bluuebunny/crossref_metadata_2025 huggingface dataset:
The Laplace transform on a class of Boehmians
Authors: Nemzer Dennis
Published: April 2009

The one-sided Laplace transform is defined on a space of generalised functions called transformable Boehmians. The space of one-sided Laplace transformable distributions is shown to be a proper subspace of transformable Boehmians. Some basic properties of the Laplace transform are investigated. An inversion formula and an Abelian theorem of the final type are obtained.
A note on analytic capacity
Authors: Uy Nguyen Xuan
Published: April 2009

Let K be a 2-dimensional Cantor set. In this note we prove, in two cases, the analytic capacity and the continuous analytic capacity of K are equal.
On the Schwarzian coefficients of univalent functions
Authors: Zemyan Stephen M.
Published: April 2009

For f ∈ S, we study the Schwarzian coefficients sn defined by {f, z} = Σ snzn. Sharp bounds on s0, s1 and s2 are given, together with an order of growth estimate as n → ∞. We use the Grunsky Inequalities to estimate combinations of coefficients.
On the number of zeros of exponential polynomials and related questions
Authors: van der Poorten A.J. , Shparlinski I.E.
Published: April 2009

We apply Straßmann's theorem to p–adic power series satisfying linear differential equations with polynomial coefficients and note that our approach leads to our estimating the number of integer zeros of polynomials on a given interval and thence to an investigation of the number of p–adic small values of a function on such an interval, that is, of the number of solutions of a congruence modulo pr.
Local invertibility in subrings of C*(X)
Authors: Byun H. Linda , Redlin Lothar , Watson Saleem
Published: April 2009

It is known that the maximal ideals in the rings C(X) and C*(X) of continuous and bounded continuous functions on X, respectively, are in one-to-one correspondence with βX. We have shown previously that the same is true for any ring A(X) between C(X) and C*(X). Here we consider the problem for rings A(X) contained in C*(X) which are complete rings of functions (that is, they contain the constants, separate points and closed sets, and are uniformly closed). For every noninvertible f ∈ A(X), we define a z–filter ZA(f) on X which, in a sense, provides a measure of where f is ‘locally invertible’. We show that the map ZA generates a correspondence between ideals of A(X) and z–filters on X. Using this correspondence, we construct a unique compactification of X for every complete ring of functions. Each such compactification is explicitly identified as a quotient of βX. In fact, every compactification of X arises from some complete ring of functions A(X) via this construction. We also describe the intersections of the free ideals and of the free maximal ideals in complete rings of functions.
Some nil ring properties related to T-nilpotence
Authors: Gardner B.J.
Published: April 2009

We examine the rings in which every sequence has either a subsequence, or a rearrangement, such that for some n the product of the first n terms in zero.
Calculus rules for combinations of ellipsoids and applications
Authors: Seeger Alberto
Published: April 2009

We derive formulas for the Minkowski sum, the convex hull, the intersection, and the inverse sum of a finite family of ellipsoids. We show how these formulas can be used to obtain inner and outer ellipsoidal approximations of a convex polytope.
Posets, near unanimity functions and zigzags
Authors: Zádori László
Published: April 2009

With every poset we associate a class of coloured posets called zigzags. By means of zigzags we show that, if we delete a convex set from a finite lattice ordered set then the resulting poset has the strong selection property. We give the complete list of finite bounded irreducible posets admitting an n-ary near unanimity function, provided n ≤ 6. We present some examples and classes of posets with full descriptions of their zigzags.
Ultrabornological Bochner integrable function spaces
Authors: Ferrando J.C.
Published: April 2009

If (Ω, Σ, μ) is a finite measure space and X is a normed space such that X* has the Radon-Nikodym property with respect to μ, we show first that each space Lp(μ, x), 1 < p < ∞, is ultrabornological whenever μ is atomless. When μ is arbitrary, we prove later on that the space Lp(μ, X) is ultrabornological if X* has the Radon-Nikodym property with respect to μ and X is itself an ultrabornological space.
The natural topology of Matlis reflexive modules
Authors: Belshoff Richard
Published: April 2009

For a complete local ring R with maximal ideal m, we define a linear topology on a Matlis reflexive R-module M which coincides with the m-adic topology on M in case M is finitely generated. We show that a Matlis reflexive module is complete in this topology.
The structure of certain group C*-algebras
Authors: Pahor Milan
Published: April 2009

Let G be a separable locally compact group which admits a non-trivial compact normal subgroup. It is shown that the group C*-algebra C*(G) of G may be decomposed as a direct sum of ideals whose structure is determined up to *-isomorphism. Applications are given to Type 1, [FD]− groups; in particular it is shown that the group C*-algebra of such a group is a direct sum of homogeneous C*-algebras.
Socles of Verma modules in quantum groups
Authors: Jeyakumar A.V. , Sarasija P.B.
Published: April 2009

In this paper the Verma modules Me(λ) over the quantum group vε(sl(n + 1), ℂ), where ε is a primitive lth root of 1 are studied. Some commutation relations among the generators of Ue are obtained. Using these relations, it is proved that the socle of Mε(λ) is non-zero.
Further results on the deficiencies of algebroid functions
Authors: Yang Lianzhong
Published: April 2009

Let f(z) be an n-valued algebroid function of finite lower order μ. In this paper, we give some further results on the deficiencies of f(z). Particularly if 0 ≤ μ ≤ 1/2, the corresponding result is best possible.
Existence theorem for proximate type of entire functions with index-pair (p, q)
Authors: Kasana H. S.
Published: April 2009

R.S.L. Srivastava and O.P. Juneja (1967) proved an existence theorem for the proximate type T (r) of an entire function with classical growth. For an interesting generalization of this theorem for an entire function with index-pair (p,q), which is due essentially to H.S. Kasana and S.K. Vaish (1984), a remarkably simple (and markedly different) construction of T (r) is presented here. The main theorem established here applies to a much larger class of entire functions with index-pair (p,q) than that considered earlier.
Division of distributively generated near-rings II
Authors: Tharmaratnam V.
Published: April 2009

The definition of division d.g. near-rings given by the author in 1976 has been found to be too restrictive. In this paper we generalise the definition of division d.g. near-rings and extend the results obtained earlier for division d.g. near-rings to the new wider class of near-rings.
Riemann derivatives and general integrals
Authors: De Sarkar S. , Das A. G.
Published: April 2009

Sargent and later Bullen and Mukhopadhyay obtained a definition of absolutely continuous functions, functions, that is related to kth Peano derivatives. The generalised notions of ACkG*, [ACkG*], ACkG* above, etcetera functions led Bullen and Mukhopadhyay to define certain general integrals of the kth order.

The present work is concerned with a further simplification of the definitions of such functions by the use of divided differences but still retaining similar fundamental properties. These concepts lead to the introduction of Denjoy and Ridder type integrals which are shown to be equivalent to a Perron type integral that corresponds to kth Riemann* derivatives. All three of these integrals are shown to be equivalent to the three integrals of Bullen and Mukhopadhyay.
Closed and prime ideals in the algebra of bounded analytic functions
Authors: Mortini Raymond
Published: April 2009

Let H∞ be the Banach algebra of all bounded analytic functions in the unit disc. We present a complete description of the closed primary (respectively prime) ideals contained in a maximal ideal of the Shilov boundary of H∞. The paper is also concerned with chains of prime ideals in H∞.
Nonlinear integral operators and chaos in Banach spaces
Authors: Diamond Phil
Published: April 2009

Sufficient conditions are given for chaotic behaviour of continuous transformations on Banach spaces. The conditions avoid the requirement that mappings be expanding on compact sets and are probably easier to verify for many classes of operator equations than existing criteria. Two classes of integral operators on C[0, 1] are considered in the light of these results: one nonlinear but compact, the second noncompact.
Bifurcating attractors and Galerkin approximates
Authors: Wells R. , Dutton J. A.
Published: April 2009

Let u̇ = A0u + μA1u + J (u) be a Navier-Stokes parameterized evolution equation in a Hilbert space H and let F1 ⊂ F2 ⊂ F3 ⊂ … be an increasing sequence of finite dimensional spaces such that every Fn ⊕ ℝ contains the center-unstable linear subspace Hu ⊕ ℝ ⊂ H ⊕ ℝ of the system u̇ = A0u + μA1u + J (u), u̇ = 0. Then each Fn ⊕ ℝ determines a Galerkin approximant of the original system, with the same center-unstable linear subspace Hu ⊕ ℝ The flow on the center-unstable manifold of the original system may be identified with a parameterized flow on Hu given by x = f∞ (x,μ). The flow on the center-unstable manifold of the Galerkin approximant determined by Fn ⊕ ℝ may be identified with a parameterized flow on Hu given by ẋ = fn (x,μ). It is proved that Theorem I holds: in the Cktopology on a compact neighborhood of the origin in Hu ⊕ ℝ From this theorem it is concluded that Theorem 2 holds: If a certain priori bound holds relating f∞ and fn and an asymptotically stable set A of ẋ = fn (x,μ) near the origin, then ẋ = f∞ (x,μ) has an asymptotically stable set near the origin with the same Borsuk shape as A. Conversely, for each asymptotically stable set near the origin of ẋ = f∞(x,μ), there is one of the same Borsuk shape for ẋ = fn (x,μ) provided n is large enough. Informally, these results amount to the statement that asymptotically stable sets of the Navier-stokes equation, bifurcating from a steady solution, are recovered up to Borsuk shape by those of large enough Galerkin approximants.
On essential extensions of rings
Authors: Puczyłwski E. R.
Published: April 2009

This paper concerns the problem of description of the set of rings containing a given ring as an essential ideal. The results obtained are applied to some problems of ring theory and radicals.
Lattice coverings and the diagonal group
Authors: Ramharter G.
Published: April 2009

LetMbe any bounded set inn-dimensional Euclidean space. Then almost alln-dimensional latticesLwith determinant1have the following property: There exists a diagonal transformationDwith determinant1(depending onL) such thatLdoes not cover space withDM. Moreover, ifMhas non-empty interior, the exceptional (null-) set contains at least enumerably many diagonally non-equivalent lattices.
On the area of planar convex sets containing many lattice points
Authors: Scott P. R.
Published: April 2009

A classical theorem of van der Corput gives a bound for the volume of a symmetric convex set in terms of the number of lattice points it contains. This theorem is here generalized and extended for a large class of non-symmetric sets in the plane.
On the one-dimensional nonlinear elastohydrodynamic lubrication
Authors: Goeleven Daniel , Nguyen Van Hien
Published: April 2009

In this paper the authors prove an abstract theorem for solutions of a variational inequality on a cone and use it to study the free boundary problem of elastohydrodynamic lubrication from mechanical engineering. The mathematical model is set in a one-dimensional geometry. The existence of a solution for every non-negative lubricant viscosity is proved, and some properties useful for the numerical analysis are obtained.
Approximation of a quasilinear elliptic equation with nonlinear boundary condition
Authors: Cranny T.R.
Published: April 2009

We consider a quasilinear elliptic partial differential equation with nonlinear boundary condition under assumptions which do not allow the application of standard degree theory results or techniques such as the method of continuity. An approximation using mollifiers is introduced, allowing the application of Leray-Schauder degree theory, and homotopy arguments are then used to prove the existence of solutions to the approximating problems. A subsequent paper will discuss the question of the convergence of these approximate solutions to a classical solution of the original problem.
Use of the rabinowitsch polynomial to determine the class groups of a real quadratic field
Authors: Mollin R.A.
Published: April 2009

The main result is a necessary and sufficient condition for the class group of a real quadratic field to be determined by primality properties of the well-known Rabinowitsch polynomial.
On projective lift and orbit spaces
Authors: Das T.K.
Published: April 2009

By constructing the projective lift of a dp-epimorphism, we find a covariant functor E from the category Cd of regular Hausdorff spaces and continuous dp-epimorphisms to its coreflective subcategory εd consisting of projective objects of Cd We use E to show that E(X/G) is homeomorphic to EX/G whenever G is a properly discontinuous group of homeomorphisms of a locally compact Hausdorff space X and X/G is an object of Cd.
Linear parabolic equations with venttsel initial boundary conditions
Authors: Zeng Yi , Luo Yousong
Published: April 2009

The Schauder estimates for solutions of linear second order parabolic equations with Venttsel initial boundary conditions are proved, and existence and uniqueness of classical solutions under such an initial boundary condition are established. An application to an engineering problem is also given.
Regularisations of convex functions and slicewise suprema
Authors: Simons S.
Published: April 2009

For a number of years, there has been interest in the regularisation of a given proper convex lower semicontinuous function on a Banach space, defined to be the episum (=inf-convolution) of the function with a scalar multiple of the norm. There is an obvious geometric way of characterising this regularisation as the lower envelope of cones lying above the graph of the original function. In this paper, we consider the more interesting problem of characterising the regularisation in terms of approximations from below, expressing the regularisation as the upper envelope of certain subtangents to the graph of the original function. We shall show that such an approximation is sometimes (but not always) valid. Further, we shall give an extension of the whole procedure in which the scalar multiple of the norm is replaced by a more general sublinear functional. As a by-product of our analysis, we are led to the consideration of two senses stronger than the pointwise sense in which a function on a Banach space can be expressed as the upper envelope of a family of functions. These new senses of suprema lead to some questions in Banach space theorey.
Rings with quasi-injective ideals
Authors: Ivanov George
Published: April 2009

A short proof determining the structure of Q-rings with infinite identities is given. The structure of pQ-rings is determined and it is shown that essentially all wQ-rings with finite identities are pQ-rings.
Remarks concerning the 2-Hilbert class field of imaginary quadratic number fields: Corrigenda
Authors: Benjamin Elliot
Published: April 2009

In my earlier paper [1] I made the claim that there are three groups in Hall and Senior's book “The Groups of Order 2n(n ≤ 6)” that are in error (groups 64/140, 64/141, 64/143). However, it has been pointed out to me by Franz Lemermeyer that I made the unfortunate oversight of using the definition [x, y] = xyx−1y−1 for the commutator whereas Hall and Senion use the definition [x, y] = x−1y−1xy (see [2]). With this correction there is no problem with the above three groups in Hall and Senior.
Conjugations on Banach algebras
Authors: Miller John Boris
Published: April 2009

An example is given of a complex unital Banach algebra carrying a continuum of conjugations, for each of which the selfconjugate subalgebra is strictly real.
Characterisations of efficient sets in vector optimisation
Authors: Boissard Nathalie
Published: April 2009

In this paper, we present characterisations of the sets of infima and efficient solutions and we give also a multiplier rule for these kinds of points. The results are established for a vector optimisation problem with C-convexlike criterion, C being a polyhedral cone.
Generalised second-order derivatives of convex functions in reflexive Banach spaces
Authors: Ndoutoume James Louis , Théra Michel
Published: April 2009

Generalised second-order derivatives introduced by Rockafellar in the finite dimensional setting are extended to convex functions defined on reflexive Banach spaces. Our approach is based on the characterisation of convex generalised quadratic forms defined in reflexive Banach spaces, from the graph of the associated subdifferentials. The main result which is obtained is the exhibition of a particular generalised Hessian when the function admits a generalised second derivative. Some properties of the generalised second derivative are pointed out along with further justifications of the concept.
Composites of translations and odd rational powers act freely
Authors: Cohen Stephen D. , Glass A.M.W.
Published: April 2009

It is shown that no non-trivial composition of translations x ↦ x + a and odd rational powers x ↦p/q, where p,q are odd co-prime integers, positive or negative with p/q≠±, acts like the identity on a field of characteristic zero. This extends a theorem of Adeleke, Glass, and Morley in which only odd positive rational powers were considered. Moreover, the nature of the proof itself (by field theory) is a simplification and natural refinement of previous proofs. It has applications in other settings.
On the average distance property in finite dimensional real Banach spaces
Authors: Wolf Reinhard
Published: April 2009

The average distance Theorem of Gross implies that for each N-dimensional real Banach space E (N ≥ 2) there is a unique positive real number r(E) with the following property: for each positive integer n and for all (not necessarily distinct) x1, x2, …, xn, in E with ‖x1‖ = ‖x2‖ = … = ‖xn‖ = 1, there exists an x in E with ‖x‖ = 1 such that

.

In this paper we prove that if E has a 1-unconditional basis then r(E)≤2−(l/N) and equality holds if and only if E is isometrically isomorphic to Rn equipped with the usual 1-norm.
On rational-derived quartics
Authors: Buchholz R.H. , Kelly S.M.
Published: April 2009

We present a characterisation of all quartic polynomials with exactly three distinct roots and the property that it and all its derivatives have rational roots. It turns out that there are an infinite number of distinct such quartics, each of which corresponds to a point on a related elliptic curve. Furthermore the collection of these points forms a proper subgroup of the group of rational points on the curve.
Approximate conversion of Bézier curves
Authors: Park Yungeom , Choi U Jin , Kimn Ha-Jine
Published: April 2009

The methods for generating a polynomial Bézier approximation of degree n − 1 to an nth degree Bézier curve, and error analysis, are presented. The methods are based on observations of the geometric properties of Bézier curves. The approximation agrees at the two endpoints up to a preselected smoothness order. The methods allow a detailed error analysis, providing a priori bounds of the point-wise approximation error. The error analysis for other authors’ methods is also presented.
The subdifferential of the sum of two functions in Banach spaces II. Second order case
Authors: Deville Robert , Haddad El Mahjoub El
Published: April 2009

We prove a formula for the second order subdifferential of the sum of two lower semi continuous functions in finite dimensions. This formula yields an Alexandrov type theorem for continuous functions. We derive from this uniqueness results of viscosity solutions of second order Hamilton-Jacobi equations and singlevaluedness of the associated Hamilton-Jacobi operators. We also provide conterexamples in infinite dimensional Hilbert spaces.
Invexity criteria for a class of vector-valued functions
Authors: Sach Pham Huu , Phuong Ta Duy
Published: April 2009

This paper gives criteria, necessary or sufficient for a vector-valued function F = (f1, f2, …, fk) to be invex. Here each fi is of the -class (that is, each fi is a function whose gradient mapping is locally Lipschitz in a neighbourhood of x0) and the invexity of F means that F(x) − F(x0) ⊂ ˚F′(X) + Q for a fixed convex cone Q of Rk and every x near x0 (˚F′ being the Jacobian matrix of F at x0).
On the join of varieties of groups
Authors: Storozhev A.
Published: April 2009

We introduce two pseudoabelian group varieties, each defined by one word in two variables, and prove that their join is not pseudoabelian. We also prove that every variety which is nilpotent of class two, is not join-inaccessible.
Expansivity of semi-hyperbolic Lipschitz mappings
Authors: Diamond P. , Kloeden P. , Kozyakin V. , Pokrovskii A.
Published: April 2009

Semi-hyperbolic dynamical systems generated by Lipschitz mappings are shown to be exponentially expansive, locally at least, and explicit rates of expansion are determined. The result is applicable to nonsmooth noninvertible systems such as those with hysteresis effects as well as to classical systems involving hyperbolic diffeomorphisms.
Some bounds for the degree of commutativity of a p-group of maximal class
Authors: Vera-López Antonio , Fernández-Alcober Gustavo A.
Published: April 2009

In this paper we obtain several lower bounds for the degree of commutativity of a p-group of maximal class of order pm. All the bounds known up to now involve the prime p and are almost useless for small m. We introduce a new invariant b which is related with the commutator structure of the group G and get a bound depending only on b and m, not on p. As a consequence, we bound the derived length of G and the nilpotency class of a certain maximal subgroup in terms of b. On the other hand, we also generalise some results of Blackburn. Examples are given in order to check the sharpness of the bounds.
Some series involving the zeta function
Authors: Choi Junesang , Srivastava H.M. , Quine J.R.
Published: April 2009

Lots of formulas for series of zeta function have been developed in many ways. We show how we can apply the theory of the double gamma function, which has recently been revived according to the study of determinants of Laplacians, to evaluate some series involving the Riemann zeta function.
A generalisation of Ahlfors-Schwarz lemma to Riemannian geometry
Authors: Chua Kok Seng
Published: April 2009

Our main result shows that a conformal mapping of hyperbolic n-space into another Riemannian manifold with scalar curvature bounded above by −n(n − 1) is necessarily distance decreasing. This is a generalisation of Ahlfors' version of the Schwarz-Pick lemma to Riemannian Geometry.
A theory of polytopes
Authors: Coppel W.A.
Published: April 2009

The basic properties of polytopes and their faces are derived from a set of axioms which are satisfied, in particular, by polytopes in Euclidean, hyperbolic or (hemi-)spherical space. The underlying space is not assumed to be either dense or unbounded.
A note on strong Ditkin algebras
Authors: Feinstein J.F.
Published: April 2009

In this note we answer a question of W. G. Bade by showing that if a normal, unital Banach function algebra A is strongly regular at one of its characters φ has a bounded approximate identity, then A has bounded relative units at φ. In particular, every strong Ditkin algebra has bounded relative units at all points of its character space. There need not, however, be a global bound available for the relative units.
On loops which have dihedral 2-groups as inner mapping groups
Authors: Niemenmaa Markku
Published: April 2009

In this paper we consider the situation that a group G has a subgroup H which is a dihedral 2-group and with connected transversals A and B in G. We show that G is then solvable and moreover, if G is generated by the set A ∪ B, then H is subnormal in G. We apply these results to loop theory and it follows that if the inner mapping group of a loop Q is a dihedral 2-group then Q is centrally nilpotent.
Separable determination of Fréchet differentiability of convex functions
Authors: Giles J.R. , Sciffer Scott
Published: April 2009

For a continuous convex function on an open convex subset of any Banach space a separability condition on its image under the subdifferential mapping is sufficient to guarantee the generic Fréchet differentiability of the function. This gives a direct insight into the characterisation of Asplund spaces.
Maximum principles for a class of semilinear elliptic boundary-value problems
Authors: Hailiang Zhang
Published: April 2009

For years it has remained a problem to find suitable functionals satisfying certain maximum principles for solutions of the equation Δu + f(x, u) = 0. In this paper, maximum principles for certain functionals which are defined on solutions of semilinear elliptic equations subject to mixed or Robin boundary conditions are obtained. The principles derived may be used to deduce bounds on important quantities in physical problems of interest.
Approximate polyhedra, density and discrete maps
Authors: Giraldo Antonio , Sanjurjo Jose M.R.
Published: April 2009

Some extension properties of maps defined on dense subsets are studied for approximate polyhedra. The latter are characterised as approximate extensors for finite maps with small oscillation.
Remarks on symmetric smooth norms
Authors: H´Jek P. , Zizler V.
Published: April 2009

A characterisation is given of separable Banach spaces with symmetric Schauder bases which admit equivalent symmetric norms that are Gâteaux differentiable or uniformly rotund in every direction. Some applications to questions on distortion of norms on l∞ are discussed.
Some utility theorems on inductive limits of preordered topological spaces
Authors: Candeal J.C. , IndurÁIn E. , Mehta G.B.
Published: April 2009

We prove the existence of an order-preserving function on a class of preordered topological spaces that are inductive limits of preordered spaces. Some applications to economics are given.
Remarks on a measure of weak noncompactness in the Lebesgue space
Authors: Bana´ Józef , Sadarangani Kishin
Published: April 2009

Using the concept of equi-integrability we introduce a measure of weak noncompactness in the Lebesgue space L1(0, l). We show that this measure is equal to the classical De Blasi measure of weak noncompactness.
Curvature evolution of plane curves with prescribed opening angle
Authors: Ishimura Naoyuki
Published: April 2009

We discuss the evolution of plane curves which are described by entire graphs with prescribed opening angle. We show that a solution converges to the unique self-similar solution with the same asymptotics.
Free Abelian topological groups and the Pontryagin-Van Kampen duality
Authors: Pestov Vladimir
Published: April 2009

We study the class of Tychonoff topological spaces such that the free Abelian topological group A(X) is reflexive (satisfies the Pontryagin-van Kampen duality). Every such X must be totally path-disconnected and (if it is pseudocompact) must have a trivial first cohomotopy group π1(X). If X is a strongly zero-dimensional space which is either metrisable or compact, then A(X) is reflexive.
Note on amenable algebras of operators
Authors: Curtis P.C. , Loy R.J.
Published: April 2009

It is shown that an amenable algebra of operators on Hibert space which is generated by its normal elements is necessarily self-adjoint, so it is a C*-algebra.
Elementary Abelian p-groups revisited
Authors: Howard Paul , Rubin Jean E.
Published: April 2009

For each prime p, a Fraenkel-Mostowski model is constructed in which there are two elementary Abelian p-groups with the same cardinality that are not isomorphic.
On the discrepancy principle and generalised maximum likelihood for regularisation
Authors: Lukas Mark A.
Published: April 2009

Let fnλ be the regularised solution of a general, linear operator equation, K f0 = g, from discrete, noisy data yi = g(xi ) + εi, i = 1, …, n, where εi are uncorrelated random errors with variance σ2. In this paper, we consider the two well–known methods – the discrepancy principle and generalised maximum likelihood (GML), for choosing the crucial regularisation parameter λ. We investigate the asymptotic properties as n → ∞ of the “expected” estimates λD and λM corresponding to these two methods respectively. It is shown that if f0 is sufficiently smooth, then λD is weakly asymptotically optimal (ao) with respect to the risk and an L2 norm on the output error. However, λD oversmooths for all sufficiently large n and also for all sufficiently small σ2. If f0 is not too smooth relative to the regularisation space W, then λD can also be weakly ao with respect to a whole class of loss functions involving stronger norms on the input error. For the GML method, we show that if f0 is smooth relative to W (for example f0 ∈ Wθ, 2, θ > m, if W = Wm, 2), then λM is asymptotically sub-optimal and undersmoothing with respect to all of the loss functions above.
On the number of conjugacy classes of the sylow p-subgroups of GL(n,q)
Authors: Vera-López Antonio , Arregi J.M. , Vera-López F.J.
Published: April 2009

If G is a finite p-group of order pn, P. Hall determined the number of conjugacy classes of G, r(G), modulo (p2 − 1)(p − 1). Namely, he proved the existence of a constant k ≥ 0 such that r(G) = n(p2 − 1) + pe + k(p2 − 1)(p − 1). In this paper, we denote by the group of the upper unitriangular matrices over , the finite field with q = pt elements, and we determine the number of classes of modulo (q − 1)5.
On uniformly contractive systems and quadratic equations in Banach space
Authors: Ruch David K.
Published: April 2009

The solution of quadratic equations using the contraction mapping principle is considered. A uniqueness result extending that given by Argyros is proved. Uniformly contractive systems theory is used to find approximate solutions and convergence criteria are given. In particular, only pointwise convergence of approximating operators is required to guarantee convergence of the approximate solutions. A theorem and algorithm for a continuation method are presented, and illustrated on Chandrasekhar's equation.
Estimates by polynomials
Authors: Aron R.M. , Choi Y.S. , Llavona J.G.
Published: April 2009

Consider the following possible properties which a Banach space X may have: (P): If (xi) and (yj) are bounded sequences in X such that for all n ≥ 1 and for every continuous n-homogeneous polynomial P on X, P(xj) − (yj) → 0, then Q(xj − yj) → 0 for all m ≥ 1 and for every continuous m-homogeneous polynomial Q on X.

(RP): If (xj)and (yj) are bounded sequences in X such that for all n ≥ 1 and for every continuous n-homogeneous polynomial P on X, P(xj − yj) → 0, then Q(xj) − Q(yj) → 0 for all m ≥ 1 and for every continuous m-homogeneous polynimial Q on X. We study properties (P) and (RP) and their relation with the Schur proqerty, Dunford-Pettis property, Λ, and others. Several applications of these properties are given.
Generic differentiability of locally Lipschitz functions on product spaces
Authors: Giles J.R.
Published: April 2009

Although it is known that locally Lipschitz functions are densely differentiable on certain classes of Banach spaces, it is a minimality condition on the subdifferential mapping of the function which enables us to guarantee that the set of points of differentiability is a residual set. We characterise such minimality by a quasi continuity property of the Dini derivatives of the function and derive sufficiency conditions for the generic differentiability of locally Lipschitz functions on a product space.
Bounds on the limiting distribution of a branching process with varying environment
Authors: Jones Owen Dafydd
Published: April 2009

Upper and lower bounds are obtained for the left tail of the normed limitW0of a supercritical branching process with varying environment, that is, for P(W0<x) for smallx. Two types of process are dealt with—öttcher type and Schröder type—which between them cover “most” processes with zero extinction probability.
Compactifications and quotient lattices of Wallman bases
Authors: Wajch Eliza
Published: April 2009

We improve the intuition and some ideas of G. D. Faulkner and M. C. Vipera presented in the article “Remainders of compactifications and their relation to a quotient lattice of the topology” [Proc. Amer. Math. Soc. 122 (1994)] in connection with the question about internal conditions for locally compact spacesXandYunder whichβX/X≅βY/Yor, more generally, under which the remainders of compactifications ofXbelong to the collection of the remainders of compactifications ofY. We point out the reason why the quotient lattice of the topology considered by Faulkner and Vipera cannot lead to a satisfactory answer to the above question. We replace their lattice by the qoutient lattice of a new equivalence relation on a Wallman base in order to describe a method of constructing a Wallman-type compactification which allows us to deduce more complete solutions to the problems investigated by Faulkner and Vipera.
Some classes of sequential spaces
Authors: Svetlichny Sergey A.
Published: April 2009

By means of defined concepts all metric spaces of given weight or cardinality and their quotients are characterised. An example of a sequential space having weight w1 which is not a quotient of any metric space of weight w1 is provided. The well-known classes of sequential spaces are also obtained as images of metric spaces by particular kinds of maps.
Locally compactly Lipschitzian mappings in infinite dimensional programming
Authors: Glover B.M.
Published: April 2009

In this note we show that a subgradient multifunction of a locally compactly Lip-schitzian mapping satisfies a closure condition used extensively in optimisation theory. In addition we derive a chain rule applicable in either separable or reflexive Banach spaces for the class of locally compactly Lipschitzian mappings using a recently derived generalised Jacobian. We apply these results to the derivation of Karush-Kuhn-Tucker and Fritz John optimality conditions for general abstract cone-constrained programming problems. A discussion of constraint qualifications is undertaken in this setting.
Subdifferentials are locally maximal monotone
Authors: Simons S.
Published: April 2009

In a recent paper, Fitzpatrick and Phelps introduced a new class of operators on a Banach space, the locally maximal monotone operators, and showed that this kind of operator can be approximated by a sequence of nicer maximal monotone operators. We give here an affirmative answer to a question posed in this paper: is the subdifferential of a proper convex lower semicontinuous function necessarily locally maximal monotone? Since a locally maximal operator is maximal monotone, our result represents a strengthening of Rockafellar's maximal monotonicity theorem.
Countably quasi-suprabarrelled spaces
Authors: Ferrando J.C. , Sánchez Ruiz L.M.
Published: April 2009

In this paper we obtain some permanence properties of a class of locally convex spaces located between quasi-suprabarrelled spaces and quasi-totally barrelled spaces, for which a closed graph theorem is given.
Denseness of operators which attain their numerical radius
Authors: Jia-Ping Wang , Tai Yu Xin
Published: April 2009

We show that a bounded linear operator on a dual Banach space X may be perturbed by a compact operator of arbitrarily small norm to yield an operator which attains its numerical radius provided the weak star and norm topologies coincide on the unit sphere of X.
On topological entropy of triangular maps of the square
Authors: Alsedà Lluís , Kolyada Sergiĭ F. , Snoha Ľubomír
Published: April 2009

We study the topological entropy of triangular maps of the square. We show that such maps differ from the continuous maps of the interval because there exist triangular maps of the square of “type 2∞” with infinite topological entropy. The set of such maps is dense in the space of triangular maps of “type at most 2∞” and the topological entropy as a function of the triangular maps of the square is not lower semicontinuous. However, we show that for these maps the characterisation of the lower bounds of the topological entropy depending on the set of periods is the same as for the continuous maps of the interval.
Necessary and sufficient fixed point critera involving attractors
Authors: Jachymski Jacek
Published: April 2009

Let f be a continuous self-map on a complete metric space X and p ∈ X. Let c be a positive real. Equivalent conditions are given for the singleton {p} to be an attractor of a set of c−fixed points of f. We also establish equivalent conditions for the existence of a contractive fixed point of f. These results subsume a body of fixed point theorems.
Elliptic integrals and limit cycles
Authors: Urbina A.M. , De La Barra M. León , De La Barra G. León , Cañas M.
Published: April 2009

By using zeros of elliptic integrals we establish an upper bound for the number of limit cycles that emerge from the period annulus of the Hamiltonian XH in the system Xε = XH + ε(P, Q), where H = y2 + x4 and P, Q are polynomials in x, y, as a function of the degrees of P and Q. In particular, if (P, Q) = , with N = 2k + 1 or 2k + 2, this upper bound is k − 1.
Universal arrows to forgetful functors from categories of topological algebra
Authors: Pestov Vladimir G.
Published: April 2009

We survey the present trends in theory of universal arrows to forgetful functors from various categories of topological algebra and functional analysis to categories of topology and topological algebra. Among them are free topological groups, free locally convex spaces, free Banach-Lie algebras, and more. An accent is put on the relationship of those constructions with other areas of mathematics and their possible applications. A number of open problems is discussed; some of them belong to universal arrow theory, and other may become amenable to the methods of this theory.
The homological dimensions of simple modules
Authors: Ding Nanqing , Chen Jianlong
Published: April 2009

We prove that (a) if R is a commutative coherent ring, the weak global dimension of R equals the supremum of the flat (or (FP–)injective) dimensions of the simple R-modules; (b) if R is right semi-artinian, the weak (respectively, the right) global dimension of R equals the supremum of the flat (respectively, projective) dimensions of the simple right R-modules; (c) if R is right semi-artinian and right coherent, the weak global dimension of R equals the supremum of the FP-injective dimensions of the simple right R-modules.
The Joly topology and the Mosco-Beer topology revisited
Authors: Azé Dominique , Penot Jean-Paul
Published: April 2009

Some extensions to the non reflexive case of continuity results for the Legendre-Fenchel transform are presented following an approach due to J.-L. Joly. We compare the topology introduced by J.-L. Joly and the Mosco-Beer topology introduced by G. Beer. In particular, in the case of the space of closed proper convex functions defined on the dual of a normed vector space they coincide.
A theorem on the spectral radius of the sum of two operators and its application
Authors: Zima M.
Published: April 2009

In the present paper a theorem on the spectral radius of the sum of linear operators is established. The application of this theorem to a functional differential equation of neutral type is also given.
Nonoscillatory solutions of neutral delay differential equations
Authors: Chen Ming-Po , Yu J.S. , Wang Z.C.
Published: April 2009

Consider the following neutral delay differential equation

wherep∈R,τ∈ (0, ∞), δ ∈R+= (0, ∞) and Q ∈ (C([t0, ∞),R). We show that if

then Equation (*)has a nonoscillatory solution whenp≠ –1. We also deal in detail with a conjecture of Chuanxi, Kulenovic and Ladas, and Györi and Ladas.
Uniqueness of limit cycles in polynomial systems with algebraic invariants
Authors: Zegeling André , Kooij Robert E.
Published: April 2009

The uniqueness of limit cycles is proved for quadratic systems with an invariant parabola and for cubic systems with four real line invariants. Also a new, simple proof is given of the uniqueness of limit cycles occurring in unfoldings of certain vector fields with codimension two singularities.
Near-rings of homotopy classes of continuous functions
Authors: Mutter Wolfgang
Published: April 2009

In this paper we show that for a compact connected abelian group G the near-ring [G, G] of all homotopy classes of continuous selfmaps of G is an abstract affine near-ring, and investigate the ideal structure of these near-rings.
Skew fields with a non-trivial generalised power central rational identity
Authors: Chiba Katsuo
Published: April 2009

Let D be a skew field with uncountable centre K. The main result in the present paper is as follows: If D satisfies a non-trivial generalised power central rational identity, then D is finite dimensional over K. As a corollary we obtain the following result. Let a be an element of D such that (a−1x−1ax)q(x) ∈ K for all x ∈ D ﹨ {0} where q(x) is a positive integer depending on x. Then a ∈ K.
A note on fragmentable topological spaces
Authors: Nagamizu Toshihiro
Published: April 2009

We extend the results of N.K. Ribarska and A.V. Arhangel'skiĭ to the class of strongly countably complete spaces. And we show another characterisation of Eberlein and Radon-Nikodým compact spaces.
A chain rule for nonsmooth composite functions via minimisation
Authors: Ralph D.
Published: April 2009

Nonsmooth calculus using the approximate subdifferential of Mordukhovich and loffe admits a sharper chain rule, hence sharper applications in optimisation, than does the generalised gradient of Clarke. We observe, however, that at a local minimum point of the composition of nonsmooth vector valued and real valued functions, the generalised gradient admits a special, relatively sharp chain rule, that yields sharper results than have been seen before in the context of the generalised gradient.
Invariant Kähler metrics and projective embeddings of the flag manifold
Authors: Yang Kichoon
Published: April 2009

We determine explicitly the space of invariant Hermitian and Kähler metrics on the flag manifold. In particular, we show that a Killing metric is not Kähler. The Chern forms are also computed in terms of the Maurer–Cartan form, and this calculation is used to prove that the flag manifold is projective algebraic. An explicit projective embedding of the flag manifold is also given.
Global attractor for the Cahn-Hilliard system
Authors: Cholewa Jan W. , Dlotko Tomasz
Published: April 2009

The Cahn-Hilliard system, a natural extension of the single Cahn-Hilliard equation in the case of multicomponent alloys, will be shown to generate a dissipative semigroup on the phase space ℋ = [H2(Ω)]m. Following Hale's ideas and based on the existence and form of the Lyapunov functional, our main result will be the existence of a global attractor on a subset of ℋ. New difficulties specific to the system case make our problem interesting.
Examples of supersoluble Lockett sections
Authors: Menth Martin
Published: April 2009

Two Lockett sections of Fitting classes of supersoluble groups are determined. One of these sections has only one member, a minimal supersoluble nonnilpotent Fitting class.
The approximation property and nilpotent ideals in amenable Banach algebras
Authors: Loy R.J. , Willis G.A.
Published: April 2009

It is well known that non-zero nilpotent ideals in amenable Banach algebras must be infinite-dimensional. We show that under certain additional hypotheses such ideals cannot even have the approximation property.
Derived Mendelsohn triple systems
Authors: Stojaković Zoran
Published: April 2009

Mendelsohn triple system of order ν which can be extended to a tetrahedral quadruple system of order ν + 1 we call a derived Mendelsohn triple system. We consider some properties of derived Mendelsohn triple systems and give some results on their existence.
Existence and multiplicity results for semicoercive unilateral problems
Authors: Goeleven D. , Nguyen V.H. , Willem M.
Published: April 2009

In this paper, we investigate a general class of variational inequalities. Existence and multiplicity results are obtained by using minimax principles for lower semicontinuous functions due to A. Szulkin.
A remark on embedding topological groups into products
Authors: Pestov Vladimir
Published: April 2009

Let P be a class of topological groups such that every topological group is isomorphic to a topological subgroup of the direct product (with Tychonoff topology) of a subfamily of P. Then every Tychonoff space is homeomorphic to a subspace of a group from P.
A class of spaces with weak normal structure
Authors: Sims Brailey
Published: April 2009

It has recently been shown that a Banach space enjoys the weak fixed point property if it is ε0-inquadrate for some ε0 < 2 and has WORTH; that is, if then, ║xn — x║ — ║xn + x║ → 0, for all x. We establish the stronger conclusion of weak normal structure under the substantially weaker assumption that the space has WORTH and is ‘ε0-inquadrate in every direction’ for some ε0 < 2.
On the convexity of Stampfli's numerical range
Authors: Agure J. O.
Published: April 2009

This paper investigates a certain type of numerical range introduced by Stampfli. In particular, we investigate the convexity of this set of elements of operators on Hilbert spaces and its relationship to the algebra numerical range implemented by elements of a W*-algebra.
Non-coprime quadratic systems
Authors: Coppel W. A.
Published: April 2009

A recent result of Huang and Reyn on quadratic systems is reformulated and given a clearer proof.
Differential inclusions and abstract control problems
Authors: Cichoń Mieczyław
Published: April 2009

We prove an existence theorem for differential inclusionsin Banach spaces. Here {A(t):t∈ [0,T]} is a family of linear operators generating a continuous evolution operatorK(t, s). We concentrate on mapsFwithF(t,·) weakly sequentially hemi-continuous.

Moreover, we show a compactness of the set of all integral solutions of the above problem. These results are also applied to a semilinear optimal control problem. Some corollaries, important in the theory of optimal control, are given too. We extend in several ways theorems existing in the literature.
On the Dunford-Pettis property in spaces of vector-valued bounded functions
Authors: Contreras Manuel D. , Díaz Santiago
Published: April 2009

We show that L∞(μ,X) has the Dunford-Pettis property for some classical Banach spaces including L1(μ), C (K), the disc algebra A and H∞.
Sign pattern matrices that allow a nilpotent matrix
Authors: Yeh Lina
Published: April 2009

We characterise some star sign pattern matrices and linear tree sign pattern matrices that allow a nilpotent matrix.
Modules arising from some relative injectives
Authors: Zhou Yiqiang
Published: April 2009

A ringRis a rightSI-ring if every singular rightR-module is injective, whileRis a rightS3I-ring if every singular semisimple rightR-module is injective. In this paper, we investigate and characterise several analogues of the two notions to modules, with many illustrative examples included.
On squares of Jacobson radical rings
Authors: Puczylowski E.R. , Zand H.
Published: April 2009

We construct several examples of Jacobson radical rings which are not squares of other rings.
Recycling circle planes
Authors: Polster Burkard
Published: April 2009

The main aim of this paper is to introduce new ways of constructing flat projective planes from spherical circle planes and cylinder circle planes. We shall also touch upon topics that have natural connections with our constructions, like the construction of spreads of pseudolines from flat projective planes, the extendability of partial spherical circle planes to spherical circle planes and giving examples of sets of 2-arcs that determine flat projective planes and ℝ2-planes.