bluuebunny/crossref_metadata_2025 huggingface dataset:
Varieties generated by finite BCK-algebras
Authors: Cornish William H.
Published: April 2009

Iséki's BCK-algebras form a quasivariety of groupoids and a finite BCK-algebra must satisfy the identity (En): xyn = xyn+1, for a suitable positive integer n. The class of BCK-algebras which satisfy (En) is a variety which has strongly equationally definable principal congruences, congruence-3-distributivity, and congruence-3-permutability. Thus, a finite BCK-algebra generates a 3-based variety of BCK-algebras. The variety of bounded commutative BCK-algebras which satisfy (En) is generated by n finite algebras, each of which is semiprimal.
Principal indecomposable modules for some three-dimensional special linear groups
Authors: Archer James
Published: April 2009

Let k be a finite field of characteristic 2, and let G be the three dimensional special linear group over k. The principal indecomposable modules of G over k are constructed from tensor products of the irreducible modules, and formulae for their dimensions are given.
An existence theorem for ordinary differential equations in Banach spaces
Authors: Boudourides Moses A.
Published: April 2009

The Cauchy problem x′ = f(t, x), x(0) = x0, is considered in a non-reflexive Banach space E, where f is weakly continuous. A local existence theorem is proved using the measure of weak noncompactness.
Operator semistable probability measures on a Hilbert space: Corrigenda
Authors: Laha R.G. , Rohatgi V.K.
Published: April 2009

A faulty typescript of [2] was, regrettably, submitted. The following changes should be made:

Page 398, line 7: replace A є G with A є L.

Page 398, line 12: replace A є G with A є L.
On normal subspaces
Authors: Gauld D.B. , Reilly I.L. , Vamanamurthy M.K.
Published: April 2009

In this paper the anti-normal property is studied. A space is anti-normal if its only normal subspaces are those whose cardinalities require them to be normal. It is shown that every topological space of at least four elements contains a normal three point subspace from which it follows that there is only one non-trivial anti-normal space.
Numbers of conjugacy classes in some finite classical groups
Authors: Macdonald I.G.
Published: April 2009

In this paper we calculate the number of congugacy classes in the following finite classical groups: GLn(Fq); PGLn(Fq), SLn(Fq), and more generally G(Fq), where G is any algebraic group isogenous to SLn; PSLn(Fq); ; , , and more generally where G is any group isogenous to SUn over Fq; and .
Randomly k-axial graphs
Authors: Burns David , Chartrand Gary , Kapoor S.F. , Saba Farrokh
Published: April 2009

A class of graphs called randomly k-axial graphs is introduced, which generalizes randomly traceable graphs. The problems of determining which bipartite graphs and which complete n-partite graphs are randomly k-axial are studied.
Some remarks on symmetry for a monoidal category
Authors: Kasangian Stefano , Rossi Fabio
Published: April 2009

It is shown that, for a monoidal category V, not every commutation is a symmetry and also that a commutation does not suffice to define the tensor product A ⊗ B of V-categorles A and B. Moreover, it is shown that every symmetry can be transported along a monoidal equivalence.
Factorisation of Lipschitz functions on zero dimensional groups
Authors: Bloom Walter R.
Published: April 2009

Let G denote a locally compact metrisable zero dimensional group with left translation invariant metric d. The Lipschitz spaces are defined by

where af: x → f(ax) and α > 0; when r = ∞ the members of Lip(α; r) are taken to be continuous. For a suitable choice of metric it is shown that , where 1 ≤ p ≤ 2, α > q−1, p, q are conjugate indices and . It is also shown that for G infinite the range of values of α cannot be extended.
A covering property of finite groups
Authors: Brandl Rolf
Published: April 2009

Finite groups G possessing a proper subgroup U such that for each element g of G there exists an automorphism of G mapping g into U are considered. The question of how the structure of U determines the structure of G is examined. For example, if G is soluble and U is nilpotent then G is nilpotent.
On exponential dichotomy in Banach spaces
Authors: Megan Mihail , Preda Petre
Published: April 2009

In this paper we study the exponential dichotomy property for linear systems, the evolution of which can be described by a semigroup of class C0 on a Banach space. We define the class of (p, q) dichotomic semigroups and establish the connections between the dichotomy concepts and admissibility property of the pair (Lp, Lq) for linear control systems. The obtained results are generalizations of well-known results of W.A. Coppel, J.L. Massera and J.J. Schäffer, K.J. Palmer.
On rings with nil commutator ideal
Authors: Abu-Khuzam Hazar
Published: April 2009

Let R be a ring in which for each x, y in R there exists a positive integer n = n(x, y) such that (xy)n − (yx)n is in the center of R. Then R has a nil commutator ideal.
Some neutral equations with a control parameter
Authors: Angelov Vasil G.
Published: April 2009

This paper presents sufficient conditions, involving accretive operators, for the existence, uniqueness and continuous dependence on a control parameter of the solutions of some initial and boundary value problems for neutral functional differential equations.
Dissipative operators and series inequalities
Authors: Gindler Herbert A. , Goldstein Jerome A.
Published: April 2009

Of concern is the best constant K in the inequality ‖Ax‖2 ≤ K‖A2x‖‖x‖ where A generates a strongly continuous contraction semigroup in a Hilbert space. Criteria are obtained for approximate extremal vectors x when K = 2 (K ≤ 2 always holds). By specializing A + I to be a shift operator on a sequence space, very simple proofs of Copson's recent results on series inequalities follow. Inequalities of the above type are also studied on LP spaces, and earlier results of the authors and of Holbrook are improved.
Manifolds of smooth maps
Authors: Nghê Truong Công
Published: April 2009

We show that the space of smooth maps from a compact smooth manifold into another smooth manifold can be endowed with the structure of a smooth manifold if we use the Γ-differentiation of Yamamuro. We then generalise the Smale Density Theorem to mappings between these manifolds.
On a theorem of Nielsen
Authors: Kaul Saroop K. , Thompson Dale V.
Published: April 2009

The following theorem proved in this paper is a generalization of a result of Jakob Nielsen. Suppose G is a group of linear fractional transformations acting on the unit disc D in the complex plane; suppose also that each element of G, except the identity, is either a hyperbolic or a parabolic transformation. Then any homeomorphism h of the open disc onto itself which satisfies the functional equation hg = g′h, for some automorphism g → g′ of G, has a unique extension to a homeomorphism of D onto itself.
Mean value theorems and a Taylor theorem for vector valued functions
Authors: Výborný Rudolf
Published: April 2009

Two mean value theorems and a Taylor theorem for functions with values in a locally convex topological vector space are proved without the use of the Hahn-Banach extension theorem.
Periodic points and chaos for expanding maps of the interval
Authors: Byers Bill
Published: April 2009

Expanding maps of the interval with unique turning points have periodic points of period 2n · 3 for some n and therefore are chaotic.
Asymptotic behavior of nonoscillatory solutions of a higher order functional differential equation
Authors: Onose Hiroshi
Published: April 2009

The asymptotic behavior of nonoscillatory solutions of nth order nonlinear functional differential equations

is investigated. Sufficient conditions are provided which ensure that all nonoscillatory solutions approach zero as t → ∞.
Differential calculus in Fréchet spaces
Authors: Duc Duong Minh
Published: April 2009

We apply Keller's method to the study of differential calculus in Frechet spaces and establish an inverse mapping theorem. A special case of this theorem is similar to a theorem of Yamamuro.
Arithmetic and analytic properties of paper folding sequences
Authors: France M. Mendès , van der Poorten A.J.
Published: April 2009

The mechanical procedure of paper folding generates an uncountable family of infinite sequences of fold patterns. We obtain the associated Fourier series and show that the sequences are almost periodic and hence deterministic. Further, we show that paper folding numbers defined by the sequences are all transcendental.
On the distribution of winning moves in random game trees
Authors: Flanigan J. A.
Published: April 2009

In a natural way, associated with each rooted tree there exists a pair of two-person games, each game possessing the root as initial position. When a rooted tree is selected at random from the set of all rooted trees which possess {1, 2, …, n} as vertex set, the number of winning moves available to the first player to move in each of the associated games is a random variable. For fixed n, we determine the distribution of this random variable. As an immediate consequence, we find the probability that the first player to move has no winning move at all. The “saddlepoint method” is applied to a certain contour integral to obtain the asymptotic distribution of the number of winning moves as n → ∞.
Some geometric characterizations of inear product spaces
Authors: Kapoor O. P. , Mathur S. B.
Published: April 2009

There are several geometric characterizations of inner product spaces amongst the normed linear spaces. Mahlon M. Day's refinement “rhombi suffice as well as parallelograms”, of P. Jordan and J. von Neumann parallelogram law is well known. There are some characterizations which employ various notions of orthogonality. For example, it is known that if in a normed linear space Birkhoff-James orthogonality implies isosceles orthogonality. For example, it is known that if in a normed linear space Birkhoff-James orthogonality implies isosceles orthogonality then the space is an inner product space; geometrically it means that if the diagonals of a rectangle, with sides perpendicular in Birkhoff-James sense, are equal then the space is an inner product space. In the main result of this note we improve upon this characterization and show that here unit squares suffice as well as rectangles.
Projective distributive p-algebras
Authors: Urquhart Alasdair
Published: April 2009

A characterization of finite (weak) projectives in an equational class of distributive pseudocomplemented lattices is given. In the class of all such lattices, a finite lattice is projective if and only if its poset of join–irreducible elements forms a semilattice in which the minimal elements below the join of x and y are exactly the mininal elements below x or y. A similar condition works for any equational subclass.
Free finitary algebras on compactly generated spaces
Authors: Day Brian J.
Published: April 2009

An explicit colimit formula is used to describe the free k-space algebra on a given k-space for any k-enriched finitary theory. A question, raised and solved affirmatively by several authors, has been that of whether the free k-space group on a weakly hausdorff k-space is again weakly hausdorff and admits a closed embedding of the generators. In the present article both these features of finitary k-space algebra are combined to answer analogous questiona regarding the free finitary k-space algebras in general, and the weakly hausdorff separation axiom. Relationships with other problems in k-space theory are described.
Symmetric dual nondifferentiable programs
Authors: Chandra S. , Husain I.
Published: April 2009

Symmetric and selfduality results are established for a general class of nonlinear programs which combine differentiable as well as non-differentiable cases appearing in the literature. Many well known results are deduced as special cases and certain natural extensions are discussed.
Asymptotics applied to nonlinear boundary-value problems
Authors: Dancer E.N.
Published: April 2009

We announce results of Landesman-Lazer type for boundary-value problems for ordinary differential equations. Details will appear elsewhere.
Normal and invertible composition operators
Authors: Singh R.K. , Gupta D.K.
Published: April 2009

Let N denote the set of natural numbers and let φ be a mapping from N into itself. Then the composition transformmation Cφ, on the weighted l2 space with weights a2n, where n ∈ N and 0 < a < 1 is defined by Cφf = f ∘ φ. If Cφ is a bounded operator, then it is called a composition operator. The adjoint of the composition operator Cφ, is computed, and it is used to characterise normal, unitary, isometric, and co-isometric composition operators. Not every invertible φ induces an invertible composition operator, as is shown by examples. At the end of this note all invertible composition operators are characterised.
Oscillation theorems for semilinear hyperbolic and ultrahyperbolic operators
Authors: Narita Mamoru
Published: April 2009

The oscillation property of the semilinear hyperbolic or ultra-hyperbolic operator L defined by

is studied. Sufficient conditions are provided for all solutions of uL[u] ≤ 0 satisfying certain boundary conditions to be oscillatory. The basis of our results is the non-existence of positive solutions of the associated differential inequalities.
Duality in finite dimensional complex space
Authors: Scott C.H. , Jefferson T.R.
Published: April 2009

The idea of duality is now a widely accepted and useful idea in the analysis of optimization problems posed in real finite dimensional vector spaces. Although similar ideas have filtered over to the analysis of optimization problems in complex space, these have mainly been concerned with problems of the linear and quadratic programming variety. In this paper we present a general duality theory for convex mathematical programs in finite dimensional complex space, and, by means of an example, show that this formulation captures all previous results in the area.
Characterisation of normed linear spaces with Mazur's intersection property
Authors: Giles J.R. , Gregory D.A. , Sims Brailey
Published: April 2009

Normed linear spaces possessing the euclidean space property that every bounded closed convex set is an intersection of closed balls, are characterised as those with dual ball having weak* denting points norm dense in the unit sphere. A characterisation of Banach spaces whose duals have a corresponding intersection property is established. The question of the density of the strongly exposed points of the ball is examined for spaces with such properties.
An analogue of Banach's contraction principle for 2-metric spaces
Authors: Lal S.N. , Singh A.K.
Published: April 2009

In this paper we establish a fixed point theorem for 2-metric spaces. Some interesting particular cases of this theorem are also obtained.
Characterizations of MacNeille completions and topological functors
Authors: Porst Hans-E.
Published: April 2009

In this note we give external characterizations of absolutely topologicai functors U: A →X (where A may be a large category) as functors which are injective with respect to all functors based on the category X, or equivalently, which do not admit essential extensions over X. From this we deduce several characterizations and properties of the MacNeille completion of faithful functors. These results generalize the work of Horst Herriich [Math. Z. 150 (1976), 101–110] in case of small categories, where the crucial point of this generalization lies in the fact that we cannot make use of the existence of MacNeille completions and we therefore have to introduce a local-initial-completion-construction.
On the natural completion functor for Cauchy spaces
Authors: Frič R. , Kent D.C.
Published: April 2009

The natural completion functor on the category of cλ-embedded Cauchy spaces induces a completion functor on a category of sequential Cauchy spaces which preserves sequential regularity.
Generalized symmetry
Authors: Wilker J.B.
Published: April 2009

Let X be a set and G a group which acts on X and is generated by two elements α and b. Motivated by a geometric problem of L. Fejes Tóth, we define a subset S ⊂ X to have [α, b]-symmetry if its images under α and b satisfy Sα ∩ Sb = S. The problem of finding all sets with [α, b]- symmetry when an arbitrary 2-generator group G acts on an arbitrary space X is shown to be equivalent to the same problem in the special case when the 2-generator free group acts on itself by right translation. This action is modelled in the hyperbolic plane in a way that helps to reveal the [α, b]- symmetric subsets of the free group.
Composition operators
Authors: Singh R.K. , Komal B.S.
Published: April 2009

A study of centered composition operators on l2 is made in this paper. Also the spectrum of surjective composition operators is computed. A necessary and sufficient condition is obtained for the closed unit disc to be the spectrum of a surjective composition operator.
Note on asymptotic equivalence for measure differential equations
Authors: Rao V. Sree Hari
Published: April 2009

Two nonlinear ordinary differential systems, one of which contains impulses are considered in this note, and assuming the existence of bounded solutions, some results on asymptotic equivalence type correspondence between them are obtained. At the end an open question is posed.
Duality in topological algebra
Authors: Day B.J.
Published: April 2009

Aspects of duality relating to compact totally disconnected universal algebras are considered. It is shown that if P is a ““basic“ set of injectives in a variety of compact totally disconnected algebras then the category P of P-copresentable objects is in duality with the class of all G-copresentable algebras on P, where G: P → Ens is the forgetful functor and an algebra is taken to mean a finite-product-preserving functor from P to Ens.
Realizing isomorphisms of category algebras
Authors: Maharam Dorothy , Stone A.H.
Published: April 2009

Let C(X) denote the complete boolean algebra of Borel sets modulo first category sets of the space X. Given an isomorphism τ between C(X) and C(Y), where X and Y are complete metric spaces, it is shown that there exists a homeomorphism T, between residual subsets A of X and B of Y, that induces τ. When X = Y one can make A = B. An analogous result is stated when τ is a complete isomorphism onto a subalgebra.
On the rate of convergence of interpolation polynomials of Hermite-Fejér type
Authors: Prasad J.
Published: April 2009

For the interpolation polynomial of Hermite-Fejér type An[f] of degree less than or equal to 4n − 1 constructed on the nodes , k = 1, 2, …, n, it is shown that for f ∈ CM(Ω) the inequality

holds where CM(Ω) is the class of continuous functions on [−1, 1] satisfying certain conditions, Ω is a certain modulus of continuity, and c3 and M are positive constants.
A sequence algebra associated with distributions
Authors: Petersen G.M.
Published: April 2009

If A = {am,n} is a regular summability matrix, the sequence s = {sn} is said to be A uniformly distributed (see L. Kuipers, H. Niederreiter, Uniform distribution of sequences, p. 221, John Wiley & Sons, New York, London, Sydney, Toronto, 1974), if

(h = 1, 2, …). In this paper we examine sequences belonging to A*, where t ∈ A* if and only if t is bounded and s + t is A uniformly distributed whenever s is A uniformly distributed. By A′ are denoted those members t of A* such that at ∈ A* for every real a. The members of A′ form a Banach algebra, A* is not connected under the sup norm, but A′ is a component.
Semisimple rings of quotients
Authors: Zelmanowitz Julius M.
Published: April 2009

Necessary and sufficient conditions on an arbitrary Gabriel filter of left ideals of a ring R are determined in order that the ring of quotients of R with respect to the filter be semi-simple artinian. Special instances include generalizations of earlier work on classical rings of quotients and maximal rings of quotients.
A result in queueing theory
Authors: Ghosal A.
Published: April 2009

In a single-server queueing system, subject to the queue discipline ‘First come first served’, the equilibrium distribution function of the waiting time of a server depends on the distribution of the random variable (u) which is the difference between the service time and the inter-arrival time. If in two queueing systems u's are equivalent in distribution, the waiting times are also equivalent in distribution (known result). It has been shown in this note that equivalence in waiting time distributions does not necessarily imply equivalence in distributions of u's. The proof is heuristic. This result has useful practical implications.
Two inequalities for convex sets in the plane
Authors: Scott P.R.
Published: April 2009

Let K be a bounded, closed, convex set in the euclidean plane having diameter d, width w, inradius r, and circumradius R. We show that

and

where both these inequalities are best possible.
On certain function spaces and group structures
Authors: Yamaguchi Hiroshi
Published: April 2009

We generalize a result of Walter Rudin about the structure of a compact abelian group G for which C(G) + H∞(G) is a closed subalgebra of L∞(G).
Existence and uniqueness regions for solutions of nonlinear equations
Authors: Andrew A.L.
Published: April 2009

A refinement of the Newton-Kantorovich Theorem, which has many-potential applications in existence - uniqueness theory, is used to strengthen a result of Lancaster and Rokne concerning existence and uniqueness regions for zeros of operator polynomials.
Action of a force near the planar surface between semi-infinite immiscible liquids at very low Reynolds numbers: Addendum
Authors: Aderogba K. , Blake J.R.
Published: April 2009

In the paper by Aderogba and Blake [1], the first order approximation to the shape of the interface between two immiscible liquids, at which surface tension acted, was obtained in the case of a point force directed parallel to the interface. In the case of the normal force no solution was obtained due to the logarithmic singularity associated with problems of this type. However, the problem is not physically well-posed in the case of the normal force. Surface tension is not suitable because it cannot alone balance the induced stress on the interface due to a point force. We need an additional force to balance the action of the point force on the interface. The obvious solution is to include a density difference Δρ* between the two fluids

where and are the densities of the lower and upper fluid respectively.
On a nonlinear differential-integral equation for ecological problems
Authors: Rao V. Sree Hari , Rao K. Kuppuswamy
Published: April 2009

In this paper we consider a nonlinear differential-integral equation which arises in the problems of ecology and study the questions of convergent solutions and asymptotic equivalence of the solutions.
On generalized Nörlund methods of summability
Authors: Tanaka Minoru
Published: April 2009

The object of this paper is to establish some relations between two generalized Nörlund methods and also between two absolute generalized Nörlund methods. Our theorems obtained here generalize many known results, including McFadden's Theorems which state the inclusion relations between two absolute Nörlund methods, and results of Ikuko Kayashima.
Orthogonality and characterizations of inner product spaces
Authors: Kapoor O.P. , Prasad Jagadish
Published: April 2009

Using the notions of orthogonality in normed linear spaces such as isosceles, pythagorean, and Birkhoff-James orthogonality, in this paper we provide some new characterizations of inner product spaces besides giving simpler proofs of existing similar characterizations. In addition we prove that in a normed linear space pythagorean orthogonality is unique and that isosceles orthogonality is unique if and only if the space is strictly convex.
Linear approximation by primes
Authors: Lau Kee-Wai , Liu Ming-Chit
Published: April 2009

In this present paper we shall prove the following. Suppose that λ1, λ2, λ3are any non-zero real numbers not all of the same sign and that λ1/λ2is irrational. If η is any real number and, 0 < α < 1/9, then there are infinitely many prime triples (p1,p2,p3) for which
The density theorem for loop near-rings
Authors: Santhakumari C.
Published: April 2009

An algebraic formulation of the density theorem for loop near-rings is presented, which generalizes the same result for near-rings.
Can a Fibonacci group be a unique products group?
Authors: Fox Colin D.
Published: April 2009

We show that a certain class of Fibonacci groups can not be right ordered. A question remaining is: Are the torsion-free members of this class unique products groups?
On stationary points and the complementarity problem
Authors: Nanda Sribatsa , Nanda Sudarsan
Published: April 2009

Let S be a closed convex cone in Cn, S* the polar cone, g a continuous map from Cn into itself, and e a fixed vector in S*. In this paper we prove that there is a connected set T in S of stationary points of (Dr (e), g) where Dr (e) is the set of all x in S with re(e, x) ≤ r. This extends the results of Lemke and Eaves to the complex nonlinear case and arbitrary closed convex cones in Cn. We show that if g is strictly monotone on S, then T is both unique as well as arcwise connected. This partly solves the open problems raised by Eaves in this more general setting. We also show that if x is a stationary point of (Dr (e), g) and re(e, x) < r then x is a stationary point of (S, g).
Intersections of finitely generated free groups
Authors: Nickolas Peter
Published: April 2009

A result of Howson is that two finitely generated subgroupsUandVof a free group have finitely generated intersection. Hanna Neumann showed further that, ifm, nandNare the ranks ofU, VandU ∩ Vrespectively, thenN ≤ 2(m−1)(n−1) + 1, and Burns strengthened this, showing thatN ≤ 2(m−1)(n−1) − m+ 2 (ifm ≤ n). This paper presents a new and simple proof of Burns' result. Further, the graph-theoretical ideas used provide still stronger bounds in certain special cases.
The subvariety lattice of the variety of distributive doublep-algebras
Authors: Dziobiak Wieslaw
Published: April 2009

LetLdenote the subvariety lattice of the variety of distributive doublep-algebras, that is, the lattice whose universe consists of all varieties of distributive doublep-algebras and whose ordering is the inclusion relation. We prove in this paper that each proper filter inLis uncountable. Moreover, we prove that except for the trivial variety (the zero inL) and the variety of Boolean algebras (the unique atom inL) every other element ofL, generated by a finite algebra, has infinitely many covers inL, among which at least one is not generated by any finite algebra. The former result strengthens a result of Urquhart who showed that the latticeLis uncountable. On the other hand, both of our results indicate a high complexity of the latticeLat least in comparison with the subvariety lattice of the variety of distributivep-algebras, since a result of Lee shows that the latter lattice forms a chain of type ω + 1 and every cover in it of the variety generated by a finite algebra is itself generated by a finite algebra.
Trajectories of set valued integrals
Authors: Papageorgiou Nikolaos S.
Published: April 2009

The purpose of this paper is to study the trajectory multifunction Φ(·) determined by the indefinite set valued integral of a measurable Banach space valued multifunction F(·), that is for all t ∈ [0, T], , where the set valued integral is interpreted in the sense of Aumann. We study the topological and algebraic properties of SΦ equaling the set of selectors of Φ(·) whose primitive is an integrable selector of F(·). We also determine several useful properties that Φ(·) possesses and finally we present some convergence and stability results using the Kuratowski-Mosco convergence of sets.
The subcomodule structure of the quantum symmetric powers
Authors: Thams Lars
Published: April 2009

In this paper we study the symmetric powers of quantum GLn. These are comodules and we give a complete description of the subcomodule structure.
On a theorem of Hughes and Thompson
Authors: Bryce R.A.
Published: April 2009

We generalise the notion of proper Hughes subgroup in a group, asking that, for some prime p, the set-complement of the union of two proper subgroups consist solely of elements of order p. A structure theorem for non-p–groups of this type is proved.
A nil-implies-nilpotent result in linearly compact rings
Authors: Xue Weimin , Herstein I.N.
Published: April 2009

Let R be a left linearly compact ring with left ideals I ⊆ J such that RJ is finitely generated and R(J/I) is Artinian. We prove that if J is nil over I then J is nilpotent over I.
Norms of powers in the Volterra algebra
Authors: Solovej Michel
Published: April 2009

We prove a conjecture of Willis saying that for each f in the Volterra algebra the sequence (‖fn‖)n is a weight sequence which is regulated at 1.
Continuity of the superposition operator on Orlicz-Sobolev spaces
Authors: Hardy G. , Thompson H.B.
Published: April 2009

We give sufficient conditions for a homogeneous superposition operator to be a continuous mapping between Orlicz-Sobolev spaces. This extends a result of Marcus and Mizel concerning mappings between Sobolev spaces.
Some coincidence theorems and applications
Authors: Ding Xie Ping , Tarafdar E.
Published: April 2009

In this paper, we establish a new coincidence theorem for a Browder type set-valued mapping and an upper semi-continuous set-valued mapping with compact acyclic values in an H-space which generalises some recent results in the literature. As applications we obtain two H a type coincidence theorems and existence theorems of maximal elements for preference correspondences.
The set of idempotents of a completely regular semigroup as a binary algebra
Authors: Broeksteeg Raymond
Published: April 2009

A semigroupSis calledE-solidif and only if for all idempotentse, f, g ∈ Ssuch thate L f R gthere exists an idempotenth ∈ Ssuch thate R h L g. Each completely regular semigroup is E-solid. We characterise the idempotents of an arbitrary E-solid regular semigroup as a set with a binary operation on it satisfying a given finite set of identities.
Piggyback-Dualitäten
Authors: Davey B.A. , Werner H.
Published: April 2009

For the class of meromorphically starlike functions of prescribed order, the concept of type has been introduced. A characterization of meromorphically starlike functions of order α and type β has been obtained when the coefficients in its Laurent series expansion about the origin are all positive. This leads to a study of coefficient estimates, distortion theorems, radius of convexity estimates, integral operators, convolution properties et cetera for this class. It is seen that the class considered demonstrates, in some respects, properties analogous to those possessed by the corresponding class of univalent analytic functions with negative coefficients.
Injectivity and related concepts in modular varieties: I. Two commutator properties
Authors: Kiss Emil W.
Published: April 2009

The first property occurred in the investigation of directly representable varieties, and was namedC2 by R. McKenzie, the second one is new. Our analysis is independent of injectivity. However, in the forthcoming second part of this paper we are going to prove that varieties with enough injectives satisfy both properties, and shall use intensively the results proved here.
Distances between convex subsets of state spaces
Authors: Ellis A.J.
Published: April 2009

Let L be a closed linear space of continuous real-valued functions, containing constants, on a compact Hausdorff space Ω. This paper gives some new criteria for a closed subset E of Ω to be an L-interpolation set, or more generally for L|E to be uniformly closed or simplicial, in terms of distances between certain compact convex subsets of the state space of L. These criteria involve the facial structure of the state space and hence are of a geometric nature. The results sharpen some standard results of Glicksberg.
Locally irreducible rings
Authors: Vinsonhaler C. , Wickless W.
Published: April 2009

In the study of torsion-free abelian groups of finite rank the notions of irreducibility, field of definition and E-ring have played significant rôles. These notions are tied together in the following theorem of R. S. Pierce:

THEOREM. Let R be a ring whose additive group is torsion free finite rank irreducible and let Γ be the centralizer of QR as a QE(R) module. Then Γ is the unique smallest field of definition of R. Moreover, Γ ∩ R is an E-ring, in fact, it is a maximal E-subring of R.

In this paper we consider extensions of Pierce's result to the infinite rank case. This leads to the concept of local irreducibility for torsion free groups.
Meromorphic univalent functions with positive coefficients
Authors: Mogra M.L. , Reddy T.R. , Juneja O.P.
Published: April 2009

For the class of meromorphically starlike functions of prescribed order, the concept of type has been introduced. A characterization of meromorphically starlike functions of order α and type β has been obtained when the coefficients in its Laurent series expansion about the origin are all positive. This leads to a study of coefficient estimates, distortion theorems, radius of convexity estimates, integral operators, convolution properties et cetera for this class. It is seen that the class considered demonstrates, in some respects, properties analogous to those possessed by the corresponding class of univalent analytic functions with negative coefficients.
Quadratic equations and applications to Chandrasekhar's and related equations
Authors: Argyros Ioannis K.
Published: April 2009

A new technique, using the contraction mapping theorem, for solving quadratic equations in Banach space is introduced. The results are then applied to solve Chandrasekhar's integral equation and related equations without the usual positivity assumptions.
Nilpotent injectors in finite groups
Authors: Förster Peter
Published: April 2009

Nilpotent injectors exist in all finite groups.

For every Fitting class F of finite groups (see [2]), InjF(G) denotes the set of all H ≤ G such that for each N ⊴ ⊴ G , H ∩ N is an F -maximal subgroup of N (that is, belongs to F and i s maximal among the subgroups of N with this property). Let W and N* denote the Fitting class of all nilpotent and quasi-nilpotent groups, respectively. (For the basic properties of quasi-nilpotent groups, and of the N*-radical F*(G) of a finite group G3 the reader is referred to [5].,X. %13; we shall use these properties without further reference.) Blessenohl and H. Laue have shown in CJ] that for every finite group G, InjN*(G) = {H ≤ G | H ≥ F*(G) N*-maximal in G} is a non-empty conjugacy class of subgroups of G. More recently, Iranzo and Perez-Monasor have verified InjN(G) ≠ Φ for all finite groups G satisfying G = CG(E(G))E(G) (see [6]), and have extended this result to a somewhat larger class M of finite groups C(see [7]). One checks, however, that M does not contain all finite groups; for example, S5 ε M.
On the computational algorithms for time-lag optimal control problems
Authors: Wong Kar Hung
Published: April 2009

In this thesis we study the following two types of hereditary optimal control problems: (i) problems governed by systems of ordinary differential equations with discrete time-delayed arguments appearing in both the state and the control variables; (ii) problems governed by parabolic partial differential equations with Neumann boundary conditions involving time-delays.
Isometric multiplication of Hardy-Orlicz spaces
Authors: Deeb W. , Khalil R. , Marzuq M.
Published: April 2009

For a modulus function φ, we define the Hardy-Orlicz space H (φ). Two main questions are discussed in this paper. First, when is a linear map mg: H (φ) → H (φ), mg (f) = g.f an isometry? Second, when is H (φ) = H1?
A reversed Hardy inequality
Authors: Renaud P. F.
Published: April 2009

We consider Hardy's classical inequality for Cesaro averages and show that a reversed version exists if we restrict ourselves to monotone sequences. Some consequences of this result as well as an integral version are also obtained.
On the frequency of 3-connected subgraphs of planar graphs
Authors: Wormald Nicholas C.
Published: April 2009

The concept of dependence of subgraphs of a plane graph is defined, as a measure of how much they overlap. It is shown that if M is a 3-connected plane graph, then the number of copies of M in a plane graph which are dependent on a given copy is bounded above by a constant c (M). The number of copies of M in any n-vertex plane graph is at most nc (m).
On the almost sure convergence of a general stochastic approximation procedure
Authors: Evans S. N. , Weber N. C.
Published: April 2009

A set of conditions for the almost sure convergence of a stochastic iterative procedure is given. The conditions are framed in terms of the behaviour of the random adjustment made the n-th step rather than in terms of some underlying regression model.
Some examples of compressible group algebras and of noncompressible group algebras
Authors: Motose Kaoru
Published: April 2009

A ring R with centre Z (R) is called compressible if Z (eRe) = eZ (R) e for any idempotent e of R. In this paper we shall give some examples of compressible group algebras and of noncompressible group algebras. These examples show that it is very difficult to judge the compressibility of a group algebra.
Lie group valued integration in well-adapted toposes
Authors: Kock Anders
Published: April 2009

In the context of synthetic differential geometry, we prove that group valued 1-forms on the unit interval are exact, provided the group in question is a Lie group. This exactness is the basic assumption in a previous paper by the author on differential forms with values in groups.
A theorem on commutativity of semi-prime rings
Authors: Quadri Murtaza A. , Ashraf Mohd.
Published: April 2009

The following Theorem is proved: LetRbe a semi-prime ring in which either (xy)n−xnynor (xy)n−ynxnis central, for allx,yinRwheren>1is a fixed integer. ThenRis commutative.
Representing a distribution by stopping a Brownian Motion: Root's construction
Authors: Sheu Shey Shiung
Published: April 2009

A closed subset c of [0,∞]×[−∞,∞] is called a barrier if

(i) (∞,x) ∈ C, ∀̱x,

(ii) (t, ±∞) ∈ C, ∀̱t,

(iii) (t, x) ∈ C implies (s, x) ∈ C, ∀̱S ≥ t.

Given a Brownian motion (B (t)) Starting at the origin and a barrier C, let τ(C) be inf{t: (t, B (t)) ∈ C}. A random variable x (or a distribution F) is called achievable if there exists a barrier C so that B (τ(C)) is distributed as x (F). In this paper we shall show that if x is bounded above or below with finite mean or if x has zero mean and E (|x| log+ |x|) < ∞ then x is achievable. This result gives a partial answer to a problem raised by Loynes [7].
A characterization of the topological group of real numbers
Authors: Morris Sidney A.
Published: April 2009

It is shown that a non-discrete locally compact Hausdorff group has each of its proper closed subgroups finite (respectively, discrete) if and only if it is topologically isomorphic to the circle group (respectively, the circle group or the group of real numbers).
New proofs of some theorems on infinitely differentiable functions
Authors: Deakin Michael A. B.
Published: April 2009

New proofs are given for the splitting lemma and two of Mather's theorems in the theory of C∞-functions. They use a Taylor series approach rather than the usual map-germ theory and are more elementary than previous proofs. A geometric characterisation of a class of degenerate functions is proved to hold in this account but not in the usual framework.
On the norming constants occuring in convergent Markov chains
Authors: Cohn Harry
Published: April 2009

Several theorems concerning the norming constants {aṇ} and {bn} making a normed Markov chain {an (Xn+bn): n ≥ 0} convergent in distribution (or in probability) are given. It is shown that if Rényi's mixing conditions holds, and , whereas in the general case with α ≠ 0 and exists and are finite. Examples regarding maxima of independent and identically distributed random variables, random walk, and branching processes are considered.
Primitive recursive algebraic theories and program schemes
Authors: Kühnel W. , Meseguer J. , Pfender M. , Sols I.
Published: April 2009

We introduce primitive recursion as a generation process for arrows of algebraic theories in the sense of Lawvere and carry over important results on algebraic theories and functorial semantics to the enriched setting of “primitive recursive algebra”: existence of free primitive recursive theories and of theories presented by operations and equations on primitive recursive functions; existence of free models presented by generators and equations. Finally semantical correctness of translations is reduced to correctness for the basic operations. There is a connection to the theory of program schemes: program schemes involving primitive recursion correspond to arrows of a primitive recursive theory freely generated over a graph of basic operations. This theory T can be viewed as a programming language with “arithmetics” given by the basic operations and with DO-loops. A machine loaded with a compiler for T can be interpreted as a T-model in Lawvere's sense, preserving primitive recursion.
On product-preserving Kan extensions
Authors: Borceux Francis , Day B. J.
Published: April 2009

In this article we examine the problem of when a left Kan extension of a finite-product-preserving functor is finite-product preserving. This extension property is of significance in the development of finitary universal algebra in a closed category, details of which will appear elsewher. We give a list of closed categories with the required extension property.
A computer aided classification of certain groups of prime power order
Authors: Ascione Judith A. , Havas George , Leedham-Green C. R.
Published: April 2009

A classification of two-generator 3-groups of second maximal class and low order is presented. All such groups with orders up to 38 are described, and in some cases with orders up to 310. The classification is based on computer aided computations. A description of the computations and their results are presented, together with an indication of their significance.
Production optimization for a monopolist who does not set prices
Authors: Armour L.J. , Gates D.J. , Rickard J.A.
Published: April 2009

Consider a monopolistic firm selling each business period's production at the end of that period at a price determined by the buyers, and wishing to determine the production for which business period profit is maximal. In this paper we announce the results of our investigations into what happens when the firm employs a certain algorithm (based on linear approximations to its average contribution profit function) in an attempt to determine this optimal production. Our results are as follows: firstly, for many apparently feasible average contribution profit functions the algorithm generates production sequences globally convergent to the optimal production, the convergence being linear with convergence ratio dependent on the average contribution profit function; secondly, in certain cases a lower bound for the initial rate of convergence of the algorithm can be obtained. Proofs are for the most part given only in outline, and will be published in full later.
Generalizations of the Poincaré Birkhoff fixed point theorem
Authors: Neumann Walter D.
Published: April 2009

It is shown how George D. Birkhoff's proof of the Poincaré Birkhoff theorem can be modified using ideas of H. Poincaré to give a rather precise lower bound on the number of components of the set of periodic points of the annulus. Some open problems related to this theorem are discussed.
Multiplicative functionals and a class of topological algebras
Authors: Joseph Gerard A.
Published: April 2009

Every multiplicative linear functional on a pseudocomplete locally convex algebra satisfying the “sequential” property of Husain and Ng is bounded (a topological algebra is called “sequential” if every null sequence contains an element whose powers converge to zero). Characterizations of such algebras are given, with some examples.
Locally compact products and coproducts in categories of topological groups
Authors: Hofmann Karl Heinrich , Morris Sidney A.
Published: April 2009

In the category of locally compact groups not all families of groups have a product. Precisely which families do have a product and a description of the product is a corollary of the main theorem proved here. In the category of locally compact abelian groups a family {Gj; j ∈ J} has a product if and only if all but a finite number of the Gj are of the form Kj × Dj, where Kj is a compact group and Dj is a discrete torsion free group. Dualizing identifies the families having coproducts in the category of locally compact abelian groups and so answers a question of Z. Semadeni.
The additive groups of subdirectly irreducible rings
Authors: Feigelstock Shalom
Published: April 2009

An abelian group G is said to be subdirectly irreducible if there exists a subdirectly irreducible ring R with additive group G. If G is subdirectly irreducible, and if every ring R with additive group G, and R2 ≠ 0, is subdirectly irreducible, then G is said to be strongly subdirectly irreducible. The torsion, and torsion free, subdirectly irreducible and strongly subdirectly irreducible groups are classified completely. Results are also obtained concerning mixed subdirectly irreducible and strongly subdirectly irreducible groups.
On Sharkovsky's cycle coexistence ordering
Authors: Kloeden Peter E.
Published: April 2009

A theorem of Sharkovsky on the coexistence of cycles for one-dimensional difference equations is generalized to a class of difference equations of arbitary dimension. The mappings defining these difference equations are such that the ith component depends only on the first i independent variables.
Weak and semi-strong solutions of the Schneider-Tricomi problem in the euclidean plane
Authors: Rassias John M.S.
Published: April 2009

Schneider (Math. Nachr. 60 (1974), 167–180) has established the following result. Consider the mixed type equation

in G ⊂ R2 which is a simply connected region, bounded for y > 0 by a piece-wise smooth curve Γ0 connecting the points A(0, 0) and B(1, 0), and for y < 0 by the solutions of k(y).(dy)2 + (dx)2 = 0 which meet at the point G(½, yc), such that for ,

S(x, y) = F(yy) + 8λ·(k/k′)2 > 0 in Ḡ ∩ {y < 0}, “Schneider's Condition”, where F(y) = 1 + 2(k/k′)′, and such that S = S(x, y) is integrable in G2, “Frankl's Condition”. Then the Tricomi Problem (T): L[u] = f with has a weak solution u ∈ L2(Ḡ) and the Adjoint Tricomi Problem (T+): L+[w] = f with has at most one semistrong solution.

In this present paper we get the above result of Schneider in a much more generalized way, so that here our uniqueness theorem and existence results include cases where S(x, y) may be negative in G2.
A Fenchel-Rockafellar type duality theorem for maximization
Authors: Singer Ivan
Published: April 2009

We prove that sup(f-h)(E) = sup(h*-f*)(E*), where f is a proper lower semi-continuous convex functional on a real locally convex space E, h: E → = [-∞, +∞] is an arbitrary-functional and, f*, h* are their convex conjugates respectively. When h = δG, the indicator of a bounded subset G of E, this yields a formula for sup f(G).
Bitangents of plane quartics
Authors: Glass J.P.
Published: April 2009

The topic dealt with in this paper arose out of a study of theta functions and the moduli of curves. It concerns itself with configurations of lines in the plane and when they can be bitangents to a quartic. The techniques used are classical.
On some Gelfand-Mazur like theorems in Banach algebras
Authors: Srinivasan V.K.
Published: April 2009

The following Gelfand-Mazur like theorems are proved in this paper:

(1) A complex Banach algebra which is locally finite, and which is also an integral domain, is isomorphic to the complex field .

(2) A complex Banach algebra which is a noetherian domain is isomorphic to .

(3) A complex Banach algebra which is a principal ideal domain is isomorphic to .

An application is given to the algebra of all complex formal power series in several variables.