bluuebunny/crossref_metadata_2025 huggingface dataset:
Extension of three theorems For Fourier series on the disc to the torus
Authors: Miamee A. G.
Published: April 2009

We extend three well-known facts of Fourier series on the disc to Fourier series on the torus, a theorem of Riesz, a theorem of Szegö, and the fact that any function in H1 can be factored as the product of two functions in H2. Here the rôle of negative integers is played by the lattice points in the third quadrant. In earlier extensions of these theorems this rôle was played by half-planes.
On some groups with trivial multiplicator
Authors: Wiegold James
Published: April 2009

I discussed the sort of thing Bernhard had in mind concerning the BFC-problem in [3], an article written for his sixieth birthday. This vigesennial contribution deals with one of the “and others”, namely the zero deficiency problem. in his article [1] bearing the same title as this one, Bernhard gave 2-generator 2-relator presentations of some metacyclic groups; if one distils and formalises the process used there, one gets the following result, to be used later in constructing some zero-deficiency finitep-groups.
Sequences and bases in p-Banach spaces
Authors: Ariño M. A.
Published: April 2009

Necessary and sufficient condition are given for an infinite dimensional subspace of a p-Banach space X with basis to contain a basic sequence which can be extended to a basis of X.
On subnormality of generalized derivations and tensor products
Authors: Magajna Bojan
Published: April 2009

Subnormal and quasinormal tensor product operators and generalized derivations on the Hilbert-Schmidt class will be characterized.
On converse duality for a nondifferentiable program
Authors: Gulati T.R.
Published: April 2009

A nonlinear nondifferentiable program with linear constraints is considered and a converse duality theorem is discussed. First we weaken an assumption previously made by Bhatia, and then give a simple proof under this weaker hypothesis, using the Fritz John conditions. Finally, defining a generalized Slater constraint qualification which implies Abadie's constraint qualification, we give a simple condition for the dual problem to satisfy this constraint qualification.
A Hilbert-Schmidt norm inequality associated with the Fuglede-Putnam theorem
Authors: Furuta Takayuki
Published: April 2009

The familiar Fuglede-Putnam theorem asserts thatAX=XBimpliesA*X=XB*whenAandBare normal. We prove thatAandB*be hyponormal operators and letCbe a hyponormal commuting withA*and also letD*be a hyponormal operator commuting withBrespectively, then for every Hilbert-Schmidt operatorX, the Hilbert-Schmidt norm ofAXD+CXBis greater than or equal to the Hilbert-Schmidt norm ofA*XD*+C*XB*. In particular,AXD=CXBimpliesA*XD*=C*XB*. If we strengthen the hyponormality conditions onA, B*, CandD*to quasinormality, we can relax Hilbert-Schmidt operator of the hypothesis onXto be every operator and still retain the inequality under some suitable hypotheses.
Approximation of entire functions over Carathéodory domains
Authors: Kapoor G.P. , Nautiyal A.
Published: April 2009

Let D be a domain bounded by a Jordan curve. For 1 ≤ p ≤ ∞, let Lp(D) be the class of all functions f holomorphic in D such that where A is the area of D. For f ∈Lp(D), set

πn consists of all polynomials of degree at most n. Recently, Andre Giroux (J. Approx. Theory 28 (1980), 45–53) has obtained necessary and sufficient conditions, in terms of the rate of decrease of the approximation error , such that has an analytic continuation as an entire function having finite order and finite type. In the present paper we have considered the approximation error (*) on a Carathéodory domain and have extended the results of Giroux for the case 1 ≤ p < 2.
A characterization of the existence of a Souslin line
Authors: Kemoto Nobuyuki
Published: April 2009

The main purpose of this paper is to show that there exists a Souslin line if and only if there exists a countable chain condition space which is not weak-separable but has a generic π-base. If I is the closure of the isolated points in a space X, then X is said to be weak-separable if a first category set is dense in X – I. A π-base is said to be generic if, whenever a member of is included in the disjoint union of members of it is included in one of them.
Spaces with homogeneous norms
Authors: Pryde A.J.
Published: April 2009

Spaces with homogeneous norms are closely related to the Beppo Levi spaces of Deny and Lions, to spaces of Riesz potentials, and to Sobolev spaces. In this paper we survey the literature on them, give a broad extension of their definition, and present their basic theory. Many of the properties of Sobolev spaces have their analogues. In fact, the two families are locally equivalent. Spaces with homogeneous norms are especially suited to the study of boundary value problems on for homogeneous elliptic operators with constant coefficients. We will use them extensively in a forthcoming paper to study elliptic partial differential equations with mixed boundary conditions on a smoothly bounded domain.
Simultaneous diophantine approximations and Hermite's method
Authors: Durand Alain
Published: April 2009

In this paper we generalize a result of Mahler on rational approximations of the exponential function at rational points by proving the following theorem: letnε N* and αl, …, αnbe distinct non-zero rational numbers; there exists a constantc=c(n, αl, …, αn) ≥ 0 such that

for every non-zero integer point (qo,ql, …,qn)andq= max {|ql|, … |qn|, 3}.
More Fibonacci varieties
Authors: Kim Ann Chi , Neumann B.H. , Rhemtulla A.H.
Published: April 2009

The Fibonacci varieties introduced by Ann Chi Kim, Bull. Austral. Math. Soc. 19 (1978), 191–196 (1979), are here generalised in an obvious way suggested by the work of D.L. Johnson, J.W. Wamsley, and D. Wright, Proc. London Math. Soc. (3) 29 (1974), 577–592. The underlying groups of algebras in these varieties are studied, and are shown to be abelian when the algebras are generated by a single element, and in general are found to be extensions of central subgroups by groups of finite exponent.
Legendre polynomials in irrationality proofs
Authors: Beukers F.
Published: April 2009

It is shown that a simple trick involving Legendre polynomials readily yields the irrationality of ea, , π2, and of the zeros of Bessel functions of integer order. Generalisation of this idea yields the irrationality of ζ(3).
Positivity notions for holomorphic line bundles over compact Riemann surfaces
Authors: Rabinowitz Joshua H.
Published: April 2009

Since the early 1950's, when Kodaira “discovered” positive line bundles, the notion of positivity has undergone a continuous evolution. This paper is intended as an introduction to the study of positivity notions. More specifically, I consider the simplest case - line bundles over compact Riemann surfaces - and compare five positivity notions for such bundles. The results obtained are certainly not new; they are, in fact, known in much greater generality. However, by restricting to the dimension one case, I am able to make use of Riemann surface techniques to significantly simplify the proofs. In fact, this article should be easily understood by anyone familiar with the contents of Gunning's Lectures on Riemann surfaces.
Uniformization of quasi-uniform spaces
Authors: Raghavan T. G. , Reilly I. L.
Published: April 2009

This paper considers the question of when a quasi-uniform space has a compatible uniform structure. Typical of the sufficient conditions provided is the result that a quasi-uniform space whose conjugate topology is compact and R0 is uniformizable.
Distributive Ockham algebras: free algebras and injectivity
Authors: Goldberg Moshe S.
Published: April 2009

This paper centres around the variety 0 of distributive Ockham algebras, and those subvarieties of 0 which are generated by a single finite subdirectly irreducible algebra A. We use H.A. Priestley's duality for bounded distributive lattices throughout. First, intrinsic descriptions of the duals of certain finite subdirectly irreducibles are given; these are later used to determine projectives in the dual categories. Next, left adjoints to the forgetful functors from 0 and Var(A) into bounded distributive lattices are obtained, thereby allowing us to describe all free algebras and coproducts of arbitrary algebras. Finally, by applying the duality, we characterize injectivity in Var(A) for each finite subdirectly irreducible algebra A.
A martingale central limit theorem without negligibility conditions
Authors: Adler Robert J.
Published: April 2009

We obtain sufficient conditions for the convergence of martingale triangular arrays to infinitely divisible laws with finite variances, without making the usual assumptions of uniform asymptotic negligibility. Our results generalise known results for both the martingale case under a negligibility assumption and the classical (independence) case without such assumptions.
Estimation of the integral of a stochastic process
Authors: Cressie Noel
Published: April 2009

Consider the class of stochastic processes with stationary independent increments and finite variances; notable members are brownian motion, and the Poisson process. Now for Xt any member of this class of processes, we wish to find the optimum sampling points of Xt, for predicting . This design question is shown to be directly related to finding sampling points of Yt for estimating β in the regression equation, Yt = β + Xt. Since processes with stationary independent increments have linear drift, the regression equation for Yt is the first type of departure we might look for; namely quadratic drift, and unchanged covariance structure.
Martingale central limit theorems without uniform asymptotic negligibility: Corrigendum
Authors: Adler R.J. , Scott D.J.
Published: April 2009

The following is a correct proof of the main theorem of [1]. It should be substituted for the published Section 3, which, as pointed out by Professor B.L.S. Prakasa Rao, contains an error in the equations following (15) on page 49.
The Bloch-Nevanlinna conjecture revisited
Authors: Campbell Douglas M. , Wickes Gene H.
Published: April 2009

In 1929 Rolf Nevanlinna posed a problem attributed to Bloch which has since been known as the Bloch-Nevanlinna conjecture. It can be stated as follows: Is the derivative of a function of bounded characteristic of bounded characteristic? A variety of different counterexamples have provided negative answers to this question. The purpose of the paper is to survey these counterexamples and then give a truly elementary proof of the following theorem.
An algebraic theory of hypergroups
Authors: McMullen J.R.
Published: April 2009

The category of groups forms a full subcategory of the category of hypergroups. This larger category also contains other group theoretic objects, such as the conjugacy class hypergroup and character hypergroup of a finite group.

Definitions of hypergroups and hypergroup morphisms are given and related to double algebras (which are simultaneously algebras and cogebras, but not Hopf algebras in general). Quotient and orbit hypergroups are defined. Coefficients are allowed in a more or less arbitrary field.

These concepts provide a new language in which groups and their character tables can be fruitfully discussed.
Duality for finite abelian hypergroups over splitting fields
Authors: McMullen J.R. , Price J.F.
Published: April 2009

A duality theory for finite abelian hypergroups over fairly general fields is presented, which extends the classical duality for finite abelian groups. In this precise sense the set of conjugacy classes and the set of characters of a finite group are dual as hypergroups.
Unsolvability of the knot problem for surface complexes
Authors: Stillwell John C.
Published: April 2009

It is shown that the problem of deciding whether a polygonal curvecin a finite surface complexKis knotted inKis complete recursively enumerable, and hence unsolvable.
Notes on irreducible ideals
Authors: Smith David J.
Published: April 2009

Every ideal of a Noetherian ring may be represented as a finite intersection of primary ideals. Each primary ideal may be decomposed as an irredundant intersection of irreducible ideals. It is shown that in the case that Q is an M-primary ideal of a local ring (R, M) satisfying the condition that Q: M = Q + Ms−1 where s is the index of Q, then all irreducible components of Q have index s. (Q is “index-unmixed”.) This condition is shown to hold in the case that Q is a power of the maximal ideal of a regular local ring, and also in other cases as illustrated by examples.
On the discrepancy of the sequence formed from multiples of an irrational number
Authors: van Ravenstein Tony
Published: April 2009

This paper demonstrates a connection between two measures of discrepancy of sequences which arise in the theory of uniform distribution modulo one. The sequence formed from the non-negative integer multiples of an irrational number ξ is investigated and, by an application of the “Steinhaus Conjecture”, some values of the two discrepancies are obtained using continued fractions.
Second-order normal vectors to a convex epigraph
Authors: Seeger Alberto
Published: April 2009

The second–order behaviour of a nonsmooth convex function f is reflected by the so–called second–order subdifferential mapping ∂2f. This mathematical object has been intensively studied in recent years. Here we study ∂2f in connection with the geometric concept of “second-order normal vector” to the epigraph of f.
On the direct sum decomposition of an algebra of continuous functions
Authors: Mehta R.D. , Vasavada M.H.
Published: April 2009

Let A and B be closed subalgebras of Cr(K) whose direct sum is Cr(K) According to a result of Stephen Fisher the set of common zeros of elements of B is a retract of K. We give examples to show that this result is not correct.
The moments of the multivariate normal
Authors: Withers C.S.
Published: April 2009

Explicit expressions are given for the noncentral moments of the multivariate normal. Finding the general moment is shown to be equivalent to finding the general derivative of the density of the multivariate normal, that is to finding an expression for the multivariate Hermite polynomial.
A duality theorem for a multiple objective fractional optimization problem
Authors: Weir T.
Published: April 2009

Characterizations of efficiency and proper efficiency are given for classes of multiple objective fractional optimization problems. These results are then applied to the case of multiple objective fractional linear problems. A dual problem is given for the multiple objective fractional problem and it is shown that for a properly efficient primal solution the dual solution is also properly efficient.
Characterisation of quasi-Anosov diffeomorphisms
Authors: Couper Graham
Published: April 2009

Let ƒ be a C1 diffeomorphism of a compact C∞ boundary–less manifold, and let ƒ# be the operator on the bounded or continuous sections of the tangent bundle (with supremum norm) defined by ƒ#η = Tƒ о η о ƒ−1. The main result of this paper is that ƒ is quasi-Anosov if and only if 1 – f# is injective and has closed range.
Best approximation and intersections of balls in Banach spaces
Authors: Yost David T.
Published: April 2009

Let E be a Banach space, M a closed subspace of E with the 3-ball property. It is known that M is proximinal in E, and that its metric projection admits a continuous selection. This means that there is a continuous (generally non-linear) map π: E → M satisfying ‖x−π(x)‖ = d(x, M) for all x in E. Here it is shown that the same conclusion holds under a much weaker hypothesis on M, which we call the 1½-ball property. We also establish that if M has the 1½-ball property in E, then there is a continuous Hahn-Banach extension map from M* to E*.
An implicit function theorem with symmetries and its application to nonlinear eigenvalue equations
Authors: Dancer E.N.
Published: April 2009

In this paper we prove a G-invariant implicit function theorem and indicate how it can be used to improve an earlier result of the author on the bifurcation of solutions of nonlinear equations in the presence of continuous groups of symmetries. We also use our theorem to show that, under reasonable hypotheses, the method of looking for solutions in invariant subspaces yields all solutions. This can be used to answer a question raised by Sattinger [J. Math. Phys. 19 (1978), 1729]. The abstract result is also of interest because it provides a theorem which should be of use in other symmetric situations.
Banach algebras with one dimensional radical
Authors: Stedman Lawrence
Published: April 2009

A Banach algebra A with radical R is said to have property (S) if the natural mapping from the algebraic tensor product A ⊗ A onto A2 is open, when A ⊗ A is given the protective norm. The purpose of this note is to provide a counterexample to Zinde's claim that when A is commutative and R is one dimensional the fulfillment of property (S) in A implies its fulfillment in the quotient algebra A/R.
Some remarks on variational-like and quasivariational-like inequalities
Authors: Dien Nguyen Huu
Published: April 2009

In this paper we study the variational-like inequalities, which generalise some results of Parida, Sahoo and Kumar, and we also investigate the quasivariational-like inequalities. We establish some existence theorems of a solution for the above problem.
On sufficiency of the Kuhn-Tucker conditions in nondifferentiable programming
Authors: Zhao Fuan
Published: April 2009

Some generalised invex conditions are given for a nondifferentiable constrained optimisation problem, generalising those of Hanson and Mond for differentiable problems. Some duality results are obtained.
On Hermite-Fejér type interpolation on the Chebyshev nodes
Authors: Byrne Graeme J. , Mills T.M. , Smith Simon J.
Published: April 2009

Given f ∈ C [−1, 1], let Hn, 3(f, x) denote the (0,1,2) Hermite-Fejér interpolation polynomial of f based on the Chebyshev nodes. In this paper we develop a precise estimate for the magnitude of the approximation error |Hn, 3(f, x) − f(x)|. Further, we demonstrate a method of combining the divergent Lagrange and (0,1,2) interpolation methods on the Chebyshev nodes to obtain a convergent rational interpolatory process.
On projectional resolution of identity on the duals of certain Banach spaces
Authors: Fabian M.
Published: April 2009

A consequence of the main proposition includes results of Tacon, and John and Zizler and says: If a Banach space X possesses a continuous Gâteaux differentiable function with bounded nonempty support and with norm-weak continuous derivative, then its dual X* admits a projectional resolution of the identity and a continuous linear one-to-one mapping into c0 (Γ). The proof is easy and selfcontained and does not use any complicated geometrical lemma. If the space X is in addition weakly countably determined, then X* has an equivalent dual locally uniformly rotund norm. It is also shown that l∞ admits no continuous Gâteaux differentiable function with bounded nonempty support.
On certain inequalities for some regular functions defined on the unit disc
Authors: Chen Ming-Po , Lan Ih-Ren
Published: April 2009

In this paper we obtain some inequalities for some regular functions f defined on the unit disc. Our results include or improve several previous results.
Induced representations twisted by cocycles
Authors: Bui Huu Hung
Published: April 2009

We define a notion of representation induced from cocycles which encompasses the case of Kawakami's generalised induced representation. Our purpose is to formulate Kawakami's construction within the context of Rieffel's formalism of induced representations of C*-algebras.
Convergence of approximate solutions of a quasilinear partial differential equation
Authors: Cranny T.R.
Published: April 2009

This article is a sequel to a paper in which a quasilinear partial differential equation with nonlinear boundary condition was approximated using mollifiers, and the existence of solutions to the approximating problem shown under quite general conditions. In this paper we show that standard a priori Hölder estimates ensure the convergence of these solutions to a classical solution of the original problem. Some partial results giving such estimates for special cases are described.
Topological transversality: applications to differential equations
Authors: Sengadir T. , Pani A.K.
Published: April 2009

In this paper, existence results for both integro-differential and functional differential equations are discussed using topological transversality arguments. As applications, third and fourth order boundary value problems are considered. For third order problems, an example has been cited to show that our results cover a wider class of problems than Theorem 2.3 of D.J. O'Regan, Topological transversality: Applications to third order boundary value problems, SIAM J. Math. Anal. 18 (1987) 630–641.
A Littlewood and Paley-type inequality on the ball
Authors: Choa Jun Soo , Kim Hong Oh
Published: April 2009

A multi-dimensional analogue of a well known inequality of Littlewood and Paley is obtained on the ball.
On strongly pi-regular rings of stable range one
Authors: Yu Hua-Ping , Camilo Victor P.
Published: April 2009

An associative ring R is said to have stable range one if for any a, b ∈ R satisfying aR + bR = R, there exists y ∈ R such that a + by is right (equivalently, left) invertible. Call a ring R strongly π-regular if for every element a ∈ R there exist a number n (depending on a) and an element x ∈ R such that an = an+1x. It is an open question whether all strongly π-regular rings have stable range one. The purpose of this note is to prove the following Theorem: If R is a strongly π-regular ring with the property that all powers of every nilpotent von Neumann regular element are von Neumann regular in R, then R has stable range one.
Smooth families of fibrations and analytic selections of polynomial hulls
Authors: Černe Miran
Published: April 2009

Constructed are strictly increasing smooth families Σt ⊆ ∂D × C2, t ∈ [0, 1], of fibrations over the unit circle with strongly pseudoconvex fibers all diffeomorphic to the ball such that there is no analytic selection of the polynomial hull of Σ0 and which end at the product fibration . In particular these examples show that the continuity method for describing the polynomial hull of a fibration over ∂D fails even if the complex geometry of the fibers is relatively simple.
On Ky Fan's covering theorems for simplexes
Authors: Ha Chung-Wei
Published: April 2009

New covering properties of simplexes are obtained which extend and complement some covering theorems for simplexes of Fan.
Two characterisations of a gamma mixture distribution
Authors: Gharib M.
Published: April 2009

Two characterisations are obtained for a gamma mixture distribution. The first is a generalisation of a result of Engel, Zijlstra and Philips [4] and the second based on Gumbel's bivariate exponential distribution. The two characterisatio are of direct relevance to some practical problems.
On the limit cycle distribution over two nests in quadratic systems
Authors: Huang Xianhua , Reyn J.W.
Published: April 2009

As a contribution to the solution of Hilbert's 16th problem the question is considered whether in a quadratic system with two nests of limit cycles at least in one nest there exists precisely one limit cycle. An affirmative answer to this question is given for the case that the sum of the multiplicities of the finite critical points in the system is equal to three.
Pluriharmonic symbols of commuting Toeplitz type operators
Authors: Lee Young Joo
Published: April 2009

Certain Toeplitz type operators acting on the Bergman space A1 of the unit ball are considered and pluriharmonic symbols of commuting Toeplitz type operators are characterised by using M-harmonic function theory.
Multipliers on spaces of functions on compact groups with p-summable Fourier transforms
Authors: Gupta Sanjiv Kumar , Madan Shobha , Tewari U.B.
Published: April 2009

Let G be a compact abelian group with dual group Γ. For 1 ≤ p < ∞, denote by Ap(G) the space of integrable functions on G whose Fourier transforms belong to lp(Γ). We investigate several problems related to multipliers from Ap(G) to Aq(G). In particular, we prove that (Ap, Ap) ⊊ (Aq, Aq). For the circle group, we characterise permutation invariant multipliers from Ap to Ar for 1 ≤ r ≤ 2.
Free commutative semifields
Authors: Gardner B.J. , Steinfeld Ottó
Published: April 2009

A description is obtained of the free semifields with both fundamental operations commutative.
A characterisation of Riemannian foliations and totally umbilical submanifolds
Authors: Tondeur Ph. , Vanhecke L.
Published: April 2009

We discuss characterisations of Riemannian foliations, totally geodesic submanifolds, and totally umbilical submanifolds by sharp inequalities. These derive from the same linear algebraic set up, characterising a linear endomorphism which is a multiple of the identity.
Quantum double finite group algebras and their representations
Authors: Gould M.D.
Published: April 2009

The quantum double construction is applied to the group algebra of a finite group. Such algebras are shown to be semi-simple and a complete theory of characters is developed. The irreducible matrix representations are classified and applied to the explicit construction of R-matrices: this affords solutions to the Yang-Baxter equation associated with certain induced representations of a finite group. These results are applied in the second paper of the series to construct unitary representations of the Braid group and corresponding link polynomials.
A note on Baric algebras
Authors: Andrade Raúl , Labra Alicia
Published: April 2009

In this paper we present a characterization of baric algebras. In particular we study those in which the identity x3 = w(x)x2 holds. Moreover, for every field K, we prove that this identity guarantees that the annihilator of Ker (w) is an ideal in A and we give example of a subspace of Ker (w) whose annihilator is not an ideal.
On the normal version of the simplicial cohomology of operator algebras
Authors: Helemskii A.Ya. , Lykova Z.A.
Published: April 2009

We show that the normal version (R, R.) of the Banach simplicial cohomology of operator algebras can be expressed in terms of the functor Ext on the category of Banach R-bimodules. As an application, we prove that (R, R*) = Hn(R, R*) and thus the latter space vanishes for some von Heumann algebras for positive τ.
A remark on a third-order three-point boundary value problem
Authors: Marano Salvatore A.
Published: April 2009

Let f be a real function defined on [0, 1] × R3 and let η ∈ (0, 1). Very recently, C.P. Gupta and V. Lakshimikantham, making use of the Leray-Schauder continuation theorem and Wirtinger-type inequalities, established an existence result for the problem

(Theorem 1 and Remark 4 of [Nonlinear Anal. 16 (1991), 949–957]).

The aim of the present paper is simply to point out how, bu means of a completely different approach, it is possible to improve that result not only by requiring much general on f, but also by giving a precise pointwise estimate on x″′
On Gaussian elimination and determinant formulas for matrices with chordal inverses: Corrigendum
Authors: Bakonyi Mihály
Published: April 2009

The statement of Proposition 2.2 (p.437) published by the author in Bull. Austral. Math. Soc. Vol. 46 (1992) pp.435–440 is incorrect. The correct version follows.
Unicity theorems for meromorphic or entire functions
Authors: Yi Hong-Xun
Published: April 2009

In this paper, we prove that there exist three finite sets Sj (j = 1, 2, 3) such that any two non-constant meromorphic functions f and g satisfying Ef(Sj) = Eg(Sj) for j = 1,2,3 must be identical. As a particular case of the above result, we obtain that there exist two finite sets Sj (j = 1, 2) such that any two non-constant entire functions f and g satisfying Ej(Sj) = Eg(Sj) for j = 1, 2 must be identical, which answers a question posed by Gross.
Pinching theorems for teardrops and footballs of revolution
Authors: Borzellino Joseph E.
Published: April 2009

We give explicit optimal curvature pinching constants for the Riemannian (p, q)- football orbifolds under the assumption that they are realised as surfaces of revolution in ℝ3. We show that sufficiently pinched sectional curvature assumptions imply that a (p, q)-football must be good.
Pre-vector variational inequalities
Authors: Lin Lai-Jiu
Published: April 2009

Existence theorems for pre-vector variational inequalities are established under different conditions on the operator T and the function η. As an application, we establish the existence of a weak minimum of an optimisation problem on η-invex functions.
Abstract Daniell-Loomis spaces
Authors: Carrillo M. Díaz , Günzler H.
Published: April 2009

In [3] for general integral metric q an integral extension of Lebesgue power was discussed. In this paper we introduce the abstract Daniell-Loomis spaces Rp, p real, 0 < p < ∞, of q-measurable functions with finite “p-norm”, and study their basic properties.
Semilinear problems on the half space with a hole
Authors: Wang Hwai-Chiuan
Published: April 2009

In this article we prove that there is a positive solution inof the equation −Δu+ λu= |u|p−2uin Ω where Ω is the half space with a hole, λ > 0 and 2 < p < 2N/(N−2).
Two characterisations of additive *-automorphisms of B(H)
Authors: Molnár Lajos
Published: April 2009

Let H be a complex Hilbert space and let B(H) denote the algebra of all bounded linear operators on H. In this paper we give two necessary and sufficient conditions for an additive bijection of B(H) to be a *-automorphism. Both of the results in the paper are related to the so-called preserver problems.
Weighted convolutions of certain polynomials
Authors: Jahangiri Massoud
Published: April 2009

For α ≥ 0 and β ≥ 0, let K(β) consist of those functions f(z), analytic and non-zero in |z| < 1, such that for θ1 < θ2 < θ1 + 2π and . It is conjectured that for 1 ≤ α ≤ β and α an integer, the weighted convolution of polynomials having their zeros on |z| = 1 and belonging to K(α, β), also belong to K(α, β). This conjecture is known to be true for the case α = 1, which leads to an alternative proof for the generalised Polya-Schoenberg conjecture. The case α = 2 is also known to be true for cubic polynomials. We prove the conjecture for certain quartic polynomials when 2 ≤ α ≤ 4.
Embedding into groups with well-described lattices of subgroups
Authors: Obraztsov Viatcheslav N.
Published: April 2009

A thrifty embedding scheme of an arbitrary set of groups in a simple infinite group with a given outer automorphism group is presented. One of the applications of this scheme is the existence (assuming CH) of an uncountable group G in which all proper subgroups are countable such that G contains every countable group.
On the structure of a real crossed group algebra
Authors: Pálfy P.P.
Published: April 2009

We prove that the crossed group algebra A of the infinite dihedral group over the real field defined by the generators a and b, relations b−1 ab = a−1, b2 = −1, and λa = aλ, λb = bλ for all real λ is a principal left ideal ring. This corrects a result of Buzási and provides the missing step towards the classification of finitely generated torsion-free RG-modules for groups G which contain an infinite cyclic subgroup of finite index.
Semigroups whose idempotents form a subsemigroup
Authors: Birget Jean-Camille , Margolis Stuart , Rhodes John
Published: April 2009

We prove that if the “type-II-construct” subsemigroup of a finite semigroup S is regular, then the “type-II” subsemigroup of S is computable (actually in this case, type-II and type-II-construct are equal). This, together with certain older results about pseudo-varieties of finite semigroups, leads to further results:

(1) We get a new proof of Ash's theorem: If the idempotents in a finite semigroup S commute, then S divides a finite inverse semigroup. Equivalently: The pseudo-variety generated by the finite inverse semigroups consists of those finite semigroups whose idempotents commute.

(2) We prove: If the idempotents of a finite semigroup S form a subsemigroup then S divides a finite orthodox semigroup. Equivalently: The pseudo-variety generated by the finite orthodox semigroups consists of those finite semigroups whose idempotents form a subsemigroup.

(3) We prove: The union of all the subgroups of a semigroup S forms a subsemigroup if and only if 5 belongs to the pseudo-variety u * G if and only if Sn belongs to u. Here u denotes the pseudo-variety of finite semigroups which are unions of groups.

For these three classes of semigroups, type-II is equal to type-II construct.
On a result of Singh
Authors: Yi Hong-Xun
Published: April 2009

In this paper relations between T(r, f) and T(r, f(k)) are established for a class of meromorphic functions f(z), where T(r, f) and T(r, f(k)) are the Nevanlinna characteristic functions f(z) and f(k)(z) respectively. An example is provided to show that a result of Singh is not true. The conclusions obtained here correct and generalise the result of Singh.
The lambda-property for generalised direct sums of normed spaces
Authors: Lohman Robert H. , Shura Thaddeus J.
Published: April 2009

This paper considers direct sums of normed spaces with respect to a Banach space with a normalised, unconditionally strictly monotone basis. Necessary and sufficient conditions are given for such direct sums to have the λ-property. These results are used to construct examples of reflexive Banach spaces U and V such that U has the uniform λ-property but U* fails to have the λ-property, while V and V* fail to have the λ-property.
On Lagrange interpolation with equally spaced nodes
Authors: Revers Michael
Published: April 2009

A well-known result due to S.N. Bernstein is that sequence of Lagrange interpolation polynomials for |x| at equally spaced nodes in [−1, 1] diverges everywhere, except at zero and the end-points. In this paper we present a quantitative version concerning the divergence behaviour of the Lagrange interpolants for |x|3at equidistant nodes. Furthermore, we present the exact rate of convergence for the interpolatory parabolas at the point zero.
Measure of weak noncompactness and real interpolation of operators
Authors: Kryczka Andrzej , Prus Stanislaw , Szczepanik Mariusz
Published: April 2009

A new measure of weak noncompactness is introduced. A logarithmic convexity-type result on the behaviour of this measure applied to bounded linear operators under real interpolation is proved. In particular, it gives a new proof of the theorem showing that if at least one of the operators T: Ai → Bi, i = 0, 1 is weakly compact, then so is T : Aθ,p → Bθ,p for all 0 < θ < 1 and 1 < P < ∞.
Linearised Moser-Trudinger inequality
Authors: Kim Meelae
Published: April 2009

As a limiting case of the Sobolev imbedding theorem, the Moser-Trudinger inequality was obtained for functions in with resulting exponential class integrability. Here we prove this inequality again and at the same time get sharper information for the bound. We also generalise the Linearised Moser inequality to higher dimensions, which was first introduced by Beckner for functions on the unit disc. Both of our results are obtained by using the method of Carleson and Chang. The last section introduces an analogue of each inequality for the Laplacian instead of the gradient under some restricted conditions.
The fixed point property and normal structure for some B-convex Banach spaces
Authors: García-Falset Jesús , Llorens-Fuster Enrique , Mazcuñán-Navarro Eva M.
Published: April 2009

We give a sufficient condition for normal structure more general than the well known ɛ0(X) < 1. Moreover we obtain sufficient conditions for the fixed point property for some B-convex Banach spaces.
On joint spectra of non-commuting hyponormal operators
Authors: Sołtysiak A.
Published: April 2009

We show that the left joint spectrum of an arbitrary n-tuple of hyponormal Hilbert space operators can be obtained from the spectral set γ introduced by McIntosh and Pryde. A dual statement for cohyponormal operators is also true. The result is a generalisation of a theorem proved by Pryde and the author for normal operators.
Gröbner bases and products of coefficient rings
Authors: Norton Graham H. , Sӑlӑgean Ana
Published: April 2009

Suppose that A is a finite direct product of commutative rings. We show from first principles that a Gröbner basis for an ideal of A[x1,…,xn] can be easily obtained by ‘joining’ Gröbner bases of the projected ideals with coefficients in the factors of A (which can themselves be obtained in parallel). Similarly for strong Gröbner bases. This gives an elementary method of constructing a (strong) Gröbner basis when the Chinese Remainder Theorem applies to the coefficient ring and we know how to compute (strong) Gröbner bases in each factor.
An explicit Hecke's bound and exceptions of even unimodular quadratic forms
Authors: Chua Kok Seng
Published: April 2009

We prove an explicit Hecke's bound for the Fourier coefficients of holomorphic cusp forms for SL2(Z) and apply it to derive effectively computable constants c (m) for each dimension m, divisible by 8, for which every even integer is always represented by every even unimodular form of m variables.
Nondualisable semigroups
Authors: Hobby David
Published: April 2009

An infinite family of finite semigroups is studied. It is shown that most of them do not generate a quasivariety which admits a natural duality.
On Fréchet algebras of power series
Authors: Bhatt S. J. , Patel S. R.
Published: April 2009

If the indeterminate X in a Fréchet algebra A of power series is a power series generator for A, then either A is the algebra of all formal power series or is the Beurling-Fréchet algebra on non-negative integers defined by a sequence of weights. Let the topology of A be defined by a sequence of norms. Then A is an inverse limit of a sequence of Banach algebras of power series if and only if each norm in the defining sequence satisfies certain closability condition and an equicontinuity condition due to Loy. A non-Banach uniform Fréchet algebra with a power series generator is a nuclear space. A number of examples are discussed; and a functional analytic description of the holomorphic function algebra on a simply connected planar domain is obtained.
On pendent drops in a capillary tube
Authors: Huisken G.
Published: April 2009

The energy functional for a pendent drop in a capillary tube is neither convex nor bounded from below. We obtain local minima of the energy by making the physically reasonable assumption that the gravitation or the prescribed volume of the drop is small.
Prolongations of linear connections to the frame bundle
Authors: Cordero Luis A. , de Leon Manuel
Published: April 2009

In this paper we construct the prolongation of a linear connection Γ on a manifold Μ to the bundle space of its frame bundle, and show that such prolongated connection coincides with the so-called complete lift of Γ to .
Monadic representability of certain binary relations
Authors: Humberstone I.L.
Published: April 2009

Call a relation R⊆A2 (A some non-empty set) monadically representable when there exist F, G⊆A such that R = {(x, y) | x ∈ F ∘ y ∈ G} for some truth-functional connective ∘. This note finds a first-order condition on R which is necessary and sufficient for R to be monadically representable.
A note on existence of envelopes and covers
Authors: Chen Jianlong , Ding Nanqing
Published: April 2009

We prove the following results for a ring R. (a) If C is a class of right R-modules closed under direct summands and isomorphisms, then every right R-module has an epic C-envelope if and only if C is closed under direct products and submodules. (b) If R is left T-coherent and pure injective as a right R-module, then every T-finitely presented right R-module has a T-flat envelope, (c) Let R be a left T-coherent ring and injective right R-modules be T-flat. If every finitely presented left R-module has a flat envelope, then every T-finitely presented right R-module has a projective cover.
Applications of Fox's derivation in determining the generators of a group
Authors: Lin Wan
Published: April 2009

We give a necessary and sufficient condition for a set of elements to be a generating set of a quotient group F/N, where F is the free group of rank n and N is a normal subgroup of F. Birman's Inverse Function Theorem is a corollary of our criterion. As an application of this criterion, we give necessary and sufficient conditions for a set of elements of the Burnside group B (n,p) of exponent p and rank n to be a generating set.
Generalised Bernoulli polynomials and series
Authors: Frappier Clément
Published: April 2009

We present several results related to the recently introduced generalised Bernoulli polynomials. Some recurrence relations are given, which permit us to compute efficiently the polynomials in question. The sums , where jk = jk (α) are the zeros of the Bessel function of the first kind of order α, are evaluated in terms of these polynomials. We also study a generalisation of the series appearing in the Euler-MacLaurin summation formula.
Asymptotic behaviour for an almost-orbit of nonexpansive semigroups in Banach spaces
Authors: Kim Jong Kyu , Li Gang
Published: April 2009

In this paper, by using the technique of product nets, we are able to prove a weak convergence theorem for an almost-orbit of right reversible semigroups of nonexpansine mappings in a general Banach spaceXwith Opial's condition. This includes many well known results as special cases. LetCbe a weakly compact subset of a Banach spaceXwith Opial's condition. LetGbe a right reversible semitopological semigroup,  = {T(t):t∈G} a nonexpansive semigroup onC, andu(·) an almost-orbit of . Then {u(t):t∈G} is weakly convergent (to a common fixed point of ) if and only if it is weakly asymptotically regular (that is, {u(ht) −u(t)} converges to 0 weakly for everyh∈G).
Continuous and discrete Halanay-type inequalities
Authors: Mohamad S. , Gopalsamy K.
Published: April 2009

We consider continuous time and discrete time Halanay-type inequalities for nonautonomous scalar systems with discrete and distributed delays. The results obtained generalise the existing results of Halanay and improve certain results of Baker and Tang. Furthermore, it is shown that the discrete time inequalities which are analogues of continuous time inequalities preserve the stability conditions corresponding to the continuous time Halanay-type inequalities.
Fixed point theory of Mönch type for weakly sequentially upper semicontinuous maps
Authors: O'Regan Donal
Published: April 2009

A variety of fixed point results are presented for weakly sequentially upper semicontinuous maps. In addition an existence result is established for differential equations in Banach spaces relative to the weak topology.
On the sum and the difference of finite sets of integers
Authors: Razen Reinhard A.
Published: April 2009

Let A = {ai} be a finite set of integers and let p and m denote the cardinalities of A + A = {ai+aj} and A - A {ai–aj}, respectively. In the paper relations are established between p and m; in particular, if max {ai–ai-1} = 2 those sets are characterized for which p = m holds.
On the canonical projection of the third dual of a Banach space onto the first dual
Authors: Brown A.L.
Published: April 2009

For a Banach space B let P denote the canonical projection of the third dual space of B onto the embedding of the first dual into the third. It is shown that if B = l1 then ‖I-P‖ = 2.

This fact shows to be mistaken a current belief in a statement which is equivalent to the statement that for all Banach spaces B the operator I – P is of norm one.
A commutativity theorem for rings
Authors: Ligh Steve , Richoux Anthony
Published: April 2009

Let R be a ring with an identity and for each x, y in R, (xy)k = xkyk for three consecutive positive integers k. It is shown in this note that R is a commutative ring.
A counterexample to the density of the space generated by the composition operators
Authors: Beattie Ronald
Published: April 2009

It is known that, for an arbitrary convergence space X, the vector space generated by X is dense in LcCc (X) where both C(X) and its dual space carry the continuous convergence structure. In this note, a natural analogue formulated for the operator space L(Cc(X), Cc(X)) is considered, namely: is the vector space generated by the composition operators associated to the continuous mappings in C(X, X) dense in Lc (Cc (X), Cc (X)) ? This question is answered in the negative by a counterexample.
On Sylow intersections
Authors: Ish-Shalom Ariel
Published: April 2009

LetGbe a finite group,pa prime divisor of |G|, andTap–subgroup ofG. Define σ(T) to be the number of Sylowp–subgroups ofGcontainingT. CallTa centralp–Sylow intersection if for some Σ ⊆ Sylp(G),T= ∩(S|Sє Σ), and if, in addition,Tcontains the center of a Sylowp–subgroup ofG. This work is inspired and motivated by work of G. Stroth [J. Algebra37 (1975), 111–120]. Generalizing an argument of his we describe finite groups in which every centralp–Sylow intersectionTwithp–rank(T) > 2 satisfies σ(T) ≤p.

Related methods yield the description of finite groups in which every centralp–Sylow intersectionTwithp–rank(T) ≥ 2 satisfies σ(T) ≤ 2p.
The automorphism group of a scattered set can be non-commutative
Authors: Fleischer Isidore
Published: April 2009

Perhaps the simplest example is the lexicographic sum of copies Zn of the integers indexed by the integers. If one performs the shift in the 0-indexed summand m0 → (m+1)0 while leaving all the other summands fixed, and follows this with the shift Zn → Zn+1 in the index set, then the element 00. will be sent on 11; whereas under these automorphisms performed in the other order, it will be sent on 01. This non-commutativity contradicts Theorem 9 in [1].
Groups of finite exponent
Authors: Gupta N.D. , Newman M.F.
Published: April 2009

The negative answer by Novikov and Adyan to the Burnside question (is every finitely generated group of finite exponent finite?) still leaves open some cases, in particular, all 2-power exponents. Some reduction results are known. In this note we present another kind of reduction result.
Counting of finite topologies and a dissection of Stirling numbers of the second kind
Authors: Krishnamurthy V.
Published: April 2009

Certain new combinatorial numbers which arise in the counting of finite topologies are introduced and formulae obtained. These numbers are used to obtain a known formula for tn, the number of labelled topologies on n points in terms of the Stirling numbers S(n, p) and dn, the number of labelled T0-topologies on n points. The numbers dn are computed for n ≤ 5 with the the help of a method of Comtet (1966) (which seems to have been missed by later authors), reinterpreted for transitive digraphs.
A convergent quasi-Hermite-Féjer interpolation process
Authors: Mills T.M.
Published: April 2009

D.L. Berman has proved several divergence theorems about “extended” Hermite-Fejér interpolation on the Chebyshev nodes of the first kind. These are surprising in light of the classical convergence theorem of L. Fejér concerning ordinary Hermite-Fejér interpolation on these nodes. However there is one case which has been neglected so far: the case of quasi-Hermite-Fejér interpolation on these nodes. In this paper it is proved that quasi-Hermite-Fejér interpolation polynomials on the Chebyshev nodes converge uniformly to the continuous function being interpolated. In addition, an estimate for the rate of convergence is established.
On a class of finite soluble groups
Authors: Karpilovsky G.
Published: April 2009

Let the group T be the direct product of groups Si (i = 1, … r) where for a given group Ai, Si is the direct product of ni factors Ai × Ai × … × Ai. Let B be a group that has a faithful permutation representation Γi of degree ni. (i = 1, …, r). Consider G, the split extension of T by B defined by letting B act on T as follows.

Each Si is normal in G. If and b ∈ B then where . It is proved that if T is an M-group and all subgroups of B are M-groups, then G is an M-group. This is a generalisation of a result of Gary M. Seitz, Math. Z. 110 (1969), 101–122, who proved the particular case where r = 1 and Γ1 is the regular representation of B.