bluuebunny/crossref_metadata_2025 huggingface dataset:
On the relationship between ordinary thin sets and full-thin sets
Authors: Hwang J. S. , Jackson H. L.
Published: April 2009

In this work we demonstrate that if Ω ⊂ Rn (n ≧ 3) is either a half space or a unit ball, and if E ⊂ ω then E is an ordinary thin set at a boundary point of Ω (including the point at infinity if Ω is a half space) if and only if it is a full-thin set at the corresponding Kuramochi boundary point of Ω. The case for n = 2 has already been considered in an earlier work.

1980 Mathematics subject classification (Amer. Math. Soc.): 31 B 05.
On odd perfect numbers (II), multiperfect numbers and quasiperfect numbers
Authors: Cohen Graeme L.
Published: April 2009

Let N be a positive integer. This paper is concerned with obtaining bounds for(p prime), when N is an odd perfect number, a multiperfect number, or a quasiperfect number, under assumptions on the existence of such numbers (where none is known) and whether 3 and 5 are divisors. We argue that our new lower bounds in the case of odd perfect numbers are not likely to be significantly improved further. Triperfect numbers are investigated in some detail, and it is shown that an odd triperfect number must have at least nine distinct prime factors.

1980 Mathematics subject classification (Amer. Math. Soc.): 10 A 20.
Major arcs in the four cubes problem
Authors: Szekeres George
Published: April 2009

There is an old conjecture that every integer can be decomposed into four (positive or negative) perfect cubes. More specifically one would like to know the asymptotic number of solutions of when a large bound N is placed on the parts mi. Using the circle method it is shown that the number of such representations of n when N → ∞ is asymptotically equal to C(n). N for a certain positive constant C(n), provided that the contribution of the minor arcs can be neglected.
Transcendence measures for exponentials and logarithms
Authors: Waldschmidt Michel
Published: April 2009

In the present paper, we derive transcendence measures for the numbers log α,eβ, αβ, (log α1)/(log α2) from a previous lower bound of ours on linear forms in the logarithms of algebraic numbers.
On some unconventional problems on the divisors of integers
Authors: Erdös P. , Hall R. R.
Published: April 2009

In this note a number of related problems about divisors are studied, and partial solutions obtained by elementary means. The problems are rather unconventional and seem to suggest interesting developments.
The Markoff spectrum of an algebraic number field
Authors: Woods A. C.
Published: April 2009

The Markoff spectrum of an algebraic number field is defined and it is proved that the spectrum of Q(✓5) is not discrete.
A diophantine equation over a function field
Authors: Cassels J. W. S.
Published: April 2009

Let x0, x1, x2, x3 be polynomials in a variable t and with coefficients in a field k of character of characteristic 0. If and , then x0 = x1 = x2 = x3 = 0. This partially answers a question of Pjatetskii-Š;apiro and Šafarevič about the K3-surface . The proof uses a technique of M. R. Christie.
From cyclic algebras of quadratic fields to central polynomials
Authors: Taussky Olga
Published: April 2009

A link between norms from quadratic fields and —det (AB−BA) for 2 × 2 matrices is reformulated via central polynomials and thereby generalized.
On some properties of group rings
Authors: Karpilovsky G.
Published: April 2009

Let Out (RG) be the set of all outer R-automorphisms of a group ring RG of arbitrary group G over a commutative ring R with 1. It is proved that there is a bijective correspondence between the set Out (RG) and a set consisting of R(G × G)-isomorphism classes of R-free R(G × G)-modules of a certain type. For the case when G is finite and R is the ring of algebraic integers of an algebraic number field the above result implies that there are only finitely many conjugacy classes of group bases in RG. A generalization of a result due to R. Sandling is also provided.
A fixed point theorem for non-expansive, condensing mappings
Authors: Chandler Eric , Faulkner Gary
Published: April 2009

A lemma is obtained which guarantees that non-expansive mappings on contractive spaces have fixed points. An example shows that Schauders's fixed point theorem cannot be extended to contractive spaces, but a theorem for contractive spaces, analogous to a result of B. N. Sadovskii on convex spaces, is derived from the lemma. Finally, some local results for ε-chainable contractive spaces are given.
Bhaskar Rao designs from cyclotomy
Authors: Street Deborah J.
Published: April 2009

A Bhaskar Rao design is obtained from the incidence matrix of a partially balanced incomplete block design with m associate classes by negating some elements of the matrix in such a way that the inner product of rows α and β is ci if α and β are ith associates. In this paper we use nested designs constructed from unions of cyclotomic classes to give Bhaskar Rao designs.
On a method for constructing Bergman kernels
Authors: Azzam A. , Kreyszig E.
Published: April 2009

We establish a method of constructing kernels of Bergman operators for second-order linear partial differential equations in two independent variables, and use the method for obtaining a new class of Bergman kernels, which we call modified class E kernels since they include certain class E kernals. They also include other kernels which are suitable for global representations of solutions (whereas Bergman operators generally yield only local representations).
Transposable and symmetrizable matrices
Authors: McCarthy David , McKay Brendan D.
Published: April 2009

A square matrix A is transposable if P(RA) = (RA)T for some permutation matrices p and R, and symmetrizable if (SA)T = SA for some permutation matrix S. In this paper we find necessary and sufficient conditions on a permutation matrix P so that A is always symmetrizable if P(RA) = (RA)T for some permutation matrix R.
Positive points in polar lattices II
Authors: Worley R. T.
Published: April 2009

The problem of positive points in polar lattices, discussed by Hossain and Worley for the distance functions Ft(x1, x2) = │x1│+│tx2 │ and , is considered for a general distance function F. Best possible results are obtained.
Six pairwise orthogonal latin squares of order 69
Authors: Zhu L.
Published: April 2009

In this note it is proved that a BIB(ν, k, l) implies N(ν −4) ≧ min (N(k–2), N(k–1) –1, N(k)–1) and that N(69)≧6.
Arithmetic properties of certain recurrence sequences
Authors: Perelli A. , Zannier U.
Published: April 2009

A classical theorem states that if a polynomial with integral coefficients is an in mth power for every integral value of its argument, then it is the mth power of a polynomial with integral coefficients.

In this paper we deal with analogous problems concerning functions which arise as solutions of recurrence equations with constant coefficients.
Pair-packings and projective planes
Authors: Stinson D. R.
Published: April 2009

An (n + 1, n2 + n + 1)-packing is a collection of blocks, each of size n + 1, chosen from a set of size n2 + n + 1, such that no pair of points is contained in more than one block. If any two blocks contain a common point, then the packing can be extended to a projective plane of order n, provided the number of blocks is sufficiently large. We study packings which have a pair of disjoint blocks (such a packing clearly cannot be extended to a projective plane of order n). No such packing can contain more than n2 + n/2 blocks. Also, if n is the order of a projective plane, then we can construct such a packing with n2 + 1 blocks.
Pairwise relatively prime solutions of linear diophantine Equations
Authors: Worley R. T.
Published: April 2009

It is shown that if a1,…,am are relatively prime integers then for every integer n the equation has infinitely many solutions in pairwise relatively prime integers x1,…,xm.
Critical associated metrics on contact manifolds
Authors: Blair David E.
Published: April 2009

Defining a function on the set of all Riemannian metrics associated to a contact form on a compact manifold by taking the integral of the Ricci curvature in the direction of the characteristic vector field, it is shown that on a compact regular contact manifold the only critical points of this function are the metrics for which the characteristic vector field generates a group of isometrics.
Calculus in f-algebras
Authors: Beukers F. , Huijsmans C. B.
Published: April 2009

Let A be an Archimedean, uniformly complete, semiprime f-algebra and F(X1,…Xn) ∈ R+ [X1,…Xn] a homogeneous polynomial of degree p (p∈ N). It is shown that (F(u 1…unn))1/p exists in A+ for all u1…un ∈ A+.
Jakubowski starlike integral operators
Authors: Kumar Vinod , Shukla S. L.
Published: April 2009

Let S(m, M) be the set of functions regular and satisfying │zf′(z)/f(z) – m│< M in │z│ <1, where│m –│ <M;≦ m; and let S*(p) be the set of starlike functions of order p, 0≦ p <1. In this paper we obtain integral operators which map S(m, M) into S(mM) and S* (p) × S(mM) into S*(p). Our results improve and generalize many recent results.
Two further Ramanujan pairs
Authors: Hirschhorn Michael D.
Published: April 2009

In a recent article, George E. Andrews considers a generalization of the Rogers-Ramanujan identities involving a pair of infinite sequences of positive integers, which he calls a Ramanujan pair. He lists the known Ramanujan pairs and conjectures that there are no more. The object of this note is to establish the existence of two further Ramanujan pairs.
On the law of the iterated logarithm in the infinite variance case
Authors: Maller R. A.
Published: April 2009

The main purpose of the paper is to give necessary and sufficient conditions for the almost sure boundedness of (Sn – αn)/B(n), where Sn = X1 + X2 + … + XmXi being independent and identically distributed random variables, and αnand B(n) being centering and norming constants. The conditions take the form of the convergence or divergence of a series of a geometric subsequence of the sequence P(Sn − αn > a B(n)), where a is a constant. The theorem is distinguished from previous similar results by the comparative weakness of the subsidiary conditions and the simplicity of the calculations. As an application, a law of the iterated logarithm general enough to include a result of Feller is derived.
Nonexistence of an extremal graph of a certain type
Authors: Stanton R. G. , Seach S. T. E. , Cowan D. D.
Published: April 2009

Cubic Moore graphs of diameter k on 3.2k−2 vertices do not exist for k > 2. This paper exhibits the first known case of nonexistence for generalized cubic Moore graphs when the number of vertices is just less than the critical number for a Moore graph: the generalized Moore graph on 44 vertices does not exist.
A generalization of the Hall semigroup of a band
Authors: Szendrei Mária B.
Published: April 2009

Let E be a band and ε a compatible partition on it. If S is an orthodox semigroup with band of idempotents E such that there exists a congruence on S inducing the partition ε then we define a homomorphism of S into a Hall semigroup whose kernel is the greatest congruence on S inducing the partition ε. On the other hand, we define a subsemigroup of the Hall semigroup WE possessing the property that S is an othodox semigroup with band of idempotents E which has a congruence inducing ε if and only if the range of the Hall homomoprhism of S into WE is contained in .
Some cancellation theorems
Authors: Shastri A. R.
Published: April 2009

If G, H and B are groups such that G × B ≃ H × B, G/[G, G]. Z(G) is free abelian and B is finitely generated abelian, then G ≃ H. The equivalence classes of triples (Vξ,A) where Vand A are finitely generated free abelian groups and ξ: V⊗ V → A is a bilinear form constitute a semigroup B undera natural external orthogonal sum. This semigroup B is cancellative. A cancellation theorem for class 2 nilpotent groups is deduced.
Some remarks on a One-dimensional skip-free process with repulsion
Authors: Pakes Anthony G.
Published: April 2009

We extend the results obtained by Hines and Thompson for a Markov chain which has a single reflecting barrier at the origin, nearest neighbour transitions and which moves from {j} to {j + l} with probability j/(j + 1). Martingale limit theorems are used to work out an asymptotic theory for a general class of such chains for which the probability above has the form l – λ(j) = O>λ(j)>1 (j ∈N),λ(j)→ O (j →∞)and Σλ(j)=∞ We discuss the case where the last sum is finite and some alternative versions of the general case.
Fixed points of certain involutions in Banach spaces
Authors: Khan M. S. , Imdad M.
Published: April 2009

Some results on fixed points of certain involutions in Banach spaces have been obtained, and whence a few coincidence theorems are also derived. These are indeed generalization of previously known results due to Browder, Goebel-Zlotkiewicz and Iséki. Illustrative examples are also given.
Positive derivations on partially ordered strongly regular rings
Authors: Hansen D. J.
Published: April 2009

The author presents a proof that a partially ordered strongly regular ring S which has the additional property that the square of each member of S is greater than or equal to zero cannot have nontrivial positive derivations.
On semi inner product spaces over quaternions
Authors: Sen Dilip Kumar
Published: April 2009

In this note semi inner product spaces over quaternions are studied. We investigate the properties of complex strict convexity over C, left and right Q-complex strict convexity over Q, and left and right quaternion strict convexity. Finally we discuss the permanence properties with respect to formation of products.
Extension and inversion of extended orthomorphisms on Riesz spaces
Authors: Duhoux Michel , Meyer Mathieu
Published: April 2009

Let E be an Archimedean Riesz space and let Orth∞(E) be the f-algebra consisting of all extended orthomorphisms on E, that is, of all order bounded linear operators T:D→E, with D an order dense ideal in E, such that T(B∩D) ⊆ B for every band B in E. We give conditions on E and on a Riesz subspace F of E insuring that every T ∈ Orth∞(F) can be extended to some ∈ Orth∞(E), and we also consider the problem of inversing an extended orthomorphism on its support. The same problems are also studied in the case of σ-orthomorphisms, that is, extended orthomorphisms with a super order dense domain. Furthermore, some applications are given.
Invex functions and duality
Authors: Craven B. D. , Glover B. M.
Published: April 2009

For both differentiable and nondifferentiable functions defined in abstract spaces we characterize the generalized convex property, here called cone-invexity, in terms of Lagrange multipliers. Several classes of such functions are given. In addition an extended Kuhn-Tucker type optimality condition and a duality result are obtained for quasidifferentiable programming problems.
Continuous programming containing arbitrary norms
Authors: Chandra S. , Craven B. D. , Husain I.
Published: April 2009

Optimality conditions and duality results are obtained for a class of cone constrained continuous programming problems having terms with arbitrary norms in the objective and constraint functions. The proofs are based on a Fritz John theorem for constrained optimization in abstract spaces. Duality results for a fractional analogue of such continuous programming problems are indicated and a nondifferentiable mathematical programming duality result, not explicitly reported in the literature, is deduced as a special case.
Measures coniques sur un espace de Banach ou son dual
Authors: Becker Richard
Published: April 2009

Si E et F sont deux espaces vectoriels en dualité séparante, M+(E, F) désigne le cône des mesures coniques positives sur E mis en dualité avec F, c'est à dire le cônes des formes postives sur le treillis de fonctions sur E engendré par F. Ce sont des objets plus généraux que les mesures cylindriques admettant des moments finis d'ordre un.

On part d'abord d'une mesure conique représentée par une mesure de Radon sur le complété faible de E et on donne des critéres (par exemple R.N.P.) pour qu'elle le soit sur l'espace E lui-même.

On étudie ensuite les cônes faiblement complets saillants (classe L) contenus dans un espace de Banach ou dans le dual d'un espace de Fréchet F; on montre notamment qu' un cône faiblement fermé contenu dans F′ est dans Lsi son polaire dans F est positivement engendré.

Si B est un espace de Banach et 11 ⊄ B, on cherche à prologner une μ ∈ M+(B′, B) en un élement de M+ (B′, B″). On montre également que, si X est un convexe compact, toute fonction vérifiant le calcul barycentrique sur X est continue sur des ensembles fixes que l'on précise.

Enfin on donne des conditions (de type bornologique) sur un e.l.c.s E, permettant d'interpréter une μ ∈ M+ (E, E′) comme une mesure conique sur un espace normé.
Multipliers of Banach valued function spaces
Authors: Lai Hang-Chin
Published: April 2009

Let A be a commutative Banach algebra with identity of norm 1, X a Banach A-module and G a locally compact abeian group with Haar measure. Then the multipliers from an A -valued function algebra into an X-valued function space is studied. We characterize the multiplier spaces as the following isometrically isomorphic relations under some appropriate conditions:
Remainder term estimates in a conditional central limit theorem for integer-valued random variables
Authors: Quine M. P.
Published: April 2009

A Berry-Esseen type result is given for the conditional distribution of a weighted sum of i.i.d. integer-valued r.v.'s given that their unweighted sum equals its expectation. The examples include the case of sampling without replacement from a finite population.
Triangles in a complete chromatic graph
Authors: Goodman A. W.
Published: April 2009

Suppose that in a complete graph on N points, each edge is given arbitrarily either the color red or the color blue, but the total number of blue edges is fixed at T. We find the minimum number of monochromatic triangles in the graph as a function of N and T. The maximum number of monochromatic triangles presents a more difficult problem. Here we propose a reasonable conjecture supported by examples.
Generalized implication equation languages
Authors: Foo Norman Y. , Riley Roslyn B.
Published: April 2009

The calculus for equational implication languages given by Selman is generalized to handle the logical equivalent if the if…then…else… construct of high level programming languages. The relevance of these results to current investigations in the algebraic specifications of data types is discussed.
Automorphisms of nilpotent groups of class two with small rank
Authors: Fournelle Thomas A.
Published: April 2009

Rational abelian groups, that is, torsion-free abelian groups of rank one, are characterized by their types. This paper characterizes rational nilpotent groups of class two, that is, nilpotent groups of class two in which the center and central factor group are direct sums of rational abelian groups. This characterization is done according to the types of the summands of the center and the central factor group. Using these types and some cohomological techniques it is possible to determine the automorphism group of the nilpotent group in question by performing essentially matrix computations.

In particular, the automorphism groups of rational nilpotent groups of class two and rank three are completely described. Specific examples are given of semicomplete and pseudocomplete nilpotent groups.
Another characterisation of Pfaffian bipartite graphs
Authors: Little Charles H. C.
Published: April 2009

It has been known for over twenty years that every planar graph is Pfaffian. Recently a characterisation of planar graphs in terms of strict maximal odd rings has been discovered. This paper attempts to elucidate the connection between the Pfaffian property and planarity by characterising Pfaffian bipartite graphs in terms of maximal odd rings.
Certain homomorphisms of the lattice of varieties of completely simple semigroups
Authors: Petrich Mario , Reilly Norman R.
Published: April 2009

Completely simple semigroups form a variety, , of algebras with the operations of multiplication and inversion. It is known that the mapping , where is the variety of all groups, is an isomorphism of the lattice of all subvarieties of onto a subdirect product of the lattice of subvarieties of and the interval . We consider embeddings of into certain direct products on the above pattern with rectangular bands, rectangular groups and central completely simple semigroups in place of groups.
Stochastic compactness and point processes
Authors: de Hann L. , Resnick S. I.
Published: April 2009

We show that stochastic compactness of partial sums with no normal limit distribution corresponds to stochastic compactness of the point processes generated by the observations so that there exist joint limit distributions for the sample sums and the sample maxima.
Partial automorphisms and the reconstruction conjecture
Authors: Kocay W. L.
Published: April 2009

Let Γ be a graph with isomorphic subgraphs G and H, and let θ: G → H be an isomorphism. If θ can be extended to an automorphism of Γ, we call θ a partial automorphism of Γ.

We consider the application of partial automorphisms to the graph reconstruction conjecture, in particular, to the problem of reconstructing graphs with two vertices of degree k – 1 and the remaining vertices of degree k.
Verbal varieties of inverse semigroups
Authors: Wilkinson Ross
Published: April 2009

A verbal product is introduced for a particular class of varieties of inverse semigroups and this product is shown to be associative. As well, the structure of this class is examined.
The projective geometry arising from a hollow module
Authors: Dawson Jeremy E.
Published: April 2009

We discuss the projective geometry defined in terms of the hollow factor modules of a given module. In particular, we derive an explicit expression for the division ring obtained in coordinatizing such a projective geometry.
Some remarks on the location of fixed points
Authors: Edelstein Michael , Tingley Daryl
Published: April 2009

Several procedures for locating fixed points of nonexpansive selfmaps of a weakly compact convex subset of a Banach space are presented. Some of the results involve the notion of an asymptotic center or a Chebyshev center.
Families of sets on a finite set
Authors: Ashman C. J. , Ficker V.
Published: April 2009

V. Krishnamurthy has shown that on a finite set X all topologies can be mapped into a certain set of matrices of zeros and ones. In this paper it is shown that all lattices, algebras and rings on a finite set X can be mapped onto particular sets of matrices of zeros and ones.
The degree of the gradient of a coercive functional
Authors: McKenzie Ross H.
Published: April 2009

An elementary proof is given of a theorem of Castro and Lazer that the degree of the gradient of a coercive functional on a large ball ofRnis one.
Cocompleteness over coverings
Authors: Betti Renato
Published: April 2009

For enriched categories the correct notion of limit involves indexing by a module. This paper studies the question of cocompletion for a given set of indexing modules. As well as providing a simplified treatment of cocompleteness for ordinary categories, associated sheaves and associated stacks are also included as cocompletion processes for appropriate bases. In fact the saturation of a general set of indexing modules has properties which justify our use of the term “covering” for members of the saturation.
Holomorphic solutions about an irregular singular point of an ordinary linear differential equation
Authors: Pearce C. E. M.
Published: April 2009

It is shown that that an ordinary linear differential equation may possess a holomorphic solution in a neighbourhood of an irregular singular point even though the usual linearly independent solutions corresponding to the two roots of the indicial equation both have zero radius of convergence.
Minimal F2-flows
Authors: Berend Daniel
Published: April 2009

Let σ be an ergodic endomorphism of the r–dimensional torus and Π a semigroup generated by two affine transformations lying above σ. We show that the flow defined by Π admits minimal sets of positive Hausdorff dimension and we give necessary and sufficient conditions for this flow to be minimal.
Reducible 2 – (11, 5, 4) and 3 – (12, 6, 4) designs
Authors: Breach D. R. , Thompson A. R.
Published: April 2009

One way of constructing a 2 – (11,5,4) design is to take together all the blocks of two 2 – (11,5,2) designs having no blocks in common. We show that 58 non-isomorphic 2 – (11,5,4) designs can be so made and that through extensions by complementation these can be packaged into just 12 non-isomorphic reducible 3 – (12,6,4) designs.
Effectivity in independence measures for values ofE-functions
Authors: Brownawell W. Dale
Published: April 2009

We establish a measure of algebraic independence for values ofE-functions which is more nearly effectively computable than the previous one. When the system of equations meets either of two criteria, then the measure becomes entirely effectively computable.
Semigroups of constant maps
Authors: Schein Boris M.
Published: April 2009

In this paper “a map” denotes an arbitrary (everywhere defined, or partial, or even multi-valued) mapping. A map is constant if any two elements belonging to its domain have precisely the same images under this map. We characterize those semigroups which can be isomorphic to semigroups of constant maps or to involuted semigroups of constant maps.
Poisson convergence for point processes on the plane
Authors: Ivanoff B. Gail
Published: April 2009

A compensator is defined for a point process in two dimensions. It is shown that a Poisson process is characterized by a continuous deterministic compensator. Sufficient conditions are given for convergence in distribution of a sequence of two-dimensional point processes in the Skorokhod topology to a Poisson process when the corresponding sequence of compensators converges pointwise in probability to a continuous deterministic function.
Homogeneous C*-algebras whose spectra are tori
Authors: Disney Shaun , Raeburn Iain
Published: April 2009

By a theorem of Fell and Tomiyama-Takesaki, an N-homogeneous C*-algebra with spectrum X has the form Γ(E) for some bundle E over X with fibre MN(C), and its isomorphism class is determined by that of E and its pull-backs f*E along homeomorphisms f of X. We describe the homogeneous C*-algebras with spectrum T2 or T3 by classifying the MN-bundles over Tk using elementary homotopy theory. We then use our results to determine the isomorphism classes of a variety of transformation group C*-algebras, twisted group C*-algebras and more general crossed products.
On semi-regularization topologies
Authors: Mršević M. , Reilly I. L. , Vamanamurthy M. K.
Published: April 2009

This paper discusses several properties of topological spaces and how they are refelected by corresponding properties of the associated semi-regularization topologies. For example a space is almost locally connected if and only if its semi-regularization is locally connected. Various separation, connectedness, covering, and mapping properties are considered.
Weakly prime one-sided ideals
Authors: Van Der Walt Andries P. J.
Published: April 2009

A left ideal P in a ring is weakly prime if L, K ⊇ P and LK ⊆ P for left ideals L and K imply L = P or K = P. A prime left ideal is weakly prime but the converse is false. Characterizations of weakly prime left ideals as well as a number of their properties are obtained. The intersection of all the weakly prime left ideals in a ring is a left ideal which in general is contained in (but not equal to) the prime radical.
Near-rings of mappings on finite topological groups
Authors: Mason Gordon
Published: April 2009

When G is a topological group, the set N(G) of continuous self-maps of G, and the subset N0(G) of those which fix the identity of G, are near-rings. In this paper we examine the (left) ideal structure of these near-rings when G is finite. N0(G) is shown to have exactly two maximal ideals, whose intersection is the radical. In the final section we investigate subnear-rings of N0(G) determined by certain continuous elements of the endomorphism near-ring.
Time-dependent Lipschitz attractors for non-semigroup evolution processes
Authors: Turinici Mihai
Published: April 2009

A maximality principle on quasi-ordered pseudo-metric spaces is used to obtain a number of Lipschitz attraction results for non-semigroup evolution processes with respect to time-dependent families. As particular cases, a multivalued version of Dieudonné's means value theorem and the Kirk-Ray lipschitzianness test are derived.
A Schunck class construction and a problem concerning primitive groups
Authors: Förster Peter
Published: April 2009

Gaschütz has introduced the concept of a product of a Schunck class and a (saturated) formation (differing from the usual product of classes) and has shown that this product is a Schunck class provided that both of its factors consist of finite soluble groups. We investigate the same question in the context of arbitrary finite groups.
The inversion of a transform related to the Laplace transform and to heat conduction
Authors: Widder David V.
Published: April 2009

In a recent paper [7] the author considered, among other things, the integral transform where is the fundamental solution of the heat equation There we gave a physical interpretation of the transform (1.1). Here we shall choose a slightly different interpretation, more convenient for our present purposes. If then u(O, t) = f(t). That is, the function f(t) defined by equation (1.1) is the temperature at the origin (x = 0) of an infinite bar along the x-axis t seconds after it was at a temperature defined by the equation .
Symmetrisable operators: Part II Operators in a Hilbert Space
Authors: Silberstein J. P. O.
Published: April 2009

In the first paper of this series [4] I gave a brief summary of the properties of symmetrisable operators in Hilbert Space. A detailed discussion of these properties will be given now, but the properties of operators symmetrisable by bounded operators will be dealt with further in Part III.
The double-six of lines over PG (3, 4)
Authors: Hirschfeld James W. P.
Published: April 2009

The object of this paper is to consider the existence of the double-six over GF(2n) and particularly over GF(4).
On finite groups whose 2-Sylow subgroups have cyclic subgroups of index 2
Authors: Wong W. J.
Published: April 2009

If the finite group G has a 2-Sylow subgroup S of order 2a+1, containing a cyclic subgroup of index 2, then in general S may be one of the following six types [8]:

(i) cyclic; (ii) Abelian of type (a, 1), a > 1; (iii) dihedral1; (iv) generalized quaternion; (v) {α, β}, α2a = β2, α2a−1+1, a ≧ 3;

(vi) {α, β}, α2a = β2, α2a−1+1, a ≧ 3.
Fixed point theorems for generalized nonexpansive mappings
Authors: Wong Chi Song
Published: April 2009

Let S, T be self-mappings on a (non-empty) complete metric space (X, d). Let ai, i = 1, 2, …, 5, be non-negative real numbers such that < 1 and for any x, y in X,
Semi-Brouwerian algebras
Authors: Murty P. V. Ramana
Published: April 2009

Ever since David Ellis has shown that a Boolean algebra has a natural structure of an autometrized space, the interest in such spaces has led several authors to study various autometrized algebras like Brouwerian algebras [9], Newman algebras [4], Lattice ordered groups [6], Dually residuated lattice ordered semigroups [7] etc. However all these spaces are lattices (with the exception of Newman algebra which is not even a partially ordered set); and a natural question would be whether there are semilattices with a natural structure of an autometrized space. In the present paper we observe that the dual of an implicative semilattice [8] is a generalization of Brouwerian algebra and it has a natural structure of an autometrized space.
Uniqueness criterion for a moment problem
Authors: Lenard A.
Published: April 2009

In an article that appeared some years ago in this journal, Takács [1] gave a uniqueness criterion for the solution of the moment problem where the Br are given numbers and the Pk are sought, Pk ≧ 0, σkPk = 1. Takács showed that if Br < ∞ for all r and then the solution is unique. In addition, he gave an explicit formula for the solution in this case where q is any number satisfying q ≧ 0 and q > p2 — 1.
The iterated equation of generalized axially symmetric potential theory, VI General solutions
Authors: Burns J. C.
Published: April 2009

The iterated equation of generalized axially symmetric potential theory [1] is the equation where, in its simplest form, the operator Lk is defined by the function f f(x, y) being assumed to belong to the class of C2n functions and the parameter l to take any real value. In appropriate circumstances, which will be indicated later, the operator can be generalized but as this can be done without altering the methods used, the operator will be taken in the form where r, θ are polar coordinates such that x = r cos θ, y = r sin μ = cosθ.
Thermal instability of Couette flow
Authors: Agrawal S. C. , Saini J. C.
Published: April 2009

The present paper investigates the thermal instability of a non-homogeneous fluid rotating between two co-axial cylinders when the inner cylinder is being heated uniformly. The conditions are established under which the oscillatory and non-oscillatory modes exist and further it has been shown that the oscillatory modes are amplified due to the adverse temperature gradient. In the case of non-oscillatory modes, sufficient conditions for stability and instability are obtained.
Quotient closed metanilpotent Fitting classes
Authors: Berger T. R. , Bryce R. A. , Cossey John
Published: April 2009

A Fitting class of finite soluble groups is one closed under the formation of normal subgroups and products of normal subgroups. It is shown that the Fitting classes of metanilpotent groups which are quotient group closed as well are primitive saturated formuations.
The structure of a group of permutation polynomials
Authors: Mullen Gary L. , Niederreiter Harald
Published: April 2009

Let Gq be the group of permutations of the finite field Fq of odd order q that can be represented by polynomials of the form ax(q+1)/2 + bx with a, b ∈ Fq. It is shown that Gq is isomorphic to the regular wreath product of two cyclic groups. The structure of Gq can also be described in terms of cyclic, dicyclic, and dihedral groups. It also turns out that Gq is isomorphic to the dymmetry group of a regular complex polygon.
Monoidal closed structures on categories with constant maps
Authors: Logar Alessandro , Rossi Fabio
Published: April 2009

The purpose of this paper is to study the so-called canonical monoidal closed structures on concrete categories with constant maps. First of all we give an example of a category of this kind where there exists a non canonical monoidal closed structure. Later, we give a technique to construct a class of suitable full subcategories of the category of T0-spaces, such that all monoidal closed structures on them are canonical. Finally we show that “almost all” useful categories of topological compact spaces admit no monoidal closed structures whatsoever.
Almost all chordal graphs split
Authors: Bender E. A. , Richmond L. B. , Wormald N. C.
Published: April 2009

A chordal graph is a graph in which every cycle of length at least 4 has a chord. If G is a random n-vertex labelled chordal graph, the size of the larget clique in about n/2 and deletion of this clique almost surely leaves only isolated vertices. This gives the asymptotic number of chordal graphs and information about a variety of things such as the size of the largest clique and connectivity.
Nil and s-prime Ω-groups
Authors: Buys A. , Gerber G. K.
Published: April 2009

The concepts nilpotent element, s-prime ideal and s-semi-prime ideal are defined for Ω-groups. The class {G|G is a nil Ω-group} is a Kurosh-Amitsur radical class. The nil radical of an Ω-group coincides with the intersection of all the s-prime ideals. Furthermore an ideal P of G is an s-semi-prime ideal if and only if G/P has no non-zero nil ideals.
Some finite groups with few defining relations
Authors: Neumann B. H.
Published: April 2009

Some new classes of finite groups with zero deficiency presentations, that is to say presentations with as few defining relations as generators, are exhibited. The presentations require 3 generators and 3 defining relations; the groups so presented can also be generated by 2 of their elements, but it is not known whether they can be defined by 2 relations in these generators, and it is conjectured that in general they can not. The groups themselves are direct products or central products of binary polyhedral groups with cyclic groups, the order of the cyclic factor being arbitrary.
K-groups of rings and the homology of their elementary matrix groups
Authors: Aisbett Janet
Published: April 2009

Low dimensional algebraic K-groups of a commutative ring are described in terms of the homology of its elementary matrix group. This approach is prompted by recent successful computations of low-dimensional K-groups using group homology methods, and it builds on the identity K2(R)=H2(ER).
A Characterization of separable polynomials over a skew polynomial ring
Authors: Szeto George
Published: April 2009

The characterization of a separable polynomial over an indecomposable commutative ring (with no idempotents but 0 and 1) in terms of the discriminant proved by G. J. Janusz is generalized to a skew polynomial ring R [ X, ρ] over a not necessarily commutative ring R where ρ is an automorphism of R with a finite order. 1980 Mathematics subject classification (Amer. Math. Soc.): 16 A 05.
On the lattice of congruences on an eventually regular semigroup
Authors: Edwards P. M.
Published: April 2009

A natural equivalence θ on the lattice of congruences λ(S) of a semigroup S is studied. For any eventually regular semigroup S, it is shown that θ is a congruence, each θ-class is a complete sublattice of λ(S) and the maximum element in each θ-class is determined. 1980 Mathematics subject classification (Amer. Math. Soc.): 20 M 10.
A free boundary problem in an annulus
Authors: Tepper David E.
Published: April 2009

If Ω is a ring region with starlike boundary components α and β, then we show for each λ > 0 there exists a ring region ω ⊂ Ω with ∂ ω = α ∪ ϒ, α ∩ ϒ = φ such that there is a harmonic function V in ω satisfying (a) V(z) = 0 for z ∈ α, (b) V(z) = 1 for z ∈ ϒ, (c) | grad V(z)| = λ for z ∈ ϒ ∩ Ω. Furthermore, we show when ω is not equal to Ω; that is, that is, there is a non-trival solution.
On right self-injective regular semigroups, II
Authors: Shoji Kunitaka
Published: April 2009

It is shown that a semigroup is right self-injective and a band of groups if and only if it is isomorphic to the spined product of a self-injective semilattice of groups and a right self-injective band. A necessary and sufficient condition for a band to be right self-injective is given. It is shown that a left [right] self-injective semigroup has the [anti-] representation extension property and the right [left] congruence extension property.
A Joint spectral theorem for unbounded normal opertors
Authors: Patel A. B.
Published: April 2009

A joint spectral theorem for an n-tuple of doubly commuting unbounded normal operators in a Hilbert space is proved by using the techniques of GB*-algebras.
Integration by parts for the generalized Riemann-Stieltjes integral
Authors: Pfeffer W. F.
Published: April 2009

Under the standard assumptions, the formula for integration by parts is obtained by a straightforward calculation.
Prefrattini groups
Authors: Förster Peter
Published: April 2009

We define and investigate H-prefrattini subgroups for Schunck classes H of finite soluble groups, and solve a problem of Gaschütz concerning the structure of H-prefrattini groups for H = {1}.
On almost locally connected spaces
Authors: Noiri Takashi
Published: April 2009

In this paper it is shown that aimost local connectedness is hereditary for the subspace that is the union of regular open sets and is preserved under almost-open (in the sense of Singal) θ-continuous surjections.
Groups sharing some varietal properties with supersoluble groups
Authors: Brandl Rolf
Published: April 2009

In this note a formation U is considered which can be defined by a sequence of laws which ‘almost’ hold in every finite supersoluble group. The class U contains all finite supersoluble groups and each group in U has a Sylow tower.

It is shown that a finite group belongs to U if and only if all of its subgroups with nilpotent commutator subgroup are supersoluble. A more general result concerning classes of this type finally proves that U is a saturated formation.
Fractional iteration of entire and rational functions
Authors: Szekeres G.
Published: April 2009

We shall be concerned with the behaviour of the fractional iterates of analytic functions which have a fixpoint ζ with multiplier 11. The general form of such a function is If ζ is finite, if ζ = ∞.
Note on Schröder's functional equation
Authors: Kuczma Marek
Published: April 2009

In the present paper we are concerned with Schröder's functional equation , where ϕ(x) is the unknown function and is a number between 0 and 1: . We shall prove a theorem which generalizes some earlier results on convex solutions of the Schröder equation [4], [5].
Twisted group algebras and their representations
Authors: Conlon S. B.
Published: April 2009

Let be a finite group, a field. A twisted group algebra A() on over is an associative algebra whose elements are the formal linear combinations and in which the product (A)(B) is a non-zero multiple of (AB), where AB is the group product of A, B ∈: . One gets the ordinary group algebra () by taking each fA, B ≠ 1.
On Runge-Kutta processes of high order
Authors: Butcher J. C.
Published: April 2009

An (explicit) Runge-Kutta process is a means of numerically solving the differential equation , at the point x = x0+h, where y, f may be vectors.
Integration of real-valued set functions in abstract Spaces
Authors: Finch P. D.
Published: April 2009

Let an abstract space of points x and let ℳ be a σ-field of subsets of , that is a class of subsets of such that (i) ∈ ℳ, (ii) if M ∈ ℳ then — M ∈ ℳ and (iii) if {Mj} is any sequence of elements of ℳ then UjMj ∈ ℳ.
Two probability theorems and their application to some first passage problems
Authors: Heyde C. C.
Published: April 2009

Let Xi, i = 1, 2, 3,··· be a sequence of independent and identically distributed random variables and write Sn = X1+X2+…+Xn. If the mean of Xi is finite and positive, we have Pr(Sn ≦ x) → 0 as n → ∞ for all x1 – ∞ < x < ∞ using the weak law of large numbers. It is our purpose in this paper to study the rate of convergence of Pr(Sn ≦ x) to zero. Necessary and sufficient conditions are established for the convergence of the two series where k is a non-negative integer, and where r > 0. These conditions are applied to some first passage problems for sums of random variables. The former is also used in correcting a queueing Theorem of Finch [4].
Recurrence properties of Processes with stationary independent increments
Authors: Kingman J. F. C.
Published: April 2009

Let X1, X2,…Xn, … be independent and identically distributed random variables, and write . In [2] Chung and Fuchs have established necessary and sufficient conditions for the random walk {Zn} to be recurrent, i.e. for Zn to return infinitely often to every neighbourhood of the origin. The object of this paper is to obtain similar results for the corresponding process in continuous time.
On a theorem of Halmos concerning unbiased estimation of moments
Authors: Konijn H. S.
Published: April 2009

In [4] Halmos considers the following situation. Let be a class of distribution functions over a given (Borel) subset E of the real line, and F a function over . He investigates which functions F admit estimates that are unbiased over and what are all possible such estimates for any given F. In particular he shows that on the basis of a sample (of size n) one can always obtain an estimate of the first moment which is unbiased in and that the central moments Fm of order m ≧ 2 have estimates which are unbiased in if and only if n ≧ m, provided satisfies the following properties: Fm exists and is finite for all distributions in and includes all distributions which assign probability one to a finite number of points of E. Halmos also finds that symmetric estimates which are unbiased on are unique1 and have smaller variances on than unsymmetric unbiased estimates.
Imbedded Markov chain analysis of single server bulk queues
Authors: Bhat U. Narayan
Published: April 2009

In this paper results from Fluctuation Theory are used to analyse the imbedded Markov chains of two single server bulk-queueing systems, (i)with Poisson arrivals and arbitrary service time distribution and (ii) with arbitrary inter-arrival time distribution and negative exponential service time. The discrete time transition probailities and the equilibrium behaviour of the queue lengths of the systems have been obtained along with distributions concerning the busy periods. From the general results several special cases have been derived.
Herbert Melvin Lieberstein
Authors: Keats R. G.
Published: April 2009

Professor Herbert Melvin Lieberstein died at Royal Newcastle Hospital on 18th August,1973, at the age of 47. As an applied mathematician, Professor Lieberstein was devoted tohis research and teaching in the application of mathematics to other disciplines; his most recent book entitled “Mathematical Physiology”, was published just before his death. Because his interests coincided so closely with the aims and aspirations of theFaculty of Mathematics at Newcastle, his appointment to that Faculty in 1971 was particularly appropriate.He lived less than two years in Australia, but during that time he consolidated his reputation as a most versatile and successful applied mathematician. His work is well known throughout Australia and, indeed, throughout the world, especially to those who work in fields to which mathematics may be profitably applied. However, his versatility and ability were not confined to mathematics, for he also made substantial contributions to a number of community projects; these contributions will be long remembered by those interested in the welfare of the Australian Aborigines, problems of the environment and associated projects.
General-well-ordered sets
Authors: Hickman J. L.
Published: April 2009

It is of course well known that within the framework of any reasonable set theory whose axioms include that of choice, we can characterize well-orderings in two different ways: (1) a total order for which every nonempty subset has a minimal element; (2) a total order in which there are no infinite descending chains.

Now the theory of well-ordered sets and their ordinals that is expounded in various texts takes as its definition characterization (1) above; in this paper we commence an investigation into the corresponding theory that takes characterization (2) as its starting point. Naturally if we are to obtain any differences at all, we must exclude the axiom of choice from our set theory. Thus we state right at the outset that we are working in Zermelo-Fraenkel set theory without choice.