bluuebunny/crossref_metadata_2025 huggingface dataset:
Topological Localization, Category and Cocategory
Authors: Toomer Graham Hilton
Published: December 2010

It is easy to see that a localization (in the sense of [9]) of a simply connected co H-space (equivalently a simply connected space of Liusternik-Schnirelman category one) is again a co H-space. (All spaces in this paper will be pointed and have the based homotopy type of a connected CW complex; and all maps will preserve base-points.) We show that the category of a simply connected space does not increase on localizing. We give an example to show that the hypothesis simple-connectivity is crucial. In strong contrast, the dual result only requires connectivity.
Two Applications of Homology Decompositions
Authors: Toomer Graham Hilton
Published: December 2010

We show that a map of rational spaces (see Definition 1) induces a map of homology sections at each stage, and that the k'-invariants are mapped naturally. This is used to characterize rational spaces in which all (matric) Massey products vanish as wedges of rational spheres, and yields the precise Eckmann-Hilton dual of a result of M. Dyer [7]. Berstein's result on co-H spaces [3] is also deduced. These results form a part of the author's doctoral dissertation at Cornell University written under Professor I. Berstein, to whom I express my sincere thanks for his patient help and encouragement. Extensions and counterexamples will appear in a future paper.
On Σ-Finite Families
Authors: Mccandless Byron H.
Published: December 2010

Let be a family of subsets of a topological space X. We do not require to be a covering of X, nor do we assume that the members of are necessarily open. In this paper we shall assume that is of a special sort, which we call Σ-Finite. We show that a Σ-Finite family is both locally finite and star-finite, and in particular that an open covering of X is Σ-Finite if and only if it is star-finite. We then prove that every Σ-Finite family is ᓂ-discrete, so that in particular, every star-finite open covering of X is (ᓂ-discrete. There seems to be some applications of this fact.
Sur Certains Sous-Espaces De BP(G)
Authors: Lohoué N.
Published: December 2010

On étudie certains sous-espaces de l'algèbre de Banach Bp(G) des multiplicateurs de AP(G). On montre entre autres que l'espace des coefficients d'une représentation de G sur un espace Lp n'est pas nécessairement fermé dans Bp(G) à moins que p soit égal à deux.
A Note on Quadratic forms Over Arbitrary Semi-Local Rings
Authors: Mandelberg K. I.
Published: December 2010

Let R be a commutative ring. A bilinear space (E, B) over R is â finitely generated projective R-module E together with a symmetric bilinear mapping B:E X E →R which is nondegenerate (i.e. the natural mapping E → HomR(E﹜ R) induced by B is an isomorphism). A quadratic space (E, B, ) is a bilinear space (E, B) together with a quadratic mapping ϕ:E →R such that B(x, y) = ϕ (x + y) — ϕ (x) — ϕ (y) and ϕ (rx) = r2ϕ (x) for all x, y in E and r in R. If 2 is a unit in R, then ϕ (x) = ½. B﹛x,x) and the two types of spaces are in obvious 1 — 1 correspondence.
On Order Properties of Order Bounded Transformations
Authors: Aliprantis Charalambos D.
Published: December 2010

W. A. J. Luxemburg and A. C. Zaanen in [7] and W. A. J. Luxemburg in [5] have studied the order properties of the order bounded linear functionals of a given Riesz space L. In this paper we consider the vector space (L, M) of the order bounded linear transformations from a given Riesz space L into a Dedekind complete Riesz space M.
Connexions and Prolongations
Authors: Patterson Leif-Norman
Published: December 2010

Computation of the velocity of a given motion depends on measurement of nearby position changes only. Computation of acceleration, on the other hand, depends on measurement of nearby changes in velocity. But since velocity vectors are attached to positions so that even nearby ones are not a priori comparable, acceleration is not computable until a rule for comparison of vectors along a curve is given. Such a rule-parallel translation or linear connexion - exists automatically in Euclidean spaces. For motions in more general manifolds, for example (semi-) Riemannian ones, parallel translation is a less obvious consequence of the metric properties.
Entire Mean Periodic Functions
Authors: Laird P. G.
Published: December 2010

Let H denote the set of all entire functions of a single complex variable equipped with the topology of convergence uniform on all compact subsets of C, the set of complex numbers. Then an entire function f is mean periodic if the subspace spanned by f and its complex translates is not dense in H. It was shown by Schwartz [13, p. 922] in 1947, to whom this definition is due, that any such function is the limit in H of a certain sequence of exponential polynomials.
Complete and Orthogonally Complete Rings
Authors: Burgess W. D. , Raphael R.
Published: December 2010

This article continues the study of Abian's order on commutative semiprime rings (for such a ring R, the relation a ≦ b if and only if ab = a2” makes R into a partially ordered multiplicative semigroup). The aim, here, is to extend as far as possible the theorem of Brainerd and Lambek which says that the completion of a Boolean ring is its complete ring of quotients. Only certain subsets of a ring may have upper bounds (in any extension ring) and these are called boundable (the notion is due to Haines). A ring will be called complete if every boundable subset has a supremum. If R ⊂ S are (commutative semiprime) rings then S will be called a completion of R if S is complete and every element of S is the supremum of a subset of R.
Numerical Invariants in Homotopical Algebra, I
Authors: Varadarajan K.
Published: December 2010

Classically CW-complexes were found to be the best suited objects for studying problems in homotopy theory. Certain numerical invariants associated to a CW-complex X such as the Lusternik-Schnirelmann Category of X, the index of nilpotency of ᘯ(X), the cocategory of X, the index of conilpotency of ∑ (X) have been studied by Eckmann, Hilton, Berstein and Ganea, etc. Recently D. G. Quillen [6] has developed homotopy theory for categories satisfying certain axioms. In the axiomatic set up of Quillen the duality observed in classical homotopy theory becomes a self-evident phenomenon, the axioms being so formulated.
Numerical Invariants In Homotopical Algebra, II-Applications
Authors: Varadarajan K.
Published: December 2010

This paper deals with some applications in the results obtained in “Numerical Invariants in Homotopical Algebra” [7]. The applications are mainly concerned with the homotopy theory of modules developed by P. J. Hilton [4]. However we have to restrict the class of rings because we want to obtain a situation where the axioms of Quillen [6] hold good. This paper is organised as follows.
The Completion of an Abelian l-Group
Authors: Otis Kenny G.
Published: December 2010

A directed partially ordered abelian group (G, ≦ ) is a tight Riesz group if for a1, a2, b1, b2 ∈ G with ai < bj, i, j = 1,2, there is an x ∈ G with ai < x < bj, i, j = 1, 2. The open interval topology on G is the topology having as a base the set of all open intervals (a, b) = {x ∈ G|a < x < b}. For any x ∈ G, a neighborhood base at x is the set of all open intervals (x — a, x + a) = x + ( — a, a) for a > 0.
Brauer Characters and Grothendieck Rings
Authors: Puttaswamaiah B. M.
Published: December 2010

Let G be a group of finite order g, A a splitting field of G of characteristic p (which may be 0) and R = AG the group algebra of G over A. In [2], the author studied some of the properties of the Grothendieck ring K(R) of the category of all finitely generated R-modules, and derived a number of consequences. This paper continues the study carried out in [2]. The study is concerned with the structure and irreducible representations of K(R). The ring K(R) is proved to be semisimple and the primitive idempotents of K(R) are explicitly constructed. If the ring K(R) is identified with the ‘algebra of representations', then Robinson's idempotent [3; 4; 5] follow from our description as a special case.
Positive Definite Functions for the Class Lp(G)
Authors: Husain T. , Warsi S. A.
Published: December 2010

There are several notions of positive definiteness for functions on topological groups, the two of which are: Bochner type positive definite functions and integrally positive definite functions. The class P(F) of positive definite functions for the class F can be defined more generally and it is interesting to observe that a change in F produces a different class P(F) of positive definite functions. The purpose of this paper is to study the functions in P(LP(G)) which are positive definite for the class LP(G) (1 ≦ p < ∞), where G is a compact or locally compact group. The relevant information about the class P(F) can be found in [1; 2; 3 and 8].
On Nilpotent Products of Cyclic Groups—Reexamined by the Commutator Calculus
Authors: Waldinger Hermann V. , Gaglione Anthony M.
Published: December 2010

Ruth R. Struik investigated the nilpotent group , where G is a free product of a finite number of cyclic groups, not all of which are of infinite order, and Gm is the mth subgroup of the lower central series of G. Making use of the “collection process” first given by Philip Hall in [8], she determined completely for 1 ≦ n ≦ p + 1, where p is the smallest prime with the property that it divides the order of at least one of the free factors of G. However, she was unable to proceed beyond n = p + 1.
Operators of Rank One in Reflexive Algebras
Authors: Longstaff W. E.
Published: December 2010

If H is a (complex) Hilbert space and is a collection of (closed linear) subspaces of H it is easily shown that the set of all (bounded linear) operators acting on H which leave every member of invariant is a weakly closed operator algebra containing the identity operator. This algebra is denoted by Alg . In the study of such algebras it may be supposed [4] that is a subspace lattice i.e. that is closed under the formation of arbitrary intersections and arbitrary (closed linear) spans and contains both the zero subspace (0) and H. The class of such algebras is precisely the class of reflexive algebras [3].
Isometry of Riemannian Manifolds to Spheres, II
Authors: Ackerman Neill H. , Hsiung C. C.
Published: December 2010

Let Mn be a Riemannian manifold of dimension n ≧ 2 and class C3, (gtj) the symmetric matrix of the positive definite metric of Mn, and (gij) the inverse matrix of (gtj), and denote by and R = gijRij the operator of covariant differentiation with respect to gij, the Riemann tensor, the Ricci tensor and the scalar curvature of Mn respectively.
Modules Over Hereditary Noetherian Prime Rings, II
Authors: Singh Surjeet
Published: December 2010

Let R be a hereditary noetherian prime ring ((hnp)-ring) with enough invertible ideals. Torsion modules over bounded (hnp)-rings were studied by the author in [10; 11]. All the results proved in [10; 11] also hold for torsion R-modules having no completely faithful submodules. In Section 2, indecomposable injective torsion R-modules which are not completely faithful are studied, and they are shown to have finite periodicities (Theorem (2.8) and Corollary (2.9)). These results are used to determine the structure of quasi-injective and quasi-projective modules over bounded (hnp)-rings (Theorems (2.13), (2.14) and (2.15)).
Finite Rings in Which 1 is a Sum of Two Non-p-thPower Units
Authors: Jacobson David
Published: December 2010

LetRbe a finite ring with 1 and letR*denote the group of units ofR.Letpbe a prime number. In this paper we consider the question of whether there exista, binR*such thataandb arenon-p-th powers whose sum is 1. If such units a,bexisting, we say that R is an N (p)-ring. Of course ifpdoes not divide |R*|, the order of R*, then every element inR*is apthpower.
On Derivations of Lie Algebras
Authors: Berman Stephen
Published: December 2010

A well known result in the theory of Lie algebras, due to H. Zassenhaus, states that if is a finite dimensional Lie algebra over the field K such that the killing form of is non-degenerate, then the derivations of are all inner, [3, p. 74]. In particular, this applies to the finite dimensional split simple Lie algebras over fields of characteristic zero. In this paper we extend this result to a class of Lie algebras which generalize the split simple Lie algebras, and which are defined by Cartan matrices (for a definition see § 1). Because of the fact that the algebras we consider are usually infinite dimensional, the method we employ in our investigation is quite different from the standard one used in the finite dimensional case, and makes no reference to any associative bilinear form on the algebras.
Sequential Compactness of X Implies a Completeness Property for C(X)
Authors: Rajagopalan M. , Wheeler R. F.
Published: December 2010

A locally convex Hausdorff topological vector space is said to be quasicomplete if closed bounded subsets of the space are complete, and von Neumann complete if closed totally bounded subsets are complete (equivalently, compact). Clearly quasi-completeness implies von Neumann completeness, and the converse holds in, for example, metrizable locally convex spaces. In this note we obtain a class of locally convex spaces for which the converse fails. Specifically, let X be a completely regular Hausdorff space, and let CC(X) denote the space of continuous real-valued functions on X, endowed with the compact-open topology.
On the Stable Equivalence of Plat Representations of Knots and Links
Authors: Birman Joan S.
Published: December 2010

We are interested in the question of the decideability of the classical knot problem. A knot is the embedded image of a circle S1 in Euclidean 3-space E3. If L1, L2 are knots, then L1 ≈ L2 if there is an orientation-preserving homeomorphism h: E3 ⟶ E3 with h(L1) = L2. By the “knot problem” we mean: given two arbitrary tame knots L1, L2 (a knot is tame if it is equivalent to a polygonal knot), decide in a finite number of steps whether L1 ≈ L2. The object of this paper is to show that the knot problem is ‘'stably equivalent“ to a problem of deciding membership in the double cosets of a distinguished subgroup K2n of the classical braid group B2n [1].
Ratio Limit Theorems
Authors: Mucci A. G.
Published: December 2010

Let be an adapted sequence of integrable random variables on the probability space . Let us set .The following result can be immediately derived from Brown [2]:
Domains of Paracompactness and Local Compactness
Authors: Warrack Brian
Published: December 2010

Given a class of topological spaces and a class of mappings of topological spaces, the -résolvant of is denned to be the class of topological spaces all of whose -images lie in . Whenever is closed under composition and includes identity maps, is easily seen to be the largest class of spaces smaller than which is closed under -images.
Linear Transformations On Matrices: The Invariance of Generalized Permutation Matrices, I
Authors: Ong Hock , Botta E. P.
Published: December 2010

Let F be a field, Mn(F) be the vector space of all w-square matrices with entries in F and a subset of Mn(F). It is of interest to determine the structure of linear maps T : Mn(F) →Mn(F) such that . For example: Let be GL(n, C), the group of all nonsingular n X n matrices over C [5]; the subset of all rank 1 matrices in MmXn(F) [4] (MmXn(F) is the vector space of all m X n matrices over F) ; the unitary group [2] ; or the set of all matrices X in Mn(F) such that det(X) = 0 [1]. Other results in this direction can be found in [3].
On the Brauer Group of Algebras Having a Grading and an Action
Authors: Orzech Morris
Published: December 2010

Beginning with Wall's introduction [19] of Z2-graded central simple algebras over a field K, a number of related generalizations of the Brauer group have been proposed. In [16] the field K was replaced by a commutative ring R, building upon the theory developed in [1]. The concept of a G-graded central simple K-algebra (G an abelian group) was first defined in [12]; this work and that of [16] was subsequently unified in [6] and [7] via the construction and computation of the graded Brauer group Bφ﹛R, G) (φ a bilinear form from G X G to U(R), the units of R).
Covering Theorems for Univalent Functions Mapping onto Domains Bounded by Quasiconformal Circles
Authors: Blevins Donald K.
Published: December 2010

Let Γ be a Jordan curve in the extended complex plane C. Γ is called a quasiconformal circle if it is the image of a circle by a homeomorphism ƒ which is quasiconformal in a neighborhood of that circle. If q(zi, z2) is the chordal distance from z1 to z2, the chordal cross ratio of a quadruple z1, z2, z3, z4 in C is
A Collectionwise Hausdorff, Non-Normal Moore Space
Authors: Wage Michael L.
Published: December 2010

A topological space X is said to be collectionwise Hausdorff if every discrete collection of points of X can be simultaneously separated by a collection of pairwise disjoint open sets. The question of whether there exists a collectionwise Hausdorff, non-normal Moore space was first asked by R. L. Moore. In 1964, J. M. Worrell announced that such a space did indeed exist (see [7]), but his proof has never appeared in print.
Spaces in Which Special Sets are z-Embedded
Authors: Blair Robert L.
Published: December 2010

A subset S of a topological space X is z-embedded in X in case each zero-set of S is the restriction to S of a zero-set of X. (A zero-set is the set of zeros of a real-valued continuous function.) For the basic theory of z-embedding, see [3] and [4] (and see [4] for a comprehensive bibliography of relevant papers).
A Combinatorial Interpretation Of The Wreath Product Of Schur Functions
Authors: Thomas Glânffrwd P.
Published: December 2010

A combinatorial interpretation of Schur functions in terms of Young tableaux is well-known. (For example, see Littlewood [1] or Thomas [4]). The purpose of this paper is to present a combinatorial interpretation of the wreath product (or plethysm) of two Schur functions.
Limit Point and Limit Circle Criteria for a Class of Singular Symmetric Differential Operators
Authors: Anderson Robert L.
Published: December 2010

For certain classes of singular symmetric differential operators L of order 2n, this paper considers the problem of determining sufficient conditions for L to be of limit point type or of limit circle type. The operator discussed here is defined by
Weierstrass Division in Quasianalytic Local Rings
Authors: Childress C. L.
Published: December 2010

In this paper we consider the problem of extending the Weierstrass division theorem to quasianalytic local rings of germs of functions of k real variables which properly contain the local ring of germs of analytic functions. After some background material (§ 2) and some technical preliminaries (§ 3), we show by examples that the so-called generic division theorem fails in such rings if k ≧ 1 and that the Weierstrass division theorem fails in such rings if k ≧ 2 (§ 4).
Sur L'Approximation Polynomiale Sur Tout L'axe Reel
Authors: Freud G. , Giroux A. , Rahman Q. I.
Published: December 2010

Soit Q(x) une fonction positive paire continûment différentiable pour — ∞ < x < ∞ telle que xQ’ (x) soit croissante pour x > 0 et que Q‘(x) → ∞ lorsque x → co. Désignons par Qn l'unique racine positive de l'équation xQ‘(x) = n. L'approximation polynomiale des fonctions continues relativement au poids e-Q(x) a été étudiée par de nombreux mathématiciens. Le résultat suivant est une conséquence d'un théorème de l'un des auteurs (voir Freud [1]): si F(x) est une fonction réelle continue pour —∞ < x < ∞ qui satisfait une condition de Lipschitz d'ordre a où 0 < a < 1, il existe une suite de polynômes ﹛Pn(x)﹜ où deg Pn ≦ n telle que
A Lattice-Theoretic Description of the Lattice of Hyperinvariant Subspaces of a Linear Transformation
Authors: Longstaff W. E.
Published: December 2010

If A is a (linear) transformation acting on a (finitedimensional, non-zero, complex) Hilbert space H the family of (linear) subspaces of H which are invariant under A is denoted by Lat A. The family of subspaces of H which are invariant under every transformation commuting with A is denoted by Hyperlat A. Since A commutes with itself we have Hyperlat A ⊆ Lat A. Set-theoretic inclusion is an obvious partial order on both these families of subspaces. With this partial order each is a complete lattice; joins being (linear) spans and meets being set-theoretic intersections. Also, each has H as greatest element and the zero subspace (0) as least element. With this lattice structure being understood, Lat A (respectively Hyperlat A) is called the lattice of invariant (respectively, hyper invariant) subspaces of A.
The Norm of the Lp-Fourier Transform, II
Authors: Russo Bernard
Published: December 2010

Let G be a locally compact separable unimodular group. The general theory [18] assigns to G a measure space (Λ, μ) whose points ƛ index a family of unitary factor representations of G in such a way that if U ƛ corresponds to ƛ and then

for all .
Infinite Systems of Differential Equations
Authors: McClure J. P. , Wong R.
Published: December 2010

In an earlier paper [7], we have studied the existence, uniqueness and asymptotic behavior of solutions to certain infinite systems of linear differential equations with constant coefficients. In the present paper we are interested in systems of nonlinear equations whose coefficients are not necessarily constants; more specifically, we are concerned with infinite systems of the form
Varieties Of Steiner Loops and Steiner Quasigroups
Authors: Quackenbush Robert W.
Published: December 2010

A Steiner Triple System (STS) is a pair (P, B) where P is a set of points and B is a set of 3-elenient subsets of P called blocks (or triples) such that for distinct p, q ∈ P there is a unique block b ∈ B with ﹛p, q) ⊂ b. There are two well-known methods for turning Steiner Triple Systems into algebras; both methods are due to R. H. Bruck [1]. Each method gives rise to a variety of algebras; in this paper we will study these varieties.
A Hierarchy on the Class of Primitive Recursive Ordinal Functions
Authors: Stahl Stanley H.
Published: December 2010

The class of primitive recursive ordinal functions (PR) has been studied recently by numerous recursion theorists and set theorists (see, for example, Platek [3] and Jensen-Karp [2]). These investigations have been part of an inquiry concerning a larger class of functions; in Platek's case, the class of ordinal recursive functions and in the case of Jensen and Karp, the class of primitive recursive set functions. In [4] I began to study PR in depth and this paper is a report on an attractive analogy between PR and its progenitor, the class of primitive recursive functions on the natural numbers (Prim. Rec).
Elimination from Homogeneous Polynomials Over a Polynomial Ring
Authors: Stevens John G.
Published: December 2010

Let Ω be a field and Γ a parameter. We designate the set of all polynomials homogeneous in (X) = (X1, … , Xn) with coefficients in Ω [Γ] by H Ω Γ[X] and write such polynomials as F, F(X), or F(X, Γ). The degree of a polynomial in H Ω Γ [X] shall mean the degree in (X). Let I = (F1 … , Fr) be a fixed ideal in H Ω Γ [X] generated by F1 … , Fr.
Bounds for a Linear Diophantine Problem of Frobenius, II
Authors: Vitek Yehoshua
Published: December 2010

Let A = ﹛a0, a1, … , a3﹜ be a set of relatively prime integers such that 0 < a0 < a1 < … < as = n. Let ϕ (A) denote the smallest integer such that, for N ≧ ϕ (A), the equation

should always have a solution in nonnegative integers.
A Conjecture of Bachmuth and Mochizuki on Automorphisms of Soluble Groups
Authors: Hartley Brian
Published: December 2010

In [1], Bachmuth and Mochizuki conjecture, by analogy with a celebrated result of Tits on linear groups [8], that a finitely generated group of automorphisms of a finitely generated soluble group either contains a soluble subgroup of finite index (which may of course be taken to be normal) or contains a non-abelian free subgroup. They point out that their conjecture holds for nilpotent-by-abelian groups and in some other cases.
Uniquely Colourable Graphs with Large Girth
Authors: Bollobás Béla , Sauer Norbert
Published: December 2010

Tutte [1], writing under a pseudonym, was the first to prove that a graph with a large chromatic number need not contain a triangle. The result was rediscovered by Zykov [5] and Mycielski [4]. Erdös [2] proved the much stronger result that for every k ≧ 2 and g there exist a k-chromatic graph whose girth is at least g.
Extensive Subcategories in Universal Topological Algebras
Authors: Choe T. H. , Hong Y. H.
Published: December 2010

Herrlich [7] has introduced the limit-operators to obtain every coreflective subcategory of the category Top of topological spaces and continuous maps. Using limit-operators, S. S. Hong [9] has constructed new reflective subcategories from a known extensive subcategory of a hereditary category of Hausdorff spaces and continuous maps.
Some Examples of Normal Moore Spaces
Authors: Ellen Rudin Mary , Starbird Michael
Published: December 2010

A normal Moore space is non-metrizable only if it fails to be ƛ-collectionwise normal for some uncountable cardinal ƛ [1].

For each uncountable cardinal X we present a class of normal, locally metrizable Moore spaces and a particular space Sλ in . If there is any space of class which is not X-collectionwise normal, then Sλ is such a space. The conditions for membership in make a space in behave like a subset of a product of a Moore space with a metric space. The class is sufficiently large to allow us to prove the following. Suppose F is a locally compact, 0-dimensional Moore space (not necessarily normal) with a basis of cardinality X and M is a metric space which is O-dimensional in the covering sense. If there is a normal, not X-collectionwise normal Moore space X where X ⊂ Y × M, then Sx is a normal, not λ-collectionwise normal Moore space.
Algebras with a Diagonable Subspace whose Centralizer Satisfies a Polynomial Identity
Authors: Goodaire E. G.
Published: December 2010

The literature concerning rings with polynomial identity contains several theorems in which the existence of a polynomial identity on a subring implies the existence of such an identity on the ring itself. Belluce and Jain showed in 1968 that a prime ring will satisfy a polynomial identity provided it contains a right ideal with zero left annihilator which satisfies a polynomial identity [2].
Isomorphism of Some Simple 2-Graded Lie Algebras
Authors: Djoković Dragomir Ž.
Published: December 2010

The grading is by integers modulo 2 and we refer to it as 2-grading. For the definition of 2-graded Lie algebras L and their properties we refer the reader to the papers [1; 2; 3]. All algebras considered here are finite-dimensional over a field F of characteristic zero.
Generalized Bloch Mappings in Complex Hilbert Space
Authors: Wicker Fletcher D.
Published: December 2010

Anderson, Clunie and Pommerenke defined and studied the family of Bloch functions on the unit disc (see [1]). This family strictly contains the space of bounded analytic functions. However, all Bloch functions are normal and therefore enjoy the “nice” properties of normal functions. The importance of the Bloch function concept is the combination of their richness as a family and their “nice” behavior.
When is a Matrix Sign Stable?
Authors: Jeffries Clark , Klee Victor , Van Den Driessche Pauline
Published: December 2010

An n X n real matrix A = (aij) is called stable (resp. semistable) if each of its eigenvalues has negative (resp. nonpositive) real part. These notions are important because of their close connection with the stability of motion, which can be described especially simply for a system
Recursive Embeddings of Partial Orderings
Authors: Apt K. R.
Published: December 2010

Let be a countable atomless Boolean algebra and let X be a countable partial ordering. We prove that there exists an embedding of X into which is recursive in X, and which destroys all suprema and infima of X which can be destroyed. We show that the above theorem is false when we try to preserve all suprema and infima of X instead of destroying them.
Continuity Properties of Operator Spectra
Authors: Bezak Nicholas J. , Eisen Martin
Published: December 2010

This paper is devoted to the study of convergence and variation of operator spectra with respect to the distance G of Gokhburg and Markus [5] for subspaces and linear operators in a Banach space. We use the convention of Kato [7] and refer to convergence with respect to G as generalizedconvergence.
Category Results for Tsuji Functions
Authors: Bonar D. D. , Carroll F. W. , Colwell Peter
Published: December 2010

Let D be the unit disk, |z| < 1, and H(D) the Fréchet space of holomorphic functions on D, provided with the topology of uniform convergence on compact subsets of D. If f is meromorphic in D, we denote by
Matrices Sous-Stochastiques et Fonctions Convexes
Authors: Fischer Pal , Holbrook John A. R.
Published: December 2010

Dans cette note on se propose d'étendre certains résultats de L. Mirsky concernant des matrices doublement sous-stochastiques [5; 6; 7].

On commence par rappeler des définitions et notations qu'on aura à utiliser par la suite.
Split Graphs Having Dilworth Number Two
Authors: Foldes Stephane , Hammer Peter L.
Published: December 2010

All graphs considered in this paper are finite, undirected, loopless and without multiple edges.

The vertex set and the edge set of a graph G will be denoted by V(G) and E(G)y respectively. Thus we have
Green's Potentials with Prescribed Boundary Values
Authors: Wu Jang-Mei G.
Published: December 2010

Let U, C denote the open unit disk and unit circumference, respectively and G(z, w) be the Green's function on U. We say v is the Green's potential of a mass distribution v on U if
A Topological Characterization of Conjugate Nets
Authors: Vincent Paul A.
Published: December 2010

One aspect of topological analysis that authors, such as G. T. Whyburn and Marston Morse, have pointed to ([16; 6] for instance) as being fundamental in the development of function theory is the topological study of the level sets of analytic and harmonic functions or of their topological analogues, light open maps and pseudo-harmonic functions. The first step in this direction seems to have been made by H. Whitney [14] when he studied families of curves, given abstractly using a condition of regularity.
On Upcrossing Probabilities
Authors: McDonald David R.
Published: December 2010

In [1] a simple but ingenious technique was developed for calculating hitting probabilities for submartingales (or martingales or supermartingales) subject to various constraints. This technique is extended here in order to find sharp bounds on upcrossing probabilities for submartingales subject to constraints.
Certain Integral Equalities which Imply Equimeasurability of Functions
Authors: Stephenson Kenneth
Published: December 2010

1.1. Two complex measurable functions/ and g on complex measure spaces (X, η) and (Y, v) are equimeasurable, abbreviated ƒ ∼ g, if

for every Borel set E ⊆ C. If Φ is a continuous complex function on C, then we make the following standing hypothesis (HI) which relates Φ, f, and g:

(HI) For all α, β ∊ C, we have
A Sufficient Condition for Solvability in Groups Admitting Elementary Abelian Operator Groups
Authors: Pettet Martin R.
Published: December 2010

Generalizing a celebrated theorem of Thompson, R. P. Martineau has established [4; 5] that a finite group which admits an elementary abelian group of automorphisms with trivial fixed-point subgroup is necessarily solvable. A critical observation in his approach to this problem is the fact that, corresponding to each prime divisor of its order, such a group contains a unique Sylow subgroup invariant (as a set) under the action. Hence, the theorem we shall derive here represents a modest extension of Martineau's result.
Finite Groups Admitting an Automorphism Trivial on a Sylow 2-Subgroup
Authors: Hayden John L. , Winter David L.
Published: December 2010

In this paper we shall consider finite groups satisfying the following hypothesis.

Hypothesis I. Let G be a finite group which admits an automorphism σ of primeorder p, (p, |G|) = 1. Assume the fixed point subgroup B = CG(σ) contains some Sylow 2-subgroup.
Approximating Approximate Fibrations by Fibrations
Authors: Husch L. S.
Published: December 2010

A map p: E → B between metric spaces has the approximate homotopy lifting property with respect to the space X if given a cover Ū of B and maps g: X → E and H: X × [0, 1] → B such that H(x, 0) = pg(x) for all x ϵ X, then there exists a map G: X × [0, 1] → E such that G(x, 0) = g(x) and pGt and Ht are Ū-close for all x ϵ X and t ϵ [0, 1]; i.e. given (x, t) ∊ X × [0, 1], there exists U × Ū such that pG(x, t) and H(x, t) are elements of U.
Linear Transformations on Matrices: The Invariance of a Class of General Matrix Functions
Authors: Ong Hock
Published: December 2010

Let F be a field, F* be its multiplicative group and Mn(F) be the vector space of all n-square matrices over F. Let Sn be the symmetric group acting on the set {1, 2, … , n}. If G is a subgroup of Sn and λ is a function on G with values in F, then the matrix function associated with G and X, denoted by Gλ, is defined by

and let

ℐ(G, λ) = { T : T is a linear transformation of Mn(F) to itself and Gλ(T(X)) = Gλ(X) for all X}.
A Contribution to the Theory of Metrization
Authors: Hung H. H.
Published: December 2010

In a paper on the same subject [28] and another coming out at the same time [27], Nagata gave his celebrated Double (treble, really) Sequence Theorem, with which he deduced easily and thus brought together the basic metrization theorems, i.e. theorems in which the conditions for metrizability are given as the availability of bases or subbases of certain descriptions.
An Operad Action on Infinite Loop Space Multiplication
Authors: Lada Thomas
Published: December 2010

It is well-known that an infinite loop space is an H-space whose multiplication enjoys nice properties concerning associativity and commutativity. A practical way of identifying infinite loop spaces is the utilization of May's recognition principle [3; 4]. To apply this principle, one requires an E∞-operad action on a space X; this action gives rise to various multiplications on X. In this note, it is shown that such multiplications enjoy an operad action up to homotopy that encodes the associativity and commutativity information, and that May's delooping theorem may be applied to them. We refer to [3] for the terminology of operads and monads.
On the Unitarized Adjoint Representation of a Semisimple Lie Group II
Authors: Lipsman Ronald L.
Published: December 2010

Let G be a connected semisimple Lie group with Lie algebra . Lebesgue measure on is invariant under the adjoint action of G; and so there is a natural unitary representation TG of G on L2 given by
Bounded Endomorphisms of Lattices of Finite Height
Authors: Adams M. E. , Sichler J.
Published: December 2010

Every monoid M is isomorphic to the monoid End0,1(L) of all (0,1)-preserving endomorphisms of a bounded lattice L, see [3]. The lattices L with M ≌ End0,1(L) that are constructed there are of an arbitrary infinite cardinality not smaller than that of M, and they all have infinite chains. The aim of the present article is to supplement these results. It will be shown that every finite monoid M is representable as End0,1(L) of a finite lattice. In addition, an account of the difficulties involved in attempting to characterize endomorphism monoids of lattices of a fixed finite height will be given.
Index Four Simple Groups
Authors: Alex Leo J. , Morrow Dean C.
Published: December 2010

An index four simple group is a finite simple
group, G, with a self-centralizing Sylow
p-subgroup whose normalizer in
G has order 4p. In this
paper index four simple groups having a non-principal ordinary irreducible
character of small degree in the principal p-block are
studied.
Weakly Confluent Mappings and Atriodic Suslinian Curves
Authors: Cook H. , Lelek A.
Published: December 2010

There are theorems in which some classes of topological spaces are
characterized by means of properties of mappings of these spaces into a single
space. For example, it is well known that a compactum X
is at most n-dimensional if and only if no mapping of X
irto an (n + l)-cube has a stable value [5, Theorems
VI. 1-2, pp. 75-77]. Also, a curve X is tree-like if
and only if no mapping of X into a figure eight is
homotopically essential [1, Theorem 1, pp. 74-75;
8, p. 91]. By a curve we mean
any at most 1-dimensional continuum; a continuum is a
connected compactum; a compactum is a compact metric
space, and a mapping is a continuous function. The aim
of the present paper is to prove another theorem of this type. We distinguish a
class of curves and show that it is characterized by imposing the condition that
no weakly confluent mapping [13] can transform the given
curve onto a simple triod (see 2.4). A related result is applied to a generalized
branch-point covering theorem (see 3.2). In addition, two results are obtained in
which we establish some characterizations of weakly confluent images and preimages
of the product of the Cantor set and an arc (see 1.1 and 2.2). Continua that are
such images turn out to be identical with regular curves (see 1.3).
The BP-Coaction for Projective Spaces
Authors: Davis Donald M.
Published: December 2010

The Brown-Peterson spectrum BP has been used
recently to establish some new information about the stable homotopy groups of
spheres [9; 11]. The best results
have been achieved by using the associated homology theory
BP*
( ), the Hopf algebra
BP*(BP), and the Adams-Novikov
spectral sequence
Measure, Compactification and Representation
Authors: Sultan Alan
Published: December 2010

The theory of measure on topological spaces has in recent years found its
most natural setting in the study of pavings and measures on such pavings (see
e.g. [1-3; 5;
6; 10; 19;
22; 32;
33]. In this setting the relationship between measure and
topology crystallizes since one concentrates primarily on the simpler internal
lattice structure associated with sublattices of the topology rather than on the
more complex topological structure.
Formal Power Series Over Commutative N-Algebras
Authors: Behrens Ernst August
Published: December 2010

A Banach algebra P over C
with identity element is called an N-algebra if any
closed ideal in P is the intersection of maximal
ideals. An example is given by the algebra of the continuous
C-valued functions on a compact Hausdorff space
X under the supremum norm; two others are discussed
in § 3.
Notes on Local Integral Extension Domains
Authors: Ratliff L. J.
Published: December 2010

All rings in this paper are assumed to be commutative with identity, and the
undefined terminology is the same as that in [3].

In 1956, in an important paper [2], M. Nagata
constructed an example which showed (among other things): (i) a maximal chain of
prime ideals in an integral extension domain R' of a
local domain (R, M) need not contract in
R to a maximal chain of prime ideals; and, (ii) a
prime ideal P in R' may be
such that height P < height
P ∩ R. In his example, Rf
was the integral closure of R and had two maximal
ideals. In this paper, by using Nagata's example, we show that there exists a
finite local integral extension domain of D =
R[X](M,X)
for which (i) and (ii) hold (see (2.8.1) and (2.10)).
Norm Decreasing Homomorphisms Between Ideals of Lp (G)
Authors: Kalton N. J. , Wood G. V.
Published: December 2010

Let G1
and G
2 be compact groups and T :
Lp(G1)
→ LP(G2) (1 ≦
P ≦ ∞ ) be an algebra homomorphism. If || T || ≦ 1
and T is either a monomorphism of an epimorphism then
T can in many cases be explicitly characterized (see
[4 ; 8 ; 9
; 11 ; 13 ;
14]). Excluding p = 2, the
outstanding cases are 1 < p < ∞ for
monomorphisms and 2 < p < ∞ for
epimorphisms (cf. [14]). One aim of the present note is to complete this work. We
also consider the problem of extending these results in some form to homomorphisms
on ideals of group algebras; the only known result in this area is for abelian
groups [3].
Characterizations of Completely Hausdorff-closed Spaces Via Graphs and
Projections
Authors: Joseph James E.
Published: December 2010

L. L. Herrington recently characterized completely Hausdorff-closed
topological spaces in terms of arbitrary filterbases and a type of convergence for
filterbases called f-convergence
[2], Before this, characterizations of these spaces via
filterbases was by open filterbases [1]. In this article,
we employ Herrington's characterizations to obtain characterizations of completely
Hausdorff-closed spaces in terms of projections and in terms of graphs of
functions into the spaces; both of these—projections and graphs—are utilized in
conjunction with a class S of spaces containing as a
subclass the Hausdorff completely normal fully normal spaces to effect the
characterizations.
The Stable Homeomorphism Conjecture in Dimension Four—An Equivalent
Conjecture
Authors: Friberg Bjorn
Published: December 2010

The stable homeomorphism conjecture in dimension
n,
SHC (n), says that every orientation preserving
homeomorphism of Sn
is stable, i.e. can be written as the composition of
homeomorphisms, each of which are the identity on some open set. This is
equivalent to the homeomorphism being isotopic to the identity
[6]. Call a homeomorphism
k-stable if it is isotopic to a homeomorphism which
is the identity on Sk ⊂ Sn.
Regular and Strongly Finitary Structures Over Strongly Algebroidal
Categories
Authors: Matthiessen Günter
Published: December 2010

Most properties an algebraist needs in categories are reflected by regular
functors, introduced in [6]. If is a regular and
strongly finitary functor and has some nice
properties, it can be shown that the left adjoint functor of
G helps to characterize finitary and strongly
finitary objects of . The property of
being algebroidal can be lifted from to
if a certain
condition holds in . As an
application, the implicational hull of subcategories can be constructed with the
help of reduced products.
Even Covers and Collectionwise Normal Spaces
Authors: Shapiro H. L. , Smith F. A.
Published: December 2010

The concept of an even cover is introduced early in elementary topology
courses and is known to be valuable. Among other facts it is known that
X is paracompact if and only if every open cover of
X is even. In this paper we introduce the concept of
an n-even cover and show its usefulness. Using
n-even we define an embedding that on closed subsets
is equivalent to collectionwise normal. We also give sufficient conditions for a
point finite open cover to have a locally finite refinement and also sufficient
conditions for this refinement to be even. Finally we show that the collection of
all neighborhoods of the diagonal of X is a uniformity
if and only if every even cover is normal. This last result is particularly
interesting in light of the fact that every normal open cover is even.
Homology Invariants
Authors: Hartley Richard , Murasugi Kunio
Published: December 2010

There have been few published results concerning the relationship between the
homology groups of branched and unbranched covering spaces of knots, despite the
fact that these invariants are such powerful invariants for distinguishing knot
types and have long been recognised as such [8]. It is well
known that a simple relationship exists between these homology groups for cyclic
covering spaces (see Example 3 in § 3), however for more complicated covering
spaces, little has previously been known about the homology group,
H1(M) of the branched
covering space or about H1(U), U
being the corresponding unbranched covering space, or about the relationship
between these two groups.
Lie Action of Certain Skews in *-Rings
Authors: Chacron M.
Published: December 2010

A *-ring is an associative ring R with an anti-automorphism * of period 2 (involution). Call x ∈ R skew (symmetric) if x = - x* (x = x*) and let K(S) be the additive subgroup of all skews (symmetries). If [a, b] denotes the Lie product of a, b ∈ R (that is, ab — ba) and if [A, B] denotes the Lie product of the additive subgroups A and B of R (that is, the additive subgroup generated by [a, b], a and b ranging over A and B) then clearly [K, K] is an additive subgroup contained in K.
A Condition for Artinian Rings to be Noetherian
Authors: Murase Ichiro
Published: December 2010

Throughout this paper the word “Artinian (Noetherian) ring” means an associative ring with minimum (maximum) condition on left ideals. According to C. Hopkins, an Artinian ring is Noetherian if it contains a left or right identity [3, p. 728]. However we shall consider Artinian rings without the assumption of existence of such an identity, and the theorem of Hopkins will be reproved.
Signatures and Semi Signatures of Abstract Witt Rings and Witt Rings of Semilocal Rings
Authors: Kleinstein Jerrold L. , Rosenberg Alex
Published: December 2010

This paper originated in an attempt to carry over the results of [3] from the case of a field of characteristic different from two to that of semilocal rings. To carry this out, we reverse the point of view of [3] and do assume a full knowledge of the theory of Witt rings of classes of nondegenerate symmetric bilinear forms over semilocal rings as given, for example, in [10; 11]. It turns out that the rings WT of [3] are just the residue class rings of W(C), the Witt ring of a semilocal ring C, modulo certain intersections of prime ideals.
On Semigroups in Rn X Lp Corresponding to Differential Equations with Delays
Authors: Bernier C. , Manitius A.
Published: December 2010

In this paper we study some properties of the semigroups associated with the linear retarded functional differential equations (FDE) in the setting of Banach spaces Rn X Lp( — h, 0, Rn), 1 < p < ∞. Earlier investigations of these equations via semigroups defined on the customary space C([ — h, 0], Rn) played an important role in problems of stability, oscillations, bifurcation, asymptotic behavior etc. [15].
Constructions and Applications of Rigid Spaces III
Authors: Kannan V. , Rajagopalan M.
Published: December 2010

One often encounters problems that are difficult as they are, but become manageable when translated to a different category. Thus very often, problems on Boolean algebras are answered by first transferring them to problems on Boolean spaces. (See, for example, [7]). It is with this spirit that we approach in this paper two problems on Boolean algebras. These problems are two decades old, and are considered to be outstanding problems in the field.
Sullivan's Minimal Models and Higher Order Whitehead Products
Authors: Andrews Peter , Arkowitz Martin
Published: December 2010

The theory of minimal models, as developed by Sullivan [6; 8; 16] gives a method of computing the rational homotopy groups of a space X (that is, the homotopy groups of X tensored with the additive group of rationals Q). One associates to X a free, differential, graded-commutative lgebra , over Q, called the minimal model of X, from which one can read off the rational homotopy groups of X.
On the Altitude of Nodes in Random Trees
Authors: Meir A. , Moon J. W.
Published: December 2010

Let Tn denote a tree with n nodes that is rooted at node r. (For definitions not given here see [4] or [10].) The altitude of a node u in Tn is the distance α = α (u, Tn) between r and u in Tn. The width of Tn at altitude is the number Wk = Wk(Tn) of nodes at altitude in Tn, where = 0, 1, …
Families of Generalized Weighing Matrices
Authors: Berman Gerald
Published: December 2010

Generalized weighing (GW) matrices are orthogonal matrices whose nonzero entries are roots of unity. Several families are constructed with the aid of finite geometries which include as special cases interesting examples of conference matrices and weighing matrices.
Curvature Bounds for the Spectrum of Closed Einstein Spaces
Authors: Simon Udo
Published: December 2010

The following is our main result.

(A) THEOREM. Let (M, g) be a closed connected Einstein space, n = dim M ≧ 2 (with constant scalar curvature R). Let K0 be the lower bound of the sectional curvature. Then either (M, g) is isometrically diffeomorphic to a sphere and the first nonzero eigenvalue ƛ1of the Laplacian fulfils