bluuebunny/crossref_metadata_2025_split huggingface dataset:
Dynamics of slowly growing entire functions
Authors: Baker I. N. 
Published: April 2009

Dedicated to George Szekeres on his 90th birthdayFor a transcendental entire function f let M(r) denote the maximum modulus of f(z) for |z| = r. Then A(r) = log M(r)/logr tends to infinity with r. Many properties of transcendental entire functions with sufficiently small A(r) resemble those of polynomials. However the dynamical properties of iterates of such functions may be very different. For instance in the stable set F(f) where the iterates of f form a normal family the components are preperiodic under f in the case of a polynomial; but there are transcendental functions with arbitrarily small A(r) such that F(f) has nonpreperiodic components, so called wandering components, which are bounded rings in which the iterates tend to infinity. One might ask if all small functions are like this.A striking recent result of Bergweiler and Eremenko shows that there are arbitrarily small transcendental entire functions with empty stable set—a thing impossible for polynomials. By extending the technique of Bergweiler and Eremenko, an arbitrarily small transcendental entire function is constructed such that F is nonempty, every component G of F is bounded, simply-connected and the iterates tend to zero in G. Zero belongs to an invariant component of F, so there are no wandering components. The Julia set which is the complement of F is connected and contains a dense subset of “buried’ points which belong to the boundary of no component of F. This bevaviour is impossible for a polynomial.
More cranks andt-cores
Authors: Garvan F. G. 
Published: April 2009

Dedicated to George Szekeres on the occasion of his 90th BirthdayIn 1990, new statistics on partitions (calledcransk) were found which combinatorially prove Ramanujan's congruences for the partition function modulo 5, 7, 11 and 25. The methods are extended to find cranks for Ramanujan's partition congruence modulo 49. A more explicit form of the crank is given for the modulo 25 congruence.
Self-splitting Abelian groups
Authors: Schultz P. 
Published: April 2009

G is reduced torsion-free A belian group such that for every direct sum ⊕G of copies of G, Ext(⊕G, ⊕G) = 0 if and only if G is a free module over a rank 1 ring. For every direct product ΠG of copies of G, Ext(ΠG,ΠG) = 0 if and only if G is cotorsion.This paper began as a Research Report of the Department of Mathematics of the University of Western Australia in 1988, and circulated among members of the Abelian group community. However, it was never submitted for publication. The results have been cited, widely, and since copies of the original research report are no longer available, the paper is presented here in its original form in Sections 1 to 5. In Section 6, I survey the progress that has been made in the topic since 1988.
Short Amicable sets and Kharaghani type orthogonal designs
Authors: Koukouvinos Christos , Seberry Jennifer 
Published: April 2009

Dedicated to Professor George SzekeresShort amicable sets were introduced recently and have many applications. The construction of short amicable sets has lead to the construction of many orthogonal designs, weighing matrices and Hadamard matrices. In this paper we give some constructions for short amicable sets as well as some multiplication theorems. We also present a table of the short amicable sets known to exist and we construct some infinite families of short amicable sets and orthogonal designs.
Total torsion of closed lines of curvature
Authors: Qin Yong-An , Li Shi-Jie 
Published: April 2009

In this article we investigate the total torsion of closed lines of curvature on a surface in 3 and obtain the following results.(1) The total torsion of a closed line of curvature on a surface is kπ where k is an integer. Conversely, if the total torsion of a closed curve is kπ for an integer k, then the curve can appear as a line of curvature on a surface. In particular, if the total torsion of a closed curve is 2kπ, then it can appear as a line of curvature on a closed, oriented surface of genus 1.(2) The total torsion of a closed line of curvature on an ovaloid is zero.
Usco selections of densely defined set-valued mappings
Authors: Moors Warren B. , Somasundaram Sivajah 
Published: April 2009

A set-valued mapping Φ : X → 2Y acting between topological spaces X and Y is said to be “lower demicontinuous” if the interior of the closure of the set Φ−1(V): = {x ∈ X : Φ(x) ∩ V ≠ ∅} is dense in the closure of Φ−1(V) for each open set V in Y. Čoban, Kenderov and Revalski (1994) showed that for every densely defined lower demicontinuous mapping Φ acting from a Baire space X into subsets of a monotonely Čech-complete space Y, there exist a dense and Gδ subset X1 ⊆ X and an usco mapping G: X1 → 2Y such that G (x) ⊆ Φ*(x), for every x ∈ X1, where the mapping Φ*: X → 2Y is the extension of Φ defined by,
W is a neighbourhood of x}.In this paper we present a proof of the above result with the notion of monotone Čcech-completeness replaced by the weaker notion of partition completeness. In addition, we observe that if the range space also lies is Stegall's class then we may assume that the mapping G is single-valued on X1.
Descent on Picard groups using functions on curves
Authors: Siksek Samir 
Published: April 2009

Let k be a perfect field, X a smooth curve over k, and denote by Xc the subset of closed points of X. We show that for any non-constant element f of the function field k (X) there exists a natural homomorphism

Where
We explain how this generalises the usual results on descents on Jacobians and Picard groups of curves.
Pseudocomplemented distributive lattices with small endomorphism monoids
Authors: Adams M.E. , Koubek V. , Sichler J. 
Published: April 2009

By a result of K.B. Lee, the lattice of varieties of pseudo-complemented distributive lattices is the ω + 1 chainwhere B−1, B0, B1 are the varieties formed by all trivial, Boolean, and Stone algebras, respectively. General theorems on relative universality proved in the present paper imply that there is a proper class of non-isomorphic algebras in B3 with finite endomorphism monoids, while every infinite algebra from B2 has infinitely many endomorphisms. The variety B4 contains a proper class of non-isomorphic algebras with endomorphism monoids consisting of the identity and finitely many right zeros; on the other hand, any algebra in B3 with a finite endomorphism monoid of this type must be finite.
Sharp estimates of approximation by some positive linear operators
Authors: Sahai Ashok , Prasad Govind 
Published: April 2009

Recently, Varshney and Singh [Rend. Mat. (6) 2 (1982), 219–225] have given sharper quantitative estimates of convergence for Bernstein polynomials, Szasz and Meyer-Konig-Zeller operators. We have achieved improvement over these estimates by taking moments of higher order. For example, in case of the Meyer-Konig-Zeller operator, they gave the following estimatewherein ∥·∥ stands for sup norm. We have improved this result toWe may remark here that for this modulus of continuity ) our result cannot be sharpened further by taking higher order moments.
Using product designs to construct orthogonal designs
Authors: Robinson Peter J. 
Published: April 2009

This paper produces new types of designs, called product designs, which prove extremely useful for constructing orthogonal designs. An orthogonal design of order 2t and typeis constructed. This design often meets the Radon bound for the number of variables.We also show that all orthogonal designs of order 2t and type (a, b, c, d, 2t-a-b-c-d), with 0 < a + b + c + d < 2t, exist for t = 5, 6, and 7.
Transformations on tensor products and the torsionless property in abelian groups: Corrigendum
Authors: Webb Cary 
Published: April 2009

Professor Paul L. Sperry, when reviewing the paper [1] for Mathematical Reviews, has drawn the author's attention to an error in the formulation of Theorem 4.The hypotheses on the abelian groups Ci, i ∈ I, in Theorem 4 were incorrectly stated. (They implied, for one thing, that the slender group A is divisible, an absurdity.) The correct formulation is as follows.
Optimal reduction in replacement systems
Authors: Staples John 
Published: April 2009

High level programming languages can generally be compiled in many different ways. Thus it is natural to ask if there is a best way, for example in the sense of achieving complete execution of the program in a minimum number of steps; such a complete, minimal execution procedure will be called optimal.In recent years this question has been studied and answered for several simple models of programming languages, and a technique for proving procedures to be optimal has gradually emerged. Even for model languages the proofs of optimality become intricate; thus it is natural to emphasize the simplicity of the underlying technique by generalising it to an abstract system. That is the purpose of this paper. The general method to be given applies to prove all theorems (on optimal executions for model languages) which are known to the author. None of the previously known proofs has explicitly used the method, but in no case is it particularly difficult to modify the known proof so as to conform with the method.
Constructions for amicable orthogonal designs
Authors: Wallis Jennifer Seberry 
Published: April 2009

Infinite families of amicable orthogonal designs are constructed with(i) both of type (1, q) in order q + 1 when q ≡ 3 (mod 4) is a prime power,(ii) both of type (1, q) in order 2(q + 1) where q ≡ 1 (mod 4) is a prime power or q + 1 is the order of a conference matrix,(iii) both of type (2, 2q) in order 2(q + 1) when q ≡ 1 (mod 4) is a prime power or q + 1 is the order of a conference matrix.
A note on zero-sets in the Stone-Čech compactification
Authors: Rudd D. 
Published: April 2009

The ring C(X) is the ring of all continuous real-valued functions on a completely regular Hausdorff space X, and βX is the Stone-Čech compactification of X.The author proves a theorem which leads to a characterization of those zero-sets in X whose closures (in βX) are zero-sets in βX, and relates this characterization to the ideals in the ring C(X).
Jackson's Theorem for finite products and homomorphic images of locally compact abelian groups
Authors: Bloom Walter R. 
Published: April 2009

Let G be a Hausdorff locally compact abelian group. The author has shown (Bull. Austral. Math. Soc. 10 (1974), 59–66) that, given ε > 0 and a certain base {Vi}i∈I of symmetric open neighbourhoods of zero, the algebra L1(G) admits a bounded positive approximate unit {ki}i∈I such that for every p–th integrable function f on G,where ω(p; f; Vi) denotes the mean modulus of continuity with exponent p of f. The purpose of this paper is to obtain {ki}i∈I (as above) with a simple dependence of supp on {ki}i∈I on Vi; this is achieved for finite products and homomorphic images of groups for which such a simple dependence is known. The results obtained are used to give a simplified proof of the classical Jackson's Theorem for the circle group, and an analogue of this theorem for the a-adic solenoid.
Multifunctions of Souslin type: Corrigendum
Authors: Leese S.J. 
Published: April 2009

In [1], Theorem 6, a sufficient condition is given for a multifunction to be “of Souslin type”. However, the proof contains an error; we are required to prove that the multifunction Ω: S→ P×NN defined byhas values which are closed subsets of P×NN (the notation is explained in [1]). The “proof” of this fact given in [1] is manifestly incorrect as it appears to assume that NN has the discrete topology.
Some fixed-point theorems on locally convex linear topological spaces
Authors: Tarafdar E. 
Published: April 2009

Let (E, τ) be a locally convex linear Hausdorff topological space. We have proved mainly the following results.(i) Let f be nonexpansive on a nonempty τ-sequentially complete, τ-bounded, and starshaped subset M of E and let (I-f) map τ-bounded and τ-sequentially closed subsets of M into τ-sequentially closed subsets of M. Then f has a fixed-point in M.(ii) Let f be nonexpansive on a nonempty, τ-sequentially compact, and starshaped subset M of E. Then f has a fixed-point in M.(iii) Let (E, τ) be τ-quasi-complete. Let X be a nonempty, τ-bounded, τ-closed, and convex subset of E and M be a τ-compact subset of X. Let F be a commutative family of nonexpansive mappings on X having the property that for some f1 ∈ F and for each x ∈ X, τ-closure of the setcontains a point of M. Then the family F has a common fixed-point in M.
Asymptotic behavior of nonoscillatory solutions of second order functional differential equations
Authors: Kusano Takaŝi , Onose Hiroshi 
Published: April 2009

The asymptotic behavior of nonoscillatory solutions of the second order functional differential equationis studied. First, in the case when a(t)is oscillatory, sufficient conditions are given in order that all bounded non-oscillatory solutions of (*) approach zero as t → ∞. Secondly, in the case when a(t) is nonnegative, conditions are provided under which all nonoscillatory solutions of (*) tend to zero as t → ∞.
On the transcendency of the solutions of a special class of functional equations
Authors: Mahler Kurt 
Published: April 2009

Let a(z) and b(w) be two rational functions in z or W with algebraic coefficients, where a(0) = 0 and letAssume that 0 < |z| < 1, that z is not a pole of for n ≥ 0, that w is neither a pole nor a zero of b(w, n) for n ≥ 1, and that the seriesfor fixed w is a transcendental function of z. Then, if z and W are algebraic numbers, f(z, w) is a transcendental number.
Double covers of graphs
Authors: Waller Derek A. 
Published: April 2009

A projection morphism ρ: G1 → G2 of finite graphs maps the vertex-set of G1 onto the vertex-set of G2, and preserves adjacency. As an example, if each vertex v of the dodecahedron graph D is identified with its unique antipodal vertex v¯ (which has distance 5 from v) then this induces an identification of antipodal pairs of edges, and gives a (2:1)-projection p: D → P where P is the Petersen graph.In this paper a category-theoretical approach to graphs is used to define and study such double cover projections. An upper bound is found for the number of distinct double covers ρ: G1 → G2 for a given graph G2. A classification theorem for double cover projections is obtained, and it is shown that the n–dimensional octahedron graph K2,2,…,2 plays the role of universal object.
On groups with extremal blocks
Authors: Herzog Marcel 
Published: April 2009

Let G be a finite group. It is shown that G is 2-closed if and only if(a) every 2-block of G has full defect, and(b) every Sylow 2-intersection is centralized by a Sylow 2-subgroup of G.As a consequence it is shown that G is a TI-group if and only if every 2-block of G has either full defect or defect zero and (b) holds. This result and a theorem of Kwok yield complete characterizations of finite groups with certain relations being satisfied by every nonprincipal irreducible character.
Note on rational approximations of the exponential function at rational points
Authors: Durand Alain 
Published: April 2009

Let p, q, u, and v be any four positive integers, and let δ be a number in the interval 0 < δ ≤ 2. In one of his papers, Kurt Mahler, Bull. Austral. Math. Soc. 10 (1974), 325–335, proved that if q satisfies the inequalitiesthenIn this note, by a slightly different treatment of some inequalities in Mahler's paper, we easily obtain the same result with q only restricted by the first condition.
On families of finite sets no two of which intersect in a singleton
Authors: Frankl Peter 
Published: April 2009

Let X be a finite set of cardinality n, and let F be a family of k-subsets of X. In this paper we prove the following conjecture of P. Erdös and V.T. Sós.If n > n0(k), k ≥ 4, then we can find two members F and G in F such that |F ∩ G| = 1.
Families of partial functions
Authors: Balanda Kevin P. 
Published: April 2009

The degree of disjunction, δ(F), of a family F of functions is the least cardinal τ such that every pair of functions in F agree on a set of cardinality less than τ.Suppose θ, μ, λ, κ are non-zero cardinals with θ ≤ μ ≤ λ. This paper is concerned with functions which map μ-sized subsets of λ into κ. We first show there is always a ‘large’ family F of such functions satisfying δ(F) ≤ θ. Next we determine the cardinalities of families F of such functions that are maximal with respect to δ(F) ≤ θ.
Beurling's ordinary value
Authors: Yamashita Shinji 
Published: April 2009

Let n(w, f) be the number of w-points of f meromorphic in D = {|z| < 1}. Beurling defined the quantity and called w an ordinary value of f if < ∞. We shall consider the intermediate quantity ṉ(w, f) in the sense that n(w, f) ≤ ṉ(w, f) , and construct two bounded holo-morphic functions f1 and f2 of finite Dirichlet integrals in D for whichand.
Characterising complete boolean algebras in terms of pure essentialness
Authors: Bhutani Kiran R. 
Published: April 2009

We discuss purity and pure essentialness of abelian groups in a topos of sheaves on a locale and show that purity is not a local property. We prove that is divisible if and only if it is pure in every extension, and give an example of a category in winch absolutely pure does not imply divisible. We discuss uniform abelian groups and show that each AU uniform in Ab does not imply that A is uniform in Banaschewski showed that the pure subgroups of are exactly of the type for the different . We show that is essential in if and only if U is dense in , Finally, we characterise as complete boolean algebras the locales for which the only pure and essential subgroup of is .
Stability and J-depth of expansions
Authors: Birget Jean-Camille 
Published: April 2009

In this paper I prove that if a semigroup S is stable then ∧L(S) and ∧R(S) (the Rhodes expansions), and ∧+(SA) (the iteration of those expansions) are also stable. I also prove that if S is stable and has a J-depth function then these expansions also have a J-depth functon. More generally, if X →→ S is a J*-surmorphism and if S is stable and has a J-depth function then X has a J-depth function. All these results are needed for the structure theory of semigroups which are stable and have a J-depth function.The techniques used were originally developed by the author to prove that ∧+(SA) is finite if S is finite (later Rhodes found a much more direct proof of that result).
Neighbourhood lattices – a poset approach to topological spaces
Authors: Prokop Frank P. 
Published: April 2009

In this paper neighbourhood lattices are developed as a generalisation of topological spaces in order to examine to what extent the concepts of “openness”, “closedness”, and “continuity” defined in topological spaces depend on the lattice structure of P(X), the power set of X.A general pre-neighbourhood system, which satisfies the poset analogues of the neighbourhood system of points in a topological space, is defined on an ∧-semi-lattice, and is used to define open elements. Neighbourhood systems, which satisfy the poset analogues of the neighbourhood system of sets in a topological space, are introduced and it is shown that it is the conditionally complete atomistic structure of P(X) which determines the extension of pre-neighbourhoods of points to the neighbourhoods of sets.The duals of pre-neighbourhood systems are used to generate closed elements in an arbitrary lattice, independently of closure operators or complementation. These dual systems then form the backdrop for a brief discussion of the relationship between preneighbourhood systems, topological closure operators, algebraic closure operators, and Čech closure operators.Continuity is defined for functions between neighbourhood lattices, and it is proved that a function f: X → Y between topological spaces is continuous if and only if corresponding direct image function between the neighbourhood lattices P(X) and P(Y) is continuous in the neighbourhood sense. Further, it is shown that the algebraic character of continuity, that is, the non-convergence aspects, depends only on the properites of pre-neighbourhood systems. This observation leads to a discussion of the continuity properties of residuated mappings. Finally, the topological properties of normality and regularity are characterised in terms of the continuity properties of the closure operator on a topological space.
Oscillation of second order neutral differential equations
Authors: Erbe L.H. , Zhang B.G. 
Published: April 2009

Some new sufficient conditions are obtained for the oscillation of the neutral differential equationwherer(t)> 0, 0 <c< 1,p(t)≥ 0, σ(t) > τ > 0 and α = 1 or 0 < α < 1.
On the conformal deformation of Riemannian structures
Authors: Jung Yoon-Tae 
Published: April 2009

In this paper, we study a nonlinear partial differential equation on a compact manifold;where a > 1 is a constant, r is a positive constant, and H is a prescribed smooth function.Kazdan and Warner showed that if λ1(g) < 0 and < 0, where is the mean of H, then there is a constant 0 < r0(H) ≤ ∞ such that one can solve this equation for 0 < r < r0(H), but not for r > r0(H). They also proved that if r0(H) = ∞, then H(x) ≤ 0 (≢0) for all x ∈ M. They conjectured that this necessary condition might be sufficient.I show that this conjecture is right; that is, if H(x) ≤ 0 (≠ 0) for all x ∈ M, then r0(H) = ∞.
Nonoscillation criteria for Emden-Fowler systems
Authors: Erbe Lynn H. , Liu Xinzhi 
Published: April 2009

A number of nonoscillation criteria for the Emden-Fowler systemwhere a(t), b(t) > 0, r1, r2 > 0 and b(t)/a(t) is locally of bounded variation, are established employing energy function techniques. The results obtained here include many known nonoscillation theorems for the classical Emden-Fowler equations as special cases. We illustrate the results obtained with several examples.
On operator ideals determined by sequences
Authors: González Manuel , Martinón Antonio 
Published: April 2009

We associate with an operator ideal 𝒜 (in the sense of Pietsch) a class of bounded sequences S𝒜 by using the 𝒜-variation of Astala. If 𝒜 and B are operator ideals, and we define (𝒜, B) as the class of operators which map a sequence of S𝒜 into a sequence of SB, we obtain the following:Theorem. If Tn: X → Y is a sequence of operators and for every sequence (xn) ⊂ X in S𝒜 there exists p such that (Tpxn) belongs to SB, then Tm ∈ (𝒜, B) for some m.The compact operators, weakly compact operators and some other operator ideals can be represented as (𝒜, B). Hence several results of Tacon and other authors are a consequence of this theorem.
The centraliser of the injective tensor product
Authors: Werner Wend 
Published: April 2009

The aim of this note is to obtain an intrinsic product formula for the centraliser of the injective tensor product of a couple of Banach spaces, Z(). More precisely, we are going to prove thatHere, the spaces and depend only on X and Y, respectively, and Xk denotes the topological k-product.A Counterexaple used to demonstrate that the k-product cannot beavoided serves as an answer to a question posed by W. Rueß and D. Werner concerning the behaviour of M-ideals on Y.
Quadratic systems with a weak focus
Authors: Pingguang Zhang , Suilin Cai 
Published: April 2009

In this paper we study the number and the relative position of the limit cycles of a plane quadratic system with a weak focus. In particular, we prove the limit cycles of such a system can never have (2, 2)-distribution, and that there is at most one limit cycle not surrounding this weak focus under any one of the following conditions:(i) the system has at least 2 saddles in the finite plane,(ii) the system has more than 2 finite singular points and more than 1 singular point at infinity,(iii) the system has exactly 2 finite singular points, more than 1 singular point at infinity, and the weak focus is itself surrounded by at least one limit cycle.