how to use k(R) to embed R in a ring R1 with identity. This unital overring of R inherits many ring properties of R; for instance, if R is artinian, noetherian, semiprime Goldie, regular, biregular or a V-ring, so too is R1. In the case of regularity (or generalizations thereof), R1 satisfies a universal property with respect to the adjunction of an identity