bluuebunny/crossref_metadata_2025 huggingface dataset:
Derivation of a general lorentz transformation without rotation
Authors: Klotz A. H.
Published: April 2009

An elementary, purely algebraic derivation of the most general Lorentz transformations without spacial rotation and of the Thomas precession is given.
A result for semi-regular continued fractions
Authors: Blanksby P. E.
Published: April 2009

If Φ is a real number with |Φ| ≧ 1, then a semiregular continuet fraction development of Φ is denoted by where the ai are integers such that |ai| ≧ 2. The expansions arise geo-. metrically by considering the sequence of divided cells of two-dimensional grids (see [1]), and are described by the following algorithm: for all n ≧ 0, taking Φ = Φ.0 Hence where in this case the square brackets are used to signify the integer-part function. It follows that each irrational Φ has uncountably many such expansions, none of which has a constantly equal to 2 (or -2) for large n.
Semigroups with few endomorphisms
Authors: Dlab Vlastimil , Neumann B. H.
Published: April 2009

Large finite groups have large automorphism groups [4]; infinite groups may, like the infinite cyclic group, have finite automorphism groups, but their endomorphism semigroups are infinite (see Baer [1, p. 530] or [2, p. 68]). We show in this paper that the corresponding propositions for semigroups are false.
A Stability theorem for the nonlinear differential equation x″+p(t)g(x)h(x′) = 0
Authors: Kartsatos A. G.
Published: April 2009

K. W. Chang generalizing a result of Lazer [3], proved in [4] the following THEOREM 1. Suppose that f:I → R+ = (0, + ∞), I = ([t0, + ∞), t0 0, is a non-decreasing function whose derivatives of orders ≧ 3 exist are continuous on ([t0, + ∞). Moreover, limt→+∞f(t) = +∞ and for some α, 1≧ α ≧ 2, and F =f-1/α then every solution x(t) of the equation tends to zero as t - + ∞.
Isomorphisms of triform semigroups
Authors: Magill Kenneth D.
Published: April 2009

For any point x, we use the symbol x to denote {(x, x)}. By a triform, we mean a triple (X, Fx, S[X]) where X is a nonempty set, Fx is a family of subsets of X, [X] is a family of subsets of X x X and the following conditions are satisfied: .
Non-existence of a certain projective plane
Authors: Denniston R. H. F.
Published: April 2009

The question whether any projective plane of order ten exists or not, is an unsolved problem that has attracted some interest (see, for instance, [2]). A method, by which a plane might have been discovered, was suggested to me by a theorem in [1]: ‘If order of a plane is greater than 10, a six-arc is not complete’. Elementary arguments do not, it appears, exclude the possibility of a complete six-arc in a plane of order ten: but they do show that such a figure would be of an extreme type, and that the whole plane would fit round it in a particular way. The limitation, in fact, is so severe that it becomes feasible to consider, for a good many of the incidences in the plane, all the alternative arrangements that seem possible. With the help of the Elliott 4130 computer of the University of Leicester, I have carried out an exhaustive search, and discovered that it is impossible to build up a projective plane by this method. So I can assert:
Note on Linearly Compact Abelian Groups
Authors: Fuchs L.
Published: April 2009

By a group A is meant throughout an additively written abelian group. A is said to have linear topology if there is a system of subgroups Ui (i∈I) of A such that, for a ∈ A, the cosets a+Ui(i∈I) form a fundamental system of neighborhoods of a. The group operations are continuous in any linear topology; the topologies are always assumed to be Hausdorff, that is, ∩iUi = 0. A linearly compact group is a group A with a linear topology such that if aj+Aj (j∈I) is a system of cosets modulo closed subgroups Aj with the finite intersection property (i.e. any finite number of aj+Aj have a non-void intersection), then the intersection ∩j(aj+Aj) of all of them is not empty.
A Note on Semigroups of Mappings on Banach Spaces
Authors: Yamamuro Sadayuki
Published: April 2009

In a series of papers K. D. Magill, Jr. (see [1] and its references) has proved that, in various semigroups of mappings on topological spaces, every automorphism is inner, where an automorphism φ of a semigroup A is a bijection of A such that for all ƒ and g in A, and it is said to be inner if there exists a bijection h ∈ A such that h−1 (the inverse of h) belongs to A and for every ƒ ∈ A.
Electrochemical dissolution of an anode
Authors: Lawden D. F.
Published: April 2009

In an electro-chemical investigation, an anode in the form of an aluminium cylinder was arranged so that one circular plane end was exposed to a dilute acid electrolyte. A measured electric current was then passed and aluminium from the anode passed into solution. Employing Faraday' laws, the mass of aluminium which was expected to pass into solution as a result of the passage of the known electric charge, was calculated. It was found that, when the current density over the exposed surface of the anode was high (e.g. 100 amp/sq.cm.), the experimental and calculated results were almost in agreement. However, for small current densities (e.g. 0.1 amp/sq.cm.), it was found that the actual loss of aluminium from the anode was about 14 % greater than that predicted by Faraday's laws.
A note on the idempotent measures on countable semigroups
Authors: Sun Tze-Chien , Tserpes N. A.
Published: April 2009

In [6] we announced the following
Conjecture: Let S be a locally compact semigroup and let μ be an idempotent regular probability measure on S with support F. Then

(a) F is a closed completely simple subsemigroup.

(b) F is isomorphic both algebraically and topologically to a paragroup ([2], p.46) X × G × Y where X and Y are locally compact left-zero and right-zero semi-groups respectively and G is a compact group. In X × G × Y the topology is the product topology and the multiplication of any two elements is defined by , x where [y, x′] is continuous mapping from Y × X → G.

(c) The induced μ on X × G × Y can be decomposed as a product measure μX × μG× μY where μX and μY are two regular probability measures on X and Y respectively and μG is the normed Haar measure on G.
The diameters of the graphs of semirings
Authors: Ratti J. S. , Lin Y.-F.
Published: April 2009

Let be a family of sets, {Fa|α∈Λ}. By the graph G of the system , we mean the graph whose set of vertices is and in which the vertices Fβ∈, are adjacent (that is, are joined by an edge) if and only if Fα ≠ Fβ and Fα ∩ Fβ □, where □denotes the empty set.
The Correlation Coefficients of the Queue Lengths of Some Stationary Single Server Queues
Authors: Pakes A. G.
Published: April 2009

Until recently there has been little systematic work on the second-order properties of queueing processes. The aim of this paper is to study systematically the second-order properties of the queue length processes embedded at departure epochs in the M/G/1 and bulk service M/G/1 queues, and at arrival epochs in the GI/M/1 queue. In the latter case our results extend those of Daley [7], while in the ordinary M/G/1 queue our work parallels Daley's [6] discussion of waiting times in the same system. In the final section we briefly discuss two discrete time queueing systems.
The Indentation of an Anisotropic Half Space by a Rigid Punch
Authors: Clements D. L.
Published: April 2009

Eshelby et al. [1] and Stroh [2] have developed the theory of anisotropic elasticity for a three dimensional state of stress in which the stress is independent of one of the Cartesian coordinates. Various problems involving dislocations in an infinite anisotropic medium are solved in the first paper, while Stroh considers dislocation problems as well as determining the stresses round a crack subjected to an arbitrary non-uniform applied stress. In this note, which follows their treatment, we consider the problem of determining the stresses produced by the indentation of the plane surface of an anisotropic half space by a rigid punch. Problems of this type have been solved by Green and Zerna [3], Lekhnitskii [4], Brilla [5], Gallin [6] and Milne-Thomson [7] but if we take Cartesian coordinates x1, x2, x3 and let the stress be independent of x3, then these authors all assume the x1x2 plane to be one of elastic symmetry. The solution presented in this paper does not require this assumption so that it has a more general application than has been the case with previous solutions to problems of this type. The first part of the analysis given here is for general anisotropy, but in order to obtain a solution to the punch problem by the method of this paper, it is necessary to consider only a particular class of anisotropic materials. The indentation of such materials by a circular block is discussed in section 4 and the results are used in section 5 to examine the case when the circular block is on a transversely isotropic half space.
On a Class of Markov Chains
Authors: Pakes A. G.
Published: April 2009

Until recently, very little work has been done on the second order properties of Markov chains. Craven [1] has studied the joint distributions of Markov chains having a Borel subset of n-dimensional Euclidean space as state space. His idea was to consider the process as a time series.
On Mappings Which Commute with Convolution
Authors: Harasymiv S. R.
Published: April 2009

The symbolDwill be written for the space of indefinitely differentiable functions on the n-dimensional Euclidean spaceRnwhich have compact support andDapos; will denote the space of Schwartz distribution onRn, the topological dual ofD. Except where contrary is explicitly stated, it will be assumed thatD′ is equipped with the strong topology β (D′,D) induced byD.
On the class of functions convex in the negative direction of the imaginary axis
Authors: Lecko Adam
Published: April 2009

In this paper we present a new proof of the equivalence of the analytic and the geometric characterization of the class of functions convex in the negative or positive direction of the imaginary axis.
Additive results for the generalized Drazin inverse
Authors: Djordjević Dragan S. , Wei Yimin
Published: April 2009

Additive perturbation results for the generalized Drazin inverse of Banach space operators are presented. Precisely, ifAddenotes the generalized Drazin inverse of a bounded linear operatorAon an arbitrary complex Banach space, then in some special cases(A + B)dis computed in terms ofAdandBd. Thus, recent results of Hartwig, Wang and Wei (Linear Algebra Appl.322 (2001), 207–217) are extended to infinite dimensional settings with simplified proofs.
On c-normality of finite groups
Authors: Asaad M. , Mohamed M. Ezzat
Published: April 2009

A subgroup H of a finite G is said to be c-normal in G if there exists a normal subgroup N of G such that G = HN with H ∩ N ≤ HG = CoreG(H). We are interested in studying the influence of the c–normality of certain subgroups of prime power order on the structure of finite groups.
On supersoluble groups of Wielandt length two
Authors: Ali Asif
Published: April 2009

This paper gives a characterisation of finite supersoluble groups of Wielandt length two of order coprime to six.
Ado-Iwasawa extras
Authors: Barnes Donald W.
Published: April 2009

Let L be a finite-dimensional Lie algebra over the field F. The Ado-Iwasawa Theorem asserts the existence of a finite-dimensional L-module which gives a faithful representation ρ of L. Let S be a subnormal subalgebra of L, let be a saturated formation of soluble Lie algebras and suppose that S ∈ . I show that there exists a module V with the extra property that it is -hypercentral as S-module. Further, there exists a module V which has this extra property simultaneously for every such S and , along with the Hochschild extra that ρ(x) is nilpotent for every x ∈ L with ad(x) nilpotent. In particular, if L is supersoluble, then it has a faithful representation by upper triangular matrices.
On Noetherian rings with essential socle
Authors: Chen Jianlong , Ding Nanqing , Yousif Mohamed F.
Published: April 2009

It is shown that if R is a right Noetherian ring whose right socle is essential as a right ideal and is contained in the left socle, then R is right Artinian. This result may be viewed as a one-sided version of a result of Ginn and Moss on two-sided Noetherian rings with essential socle. This also extends the work of Nicholson and Yousif where the same result is obtained under a stronger hypothesis. We use our work to obtain partial positive answers to some open questions on right CF, right FGF and right Johns rings.
Harmonic maps and cosymplectic manifolds
Authors: Boeckx E. , Gherghe C.
Published: April 2009

We study the harmonicity of maps to or from cosymplectic manifolds by relating them to maps to or from Kähler spaces.
Fitting classes and lattice formations I
Authors: Arroyo-Jordá M. , Pérez-Ramos M. D.
Published: April 2009

A lattice formation is a class of groups whose elements are the direct product of Hall subgroups corresponding to pairwise disjoint sets of primes. In this paper Fitting classes with stronger closure properties involving F-subnormal subgroups, for a lattice formation F of full characteristic, are studied. For a subgroup-closed saturated formation G, a characterisation of the G-projectors of finite soluble groups is also obtained. It is inspired by the characterisation of the Carter subgroups as the N-projectors, N being the class of nilpotent groups.
Average co-ordinate entropy
Authors: Mortiss Genevieve
Published: April 2009

A notion of entropy for the non-singular action of finite co-ordinate changes on is introduced. This quantity-average co-ordinate or AC entropy-is calculated for product measures and G-measures. It is shown that the type III classes can be subdivided using AC entropy. An equivalence relation is established for which AC entropy is an invariant.
An application of Moser iteration to complete minimal submanifolds in a sphere
Authors: Cheung Leung-Fu , Leung Pui-Fai
Published: April 2009

We apply the Moser iteration method to obtain a pointwise bound on the norm of the second fundamental form from a bound on its Ln norm for a complete minimal submanifold in a sphere. As an application we show that a complete minimal submanifold in a sphere with finite total curvature and Ricci curvature bounded away from -∞ must be compact. This complements similar results of Osserman and Oliveira in the case the ambient space is the Euclidean and the hyperbolic space respectively.
Boundedness of vector-valued martingale transforms on extreme points and applciations
Authors: Martínez Teresa , Torrea José L.
Published: April 2009

Let Β1, Β2be a pair of Banach spaces andTbe a vector valued martingale transform (with respect to general filtration) which maps Β1-valued martingales into Β2-valued martingales. Then, the following statements are equivalent:Tis bounded fromintofor somep(or equivalently for everyp) in the range 1 <p< ∞;Tis bounded fromintoBMOB2;Tis bounded fromBMOB1intoBMOB2;Tis bounded frominto. Applications toUMDand martingale cotype properties are given. We also prove that the Hardy spacedefined in the case of a general filtration has nice dense sets and nice atomic decompositions if and only if Β has the Radon-Nikodým property.
Generalized Weyl's theorem and hyponormal operators
Authors: Berkani M. , Arroud A.
Published: April 2009

Let T be a bounded linear operator acting on a Hilbert space H. The B-Weyl spectrum of T is the set σBW(T) of all λ ∈ Сsuch that T − λI is not a B-Fredholm operator of index 0. Let E(T) be the set of all isolated eigenvalues of T. The aim of this paper is to show that if T is a hyponormal operator, then T satisfies generalized Weyl's theorem σBW(T) = σ(T)/E(T), and the B-Weyl spectrum σBW(T) of T satisfies the spectral mapping theorem. We also consider commuting finite rank perturbations of operators satisfying generalized Weyl's theorem.
Rings in which certain right ideals are direct summands of annihilators
Authors: Zhou Yiqiang
Published: April 2009

This paper is a contiunation of the study of the rings for which every principal right ideal (respectively, every right ideal) is a direct summand of a right annihilator initiated by Stanley S. Page and the author in [20, 21].
On the notion of residual finiteness for G-spaces
Authors: Mukherjee Goutam , Naolekar Aniruddha C.
Published: April 2009

We define equivariant completion of a G-complex and define residually finite G-spaces. We show that the group of G-homotopy classes of G-homotopy self equivalences of a finite, residually finite G-complex, in residually finite. This generalizes some results of Roitberg.
Error estimates for asymptotic representations of integrals
Authors: Mahony J. J.
Published: April 2009

Abstract. For large real positive values of the parameter k asymptotic representations of integrals of the form , where f and g are analytic functions, can be obtained by using methods such as steepest desents. Here methods are considered for obtaining estimates, for fixed values of k, of the minimum errors achievable when such asymptotic representations are appropriately curtailed. A priori criteria are derived for the optimum point at which to curtail such asymptotic representations are appropriately curtailed. A priori criteria are derived for the optimum point at which to curtail such asymptotic representations. Both the curtailment points and the minimum errors are related to the distance between certain marked points on the path of integration and the singular points of f(u) and the zeros of g(u). The analysis permits the determination of errors whose presence is not indicated by the numerical behaviour of the asymptotic representations. It is also capable of extension to complex parameters k and to the derivation of asymptotic representations for the most significant errors. It can therefore be used to extend the domain of k for which asymptotic representations are available.
A note on the matrix renewal function
Authors: Kshirsagar A. M. , Gupta Y. P.
Published: April 2009

The Laplace-Stieltjes Transform m(s) of the matrix renewal function M(t) of a Markov Renewal process is expanded in powers of the argument s, in this paper, by using a generalized inverse of the matrix I–P0, where P0 is the transition probability matrix of the imbedded Markov chain. This helps in obtaining the values of moments of any order of the number of renewals and also of the moments of the first passage times, for large values of t, the time. All the results of renewal theory are hidden under the Laplacian curtain and this expansion helps to lift this curtain at least for large values of t and is thus useful in predicting the number of renewals.
On a sublattice of the lattice of congruences on a simple regular ω-semigroup
Authors: Baird G. R.
Published: April 2009

The set E of idemponents of a semigroup S can be partially ordered by defining e ≦f and only if ef = fe = e (e,f ∈ E). If E = {ei: i = i = 0,1…} and under this ordering e0 > e1 > e2… then we call S an ω-semigroup. Munn [10] has given a complete classification of simple regular ω-semigroups in terms of groups and group homomorphisms. Let ∧0(S) denote the set of congruences on a simple regular w-semigroup S consisting of those congruences which either are idempotent-separating or are group congruences on S. It is evident that ∧0(S) is a sublattice of the lattice of all congruences on S.
Regular rings and modules
Authors: Fieldhouse David J.
Published: April 2009

P. M. Cohn [7] calls a submodule P of the left A-module M pure iff 0 → E ⊗ P → E ⊗ M is exact for all right modules E. This definition of purity, which Cohn [7] has shown to be equivalent to the usual one when A is a PID (= Principal Ideal Domain), was studied in [9] and [10]. Here we show that the ring A is (von Neumann) regular if every left (or right) ideal is pure. This leads us to define regular modules as modules all of whose submodules are pure. The ring A is then regular if all its left (or right) A-modules are regular. A regular socle, analogous to the usual socle is defined. For commutative A, some localization theorems are proved, and used to settle a conjecture of Bass [1] concerning commutative perfect rings.
The higher order commutators of the fractional integrals on Hardy spaces
Authors: Long Shunchao , Wang Jian
Published: April 2009

In this paper we investigate the boundedness on Hardy spaces for the higher order commutator Tb, m generated by the BMO function b and fractional integral type operator Tτ, and establish the boundness theorems for Tτb, m from Hp1.q1.sb, m to Lp2 and to Hp2 (0 < p1 ≤ 1), and from H Ka. p1.sq1, b, m to Ka.p2q2 and to H Ka. p2q2, respectively, for certain ranges of α, p1, q1, p2, q2 and s.
Bounds and quotient actions of innately transitive groups
Authors: Bamberg John
Published: April 2009

Finite innately transitive permutation groups include all finite quasiprimitive and primitive permutation groups. In this paper, results in the theory of quasiprimitive and primitive groups are generalised to innately transitive groups, and in particular, we extend results of Praeger and Shalev. Thus we show that innately transitive groups possess parameter bounds which are similar to those for primitive groups. We also classify the innately transitive types of quotient actions of innately transitive groups.
On lattices of varieties of metabelian groups
Authors: Brooks M. S.
Published: April 2009

This paper presents an example to show that the lattice of subvarieties of 3, 9 Λ11 is non-distributive. The example is used further to show that a certain ‘canonic” description for non-nilpotent subvarieties of pp2, p prime, is generally not unique.
Remarks about the digits of integers
Authors: Alexander Ralph
Published: April 2009

Let n1 < n2 < … be the sequence of positive integers whose base b representations involve the digit t ≦ b —1 at most d—1 times. B. D. Craven [2] shows that Σi1/ni converges by giving an upper bound for this sum as a function of b and d.
On the cohomology of local groups
Authors: Świerczkowski S.
Published: April 2009

Most known homology theories (e.g. the homology of modules, rings, groups, sheaves, …) have been found to be special cases of a general theory proposed by M. Barr and J. Beck [1], [2]. The aim of this paper is to show that the cohomology of a local group, as defined by W. T. van Est [4], also fits the scheme of Barr and Beck. At the same time it will be shown that local group cohomology is a relative derived functor in the sense of S. Eilenberg and J. C. Moore [3].
Linear mappings between topological vector spaces
Authors: Craven B. D.
Published: April 2009

If A and B are locally convex topological vector spaces, and B has certain additional structure, then the space L(A, B) of all continuous linear mappings of A into B is characterized, within isomorphism, as the inductive limit of a family of spaces, whose elements are functions, or measures. The isomorphism is topological if L(A, B) is given a particular topology, defined in terms of the seminorms which define the topologies of A and B. The additional structure on B enables L(A, B) to be constructed, using the duals of the normed spaces obtained by giving A the topology of each of its seminorms separately.
Asymptotic Gauss Quadrature Errors as Fourier Coefficients of the Integrand
Authors: Chawla M. M.
Published: April 2009

The purpose of this paper is to derive asymptotic relations giving the error of a Gauss type quadrature, applied to analytic functions, in terms of certain coefficients in the orthogonal expansion of the integrand. The Fourier expansions of the integrand we consider here are those in terms of the Legendre and the Chebyshev polynomials. In Section 3 we obtain the error of the Gauss-Legendre quadrature expressed in terms of the Legendre-Fourier coefficients of the integrand. In Section 4 the errors of Gauss-Legendre, Lobatto and Radau quadrature formulas are obtained, for large n, expressed in terms of the Chebyshev-Fourier coefficients of the integrand. In deriving these estimates we have used complex variable methods restricting ourselves to the class of analytic integrands; this allows us to obtain simple contour integral representations for the errors of these quadratures for large values of n. However, the form of the estimates obtained indicate that these are applicable to a much wider class of functions.
Some remarks on flocks
Authors: Bader Laura , O'Keefe Christine M. , Penttila Tim
Published: April 2009

New proofs are given of the fundamental results of Bader, Lunardon and Thas relating flocks of the quadratic cone in PG(3, q), q odd, and BLT-sets of Q(4, q). We also show that there is a unique BLT-set of H(3, 9). The model of Penttila for Q(4, q), q odd, is extended to Q(2m, q) to construct partial flocks of size qm/2+m/2 – 1 of the cone kin PG(2m – 1, q) with vertex a point and base Q(2m – 2, q), where q is congruent to 1 or 3 modulo 8 and m is even. These partial flocks are larger than the largest previously known for m > 2. Also, the example of O'Keefe and Thas of a partial flock of k in PG(5, 3) of size 6 is generalised to a partial flock of the cone k of PG(2pn – 1, p) of size 2pn, for any prime p congruent to 1 or 3 modulo 8, with the corresponding partial BLT-set of Q(2pn, p) admitting the symmetric group of degree 2pn + 1.
Normal lattices
Authors: Cornish William H.
Published: April 2009

If L is a distributive lattice with 0 then it is shown that each prime ideal contains a unique minimal prime ideal if and only if, for any x and y in L, x ∧ y = 0 implies (x]*) ∨ (y]* L). A distributive lattice with 0 is called normal if it satisfies the conditions of this result. This terminology is appropriate for the following reasons. Firstly the lattice of closed subsets of a T1-space is normal if and only if the space is normal. Secondly lattices satisfying the above annihilator condition are sometimes called normal by those mathematicians interested in (Wallman-) compactications, for example see [2].
The pn-integral
Authors: Bullen P. S.
Published: April 2009

In [5] James defined an nth order Perron integral, the Pn- ntegral, and developed its properties. His proofs are often indirect, using properties of the CkP-integrals of Burkill, [3]. In this paper a simpler definition of the Pn-integral is given — the original and not completely equivalent definition, was probably chosen as James considered this integral as a special case of one defined in terms of certain symmetric derivatives, [5], when end points of the interval of definition had naturally to be avoided. We then give direct proofs of the basic results, give a characterization of Pn-primitives, and connect the integral with certain work of Denjoy, [4].
An uncertainty principle like Hardy's theorem for nilpotent Lie groups
Authors: Kumar Ajay , Bhatta Chet Raj
Published: April 2009

We extend an uncertainty principle due to Cowling and Price to threadlike nilpotent Lie groups. This uncertainty principle is a generalization of a classical result due to Hardy. We are thus extending earlier work on Rnand Heisenberg groups.
Ideals of compact operators
Authors: Lima Åsvald , Oja Eve
Published: April 2009

We give an example of a Banach spaceXsuch thatK(X, X) is not an ideal inK(X, X**). We prove that ifz* is a weak* denting point in the unit ball of Z* and ifXis a closed subspace of a Banach spaceY, then the set of norm-preserving extensionsH B(x* ⊗z*) ⊆(Z*,Y)* of a functionalx* ⊗Z* ∈ (Z⊗X)* is equal to the setH B(x*) ⊗ {z*}. Using this result, we show that ifXis anM-ideal inYandZis a reflexive Banach space, thenK(Z, X) is anM-ideal inK(Z, Y) wheneverK(Z, X) is an ideal inK(Z, Y). We also show thatK(Z, X) is an ideal (respectively, anM-ideal) inK(Z, Y) for all Banach spaces Z whenever X is an ideal (respectively, anM-ideal) inYandX* has the compact approximation property with conjugate operators.
Involutions on finite-dimensional algebras over real closed fields
Authors: Munn W. D.
Published: April 2009

It is shown that the following conditions on a finite-dimensional algebra A over a real closed field or an algebraically closed field of characteristic zero are equivalent: (i) A admits a special involution, in the sense of Easdown and Munn, (ii) A admits a proper involution, (iii) A is semisimple.
On spaces which are essentially T1
Authors: Hall Dick Wick , Murphy Sheila K. , Rozycki Eugene P.
Published: April 2009

Let S be a pseudo-metric space with pseudo-metric d. Then for each nonempty A ⊆ S, x ∈ cl (A) if and only if d(x, A) = 0, and d(x, y) = d(y, x) for all x, y ∈S. Thus, if d(x, y) = 0, then x∈cl({Y}) by the first requirement and Y∈cl({x}) by the second requirement. It is natural then to expect that if a topological space S is to be pseudo-metrizable, it should at least satisfy the requirement:
Operator algebras related to Thompson's group F
Authors: Jolissaint Paul
Published: April 2009

Let F′ be the commutator subgroup of F and let Γ0 be the cyclic group generated by the first generator of F. We continue the study of the central sequences of the factor L(F′), and we prove that the abelian von Neumann algebra L(Γ0) is a strongly singular MASA in L(F). We also prove that the natural action of F on [0, 1] is ergodic and that its ratio set is {0} ∪ {2k; k ∞ Z}.
Spreadable arrays and martingale structures
Authors: Ivanoff B. Gail , Weber N. C.
Published: April 2009

Kallenberg has introduced the concept of conditional spreadability for random sequences and has developed characterizations of this property in terms of one dimensional martingales and optional times, and as well has proven a predictable sampling theorem. This paper investigates the relationship between planar martingale structures and the natural analogues of conditional spreadability when extended to arrays of random elements. Analogues of the predictable sampling theorem are also established for spreadable arrays.
On typical means of fourier series of continuous functions
Authors: Kwee B.
Published: April 2009

Let f(x) be continuous in (-π, π) and periodic with period 2π and let , The aim of this paper is to prove the following theorem.
Buckling of elastic plates by the method of constant deflection lines
Authors: Mazumdar J.
Published: April 2009

In a previous paper of this series – hereinafter to be referred to as [1] – the author introduced a new method for a large class of boundary value problems connected with the flexure analysis of elastic plates of arbitrary shape where the concept of ‘Lines of Equal Deflection’, i.e. lines which are obtained by intersecting the bent plate by planes parallel to the original plane of the plate, was introduced. The present paper extends this analysis to the buckling analysis of thin elastic plates with various forms of boundary conditions. It is shown that the proposed method appears to be a powerful tool for the investigation of those problems of elastic stability which could not be solved by conventional methods because of the difficulty of the mathematical treatment.
The deficiency and the multiplicator of finite nilpotent groups
Authors: Wamsley J. W.
Published: April 2009

I. Šafarevič [2] proves that for a pro-finite p-group G, the deficiency of G (in the topological sense) equals the negative of d(m(G)). This means that if G is a finite p-group, where d(m(G)) = n, then there exists a group K with deficiency −n, such that G is the maximal p factor of K.
Improjective operators and ideals in a category of Banach spaces
Authors: Tarafdar E.
Published: April 2009

Kato [3] has introduced a class of operators called strictly singular operators. These operators have many properties in common with compact operators. In fact the concept of a strictly singular operator is an extension of the concept of a compact operator. Kato has proved that if X and X′ are Banach Spaces, then the singular operators of X into X′ forms a closed subspace of the space of bounded linear operators of X into X′ and if X = X′, then these operators forms a two-sided ideal in the ring of bounded linear operators on X. He has also shown that the Riers-Schauder theorem holds for the spectrum of a strictly singular operator. Gohberg, Feldman and Markus [23] have treated the same class of operators with an equivalent definition.
The probability generating functional
Authors: Westcott M.
Published: April 2009

This paper is concerned with certain aspects of the theory and application of the probability generating functional (p.g.fl) of a point process on the real line. Interest in point processes has increased rapidly during the last decade and a number of different approaches to the subject have been expounded (see for example [6], [11], [15], [17], [20], [25], [27], [28]). It is hoped that the present development using the p.g.ﬀ will calrify and unite some of these viewpoints and provide a useful tool for solution of particular problems.
Convex sum of univalent functions
Authors: Chichra Pran Nath , Singh Ram
Published: April 2009

Let f(z)=z + … be regular in the unit disc |z| < 1 (hereafter called E). In a recent paper Trimble [7] has proved that if f(z) be convex in E, then F(z) = (1 − λ)z + λf(z) is starlike with respect to the origin in E for (2/3) ≦ λ ≦ 1. The purpose of this note is to show that if certain additional restrictions be imposed on f(z), then F(z) becomes starlike for all λ, 0 ≦ λ ≦ 1. Also we consider some related problems.
Perspective simplexes and tucker quadrics
Authors: Konnully Augustine O.
Published: April 2009

The sides of a triangle are met by the sides of a triangle in perspective with it in nine points of which three lie on the axis of perspectivity of the triangles and the other six, as we have it from the converse of Pascal's theorem, lie on a conic. When the centre of perspectivity is the Lemoine point of the triangle and the axis of perspectivity is the line at infinity this conic is a circle known as a Tucker circle [1]. In this paper, analogously we prove that given a simplex inn-space, the traces on its edges of the prime faces of any simplex in perspective with it, all except those falling on the prime of perspectivity, lie on a quadric which we call a Tucker quadric. And further we consider the special case when this quadric becomes a hypersphere.
One-sided ideals in near-rings of transformations
Authors: Heatherly H. E.
Published: April 2009

Let (G, +) be an arbitrary group and let T0(G) = {f∈ Map(G, G): 0f = 0}; the system composed of T0(G) and the operations of pointwise addition and composition of functions form a (left) near-ring. Berman and Silverman, in their investigation of near-rings of transformations [3], found that for every group G the associated near-ring of transformations T0(G) has no proper ideals. In the present paper left and right ideals of T0(G) are considered.
On the iterative solution of linear operator equations with self-adjoint operators
Authors: Koliha J. J.
Published: April 2009

In this paper we deal with a linear equationAu = fin a Hilbert space using a general iterative method with a constant iterative operator for the approximate solution. The method has been studied in many papers [1, 2, 4, 9, 13, 14] and thoroughly treated by Householder [3] for matrix equations and by Petryshyn [7] for operator equations in considerably general and unified manner.
Maximal transference and summability of multilinear Fourier series
Authors: Grafakos Loukas , Honzík Petr
Published: April 2009

We obtain a maximal transference theorem that relates almost everywhere convergence of multilinear Fourier series to boundedness of maximal multilinear operators. We use this and other recent results on transference and multilinear operators to deduce Lp and almost everywhere summability of certain m–linear Fourier series. We formulate conditions for the convergence of multilinear series and we investigate certain kinds of summation.
Some completely monotonic functions involving the gamma and polygamma functions
Authors: Qi Feng , Guo Bai-Ni , Chen Chao-Ping
Published: April 2009

The function [Γ(x + 1)]1/x(1 + 1/x)x/x is strictly logarithmically completely monotonic in (0, ∞). The function ψ″ (x + 2) + (1 + x2)/x2(1 + x)2 is strictly completely monotonic in (0, ∞).
On p-adic L-functions and elliptic units
Authors: Coates J. , Wiles A.
Published: April 2009

The aim of the paper is to prove an elliptic analogue of a deep theorem of Iwasawa on cyclotomic fields.

Subject classification(Amer. Math. Soc. (MOS) 1970): primary 12 A 35, 12 A 65.
On multiply transitive permutation groups
Authors: Monro G. P. , Taylor D. E.
Published: April 2009

We present a direct combinatorial proof of the characterization of the degree of transivity of a finite permutation group in terms of the Bell numbers.

Subject classification (Amer. Math.Soc. (MOS) 1970): 20 B 20.
A commutator identity for basic p-groups
Authors: Weichsel Paul M.
Published: April 2009

The consequences of the law (Ga(1), hellip, Ga(n)) = 1 in a basic p-group are examined. The principal tools are a combinatorial analysis of the lattice of n-tuples of positive integers and a theorem of the author about higher-commutator subgroups.

Subject classification (Amer. Math. Soc. (MOS) 1970): 20 D 15.
Hamiltonian cycles in certain graphs
Authors: Heinrich Katherine , Wallis W. D.
Published: April 2009

It is observed that arrays which arise in the scheduling of tournaments exist if and only if there are Hamiltonian cycles in certain graphs. The graphs are generalizations of those which arise in the “Footballers of Croam” problem. It is proven that such Hamiltonian cycles exist in infinite classes of the graphs.

Subject classification (Amer. Math. Soc. (MOS) 1970): 05 C 35, 05 B 30.
Chebyshev subspaces of finite codimension in spaces of continuous functions
Authors: Brown A. L.
Published: April 2009

A. L. Garkavi in 1967 characterized those compact metric spaces X with the property that the space C(X) of real-valued continuous functions possesses Chebyshev subspaces of fine codimension ≥ 2. Here compact Hausdorif spaces with the same property are characterized in terms of certain standard subspaces of the space [0, 1] × {0, 1} equipped with a lexicographic order topology. Garkavi's result for metric spaces is exhibited as a corollary. The proof depends upon a simplification of a characterization by Garkavi of the Chebyshev subspaces of finite codimension in C(X).

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 41 A 65, 46 E 15; secondary 54 G 99.
Totally umbilical submanifolds of quaternion-space-forms
Authors: Chen Bang-Yen
Published: April 2009

Totally umbilical submanifolds of dimension greater than four in quaternion-space-forms are completely classified.
Pseudocomplemented algebras with Boolean congruence lattices
Authors: Beazer R.
Published: April 2009

Complemented congruences in the classes of pseudocomplemented semilattices, p-algebras and double p-algebras are described. The descriptions are applied to give intrinsic characterizations of those algebras in the aforementioned classes whose congruence lattice is a Boolean algebra.
On Fan's extensions of Browder's fixed point theorems for multi-valued inward mappings
Authors: Lee Cheng-Ming , Tan Kok-Keong
Published: April 2009

Some fixed point theorems are obtained for weekly inward mappings which extend or generalize those results by K. Fan, B. Halpern or S. Reich. Various formulations of inward and outward concepts are also briefly discussed.
Rigid cohomology of topological groupoids
Authors: MacKenzie K. A.
Published: April 2009

A cohomology theory for locally trivial, locally compact topological groupoids with coefficients in vector bundles is constructed, generalizing constructions of Hochschild and Mostow (1962) for topological groups and Higgins (1971) for discrete groupoids. It is calculated to be naturally isomorphic to the cohomology of the vertex groups, and is thus independent of the twistedness of the groupoid. The second cohomology space is accordingly realized as those “rigid” extensions which essentially arise from extensions of the vertex group; the cohomological machinery now yields the unexpected result that in fact all extensions, satisfying some natural weak conditions, are rigid.
Finite 2-groups of class two with cyclic centre
Authors: Leong Y. K.
Published: April 2009

In conjunction with an earlier work by Leong (1974a), this paper completes the solution of the isomorphism problem for finite nilpotent groups of class two with cyclic centre. A canonical decomposition for 2-groups of such type is obtained and proved.
On semigroups of endomorphisms of biregular algebras
Authors: Yzung Fu-Chien
Published: April 2009

Let A be a finite dimensional algebra over a field F. Let R and S be biregular algebras over F such that 1R ∈ R and 1S ∈ S. We show that if R/P≃A≃ S/M for each primitive ideal P in A and each primitive ideal M in S then End FR≃ End S implies R≃S.
Radicals related to the Brown-McCoy radical in some varieties of algebras
Authors: Gardner B. J.
Published: April 2009

The Brown-McCoy radical is the upper radical defined by the class of simple rings with identities. For associative or alternative rings the Brown-McCoy radical is hereditary, and its semi-simple class consists of all subdirect products of simple rings with identities. In this paper we present some classes of simple non-associative algebras whose upper radicals behave similarly. Classifications are then obtained of ‘most’ semi-simple radical classes of (γ, δ) and right alternative rings.
Special pairs of semi-bilogic and bilogic tetrahedra
Authors: Mandan Sahib Ram
Published: April 2009

Let (A), (B) be a special pair of perspective tetrahedra such that the 4 joins of their corresponding vertices are perpendicular to their plane of perspectivity. It has been already established (Mandan (1977a), p. 573) that they are, in general, skew-orthologic such that the perpendiculars from the vertices of one to the corresponding opposite faces of the other lie in a regulus. Here we give a construction of a special pair of semi-orthologic and orthologic tetrahedra, the said regulus degenerating into 2 pairs of intersecting lines and 4 concurrent lines respectively. Following Thébault ((1952), p. 25; (1955), p. 67), we call them semi-bilogic and bilogic respectively.
Certain generalizations of presetarlike functions
Authors: Al-Amiri H. S.
Published: April 2009

The classes of prestarlike functionsRα, α ≧ – 1, were studied recently by St. Ruscheweyh. The author generalizes and extends these classes. In particular the author obtains the radius ofRa+1for the classRα, α ≧ –1.
Inertial subalgebras of algebras possessing finite automorphism groups
Authors: Ford Nicholas S.
Published: April 2009

Let R be a commutative ring with identity, and let A be a finitely generated R-algebra with Jacobson radical N and center C. An R-inertial subalgebra of A is a R-separable subalgebra B with the property that B+N=A. Suppose A is separable over C and possesses a finite group G of R-automorphisms whose restriction to C is faithful with fixed ring R. If R is an inertial subalgebra of C, necessary and sufficient conditions for the existence of an R-inertial subalgebra of A are found when the order of G is a unit in R. Under these conditions, an R-inertial subalgebra B of A is characterized as being the fixed subring of a group of R-automorphisms of A. Moreover, A ⋍ B ⊗R C. Analogous results are obtained when C has an R-inertial subalgebra S ⊃ R.
On group rings of finite metabelian groups
Authors: Karpilovsky G.
Published: April 2009

It is proved that a finite metabelian groupGis determined by its group ringKGwhere the ringKsatisfies the following conditions.
Radical properties defined locally by polynomial identities I
Authors: Gardner B. J.
Published: April 2009

Bijective correspondences are established between the radical classes R (in a variety W of rings) with the property that a ring A is in R exactly when its finitely generated subrings are all in R, and certain filters of ideals in a free W-ring. It follows that such classes are determined by the polynomial identities satisfied by the finite subsets of their members. Analogous considerations are applied to radical classes R which, for a fixed integer n, have the property that a ring is in R if and only if its subrings generated by at most n elements are in R.
Flat spots on unit spheres
Authors: Van Dulst D.
Published: April 2009

A flat spot in a Banach space X is an element x ∈ Sx = {x ∈ X: ‖x‖ = 1} with the property that the infimum m(x) of the lengths of all curves in Sx joining x to −x is 2. Flat spots occur in every non-superreflexive space when suitably renormed. A study is made of the geometric implications of the existence of flat spots. Connections with other notions such as differentiability, decomposition constants and Kadec-Klee norms are explored and some renorming results for non-superreflexive spaces are proved.
Multidimensional Volterra integral equations of convolution type
Authors: Laird P. G.
Published: April 2009

In this article, it is shown that the Volterra integral equation of convolution type w − w⊗g = f has a continuous solution w when f, g are continuous functions on Rx and ⊗ denotes a truncated convolution product. A similar result holds when f, g are entire functions of several complex variables. Also simple proofs are given to show when f, g are entire, f⊗g is entire, and, if f⊗g=0, then f = 0 or g = 0. Finally, the set of exponential polynomials and the set of all solutions to linear partial differential equations are considered in relation to this convolution product.
A remark on irreducible representations of Lie algebras
Authors: Bahturin JU. A.
Published: April 2009

In addition to the results of the paper (Bachturin (1974)) we give the precise form of the necessary and sufficient conditions ensuring that all irreducible representations of a Lie algebra were of finite bounded degree.
Residual finiteness and ‘free’ distributively generated near-rings
Authors: John David J.
Published: April 2009

Let V be a variety of groups in which the free group is residually finite, and let S be a residually finite semigroup. Let Nv(S) be the ‘free’ distributively generated near-ring constructed from S and V. Theorem; Nv(S) is residually finite.
Nilpotents and units in skew polynomial rings over commutative rings
Authors: Rimmer M. , Pearson K. R.
Published: April 2009

Let R be a commutative ring with an automorphism ∞ of finite order n. An element f of the skew polynomial ring R[x, α] is nilpotent if and only if all coefficients of fn are nilpotent. (The case n = 1 is the well-known description of the nilpotent elements of the ordinary polynomial ring R[x].) A characterization of the units in R[x, α] is also given.
Completions of certain nilpotent groups
Authors: Moran Siegfried , Williams Janet
Published: April 2009

The completions of certain nilpotent groups with respect to some ascending sequences of integral domains are constructed. These completions are generalizations of Lazard completions for the groups under consideration and they are Lie algebras over the first integral domain in the sequence. The construction is possible in particular for finite p-groups of exponent p and class < p.
Harmonic inversions in PG (4, 3) and some related configurations
Authors: Basu Nirmal Kumar
Published: April 2009

Geometries of one, two and three dimensional spaces over GF(3) have been considered in [2]. A line in a space over GF(3) contains 4 points and every pair of points is harmonic to its complementary pair. This feature makes the transformation of harmonic inversion interesting in a space over GF(3).
Annulets and α-ideals in a distributive lattice
Authors: Cornish William H.
Published: April 2009

In a distributive lattice L with 0 the set of all ideals of the form (x]* can be made into a lattice A0(L) called the lattice of annulets of L. A0(L) is a sublattice of the Boolean algebra of all annihilator ideals in L. While the lattice of annulets is no more than the dual of the so-called lattice of filets (carriers) as studied in the theory ofl-groups and abstractly for distributive lattices in [1, section4] it is a useful notion in its own right. For example, from the basic theorem of [3] it follows that A0(L) is a sublattice of the lattice of all ideals of L if and only if each prime ideal in L contains a unique minimal prime ideal.