bluuebunny/crossref_metadata_2025 huggingface dataset:
A criterion for the Hall-closure of Fitting classes
Authors: Brison Owen J.
Published: April 2009

In a recent paper, Cusack has given a criterion, in terms of the Fitting class “join” operation, for a normal Fitting class to be closed under the taking of Hall π-subgroups. Here we show that Cusack's result can be slightly modified so as to give a criterion for any Fitting class of finite soluble groups to be closed under taking Hall π-subgroups.
Tolerance relations on lattices
Authors: Bandelt Hans-J.
Published: April 2009

The lattice of all tolerance relations (that is, reflexive, symmetric compatible relations) on a lattice is investigated. For modular lattices some examples are given which show that such relations do naturally occur.
Some degeneracy and pathology in non-associative radical theory II
Authors: Gardner B. J.
Published: April 2009

It is shown that in the universal classes of

(i) all commutative algebras,

(ii) all anti-commutative algebras and

(iii) all algebras satisfying x2 = 0 (over any commutative, associative, unital ring)

the only radical classes with hereditary semi-simple classes are those for which membership is determined by additive structure. Some examples of non-hereditary semi-simple classes in the class of all power-associative algebras are also presented.
Viscous motion in an oceanic circulation model
Authors: Bennett A. F. , Kloeden P. E.
Published: April 2009

The barotropic motion of a viscous fluid in a laboratory simulation of ocean circulation may be modelled by Beards ley's vorticity equations. It is established here that these equations have unique smooth solutions which depend continuously on initial conditions. To avoid a boundary condition which involves an integral operator, the vorticity equations are replaced by an equivalent system of momentum equations. The system resembles the two-dimensional incompressible Navier-Stokes equations in a rotating reference frame. The existence of unique generalized solutions of the system in a square domain is established by modifying arguments used by Ladyzhenskaya for the Navier-Stokes equations. Smoothness of the solutions is then established by modifying Golovkin's arguments, again originally for the Navier- Stokes equations. A numerical procedure for solving the vorticity equations is discussed, as are the effects of reentrant corners in the domain modelling islands and peninsulae.
On some Gelfand-Mazur like theorems in Banach algebras: On some Gelfand-Mazur like theorems in P-normed algebras: Corrigenda
Authors: Srinivasan V. K.
Published: April 2009

REMARK 1. In my paper “On some Gelfand-Mazur like theorems in Banach algebras” [2], I stated as Theorem 3.1 the following result: If A is a complex Banach algebra, which is locally finite and if A is an integral domain then A is isomorphic to C. The proof given there is wrong. The mistake occurred when the principal ideal (h) was considered. Certainly (h) is finitely generated as an ideal, but not necessarily as an algebra. However thanks to the following theorem of Heinze [1], the stated Theorem 3.1 of my paper [2] is still correct. Heinze's results states: An associative locally finite algebra which is also an integral domain, over an algebraically closed field is isomorphic to the ground field. The other theorems stated in [2] are correct.
Force distribution on a slender body close to an interface
Authors: Blake J.R. , Fulford G.R.
Published: April 2009

The motion of a slender body parallel and very close to a flat interface which separates two immiscible liquids of differing density and viscosity is considered for very small Reynolds numbers. Approximate analytical expressions are obtained for the distribution of forces acting on the slender body. The limiting case of a rigid plane wall yields results obtained previously.
On k-quasihyponormal operators II
Authors: Gupta B.C. , Ramanujan P.B.
Published: April 2009

An operator T on a Hilbert space is in the class of k-quasihyponormal operators Q(k), if T*k(T*T−TT*)Tk ≥ 0. It is shown that if T is in Q(k) and S is normal such that TX = XS, where X is one to one with dense range, then T is normal; and is unitarily equivalent to S. It is proved that S can be replaced by a cohyponormal operator, if T in Q(1) is one to one. It is also shown that two quasisimilar operators in Q(k) have equal spectra, and every reductive operator quasisimilar to a normal operator is normal.
A class of projective Stone algebras
Authors: Düntsch Ivo
Published: April 2009

We prove that a regular double Stone algebra is protective in the category of Stone algebras if and only if its centre is a projective Boolean algebra and its dense set is countably generated as a filter. It follows that every countable regular double Stone algebra is projective as a Stone algebra.
On extensions of nilpotent torsion rings by semisimple rings
Authors: Amin Ismail A. , Szász Ferenc A.
Published: April 2009

A class of rings in which each member is the extension of a nilpotent torsion ring by a semisimple semiartinian ring is presented.
On r-regular r-connected non-hamiltonian graphs
Authors: Jackson Brad , Parsons T. D.
Published: April 2009

Some methods are given for constructing regular r-valent r-connected non-hamiltonian graphs; often the graphs are also non-r-edge-colorable. The extent of the class of such graphs constructible from these methods and previous methods is discussed.
On the degree of approximation by Szász operators
Authors: Singh Suresh Prasad
Published: April 2009

The aim of the present note is to give the degree of approximation by Szász operators.
On a characterization of planar graphs
Authors: Chen C. C.
Published: April 2009

By introducing the concept of a polygon-extension of a planar graph, we provide a simple proof that a graph is planar if and only if every strict elegant ring in the graph is even.
Differentiable retracts and a modified inverse function theorem
Authors: Barit W. , Wood G.R.
Published: April 2009

A lemma is presented which is a weak version of the inverse function theorem, in that differentiability is assumed instead of continuous differentiability. The result holds only for finite dimensional spaces; a counter-example is given for the infinite dimensional analogue. The lemma is used to answer a question posed by Nadler concerning differentiable retracts.
A functorial version of a construction of Hochschild and Mostow for representations of Lie algebras
Authors: Wilson William H.
Published: April 2009

Let be a Lie algebra, a complemented ideal of , and W an -module. Hochschild and Mostow have described the construction of a -module “induced” from W, which is finite-dimensional provided W is finite-dimensional and satisfies a nilpotent action condition. This note describes a modification of their construction which is functorial and a weak adjoint to the restriction functor from –modules to -modules.
A generalization of Lagrange multipliers: Corrigendum
Authors: Craven B.D.
Published: April 2009

There is a lacuna in the proof of Lemma 1 of [1]; the projector q is assumed without proof. An alternative, valid proof is as follows.

LEMMA 1. Let S, U0, V0 be real Banach spaces; let A : S → U0 and B : S → V0 be continuous linear maps, whose null spaces are N(A) respectively N(B); let N(A) ⊂ N(B) : let A map S onto U0. Then there exists a continuous linear map C : U0 → V0 such that B = C ° A.
A note on generalised linear complementarity problems
Authors: Parida J. , Sahoo B.
Published: April 2009

Given ann×nmatrixA, ann-dimensional vectorq, and a closed, convex coneSofRn, the generalized linear complementarity problem considered here is the following: find az∈Rnsuch that

wheres* is the polar cone ofS. The existence of a solution to this problem for arbitrary vectorqhas been established both analytically and constructively for several classes of matricesA. In this note, a new class of matrices, denoted byJ, is introduced.Ais aJ-matrix if

The new class can be seen to be broader than previously studied classes. We analytically show that for anyAin this class, a solution to the above problem exists for arbitrary vectorq. This is achieved by using a result on variational inequalities.
A structure theorem for operators with closed range
Authors: Guyker James
Published: April 2009

A characterization has previously been given for linear transformations in Hilbert space whose first N + 1 powers are partial isometries. An analogous characterization is now obtained for transformations whose first N+ 1 powers have closed ranges. A hypothesis (that transformations have no isometric part) is found to be unnecessary in previous work.
Finite zero-simple semigroups over an elementary abelian group
Authors: Houghton C.H.
Published: April 2009

Finite O-simple semigroups with a Rees representation over an elementary abelian group are considered. The isomorphism classes of such semigroups with class graph γ and coefficient group of order pd are shown to correspond to the orbits under the automorphism group of γ of those subspaces of the circuit space of γ over Zp which have codimension at most d. A semigroup interpretation of the inclusion relation between subspaces is given and results are obtained on the structure of the automorphism group and the enumeration of the semigroups under consideration.
Stein quasigroups I: Combinatorial aspects
Authors: Pelling M.J. , Rogers D.G.
Published: April 2009

This paper, in conjunction with its algebraic sequel, aims to provide a foundation, long outstanding, to the theory of quasigroups obeying the law x(xy) = yx , otherwise known as Stein quasigroups.
Resolving actions of compact Lie groups
Authors: Field M.J.
Published: April 2009

A general process for the desingularization of smooth actions of compact Lie groups is described. If G is a compact Lie group, it is shown that there is naturally associated to any compact G manifold M a compact G × (Z/2)p manifold on which G acts principally. Here Z/2 denotes the cyclic group of order two and p + 1 is the number of orbit types of the G action on M.
Measure theoretic techniques in topology and mappings of replete and measure replete spaces
Authors: Bachman George , Sultan Alan
Published: April 2009

We prove in this paper several results on lattice related measures and images of such measures under mappings. If we apply these to various areas of point set topology we obtain as corollaries many known and new results on sequential compactness, repleteness, and measure repleteness – areas of recent considerable interest to mathematicians.
The enumeration and bifurcations of ranking functions
Authors: Walker W.J.
Published: April 2009

Suppose n competitors each compete in r races and a ranking function F assigns a score F(j) to the competitor finishing in the jth position in each race. The sum of the scores over r races gives each competitor a final ranking. If n is fixed, the ranking function F bifurcates as r increases. The complete bifurcation behaviour is determined for n = 3 and some information obtained for n > 3.
A counter-example to a conjecture by Deakin
Authors: Arkeryd Leif
Published: April 2009

Michael A.B. Deakin (Bull. Austral. Math. Soc. 17 (1977), 161–175) states (on p. 173) a conjecture, which, if true, would lead to simpler proofs of a number of known theorems. This conjecture is, however, shown to be false by means of a counter-example.
On Stieltjes-Volterra integral equations
Authors: Pandit S.G.
Published: April 2009

A Stieltjes-Volterra integral equation system

is firstly considered. Pointwise estimates and boundedness of its solutions are obtained under various conditions on the functionK. To do this, the well-known Gronwall-Bellman integral inequality is generalized. For a particular choice ofu, it is shown that the integral equation reduces to a difference equation. The problem of existence (and non-existence), uniqueness (and non-uniqueness) of the difference equation is discussed. Gronwall-Bellman inequality is further generalized tonlinear terms and is subsequently applied to obtain sufficient conditions in order that a certain stability of the unperturbed Volterra system

implies the corresponding local stability of the (discontinuously) perturbed system
Action of a force near the planar surface between two semi-infinite immiscible liquids at very low Reynolds numbers
Authors: Aderogba K. , Blake J.R.
Published: April 2009

Explicit expressions for the Green's functions due to a point force in one of two half space fluids are presented for the case when inertial effects of the fluid are negligible (Stokes flow) and the interface between the two fluids is considered to be flat due to the action of surface tension. The analytic expressions are discussed in terms of singularity diagrams. For the case of a force parallel to the interface a first approximation to the interface displacement is made.
An oscillation theorem for a superlinear functional differential equation with general deviating arguments
Authors: Kitamura Yuichi , Kusano Takaŝsi
Published: April 2009

An oscillation criterion is established for a class of functional differential equations including the generalized Emden-Fowler equation

as a special case. The deviating arguments involved may be retarded or advanced or otherwise. The result extends and improves known fundamental oscillation criteria for superlinear differential equations with retarded arguments.
Tall profinite groups
Authors: Hutchinson M.F.
Published: April 2009

A classical theorem of Camille Jordan concerning finite linear groups is used to give two structural characterisations of profinite groups which have only finitely many pairwise inequivalent, continuous, irreducible, unitary representations of each degree. Our characterisations of such groups involve properties of their open normal subgroups.
Topological spaces and Abian structures
Authors: Fox Ralph , Reilly Ivan L.
Published: April 2009

This paper characterizes topological spaces which have an Abian structure - a uniform-like structure of the covering type.
On the distance of non-reflexive spaces to the collection of all conjugate spaces
Authors: Singer Ivan
Published: April 2009

We show that there exists a conjugate Banach space E = B* with a basis, such that the distance from E to the collection of all conjugate Banach spaces can be made arbitrarily large, by suitable renorming of E. This solves a problem raised by B.V. Godun, Dokl. Akad. Nauk SSSR. 236 (1977), 18–20.
On the Lie ring of a group of prime exponent II
Authors: Wall G.E.
Published: April 2009

Letpbe a prime number. The Lie ring of the largest finite group of exponentpand nilpotency class 3p− 3 is determined under certain assumptions (which are conjectured always to hold).
An existence theorem for the generalized complementarity problem
Authors: Parida J. , Sahoo B.
Published: April 2009

Given a closed, convex cone S, in Rn, its polar S* and a mapping g from Rn into itself, the generalized nonlinear complementarity problem is to find a z ∈ Rn such that

Many existence theorems for the problem have been established under varying conditions on g. We introduce new mappings, denoted by J(S)-functions, each of which is used to guarantee the existence of a solution to the generalized problem under certain coercivity conditions on itself. A mapping g:S → Rn is a J(S)-function if

imply that z = 0. It is observed that the new class of functions is a broader class than the previously studied ones.
A note on a paper of E.R. Love
Authors: Fehér F.
Published: April 2009

Applying a new and very elegant method of proof of the Schur-Hardy inequality, given by E.R. Love at the Oberwolfach conference on Linear Spaces and Approximation (1977), norm estimates of integral operators with homogeneous kernels are established in the setting of abstract function norms. Applications to Flett's inequality, to integral means, and to fractional integrals are given.
Minimally locally 1-connected graphs
Authors: Kulkarni K.H.
Published: April 2009

The local connectivity, νk(G), of a graphGis the minimum of the connectivities of neighbourhoods of the vertices ofG.Gis minimally locallyn-connected if νk(G) =nand for every edgexofG, νk(G−x) =n− 1. A necessary and sufficient condition for a locally connected graph to be minimally locally 1-connected is given, and it is shown that forn≥ 7,is minimally locally 1-connected.
Dedekind-finite fields
Authors: Hickman J.L.
Published: April 2009

Let p be a prime and let (mk)k<ω be a strictly increasing sequence of positive integers such that m0 = 1 and mk divides mk+1. A field F is said to be of type (p, (mk)k<ω) if it is the union of an increasing sequence (Fk)k<ω of fields such that Fk has pmk elements. A set X is called “finite” if it has n elements for some nonnegative integer n, and “Dedekind-finite” if every injection f: X → X is a bijection. If the Axiom of Choice is rejected, then it is relatively consistent to assume the existence of medial (that is, infinite, Dedekind-finite) sets. In this paper it is shown that given any type (p, (mk)k<ω) as above, it is relatively consistent with the usual axioms of set theory (minus Choice) to assume the existence of a medial field of type (p, (mk)k<ω). Conversely, it is shown that any medial field must be of type (p, (mk)k<ω) for some (p, (mk)k<ω) as above. The paper concludes with a few observations on Dedekind-finite rings. In the first part of the paper, a general knowledge of Fraenkel-Mostowski set theory and of the Jech-Sochor Embedding Theorems is assumed.
Duality in topological algebra: Addendum
Authors: Day B.J.
Published: April 2009

It has been observed by Banaschewski [1], Proposition 1, that, in the notation of the author's paper [2], if P ⊆ FU is hereditary and finitely productive. This fact does not require the use of injectives as in [2].
New proofs of some theorems on infinitely differentiable functions: Corrigenda
Authors: Deakin Michael A.B.
Published: April 2009

In a recent note [1], Arkeryd presents a counterexample to my conjecture [2]. The same example appears in a preprint by von Grudzinski [3], who also points out that the corollary to Theorem 2 does not follow from the proof of the theorem as stated. The fact that x3 + xy3 and x3 + xy3y3 are right equivalent, but not under quasi-identity, provides a counterexample. The proof on p. 170 of [2] that is also incorrect. In order to establish this result, we note that, from equation (31), it suffices to show that ξ(0, t) = 0 for all t. But, from equation (30), f(ξ(0, t)) = 0. If now 0 is an isolated zero of f, we are done. If not, we may assume ξ(0, t) = 0 without loss of generality. The corollary to Theorem 4 shows that this latter case is, in fact, vacuous.
The interruption phenomenon for generalized continued fractions
Authors: de Bruin M.G.
Published: April 2009

After defining a generalized C-fraction (a kind of Jacobi-Perron algorithm) for an n-tuple of formal power series over (n ≥ 2), the connection between interruptions in the algorithm and linear dependence over [x] of the power series is studied.

Examples will be given showing that the algorithm behaves in a way similar to the Jacobi-Perron algorithm for an n-tuple of real numbers (the gcd-algorithm): there do exist n-tuples of formal power series f(1), f(2), …, f(n) with a C-n-fraction without interruptions but for which 1, f(1), f(2), …, f(n) is nevertheless linearly dependent over [x].

Moreover an example will be given of algebraic functions f, g of degree n over [x] (formally defined) for which the C-n-fraction for f, f2, …, fn has just one interruption and that for g, g2, …, gn 1 none, while of course 1. f, f2, …, fn and 1, g, g2, …, gn admit (only) one dependence relation over [x].
Limit theorems for semi-Markov processes
Authors: Athreya K.B. , Ney P.E.
Published: April 2009

A new construction of regeneration times is exploited to prove ergodic and renewal theorems for semi-Markov processes on general state spaces. This work extends results of the authors in Ann. Probability (6 (1978), 788–797).
A note on Omori-Lie groups
Authors: Yamamuro Sadayuki
Published: April 2009

The theory of differentiation in locally convex spaces constructed by the author in Memoirs Amer. Math. Soc. 17 (1979) is used to give a new form of the definition of Omori-Lie groups.
Large algebraic theories with small algebras
Authors: Reiterman Jan
Published: April 2009

The aim of the paper is to study the interrelation between several natural smallness conditions on an algebraic theory with a proper class of operations. The conditions concern the existence of sets of data determining algebras, homomorphisms, subalgebras, and congruences.
Isotopy in surface complexes from the computational viewpoint
Authors: Stillwell John C.
Published: April 2009

It is shown that the problem of deciding whether a curve in a finite surface complex is isotopic to a point is NP-complete. This contrasts with the recursively enumerable (RE)-completeness of the corresponding homotopy problem, and exhibits surface complexes as a common framework for NP-complete and RE-complete algorithmic problems.
On profiniteness of compact totally disconnected algebras
Authors: Day B.J.
Published: April 2009

The paper presents a necessary and sufficient condition for a given compact totally disconnected space C to be the projective limit of a given directed cone of epimorphisms onto finite discrete quotients of C. This problem is related to the question of when a compact totally disconnected algebra is profinite and some observations in this direction are recorded.
The equivalence of some variational problems for surfaces of prescribed mean curvature
Authors: Williams Graham H.
Published: April 2009

One method of finding non-parametric hypersurfaces of prescribed mean curvature which span a given curve inRnis to find a function which minimizes a particular integral amongst all smooth functions satisfying certain boundary conditions. A new problem can be considered by changing the integral slightly and then minimizing over a larger class of functions. It is possible to show that a solution to this new problem exists under very general conditions and it is usually known as the generalized solution. In this paper we show that the two problems are equivalent in the sense that the least value for the original minimization problem and the generalized problem are the same even though no solution may exist. The case where the surfaces are constrained to lie above an obstacle is also considered.
Wilansky's query on outer measures
Authors: Kim Choo-Whan
Published: April 2009

On a set X, let μ* be an outer measure and μ the measure induced by μ*. We show that if X is a finite set, then the measure μ is saturated. We give two examples of non-regular outer measures on an infinite set X which induce non-saturated and saturated measures, respectively. These answer a query posed by Wilansky.
Normal and subnormal subgroups in the group of units of group rings
Authors: Goncalves Jairo Zacarias
Published: April 2009

Let KG be the group ring of the group G over the infinite field K, and let U(KG) be its group of units. If G is torsion, we obtain necessary and sufficient conditions for a finite subgroup H of G to be either normal or subnormal in U(KG). Actually, if H is subnormal in U(KG), we can handle not only the case H finite, but the precise assumptions depend on the characteristic of K.
On a commutativity theorem for semi-simple rings
Authors: Quadri Murtaza A. , Ashraf Mohd.
Published: April 2009

In this note a theorem proved by Abu-Khuzam and Yaqub has been improved as follows: let R be a semi-simple ring such that for all x, y in R there exists a positive integer n = n(x, y) for which either (xy)n + (yx)n or (xy)n – (yx)n is central. Then R is commutative.
On convergence of closed sets in a metric space and distance functions
Authors: Beer Gerald
Published: April 2009

Let CL(X) denote the nonempty closed subsets of a metric space X. We answer the following question: in which spaces X is the Kuratowski convergence of a sequence {Cn} in CL(X) to a nonempty closed set C equivalent to the pointwise convergence of the distance functions for the sets in the sequence to the distance function for C ? We also obtain some related results from two general convergence theorems for equicontinuous families of real valued functions regarding the convergence of graphs and epigraphs of functions in the family.
Periodic points and chaos for expanding self-maps of the interval
Authors: Zhenhua Zhang
Published: April 2009

It is shown that expanding self-maps of the interval with a finite number of turning points must have periodic points whose periods are not integral power of 2 and therefore are chaotic.
The Farkas lemma of Shimizu, Aiyoshi and Katayama
Authors: Swartz Charles
Published: April 2009

Shimizu, Aiyoshi and Katayama have recently given a finite dimensional generalization of the classical Farkas Lemma. In this note we show that a result of Pshenichnyi on convex programming can be used to give a generalization of the result of Shimizu, Aiyoshi and Katayama to infinite dimensional spaces. A generalized Farkas Lemma of Glover is also obtained.
An Egerev's theorem for vector functions
Authors: Guerra P. Jimenez , de Maria Gonzalez Jose L.
Published: April 2009

In this paper some results of Egorov's theorem type are given for functions with values in locally convex spaces and Riesz's theorem is proved for functions taking values in a sequentially complete locally convex space.
On the Pettis measurability theorem
Authors: Helmer Dietrich
Published: April 2009

It is shown that, in Pettis's criterion for Bochner measurability of a vector-valued function f:S→X, scalar measurability offcan be weakened to requiring thatuof be measurable foruin some subset of the dualX* separating the points ofX. Even then, the separability hypotheses in Pettis's Theorem can be weakened as well.
Analysis on superspace: an overview
Authors: Pestov Vladimir G.
Published: April 2009

The concept of superspace is fundamental for some recent physical theories, notably supersymmetry, and a mathematical feedback for it is provided by superanalysis and supergeometry. We survey the state of affairs in superanalysis, shifting our attention from supermanifold theory to “plain” superspaces. The two principal existing approaches to superspaces are sketched and links between them discussed. We examine a problem by Manin of representing even geometry (analysis) as a collective effect in infinite-dimensional purely odd geometry (analysis), by applying the technique of nonstandard (infinitesimal) analysis.
Injectivity and related concepts in modular varieties: II. The congruence extension property
Authors: Kiss Emil W.
Published: April 2009

Varieties with enough injectives satisfy the congruence extension property (CEP). We investigate the CEP in modular varieties by using the techniques developed in the first part of the present paper. As corollaries, we obtain the results of B. Davey and J. Kollár for the congruence distributive case as well as the description of all varieties of groups and rings with CEP, given by B. Biró, E.W. Kiss and P.P. Pálfy.
On existence theorems for differential equations in Banach spaces
Authors: Banaś Józef
Published: April 2009

In this paper we show that a number of existence theorems for the Cauchy problem of ordinary differential equations in Banach spaces are only apparent generalizations of the previous ones.
Clifford semigroups and monotonicity
Authors: Hays T.E.
Published: April 2009

A semigroup S is said to be monotone if its binary operation is a monotone function from S × S into S. This paper utilizes some of the known algebraic structure of Clifford semigroups, semigroups which are unions of groups, to study topological Clifford semigroups which are monotone. It is shown that such semigroups are preserved under products, homomorphisms, and, under certain conditions, closures. Necessary and sufficient conditions for monotonicity of groups, paragroups, bands, compact orthodox Clifford semigroups, and compact bands of groups are developed.
Absolute Riesz summability of a Fourier related series, II
Authors: Dikshit G.D.
Published: April 2009

This paper is an endeavour to improve upon the work begun in an earlier paper with the same title. We prove a general theorem on the summability |R, exp((log ω)β+1), ρ| of the series ∑ {sn(x)−s}/n, where {sn(x)} is the sequence of partial sums at a point x of the Fourier series of a Lebesgue integrable 2π-periodic function and s is a suitable constant. While the theorem improves upon the main result contained in the previous paper, corollaries to it include recent results due to Chandra and Yadava.
Radon polymeasures
Authors: Jefferies Brian
Published: April 2009

The Radon-Nikodým theorem and a sequential convergence result are given for integrals with respect to a Radon polymeasure on a finite product space.
Starlike integral operators
Authors: Ahmad Faiz
Published: April 2009

We study integral transforms of functions belonging to the Jakubowski class S(m, M) and determine the range of values of the exponent for which the integral is a convex or a close to convex function.
Topological vitali measure spaces
Authors: Sarkhel D.N. , Chakraborti T.
Published: April 2009

The properties of Lebesgue outer measures embodied in the Vitali covering theorem, the Vitali-Carathéodory theorem, the Lusin theorem, the density theorem, outer regularity and inner regularity, and the relation between measurability and approximate continuity are studied in a general abstract space, called a topological Vitali measure space. The main theme is the mutual equivalence of these properties.
On the implicit complementarity problem in Hilbert spaces
Authors: Isac G.
Published: April 2009

We consider in this paper the implicit complementarity problem imposed by quasi-variational inequalities and stochastic optimal control. The principal result is an existence theorem for the implicit complementarity problem in Hilbert spaces.
Characterization of a class of infinite matrices with applications
Authors: Natarajan P. N.
Published: April 2009

In this paper,Kdenotes a complete, non-trivially valued, non-archimedean field. The class (lα,lα) of infininite matrices transforming sequences overKinlαto sequences inlαis characterized. Further a Mercerian theorem is proved in the context of the Banach algebra (lα,lα), α ≥1and finally a Steinhaus type result is proved for the spacelα. In the case of ℝ or ℀, on the other hand, the best known result so far seems to be a characterization of positive matrix transformations of the class (lα,lβ), ∞ > α ≥ β >1.
On an integral operator for convex univalent functions
Authors: Kumar Vinod , Shukla S. L.
Published: April 2009

Let K (m,M) denote the class of functions regular and satisfying |1 + zf″(z)/f′(z)− m| < M in |z| < 1, where |m−1| < M ≤ m. Recently, R.K. Pandey and G. P. Bhargava have shown that if f ε K (m,M), then the function du also belongs to K (m,M) provided α is a complex number satisfying the inequality |α| ≤ (1−b)/2, where b = (m-1)/M. In this paper we show by a counterexample that their inequality is in general wrong, and prove a corrected version of their result. We show that F ε K (m,M) provided that α is a real number satisfying −φ ≤ α ≤1, φ = (M−|m−1|)/(M + |m−1|), or a complex number satisfying |α| ≤ φ. In both cases the bounds for α are sharp.
A wide Perron integral
Authors: Sarkhel D. N.
Published: April 2009

In terms of an arbitrary limit process T, defined abstractly for real functions, we define in a novel way a T-continuous integral of Perron type, admitting mean value theorems, integration by parts and the analogue of the Marcinkiewicz theorem for the ordinary Perron integral. The integral is shown to include, as particular cases, the various known continuous, approximately continuous, cesàro-continuous, mean-continuous and proximally Cesàro-continuous integrals of Perron and Denjoy types. An interesting generalization of the classical Lebesgue decomposition theorem is also obtained.
A nil-implies-nilpotent result in Artinian rings
Authors: Meyer J. H.
Published: April 2009

It is shown that if the ring A is left Artinian and L1 and L2 are left ideals of AL1 is nilpotent modulo L2 if L1 is nil modulo L2.
Contractive projections on Banach space
Authors: Spivack Mark
Published: April 2009

In this note we prove the uniqueness of a projection onto a given subspace with strictly contractive complement. We also show that, if one completely contractive projection is invariant under another, then the two commute.
A commutativity theorem for semi-primitive rings
Authors: Tominaga Hisao
Published: April 2009

In this brief note, we prove the following: Let R be a semi-primitive ring. Suppose that for each pair x, y ε R there exist positive integers m = m (x,y) and n = n (x,y) such that either [xm,(xy) n − (yx) n] = 0 or [xm,(xy) n + (yx) n] = 0. Then R is commutative.
On a maximal outer area problem for a class of meromorphic univalent fuctions
Authors: Zemyan Stephen M.
Published: April 2009

For 0 < p < 1, let Sp denote the class of functions f (z) which are meromorphic and univalent in the unit disk U, with the normalisations f (0) = 0, f′(0) = 1 and f (p) = ∞, and let Sp (a) denote subclass of Sp consisting of those functions in Sp whose residue at the pole in equal to a. In this paper, we determine, for values of the residue a in a certain disk Δp, the greatest possible outer area over all functions in the class Sp (a). We also determine additional information concerning extremal function if the reside a dose not lie in Δp.
Finite simple groups with no elements of order six
Authors: Gordon L. M.
Published: April 2009

The aim of this paper is to completely classify the finite simple groups with no elements of order 6. The proof is by induction and involves an analysis of the structure of the 2-local subgroups of a counterexample of minimum order. A recent result of Glauberman plays an essential role.
A computer aided classification of certain groups of prime power order: Corrigendum
Authors: Ascione Judith A. , Havas George , Leedham-Green C.R.
Published: April 2009

The first four paragraphs of [1, p. 258] are a mildly erroneous over simplification of the situation. A more accurate description follows.

The analysis of two-generator 3-groups of second maximal class goes along the following lines. We first define a class of group whose structure is particularly amenable to theoretical analysis.
On character values in finite groups
Authors: Herzog Marcel , Praeger Cheryl E.
Published: April 2009

Let u be a nonidentity element of a finite group G and let c be a complex number. Suppose that every nonprincipal irreducible character X of G satisfies either X(l) − X(u) = c or X(u) = 0. It is shown that c is an even positive integer and all such groups with c ≤ 8 are described.
An embedding theorem for ordered groups: Addendum
Authors: Fox Colin D.
Published: April 2009

A simple argument yields the following generalization of Theorem 6 of [1] (whose notation is retained without further explanation).
Interchange of vector valued integrals when the measures are Bochner or Pettis indefinite integrals
Authors: de Korvin Andre , Roberts Charles E.
Published: April 2009

Necessary and sufficient conditions for the interchange of two Bochner integrals and for the interchange of two Pettis integrals are obtained. These conditions are different from those generally required in classical Fubini theorems since they do not require the construction of the cross product measure. The proof makes use of the Vitali-Hahn-Saks Theorem. It should be noted that while Fubini theorems use the cross product measure, one of the difficulties encountered is that the product measure fails to be countable additive – this is pointed out in M. Bhaskara Rao (Indiana Univ. Math. J. 21 (1972), 847–848) and Charles Swartz (Bull. Austral. Math. Soc. 8 (1973), 359–366). Most applications require the interchange of the two integrals rather than integration with respect to the product measure.
A uniqueness theorem for the Chaplygin-Frankl problem
Authors: Rassias John M.S.
Published: April 2009

In a paper dealing with trans-sonic jet flows Frankl (Bull. Acad. Sci. URSS Sér. Math. [Izv. Akad. Nauk SSSE] 9 (1945), 121–143) considered the following problem (T) by applying the condition

where k = k(y) is a monotone increasing function with a continuous second derivative, k(0) = 0, F(0) > 0, k′(y) ≠ 0 for y < 0. Consider an equation of the form

which is elliptic for y > 0, hyperbolic for y < 0, and parabolic for y = 0. Consider equation (2) in a bounded simply connected region D ⊂ R2 which is bounded by the following three curves: a piecewise smooth curve Γ0 lying in the half-plane y > 0 which intersects the line y = 0 at the points A(0, 0) and B(l, 0); for y < 0 by a smooth curve Γ2 through B which meets the characteristic of (2) issuing from A(0, 0) at the point P; and the curve Γ1 which consists of the portion PA of the characteristic through A. The problem (T) (or problem of Tricomi-Frankl) consists of finding a solution u = u(x, y) ∈ C2(D) assuming prescribed values on Γ0 ∪ Γ2. In the present paper we generalize Frankl's uniqueness theorem; our uniqueness theorem includes cases where F(y) may be negative.
Points in topoi of sheaves over distributive lattices
Authors: Adelman M.
Published: April 2009

This article generalizes the well known theorem that the geometric morphisms from the category of sets to a category of set-valued sheaves on a topological space correspond to the irreducible components of the topological space. As irreducible components are not available in any topos more general than a spatial one, they are characterized in terms of filters of open sets - which are available in any topos. It is then seen that the theorem phrased in these terms generalizes to sheaves on any lattice with reasonable distributivity conditions.
On the Morse-Smale characteristic of a differentiable manifold
Authors: Rassias George M.
Published: April 2009

In this note, the Morse-Smale characteristic of a differentiable manifold is defined and certain of its properties are studied.
A note on rational approximation
Authors: Davis C.S.
Published: April 2009

It is shown that the inequality

holds for an infinity of integers p, q and that here the factor ½ may not be replaced by a smaller number. Corresponding best possible inequalities are given for the numbers e±2/t, where t is a positive integer.
A note on induced central extensions
Authors: Vermani L.R.
Published: April 2009

A characterization of induced central extensions which gives an explicit relationship between induced central extensions and n-stem extensions is obtained. Using the characterization, necessary and sufficient conditions for a central extension of an abelian group by a nilpotent group of class n to be a Baer sum of an induced central extension and an extension of class n are obtained.
A note on the omega lemma
Authors: Yamamuro Sadayuki
Published: April 2009

A class of locally convex spaces, a B-subfamily of finite order, is defined and the omega lemma for spaces belonging to this family is proved.
Perfect maps on convergence spaces
Authors: Herrmann Robert A.
Published: April 2009

The concept of the perfect map on a convergence space (X, q), whereqis a convergence function, is introduced and investigated. Such maps are not assumed to be either continuous or surjective. Some nontrivial examples of well known mappings between topological spaces, nontopological pretopological spaces and nonpseudotopological convergence spaces are shown to be perfect in this new sense. Among the numerous results obtained is a covering property for perfectness and the result that such maps are closed, compact, and for surjections almost-compact. Sufficient conditions are given for a compact (respectively almost-compact) map to be perfect. In the final section, a major result shows that iff: (X, q) → (Y, p) is perfect andg: (X, q) → (Z, s) is weakly-continuous into HausdorffZ, then (f, g): (X, q) → (Y×Z,p×s) is perfect. This result is given numerous applications.
Rates of convergence for U-Statistics with varying kernels
Authors: Weber N.C.
Published: April 2009

Let Un be a U-statistic whose kernel depends on the size n of the sample under consideration. It is shown that when Un is suitably normalised its distribution function differs in Lp norm from the distribution function of a standard normal variable by a term of O(n-½).
Trivializing ribbon links by Kirby moves
Authors: Hillman Jonathan A.
Published: April 2009

In this note it is shown that any ribbon link is a sublink of a ribbon link for which surgery on the longitudes gives a connected sum of copies of S1 x S2. In particular there are many links for which the analogue of the knot theoretic Property R fails, and sublinks of homology boundary links need not be homology boundary links. Higher dimensional analogues of these results are also given and it is shown that if n ≥ 2 the group of a ν-component ribbon n-link has a presentation of deficiency ν. Hence there are high dimensional slice knots which are not ribbon knots.
Radii of convexity of two classes of regular functions
Authors: Tuan P.D. , Anh V.V.
Published: April 2009

This paper establishes the radii of convexity of the following two classes of regular functions,

where

.
Existence and uniqueness of weak solutions of the Cauchy problem for parabolic delay-differential equations
Authors: Nababan S. , Teo K.L.
Published: April 2009

In this paper, a class of systems governed by second order linear parabolic partial delay-differential equations in “divergence form” with Cauchy conditions is considered. Existence and uniqueness of a weak solution is proved and its a priori estimate is established.
On flat finitely generated ideals
Authors: Dobbs David E.
Published: April 2009

It is shown that if I is a finitely generated ideal of a commutative ring R such that the multiplication map I ⊗RI → I is an injection, then I is locally principal. As a corollary, one obtains a new homological characterization of Prüfer domains.
Functional equations occurring in the theory of delayed differential equations
Authors: Banaś Józef , Wędrychowicz Stanisław
Published: April 2009

This paper is devoted to duscussion of some functional equations obtained in the theory of delayed differential equations. By means of the Laplace transform distribution solutions of the considered equations are constructed.
Hilbert spaces have the Banach-Stone property for Bochner spaces
Authors: Greim Peter
Published: April 2009

Let (ωi, σi, μi.) be two positive finite measure spaces, V a non-zero Hilbert space, and 1 ≤ p < ∞, p # 2. In this article it is shown that each surjective linear isometry between the Bochner spaces induces a Boolean isomorphism between the measure algebras , thus generalizing a result of Cambern's for separable Hilbert spaces.

This Banach–Stone type theorem is achieved via a description of the Lp-structure of .
A continuity property related to an index of non-separability and its applications
Authors: Moors Warren B.
Published: April 2009

For a set E in a metric space X the index of non-separability is β(E) = inf{r > 0: E is covered by a countable-family of balls of radius less than r}.

Now, for a set-valued mapping Φ from a topological space A into subsets of a metric space X we say that Φ is β upper semi-continuous at t ∈ A if given ε > 0 there exists a neighbourhood U of t such that β(Φ(U)) < ε. In this paper we show that if the subdifferential mapping of a continuous convex function Φ is β upper semi-continuous on a dense subset of its domain then Φ is Fréchet differentiable on a dense Gδ subset of its domain. We also show that a Banach space is Asplund if and only if every weak* compact subset has weak* slices whose index of non-separability is arbitrarily small.
Right alternative algebras with commutators in a nucleus
Authors: Kleinfeld Erwin , Smith Harry F.
Published: April 2009

Let A be a right alternative algebra, and [A, A] be the linear span of all commutators in A. If [A, A] is contained in the left nucleus of A, then left nilpotence implies nilpotence. If [A, A] is contained in the right nucleus, then over a commutative-associative ring with 1/2, right nilpotence implies nilpotence. If [A, A] is contained in the alternative nucleus, then the following structure results hold: (1) If A is prime with characteristic ≠ 2, then A is either alternative or strongly (–1, 1). (2) If A is a finite-dimensional nil algebra, over a field of characteristic ≠ 2, then A is nilpotent. (3) Let the algebra A be finite-dimensional over a field of characteristic ≠ 2, 3. If A/K is separable, where K is the nil radical of A, then A has a Wedderburn decomposition
Convex spaces: Classification by differentiable convex functions
Authors: Eyland Roger , Sharp Bernice
Published: April 2009

The differentiability, of a specified strength, of a convex function at a point, is shown to be characterised by the convergence of subdifferentials in the appropriate topology on the dual space. This is used to prove that if each gauge is densely differentiable then so is each convex function. The generic version of this is equivalent to a conjecture which, for Gateaux differentiability and Banach spaces, is the long standing open question of whether X × ℝ is Weak Asplund whenever X is. Some progress is made towards a resolution.
Some further results on oscillation of neutral differential equations
Authors: Yu Jianshe , Wang Zhicheng
Published: April 2009

We obtain new sufficient conditions for the oscillation of all solutions of the neutral differential equation with variable coefficients

whereP, Q, R∈C([t0, ∞),R+),r∈ (0, ∞) and τ, σ ∈ [0, ∞). Our results improve several known results in papers by: Chuanxi and Ladas; Lalli and Zhang; Wei; Ruan.
Dirichlet series with positive real part
Authors: Samaris N.
Published: April 2009

We consider the sequence Λ = {0 < λ2 < λ2 < …}, for which λn → +∞. We denote by PD(Λ) the class of Dirichlet's series having the form F(s) = defined in the half plan Re s > 0 converging absolutely and Re F ≥ 0. If N0 = {0, 1,2, …} then the class PD(N0) coincides with the Caratheodory's class P. In this paper some classical results holding for the class P are generalised in any class PD(Λ). In special cases for the sequence Λ extreme problems are examined in the class PD(Λ).
On the prediction error for two-parameter stationary random fields
Authors: Cheng R.
Published: April 2009

A number of Szegö-type prediction error formulas are given for two-parameter stationary random fields. These give rise to an array of elementary inequalities and illustrate a general duality relation.
Isometric immersion of a compact Riemannian manifold into a Euclidean space
Authors: Deshmukh Sharief
Published: April 2009

We show that an isometric immersion of an n−dimensional compact Riemannian manifold of non-negative Ricci curvature with scalar curvature always less than n(n−1)λ−2 into a Euclidean space of dimension n + 1 can never be contained in a ball of radius λ.
Multipliers in continuous vector-valued function spaces
Authors: Haro J.C. Candeal , Lai H.C.
Published: April 2009

We identify the multiplier space of continuous vector-valued function spaces as the bounded continuous multiplier-valued space in the strong topology.
Representations of finite groups and Cuntz-Krieger algebras
Authors: Mann M.H. , Raeburn Iain , Sutherland C.E.
Published: April 2009

We investigate the structure of the C*-algebras 𝒪ρ constructed by Doplicher and Roberts from the intertwining operators between the tensor powers of a representation ρ of a compact group. We show that each Doplicher-Roberts algebra is isomorphic to a corner in the Cuntz-Krieger algebra 𝒪A of a {0,1}-matrix A = Aρ associated to ρ. When the group is finite, we can then use Cuntz's calculation of the K-theory of 𝒪A to compute K*(𝒪ρ).
On periodic solutions of a semilinear hyperbolic parabolic equation
Authors: Nakao Mitsuhiro , Kato Hisako
Published: April 2009

Uniqueness and regularity of periodic solutions to the semilinear dissipative wave equation with small parameter ∈ > 0,

are investigated when g(u) has a certain ‘critical’ nonlinearity.
Generalisation of an inequality of C.T. Chuang to vector meromorphic functions
Authors: Lahiri Indrajit
Published: April 2009

We generalise Chuang's inequality to vector meromorphic functions, which is originally a sort of extension of Nevanlinna's second fundamental theorem.