bluuebunny/crossref_metadata_2025 huggingface dataset:
Essential extensions in radical theory for rings
Authors: Heyman G. A. P. , Roos C.
Published: April 2009

The essential coverMkof a classMis defined as the class of all essential extensions of rings belonging toM.Mis called essentially closed ifMk=M. Every classMhas a unique essential closure, i.e. a smallest essentially closed class containingM.

LetMbe a hereditary class of (semi)prime rings. ThenMis proved to be a (weakly) special class if and only ifMis essentially closed. A main result is thatMkis the smallest (weakly) special class containingM. Further it is shown that the upper radicalUMdetermined byM, is hereditary if and only ifUMhas the intersection property with respect toMk.
Free topological groups
Authors: Borges Carlos R.
Published: April 2009

Let X be any Tychonoff space and βX the Stone—Čech compactification of X. Let F(βX) be the Graev free group of βX and let be the subspace topology on the Graev group F(X). Our results demonstrate that this topology is useful and behaves extremely well; the behavior of the free topology still remains enigmatic.

There are various applications, some of which clarify the free topology on F(X), while others improve various results recently published.
An algebraic characterization of groups with soluble word problem
Authors: Boone William W. , Higman Graham
Published: April 2009

The following theorem is the focal point of the present paper. It stipulates an algebraic condition equivalent, in any finitely generated group, to the solubility of the word problem.

THEOREM I. A necessary and sufficient condition that a finitely generated group G have a soluble word problem is that there exist a simple group H, and a finitely presented group K, such that G is a subgroup of H, and H is a subgroup of K.
Uniqueness of solutions of improperly posed problems for singular ultrahyperbolic equations
Authors: Young Eutiquio C.
Published: April 2009

In [1], Owen gave sufficient conditions for the uniqueness of certain mixed problems having elliptic and hyperbolic nature for the ultrahyperbolic equation. Recently, Diaz and Young [2] has obtained necessary and sufficient conditions for the uniqueness of solutions of the Dirichlet and Neumann problems involving the more general ultrahyperbolic equation The purpose of this paper is to present corresponding uniqueness conditions for the Dirichlet and Neumann problems for the singular ultrahyperbolic equation for all values of the parameter, α −∞ > α > ∞. The symbol Δ denotes the Laplace operator in the variables x1, …, xm, Dj indicates partial differentiation with respect to the variable yj (1 ≧ J ≧ n), and the summation convention is adopted for repeated indices including (iu2), where denotes differentiation with respect to the variable xi.
Signed sums of reciprocals II
Authors: Worley R. T.
Published: April 2009

The author investigates M(n, α) = min ¦α – Σηkk−1¦ where the minimum is over all sets of signs η1 = ± 1 and shows .
Concerning periodicity in the asymptotic behaviour of partition functions
Authors: Erdös P. , Richmond B.
Published: April 2009

Let PA(n) denote the number of partitions of n into summands chosen from the set A = {a1, a2, …}. De Bruijn has shown that in Mahler's partition problem (aν = rν) there is a periodic component in the asymptotic behaviour of PA(n). We show by example that this may happen for sequences that satisfy aν ν and consider an analogous phenomena for partitions into primes. We then consider corresponding results for partitions into distinct summands. Finally we obtain some weaker results using elementary methods.
A class of D-extreme Minkowski-reduced forms
Authors: Trenerry D. W.
Published: April 2009

Barnes (1978, 1979) introduced the concept of a -extreme form, which is a Minkowski-reduced positive definite quadratic form having prescribed diagonal coefficients α1, α2, …, αn and providing a local minimum of the determinant of the form over all such forms. Here a class of forms which are -extreme for all α and all n is described.
Regular Wallman compactifications of rim-compact spaces
Authors: Njåstad Olav
Published: April 2009

A compact Hausdorff space is regular Wallman if it possesses a separating ring of regular closed sets, an s-ring. It was proved by P. C. Baayen and J. van Mill [General Topology and Appl. 9 (1978), 125–129] that if a locally compact Hausdorff space possesses an s-ring, then every Hausdorff compactification with zero-dimensional remainder is regular Wallman.

In this paper the reasoning leading to this result is modified to work in a more general setting. Iet αX be a Hausdorff compactification of a space X, and let be the family of those closed sets in αX whose boundaries are contained in X. A main result is the following: If contains an s-ring for some Hausdorff compactification γX, then every larger Hausdorff compactification αX for which is a base for the closed sets on αX — X, is regular Wallman. Various consequences concerning compactifications of a class of rim-compact spaces (called totally rim-compact spaces) are discussed.
Some results concerning frames, Room squares, and subsquares
Authors: Stinson D. R.
Published: April 2009

Frames have been defined as a certain type of generalization of Room square. Frames have proven useful in the construction of Room squares, in particular, skew Room squares.

We generalize the definition of frame and consider the construction of Room squares and skew Room squares using these more general frames.

We are able to construct skew Room squares of three previously unknown sides, namely 93, 159, and 237. This reduces the number of unknown sides to four: 69, 87, 95 and 123. Also, using this construction, we are able to give a short proof of the existence of all skew Room squares of (odd) sides exceeding 123.

Finally, this frame construction is useful for constructing Room squares with subsquares. We can also construct Room squares “missing” subsquares of sides 3 and 5. The “missing” subsquares of sides 3 and 5 do not exist, so these incomplete Room squares cannot be completed to Room squares.
The conjugacy problem and cuclic HNN constructions
Authors: Larsen Leif
Published: April 2009

We consider two related classes of groups. For any group G of the first of these — the smallest class containing all finitely generated free groups and closed under cyclic amalgamations — we show that for any U, W ∈ G we can “effectively describe” the set of all x and y with U* and W* conjugate in G. For the second class, which consists of all groups obtained from the first class through cyclic HNN constructions, we solve the conjugacy and power-conjugacy problems.
On functions derived from regularly varying functions
Authors: Haan Laurens De
Published: April 2009

A generalization of Karamata's theorem on integrals of regularly varying functions is proved. Using Laplace-Stieltjes transforms it is shown that any regularly varying function with exponent α (α + 1 ∉ N) is asymptotic to another regularly varying function all of whose derivations are regularly varying.
Some results on a combinatorial problem of Cordes
Authors: McCarthy D. , Rees G. H. J. van
Published: April 2009

Cordes (1976) introduced the problem of determining the maximum number of resolution classes of a finite set partitioned into equicardinal subsets such that the number of pairs common to any 2 classes is minimized. A later paper of Mullin and Stanton (1976) investigated those conditions under which the configurations were actually BIBD's. They obtained a bound for these special configurations and conjectured it applied in general. We prove this in the present paper. A recursive and a direct construction are also given for a special class of configurations.
On minimal Hausdorff spaces
Authors: Joseph James E.
Published: April 2009

In this paper, several characterizations of minimal Hausdorff spaces are given.
Recursive equivalence types and octahedra
Authors: Dekker J. C. E.
Published: April 2009

Let the word “graph” be used in the sense of a countable, connected, simple graph with at least one vertex. We write Qn and Ocn for the graphs associated with the n-cube Qn and the n-octahedron Ocn respectively. In a previous paper (Dekker, 1981) we generalized Qn and Qn to a graph QN and a cube QN, for any nonzero recursive equivalence type N. In the present paper we do the same for Ocn and Ocn. We also examine the nature of the duality between QN and OcN, in case N is an infinite isol. There are c RETs, c denoting the cardinality of the continuum.
On ω-approximately continuous Perron-Stieltjes and Denjoy-Stieltjes integral
Authors: Sarkhel D. N.
Published: April 2009

The aim of the present paper is to introduce a definition of the Perron-Stieltjes integral employing the notion of approximate derivative with respect to a nondecreasing function ω and to study some of the properties of the integral. Various authors have studied the Perron integral and Perron-Stieltjes integral in different ways, most of which can be found in the references appended in the list of the bibliography. Among them Ridder [10] uses the concept of approximate co-derivative but he assumes that the monotone function a associated with co is continuous. Finally we consider a more general type of integral, the co-approximately continuous Denjoy-Stieltjes integral, defined descriptively by the method of Saks [11].
The order dual of an abelian von Neumann algebra
Authors: Dodds Peter G.
Published: April 2009

The usual technique for dealing with an abelian W*-algebra is to consider it, via the Gelfand theory, as the algebra of all continuous complex-valued functions on an extremally disconnected compact Hausdorff space with a separating family of normal linear functionals. An alternative approach, outlined in [2] and [10], is to develop the theory within the framework of Riesz spaces (linear vector lattices) where the order properties of the self-adjoint operators play an important and natural role. It has been known for a long time that the self-adjoint part of an abelian W*-algebra is a Dedekind complete Riesz space under the natural ordering of self-adjoint operators, but it is only relatively recently that a proof of this fact has been given that is independent of the Gelfand theory, and the interested reader may consult [2] or [10] for the details. This approach is essentially foreshadowed in [6] and provides a very satisfying introduction to the theory of commutative rings of operators. From this point of view, the spectral theorem for self-adjoint operators falls naturally into place as an easy consequence of the spectral theorem of H. Freudenthal. In this paper, the line of approach via Riesz spaces is developed further and several well known results are shown to follow as elementary consequences of the order structure of the algebra.
Restricted homological properties of modules
Authors: Hill David A.
Published: April 2009

Let R be a ring and M a left R-module. We investigate when the functors HomR(M, —), HomR( —, M), and — ⊗RM are exact for certain restricted subcategories of modules.
On a relationship between magnetohydrodynamic planetary eigenmodes and second-class inertial elgenmodes
Authors: Rickard J. A.
Published: April 2009

Stewartson [5] considered second class oscillations in a spherical shell in the presence of a toroidal magnetic field. He followed Hide [2] and supposed the toroidal field to be uniform.
Some examples of nonmeasurable sets
Authors: Hewitt Edwin , Stromberg Karl
Published: April 2009

In a recent issue of this Journal, Pu [3] has given an interesting construction of a nonmeasurable subset A of R such that for all intervals I in R. [Throughout this note, the symbol λ denotes Lebesgue outer measure on R or Haar outer measure on a general locally compact group.] This solves a problem stated in [2], p. 295, Exercise (18.30).
Pseudo-complemented modular semilattices
Authors: Cornish William H.
Published: April 2009

Chen and Grätzer [3], [4] have had great success in describing the properties of Stone lattices by way of representing them as triples. Their triple representation has recently been generalized to distributive pseudo-complemented lattices by Katriňák [6]. By varying the approach slightly Katriňák [5] has been able to obtain a triple representation for distributive pseudo-complemented semilattices that enabled him to characterize semilattices from distributive pseudo-complemented semilattices through to Stone lattices and Brouwer lattices in an elegant unified manner.
N-Semigroups and their translation semigroups
Authors: Tamura Takayuki
Published: April 2009

Ifhis a homomorphism of anN-semigroup onto anN-semigroupS′, thenhinduces a homomorphismhof the translation semigroup Λ(S) ofSinto Λ(S′) ofS′. We will study the relations between the structures ofS,S′ and Λ(S), Λ(S)′, and will introduce the specialized concepts ofN-semigroupsS. In particular, we will be interested in power-joined steady or endlessN-semigroups. Finally, we will consider admissibility of torsion abelian groups, that is, consider what torsion abelian group can be a structure group of a power-joined steadyN-semigroup.
Recursive constructions for equidistant permutation arrays
Authors: Schellenberg P. J. , Vanstone S. A.
Published: April 2009

An equidistant permutation array (EPA) is a ν ×rarray defined on anr-set,R, such that (i) each row is a permutation of the elements ofRand (ii) any two distinct rows agree in λ positions (that is, the Hamming distance is (r−λ)).

Such an array is said to have order ν. In this paper we give several recursive constructions for EPA's.

The first construction uses a resolvable regular pairwise balanced design of ordervto construct an EPA of order ν. The second construction is a generalization of the direct product construction for Room squares.

We also give a construction for intersection permutation arrays, which arrays are a generalization of EPA's.
Maximal quotient rings of prime group algebras. II Uniform right ideals
Authors: Hannah John
Published: April 2009

Suppose KG is a prime nonsingular group algebra with uniform right ideals. We show that G has no nontrivial locally finite normal subgroups. If G is soluble or residually finite, or if K has zero characteristic and G is linear, then the maximal right quotient ring of KG is simple Artinian.
Projectively torsion-free modules
Authors: Evans M. W.
Published: April 2009

A right R-module AR will be said to be right projectively torsion-free (AR is PTF) if for every a ∈ A, there exist subsets {a1, a2, …, an,} ⊆ A and {x1, x2, …, xn} ⊆ R such that a = Σni = 1 aixi and for all x ∈ R, if ax = 0 then xix = 0 for all 1 ≦ i ≦ n.
Embedding a semigroup of transformations
Authors: Symons J. S. V.
Published: April 2009

Let X be an arbitrary set and θ a transformation of X. One may use θ to induce an associative operation in Jx, the set of all mappings of X to itself as follows: . We denote the resulting semigroup by {Jx;θ) Magill (1967) introduced this structure and it has been studied by Sullivan and by myself.
Multiple points and Wallman compactifications
Authors: Njastad Olav
Published: April 2009

Banaschewski (1963) and Frink (1964) generalized the compactification procedure of Wallman to obtain Hausdorff compactifications of Tychonoff spaces. Numerous papers have been devoted to the problem whether all Hausdorff compactifications may be obtained in this way, and for many classes of compactifications an affirmative answer has been given. This note is a contribution in this direction. We show that if a (Hausdorff) compactification αX of X is the quotient space of a Wallman compactification γX in such a way that the set of multiple points of αX with respect to γX is not too large, then αX too is a Wallman compactification. The results are generalizations of earlier results of Steiner and Steiner (1968) and by the author (1966) for the special case that γX is the Stone Čech-compactification.
Regular graphs and stability
Authors: Holton D. A. , Grant Douglas D.
Published: April 2009

We show that a graph G is semi-stable at vertex v if and only if the set of vertices of G adjacent to v is fixed by the automorphism group of Gv, the subgraph of G obtained by deleting v and its incident edges. This result leads to a neat proof that regular graphs are semi-stable at each vertex. We then investigate stable regular graphs, concentrating mainly on stable vertex-transitive graphs. We conjecture that if G is a non-trivial vertex-transitive graph, then G is stable if and only if γ(G) contains a transposition, offering some evidence for its truth.
Arithmetic properties of certain functions in several variables II
Authors: Loxton J. H. , van der Poorten A. J.
Published: April 2009

If T = (tij) is an n x n matrix with non-negative integer entries, we define a transformation T: Cn → Cn by z' = Tz where

.
Inhomogeneous products of cyclic irreducible nonnegative matrices
Authors: Taylor G. C.
Published: April 2009

The now well-known Coale–Lopez theorem, and variants of it, state that, under certain conditions, the product of the first r members of an infinite inhomogeneous sequence of nonnegative matrices approaches, as r → ∞, the class of matrices which, apart from scalar multiples, have only one distinct column. The aim of the present paper is to lay down conditions under which such products approach the class of matrices which, apart from scalar multiples, have no more than d distinct columns. A stronger result is then obtained by considering stochastic matrices instead of just nonnegative ones.
Extension theorems for smooth functions on real analytic spaces and quotients by Lie groups and smooth stability
Authors: Wells G. S.
Published: April 2009

Extension theorems are proved for smooth functions on a coherent real analytic space for which local defining functions exist which are finitely determined in the sense of J. Mather, (1968), and for smooth functions invariant under the action of a compact lie groupG. thus providing the main step in the proof that smooth infinitesimal stability implies smooth stability in the appropriate categories. In addition the remaining step for the category ofCxG-manifolds of finite orbit type is filled in.
The root system of primes of a Hahn group
Authors: Anderson Marlow , Kenny Otis
Published: April 2009

Let δ be a root system and let V be the Hahn group of real-valued functions on δ Then δ can be order-embedded into P(δ), the root system of prime l-ideals of V. In this note we identify P(δ) in terms of δ without explicit reference to V, up to the convex subgroup structure of the additive groups of real closed η1-fields. In particular, we characterize the minimal prime 1-ideals of V in terms of δ by an ultrafilter construction which generalizes the well-known method when δ is trivially ordered.
Some multipliers on H1P(G)
Authors: Yamaguchi Hiroshi
Published: April 2009

In this paper, we define the function space H1P(G) on a LCA group G with the algebraically ordered dual, and construct a multiplier on H1P(G) similar to the one given by Gaudry (1968).
Relations between the amalgamation property and algebraic equations
Authors: Hule Harald
Published: April 2009

A variety B is called solutionally complete if any system of algebraic equations over an algebra A in B has a solution in A provided it is solvable in B and has at most one solution in any extension of A in B. B is called solutionally compatible if every solvable system of equations over an algebra in B is also solvable over any extension of that algebra. It is shown that solutional compatibility is equivalent with the amalgamation property and that a weaker form of the strong amalgamation property is sufficient but not necessary for equational completeness.
A converse to Lagrange's theorem
Authors: Berger T. R.
Published: April 2009

An integer n >0 is called a CLT-number if any group of order n has subgroups of order d for every divisor d of n. The Set of CLT-numbers n is characterized by properties of the prime factorization of n. In addition, if G has order dividing a CLT-number then the structure of G/CG(U) is given where U is a chief factor of G. As a consequence, it is shown that G is solvable of Fitting height at most 3.
Probabilities of very large deviations
Authors: Book Stephen A.
Published: April 2009

If {Xn: 1 ≦ n < ∞} are independent, identically distributed random variables having E(X1) = 0 and Var(X1) = 1, the most elementary form of the central limit theorem implies that P(n-½Sn≧ zn) → 0 as n → ∞, where Sn = Σnk=1 X,k, for all sequences {zn:1 ≧ n gt; ∞} for which zn → ∞. The probability P(n-½ Sn ≧ zn) is called a “large deviation probability”, and the rate at which it converges to 0 has been the subject of much study. The objective of the present article is to complement earlier results by describing its asymptotic behavior when n-½zn → ∞ as n → ∞, in the case of absolutely continuous random variables having moment-generating functions.
Mal'tsev conditions and spectra
Authors: Taylor Walter
Published: April 2009

Let J be a cofinite set of positive integers which contains 1. In (1973) I proved that the following condition on a variety (equational class) is Mal'tsev-definable: if υ ∈and υ is finite, then |υ| ∈J. This article contains some subsidiary results, concerned mainly with a more detailed description of these Mal'tsev conditions. Many of our results arose upon considering a recent article of W. D. Neumann (1978).
The Lie ring of symmetric derivations of a ring with involution
Authors: Jordan D. A.
Published: April 2009

In this paper we investigate how the ideal structure of the Lie ring of symmetric derivations of a ring with involution is determined by ideal structure of the ring.
A characterization of the semigroup of matrix units
Authors: Gelbaum Bernard R. , Schanuel Stephen
Published: April 2009

Let I be a set and let (I) denote the set consisting of the 0 matrix over I × I and the matrix units over I × I. Then for x, z in (I) and x≠0≠z, xyz≠0 has precisely one solution y. This and several other statements are shown to be equivalent characterizations of (I) regarded as a semigroup with zero.

1980 Mathematics subject classification (Amer. Math. Soc.): 20 M 10.
Groups of height four
Authors: Hales Alfred W.
Published: April 2009

If G and H are infinite groups then G is said to be larger than H (H≼G) if there are subgroups A of G, B of H, each of finite index, such that B is an epimorphic image of A. Pride (1979) showed that if G has finite ‘height’ with respect to the quasi-order ≼ then there are only finitely many (classes of) minimal groups H with H ≼G, and asked whether this were true without the minimality restriction on H. This paper gives a negative answer to his question by exhibiting a group G of height four with infinitely many (classes of) groups H satisfying H≼G.

1980 Mathematics subject classification (Amer. Math. Soc.): 20 E 99, 20 K 15.
Automorphisms of semigroups of continuous functions
Authors: Wood G. R.
Published: April 2009

Certain semigroups of continuous selfmaps of the closed unit interval are shown to have the property that all their automorphisms are inner. Contrary to expectation, certain other such semigroups do have outer automorphisms.

1980 Mathematics subject classification (Amer. Math. Soc.): primary 20 M 20; secondary 54 C 40.
Note on support-concentrated Borel measures
Authors: Adamski Wolfgang
Published: April 2009

Every τ-smooth Borel measure is support-concentrated. We shall prove in this note that the converse of this statement is not true, in general. Furthermore, we shall give some conditions assuring that a support-concentrated Borel measure be τ-smooth.

1980 Mathematics subject classification (Amer. Math. Soc.): 28 C 15.
On strong pseudoprimes in arithmetic progressions
Authors: Poorten A. J. van der , Rotkiewicz A.
Published: April 2009

A composite integer N is said to be a strong pseudoprime for the base C if with N – 1 = 2sd, (2, d) = 1 either Cd = 1, or C2r ≡ 1 (mod N) some r, 0 ≤ r < s. It is shown that every arithmetic progression ax+b (x = 0,1, …) where a, b are relatively prime integers contains an infinite number of odd strong pseudoprimes for each base C ≤ 2.

1980 Mathematics subject classification (Amer. Math. Soc.): 10 A 15.
Right inverse semigroups
Authors: Madhavan S.
Published: April 2009

In a recent paper of the author the well-known Vagner-Preston Theorem on inverse semigroups was generalized to include a wider class of semigroups, namely right normal right inverse semigroups. In an attempt to generalize the theorem to include all right inverse semigroups, the notion of μ – μi transformations is introduced in the present paper. It is possible to construct a right inverse band BM(X) of μ – μi transformations. From this a set AM(X) for which left and right units are in BM(X) and satisfying certain conditions is constructed. The semigroup AM(X) so constructed is a right inverse semigroup. Conversely every right inverse semigroup can be isomorphically embedded in a right inverse semigroup constructed in this way.

1980 Mathematics subject classification (Amer. Math. Soc.): 20 M 20.
Geometric representation of recurring sequences
Authors: Lekkerkerker C. G.
Published: April 2009

The asymptotic behaviour of second-order recurring seequences is studied.
Rudin synthesis on homogeneous Banach algebras
Authors: Jih Rong-Song , Wang Hwai-Chiuan
Published: April 2009

The main results of this article are (I) Let B be a homogeneous Banach algebra, A a closed subalgebra of B, and I the largest closed ideal of B contained in A. We assert that for some closed subalgebra J of B. Furthermore, under suitable conditions, we show that A is an R-subalgebra if and only if J is an R-subalgebra. A number of concrete closed subalgebras of a homogeneous Banach algebra therefore are R-subalgebras. For the definition of P(A) and that of an R-subalgebra, see the introduction in Section 1. (II) We give sufficient and necessary conditions for a closed subalgebra of Lp(G), 1 ≦ p ≦ ∞, to be an R-subalgebra.
On the Wall polynomials and the L-M-W conjectures
Authors: Andrews George E.
Published: April 2009

This paper provides explicit formulas for the Wall polynomials which arise in Wall's work on conjugacy classes in the unitary, symplectic and orthogonal groups. From these explicit formulas are easily derived six interesting limiting idetities incuding the two that arise in the Luszing-Macdonald Wall conjectures.
Generlized Fredholm transformations
Authors: Tacon D. G.
Published: April 2009

In an earlier paper we showed that the set ψ+ (X, Y) of super Tauberian transformations between two Banach spaces X and Y forms an open subset of B(X, Y) which is closed under perturbation by super weakly compact transformations. In this note we characterize a class dual to ψ+ (X, Y) which we denote by ψ-(X, Y). We show that T∈ψ+(X, Y) if and only if T′ ∈ ψ-(Y′, X′) and that T′∈ψ+(Y′, X′) if and only if T ∈ ψ-(X, Y) and provide standard and nonstandard characterizations of elements of ψ-(X, Y). These two classes thus play in some ways analogous roles to the sets of semi-Fredholm transforms ϕ+ (X, Y) and ϕ-(X, Y).

Moreover en forms an open subset of B(X, Y) closed under the taking of adjoints, under the taking of nonstandard hull extensions, and under perturbation by super weakly compact transformations.
The Euler-Maclaurin sum formula for a closed derivation
Authors: Miller John Boris
Published: April 2009

An operator form of the Euler-Maclaurin sum formula is obtained, expressing the sum of the Euler-Maclaurin infinite series in a closed derivation, whose spectrum is compact, not equal to {0}, and does not have 0 as a clusterpoint, as the difference between a summation operator and an antiderivation which is the local inverse of the derivation.
On translation-bounded measures
Authors: Robertson A. P. , Thornett M. L.
Published: April 2009

It is shown that a positive measure μ on the Borel subsets of Rk is translation-bounded if and only if the Fourier transform of the indicator function of every bounded Borel subset of Rk belongs to L2(μ).
The endomorphism near-rings of the symmetric groups of degree at least five
Authors: Fong Y. , Meldrum J. D. P.
Published: April 2009

The near-ring distributively generated by the semigroup of all endomorphisms of Sn, the symmetric group of degree n, for n ≥ 5, is close to being the near-ring of all mappings from Sn to itself respecting the identity. In this paper, the structure of these near-rings is studied in detail. In particular, addition and multiplication rules for the elements given in canonical form are determined. A complete list of all right ideals, left ideals, right invariant and left invariant subgroups is given.
Prime ideal characterization of chain based lattices
Authors: Swamy U. Maddna , Rao G. C. , Manikyamba P.
Published: April 2009

Epstein and Horn, in their paper ‘Chain based lattices’, characterized P1-lattices, and P2-lattices in terms of their prime ideals. But no such prime ideal characterization for P0-lattices was given. Our main aim in this paper is to characterize P0-lattices in terms of their prime ideals. We also give a necessary and sufficient condition for a P-algebra to be a P0-lattice (and hence a P2-lattice).
Graphs, groups and pseudo-similar vertices
Authors: Kocay W. L.
Published: April 2009

Vertices u0, u1, …, uk−1 of a graph X are mutually pseudo-similar if X − u0 ≌ X − u1 ≌ … ≌ X − uk−1, but no two of the vertices are related by an automorphism of X. We describe a method for constructing graphs with a set of k≥2 mutually pseudo-similar vertices, using a group with a special subgroup. We show that in all graphs with pseudo-similar vertices, the vertices are pseudo-similar due to the action of a group on the cosets of some subgroup.
Denjoy-Bochner almost periodic functions
Authors: Pal B. K. , Mukhopadhyay S. N.
Published: April 2009

The special Denjoy-Bochner integral (the D*B-integral) which are generalisations of Lebesgue-Bochner integral are discussed in [7, 6, 5]. Just as the concept of numerical almost periodicity was extended by Burkill [3] to numerically valued D*- or D-integrable function, we extend the concept of almost periodicity for Banach valued function to Banach valued D*B-integrable function. For this purpose we introduce as in [3] a distance in the space of all D*B-integrable functions with respect to which the D*B-almost periodicity is defined. It is shown that the D*B-almost periodicity shares many of the known properties of the almost periodic Banach valued function [1, 4].
On the reconstruction of a star-shaped body from its “half-volumes”
Authors: Campi Stefano
Published: April 2009

The problem is the reconstruction of the shape of an object, whose shell is a surface star-shaped with respect to a point 0, from the knowledge of the volume of every “half-object” obtained by taking any plane through 0. Conditions for the existence and uniqueness of the solution are given. The main result consists in showing that any uniform a-priori bound on the mean curvature of the shell reestablishes continuous dependence on the data for bodies satisfying a certain symmetry condition.
Small varieties of finite semigroups and extensions
Authors: Pin Jean-Eric , Straubing Howard , Therien Denis
Published: April 2009

We find the atoms of certain subclasses of varieties of finite semigroups and the corresponding varieties of languages. For example we give a new description of languages whose syntactic monoids are R-trivial and idempotent. We also describe the least variety containing all commutative semigroups and at least one non-commutative semigroup. Finally we extend to varieties of finite semigroups some classical results about semilattice decomposition of semigroups.
Some covering theorems for locally inverse semigroups
Authors: McAlister D. B.
Published: April 2009

A regular semigroup S is said to be locally inverse if each local submonoid eSe, with e an idempotent, is an inverse semigroup. In this paper we apply known covering theorems for inverse semigroups and a covering theorem for locally inverse semigroups due to the author to obtain some covering theorems for locally inverse semigroups. The techniques developed here permit us to give an alternative proof for, and sligbt strengthening of, an important covering theorem for locally inverse semigroups due to F. Pastijn.
A homotopy type of a p–group with cyclic centre
Authors: Conlon S. B.
Published: April 2009

Let G be a p–group with cyclic L(G) = Z. Then L(G) = {Z < H ≦ G|H′ ∩ Z = (1)}, a poset ordered under inclusion. Then the associated simplicial complex |L(G)| is homotopic to a bouquet of spheres. A subgroup E of G is called a CES if CG (E) = Z = L(E) and if E/Z is elementary. Then |L(G)| is homotopic to the one-point union of the |L(E)| for all CES's E in G. If |E/Z| = p2n then |L(E)| is homotopic to a one-point union of pn2 (n– 1)-spheres.
Uniform convergence of regularization methods for Fredholm equations of the first kind
Authors: Groetsch C. W.
Published: April 2009

For Fredholm equations of the first kind with continuous kernels we investigate the uniform convergence of a general class of regularization methods. Applications are made to Tikhonov regularization and Landweber's iteration method.
On a convergence test of Hardy-Littlewood's type for fourier series
Authors: Hsiang Fu Cheng
Published: April 2009

Let ф(t) be an even function integrable in the Lebesgue sense and periodic with period 2п. Let Write By an indirect method based on the method of Riesz summability for the Fourier series, the author has established the following convergence test for the oscifiating series Σan. The theorem is as follows:

THEOREM A [1]. If, for some Δ > 0 as t → +0 andthen фan converges to the sums = 0. Here K is an absolute constant independent of n.
On perfect and extreme forms
Authors: Scott P. R.
Published: April 2009

Let(х) =(x1,x2, …xn) = ΣiΣiaij,xixf(aij= aij) be a positive quadratic form with determinantD, and letMbe the minimum offor integral x ≠ 0. Thenattains the valueMfor a finite number of integral x = ±mk( k = 1, …, s) called itsminimal vectors.
Categories of certain minimal topological spaces
Authors: Berri Manuel P.
Published: April 2009

The main purpose of this paper is to discuss the categories of the minimal topological spaces investigated in [1], [2], [7], and [8]. After these results are given, an application will be made to answer the following question: If is the lattice of topologies on a set X and is a Hausdorff (or regular, or completely regular, or normal, or locally compact) topology does there always exist a minimal Hausdorff (or minimal regular, or minimal completely regular, or minimal normal, or minimal locally compact) topology weaker than ?
On projective-symmetric spaces
Authors: Gupta Bandana
Published: April 2009

This paper deals with a type of Remannian space Vn (n ≧ 2) for which the first covariant dervative of Weyl's projective curvature tensor is everywhere zero, that is where comma denotes covariant differentiation with respect to the metric tensor gij of Vn. Such a space has been called a projective-symmetric space by Gy. Soós [1]. We shall denote such an n-space by ψn. It will be proved in this paper that decomposable Projective-Symmetric spaces are symmetric in the sense of Cartan. In sections 3, 4 and 5 non-decomposable spaces of this kind will be considered in relation to other well-known classes of Riemannian spaces defined by curvature restrictions. In the last section the question of the existence of fields of concurrent directions in a ψ will be discussed.
Inversive semirings
Authors: Karvellas Paul H.
Published: April 2009

A semiring (S, +,·) is a nonempty set S, endowed with associative operations of addition and multiplication, such that the multiplicative semigroup (S, ·) distributes over the addition. That is: x(y +z) = xy + xz and (x + y)z = xz + yz for all x, y and z in S. A topological semiring is a semiring, defined on a Hausdorff space, such that both of the operations are jointly continuous.
Kernels of inverse semigroup homomorphisms
Authors: Scheiblich H. E.
Published: April 2009

The aim of this note is to give an analogue, for an inverse semigroup S, of the theorem for a group G which says that if G is the set of normal subgroups of G, then the map N → (N) = {(a, b) ∈ G x G: ab-1 ∈ N}; for N ∈ G is a 1: 1 order preserving map of G onto ∧(G), the lattice of congruences on G. It will be shown that if E is the semilattice of idempotents of S, P = {E: α ∈ J} is a normal partition of E, and K is a certain collection of self conjugate inverse subsemigroups of S, then the map K →(X) = {(a, b)∈ S x S: a-la, b-1b∈ Eα for some α ∈ J and ab-l ∈ K) for K e Jf is a 1:1 map of K onto the set of congruences on S which induce P.
Completely rigid graphs
Authors: Symons J. S. V.
Published: April 2009

In general, a structure is called rigid if it admits only the trivial structure preserving transformations. Of course, what is trivial depends on the context. In [7] the authors understand by a rigid graph one which has the property that the only edge preserving transformation of the vertices is the identity map. In other contexts, however, it is convenient to regard the constant maps as trivial also. (See [2] where a topological space is given which admits as continuous transformations only the identity and the constants.) The purpose of this note is to construct graphs rigid in the later sense; we call them completely rigid.
Complex inversion theorems for generalized Stieltjes transforms
Authors: Byrne Angelina , Love E. R.
Published: April 2009

In this paper we seek to establish some “complex inversion formulae” for the generalized Stieltjes transformfor all s in the cut plane, supposing thatpis any complex number except zero and the negative integers. The “cut plane” means all complex numbers except those which are negative real or zero.
Bernstein and Jackson theorems for the Heisenberg group
Authors: Giulini Saverio
Published: April 2009

We describe on the Heisenberg group Hn a family of spaces M(h, X) of functions which play a role analogous to the trigonometric polynomials in Tn or the functions of exponential type in Rn. In particular we prove that for the space M(h, X), Jackson's theorem holds in the classical form while Bernstein's inequality hold in a modified form. We end of the paper with a characterization of the functions of the Lipschitz space by the behavior of their best approximations by functions in the space M(h, X).
Some direct and inverse theorems in approximation of functions
Authors: Mohapatra R. N. , Russell D. C.
Published: April 2009

The paper is concerned with the determination of the degree of convergence of a sequence of linear operators connected with the Fourier series of a function of class Lp (p > 1) to that function and some inverse results in relating the convergence to the classes of functions. In certain cases one can obtain the saturation results too. In all cases Lp norm is used.
Extensions of a theorem of Jordan on primitive permutation groups
Authors: Liebeck Martin W.
Published: April 2009

Let G be a primitive permutation group of finite degree n containing a subgroup H which fixes k points and has r orbits on Δ, the set of points it moves. An old and important theorem of Jordan says that if r = 1 and k ≥ 1 then G is 2-transitive; moreover if H acts primitively on Δ then G is (k + 1)-transitive. Three extensions of this result are proved here: (i) if r = 2 and k ≥ 2 then G is 2-transitive, (ii) if r = 2, n > 9 and H acts primitively on both of its two nontrivial orbits then G is k-primitive, (iii) if r = 3, n > 13 and H acts primitively on each of its three nontrivial orbits, all of which have size at least 3, then G is (k − 1)-primitive.
Strongly reversible manifolds
Authors: Hocking J. , Doyle P.
Published: April 2009

The results here concern bijective continous functions from one connected separable n-manifold M to another N. If M has the property that every such function is necessarily a homeomorphism, then M is said to be strongly reversible. Strongly reversible manifolds having only compact boundary components are completely charaterized.
Some Inequalities arising from a Banach algebra norm
Authors: Russell A. M.
Published: April 2009

We derive some specific inequalities involving absolutely continuous functions and relate them to a norm inequality arising from Banach algebras of functions having bounded k th variation.
Bipackings of pairs into triples, and isomorphism classes of small bipackings
Authors: Stanton R. G. , Rogers M. J. , Quinn R. F. , Cowan D. D.
Published: April 2009

The (2, 3, ν) bipacking number is determined for all integers ν, and the number of non-isomorphic bipackings is found for small values of ν. The general solution for lambada packings of pairs into triples is deduced from the results for λ = 1 and λ = 2.
Fractional iteration near a fixpoint of multiplier 1.
Authors: Baker I. N.
Published: April 2009

An analytic function f(z) is said to have a fixpoint ξ ≠ ∞ of multiplier 1 if f(ξ) = ξ, f'(ξ) = 1. The function then has an expansion .
On linear p-groups
Authors: Wong W. J.
Published: April 2009

A quasi-permutation group of degree n was defined in [3] to be a finite group with a faithful representation of degree n whose character has only non-negative rational integral values. If G is such a group, then the following simple properties of permutation groups of degree n were proved to hold also for G:

(i) the order of G is a divisor of the order of the symmetric group Sn of degree n; and (ii) if G is a p-group and n < p2, then G has exponent at most p and derived length at most 1 (i.e. G is elementary Abelian).
On products of vector measures
Authors: Bandyopadhyay U. K.
Published: April 2009

Products of positive measures play a very important role in analysis. The purpose of this paper is to construct a theory of products of two measures taking values in two (possibly different) Banach spaces. A Fubini theorem is obtained which generalizes the Fubinitheorem for the Bochner integral (Dunford and Schwartz (1958), Theorem 9, page 190), and hence also the classical result.

We use the theory of vector integration presented in Dinculeanu (1967). Our arguments rely upon a standard sort of application of the dominated convergence theorem (cf. Dunford and Schwartz (1958), Theorem 9, page 190), and therefore do not appear to generalize to any theory of integration where this theorem is lacking (e.g. Bartle (1956)).
On absolute riesz summability of Fourier series
Authors: Dikshit G. D.
Published: April 2009

Let and .

In 1951 Mohanty proved the following theorem: .

In this paper a general theorem on summability |R,l (w), 1 | of Σ An(x) has been given which improves upon Mohanty's result in different ways (see Corollaries 1, 2 and 3) and it is also shown that some of the results of this note are the best possible.
Integral bases of dihedral numberfields. I
Authors: Ledermann Walter , Van Der Ploeg Carol
Published: April 2009

A dihedral number field is a non-normal quartic field K which possesses a quadratic subfield k. That is, for some integer α of k. Integral bases of these fields were known by Sommer (1907), but the form in which they were known was of little use for computational purposes. In this paper we construct integral bases of those dihedral fields with quadratic subfield of the form , d ≢ 1 (mod 8), for which only rational quantities need be determined. Although the general theory may easily be generalized to the case d ≡ 1 (mod 8), the actual determination of integral bases in this case is left to a later paper.
Some properties of periodic modules
Authors: Bessenrodt Christine
Published: April 2009

In this paper periodic modules over group rings and algebras are considered. A new lower bound for the p-part of the rank of a periodic module with abeian vertex is given, and results on periodic modules with odd/even and small periods are obtained. In particular, it is shown that characters afforded by periodic lattices of odd period satisfy strong properties and that irreducible periodic lattices are always of even period.
Nil ideals of power series rings
Authors: Puczyłowski Edmund R.
Published: April 2009

Some characterizations of nil radical and nil semisimple power series rings are given. The upper nil radical of a power series ring in an uncountable set of non-commutative indeterminates is completely described.
Definability problems in elementary topology
Authors: Yasugi Mariko
Published: April 2009

The elementary part of general topology is carried out in a system which is based on the arithmetically definable theory of the reals with definitions by definable induction (DDI), where a formal object is said to be definable if the quantifiers are restricted to the rationals, the names of the base members and the elements of the spaces.
A remark on convergence of test functions
Authors: Moss W. F.
Published: April 2009

In this note it is shown in the most frequently encountered spaces of test functions in the theory of generalized functions that the customary definitions of convergence are equivalent to apparently much weaker definitions. For example, in the space g the condition of uniform convergence of the functions together with all derivatives (which appears in the definition of convergence) is equivalent to the condition of pointwise convergence of the functions alone. Thus verification of convergence is simplified somewhat.
Integral closure of some co-ordinate rings
Authors: Smith David J.
Published: April 2009

In this paper, some methods are developed for obtaining explicitly a basis for the integral closure of a class of coordinate rings of algebraic space curves.

The investigation of this problem was motivated by a need for examples of integrally closed rings with specified subrings with a view toward examining questions of unique factorization in them. The principal result, giving the elements to be adjoined to a ring of the form k[x1, …,xn] to obtain its integral closure, is limited to the rather special case of the coordinate ring of a space curve all of whose singularities are normal. But in numerous examples where the curve has nonnormal singularities, the same method, which is essentially a modification of the method of locally quadratic transformations, also gives the integral closure.
Right invariant integrals on locally compact semigroups
Authors: Michael J. H.
Published: April 2009

An integral on a locally compact Hausdorff semigroup ς is a non-trivial, positive, linear functional μ on the space of continuous real-valued functions on ς with compact supports. If ς has the property: (A) for each pair of compact sets C, D of S, the set is compact; then, whenever and a ∈ S, the function fa defined by is also in . An integral μ on a locally compact semigroup S with the property (A) is said to be right invariant if for all j ∈ and all a ∈ S.
On the radical of a category
Authors: Kelly G. M.
Published: April 2009

In [1] the concept of completeness of a functor was introduced and, in the cse of additive * categories and and an additive functor T: → , a criterion for T (supposed surjective) to be complete was given in terms of the kernel of T: this was that for each object A of the ideal A should be containded in the (Jacobson) radical of A. (The meaning of this notation and nomemclature is recalled in § 2 below). The question arises whether in any additive category there is a greatest ideal with this property, so that the canonical functor T: → / is in some sense the coarsest that faithfully represents the objects (but not the maps) of .
The solutions to two problems on permutational products
Authors: Allenby R. B. J. T.
Published: April 2009

The two problem, both raised in the literature, are: (I) Is there, amongst all the permutational products (p.p.s.) on the amalgam= (A, B; H) at least one which is a minimal generalized regular product? (II) If one of the p.p.s. onis isomorphic to the generalized free product (g.f.p.)FonUare they all? We answer both of them negatively.
Boundary behaviour of meromorphic functions along Green's lines
Authors: Niimura Mikio
Published: April 2009

In this note we study the boundary behavior of meromorphic functions in bounded plane regions along Green's lines. As applications we obtatin extensions of Lohwater's theorems and Seidel's theorems concerning radial cluster sets.