bluuebunny/crossref_metadata_2025 huggingface dataset:
Derived intertwining norms for reducible spherical principal series
Authors: Gilbert J. E. , Kunze R. A. , Meaney C.
Published: April 2009

We use the second derivative of intertwining operators to realize a unitary structure for the irreducible subrepresentations in the reducible spherical principal series of U(1, n). These representations can also be realized as the kernels of certain invariant first-order differential operators acting on sections of homogeneous bundles over the hyperboloid (U(1) × U(n))/U(1, n).
C*-crossed products by partial actions and actions of inverse semigroups
Authors: Sieben Nándor
Published: April 2009

The recently developed theory of partial actions of discrete groups on C*-algebras is extended. A related concept of actions of inverse semigroups on C*-algebras is defined, including covariant representations and crossed products. The main result is that every partial crossed product is a crossed product by a semigroup action.
Representations of triangular subalgebras of groupoid C*-algebras
Authors: Muhly Paul S. , Solel Baruch
Published: April 2009

We investigate the invariant subspace structure of subalgebras of groupoid C*-algebras that are determined by automorphism groups implemented by cocycles on the groupoids. The invariant subspace structure is intimately tied to the asymptotic behavior of the cocycle.
On complete integral closure and Archimedean valuation domains
Authors: Gilmer Robert
Published: April 2009

SupposeDis an integral domain with quotient fieldKand thatLis an extension field ofK. We show in Theorem 4 that if the complete integral closure ofDis an intersection of Archimedean valuation domains onK, then the complete integral closure ofDinLis an intersection of Archimedean valuation domains onL; this answers a question raised by Gilmer and Heinzer in 1965.
More generalised Sylow theorems
Authors: Hawthorn I. J.
Published: April 2009

The study of classes of finite groups is divided into two parts. The projective theory studies formations and Schunck classes. The dual injective theory studies Fitting classes. In each type of class a generalisation of Sylow's theorem holds. In this paper we seek further generalisations of Sylow's theorem which hold for classes which are neither injective nor projective, but obey other related properties. Firstly a common framework for the injective and projective theories is constructed. Within the context of this common framework further types of Sylow theorem can then be sought. An example is given of a property which is a simple hybrid of injectivity and projectivity which we will call ‘interjectivity’. A generalised Sylow theorem is then proved in the interjective case.
Two estimates concerning asymptotics of the minimizations of a Ginzburg-Landau functional
Authors: Hong Min-Chun
Published: April 2009

We prove two asymptotical estimates for minimizers of a Ginzburg-Landau functional of the form .
Compressible ends of leaves in foliated 3-manifolds
Authors: Charitos Charalambos
Published: April 2009

In this paper we study the asymptotic behavior of cylindrical ends in compact foliated 3-manifolds and give a sufficient condition for these ends to spiral onto a toral leaf.
On some regularity conditions of Borel measures on R
Authors: Nasr F. Ben
Published: April 2009

The aim of this paper is to resolve Taylor's question concerning certain regularity conditions on a Borel measure. The proposed solution is given in the framework of Brown, Michon and Peyrière, and Olsen.
Even compositions of entire functions and related matters
Authors: Horwitz Alan
Published: April 2009

We examine when the composition of two entire functions f and g is even, and extend some of our results to cyclic compositions in general. If p is a polynomial, then we prove that f ^ p is even for a non-constant entire function f if and only if p is even, odd plus a constant, or a quadratic polynomial composed with an odd polynomial. Similar results are proven for odd compositions. We also show that p ^ f can be even when f and no derivative of f are even or odd, where p is a polynomial. We extend some results of an earlier paper to cyclic compositions of polynomials. We also show that our results do not extend in general to rational functions or polynomials in two variables.
Duality on tori and multiplicative dependence relations
Authors: Bertrand Daniel
Published: April 2009

In this paper, we give multihomogeneous estimates for the group of relations linking multiplicatively dependent algebraic numbers. In the process, we raise a question in the style of Lehmer's problem, concerning multidimensional covolumes in the lattice of units. The proofs are based on the Brill-Gordan duality theorem on orthogonal lattices, and the paper closes with an algebraic version of the theorem, concerning orthogonal abelian subvarieties of an arbitrarily polarized abelian variety.
Uniform consistency of the partitioning estimate under ergodic conditions
Authors: Laib Naâmane
Published: April 2009

We establish the uniform almost sure convergence of the partitioning estimate, which is a histogram-like mean regression function estimate, under ergodic conditions for a stationary and unbounded process. The main application of our results concerns time series analysis and prediction in the Markov processes case.
Existence and uniqueness of a solution for a minimization problem with a generic increasing function
Authors: Rubinov A. M. , Zaslavski A. J.
Published: April 2009

In this paper we study the existence and uniqueness of a solution for minimization problems with generic increasing functions in an ordered Banach space X. The standard approaches are not suitable in such a setting. We propose a new type of perturbation adjusted for the problem under consideration, prove the existence and point out sufficient conditions providing the uniqueness of a solution. These results are proved by assuming that the space X enjoys the following property: each decreasing norm-bounded sequence has a limit. We supply a counterexample, which shows that this property is essential and give a modification of obtained results for the space C(T), which does not possess this property.
Second-order strongly elliptic operators on Lie groups with Hölder continuous coefficients
Authors: Elst A. F. M. Ter , Robinson Derek W.
Published: April 2009

LetGbe a connected Lie group with Lie algebra g anda1, …,adan algebraic basis of g. Further letAidenote the generators of left translations, acting on theLp-spacesLp(G; dg)formed with left Haar measuredg, in the directions ai. We consider second-order operatorsin divergence form corresponding to a quadratic form with complex coefficients, bounded Hölder continuous principal coefficientscijand lower order coefficientsci, c′ii, c0∈L∞such that the matrixC= (cij)of principal coefficients satisfies the subellipticity conditionuniformly overG.

We discuss the hierarchy relating smoothness properties of the coefficients ofHwith smoothness of the kernel and smoothness of the domain of powers ofHon theLρ-spaces. Moreover, we present Gaussian type bounds for the kernel and its derivatives.

Similar theorems are proved for strongly elliptic operatorsin non-divergence form for which the principal coefficients are at least once differentiable.
Invariant submanifolds in flow geometry
Authors: González-Dávila J. C. , González-Dávila M. C. , Vanhecke L.
Published: April 2009

We begin a study of invariant isometric immersions into Riemannian manifolds (M, g) equipped with a Riemannian flow generated by a unit Killing vector field ξ. We focus our attention on those (M, g) where ξ is complete and such that the reflections with respect to the flow lines are global isometries (that is, (M, g) is a Killing-transversally symmetric space) and on the subclass of normal flow space forms. General results are derived and several examples are provided.
On the action of the unitary group on the projective plane over a local field
Authors: Voskuil Harm
Published: April 2009

Let G be a unitary group of rank one over a non-archimedean local field K (whose residue field has a characteristic ≠ 2). We consider the action of G on the projective plane. A G(K) equivariant map from the set of points in the projective plane that are semistable for every maximal K split torus in G to the set of convex subsets of the building of G(K) is constructed. This map gives rise to an equivariant map from the set of points that are stable for every maximal K split torus to the building. Using these maps one describes a G(K) invariant pure affinoid covering of the set of stable points. The reduction of the affinoid covering is given.
Algebraic characterizations of locally compact groups
Authors: Font Juan J. , Hernández Salvador
Published: April 2009

Let G1, G2 be locally compact real-compact spaces. A linear map T defined from C(G1) into C(G2) is said to be separating or disjointness preserving if f = g ≡ 0 implies Tf = Tg ≡ 0 f or all f, g ∈ C(G1). In this paper we prove that both a separating map which preserves non-vanishing functions and a separating bijection which satisfies condition (M) (see Definition 4) are automatically continuous and can be written as weighted composition maps. We also study the effect of separating surjections (respectively injections) on the underlying spaces G1 and G2.

Next we apply the above results to give an algebraic characterization of locally compact Abelian groups, similar to the one given in [7] for compact Abelian groups in the presence of ring isomorphisms.

Finally, locally compact (not necessarily Abelian) groups are considered. We provide a sharpening of a result of Edwards and study the effect of onto (respectively injective) weighted composition maps on the groups G1 and G2.
A group with very strange decomposition properties
Authors: Dunwoody M. J. , Jones J. M.
Published: April 2009

An example is given of a finitely generated group G for which G ≅ G*cG, where C is infinite cyclic.
Some challenging group presentations
Authors: Havas George , Holt Derek F. , Kenne P. E. , Rees Sarah
Published: April 2009

We study some challenging presentations which arise as groups of deficiency zero. In four cases we settle finiteness: we show that two presentations are for finite groups while two are for infinite groups. Thus we answer three explicit questions in the literature and we provide the first published deficiency zero presentation for a group with derived length seven. The tools we use are coset enumeration and Knuth-Bebdix rewriting, which are well-established as methods for proving finiteness or otherwise of a finitely presented group. We briefly comment on their capabilities and compare their performance.
Computation of nilpotent engel groups
Authors: Nickel Werner
Published: April 2009

This paper reports on a facility of the ANU NQ program for computation of nilpotent groups that satisfy an Engel-n identity. The relevant details of the algorithm are presented together with results on Engel-n groups for moderate values of n.
Composition operators between weighted Banach spaces of analytic functions
Authors: Bonet J. , Domański P. , Lindström M. , Taskinen J.
Published: April 2009

We characterize those analytic self-maps ϕ of the unit disc which generate bounded or compact composition operators Cϕ between given weighted Banach spaces H∞v or H0v of analytic functions with the weighted sup-norms. We characterize also those composition operators which are bounded or compact with respect to all reasonable weights v.
Functional equations in total negation
Authors: McMaster T. B. M. , Turner C. R.
Published: April 2009

It is known that the only topological invariantsPfor which anti(P) = anti2(P), anti( ) denoting Bankston's total negation operator, are those which are determined purely by the cardinality of the underlying point-set. We examine equations of the form antin(P) = antin(notP), reaching similar conclusions forn≤ 2 but weaker ones forn> 3. A corresponding investigation for total negation within a constraint is initiated.
Congruence Representations of Join-homomorphisms of Finite Distributive Lattices: Size and Breadth
Authors: Grätzer G. , Lakser H. , Schmidt E. T.
Published: April 2009

Let K and L be lattices, and let ϕ be a homomorphism of K into L.Then ϕ induces a natural 0-preserving join-homomorphism of Con K into Con L.

Extending a result of Huhn, the authors proved that if D and E are finite distributive lattices and ψ is a 0-preserving join-homomorphism from D into E, then D and E can be represented as the congruence lattices of the finite lattices K and L, respectively, such that ψ is the natural 0-preserving join-homomorphism induced by a suitable homomorphism ϕ: K → L. Let m and n denote the number of join-irreducible elements of D and E, respectively, and let k = max (m, n). The lattice L constructed was of size O(22(n+m)) and of breadth n+m.

We prove that K and L can be constructed as ‘small’ lattices of size O(k5) and of breadth three.
Space-like submanifolds with parallel mean curvature in de Sitter spaces
Authors: Ouyang Chongzhen , Li Zhenqi
Published: April 2009

This paper investigates complete space-like submainfold with parallel mean curvature vector in the de Sitter space. Some pinching theorems on square of the norm of the second fundamental form are given
Essential ideals of incidence algebras
Authors: Spiegel Eugene
Published: April 2009

It is determined when there exists a minimal essential ideal, or minimal essential left ideal, in the incidence algebra of a locally finite partially ordered set defined over a commutative ring. When such an ideal exists, it is described.
Finite dinilpotent groups of small derived length
Authors: Cossey John , Wang Yanming
Published: April 2009

A finite dinilpotent groupGis one that can be written as the product of two finite nilpotent groups,AandBsay. A finite dinilpotent group is always soluble. IfAis abelian andBis metabelian, with |A| and|B| coprime, we show that a bound on the derived length given by Kazarin can be improved. We show thatGhas derived length at most 3 unlessGcontains a section with a well defined structure: in particular ifGis of odd order,Ghas derived length at most 3.
Soluble groups isomorphic to their non-nilpotent subgroups
Authors: Smith Howard , Wiegold James
Published: April 2009

A group G belongs to the class W if G has non-nilpotent proper subgroups and is isomorphic to all of them. The main objects of study are the soluble groups in W that are not finitely generated. It is proved that there are no torsion-free groups of this sort, and a reasonable classification is given in the finite rank case.
On the homotopy type of the p-subgroup complex for finite solvable groups
Authors: Pulkus Jürgen , Welker Volkmar
Published: April 2009

We provide a wedge decomposition of the homotopy type of the p-subgroup complex in the case of a finite solvable group G. In particular, this includes a new proof of the result of Quillen which says that this complex is contractible if and only if there is a non-trivial normal p-subgroup in G. We also provide reduction formulas for the G-module structure of the homology groups. Our results are obtained with diagram-methods by gluing the p-subgroup complex of G along the p-subgroup complex of = G/N for a normal p′-subgroup of G.
The bounded vector measure associated to a conical measure and pettis differentiability
Authors: Rodriguez-Piazza L. , Romero-Moreno M. C.
Published: April 2009

Let X be a locally convex space. Kluvánek associated to each X-valued countably additive vector measure a conical measure on X; this can also be done for finitely additive bounded vector measures. We prove that every conical measure u on X, whose associated zonoform Ku is contained in X, is associated to a bounded additive vector measure σ(u) defined on X, and satisfying σ(u)(H) ∈ H, for every finite intersection H of closed half-spaces. When X is a complete weak space, we prove that σ(u) is countably additive. This allows us to recover two results of Kluvánek: for any X, every conical measure u on it with Ku ⊆ X is associated to a countably additive X-valued vector measure; and every conical measure on a complete weak space is localizable. When X is a Banach space, we prove that σ(u) is countably additive if and only if u is the conical measure associated to a Pettis differentiable vector measure.
m-Wielandt series in infinite groups
Authors: Franchi Clara
Published: April 2009

In a group G, um (G) denotes the subgroup of the elements which normalize every subnormal subgroup of G with defect at most m. The m-Wielandt series of G is then defined in a natural way. G is said to have finite m-Wielandt length if it coincides with a term of its m-Wielandt series. We investigate the structure of infinite groups with finite m-Wielandt length.
On real forms of a complex algebraic curve
Authors: Bujalance E. , Gromadzki G. , Izquierdo M.
Published: April 2009

Two projective nonsingular complex algebraic curves X and Y defined over the field R of real numbers can be isomorphic while their sets X(R) and Y(R) of R-rational points could be even non homeomorphic. This leads to the count of the number of real forms of a complex algebraic curve X, that is, those nonisomorphic real algebraic curves whose complexifications are isomorphic to X. In this paper we compute, as a function of genus, the maximum number of such real forms that a complex algebraic curve admits.
Double circulant constructions of the Leech lattice
Authors: Chapman Robin
Published: April 2009

We consider the problem of finding, for each even number m, a basis of orthogonal vectors of length in the Leech lattice. We give such a construction by means of double circulant codes whenever m = 2p and p is a prime not equal to 11. From this one can derive a construction for all even m not of the form 2· 11r.
Sums of squares of integral linear forms
Authors: Sasaki Hideyo
Published: April 2009

In this paper we prove that every positive definite n-ary integral quadratic form with 12 < n < 13 (respectively 14 ≦ n ≤ 20) that can be represented by a sum of squares of integral linear forms is represented by a sum of 2 · 3n + n + 6 (respectively 3 · 4n + n + 3) squares. We also prove that every positive definite 7-ary integral quadratic form that can be represented by a sum of squares is represented by a sum of 25 squares.
The structure of finite groups in which permutability is a transitive relation
Authors: Robinson Derek J. S.
Published: April 2009

The structure of finite groups in which permutability is transitive (PT-groups) is studied in detail. In particular a finitePT-group has simple chief factors and thep-chief factors fall into at most two isomorphism classes. The structure of finiteT-groups, that is, groups in which normality is transitive, is also discussed, as is that of groups generated by subnormal or normalPT-subgroups.
Last passage times of minimum contrast estimators
Authors: Bose Arup , Chatterjee Snigdhansu
Published: April 2009

We study the last passage time and its asymptotic distribution for minimum contrast estimators defined through the minimization of a convex criterion function based on U-functionals. This includes cases of non-smooth estimators for vector valued parameters. We also derive a Bahadur-type representation and the law of iterated logarithms for such estimators.
On (2, 3, 7)-generation of maximal parabolic subgroups
Authors: Martino L. Di , Tamburini M. C.
Published: April 2009

Let R be a ring with 1 and En (R) be the subgroup of GLn(R) generated by the matrices I + reij, r ∈ R, i ≠ j. We prove that the subgroup of consisting of the matrices of shape , where and , is (2, 3, 7)-generated whenever R is finitely generated and n, are large enough.
Automorphisms of Cayley graphs of metacyclic groups of prime-power order
Authors: Li Caiheng , Sim Hyo-Seob
Published: April 2009

This paper inverstigates the automorphism groups of Cayley graphs of metracyclicp-gorups. A characterization is given of the automorphism groups of Cayley grahs of a metacyclicp-group for odd primep. In particular, a complete determiniation of the automophism group of a connected Cayley graph with valency less than 2pof a nonabelian metacyclicp-group is obtained as a consequence. In subsequent work, the result of this paper has been applied to solve several problems in graph theory.
Ensuring commutativity of finite groups
Authors: Neumann B. H.
Published: April 2009

Comments are made on the following question. Let m, n be positive integers and g a finite group. Suppose that for all choices of a subset of cardinality m and of a subset of cardinality n in g some member of the first commutes with some member of the second. Under what conditions on m, n is the group abelian?
Restricted Lazard elimination and modular Lie powers
Authors: Stöhr Ralph
Published: April 2009

We exhibit a variation of the Lazard Elimination theorem for free restricted Lie algebras, and apply it to two problems about finite group actions on free Lie algebras over fields of positive characteristic.
A simple remark on Dirichlet series
Authors: Kohnen Winfried
Published: April 2009

It is shown that a twist of a Dirichlet series by a Dirichlet character may lead to very different analytic properties.
On the geometry of Lp (μ) with applications to infinite variance processes
Authors: Cheng R. , Miamee A. G. , Pourahmadi M.
Published: April 2009

Some geometric properties of Lp spaces are studied which shed light on the prediction of infinite variance processes. In particular, a Pythagorean theorem for Lp is derived. Improved growth rates for the moving average parameters are obtained.
An integral formula for compact hypersurfaces in space forms and its applications
Authors: Alías Luis J.
Published: April 2009

In this paper we establish an integral formula for compact hypersurfaces in non-flat space forms, and apply it to derive some interesting applications. In particular, we obtain a characterization of geodesic spheres in terms of a relationship between the scalar curvature of the hypersurface and the size of its Gauss map image. We also derive an inequality involving the average scalar curvature of the hypersurface and the radius of a geodesic ball in the ambient space containing the hypersurface, characterizing the geodesic spheres as those for which equality holds.
A decomposition theorem for homogeneous algebras
Authors: Sweet L. G. , Macdougall J. A.
Published: April 2009

An algebra A is homogeneous if the automorphism group of A acts transitively on the one dimensional subspaces of A. Suppose A is a homogeneous algebra over an infinite field k. Let La denote left multiplication by any nonzero element a ∈ A. Several results are proved concerning the structure of A in terms of La. In particular, it is shown that A decomposes as the direct sum A = ker La Im La. These results are then successfully applied to the problem of classifying the infinite homogeneous algebras of small dimension.
About a problem of Hermite and Biehler
Authors: Stoyanov Todor
Published: April 2009

A point of departure for this paper is the famous theorem of Hermite and Biehler: If f (z) is a polynomial with complex coefficients ak and its zeros zk satisfy Im Zk < 0, then the polynomials with coefficients Re ak, and Im ak have only real zeros.

We generalize this theorem for some entire functions. The entire functions in Theorem 2 and Theorem 3 are of first and second genus respectively.
Growth of functions in cercles de remplissage
Authors: Fenton P. C. , Rossi John
Published: April 2009

Suppose that f is meromorphic in the plane, and that there is a sequence Zn → ∞ and a sequence of positive numbers ∈n → 0, such that ∈n|zn|f#(zn)/log|zn| → ∞. It is shown that if f is analytic and non-zero in the closed discs Δn = {z: |z – zn| ≦∈n|zn|}, n = 1, 2, 3 …, then, given any positive integer K, there are arbitrarily large values of n and there is a point z in Δn such that │f (z)| 〉 |Z│k. Examples are given to show that the hypotheses cannot be relaxed.
On graphC*-algebras
Authors: Goldstein P.
Published: April 2009

CertainC*-algebras on generators and relations are associated to directed graphs. For a finite graph γ,C*-algebrais canonically isomorphic to Cuntz-Krieger algebra corresponding to the adjacency matrix of γ. It is shown that if a countably infinite graph γ is strongly connected,γis simple and purely infinite.
Free algebras in the variety of three-valued closure algebras
Authors: Abad M. , Varela J. P. Díaz
Published: April 2009

In this paper, the variety of three-valued closure algebras, that is, closure algebras with the property that the open elements from a three-valued Heyting algebra, is investigated. Particularly, the structure of the finitely generated free objects in this variety is determined.
Ergodic path properties of processes with stationary increments
Authors: Kella Offer , Stadje Wolfgang
Published: April 2009

For a real-valued ergodic process X with strictly stationary increments satisfying some measurability and continuity assumptions it is proved that the long-run ‘average behaviour’ of all its increments over finite intervals replicates the distribution of the corresponding increments of X in a strong sense. Moreover, every Lévy process has a version that possesses this ergodic path property.
On the Toeplitz algebras of right-angled and finite-type Artin groups
Authors: Crisp John , Laca Marcelo
Published: April 2009

The graph product of a family of groups lies somewhere between their direct and free products, with the graph determining which pairs of groups commute. We show that the graph product of quasi-lattice ordered groups is quasi-lattice ordered, and, when the underlying groups are amenable, that it satisfies Nica's amenability condition for quasi-lattice orders. The associated Toeplitz algebras have a universal property, and their representations are faithful if the generating isometries satisfy a joint properness condition. When applied to right-angled Artin groups this yields a uniqueness theorem for the C*-algebra generated by a collection of isometries such that any two of them either *-commute or else have orthogonal ranges. The analogous result fails to hold for the nonabelian Artin groups of finite type considered by Brieskorn and Saito, and Deligne.
The iterated equation of generalized axially symmetric potential theory. III. Conjugate general solutions
Authors: Burns J. C.
Published: April 2009

The iterated equation of generalized axially symmetric potential theory (GASPT), in the notation of the first paper of this series [1] which will be designated I, is the equation where the operator Lk is defined by
A Helly-type theorem on a sphere
Authors: Baker M. J. C.
Published: April 2009

The purpose of this paper is to prove that if n+3, or more, strongly convex sets on an n dimensional sphere are such that each intersection of n+2 of them is empty, then the intersection of some n+1 of them is empty. (The n dimensional sphere is understood to be the set of points in n+1 dimensional Euclidean space satisfying x21+x22+ …+x2n+1 = 1.)
Verbal wreath products and certain product varieties of groups
Authors: Burns R. G.
Published: April 2009

Recently A. L. Šmel'kin [14] proved that a product variety1 is generated by a finite group if and only if is nilpotent, is abelian, and the exponents of and are coprime. Alternatively, by the theorem of Oates and Powell [13], we may say that a Cross variety is decomposable if and only if it is of the above form.
Functions over the residue field modulo a prime
Authors: London David , Ziegler Zvi
Published: April 2009

Let Fp be the residue field modulo a prime number p. The mappings of Fp, into itself are viewed as functions in one variable over Fp. When the mapping is onto, the function is a permutation.
On the complete integral closure of an integral domain
Authors: Gilmer Robert W. , Heinzer William J.
Published: April 2009

We consider in this paper only commutative rings with identity. When R is considered as a subring of S it will always be assumed that R and S have the same identity. If R is a subring of S an element s of S said to be integral over R if s is the root of a monic polynomial with coefficients in R. Following Krull [8], p. 102, we say s is almost integral over R provided all powers of s belong to a finite R-submodule of S. If R1 is the set of elements of S almost integral over R we say R1 is the complete integral closure of R in S.
Relativity, uncertainty and electrodynamics
Authors: Klotz A. H.
Published: April 2009

It is known that the Unified Field Theories of Weyl [14] and of Einstein [4] give no indication of how Relativity and Quantum Theories should be connected into a comprehensive field theory of physics. Indeed, the only determined attempt to establish such a theory, due to Eddington [3] and [6], failed through lack of contact with the contemporary developments, especially in quantum electrodynamics and elementary particles. Its author tried to explain curvature of the space-time in terms of statistical fluctuations partly of a physical origin defined within a mechanical system, and partly of a geometrical origin of coordinates superimposed on the latter. It is clear however that both the fluctuations of Eddington refer to purely mathematical frames. The probabilistic nature of his theory takes no account of physical objects, such as particles or energy distributions. It is the author's belief that this is the cause of difficulties associated with the otherwise admirable work of Eddington.
Relations on topological spaces: Urysohn's lemma
Authors: Lin Y.-F.
Published: April 2009

Let X be a topological space equipped with a binary relation R; that is, R is a subset of the Cartesian square X×X. Following Wallace [5], we write Deviating from [7], we shall follow Wallace [4] to call the relation R continuous if RA*⊂(RA)* for each A⊂X, where * designates the topological closure. Borrowing the language from the Ordered System, though our relation R need not be any kind of order relation, we say that a subset S of X is R-decreasing (R-increasing) if RS ⊂ S(SR ⊂ S), and that S is Rmonotone if S is either R-decreasing or R-increasing. Two R-monotone subsets are of the same type if they are either both R-decresaing or both Rincreasing.
Positive values of inhomogeneous quaternary quadratic forms, I
Authors: Dumir Vishwa Chander
Published: April 2009

Let Q(x1, …, xn) be an indefinite quadratic form in n-variables with real coefficients, determinant D ≠ 0 and signature (r, s), r+s = n. Then it is known (e.g. see Blaney [2]) that there exist constants Γr, s depending only on r and s such for any real numbers c1, …, cn we can find integers x1, …, xn satisfying
A generalisation of Minkowski's second inequality in the geometry of numbers
Authors: Woods A. C.
Published: April 2009

Let K be a bounded open convex set in euclidean n-space Rn symmetric in the origin 0. Further let L be a discrete point set in Rn containing 0 and at least n linearly independent points of Rn. Put mi = inf ui extended over all positive real numbers ui for which uiK contains i linearly independent points of L, i = 1, 2, …, n.
Rational polygons
Authors: Sheng T. K.
Published: April 2009

A polygon is said to be rational if all its sides and diagonals have rational lengths. I. J. Schoenberg has posed the interesting problem, “Can any polygon be approximated as closely as we like by a rational polygon?” Besicovitch [2] proved that right-angled triangles and parallelograms can be approximated in Schoenberg's sense, the proofs were improved by Daykin [5]. Mordell [7] proved that any quadrilateral can be approximated by a rational quadrilateral. By adapting Mordell's proof, Almering [1] generalised Mordell's result by showing that, if A, B, C are three distinct points with the distances AB, BC, CA all rational, then the set of points P for which PA, PB, PC are rational is everywhere dense in the plane that contains ABC. Daykin [4] extended the results of Besicovitch [3] and Mordell [7] by adding the requirement that the approximating quadrilaterals have rational area.
Summation of infinite series
Authors: Manocha H. L. , Sharma B. L.
Published: April 2009

In this paper we obtain the sum of some infinite series involving hypergeometric functions of one or more variables.
Involutory automorphisms of groups of odd order
Authors: Ward J. N.
Published: April 2009

Let G be a finite group of odd order with an automorphism ω of order 2. The Feit-Thompson theorem implies that G is soluble and this is assumed throughout the paper. Let Gω denote the subgroup of G consisting of those elements fixed by ω. If F(G) denotes the Fitting subgroup of G then the upper Fitting series of G is defined by F1(G) = F(G) and Fr+1(G) = the inverse image in G of F(G/Fr(G)). G(r) denotes the rth derived group of G. The principal result of this paper may now be stated as follows: THEOREM 1. Let G be a group of odd order with an automorphism ω of order 2. Suppose that Gω is nilpotent, and that G(r)ω = 1. Then G(r) is nilpotent and G = F3(G).
Density and representation theorems for multipliers of type (p, q)
Authors: Figà-Talamanca Alessandro , Gaudry G. I.
Published: April 2009

Let G be a locally compact Abelian Hausdorff group (abbreviated LCA group); let X be its character group and dx, dx be the elements of the normalised Haar measures on G and X respectively. If 1 < p, q < ∞, and Lp(G) and Lq(G) are the usual Lebesgue spaces, of index p and q respectively, with respect to dx, a multiplier of type (p, q) is defined as a bounded linear operator T from Lp(G) to Lq(G) which commutes with translations, i.e. τxT = Tτx for all x ∈ G, where τxf(y) = f(x+y). The space of multipliers of type (p, q) will be denoted by Lqp. Already, much attention has been devoted to this important class of operators (see, for example, [3], [4], [7]).
Arrays and brooks
Authors: Bennett B. T. , Potts R. B.
Published: April 2009

Consider an m × n rectangular array whose m rows are permutations of 1, 2, …, n. Such an array will be called a constant-sum array if the sum of the elements in each column is the same (and equal to ½m (n+1)). An example of a 3×9 constant-sum array is In contrast to a Latin rectangle, elements in the same column of a constantsum array may be equal. It will be convenient to assume arrays normalised in the sense that the columns are arranged so that, as in (1), the first row is in the standard order 1, 2, …, n.
A note on the propagation of plane waves in elastic and plastic solids
Authors: Cooper G. J. , Craggs J. W.
Published: April 2009

Some further numerical results are obtained for plane waves propagated into elastic and plastic solids. Quantitative agreement with experimental results indicates that rate of strain effects are not significant.
On an integral involving the H-function
Authors: Jain U. C.
Published: April 2009

The aim of this note is to evaluate an integral involving the product of two H-functions.
Conformality and p-isomorphism in finite nilpotent groups
Authors: Cooper C. D. H.
Published: April 2009

This paper discusses the relationship between two equivalence relations on the class of finite nilpotent groups. Two finite groups are conformal if they have the same number of elements of all orders. (Notation: G ≈ H.) This relation is discussed in [4] pp 107–109 where it is shown that conformality does not necessarily imply isomorphism, even if one of the groups is abelian. However, if both groups are abelian the position is much simpler. Finite conformal abelian groups are isomorphic.
On the absolute Nörlund summability of a Fourier series
Authors: Hsiang Fu Cheng
Published: April 2009

Let Σn−0∞an, be a given infinite series and {sn} the sequence of its partial sums. Let {pn} be a sequence of constants, real or complex, and let us write

If

as n → ∞, then we say that the series is summable by the Nörlund method (N, pn) to σ And the series a,Σan, is said to be absolutely summable (N, pn) or summable |N, Pn| if {σn} is of bounded variation, i.e.,
Matrix Representations of Inverse Semigroups
Authors: Preston G. B.
Published: April 2009

In his paper [1], W. D. Munn determines the irreducible matrix representations of an arbitrary inverse semigroup. Munn also gives a necessary and sufficient condition upon a 0-simple inverse semigroup for it to have a non-trivial matirx representation and for such semigroups gives a complete account of their representations. Munn's results rest upon the earlier work of Clifford [2] in which the representations of Brandt semigroups were determined. An alternative account of such representations was given by Munn in [3]. This earlier work is presented in Sections 5.2 and 5.4 of [4].
The Iterated Equation of Generalized Axially Symmetric Potential Theory
Authors: Burns J. C.
Published: April 2009

Milne-Thomson's well-known circle theorem [1] gives the stream function for steady two-dimensional irrotational flow of a perfect fluid past a circular cylinder when the flow in the absense of the cylinder is known. Butler's sphere theorem [2] gives the corresponding result for axially symmetric irrotational flow of a perfect fluid past a sphere. Collins [3] has obtained a sphere theorem for axially symmetric Stokes flow of a viscous liquid which gives a stream function satisfying the appropriate viscous boundary conditions on the surface of a sphere when the stream function for irrotational flow in the absence of the sphere is known.
On Properties Possessed by Solvable and Nilpotent Groups
Authors: Ayoub Christine
Published: April 2009

The object of this note is to study two properties of groups, which we will denote by (*) and (**). The property (*) is possessed by solvable groups (and in fact, by groups which have a solvable invariant system) and the property (**) is possessed by nilpotent groups (and in fact, by groups which have a central system).
Operators with Powers close to a Fixed Operator
Authors: Embry Mary R.
Published: April 2009

It is intuitively obvious that if z is a complex number such that ∣1–zv∣ ≤ b ≺ 1 for all positive integers p and some real number b, then z = 1. The purpose of this note is to exhibit a proof of the following generalisation of this observation: THEOREM. Let A be continuous linear operator on a reflexive Banachspace B. If there exists a continuous linear operator T on B, a real number b, and a positive integer p' such that, p an integer and , then A = I. Moreover, in this case ∥I—T∥.
Note on Finite Topological Spaces
Authors: Knopfmacher J.
Published: April 2009

In a recent paper [4], H. Sharp, Jr., has discussed the problem of finding formulae for the following naturally defined integers: the numbers t(n), tc(n), t0(n), tc0(n), and ts(n) of all homeomorphism classes of finite topological spaces with n elements, which are respectively (i) arbitrary, (ii) connected, (iii) T0, (iv) connected and T0, (v) symmetric. Here, a finite topological space X is called symmetric provided the following relation ≦ is symmetric: x ≦ y if and only if x ∈ Uv, the intersection of all open sets containing y.
An extremal problem in graph theory
Authors: Erdös P. , Moser L.
Published: April 2009

G(n;l) will denote a graph of n vertices and l edges. Let f0(n, k) be the smallest integer such that there is a G (n;f0(n, k)) in which for every set of k vertices there is a vertex joined to each of these. Thus for example fo = 3 since in a triangle each pair of vertices is joined to a third. It can readily be checked that fo = 5 (the extremal graph consists of a complete 4-gon with one edge removed). In general we will prove: Let n > k, andthen f0(n, k) = f(n, k).
On the Mathieu groups M22 and M11
Authors: Parrott David
Published: April 2009

In the list of known finite non-abelian simple groups there are infinitely many pairs of non-isomorphic simple groups which have the same order. The smallest known example of two such groups are the simple groups A8 and PSL(3, 4), of order 20,160.
Some restricted partition functions: Congruences modulo 3
Authors: Lahiri D. B.
Published: April 2009

In a previous communication [5] the author has dealt with the congruence properties of some restricted partition functions. The general category of such functions may be denoted.
Diassociative groupoids are not finitely based
Authors: Clark David M.
Published: April 2009

In [2] Evans and Neumann raised the question of whether diassociativity in groupoids or loops is equivalent to a finite set of identities and in [3], Neumann still lists the problem as unsolved. It is the purpose of this paper to show that the answer to the question for groupoids is negative.
One-step methods for the numerical solution of linear differential equations based upon Lobatto quadrature formulae
Authors: Sharma K. D.
Published: April 2009

The necessity of accurate numerical approximations to the solutions of differential equations governing physical systems has always been an important problem with scientists and engineers. Hammer and Hollingsworth [11] have used Gaussian quadrature for solving the linear second order differential equations. This method has been further developed by Morrison and Stoller [3], Korganoff [1], Kuntzman [9], Henrici [12] and Day [7, 8]. Quadrature methods based upon Lobatto quadrature formulae have recently been considered by Day [6, 8] and Jain and Sharma [10] and seem to give better results.
On the Gauss-Green theorem
Authors: Craven B. D.
Published: April 2009

In a previous paper [1], Green's theorem for line integrals in the plane was proved, for Riemann integration, assuming the integrability of Qx−Py, where P(x, y) and Q(x, y) are the functions involved, but not the integrability of the individual partial derivatives Qx and Py. In the present paper, this result is extended to a proof of the Gauss-Green theorem for p-space (p ≥ 2), for Lebesgue integration, under analogous hypotheses. The theorem is proved in the form where Ω is a bounded open set in Rp (p-space), with boundary Ω; g(x) =(g(x1)…, g(xp)) is a p-vector valued function of x = (x1,…,xp), continuous in the closure of Ω; μv,(x) is p-dimensional Lebesgue measure; v(x) = (v1(x),…, vp(x)) and Φ(x) are suitably defined unit exterior normal and surface area on the ‘surface’ ∂Ω and g(x) · v(x) denotes inner product of p-vectors.
A construction for a self-polar double-N associated with a pair of normal rational curves
Authors: Kirkpatrick P. B.
Published: April 2009

In [2] the author introduced a self-polar double-N(“CD”): this double-N is associated with a pair of very specially related (“-related”) normal rational curves, in that the spaces Hi, of one row of the double-N are chordal to one of the curves while the spaces Ki of the other row are chordal to the other curve. The double-N might be said to be “associated with” the triple consisting of these two curves and the polarizing quadric.
On the product of two linear forms, one homogeneous and one inhomogeneous
Authors: Blanksby P. E.
Published: April 2009

This paper is devoted to a complete investigation into a problem initiated by Davenport [4], and further studied by Kanagasabapathy [6], [7], from whom I borrow the title. The question is a hybrid of the two classical results of Hurwitz and Minkowski on indefinite binary quadratic forms.
A characterisation of PSL2(Zþλ) and PGL2(Zþλ)
Authors: Wall G. E.
Published: April 2009

Let Fq denote the finite field with q elements, Zm the residue class ring Z/mZ. It is known that the projective linear groups G = PSL2(Fq) and PGL2(Fq) (q a prime-power ≥ 4) are characterised among finite insoluble groups by the property that, if two cyclic subgroups of G of even order intersect non-trivially, they generate a cyclic subgroup (cf. Brauer, Suzuki, Wall [2], Gorenstein, Walter [3]). In this paper, we give a similar characterisation of the groups G = PSL2 (Zþt+1) and PGL2 (Zþt+1) (p a prime ≥ 5, t ≥ 1).
The Archimedean property in an ordered semigroup
Authors: Saitô Tôru
Published: April 2009

By an ordered semigroup we mean a semigroup with a simple order which is compatible with the semigroup operation. Several authors, for example Alimov [1], Clifford [2], Conrad [4] and Hion [7], studied the archimedean property in some special kinds of ordered semigroups. For a general ordered semigroup, Fuchs [6] defined the archimedean equivalence as follows: a ~ b if and only if one of the four conditionsholds for some positive integer n.
A note on free products with a normal amalgamation
Authors: Bryce R. A.
Published: April 2009

It is a consequence of the Kurosh subgroup theorem for free products that if a group has two decompositions where each Ai and each Bj is indecomposable, then I and J can be placed in one-to-one correspondence so that corresponding groups if not conjugate are infinite cycles. We prove here a corresponding result for free products with a normal amalgamation.
The second duals of certain spaces of analytic functions
Authors: Rubel L. A. , Shields A. L.
Published: April 2009

Let ϕ be a continuous, decreasing, real-valued funtion on 0 ≦ r ≦ 1 with ϕ(1) = 0 and ϕ(r) > 0 for r < 1. Let E0 be the Banach space of analytic function f on the open unit disc D, such that f(z)φ(|z|) → 0 as |z| → 1, with norm , where we write ϕ(z) = ϕ(z) for z ∈ D. Let E be the Banach space of analytic functions f on D for which fφ is bounded in D, with the same norm as E0. It is easy to see that E is complete in this norm, and that E0 is a closed subspace of E.
Maximal ideal spaces of Banach algebras of derivable elements
Authors: Loy R. J.
Published: April 2009

Let A be a commutative Banach algebra, D a closed derivation defined on a subalgebra Δ of A, and with range in A. The elements of Δ may be called derivable in the obvious sense. For each integer k ≦.l, denote by Δk the domain of Dk (so that Dgr;1 = Δ); it is a simple consequence of Leibniz's formula that each Δk is an algebra. The classical example of this situation is A = C(O, 1) under the supremum norm with D ordinary differentiation, and here Δk = Ck(0, 1) is a Banach algebra under the norm ∥.∥k: Furthermore, the maximal ideals of Ak are precisely those subsets of Δk of the form M ∩ Δk where M is a maximal ideal of A, and = M, the bar denoting closure in A. In the present note we show how this extends to the general case.
An application of Nevanlinna-pólya theorem to a cosine functional equation
Authors: Haruki Hiroshi
Published: April 2009

We consider the cosine functional equation (see [1, 2, 3]) , where f(z) is an entire function of a complex variable z and x, y are complex variables.
Examples of semirings of endomorphisms of semigroups
Authors: Grillet Mireille P.
Published: April 2009

Semirings of endomorphisms of semigroups form an important class of semirings. All examples which can be found in the literature concern semigroups with a subcommutative operation. We show that there exists a non-subcommutative semigroup whose endomorphisms form a semiring (this answers a question raised by Professor A. H. Clifford). We also give an example of a semigroup whose set of endomorphisms is not embeddable into a semiring; however it is the disjoint union of two semirings, but one of these semirings is not embeddable into a semiring with identity.
Direct-sum decomposition of atomic and orthogonally complete rings
Authors: Abian Alexander
Published: April 2009

In this paper we give a necessary and sufficient condition for decomposition (as a direct sum of fields) of a ring R in which for every x ∈ R there exists a (and hence the smallest) natural number n(x) > 1 such that . We would like to emphasize that in what follows R stands for a ring every element x of which satisfies (1).
On a problem of ore on maximal trees
Authors: Rao S. B.
Published: April 2009

We consider only graphs without loops or multiple edges. Pertinent definitions are given below. For notation and other definitions we generally follow Ore [1].

A connected graph G = (X, E) is said to have the property P if for every maximal tree T of G there exists a vertex aT of G such that distance between aT and x is same in T as in G for every x in X. The following problem has been posed by Ore (see [1] page 103, problem 4): Determine the graphs with property P. This paper presents a solution to the above problem in the finite case.
A ote on approximation of distributions by quasi-analytic functions
Authors: Harasymiv S. R.
Published: April 2009

Throughout this note Rn denotes the n-dimensional Euclidean space. Addition and multiplication in Rn are defined component-wise. If k ≦ n is a positive integer and x ∈ Rn, we write xk for the k-th component of x. The set {x ∈ Rn: xk ≠ 0 for each k ≦ n} is designated by R#.