bluuebunny/crossref_metadata_2025_split huggingface dataset:
On Homeomorphic Embeddings of Km,n in the Cube
Authors: Hartman Jehuda 
Published: December 2010

Homeomorphic embeddings of Knin the m-cube were investigated in [6]. In particular, it was proved that any homeomorph of Kn+1embedded in the m-cube has at least n2edges. Furthermore, homeomorphic embeddings of Kn+1having exactly n2edges are unique up to isomorphism. In this paper a similar problem for the complete bipartite graph is considered.We adopt the notation and terminology of [5].All graphs considered are without loops and multiple edges.Let x = uv be an edge of a graph G; x will be called subdivided if it is replaced by a vertex ω and by edges uω and ωv. A graph G’ is called a subdivision of G if it is obtained from G by a subdivision of an edge of G. A refinement Ĝ of G, is a graph isomorphic to a graph obtained from G by a finite sequence of subdivisions.
Order-Cauchy Completions of Rings and Vector Lattices of Continuous Functions
Authors: Dashiell F. , Hager A. , Henriksen M. 
Published: December 2010

This paper studies sequential order convergence and the associated completion in vector lattices of continuous functions. Such a completion for lattices C(X) is related to certain topological properties of the space X and to ring properties of C(X). The appropriate topological condition on the space X equivalent to this type of completeness for the lattice C(X) was first identified, for compact spaces X, in [6]. This condition is that every dense cozero set S in X should be C*-embedded in X (that is, all bounded continuous functions on S extend to X). We call Tychonoff spaces X with this property quasi-F spaces (since they generalize the F-spaces of [12]).In Section 1, the notion of a completion with respect to sequential order convergence is first described in the setting of a commutative lattice group G.
Akcoglu's Ergodic Theorem for Uniform Sequences
Authors: Olsen James H. 
Published: December 2010

Let (X, F,) be a sigma-finite measure space. In what follows we assume p fixed, 1 < p < ∞ . Let T be a contraction of Lp(X, F, μ) (‖T‖,p ≦ 1). If ƒ ≧ 0 implies Tƒ ≧ 0 we will say that T is positive. In this paper we prove that if is a uniform sequence (see Section 2 for definition) and T is a positive contraction of Lp, thenexists and is finite almost everywhere for every ƒ ∊ Lp(X, F, μ).
Nonzero Symmetry Classes of Smallest Dimension
Authors: Chan G. H. , Lim M. H. 
Published: December 2010

Let U be a k-dimensional vector space over the complex numbers. Let ⊗m U denote the mth tensor power of U where m ≧ 2. For each permutation σ in the symmetric group Sm, there exists a linear mapping P(σ) on ⊗mU such thatfor all x1, …, xm in U.Let G be a subgroup of Sm and λ an irreducible (complex) character on G. The symmetrizeris a projection of ⊗ mU. Its range is denoted by Uλm(G) or simply Uλ(G) and is called the symmetry class of tensors corresponding to G and λ.
Integral Means of Functions with Positive Real Part
Authors: Holland F. , Twomev J. B. 
Published: December 2010

We denote by the class of functions of the formthat are regular in Δ = {z:|;z| < 1} and satisfy Re h(z) > 0 there. For 0 ≦ r < 1, we writeWe note that, for , the inequalityis classical.
Longest Cycles in 2-Connected Graphs with Prescribed Maximum Degree
Authors: Bondy J. A. , Entringer R. C. 
Published: December 2010

The relationship between the lengths of cycles in a graph and the degrees of its vertices was first studied in a general context by G. A. Dirac. In [5], he proved that every 2-connected simple graph on n vertices with minimum degree d contains a cycle of length at least min{2d, n};. Dirac's theorem was subsequently strengthened in various directions in [7], [6], [13], [12], [2], [1], [11], [8], [14], [15] and [16].Our aim here is to investigate another aspect of this relationship, namely how the lengths of the cycles in a 2-connected graph depend on the maximum degree. Let us denote by ƒ(n, d) the largest integer k such that every 2-connected simple graph on n vertices with maximum degree d contains a cycle of length at least k. We prove in Section 2 that, for d ≧ 3 and n ≧ d + 2,
Invariance of Torsion and the Borsuk Conjecture
Authors: Chapman T. A. 
Published: December 2010

The following results of Whitehead and Wall are well-known applications of the algebraic K-theoretic functors K0 and K1 to basic homotopy questions in topology.THEOREM 1 [20]. If f : X → Y is a homotopy equivalence between compact CW complexes, then there is a torsion τ(ƒ) in the algebraically-defined Whitehead group Wh π1(Y) which vanishes if and only if f is a simple homotopy equivalence.THEOREM 2 [18]. If X is an arbitrary space which is finitely dominated (i.e., homotopically dominated by a compact polyhedron), then there is an obstruction σ(X) in the algebraically-defined reduced projective class group which vanishes if and only if X is homotopy equivalent to some compact polyhedron.If we direct sum over components, then the above statements make good sense even if the spaces involved are not connected.
Local-Global Criteria for Outer Product Rings
Authors: Estes Dennis R. , Matijevic Jacob R. 
Published: December 2010

Let R be a commutative ring with multiplicative identity. We say that R is an outer product ring (OP-ring) if each vector v in the exterior power ⋀nRn+1 is decomposable; i.e. v = v1 ⋀ v2 ⋀ … ⋀ vn with vi ∈ Rn+1 (alternatively, each n + 1 tuple of elements in R is the tuple of n × n minors of some n × (n + 1) matrix with entries in R).Lissner initiated the study of which commutative rings are OP-rings, showing that any Dedekind domain is an OP-ring [13]. Towber classified the local Noetherian OP-rings as those with maximal ideal generated by two elements, and Hinohara's reformulation of Towber's result extended the context to semi-local rings [18, 11]. Assuming the stronger condition that all Pliicker vectors are decomposable and designating such rings as Towber rings, Lissner and Geramita gave necessary conditions for a Noetherian ring to be a Towber ring [14].
A Note on Young's Raising Operator
Authors: Thomas Glânffrwd P. 
Published: December 2010

Consider the following formula due to Young [7] for the calculation of the homogeneous product sum, hλ, in terms of Schur functions;where the operation Srs is defined as follows:Y1: Srs, where r < s, “represents the operation of moving one letter from the s-th row up to the r-th row; and the resulting term is regarded as zero, when any row becomes less than a row below it, or when letters from the same row overlap; as, for instance, happens when λ1 = λ2 in the case of S13S23.“The following example of the above is given by Robinson [4].Calculation by other means shows that the above analysis of h(3,2,1) is correct; however, it will be noticed that the operator S123S23 does not appear in the above yet it is not specifically excluded by the rule Y1.
Generators of Orthogonal Groups over Valuation Rings
Authors: Ishibashi Hiroyuki 
Published: December 2010

Let be a valuation ring with unit element, i.e., is a commutative ring such that for any a and b in , either a divides b or b divides a. We assume 2 is a unit of . V is an n-ary nonsingular quadratic module over , O(V) or On(V) is the orthogonal group on V, and S is the set of symmetries in O(V). We define l(σ) to be the minimal number of factors in the expression of a of O(V) as a product of symmetries on V. For the case where is a field, l(σ) has been determined by P. Scherk [6] and J. Dieudonné [1]. In [3] I have generalized the results of Scherk to orthogonal groups over valuation domains. In the present paper I generalize my results of [3] to orthogonal groups over valuation rings.Since is a valuation ring, it is a local ring with the maximal ideal A which consists of all nonunits of .
Markov's and Bernstein's Inequalities on Disjoint Intervals
Authors: Borwein Peter B. 
Published: December 2010

In 1889, A. A. Markov proved the following inequality:INEQUALITY 1. (Markov [4]). If pn is any algebraic polynomial of degree at most n thenwhere ‖ ‖A denotes the supremum norm on A.In 1912, S. N. Bernstein establishedINEQUALITY 2. (Bernstein [2]). If pn is any algebraic polynomial of degree at most n thenfor x ∈ (a, b).In this paper we extend these inequalities to sets of the form [a, b] ∪ [c, d]. Let Πn denote the set of algebraic polynomials with real coefficients of degree at most n.THEOREM 1. Let a < b ≦ c < d and let pn ∈ Πn. Thenfor x ∈ (a, b).
Necessary and Sufficient Conditions for the Discreteness of the Spectrum of Certain Singular Differential Operators
Authors: Ahlbrandt Calvin D. , Hinton Don B. , Lewis Roger T. 
Published: December 2010

1. Introduction. Let P(x) be an m × m matrix-valued function that is continuous, real, symmetric, and positive definite for all x in an interval J , which will be further specified. Let w(x) be a positive and continuous weight function and define the formally self adjoint operator l bywhere y(x) is assumed to be an m-dimensional vector-valued function. The operator l generates a minimal closed symmetric operator L0 in the Hilbert space ℒm2(J; w) of all complex, m-dimensional vector-valued functions y on J satisfyingwith inner productwhere . All selfadjoint extensions of L0 have the same essential spectrum ([5] or [19]). As a consequence, the discreteness of the spectrum S(L) of one selfadjoint extension L will imply that the spectrum of every selfadjoint extension is entirely discrete.
Localization and Completion at Primes Generated by Normalizing Sequences in Right Noetherian Rings
Authors: Heinicke A. G. 
Published: December 2010

If P is a right localizable prime ideal in a right Noetherian ring R, it is known that the ring RP is right Noetherian, that its Jacobson radical is the only maximal ideal, and that RP/J(RP) is simple Artinian: in short it has several properties of the commutative local rings.In the present work we examine the properties of RP under the additional assumption that P is generated by, or is a minimal prime above, a normalizing sequence. It is shown that in such cases J(RP) satisfies the AR-property (i.e., P is classical) and that the rank of P coincides with the Krull dimension of RP. The length of the normalizing sequence is shown to be an upper bound for the rank of P, and if P is generated by a normalizing sequence x1, x2, …, xn then the rank of P equals n if and only if the P-closures of the ideals Ij generated by x1, x2, …, xj (j = 0, 1, …, n), are all distinct primes.
Signatures of Covering Links
Authors: Gordon C. Mca. , Litherland R. A. , Murasugi K. 
Published: December 2010

A (tame) knotkninS3is said to haveperiod nif there exists a homeomorphismϕ:S3→S3, necessarily orientationpreserving, such that(i) the fixed point set ofϕis a circle disjoint fromkn(ii)ϕ(kn) =kn;(iii)ϕhas ordern.Several necessary conditions for a knot to have periodnhave already been established in the literature; see[3] [11] [14] [18]. Here we establish the following further condition, involving the signatureσ(kn) of (kn).
Spaces of Maps into Eilenberg-Maclane Spaces
Authors: Hansen Vagn Lundsgaard 
Published: December 2010

In this note we provide alternative and unified proofs for two theorems on the homotopy groups of spaces of (continuous) maps into Eilenberg-MacLane spaces. The first theorem is due to Thorn, and independently Federer, and deals with spaces of maps into Eilenberg- MacLane spaces of type (π, n) for n ≧ 1 with π abelian. The second theorem is due to Gottlieb and deals with spaces of maps into Eilenberg- MacLane spaces of type (π, 1) with π nonabelian. As a main tool we shall use the homotopy sequences for certain fibrations of spaces of maps.2. Basic notation and some preliminary remarks. For any pair of connected CW-complexes X and Y with base points, we denote by M(X, Y), respectively F(X, Y), the space of free maps, respectively based maps, of X into Y.
The Translation Planes of Dempwolff
Authors: Johnson N. L. 
Published: December 2010

In [2], Dempwolff constructs three translation planes of order 16 using sharply 2-transitive sets of permutations in S16. That is, if acting on Λ is a sharply 2-transitive set of permutations then an affine plane of order n may be defined as follows: The set of points = {(x, y)|x, y ∊ Λ} and the lines = {(x, y)|y = xg for fixed }, {(x, y)|x = c}, {(x, y)|y = c} for c ∊ Λ.Let V be a vector space of dimension k over F ≅ GF(pr). A translation plane may be defined by finding a set M of pkr – 1 linear transformations such that xy–l is fixed point free on for all x ≠ y in M.Notice that if we allow V to act on itself then MV is a sharply 2-transitive set on V if and only if xy–1 is fixed point free on for all x ≠ y in M.
Generalized Resolvent Equations and Unsymmetric Dirichlet Spaces
Authors: Elliott Joanne 
Published: December 2010

Let (X, , μ) and (X, , μ′) be measure spaces with the measures μ and μ′ totally finite. Suppose {Uλ: λ > 0} is a family of positive (i.e., ϕ ≧ 0 ⇒ Uλϕ ≧ 0) continuous linear operators from L2(X, dμ′) to L2(X,dμ) with the following additional properties: if ϕ ≧ 0 then Uλϕ is non-decreasing as λ increases, while λ−1Uλϕ is nonincreasing.A family {Mλ:λ > 0} of continuous linear operators from L2(X, dμ) to L2(X, dμ′) satisfies the “generalized resolvent equation” relative to {Uλ} if(0.1)for positive λ and v. If Uλ = λI, then (0.1) is just the well-known resolvent equation. The family {Mλ} is called submarkov if Mλ is a positive operator and(0.2)it is conservative if(0.3)
Isometries of Bergman Spaces over Bounded Runge Domains
Authors: Kolaski Clinton J. 
Published: December 2010

1.1. The isometries of the Hardy spaces Hp(0 < p < ∞, p ≠ 2) of the unit disc were determined by Forelli in [2]. Generalizations to several variables: For the polydisc the isometries of Hp onto itself were characterized by Schneider [9]. For the unit ball the case p > 2 was then done by Forelli [3]; Rudin [8] removed the restriction p > 2 by proving a theorem on equimeasurability. Finally, Koranyi and Vagi [6] noted that the methods developed by Forelli, Rudin and Schneider applied to bounded symmetric domains.In this note it will be shown that their methods also apply to the Bergman spaces over bounded Runge domains. The isometries which are onto are completely characterized; the special cases of the ball and polydisc are particularly nice and are given separately.
Weak Solutions for Semi-Martingales
Authors: Pellaumail J. 
Published: December 2010

The fundamental theorem of this paper is stated in Section 8. In this theorem, the stochastic differential equation dX = a(X)dZ is studied when Z is a *-dominated (cf. [15]) Banach space valued process and a is a predictable functional which is continuous for the uniform norm.For such an equation, the existence of a “weak solution” is stated; actually, the notion of weak solution here considered is more precise than this one introduced by Strook and Varadhan (cf. [30], [31], [23]).Namely, this weak solution is a probability, so-called “rule,” defined on (DH × Ω), DH being the classical Skorohod space of all the cadlag sample paths and Ω is the initial space which Z is defined on: the marginal distribution of R on Ω is the given probability P on Ω. This concept of rule is defined in Section 3.
Separating Closed Sets by Continuous Mappings into Developable Spaces
Authors: Brandenburg Harald 
Published: December 2010

A topological space X is called developable if it has a development, i.e., a sequence of open covers of X such that for each x ∈ X the collection is a neighbourhood base of x, whereThis class of spaces has turned out to be one of the most natural and useful generalizations of metrizable spaces [23]. In [4] it was shown that some well known results in metrization theory have counterparts in the theory of developable spaces (i.e., Urysohn's metrization theorem, the Nagata-Smirnov theorem, and Nagata's “double sequence theorem”). Moreover, in [3] it was pointed out that subspaces of products of developable spaces (i.e., D-completely regular spaces) can be characterized in much the same way as subspaces of products of metrizable spaces (i.e., completely regular T1-spaces).
Some Obstacles to Duality in Topological Algebra
Authors: Bankston Paul 
Published: December 2010

0. Introduction. Functors form an equivalence of categories (see [8,]) if Γ(Φ(A)) ≅ A and Φ (Γ(B)) ≅ B naturally for all objects A from and B from . Letting denote the opposite of we say that and are dual if there is an equivalence between and .Let τ be a similarity type of finitary operation symbols. We let Lτ denote the first order language (with equality) using nonlogical symbols from τ, and consider the class of all algebras of type τ as a category by declaring the morphisms to be all homomorphisms in the usual sense (i.e., those functions preserving the atomic sentences of Lτ). If is a class in (i.e., and is closed under isomorphism), we view as a full subcategory of , and we define the order of to be the number of symbols occurring in τ.
A Construction for Vertex-Transitive Graphs
Authors: Alspach Brian , Parsons T. D. 
Published: December 2010

A useful general strategy for the construction of interesting families of vertex-transitive graphs is to begin with some family of transitive permutation groups and to construct for each group Γ in the family all graphs G whose vertex–set is the orbit V of Γ and for which Γ ≦ Aut (G), where Aut (G) denotes the automorphism group of G. For example, if we consider the family of cyclic groups 〈(0 1 … n – 1)〉 generated by cycles (0, 1 … n – 1) of length n, then the corresponding graphs are the n-vertex circulant graphs.In this paper we consider transitive permutation groups of degree mn generated by a “rotation” ρ which is a product of m disjoint cycles of length n and by a “twisted translation” t; such that τρτ–l = ρα for some α.
A Theorem on Derivations of Prime Rings with Involution
Authors: Herstein I. N. 
Published: December 2010

In a recent note [2] we showed that if R is a prime ring and d ≠ 0 a derivation of R such that d(x)d(y) = d(y)d(x) for all x, y ∈ R then, if R is not a characteristic 2, R must be commutative. (If char R = 2 we showed that R must be an order in a 4-dimensional simple algebra.)In this paper we shall consider a similar problem, namely, that of a prime ring R with involution * where d(x)d(y) = d(y)d(x) not for all x, y ∈ R but merely for symmetric elements x* = x and y* = y. Although it is clear that some results can be obtained if R is of characteristic 2, we shall only be concerned with the case char R ≠ 2. Even in this case one cannot hope to extend the result cited in the first paragraph, that is, to show that R is commutative.
Properties of a Class of (0,1)-Matrices Covering a given Matrix
Authors: Anstee R. P. 
Published: December 2010

We wish to consider the class of (0,1)-matrices with prescribed row and column sums. LetR= (r1,r2, …,rm) andS= (s1,s2, …,sn) be vectors with nonnegative integral entries andr1+r2+ … +rm=s1+s2+ … +sn. We define the classto be the set ofm×n(0, 1)-matrices withithrow sumriandjthcolumn sumsjfor 1 ≦i≦mand 1 ≦j≦n.Gale and Ryser independently found simple necessary and sufficient conditions forto be nonempty [9,14]. FromR, we form anm×n(0, 1)-matrixĀas follows. Theith row sum ofĀisriand the 1‘s are as far to the left as possible. Letbe thejthcolumn sum ofA. We define the sequenceto be theconjugateof the sequence (ri).
A Polynomial Algorithm for Constructing a Large Bipartite Subgraph, with an Application to a Satisfiability Problem
Authors: Poljak Svatopluk , Turzík Daniel 
Published: December 2010

Let G be a symmetric connected graph without loops. Denote by b(G) the maximum number of edges in a bipartite subgraph of G. Determination of b(G) is polynomial for planar graphs ([6], [8]); in general it is an NP-complete problem ([5]). Edwards in [1], [2] found some estimates of b(G) which give, in particular,for a connected graph G of n vertices and m edges, whereand ﹛x﹜ denotes the smallest integer ≧ x.We give an 0(V3) algorithm which for a given graph constructs a bipartite subgraph B with at least f(m, n) edges, yielding a short proof of Edwards’ result.Further, we consider similar methods for obtaining some estimates for a particular case of the satisfiability problem. Let Φ be a Boolean formula of variables x1, …, xn.
The Generalized Orthocompletion and Strongly Projectable Hull of a Lattice Ordered Group
Authors: Ball Richard N. 
Published: December 2010

The central result is the existence and uniqueness for an arbitrary l-group G of two hulls, Ḡ and Ḡω, which in the representable case coincide with the orthocompletion and strongly protectable hull of G. This is done by introducing two notions of extension, written ≼ and ≼ω, and proving that each G has a maximal ≼ extension Ḡ and a maximal ≼ω extension Ḡω. Two constructions of Ḡ and Ḡω are-given: an l-permutation construction leads to descriptive structural information, and a construction by “consistent maps” leads to a strong universal mapping property.The notion of a strongly projectable hull has a lengthy history. The concept of an orthocompletion, together with the first proof of its existence and uniqueness, is due to Bernau [4]. Conrad summarized and extended all these results in an important paper [10].
The Measure Spectrum of a Uniform Algebra and Subharmonicity
Authors: Kumagai Donna 
Published: December 2010

Let A be a uniform algebra on a compact Hausdorff
space X. The spectrum, or the maximal ideal space, MA, of A is given byWe define the measure spectrum, SA, of A bySA is the set of all representing measures on X for all Φ ∈ MA. (A representing measure for Φ ∈ MA is a probability measure μ on X satisfyingThe concept of representing measure continues to be an effective tool in the study of uniform algebras. See for example [12, Chapters 2 and 3], [5, pp. 15-22] and [3]. Most of the known results on the subject of representing measures, however, concern measures associated with a single homomorphism.
Homology Operations Revisited
Authors: Fiedorowicz Z. , May J. P. 
Published: December 2010

There are two principal kinds of input data for infinite loop space theory, namelyE∞spaces à la Boardman-Vogt [3] and May [7] and Γ-spaces à la Segal [14]. May and Thomason [13] introduced a common generalization and used it to prove the equivalence of the output obtained from these two kinds of input.This suggests that any invariants of one kind of input should have analogs for the other. Homology operations are among the most basic invariants ofE∞spaces, and we here establish the analogous invariants for Γ-spaces. The definition is transparently obvious from the point of view of the common generalization but is at first sight rather surprising and unnatural from the point of view of Γ-spaces alone. Probably for this reason, there is no hint of the possibility of a direct definition of homology operations for Γ-spaces in the literature.
Inequalities for Polynomials with a Prescribed Zero
Authors: Aziz Abdul 
Published: December 2010

If P(z) is a polynomial of degree n, then the inequality1is trivial. It was asked by Callahan [1], what improvement results from supposing that P(z) has a zero on |z| = 1 and he answered the question by showing that if P( l ) = 0, then2Donaldson and Rahman [3] have shown that if P(z) is a polynomial of degree n such that P(β) = 0 where β is an arbitrary non-negative number, then3whereas if the polynomial P(z) is such that P(l) = 0, then [4]4