bluuebunny/crossref_metadata_2025 huggingface dataset:
A note on group extensions
Authors: Vermani L. R.
Published: April 2009

In [2] Hauptfleisch proved that if A, B, H, K are Abelian groups, φ:A → H and ψ:B → K are epimorphisms, then every central group extension G of H by K is homomorphic image of a central loop extension L of A by B. The aim of the present note is to prove (using almost the same argument as in [2])
Permutation polynomials in several variables over residue class rings
Authors: Kaiser H. K. , Nöbauer W.
Published: April 2009

The concept of a permutation polynomial function over a commutative ring with 1 can be generalized to multiplace functions in two different ways, yielding the notion of a k-ary permutation polynomial function (k > 1, k ∈ N) and the notion of a strict k-ary permutation polynomial function respectively. It is shown that in the case of a residue class ring Zm of the integers these two notions coincide if and only if m is squarefree.
Enumerating subgroups
Authors: Cook R. J. , Wiecold James , Wellamson A. G.
Published: April 2009

It is proved that a finite soluble group of order n has at most (n − 1)/(q − 1) maximal subgroups, where q is the smallest prime divisor of n.
Some properties of vector measures taking values in a topological vector space
Authors: Giannakoulias Efstathios
Published: April 2009

In this paper we study some properties of vector measures with values in various topological vector spaces. As a matter of fact, we give a necessary condition implying the Pettis integrability of a function f: S → E, where S is a set and E a locally convex space. Furthermore, we prove an iff condition under which (Q, E) has the Pettis property, for an algebra Q and a sequentially complete topological vector space E. An approximating theorem concerning vector measures taking values in a Fréchet space is also given.
Characterisation theorems for compact hypercomplex manifolds
Authors: Nag S. , Hillman J. A. , Datta B.
Published: April 2009

We have defined and studied some pseudogroups of local diffeomorphisms which generalise the complex analytic pseudogroups. A 4-dimensional (or 8-dimensional) manifold modelled on these ‘Further pseudogroups’ turns out to be a quaternionic (respectively octonionic) manifold.

We characterise compact Further manifolds as being products of compact Riemann surfaces with appropriate dimensional spheres. It then transpires that a connected compact quaternionic (H) (respectively O) manifold X, minus a finite number of circles (its ‘real set’), is the orientation double covering of the product Y × P2, (respectively Y×P6), where Y is a connected surface equipped with a canonical conformal structure and Pn is n-dimensonal real projective space.

A corollary is that the only simply-connected compact manifolds which can allow H (respectively O) structure are S4 and S2 × S2 (respectively S8 and S2×S6).

Previous authors, for example Marchiafava and Salamon, have studied very closely-related classes of manifolds by differential geometric methods. Our techniques in this paper are function theoretic and topological.
Uniqueness and non-uniqueness of solutions of Vlasov-McKean equations
Authors: Scheutzow Michael
Published: April 2009

We study the equation dY(t)/dt = f(Y(t), Eh(Y(t))) for random initial conditions, where E denotes the expected value. It turns out that in contrast to the deterministic case local Lipschitz continuity of f and h are not sufficient to ensure uniqueness of the solutions. Finally we also state some sufficient conditions for uniqueness.
The Voronoi region of E*6
Authors: Worley R. T.
Published: April 2009

The Voronoi region and covering radius of the lattice E*6 are determined, and the normalised second moment is calculated, confirming the estimate given by Conway and Sloane.
A class of simple groups with no doubly transitive representations
Authors: Clarke R. J.
Published: April 2009

The first counterexample to the conjecture that all non a belian simple groups have doubly transitive permutation representations was pointed out by Parker in (1954), where he showed that the unitary groups PSU(4,4) had no doubly transitive representations. In this paper we generalize Parker's result to give an infinite class of simple groups having no doubly transitive permutation repreaentations. In this paper we generalize Parker's result to give an infinite class of simple groups having no doubly transitive permutation representations. Specifically, we prove THEOREM 1. The projective symplectic group PSp(4, q) has no doubly transitive permutation representation for q >2.
Linear regression in continuous time
Authors: Hannan E. J.
Published: April 2009

We consider a regression relation of the fromwhereiny(t) andx(t) are real (column) vectors ofqandpcomponents ande(t) is real and is generated by a stationary generalised vector process ofqcomponents with zero mean and covariance function (aqrowed matrix) Γ(t–s) =E{x(s)x(t)′}. (See Hannan (1970; pages 23–26, 91–94) and references therein for definitions of terms used.) We assumee(t) to be independent ofx(s) for alls,t. Thus we may regardx(t) as a fixed time function and not stochastic and we shall henceforth do that. We take Γ(t) to be continuous and to correspond to an absolutely continuous spectral function with spectral density which is uniformly bounded and continuous. Then we haveWe do not exclude the possibility that for theyth diagonal element,fjj, offwe have
A partial Baer *-semigroup of relations
Authors: Schelp R. H.
Published: April 2009

It is shown in Gudder and Schelp (1970) that partial Baer *-semigroups coordinatize orthomodular partially ordered sets (orthomodular posets). This means forPan orthomodular poset there exists a partial Baer *-semigroup whose closed projections are order isomorphic toPpreserving ortho-complementation. This coordinatization theorem generalizes Foulis (1960) in which orthomodular lattices are coordinatized by Baer *-semigroups. In particular Foulis (unpublished) shows that any complete atomic Boolean lattice is coordinatized by a Bear *-semigroup of relations. Since Greechie (1968), (1971) shows that a whole class of orthomodular posets can be formed by “pasting” together Boolean lattices, it is natural to consider the following problem. Let y be a family of Baer *-semigroups of relations which coordinatize the family B of complete atomic lattices. Is it possible to construct a partial *-semigroup of relations R which contains each member of Y such that whenPis an orthomodular poset obtained by a “Greechie pasting” of members of 38 then 91 coordinatizes R This question is considered in the sequel and answered affirmatively for a certain subclass of “Greechie pasted” orthomodular posets. In addition the construction of 8)t nicely fulfills another objective in that it provides us with “nontrivial” coordinate partial Baer *-semigroups for a whole family of well known orthomodular posets. This is particularly significant since the only other known coordinate partial Baer *-semigroups, for those posets in this family which are not lattices, are the “minimal” ones given in Gudderand and Schelp (1970).
Commutative distributive laws
Authors: Wolff Harvey
Published: April 2009

Kock (1970) defined the notion of a commutative monad in a symmetric monoidal closed category V and in Kock (1971) showed that the algebras for such a monad had a canonical structure as a closed category and that the monad had a canonical closed structure. In this paper we are concerned with the relationship between distributive laws and commutivity. In particular, the following question arises: given a distributive law between two monads on V when is the composite monad commutatice? To answer this question we define commutative distributive laws and show that if the composite is commutative then the distributiove law must be commutative. We also show that if Y and J are commutative monads in V with a commutative distributive law between them then the composite is commutative. So we get that if Y and J are commutative then the composite is commutative if and only if the distributive law is commutative. In addition we show that if the monads and the distributive law are commutative then the lifting of the monad Y to the category of J-algebras has a canonical structure as a closed monad (closed relative to the canonical closed category structure on the J algebras).
On the error in a certain interpolation formula and in the Gaussian integration formula
Authors: Luke Yudell L.
Published: April 2009

We first prove a basic theorem that if a set of polynomials satisfies an orthogonality relation with respect to integration, the set also satisfies an orthogonality relation with respect to summation. This result is then used to derive the Gaussian quadrature formula. The orthogonality relations give rise to interpolation formulas and a connection between the coefficients in these interpolation formulas is established. Finally, the analysis is used to get an estimate of the error in the Gaussian quadrature formula. Some error coefficients are evaluated in the cases where the orthogonal polynomials are those of Jacobi, Laguerre, Hermite and Bessel.
Eigenvalues in trailing edge flows
Authors: Capell K.
Published: April 2009

Abstract A wake similarity solution for symmetric uniform shear flows merging at the trailing edge of a flat plate has associated with it an eigenfunction problem which was overlooked by Hakkinen and O'Neil (1967). An asymptotic formula for large eigenvalues is obtained and compared with another such formula related to both the Goldstein (1930) inner wake solution and Tillett's (1968) similarity solution for a jet emerging from a two-dimensional channel.
The Ramsey number for stripes
Authors: Cockayne E. J. , Lorimer P. J.
Published: April 2009

If G1,…,Gc are graphs without loops or multiple edges there is a smallest integer r(G1,…,Gc) such that if the edges of a complete graph Kn, with n ≧ r(G1,…,Gc), are painted arbitrarily with c colours the ith coloured subgraph contains Gi as a subgraph for at least one i. r(G1,…Gc) is called the Ramsey number of the graphs G1,…,Gc.
Pointwise Convergence of Trigonometric Series
Authors: Chen Chang-Pao
Published: April 2009

We establish two results in the pointwise convergence problem of a trigonometric series for some nonnegative integer m. These results not only generalize Hardy's theorem, the Jordan test theorem and Fatou's theorem, but also complement the results on pointwise convergence of those Fourier series associated with known L1-convergence classes. A similar result is also established for the case that , where {ln} satisfies certain conditions.
Consequences of the Pseudo Orbits Tracing Property and Expansiveness
Authors: Ombach Jerzy
Published: April 2009

Let f be an expansive homeomorphism with the pseudo orbits tracing property on a compact metric space. There are stable and unstable “manifolds” with similar properties as in the hyperbolic case, and similar behavior near periodic points is observed. Per (f) = Ω(f) = CR(f). Mappings Ω and CR are continuous at f.
A Note On the Hadamard Kth Root of a Rational Function
Authors: Rumely Roberts , Van der Poorten A. J.
Published: April 2009

Suppose the sequence of Taylor coefficients of a rational function f consists of kth powers of elements all belonging to some finitely generated extension field F of Q. Then it is a generalisation of a conjecture of Pisot that there is a rational function with Taylor coefficients term-by-term kth roots of those of f. The authors show that it suffices to prove the conjecture in the case that the field of definition is a number field and prove the conjecture in that case subject to the constraint that f has a dominant pole, that is, that there is a valuation with respect to which f has a unique pole either of maximal or of minimal absolute value.
Correction to “Construction methods for Bhaskar Rao and related designs”
Authors: Gibbons Petter B. , Mathon Rudolf
Published: April 2009

The above paper, by Peter B. Gibbons and Rudolf Mathon, appeared in Volume 42 (1987), 5-30.

Pages 10 and 11 are misplaced, and should appear between pages 17 and 18
On Homomorphisms of an Orthogonally Decomposable Hilbert Space II
Authors: Yamamuro S.
Published: April 2009

We present two more characterizations of maps which preserve orthogonal decompositions defined on Hilbert spaces ordered by natural cones.
Cumulants and Partition Lattices V. Calculating Generalized k-Statistics
Authors: Speed T. P. , Silcock H. L.
Published: April 2009

A method is developed for obtaining compact, easily computed and statistically interpretable expressions for the generalized k-statistics associated with multiply-indexed arrays of random variables such as those which arise in variance component analysis. These expressions will be used in the next paper in this series to give formulae for variances and covariances of estimates of components of variance.
On the Bitopological Extension of the Bing Metrization Theorem
Authors: Romaguera Salvador , Marín Josefa
Published: April 2009

Based on a Junnila's paracompactness characterization we give a definition of pairwise paracompact space which permits us to prove that a bitopological space is quasi-metrizable if, and only if, it is a pairwise developable and pairwise paracompact space. An easy consequence of this result is the biquasi-metric form of the Morita metrization theorem. We also give some results on open mappings and strong quasi-metrics.
The Hausdorff Dimension of a Set of Normal Numbers II
Authors: Pollington A. D.
Published: April 2009

Let R, S be a partition of 2, 3,… so that rational powers fall in the same class. Let (λn) be any real sequence; we show that there exists a set N, of dimension 1, so that (x + λn) (n = 1,2, …) are normal to every base from R and to no base from S, for every x ∈ N.
On Normal Subgroups of Products of Nilpotent Groups
Authors: Amberg Bernhard , Franciosi Silvana , De Giovanni Francesco
Published: April 2009

Let G be a group factorized by finitely many pairwise permutable nilpotent subgroups. The aim of this paper is to find conditions under which at least one of the factors is contained in a proper normal subgroup of G.
A unified approach to continuous and certain non-continuous functions
Authors: Kohli J. K.
Published: April 2009

A unified theory of continuous and certain non-continuous functions is proposed and developed. The proposed theory encompasses in one the theories of continuous functions, upper (lower) semicontinuous functions, almost continuous functions, c-continuous functions, c*-continuous functions, s-continuous functions, l-continuous functions, H-continuous functions, and the ε-continuous functions of Klee.
Finite groups which admit a fixed-point-free automorphism group isomorphic to S3
Authors: Parrott David
Published: April 2009

Let G be a finite group of even order coprime to 3. If G admits a fixed-point-free automorphism group isomorphic to the symmetric group on three letters, then we prove that G is soluble.
Coefficients of differentially algebraic series
Authors: Laohakosol Vichian , Kongsakorn Kannika , Ubolsri Patchara
Published: April 2009

An Eisenstein-like criterion is proved for power series with algebraic coefficients satisfying algebraic differential equations of a certain general kind. The proof is elementary and the result extends earlier results of Hurwitz, Pólya and Popken
Complex Clifford analysis and domains of holomorphy
Authors: Ryan John
Published: April 2009

Integrals related to Cauchy's integral formula and Huygens' principle are used to establish a link between domains of holomorphy in n complex variables and cells of harmonicity in one higher dimension. These integrals enable us to determine domains to which analytic functions on real analytic surface in Rn+1 may be extended to solutions to a Dirac equation.
Simple surjective algebras having no proper subalgebras
Authors: Szendrei Ágnes
Published: April 2009

We prove that every finite, simple, surjective algebra having no proper subalgebras is either quasiprimal or affine or isomorphic to an algebra term equivalent to a matrix power of a unary permutational algebra. Consequently, it generates a minimal variety if and only if it is quasiprimal. We show also that a locally finite, minimal variety omitting type 1 is minimal as a quasivariety if and only if it has a unique subdirectly irreducible algebra.
On Hermite-Fejér interpolation with equidistant nodes
Authors: Baker G. B. , Mills T. M. , Vértesi P.
Published: April 2009

This paper deals with Hermite-Fejér interpolation of functions defined on a semi-infinite interval but the nodes are equally spaced. It is shown that, under certain conditions, the interpolation process has poor approximation properties.
Derived functors as homotopy groups
Authors: Modawi A. K.
Published: April 2009

In this paper a generalization of the interpretation of Robinson of torsion products as homotopy groups is given. This generalization allows us to define right derived functors of a coproduct preserving functor defined on a small category with all finite colimits to the category of abelian groups. We show that when the category is additive the definition coincides with the definitions of the right derived functors of Cartan and Eilenberg.
Presentations of some finite simple groups
Authors: Đoković Dragomir Ž.
Published: April 2009

We give new presentations of the five Mathieu groups, the simple groups J1, J2, HS, McL, Co3, and some other simple and related groups. All generators in these presentations are involutions. Our presentations are simpler than the known presentations of this type for the groups mentioned above.
Monotonic norms in ordered Banach spaces
Authors: Ng K. F. , Law C. K.
Published: April 2009

Let B be an ordered Banach space with ordered Banach dual space. Let N denote the canonical half-norm. We give an alternative proof of the following theorem of Robinson and Yamamuro: the norm on B is α-monotone (α ≥ 1) if and only if for each f in B* there exists g ∈ B* with g ≥ 0, f and ∥g∥ ≤ α N(f). We also establish a dual result characterizing α-monotonicity of B*.
Prime and special ideals in structural matrix rings over a ring without unity
Authors: Wyk L. Van
Published: April 2009

A. D. Sands showed that there is a 1–1 correspondence between the prime ideals of an arbitraty associative ring R and the complete matrix ring Mn(R) via P→ Mn(P). A structural matrix ring M(B, R) is the ring of all n × n matrices over R with 0 in the positions where the n × n boolean matrix B, B a quasi-order, has 0. The author characterized the special ideals of M(B, R′), in case R′ has unity, for certain special lasses of rings. In this note results of sands and the author are generalized to structural matrix rings over rings without unity. I t turns out that, although the class of prime simple rings is not a special class, Nagata's M-radical has the same form in structural matrix rings as the special radicals studied by the author.
Maximal-clique partitions of interval graphs
Authors: Shaohan Ma , Wallis W. D.
Published: April 2009

It is shown that if an interval graph possesses a maximal-clique partition then its clique covering and clique partition numbers are equal, and equal to the maximal-clique partition number. Moreover an interval graph has such a partition if and only if all its maximal cliques are edge-disjoint.
Some quantitative results related to Roth's Theorem
Authors: Bombieri E. , van der Poorten A. J.
Published: April 2009

We employ the Dyson's Lemma of Esnault and Viehweg to obtain a new and sharp formulation of Roth's Theorem on the approximation of algebraic numbers by algebraic numbers and apply our arguments to yield a refinement of the Davenport-Roth result on the number of exceptions to Roth's inequality and a sharpening of the Cugiani-Mahler theorem. We improve on the order of magnitude of the results rather than just on the constants involved.
A comment on certain p–shift algebras
Authors: Stacey P. J.
Published: April 2009

Let G = ⊕∞i=0Zp, where p is a prime, let s be the shift mapping the i th summand of G to the (i+1) st and let ω be a 2 cocycle on G with values in S1, for which ω (s(g), s(h)) = ω (g, h). If Ω (ej, ek) = Ω (ek, ej) whenever │j - k│ is sufficiently large, where ei is the generator of the i th summand of G, then it is shown that the twisted group C* -algebra C*(G, ω) is isomorphic to the UHF algebra UHF (p∞). An immediate consequence, by results of Bures and Yin, is the existence of infinitely many non-conjugate shifts on UHF (p∞).
On O. Bonnet III-isometry of surfaces in three dimensional Euclidean space
Authors: Yang Wenmao
Published: April 2009

In this paper we consider O. Bonnet III-isometry (or BIII-isometry) of surfaces in 3-dimensional Euclidean space E3 Suppose a map F: M → M* is a diffeomorphism, and F* (III*) = III, ki(m) = k*i (m*), i = 1, 2, where m ∈ M, m* ∈ M*, m* = F (m), ki and k*i are the principal curvatures of surfaces M and M* at the points m and m*, respectively, III and III* are the third fundmental forms of M and M*, respectively. In this case, we call F an O. Bonnet III-isometry from M to M*. O. Bonnet I-isometries were considered in references [1]-[5].

We distinguish three cases about BIII-surfaces, which admits a non-trivial BIII-ismetry. We obtain some geometric properties of BIII-surfaces and BIII-isometries in these three cases; see Theorems 1, 2, 3 (in Section 2). We study some special BIII-surfaces: the minimal BIII-surfaces; BIII-surfaces of revolution; and BIII-surfaces with constant Gaussian curvature; see Theorems 4, 5, 6 (in Section 3).
Matching theorems, fixed point theorems and minimax inequalities without convexity
Authors: Ding Xie-Ping , Tan Kok-Keong
Published: April 2009

Matching theorems, fixed point theorems and minimax inequalities are obtained inH-spaces which generalize the corresponding results of Bae-Kim-Tan, Browder, Fan, Horvath, Kim, Ko-Tan, Shih-Tan, Takahashi, Tan and Tarafdar to non-compact and/or non-convex settings.
On the average number of real zeros of a class of random algebraic equations
Authors: Nayak N. N. , Bagh S.
Published: April 2009

Let g1, g2, …, gn be a sequence of mutually independent, normally distributed, random variables with mathematical expectation zero and variance unity. In this work, we obtain the average number of real zeros of the random algebraic equations Σnk=1 Kσ gk(ω)tk = C, where C is a constant independent of t and not necessarily zero. This average is (1/π) log n, when n is large and σ is non-negative.
Constructions of Σ-groups, relatively free Σ-groups
Authors: Brunker Don , Higgs Denis
Published: April 2009

A Σ-group is an abelian group on which is given a family of infinite sums having properties suggested by, but weaker than, those which hold for absolutely convergent series of real or complex numbers. Two closely related questions are considered. The first concerns the construction of a Σ-group from an arbitrary abelian group on which certain series are given to be summable, certain of these series being required to sum to zero. This leads to a Σ-theoretic construction of R from Q and in general of the completion of an arbitrary metrizable abelian group (with the associated unconditional sums) from that group. The second question is whether, in a given Σ-group, the values of the infinite sums may be determined solely from a knowledge of which series are summable. Such a Σ-group is said to be relatively free and it is shown that all metrizable abelian groups are relatively free.
Integrable solutions of Hammerstein and Urysohn integral equations
Authors: Banaś Józef
Published: April 2009

In this paper we prove theorems on the existence of integrable and monotonic solutions of Hammserstein and Urysohn integral equations. The basic tool used in the proof is the fixed point principle for contractions with respect to the so-called measure of weak noncompactness.
Ordered probabilistic metric spaces
Authors: Kent D. C. , Richardson G. D.
Published: April 2009

Probabilistic quasi-metric spaces are introduced and used to define ordered probabilistic metric spaces. The latter spaces arise naturally in the study of probability and statistics; they closely resemble the uniform ordered spaces of L. Nachbin. A procedure is described for constructing ordered probabilistic metric spaces from quasi-simple spaces, and a completions theory is developed simultaneously for probabilistic quasi-metric spaces and ordered probabilistic metric spaces.
Quasi-suprabarrelled spaces
Authors: Ferrando J. C. , López-Pellicer M.
Published: April 2009

In this paper a proper class of barrelled spaces which strictly contains the suprabarrelled spaces is considered. A closed graph theorem and some permanence properties are given. This allows us to prove the necessity of a condition of a theorem of S. A. Saxon and P. P. Narayanaswami by constructing an example of a non-suprabarrelled Baire-like space which is a dense subspace of a Fréchet space and is not an (LF)-space under any strong locally convex topology.
Maximal immediate extensions are not necessarily maximally complete
Authors: Brungs Hans Heinrich , Törner Günter
Published: April 2009

An extensionR1of a right chain ringRis called immediate ifR1has the same residue division ring and the same lattice of principal right ideals asR. Properties of such immediate extensions are studied. It is proved that for everyR, maximal immediate extensions exist, but that in contrast to the commutative case maximal right chain rings are not necessarily linearly compact.
Allgemeines Über Äussere Fittingpaare
Authors: Pense Joachim
Published: April 2009

We discuss some general properties and limitations of the concept of outer Fitting pairs introduced earlier by the author. We describe an outer Fitting pair as a co-cone in the category of what we call outer groups (roughly speaking the category of groups modulo inner automorphisms). It is shown that generally no universal outer Fitting pair exists, whence this category is not co-complete. Additionally it is shown that if the target group of an outer Fitting pair is finite, then the much more amenable concept of normal Fitting pairs (that is, co-cones in the category of groups) applies.
Operator approximations with stable elgenvalues
Authors: Bouldin Richard
Published: April 2009

Suppose λ is an isolated eigenvalue of the (bounded linear) operator T on the Banach space X and the algebraic multiplicity of λ is finite. Let Tn be a sequence of operators on X that converge to T pointwise, that is, Tnx → Tx for every x ∈ X. If ‖(T − Tn)Tn‖ and ‖Tn(T − Tn)‖ converge to 0 then Tn is strongly stable at λ.
Normality of some p—adic product expansions
Authors: Knopfmacher Arnold , Knopfmacher John
Published: April 2009

We consider two unique products for a given p—adic integer x with leading coefficient 1, where anbn ∈ {0, 1,… p − 1}. It is shown that, for almost all such x relative to Haar measure on the p—adic integers, the sequences (an), (bn) are normal to base p, and have standard normal distribution functions.
Notes on uniform distribution modulo one
Authors: Myerson G. , Pollington A. D.
Published: April 2009

We exhibit a sequence (un) which is not uniformly distributed modulo one even though for each fixed integer k ≥ 2 the sequence (kun) is u.d. (mod 1). Within the set of all such sequences, we characterize those with a well-behaved asymptotic distribution function. We exhibit a sequence (un) which is u.d. (mod 1) even though no subsequence of the form (ukn + j) is u.d. (mod 1) for any k ≥ 2. We prove that, if the subsequences (ukn) are u.d. (mod 1) for all squarefree k which are products of primes in a fixed set P, then (un) is u.d. (mod I) if the sum of the reciprocals of the primes in P diverges. We show that this result is the best possible of its type.
Left self distributive near-rings
Authors: Birenmeier Gary , Heatherly Henry
Published: April 2009

This paper considers (left) near-rings which satisfy the left self distributive (LSD) identity: abc = abac. This is exactly the class of near-rings for which each left multiplication mapping, τa: x → ax, is a near-ring endomorphism. Simple and subdirectly irreducible ones are classified and semidirect sum decompositions into reduced and nilpotent pieces are given. LSD near-rings with restrictive conditions on nilpotent elements or annihilating sets are considered. Type 1 prime (semiprime) ideals in an LSD near-ring are completely prime (semiprime). Further results on prime and maximal ideals are given. Numerous examples are given to illuminate the theory and to illustrate its limitations. Some analogous theory for right self distributive near-rings is given (those satisfying the identity: abc = acbc).
On some reverse integral inequalities
Authors: Nania Luciana
Published: April 2009

We prove the higher integrability of nonnegative decreasing functions, verifying a reverse inequality, and we calculate the optimal integrability exponent for these functions.
Spectrality of elementary operators
Authors: Hladnik Milan
Published: April 2009

Spectrality and prespectrality of elementary operators , acting on the algebra B(k) of all bounded linear operators on a separable infinite-dimensional complex Hubert space K, or on von Neumann-Schatten classes in B(k), are treated. In the case when (a1, a2, …, an) and (b1, b2, …, bn) are two n—tuples of commuting normal operators on H, the complete characterization of spectrality is given.
Lattices of pseudovarieties
Authors: Agliano P. , Nation J. B.
Published: April 2009

We consider the lattice of pseudovarieties contained in a given pseudovariety P. It is shown that if the lattice L of subpseudovarieties of P has finite height, then L is isomorphic to the lattice of subvarieties of a locally finite variety. Thus not every finite lattice is isomorphic to a lattice of subpseudovarieties. Moreover, the lattice of subpseudovarieties of P satisfies every positive universal sentence holding in all lattice of subvarieties of varieties V(A) ganarated by algebras A ε P.
Fourier series with small gaps
Authors: Isaza P. , Waterman D.
Published: April 2009

A trigonometric series has “small gaps” if the difference of the orders of successive terms is bounded below by a number exceeding one. Wiener, Ingham and others have shown that if a function represented by such a series exhibits a certain behavior on a large enough subinterval I, this will have consequences for the behavior of the function on the whole circle group. Here we show that the assumption that f is in any one of various classes of functions of generalized bounded variation on I implies that the appropriate order condition holds for the magnitude of the Fourier coefficients. A generalized bounded variation condition coupled with a Zygmundtype condition on the modulus of continuity of the restriction of the function to I implies absolute convergence of the Fourier series.
On the small and essential ideals in certain classes of rings
Authors: Green B. W. , van Wyk L.
Published: April 2009

It is well known that for a ring with identity the Brown-McCoy radical is the maximal small ideal. However, in certain subrings of complete matrix rings, which we call structural matrix rings, the maximal small and minimal essential ideals coincide.

In this paper we characterize a class of commutative and a class of non-commutative rings for which this coincidence occurs, namely quotients of Prüfer domains and structural matrix rings over Brown-McCoy semisimple rings. A similarity between these two classes is obtained.
Projective characters of degree one and the inflation-restriction sequence
Authors: Higgs R. J.
Published: April 2009

Let G be a finite group, α be a fixed cocycle of G and Proj (G, α) denote the set of irreducible projective characters of G lying over the cocycle α.

Suppose N is a normal subgroup of G. Then the author shows that there exists a G- invariant element of Proj(N, αN) of degree 1 if and only if [α] is an element of the image of the inflation homomorphism from M(G/N) into M(G), where M(G) denotes the Schur multiplier of G. However in many situations one can produce such G-invariant characters where it is not intrinsically obvious that the cocycle could be inflated. Because of this the author obtains a restatement of his original result using the Lyndon-Hochschild-Serre exact sequence of cohomology. This restatement not only resolves the apparent anomalies, but also yields as a corollary the well-known fact that the inflation-restriction sequence is exact when N is perfect.
An algorithm for the ear decomposition of a 1-factor covered graph
Authors: Little C. H. C. , Rendl F.
Published: April 2009

We give a constructive proof for the theorem of Lovász and Plummer which asserts the existence of an ear decomposition of a 1-factor covered graph.
On the Projective Cover of an orbit space
Authors: Azad K. K. , Agrawal Gunjan
Published: April 2009

In this paper, we obtain the projective cover of the orbit space X/G in terms of the orbit space of the projective space of X, when X is a Tychonoff G-space and G is a finite discrete group. An example shows that finiteness of G is needed.
The structure of hypergroup measure algebras
Authors: Lang W. Christopher
Published: April 2009

A close analogue for some hypergroup measure algebras of the structure semigroup theorem of J. L. Taylor for convolution measure algebras is constructed: a structure semihypergroup representation is made for the hypergroup measure and its spectrum. This is done for those hypergroup measure algebras that satisfy a condition known as the structure-strong condition. This condition is that the norm-closure of the linear span of the spectrum of the hypergroup measure algebra is a commutativeB*-algebra. Then examples of hypergroups whose measure algebras satisfy this condition are given. They include the space ofB-orbits ofG, whereBis a finite solvable group of automorphisms on a locally compact abelian groupG. (The hypergroup measure algebra may be identified with the algebra ofB-invariant measures onG.) Other examples are the algebra of central measures on a compact, connected, semisimple Lie group, and the algebra of rotation invariant measures on the plane.
Homogeneous models and almost decidability
Authors: Millar Terry
Published: April 2009

Countable homogeneous models are ‘simple’ objects from a model theoretic point of view. From a recursion theoretic point of view they can be complex. For instance the elementary theory of such a model might be undecidable, or the set of complete types might be recursively complex. Unfortunately even if neither of these conditions holds, such a model still can be undecidable. This paper investigates countable homogeneous models with respect to a weaker notion of decidability called almost decidable. It is shown that for theories that have only countably many type spectra, any countable homogeneous model of such a theory that has a Σ2 type spectrum is almost decidable.
Meromorphic products determining near-fields
Authors: Fuchs Peter , Maxson C. J.
Published: April 2009

In this paper we continue our investigations of a construction method for subnear-rings ofM(G)proposed by H. Wielandt. For a meromorphic productH, H ⊂ Gk, Gfinite, we obtain necessary and sufficient conditions forM(G, k, H)to be a near-field.
Some new series of Hadamard matrices
Authors: Yamada Mieko
Published: April 2009

The purpose of this paper is to prove (1) if q ≡ 1 (mod 8) is a prime power and there exists a Hadamard matrix of order (q − 1)/2, then we can construct a Hadamard matrix of order 4q, (2) if q ≡ 5 (mod 8) is a prime power and there exists a skew-Hadamard matrix of order (q + 3)/2, then we can construct a Hadamard matrix of order 4(q + 2), (3) if q ≡ 1 (mod 8) is a prime power and there exists a symmetric C-matrix of order (q + 3)/2, then we can construct a Hadamard matrix of order 4(q + 2).

We have 36, 36 and 8 new orders 4n for n ≤ 10000, of Hadamard matrices from the first, the second and third theorem respectively, which were known to the list of Geramita and Seberry. We prove these theorems by using an adaptation of generalized quaternion type array and relative Gauss sums.
An infinite class of Hadamard matrices
Authors: Koukouvinos Christos , Kounias Stratis
Published: April 2009

An infinite class of T-matrices is constructed using Golay sequences. A list is given with new Hadamard matrices of order 2t. q, q odd, q < 10000, improving the known values of t.

Finally T-matrices are given of order 2m + 1, for small values of m ≤ 12 which do not coincide with those generated by Turyn sequences.
A generalization of Rolle's Theorem and an application to a nonlinear equation
Authors: Tineo Antonio
Published: April 2009

Given two C1 -functions g: R → R, u: [0,1] → R such that u(0) = u(1) = 0, g(0) = 0, we prove that there exists c, with 0 < c < 1, such that u′(c) = g(u(c)). This result implies the classical Rolle's Theorem when g ≡ 0. Next we apply our result to prove the existence of solutions of the Dirichlet problem for the equation x′ = f(t, x, x′).
Lp-improving measures on compact non-abelian groups
Authors: Hare Kathryn E.
Published: April 2009

A Borel measure μ on a compact group G is called Lp-improving if the operator Tμ: L2(G) → L2(G), defined by Tμ(f) = μ * f, maps into Lp(G) for some P > 2. We characterize Lp-improving measures on compact non-abelian groups by the eigenspaces of the operator Tμ if |Tμ|. This result is a generalization of our recent characterization of Lp-improving measures on compact abelian groups.

Two examples of Riesz product-like measures are constructed. In contrast with the abelian case one of these is not Lp-improving, while the other is a non-trivial example of an Lp improving measure.
Fourier inversion formula for discrete nilpotent groups
Authors: Kajiwara Tsuyoshi
Published: April 2009

Let G be a countable torsion free finitely generated nilpotent group. Then the Fourier transform can be considered as a map from the space of bounded degree 1 random operators to the Fourier algebra A(G). In this paper, we recover the matrix elements of a positive random variable from the corresponding positive definite function in A(G) for such a group.
On exponential sums over prime numbers
Authors: Sárközy A. , Stewart C. L.
Published: April 2009

In this article we establish an estimate for a sum over primes that is the analogue of an estimate for a sum over consecutive integers which has proved to be very useful in applications of exponential sums to problems in number theory.
Pairs of additive congruences to a large prime modulus
Authors: Atkinson O. D. , Cook R. J.
Published: April 2009

This paper is concerned with non-trivial solvability in p–adic integers, for relatively large primes p, of a pair of additive equations of degree k > 1: where the coefficients a1,…, an, b1,…, bn are rational integers.

Our first theorem shows that the above equations have a non-trivial solution in p–adic integers if n > 4k and p > k6. The condition on n is best possible.

The later part of the paper obtains further information for the particular case k = 5. specifically we show that when k = 5 the above equations have a non-trivial solution in p–adic integers (a) for all p > 3061 if n ≥ 21; (b) for all p execpt p = 5, 11 if n ≥ 26.
An indeterminate in number theory
Authors: Lehmer Emma
Published: April 2009

This paper studies quintic residuacity of primes p of the form for which the expression for 4f modulo p given in the first volume of this journal becomes indeterminate, and replaces it by a much simpler expression.
On homomorphisms of an orthogonally decomposable Hilbert space, III
Authors: Hiai Fumio , Yamamuro Sadayuki
Published: April 2009

A hyperfinite von Neumann algebra satisfies the condition that every o.d. homomorphism is a normal operator if and only if it is a factor of type In.
Cohomology with exotic supports and the generalized excision
Authors: Deo Satya , Jamwal Dalip Singh , Krishan Ram
Published: April 2009

The main result proved in this paper is the following. SupposeX1,X2are two subspaces of a spaceXsuch thatX= Int(X1)∪X2=X1∪ Int(X2). Then the pair (X1,X2) is a ϕ onX. This result settles an open question and includes all known results on ϕ-excisiveness in sheaf cohomology as its special cases. We construct several several examples to illustrate our main theorem and to show that it is, in fact, quite sharp.
The minimal faithful degree of a semilattice of groups
Authors: Easdown David
Published: April 2009

This paper constructs a minimal faithful representation of a semilattice of groups by partial transformations. The solution is expressed in terms of join irreducible elements of the semilattice and minimal faithful representations of groups with respect to certain normal subgroups.
Openness of vector measures and their integral maps
Authors: Spakowski Andrzej
Published: April 2009

We prove that finite dimensional nonatomic vector measures and their integral maps are open maps. These results can be found in the literature, but unfortunately the proofs presented there are not complete.
The Three Gap Theorem (Steinhaus Conjecture)
Authors: van Ravenstein Tony
Published: April 2009

This paper is concerned with the distribution of N points placed consecutively around the circle by an angle of α. We offer a new proof of the Steinhaus Conjecture which states that, for all irrational α and all N, the points partition the circle into arcs or gaps of at least two, and at most three, different lengths. We then investigate the partitioning of a gap as more points are included on the circle. The analysis leads to an interesting geometrical interpretation of the simple continued fraction expansion of α.
Some topological properties of vector measures and their integral maps: Errata
Authors: Anantharaman R. , Garg K. M.
Published: April 2009

It was kindly pointed out to the authors by Z. Lipecki and A. Spakowski that the proofs of Theorem 2.3 and Proposition 3.8 of [1] are incomplete; the gaps are on lines 15–14 from the bottom of page 457 and line 2 from the bottom of page 463 respectively. The openness of a non atomic measure in finite dimensions has also been treated in [2], [3], and [4]. A complete proof may be found in [2].
Chain conditions and semigroup graded rings
Authors: Jespers E.
Published: April 2009

The following questions are studied: When is a semigroup graded ring left Noetherian, respectively semiprime left Goldie? Necessary sufficient conditions are proved for cancellative semigroup-graded subrings of rings weakly or strongly graded by a polycyclic-by-finite (unique product) group. For semigroup rings R[S] we also give a solution to the problem in case S is an inverse semigroup.
Rates of convergence for renewal sequences in the null-recurrent case
Authors: Isaac Richard
Published: April 2009

Motivated by work of Garsia and Lamperti we consider null-recurrent renewal sequences with a regularly varying tail and seek information about their rate of convergence to zero. The main result shows that such sequences subject to a monotonicity condition obey a limit law whatever the value of the exponent α is, 0 < α < 1. This monotonicity property is seen to hold for a large class of renewal sequences, the so-called Kaluza sequences. This class includes moment sequences, and therefore includes the sequences generated by reversible Markov chains. Several subsidiary results are proved.
Subnormal embedding of relatively complete groups
Authors: Heineken Hermann , Soules Panagiotis
Published: April 2009

In this paper we show that a group A is embedded in any finite group G as a subnormal subgroup with low degree of complication, provided that the automorphism group of A satisfies a condition depending on some Fitting class (which coincides with completeness for the Fitting class of all groups). A criterion is given for these groups as to whether they can be embedded subnormally in the commutator subgroup of some finite group or not.
Scalar operators and integration
Authors: Kluvánek Igor
Published: April 2009

The notion of a scalar operator on a Banach space, in the sense of N. Dunford, is widened so as to cover those operators which can be approximated in the operator norm by linear combinations of disjoint values of an additive and multiplicative operator valued set function, P, on an algebra of sets in a space Ω such that P(Ω) = I, subject to some conditions guaranteeing that this definition is unambiguous. An operator T turns out to be scalar in this sense, if and only if, there exists a (not necessarily bounded) Boolean algebra of bounded projections such that the Banach algebra of operators it generates is semisimple and contains T.
Pasting infinite lattices
Authors: Fried E. , Grātzer G.
Published: April 2009

In an earlier paper, we investigated for finite lattices a concept introduced by A. Slavik: LetA, B,andSbe sublattices of the latticeL,A∩B=S,A∪B=L. ThenL pastes AandBtogether overS, if every amalgamation ofAandBoverScontainsLas a sublattice. In this paper we extend this investigation to infinite lattices. We give several characterizations of pasting; one of them directly generalizes to the infinite case the characterization theorem of A. Day and J. Ježk. Our main result is that the variety of all modular lattices and the variety of all distributive lattices are closed under pasting.
A new proof of the Doyen-Wilson theorem
Authors: Stinson D. R.
Published: April 2009

We describe several recursive constructions for designs which use designs with “holes”. As an application, we give a short new proof of the Doyen-Wilson Theorem.
Major n-connected graphs
Authors: Oellermann Ortrud R.
Published: April 2009

An induced subgraph H of connectivity (edge-connectivity) n in a graph G is a major n-connected (major n-edge-connected) subgraph of G if H contains no subgraph with connectivity (edge- connectivity) exceeding n and H has maximum order with respect to this property. An induced subgraph is a major (major edge-) subgraph if it is a major n-connected (major n-edge-connected) subgraph for some n. Let m be the maximum order among all major subgraphs of C. Then the major connectivity set K(G) of G is defined as the set of all n for which there exists a major n-connected subgraph of G having order m. The major edge-connectivity set is defined analogously. The connectivity and the elements of the major connectivity set of a graph are compared, as are the elements of the major connectivity set and the major edge-connectivity set of a graph. It is shown that every set S of nonnegative integers is the major connectivity set of some graph G. Further, it is shown that for each positive integer m exceeding every element of S, there exists a graph G such that every major k-connected subgraph of G, where k ∈ K(G), has order m. Moreover, upper and lower bounds on the order of such graphs G are established.
Some embeddings related to C*-embeddings: Corrigenda
Authors: Aull C. E.
Published: April 2009

The first sentence of [1, Definition 1.1] should read as follows. It is correctly given in the abstract of [1].
On the existence of sequences of co-prime pairs of integers
Authors: Dowe David L.
Published: April 2009

We say that a positive integer d has property (A) if for all positive integers m there is an integer x, depending on m, such that, setting n = m + d, x lies between m and n and x is co-prime to mn. We show that infinitely many even d and infinitely many odd d have property (A) and that infinitely many even d do not have property (A). We conjecture and provide supporting evidence that all odd d have property (A).

Following A. R. Woods [3] we then describe conditions (Au) (for each u) asserting, for a given d, the existence of a chain of at most u + 2 integers, each co-prime to its neighbours, which start with m and increase, finishing at n = m + d. Property (A) is equivalent to condition (A1), and it is easily shown that property (Ai) implies property (Ai+1). Woods showed that for some u all d have property (Au), and we conjecture and provide supporting evidence that the least such u is 2.