bluuebunny/crossref_metadata_2025_split huggingface dataset:
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.
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 equationwherep∈R,τ∈ (0, ∞), δ ∈R+= (0, ∞) and Q ∈ (C([t0, ∞),R). We show that ifthen Equation (*)has a nonoscillatory solution whenp≠ –1. We also deal in detail with a conjecture of Chuanxi, Kulenovic and Ladas, and Györi and Ladas.
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.
Periodic solutions of a second order nonlinear differential equation
Authors: Mehri Bahman 
Published: April 2009

We consider the following non-linear nonautonomous second order differential equationwhere h(x) is continuous, f, p are continuous and periodic with respect to t of period w. Using the Leray-Schauder fixed point technique we prove that the above equation possesses at least one non-trivial periodic solution of period w.
On the inversion of Fourier transforms
Authors: Asmar Nakhlé H. , Merryfield Kent G. 
Published: April 2009

Let G be a locally compact abelian group, with character group Ĝ. Let ψ be an arbitrary continuous real-valued homomorphism defined on Ĝ. For f in LP(G), 1 < p ≤ 2, letwhere 1[−ν, ν] is the indicator function of the interval [ − ν, ν ], and I is an unbounded increasing sequence of positive real numbers. Then there is a constant Mp, independent of f, such that ‖M#f‖p ≤ Mp ‖f‖p. Consequently, the pointwise limit of the function exists, almost everywhere on G, as ν tends to infinity. Using this result and a generalised version of Riesz's theorem on conjugate functions, we obtain a pointwise inversion for Fourier transforms of functions on Ra × Tb, where a and b are nonnegative integers, and on various other locally compact abelian groups.
A generalised quasi-variational inequality without upper semicontinuity
Authors: Cubiotti Paolo , Yuan Xian-Zhi 
Published: April 2009

In this note we deal with the following problem: given a nonempty closed convex subset X of Rn and two multifunctions Γ : X → 2X and , to find ( such thatWe prove a very general existence result where neither Γ nor Φ are assumed to be upper semicontinuous. In particular, our result give a positive answer to an open problem raised by the first author recently.
Nonuniqueness and wellposedness of abstract Cauchy problems in a Fréchet space
Authors: Kunstmann Peer Christian 
Published: April 2009

Suppose that A is a closed linear operator in a Fréchet space X. We show that there always is a maximal subspace Z containing all x ∈ X for which the abstract Cauchy problem has a mild solution, which is a Fréchet space for a stronger topology. The space Z is isomorphic to a quotient of a Fréchet space F, and the part Az of A in Z is similar to the quotient of a closed linear operator B on F for which the abstract Cauchy problem is well-posed. If mild solutions of the Cauchy problem for A in X are unique it is not necessary to pass to a quotient, and we reobtain a result due to R. deLaubenfels.Moreover, we obtain a continuous selection operator for mild solutions of the inhomogeneous equation.
The Perimeter of optimal convex lattice polygons in the sense of different metrics
Authors: Stojaković Miloš 
Published: April 2009

Classes of convex lattice polygons which have minimal lp-perimeter with respect to the number of their vertices are said to be optimal in the sense of the lp-metric.It is proved that if p and q are arbitrary integers or ∞, the asymptotic expression for the lq-perimeter of these optimal convex lattice polygons Qp(n) as a function of the number of their vertices n is
. for arbitrary ɛ > 0,
where
.
and Ap is equal to the area of the planar shape |x|p + |y|p ≤ 1.
Brauer points on Fermat curves
Authors: McCallum William G. 
Published: April 2009

In honour of George Szekeres on his 90th birthdayIf X is a variety over a number field K, the set of K-rational points on X is contained in the subset of the adelic points cut out by the Brauer group; we call this set the set of Brauer points on the variety. If S is a set of valuations of K, we also define S-Brauer points in a natural way. It is natural to ask how good a bound on the rational points is provided by the Brauer (or S-Brauer) points.Let p > 3 be a prime number, and let X be the Fermat curve of degree p, xp + yp = 1. Let K be the field of p-th roots of unity, and let r be the p-rank of the class group of K. In this paper we show that if r < (p + 3)/8, then the set of p-Brauer points on X has cardinality at most p. We construct elements of the Brauer group of X by relating it to the Weil-Chatelet group of the jacobian of X, then use the method of Coleman and Chabauty to bound the points cut out by these elements.
The pseudoidentity problem and reducibility for completely regular semigroups
Authors: Almedia Jorge , Trotter Peter G. 
Published: April 2009

Dedicated to George Szekeres on the occasion of his 90th birthdayNecessary and sufficient conditions for equality over the pseudovariety CR of all finite completely regular semigroups are obtained. They are inspired by the solution of the word problem for free completely regular semigroups and clarify the role played by groups in the structure of such semigroups. A strengthened version of Ash's inevitability theorem (κ-reducibility of the pseudovariety G of all finite groups) is proposed as an open problem and it is shown that, if this stronger version holds, then CR is also κ-reducible and, therefore, hyperdecidable.
Graphs without cycles of even length
Authors: Lam Thomas 
Published: April 2009

Dedicated to George Szekeres on his ninetieth birthdayIn this paper we prove that a bipartite graph with parts of sizes M and N, having no cycles of even length less that or equal to 2(2k + 1), where k is a positive integer, has at most (NM)(k+1)/(2k+1) + Dk(N + M) edges, where Dk only depends on k.In particular, we show that when k = 1, D1 = 1 is possible.
Inverse semigroup homomorphisms via partial group actions
Authors: Steinberg Benjamin 
Published: April 2009

This papar constructs all homomorphisms of inverse semigroups which factor through anE-unitary inverse semigroup; the construction is in terms of a semilattice component and a group component. It is shown that such homomorphisms have a unique factorisation βα with α preserving the maximal group image, β idempotent separating, and the domainIof βE-unitary; moreover, theP-representation ofIis explicitly constructed. This theory, in particular, applies whenever the domain or codomain of a homomorphism isE-unitary. Stronger results are obtained for the case ofF-inverse monoids.Special cases of our results include theP-theorem and the factorisation theorem for homomorphisms fromE-unitary inverse semigroups (via idempotent pure followed by idempotent separating). We also deduce a criterion of McAlister–Reilly for the existence ofE-unitary covers over a group, as well as a generalisation toF-inverse covers, allowing a quick proof that every inverse monoid has anF-inverse cover.
On analytic functions with reference to an integral operator
Authors: Parvatham R. , Shanmugam T.N. 
Published: April 2009

Let E = {z: |z| < 1} and let H = {w : regular in E, w(0) = 0, |w(z)| < l, z ∈ E}.Let P(A, B) denote the class of functions in E which can be put in the form (1 + Aw(z))/(1 + Bw(z)), −1 ≤ A < B ≤ 1, w(z) ∈ H. Let S*(A, B) denote the class of functions f(z) of the form such that zf′(z)/f(z) ∈ P(A, B). If f(z) ∈ S*(A, B) and g(z) ∈ S*(C, D) then, in this paper the radius of starlikeness of order β (β ∈ [0, 1]) of the following integral operatoris determined. Conversely, a sharp estimate is obtained for the radius of starlikeness of the class of functionswhere g(z) and F(z) belong to the class S*(A, B).
Univalent functions with univalent Gelfond-Leontev derivatives
Authors: Juneja O.P. , Shah S.M. 
Published: April 2009

Let be a nondecreasing sequence of positive numbers. We consider Gelfond-Leontev derivative Df(z), of a function , defined by for univalence and growth properties, and extend some results of Shah and Trimble. Set en = {d1d2 … dn), n≥l, e0 = 1, . Let r be the radius of convergence of p(z). We state parts of Theorem 1 and Corollaries. Let f and all Dkf, k = 1, 2,…, be analytic and univalent in the unit disk U. Then(iii) if p is entire and of growth (ρ, T) then f must be entire and of growth not exceeding (ρ, 2d2T),(iv) if D corresponds to the shift operator (dn ≡ l), then .Another class of functions is defined by a condition of the form |an+1/an| ≤ bn+1/dn+1, where is a sequence of positive numbers satisfying and inequality, and it is shown that all functions in this class along with all their Gelfond–Leontev successive derivatives are regular and univalent in U. An extension of the definition of a linear invariant family is given and results analogous to (i) and (ii) are stated.
On the construction of soluble groups satisfying the minimal condition for normal subgroups
Authors: Silcock Howard L. 
Published: April 2009

A general method is described for constructing examples of soluble groups whose normal subgroups form a well-ordered chain under the ordering of inclusion. This method is a variant of one introduced in a recent paper by Heineken and Wilson. Each of the resulting groups is obtained by an embedding procedure from a pair of iterated wreath products A1 wr A2 wr … wr An, B1 wr B2 wr … wr Bn, where the constituent groups Ai., Bi are each either cyclic of prime power order or quasicyclic. Here n may be chosen arbitrarily, and the choice of constituent groups is subject only to a condition on the sequences of prime numbers that may occur as orders of elements in the groupsrespectively. The construction is applied to give certain examples which illustrate the limitations of results on particular classes of soluble groups satisfying the minimal condition for normal subgroups obtained in recent papers by Hartley, McDougall, and the present author.
Approximative compactness and continuity of metric projections: Corrigendum
Authors: Panda B.B. , Kapoor O.P. 
Published: April 2009

There is a small error in the proof of Lemma 1 [1], namely, that there may not be a subsequence of the sequence {Φn} converging to Φ in the weak*-topology. Thus equation (5) should read: In view of continuity of Pk we haveThe same error occurs in the proof of Theorem 1 and Lemma 2 also. Therefore, equation (7) should readand this leads to lim . Similarly, equation (8) should readwhich implies that Ψn (x) → ‖x‖. Then there is no need of taking a subsequence.All the same the results are not affected by the above error.
On the existence and uniqueness of solutions of parabolic equations
Authors: Teo K.L. 
Published: April 2009

Recently, Eklund (Proc. Amer. Math. Soc. 47 (1975), 137–142) has shown that to each continuous function F on ∂pQ −⊲ {∂Ω × [0, T]} ∪ {Ω × (0)} there is a unique solution to the boundary value problemwhere L is a linear second order parabolic operator in divergence form, Ω ⊂ Rn is a bounded domain with compact closure and ∂Ω denotes its boundary. In this note, it is shown that the existence theorem of Eklund remains valid for the following boundary problem
On the complex nonlinear complementary problem
Authors: Parida J. , Sahoo B. 
Published: April 2009

The complex nonlinear complementarity problem considered here is the following: find z such thatwhere S is a polyhedral cone in Cn, S* the polar cone, and g is a mapping from Cn into itself. We study the extent to which the existence of a z ∈ S with g(z) ∈ S* (feasible point) implies the existence of a solution to the nonlinear complementarity problem, and extend, to nonlinear mappings, known results in the linear complementarity problem on positive semi-definite matrices.
A comparison theorem for functional differential equations
Authors: Kartsatos Athanassios G. , Onose Hiroshi 
Published: April 2009

In this paper, we study the oscillation of nth-order differential equations. Recently, Atkinson and the present authors studied (separately) the comparison properties of differential inequalities. Kartsatos treated the nth-order ordinary case and proposed several open problems.The purpose of this paper is to answer one of them in the affirmative concerning more general functional differential equations. The result is that if under several conditions, the equationis oscillatory for n even or a solution x(t) of (1) is oscillatory or for n odd, then this is also the case for the equation
Free k-tuples in linear groups
Authors: Mandel Arnaldo , Gonçalves Jairo Z. 
Published: April 2009

Let PGL(P) be the group of projective linear transformations of the n-dimensional projective space P over a field F. A topology is given on F, and it is assumed that F is locally-compact; PGL(P) is endowed with the quotient topology from the canonical projection map GL(n, F) → PGL(P), where.For any given k, it is shown that the set of k–tuples (g1, g2, … gk) ɛ PGL(P)k which freely generate a free sub-group of PGL(P) and has a nonvoid interior.
The persistence of universal formulae in free algebras
Authors: Gaglione Anthony M. , Spellman Dennis 
Published: April 2009

Gilbert Baumslag, B.H. Neumann, Hanna Neumann, and Peter M. Neumann successfully exploited their concept of discrimination to obtain generating groups of product varieties via the wreath product construction. We have discovered this same underlying concept in a somewhat different context. Specifically, let V be a non-trivial variety of algebras. For each cardinal α let Fα(V) be a V-free algebra of rank α. Then for a fixed cardinal r one has the equivalence of the following two statements:(1) Fr(V) discriminates V. (1*) The Fs(V) satisfy the same universal sentences for all s≥r. Moreover, we have introduced the concept of strong discrimination in such a way that for a fixed finite cardinal r the following two statements are equivalent:(2) Fr(V) strongly discriminates V. (2*) The Fs(V) satisfy the same universal formulas for all s ≥ r whenever elements of Fr(V) are substituted for the unquantified variables. On the surface (2) and (2*) appear to be stronger conditions than (1) and (1*). However, we have shown that for particular varieties (of groups) (2) and (2*) are no stronger than (1) and (1*).
Optimal results in local bifurcation theory
Authors: Esquinas J. , López-Gómez J. 
Published: April 2009

Let us consider the abstract equation(0.1) L (ɛ) u + F (ɛ,u) = 0,where F (ɛ,u) = 0 (|u|2) for ɛ near zero. In this paper we define a multiplicity depending only on L (ɛ) allowing us to obtain the following result: “Odd multiplicity entails bifurcation and, if the multiplicity is even, it is possible to find F (ɛ,u) such that the only solution to (0.1) near the origin are the trivial ones”.
Some aspects of relative injectivity
Authors: Feigelstock S. , Raphael R. 
Published: April 2009

If H and M are right R-modules, H is M-injective if every R-homonorphism N → H, N a right R-submodule of M, can be extended to an R-homonorphism from M to H.H is strongly M-injective if H is injective for inclusions whose cokernels are isomorphic to factor modules of M.For the case of abelian groups H and M, one settles the questions “when is H M-injective” and “when is H strongly M-injective”. The latter can be characterized in terms of the vanishing of Ext. Results for general module categories are also given.
Operators on locally convex spaces of vector-valued continuous functions
Authors: López A. García 
Published: April 2009

LetEandFbe locally convex spaces and letKbe a compact Hausdorff space.C(K,E) is the space of allE-valued continuous functions defined onK, endowed with the uniform topology.Starting from the well-known fact that every linear continuous operatorTfromC(K,E) toFcan be represented by an integral with respect to an operator-valued measure, we study, in this paper, some relationships between these operators and the properties of their representing measures. We give special treatment to the unconditionally converging operators.As a consequence we characterise the spacesEfor which an operatorTdefined onC(K,E) is unconditionally converging if and only if (Tfn) tends to zero for every bounded and converging pointwise to zero sequence (fn) inC(K,E).
On the structure of a real crossed group algebra
Authors: Buzási K. 
Published: April 2009

The main result of this paper is that there exist non-principal left ideals in a certain twisted group algebraAof the infinite dihedral group ≤a, b|b−1ab=a−1,b2= 1 ≥ over the field R of real numbers: namely in theAdefined byb−lab = a−1, b2= −1, and λa=aλ, λb=bλ for all real λ.The motivation comes from the study (in a series of papers by Berman and the author) of finitely generated torsion-free RG-modules for groupsGwhich have an infinite cyclic subgroup of finite index. In a sense, this amounts to studying modules over (full matrix algebras over) a finite set of R-algebras [namely, for the groups in question, these algebras take on the role played by R, C and H (the real quaternions) in the theory of real representations of finite groups]. For all but two algebras in that finite set, satisfying results have been obtained by exploiting the fact that each of them is either a ring with zero divisors or a principal left ideal ring. The other two are known to have no zero divisors. One of them is the presentA. The point of the main result is that new ideas will be needed for understandingA-modules.A number of subsidiary results are concerned with convenient generating sets for left ideals inA.
Meromorphic Lipschitz functions
Authors: Yamashita Shinji 
Published: April 2009

Let f be a function meromorphic in D = {|z| < 1} and let X be the chordal distance on the Riemann sphere. Then f satisfies the Lipschitz conditionin D if and only if |f′(z)|/(1 + |f(z)|2) = O((1 – |z|)α−1) and |z| → 1.
A distance function property implying differentiability
Authors: Giles J.R. 
Published: April 2009

In a real normed linear spaceX, properties of a non-empty closed setKare closely related to those of the distance functiondwhich it generates. IfXhas a uniformly Gâteaux (uniformly Fréchet) differentiable norm, thendis Gâteaux (Fréchet) differentiable atx∈X/Kif there exists ansuch thatand is Géteaux (Fréchet) differentiable onX/Kif there exists a setP+(K) dense inX/Kwhere such a limit is approached uniformly for allx∈P+(K). WhenXis complete this last property implies thatKis convex.
Cauchy representation of distributions and applications to probability
Authors: Chaudhry M. Aslam 
Published: April 2009

The Cauchy representation is not valid for every Schwartz distribution f ∈ (D(R))′ because (t – x)−l ∉ D(R). Since for all z ∈ {z: Im z ≠ 0} the kernel (t – z)−l belongs to (R) (1 > p > ∞), the Cauchy representation of the distributions in ((R))′ seems possible.In this paper, we prove this fact. It is also proved that every probability density defines a generalised function on the space (R)(1 < p < ∞), of test functions. Applications of these results in probability theory are discussed.
Separable measures and the Dunford-Pettis property
Authors: Aguayo José , Sánchez José 
Published: April 2009

Let X be a complete regular space. We denote by Cb(X) the Banach space of all real-valued bounded continuous functions on X endowed with the supremumnorm.In this paper we give a characterisation of weakly compact operators defined from Cb(X) into a Banach space E which are β∞-continuous, where β∞ is a locally convex topology on Cb(X) introduced by Wheeler. We also prove that (Cb(X), β∞) has the strict Dunford-Pettis property and, if X is a σ-compact space, (Cb(X), β∞), has the Dunford-Pettis property.
The primes of S(R)
Authors: Magill K.D. 
Published: April 2009

S(R) is the semigroup, under composition, of all continuous selfmaps of the space R of real numbers. We show that the primes of S(R) are precisely those continuous selfmaps which are surjective and have exactly two local extrema. Additional results are then derived from this. For example, if f is any surjective continuous selfmap of R with n ≥ 2 local extrema, then there exist homeomorphisms from R onto R such that m ≤ 1 + n/2 andwhere P is the polynomial defined by P(x) = x3 − x. It follows from this that the homeomorphisms together with the polynomial P generate a dense subsemigroup of S(R) where the topology on S(R) is the compact-open topology.
Averaging distances in certain Banach spaces
Authors: Wolf Reinhard 
Published: April 2009

Let E be a Banach space. The averaging interval AI(E) is defined as the set of positive real numbers α, with the following property: For each n ∈ ℕ and for all (not necessarily distinct) x1, x2, … xn ∈ E with ∥x1∥ = ∥x2∥ = … = ∥xn∥ = 1, there is an x ∈ E, ∥x∥ = 1, such thatIt follows immediately, that AI(E) is a (perhaps empty) interval included in the closed interval [1,2]. For example in this paper it is shown that AI(E) = {α} for some 1 < α < 2, if E has finite dimension. Furthermore a complete discussion of AI(C(X)) is given, where C(X) denotes the Banach space of real valued continuous functions on a compact Hausdorff space X. Also a Banach space E is found, such that AI(E) = [1,2].
On the critical points of a polynomial
Authors: Aziz Abdul , Zargar B.A. 
Published: April 2009

Let p be a complex polynomial, of the form , where |zk| ≥ 1 when 1 ≤ k ≤ n − 1. Then p′(z) ≠ 0 if |z| /n.Let B(z, r) denote the open ball in with centre z and radius r, and denote its closure. The Gauss-Lucas theorem states that every critical point of a complex polynomial p of degree at least 2 lies in the convex hull of its zeros. This theorem has been further investigated and developed. B. Sendov conjectured that, if all the zeros of p lie in then, for any zero ζ of p, the disc contains at least one zero of p′; see [3, Problem 4.1]. This conjecture has attracted much attention-see, for example, [1], and the papers cited there. In connection with this conjecture, Brown [2] posed the following problem.