bluuebunny/crossref_metadata_2025_split huggingface dataset:
A remark on boundedness of Bloch functions
Authors: Samotij Krzysztof 
Published: April 2009

Two consequences of a theorem of Dahlberg are derived. Let f be a holomorphic function in the unit disk D of the complex plane, and let E be an Fσ subset of the unit circle T. Suppose that |f(rw)| ≤ M, ω ∈ T/E, for some constant M.Then f is bounded in either of the two cases:(i) if f is in the Bloch space and E is of zero measure with respect to the Hausdorff measure associated with the function ψ(t) = t log log (2πee/t),(ii) if f is integrable with respect to the planar Lebesgue measure on D and E is of zero measure with respect to the Hausdorff measure associated with the function ψ(t) = t log(2πee/t).
Existence theorems for a multivalued boundary value problem
Authors: Marano Salvatore A. 
Published: April 2009

Let F be a multifunction from [a, b] × ℝn × ℝn into ℝn, with non-empty closed convex values. In this paper we prove that, under suitable assumptions, the multivalued boundary value problemhas at least one solution u ∈ W2, p([a, b], ℝn). Next we point out some particular cases.
Hopfian and co-Hopfian groups
Authors: Deo Satya , Varadarajan K. 
Published: April 2009

The main results proved in this note are the following:(i) Any finitely generated group can be expressed as a quotient of a finitely presented, centreless group which is simultaneously Hopfian and co-Hopfian.(ii) There is no functorial imbedding of groups (respectively finitely generated groups) into Hopfian groups.(iii) We prove a result which implies in particular that if the double orientable coverNof a closed non-orientable aspherical manifoldMhas a co-Hopfian fundamental group then π1(M) itself is co-Hopfian.
Finite dimensional H-invariant spaces
Authors: Hare K.E. , Ward J.A. 
Published: April 2009

A subset V of M(G) is left H-invariant if it is invariant under left translation by the elements of H, a subset of a locally compact group G. We establish necessary and sufficient conditions on H which ensure that finite dimensional subspaces of M(G) when G is compact, or of L∞(G) when G is locally compact Abelian, which are invariant in this weaker sense, contain only trigonometric polynomials. This generalises known results for finite dimensional G-invariant subspaces. We show that if H is a subgroup of finite index in a compact group G, and the span of the H-translates of μ is a weak*-closed subspace of L∞(G) or M(G) (or is closed in Lp(G)for 1 ≤ p < ∞), then μ is a trigonometric polynomial.We also obtain some results concerning functions that possess the analogous weaker almost periodic condition relative to H.
The modular counterparts of Cayley's hyperdeterminants
Authors: Glynn David G. 
Published: April 2009

LetHbe a hypersurface of degreeminPG(n, q),q=ph,pprime.(1) Ifm<n+ 1,Hhas 1 (modp) points.(2) Ifm=n+ 1,Hhas 1 (modp) points ⇔Hp−1has no termWe show some applications, including the generalised Hasse invariant for hypersurfaces of degreen+ 1 inPG(n, F), various porperties of finite projective spaces, and in particular ap-modular invariant detpof any (n+ 1)r+2= (n+ 1)×…×(n+ 1) array on hypercubeAover a field characteristicp. This invariant is multiplicative in that detp(AB) = detp(B), whenever the product (or convolution of the two arraysAandBis defined, and both arrays are not 1-dimensional vectors. (IfAis (n+ 1)r+2andBis (n+ 1)s+2, thenABis (n+ 1)r+s+2.) The geometrical meaning of the invariant is that over finite fields of characteristicpthe number of projections ofAfromr+ 1 points in any givenr+ 1 directions of the array to a non-zero point in the final direction is 0 (modp). Equivalently, the number of projections ofAfromrpoints in any givenrdirections to a non-singular (n+ 1)2matrix is 0 (modp). Historical aspects of invariant theory and connections with Cayley's hyperdeterminant Det for characteristic 0 fields are mentioned.
Annular Dehn functions of groups
Authors: Brick Stephen G. , Corson Jon M. 
Published: April 2009

For a finite presentation of a group, or more generally, a two-complex, we define a function analogous to the Dehn function that we call the annular Dehn function. This function measures the combinatorial area of maps of annuli into the complex as a function of the lengths of the boundary curves. A finitely presented group has solvable conjugacy problem if and only if its annular Dehn function is recursive.As with standard Dehn functions, the annular Dehn function may change with change of presentation. We prove that the type of function obtained is preserved by change of presentation. Further we obtain upper bounds for the annular Dehn functions of free products and, more generally, amalgamations or HNN extensions over finite subgroups.
Dynamics of homeomorphisms on minimal sets generated by triangular mappings
Authors: Forti Gian Luigi , Paganoni Luigi , Smítal Jaroslav 
Published: April 2009

The main goal of the paper is the construction of a triangular mapping F of the square with zero topological entropy, possessing a minimal set M such that F|M is a strongly chaotic homeomorphism, as well as other properties that are impossible for continuous maps on an interval.To do this we define a parametric class of triangular maps on Q × I, where Q is an infinite minimal set on the interval, which are extendable to continuous triangular maps F: I2 → I2. This class can be used to create other examples.
An Euler-type volume identity
Authors: Callahan Kevin , Hann Kathy 
Published: April 2009

In this paper we present an elementary proof of a congruence by subtraction relation. In order to prove congruence by subtraction, we produce a dissection relating equal sub-polytopes. An immediate consequence of this relation is an Euler-type volume identity in ℝ3 which appeared in the Unsolved Problems section of the December 1996 MAA Monthly.This Euler-type volume identity relates the volumes of subsets of a polytope called wedges that correspond to its faces, edges, and vertices. A wedge consists of the inward normal chords of the polytope emanating from a face, vertex, or edge. This identity is stated in the theorem below.Euler Volume Theorem. For any three dimensional convex polytope PThis identity follows immediately from
Generation of diagonal acts of some semigroups of transformations and relations
Authors: Gallagher Peter , Ruškuc Nik 
Published: April 2009

The diagonal right (respectively, left) act of a semigroup S is the set S × S on which S acts via (x, y) s = (xs, ys) (respectively, s (x, y) = (sx, sy)); the same set with both actions is the diagonal bi-act. The diagonal right (respectively, left, bi-) act is said to be finitely generated if there is a finite set A ⊆ S × S such that S × S = AS1 (respectively, S × S = S1A, S × S = SlASl).In this paper we consider the question of finite generation for diagonal acts of certain infinite semigroups of transformations and relations. We show that the semi-groups of full transformations, partial transformations and binary relations on an infinite set each have cyclic diagonal right and left acts. The semigroup of full finite-to-one transformations on an infinite set has a cyclic diagonal right act but its diagonal left act is not finitely generated. The semigroup of partial injections on an infinite set has neither finitely generated diagonal right nor left act, but has a cyclic diagonal bi-act. The semigroup of bijections (symmetric group) on an infinite set does not have any finitely generated diagonal acts.
Bifurcation of positive entire solutions for a semilinear elliptic equation
Authors: Hsu Tsing-San , Lin Huei-Li 
Published: April 2009

In this paper, we consider the nonhomogeneous semilinear elliptic equation,where λ ≥ 0, 1 < p < (N + 2)/(N − 2), if N ≥ 3, 1 < p < ∞, if N = 2, h(x) ∈ H−l(ℝN), 0 ≢ h(x) ≥ 0 in ℝN, K(x) is a positive, bounded and continuous function on ℝN. We prove that if K(x) ≥ K∞ > 0 in ℝN, and lim∣x∣⃗∞K(x) = K∞, then there exists a positive constant λ✶ such that (✶)λ has at least two solutions if λ ∈ (0, λ✶) and no solution if λ > λ✶. Furthermore, (✶)λ has a unique solution for λ = λ✶ provided that h(x) satisfies some suitable conditions. We also obtain some further properties and bifurcation results of the solutions of (1.1)λ at λ = λ✶.
A strong convergence theorem for contraction semigroups in Banach spaces
Authors: Xu Hong-Kun 
Published: April 2009

We establish a Banach space version of a theorem of Suzuki [8]. More precisely we prove that if X is a uniformly convex Banach space with a weakly continuous duality map (for example, lp for 1 < p < ∞), if C is a closed convex subset of X, and if F = {T (t): t ≥ 0} is a contraction semigroup on C such that Fix(F) ≠ ∅, then under certain appropriate assumptions made on the sequences {αn} and {tn} of the parameters, we show that the sequence {xn} implicitly defined byfor all n ≥ 1 converges strongly to a member of Fix(F).
Equivalent conditions of a tree map with zero topological entropy
Authors: Sun Taixiang , Xie Mingde , Zhao Jinfeng 
Published: April 2009

Let f: T → T be a tree map with n end-points, SAP(f) the set of strongly almost periodic points of f and CR(f) the set of chain recurrent points of f. Write E(f,T) = {x: there exists a sequence {ki} with 2 ≤ ki ≤ n such that and g = f\CR(f). In this paper, we show that the following three statements are equivalent:(1) f has zero topological entropy.(2) SAP(f) ⊂ E(f,T).(3) Map ωg: x → ω(x,g) is continuous at p for every periodic point p of f.
An inequality with application to a difference equation
Authors: Chen Jong-Yi , Chow Yunshyong 
Published: April 2009

In this paper we shall prove that for any 0 < d ≤ 2,
holds for n ≥ 1.As an application, we shall then show that the following recursively defined sequence
satisfies
The difference equation above originates from a heat conduction problem studied by Myshkis (J. Difference Equ. Appl. 3(1997), 89–91).
Computing the effectively computable bound in Baker's inequality for linear forms in logarithms
Authors: van der Poorten A.J. , Loxton J.H. 
Published: April 2009

For certain number theoretical applications, it is useful to actually compute the effectively computable constant which appears in Baker's inequality for linear forms in logarithms. In this note, we carry out such a detailed computation, obtaining bounds which are the best known and, in some respects, the best possible. We show inter alia that if the algebraic numbers α1, …, αn all lie in an algebraic number field of degree D and satisfy a certain independence condition, then for some n0(D) which is explicitly computed, the inequalities (in the standard notation)have no solution in rational integers b1, …, bn (bn ≠ 0) of absolute value at most B, whenever n ≥ n0(D). The very favourable dependence on n is particularly useful.
Families of finite sets satisfying an intersection condition
Authors: Frankl Peter 
Published: April 2009

The following theorem is proved.Let X be a finite set of cardinality n ≥ 2, and let F be a family of subsets of X. Suppose that for F1, F2, F3 ∈ F we have |F1 ∩ F2 ∩ F3| ≥ 2. Then |F| ≤ 2n−2with equality holding if and only if for two different elements x, y of X, F = {F ⊆ X | x ∈ F, y ∈ F}.
Asymptotic centres of filters on uniformly rotund spaces
Authors: Staples John 
Published: April 2009

The notion of asymptotic centre of a bounded sequence of points in a uniformly convex Banach space was introduced by Edelstein in order to prove, in a quasi-constructive way, fixed point theorems for nonexpansive and similar maps.Similar theorems have also been proved by, for example, adding a compactness hypothesis to the restrictions on the domain of the maps. In such proofs, which are generally less constructive, it may be possible to weaken the uniform convexity hypothesis.In this paper Edelstein's technique is extended by defining a notion of asymptotic centre for an arbitrary set of nonempty bounded subsets of a metric space. It is shown that when the metric space is uniformly rotund and complete, and when the set of bounded subsets is a filter base, this filter base has a unique asymptotic centre. This fact is used to derive, in a uniform way, several fixed point theorems for nonexpansive and similar maps, both single-valued and many-valued.Though related to known results, each of the fixed point theorems proved is either stronger than the corresponding known result, or has a compactness hypothesis replaced by the assumption of uniform convexity.
A nonlinear ergodic theorem for asymptotically nonexpansive mappings
Authors: Tan Kok-Keong , Xu Hong-Kun 
Published: April 2009

Let X be a real uniformly convex Banach space satisfying the Opial's condition, C a bounded closed convex subset of X, and T: C → C an asymptotically non-expansive mapping. Then we show that for each x in C, the sequence {Tnx} almost converges weakly to a fixed point y of T, that is,This implies that {Tnx} converges weakly to y if and only if T is weakly asymptotically regular at x, that is, weak- . We also present a weak convergence theorem for asymptotically nonexpansive semigroups.
On the duality of some martingale spaces
Authors: Bassily N.L. , Abdel-Fattah A.M. 
Published: April 2009

Fefferman has proved that the dual space of the martingale Hardy space H1 is the BMO1-space. Garsia went further and proved that the dual of Hp is the so-called martingale Kp-space, where p and q are two conjugate numbers and 1 ≤ p < 2.The martingale Hardy spaces HΦ with general Young function Φ, were investigated by Bassily and Mogyoródi. In this paper we show that the dual of the martingale Hardy space HΦ is the martingale Hardy space HΦ where (Φ, Ψ) is a pair of conjugate Young functions such that both Φ and Ψ have finite power. Moreover, two other remarkable dualities are presented.
Some nilpotent Lie algebras of even dimension
Authors: Seeley Craig 
Published: April 2009

For each even dimension greater than or equal to 8, an infinite family of 3-step nilpotent Lie algebras over ℂ is constructed. In dimension m, the family contains isomorphism classes parameterised locally by approximately m3/48 essential parameters.One particular case is studied further to get some global information about the variety of all nilpotent Lie algebras of dimension 8. Using the results obtained here, and some known facts, it is shown that there is a component consisting of algebras not having minimal possible central dimensions.
Cardinalities of locally compact groups and their Stone-Čech compactifications
Authors: Itzkowitz Gerald L. , Morris Sidney A. , Tkachuk Vladimir V. 
Published: April 2009

Dedicated to Edwin HewittIf G is any Hausdorff topological group and βG is the Stone-Čech compactification then where |G| denotes the cardinalty of G It is known that if G is a discrete group then and if G is the additive group of real numbers with the Euclidean topology, then |βG| = 2|G|. In this paper the cardinality and weight of βG, for a locally compact group G, is calculated in terms of the character and Lindelöf degree of G The results make it possible to give a reasonably complete description of locally compact groups G for which |βG| = 2|G| or even |βG| = |G|.
Erratum: Two hyperbolic Shwarz lemmas
Authors: Bernal-González L. , Calderón-Moreno M. C. 
Published: April 2009

In [1] there is an error, as pointed out to us by J.M. Isidro. In that paper we consider the set Rm of all m-rotations, that is, Rm = {czm: |c| = 1}; the set Aut() of the automorphisms of the unit disc  and the set of the m-automorphisms of , Autm () = {ψ ∘ R ∘ ϕ : ψ, ϕ ∈ Aut(), R ∈ Rm}. We asserted thatwhere ϕa(Z) = (a − z)/(1 − āz). Equality (1) is not true. For instance, it suffices to consider f (z) = ϕ¼ ∘ ∘ z2 ∘ ϕ½. We have that f ∈ Aut2 (), f (0) = (0) and, after calculations, f (z) = (7z2 − 6z)/(6z − 7). Then it is evident that will never hold f (z) = ϕ0 ∘ R ∘ ϕ0 with R ∈ R2, because ϕ0 is equal to identity.
Spectrally bounded traces on C*-algebras
Authors: Mathieu Martin 
Published: April 2009

A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is called spectrally bounded if there is a constant M ≥ 0 such that r(T x) ≤ Mr(x) for all x ∈ E, where r (·) denotes the spectral radius. We establish the equivalence of the following properties of a unital linear mapping T from a unital C* -algebra A into its centre:(a) T is spectrally bounded;(b) T is a spectrally bounded trace;(c) T is a bounded trace.
On 3-dimensional contact slant submanifolds in Sasakian space forms
Authors: Mihai Ion , Tazawa Yoshihiko 
Published: April 2009

Recently, B.-Y. Chen obtained an inequality for slant surfaces in complex space forms. Further, B.-Y. Chen and one of the present authors proved the non-minimality of proper slant surfaces in non-flat complex space forms. In the present paper, we investigate 3-dimensional proper contact slant submanifolds in Sasakian space forms. A sharp inequality is obtained between the scalar curvature (intrinsic invariant) and the main extrinsic invariant, namely the squared mean curvature.It is also shown that a 3-dimensional contact slant submanifold M of a Sasakian space form M̆(c), with c ≠ 1, cannot be minimal.
Two necessary and sufficient conditions for the extension of Möbius groups
Authors: Wang Xiantao , Xiong Shouyao 
Published: April 2009

Let SL(2, Γn) be the n-dimensional Clifford matrix group and G ⊂ SL(2, Γn) be a non-elementary subgroup. We show that G is the extension of a subgroup of SL(2, ℂ) if and only if G is conjugate in SL(2, Γn) to a group G′ which satisfies the following properties:(1) there exist loxodromic elements g0, h ∈ G′ such that fix(g0) = {0, ∞}, fix(g0) ∩ fix(h) = ∅ and fix(h) ∩ ℂ ≠ ∅;(2) tr(g) ∈ ℂ for each loxodromic element g ∈ G′.Further G is the extension of a subgroup of SL(2, ℝ) if and only if G is conjugate in SL(2, Γn) to a group G′ which satisfies the following properties:(1) there exists a loxodromic element g0 ∈ G′ such that fix(g0) ∩ {0, ∞} ≠ ∅;(2) tr(g) ∈ ℝ for each loxodromic element g ∈ G′.The discreteness of subgroups of SL(2, Γn) is also discussed.
On the distribution of angles of the Salié sums
Authors: Shparlinski Igor E. 
Published: April 2009

For a primepand integersaandb, we consider Salié sumswhere χ2(x) is a quadratic character and x¯ is the modular inversion ofx, that is,xx¯≡ 1 (modp). One can naturally associate withSp(a, b) a certain angle θp(a, b) ∈ [0, π]. We show that, for any fixed ε > 0, these angles are uniformly distributed in [0, π] whenaandbrun over arbitrary sets , ℬ ⊆ {0, 1, …,p− 1} such that there are at leastp1+εquadratic residues modulopamong the productsab, where (a, b) ∈  × ℬ.
Composition operators on weighted Bergman-Orlicz spaces
Authors: Sharma Ajay K. , Sharma S. D. 
Published: April 2009

In this paper, composition operators acting on Bergman-Orlicz spaces
are studied, where ψ is a non-constant, non-decreasing convex function defined on (-∞, ∞) which satisfies the growth condition . In fact, under a mild condition on ∞, we show that every holomorphic-self map ∞ of induces a bounded composition operator on and C∞ is compact on if and only if it is compact on .
Unique extremality, local extremality and extremal non-decreasable dilatations
Authors: Yao Guowu 
Published: April 2009

Given a quasi-symmetric self-homeomorphism h of the unit circle Sl, let Q(h) be the set of all quasiconformal mappings with the boundary correspondence h. In this paper, it is shown that there exists certain quasi-symmetric homeomorphism h, such that Q(h) satisfies either of the conditions,(1) Q(h) admits a quasiconformal mapping that is both uniquely locally-extremal and uniquely extremal-non-decreasable instead of being uniquely extremal;(2) Q(h) contains infinitely many quasiconformal mappings each of which has an extremal non-decreasable dilatation.An infinitesimal version of this result is also obtained.
A rank for right congruences on inverse semigroups
Authors: Gould Victoria 
Published: April 2009

The S-rank (where ‘S’ abbreviates ‘sandwich’) of a right congruence ρ on a semigroup S is the Cantor-Bendixson rank of ρ in the lattice of right congruences ℛ of S with respect to a topology we call the finite type topology. If every ρ ϵ ℛ possesses S-rank, then S is ranked. It is known that every right Noetherian semigroup is ranked and every ranked inverse semigroup is weakly right Noetherian. Moreover, if S is ranked, then so is every maximal subgroup of S. We show that a Brandt semigroup 0(G, I) is ranked if and only if G is ranked and I is finite.We establish a correspondence between the lattice of congruences on a chain E, and the lattice of right congruences contained within the least group congruence on any inverse semigroup S with semilattice of idempotents E(S) ≅ E. Consequently we argue that the (inverse) bicyclic monoid B is not ranked; moreover, a ranked semigroup cannot contain a bicyclic -class. On the other hand, B is weakly right Noetherian, and possesses trivial (hence ranked) subgroups.Our notion of rank arose from considering stability properties of the theory Ts of existentially closed (right) S-sets over a right coherent monoid S. The property of right coherence guarantees that the existentially closed S-sets form an axiomatisable class. We argue that B is right coherent. As a consequence, it follows from known results that TB is a theory of B-sets that is superstable but not totally transcendental.
Existence conditions for a class of modular subgroups of genus zero
Authors: Hempel Joachim A. 
Published: April 2009

Every subgroup of finite index of the modular groupPSL(2, ℤ) has asignatureconsisting of conjugacy-invariant integer parameters satisfying certain conditions. In the case of genus zero, these parameters also constitute a prescription for the degree and the orders of the poles of a rational functionFwith the property:Functions correspond to subgroups, and we use this to establish necessary and sufficient conditions for existence of subgroups with a certain subclass of allowable signatures.
Families of weighing matrices
Authors: Geramita Anthony V. , Pullman Norman J. , Wallis Jennifer S. 
Published: April 2009

A weighing matrix is an n × n matrix W = W(n, k) with entries from {0, 1, −1}, satisfying = WWt = KIn. We shall call k the degree of W. It has been conjectured that if n ≡ 0 (mod 4) then there exist n × n weighing matrices of every degree k ≤ n.We prove the conjecture when n is a power of 2. If n is not a power of two we find an integer t < n for which there are weighing matrices of every degree ≤ t.
Adjunction semigroups
Authors: Borrego J. T. 
Published: April 2009

Let S and T be compact (topological) semigroups, A be a closed subsemigroup of S, and f be a continuous homomorphism of A onto T. It is a natural question to ask is there a compact semigroup Z containing T and a continuous homomorphism φ of S onto Z such that φ restricted to A is f?In the category of compact Hausdorff spaces, the answer to the analogous question may be given by the following construction due to Borsuk. Let X and Y be compact Hausdorff spaces, A be a closed subspace of X and f a continuous function of A onto Y. Then R(f, X) = {(x, y)|f(x) = f(y) or x = y} is a closed equivalence relation on X. The adjunction space Z(f, x) is X/R(f, X). The purpose of this note is to investigate this construction in semigroups.
A theorem on homeomorphism groups and products of spaces
Authors: Vobach A. R. 
Published: April 2009

Let H(C) be the group of homeomorphisms of the Cantor set, C, onto itself. Let p: C → M be a map of C onto a compact metric space M, and let G(p, M) be is a group.The map p: C → M is standard, if for each (x, y) ∈ C × C such that p(x) = p(y), there is a sequence and a sequence such that xn → x and hn (xn) → y Standard maps and their associated groups characterize compact metric spaces in the sense that: Two such spaces, M and N, are homeomorphic if and only if, given p standard from C onto M, there is a standard q from C onto N for which G(p, M) = h−1G(q, N)h, for some h ∈ H(C) The present paper exhibits a structure theorem connecting these characterizing subgroups of H(C) and products of spaces: Let M1 and M2 be compact metric spaces. Then there are standard maps p: C → M1 × M2 and pi: C → Mi, i = 1, 2, such that G(p, M1 × M2) = G(p1, M1) ∩ G(p2, M2).