bluuebunny/crossref_metadata_2025 huggingface dataset:
Sur des Classes de Fonctions Analytiques Dans Le Disque et Indéfiniment Dérivables à La Frontière
Authors: Chollet A.-M.
Published: December 2010

On note D le disque unité ouvert du plan complexe, le disque fermé et T l'ensemble des réels modulo 2π.

Soit une suite de réels positifs; on désigne par {Nn}+ la classe des fonctions f, analytiques dans D, continues ainsi que toutes leurs dérivées dans , qui vérifient la propriété suivante: il existe des constantes Af et Mf telles que pour tout z dans et tout entier n positif ou nul .
On the Existence of Normal Metacompact Moore Spaces which are not Metrizable
Authors: Tall Franklin D.
Published: December 2010

It is known that the following classes of spaces (all spaces in this article are assumed T1) are identical:

1. Images of metric spaces under continuous open maps with compact point inverses.

2. Spaces with uniform bases (in the sense of Alexandrov [1]).

3. Metacompact developable spaces.

4. Spaces with σ-point-finite bases in which closed sets are Gδ's.
Which Abelian Groups Can be Fundamental Groups of Regions in Euclidean Spaces?
Authors: Chang Bai Ching
Published: December 2010

It is known that there are a lot of properties of the group of a knot inS3which fail to generalize to the group of a knotted sphere inS4; among them are included Dehn's lemma, Hopf's conjecture, and the aspherity of knots. In this paper, we shall investigate the properties of the fundamental groups of regions inS3and inS4, with examples to show that they are not quite the same. Some special consideration will be given to regions that are the complements inS3or inS4of a finite number of tamely imbedded manifolds of co-dimension 2, and, more generally, to regions that are the complements of subcomplexes inS3or inS4.
Rank r Solutions to the Matrix Equation XAXT = C, A Nonalternate, C Alternate, Over GF(2y).
Authors: Buckhiester Philip G.
Published: December 2010

Let GF(q) denote a finite field of order q = py, p a prime. Let A and C be symmetric matrices of order n, rank m and order s, rank k, respectively, over GF(q). Carlitz [6] has determined the number N(A, C, n, s) of solutions X over GF(q), for p an odd prime, to the matrix equation

1.1

where n = m. Furthermore, Hodges [9] has determined the number N(A, C, n, s, r) of s × n matrices X of rank r over GF(q), p an odd prime, which satisfy (1.1). Perkin [10] has enumerated the s × n matrices of given rank r over GF(q), q = 2y, such that XXT = 0. Finally, the author [3] has determined the number of solutions to (1.1) in case C = 0, where q = 2y.
Operators with Compact Self-Commutator
Authors: Pearcy Carl , Salinas Norberto
Published: December 2010

Let be a fixed separable, infinite dimensional complex Hilbert space, and let () denote the algebra of all (bounded, linear) operators on . The ideal of all compact operators on will be denoted by and the canonical quotient map from () onto the Calkin algebra ()/ will be denoted by π.

Some open problems in the theory of extensions of C*-algebras (cf. [1]) have recently motivated an increasing interest in the class of all operators in () whose self-commuta tor is compact.
Some C*-Algebras with Outer Derivations, II
Authors: Elliott George A.
Published: December 2010

In this paper we shall consider the class of C*-algebras which are inductive limits of sequences of finite-dimensional C*-algebras. We shall give a complete description of those C*-algebras in this class every derivation of which is inner.

Theorem. Let A be a C*-algebra. Suppose that A is the inductive limit of a sequence of finite-dimensional C*-algebras. Then the following statements are equivalent:

(i) every derivation of A is inner;

(ii) A is the direct sum of a finite number of algebras each of which is either commutative, the tensor product of a finite-dimensional and a commutative with unit, or simple with unit.
Construction of Steiner Triple Systems Having Exactly One Triple in Common
Authors: Lindner Charles C.
Published: December 2010

A Steiner triple system is a pair (Q, t) where Q is a set and t a collection of three element subsets of Q such that each pair of elements of Q belong to exactly one triple of t. The number |Q| is called the order of the Steiner triple system (Q, t). It is well-known that there is a Steiner triple system of order n if and only if n ≡ 1 or 3 (mod 6). Therefore in saying that a certain property concerning Steiner triple systems is true for all n it is understood that n ≡ 1 or 3 (mod 6). Two Steiner triple systems (Q, t1) and (Q, t2) are said to be disjoint provided that t1 ∩ t2 = Ø. Recently, Jean Doyen has shown the existence of a pair of disjoint Steiner triple systems of order n for every n ≧ 7 [1].
Compactifications
Authors: Wasileski J. S.
Published: December 2010

Every completely regular space has at least one Hausdorff compactification
and much research in Topology has been devoted to methods of constructing the
compactifications of completely regular spaces. These methods fall into two
general categories: internal methods and external methods. External methods are
characterized by their reliance on structures which are not topological or outside
the immediate topological structure of the space in question; examples of the
former are A. Weil [20] - uniform structures and Yu. Smirnov [15] who uses the
proximity structures of Efremovich; using the continuous real-valued functions to
produce an embedding of the space serves as an example of the latter.
Almost Convergence, Summability And Ergodicity
Authors: Duran J. Peter
Published: December 2010

The notion of almost convergence introduced by Lorentz [15] has been generalized in several directions (see, for example [1; 8; 11 ; 14; 17]). I t is the purpose of this paper to give a generalization based on the original definition in terms of invariant means. This is effected by replacing the shift transformation by an "ergodic" semigroupof positive regular matrices in the definition of invariant mean. The resulting "- invariant means" give rise to a summability method which we dub-almost convergence.
Valuations and Prufer Rings
Authors: Griffin Malcolm
Published: December 2010

The word ring is used to mean commutative ring. Just as valuations on fields
are used to study domains, so valuations on rings can be used to study rings;
these rings need not have units [12]. We introduce slightly weaker conditions than
having identity in order to get a more general theory. A Prufer ring
A is one in which every finitely generated regular
ideal is invertible. If we replace invertibility in the total quotient ring
K, by invertibility in a ring
R where A ⊆
R ⊆ K we get an
R-Prufer ring. These rings do occur, for example the
Witt ring of a non-Pythagorean field or a ring of bounded continuous
functions.
Multiplication Rings Via Their Total Quotient Rings
Authors: Griffin Malcolm
Published: December 2010

In the following paper ring will always mean commutative ring which may or may not have an identity. We use the letterNexclusively for nilpotents of the ringA.

A ring such that, given any two idealsLandMwithL⊆Mthere exists an idealQsuch thatL=QMis called amultiplication ring. For references to early papers on multiplication rings by Krull and Mori the reader is referred to [2]. A ring in which every regular ideal is invertible is called aDedekind ring.
Convex Directed Subgroups of a Group of Divisibility
Authors: Mott Joe L.
Published: December 2010

If D is an integral domain with quotient field K, the group of divisibility G(D) of D is the partially ordered group of non-zero principal fractional ideals with aD ≦ bD if and only if aD contains bD. If K* denotes the multiplicative group of K and U(D) the group of units of D, then G(D) is order isomorphic to K*/U(D), where aU(D) ≦ bU(D) if and only if b/a ∊ D.
Invariant Polynomials of Weyl Groups and Applications to the Centres of Universal Enveloping Algebras
Authors: Lee C. Y.
Published: December 2010

An element in the centre of the universal enveloping algebra of a semisimple Lie algebra was first constructed by Casimir by means of the Killing form. By Schur's lemma, in an irreducible finite-dimensional representation elements in the centre are represented by diagonal matrices of all whose eigenvalues are equal. In section 2 of this paper, we show the existence of a complete set of generators whose eigenvalues in an irreducible representation are closely related to polynomial invariants of the Weyl group W of the Lie algebra (Theorem 1).
Mackey Borel Structure for the Quasi-Dual of a Separable C*-Algebra
Authors: Halpern Herbert
Published: December 2010

Let A be a separable C*-algebra. Two representations π and π1 of A on the Hilbert spaces H and H1, respectively are said to be quasi-equivalent (denoted by π ~ π1) if projections of H ⊕ H1 on the invariant subspaces H and H1 of (π ⊕ π1)(A) have the same central support in the commutant (π ⊕ π1) (A)′ of (π ⊕ π1) (A), or equivalently, if there is an isomorphism ϕ of π(A)″ onto π1(A)″ such that ϕ(π(x)) = π(x) for all x ∊ A (cf. [5, § 5]). A representation π of A is said to be a factor representation if the center of π(A)″ consists of scalar multiples of the identity.
Finite p-groups with Homogyclic Central Factors
Authors: Gallian Joseph A.
Published: December 2010

If G has nilpotence class c(G) = c, let G = L1(G) > L2 (G)> . . . > Lc+1(G) = 1 and 1 = Z0(G) < Z1(G) < . . . < Zc(G) = G denote the lower central series and upper central series of G respectively. When there is no possibility of confusion we use Li for Li(G) and Zi for Zi(G). Throughout the paper we assume that G is a finite p-group of class greater than two. Let B (c, pr) denote the collection of all G of class c for which Li/Li+i is cyclic of order pr for i = 2, . . . , c and UC(c, pr) the collection of all G of class c for which Zi/Zi-1 is cyclic of order pr for i = 1, . . . , c – 1.
On Rings with Involution
Authors: Herstein I. N.
Published: December 2010

In this note we prove some results which assert that under certain conditions the involution on a prime ring must satisfy a form of positive definiteness. As a consequence of the first of our theorems we obtain a fairly short and simple proof of a recent theorem of Lanski [3]. In fact, in doing so we actually generalize his result in that we need not avoid the presence of 2-torsion. One can easily adapt Lanski's original proof, also, to cover the case in which 2-torsion is present. This result of Lanski has been greatly generalized in a joint work by Susan Montgomery and ourselves [2].
Counterexamples in the Theory of ω-functions
Authors: Applebaum C. H.
Published: December 2010

Let ϵ stand for the set of nonnegative integers (numbers), V for the class of all subcollections of ϵ (sets), Λ for the set of isols, and ΛR for the set of regressive isols. A function, f, is a mapping from a subset of ϵ into ϵ and δf and ρf denote the domain and range of f respectively. The relation of inclusion is denoted by ⊂ and that of proper inclusion by ⊊. The sets α and β are recursively equivalent (written α ≃ β), if δf = α and ρf = β for some function f with a one-to-one partial recursive extension.
Extrema of a Class of Functions on a Finite Set
Authors: Lebensold Kenneth W.
Published: December 2010

In this paper, we are concerned with the following problem: Let S be a finite set and Sm* ⊂ 2S a collection of subsets of S each of whose members has m elements (m a positive integer). Let f be a real-valued function on S and, for p ∊ Sm*, define f(P) as Σs∊pf (s). We seek the minimum (or maximum) of the function f on the set Sm*.

The Traveling Salesman Problem is to find the cheapest polygonal path through a given set of vertices, given the cost of getting from any vertex to any other. It is easily seen that the Traveling Salesman Problem is a special case of this system, where S is the set of all edges joining pairs of points in the vertex set, Sm* is the set of polygons, each polygon has m elements (m = no. of points in the vertex set = no. of edges per polygon), and f is the cost function.
Ramification Theory for Valuations of Arbitrary Rank
Authors: Marshall Murray A.
Published: December 2010

Throughout, we consider a finite Galois extension L|K of non-archimedian valued fields which are maximally complete [2, Chapter 2], Let v denote the valuation on L and let L* denote the group of non-zero elements of L. We mayidentify the value group v(L*) of L with a subgroup of D, where D denotes the minimal divisible ordered group containing v(K*). We denote the residue field of L by , and will always assume that the field extension is separable. The characteristic of will invariably be denoted by p ; much of what follows is trivial in case p = 0.
Zero-Dimensional Compactifications of Locally Compact Spaces
Authors: Woods R. Grant
Published: December 2010

Let X be a locally compact Hausdorff topological space. A compactification of X is a compact Hausdorff space which contains X as a dense subspace. Two compactifications αX and γX of X are equivalent if there is a homeomorphism from αX onto γX that fixes X pointwise. We shall identify equivalent compactifications of a given space. If is a family of compactifications of X, we can partially order by saying that αX ≦ γX if there is a continuous map from γX onto αX that fixes X pointwise.
Sufficiency Conditions for the Existence of Transversals
Authors: Milner E. C. , Shelah S.
Published: December 2010

A transversal of a family of non-empty sets is a 1-1 map

such that φ(v) ∊ Fv (v ∊ I) . A number of problems in combinatorial mathematics reduce to the question of whether or not a certain family of sets has a transversal. An up-to-date account of this theory is to be found in the book by Mirsky [9]. The best known result of this kind is the following theorem.
The Polycyclic Length of Linear and Finite Polycyclic Groups
Authors: Fisher R. K.
Published: December 2010

In what follows, a polycyclic series, for the group G, is any finite series

G = G0 ≧ G1 ≧ . . . ≧ Gl = 1

of subgroups of G, such that Gi+1 ⊲ Gi and Gi/Gi+1 is cyclic, for all i = 0, . . ., l — 1. A group that has a polycyclic series is called a polycyclic group, and if G is a polycyclic group, then the polycyclic length of G, which we denote by ρ(G), is the number of non-trivial factors of a polycyclic series for G of shortest length.
Algebraically Closed Regular Rings
Authors: Carson Andrew B.
Published: December 2010

In this paper all rings are commutative and have a unity. All ring homomorphisms preserve the unity. We let L denote the standard language for rings with two distinct constants, 0 and 1, playing the role of the zero and the unity respectively. A ring is regular if it satisfies the axiom (∀r) (∃r′)(rr′r = r) and it is algebraically closed if, for each integer n ≧ 1, it satisfies the sentence
On The Number of Classes of a Finite Group Invariant for Certain Substitutions
Authors: van Zanten A. J. , de Vries E.
Published: December 2010

In this paper we consider representations of groups over the field of the complex numbers.

The nth-Kronecker power σ⊗n of an irreducible representation σ of a group can be decomposed into the constituents of definite symmetry with respect to the symmetric group Sn. In the special case of the general linear group GL(N) in N dimensions the decomposition of the defining representation at once provides irreducible representations of GL(N) [9; 10; 11].
Homomorphisms of Rings with Involution
Authors: Lanski Charles
Published: December 2010

The purpose of this paper is to examine the extent to which a homomorphism of a ring with involution is determined by its action on the symmetric elements of the ring. Assuming that the ring is "suitably free" of 2 × 2 matrix rings, we show that any homomorphism is uniquely determined if its image is semi-prime without nonzero central ideals. To obtain this result we first investigate automorphisms of quotients of rings with involution.
Irreducible Representations of Algebras
Authors: Goodaire Edgar G.
Published: December 2010

The concept of the universal enveloping algebra of a (not necessarily associative) algebra X is basic to the study of the representations of X, because there is a one-to-one correspondence between the representations of X and . If one is only interested in studying a certain class of the representations of X, the thought occurs that there may exist a more suitable universal object.
Pseudodifferential Resolvent for a Certain Non-Locally-Solvable Operator
Authors: Hoel C.
Published: December 2010

In this note we construct a pseudo-differential resolvent for by the method of [3] and study the dependence on the parameter λ as λ → 1. Grushin [2] first pointed out that P is solvable and hypoelliptic if λ is not an odd integer, whereas P is neither locally solvable at the origin nor hypoelliptic if λ is an odd integer. Gilioli and Trèves [1] showed that this discrete nature of the condition for solvability persists to a more general class of operators.
The Additive Group of an f-ring
Authors: Conrad Paul
Published: December 2010

The intent of this paper is to show that the additive l-group of an f-ring S determines the ring structure. This is why there are so many papers that simply extend known results for abelian l-groups to f-rings. Theorem 3.1 asserts that there is a one-to-one correspondence between the f-multiplications on S and a set of homomorphisms from the positive cone of the l-group S into the positive cone of the ring (S) of polar preserving endomorphisms of the l-group S. In fact, each f-multiplication of S is determined by a homomorphism of S+ into (S)+.
Le Spectre des Opérateurs de Composition Sur C[0,1]
Authors: Montador Bruce
Published: December 2010

Soit f: [0,1] → [0,1] une fonction continue. C[0,1] est l'espace (de Banach) des fonctions continues à valeurs complexes définies sur [0, 1], muni de la norme définie par le suprémum. L'opérateur de composition [f] se définit très naturellement sur cet espace:
Iterated Limits of Lattices
Authors: Platt Craig
Published: December 2010

In this paper the results of [5] are extended to classes of lattices. We assume familiarity with [5], but we recall for convenience the principal definitions and notations. If is a category and if is a direct [resp., inverse] limit system in , then is the direct [resp., inverse] limit of (determined only up to isomorphism in ). If is an inverse limit system of sets or universal algebras, let denote the canonical construction of inverse limit described for example in [1, Chapter 3].
Some Extensions of a Theorem of Hardy, Littlewood and Pólya and Their Applications
Authors: Chong Kong-Ming
Published: December 2010

In [6], by means of convex functions Φ :R→R, Hardy, Littlewood and Pólya proved a theorem characterizing the strong spectral order relation for any two measurable functions which are defined on a finite interval and which they implicitly assumed to be essentially bounded (cf. [6, the approximation lemma on p. 150 and Theorem 9 on p. 151 of their paper]; see also L. Mirsky [10, pp. 328-329] and H. D. Brunk [1,Theorem A, p. 820]).
R-separating Sets
Authors: Gomory R. E. , Hu T. C. , Yohe J. M.
Published: December 2010

This study of r-separating sets was originally motivated by the maximum-flow-minimum-cut theorem of finite networks [1 ; 2]. In working toward a continuous version of the maximum-flow-minimum-cut theorem from the usual discrete version, one is led directly to the notion of r-connectedness of a set as defined below. This notion of r-connectedness also has a very simple intuitive interpretation. Intuitively speaking, a set of points in the plane is r-connected if a person starting at any one point of the set is able to reach any other point of the set by jumping from point to point within the set, but never jumping a distance exceeding r in any one jump.
On Continuous Images of Moore Spaces
Authors: Reed G. M.
Published: December 2010

In [4-8], the author has obtained several counterexamples to conjectures involving chain conditions, normality conditions, completeness, and the existence of point countable bases in Moore spaces. Each of these examples was obtained by constructing, by various means, a Moore space based on another space X0. In this paper, the author unifies these construction techniques and states some of the relationships between the original spaces and the derived Moore spaces.
Regular Neighborhoods of Immersed Manifolds
Authors: Maxwell J. W.
Published: December 2010

Let X and Y denote polyhedra, i : X → Y a PL immersion. A regular neighborhood of X associated with i is a regular neighborhood (e, Ri(X)) of X together with an immersion j : Ri(X) → Y

such that the diagram.
Homeomorphism and Isomorphism of Abelian Groups
Authors: Scheinberg Stephen
Published: December 2010

An abelian topological group can be considered simply as an abelian group or as a topological space. The question considered in this article is whether the topological group structure is determined by these weaker structures. Denote homeomorphism, isomorphism, and homeomorphic isomorphism by ≈, ≅ , and =, respectively. The principal results are these.

Theorem 1. If G1andG2are locally compact and connected, then G1≈ G2implies G1= G2.
Ln Sets and the Closures of Open Connected Sets
Authors: Stavrakas Nick M.
Published: December 2010

F. A. Valentine in [4] proved the following two theorems.

THEOREM 1. Let S be a closed connected subset of Rd which has at most n points of local nonconvexity. Then S is an Ln+i set.

THEOREM 2. Let S be a closed connected subset of Rd whose points of local nonconvexity are decomposable into n closed convex sets. Then S is an L2n+i set.

These results have been extended by a number of authors, but always with stronger hypothesis. (See [1] and [2].) Using a minimal arc technique, new pr∞fs of Theorems 1 and 2 were given in [3].

Valentine remarks in [4] that Theorem 2 might be improved in the case that 5 is the closure of an open connected set. The goal of this paper is to give such an improvement for sets satisfying a particular local connectivity property.
On The Mapping Properties of Certain Exceptional Sets in R2
Authors: Jackson H. L.
Published: December 2010

It is known that minimally thin and semithin sets in R2 are preserved by conformai mappings (see [3]) but it is not known whether or not analogous results hold true for ordinary thin and semithin sets respectively. In an unpublished work, Brelot has shown that ordinary thin sets at the origin are preserved by mappings of the form f(z) = z∝ (∝ > 0) where one always considers the principal branch of the mapping. We shall prove this result along with an analogous one for ordinary semithin sets and will see that the implications established by Jackson (see [4, Theorem 4]), for ordinary and minimally thin sets and by Brelot (see [2, p. 152]) for semithin sets in a half plane hold true for any wedge shaped region with vertex at the origin.
Filter Monads, Continuous Lattices and Closure Systems
Authors: Day Alan
Published: December 2010

The notion of a monad (triple) has become increasingly important as an extension of the classical universal algebraic approach to “algebraic” categories. Indeed the categories of algebras arising from a monad seem to be the most natural generalization of Birkhoffs equational classes. Moreover in [2], Barr's concept of a relational model of a monad also coincides nicely with both the concepts of partial algebras (when suitably restricted) and (Moore) closure systems.

In this paper, we wish to examine two particular monads determined by filters. The first is the filter monad F = (F, η, 𝛍) over Sets where FX is the set of all (not necessarily proper) filters on X.
Going Down and Open Extensions
Authors: McAdam Stephen
Published: December 2010

We call an extension of commutative rings, R ⊂ T, open if the spec mapping from spec (T) to spec (R), which sends the prime Q of T to Q ∩ R, is an open mapping. It is easy to show, as for example in [1], that if R ⊂ T is open then it satisfies going down. In general, the converse is false, as is shown by Z ⊂ (2z) with Z the integers. To the best of this author's knowledge, it is an open question whether for an integral extension, going down and open are equivalent.
Character Degrees and Derived Length of a Solvable Group
Authors: Isaacs I. M.
Published: December 2010

Let G be a finite group. (All groups considered here are finite). There exist several results which control the structure of G in terms of cd(G), the set of degrees of the irreducible complex characters of G. Here, we are concerned with the situation where only the cardinality of cd(G) is given. If |cd(G)| ≦ 3,, then it is known [9 ; 7] that G is solvable and the derived length dl (G) ≦ cd (G) |., If |cd(G)| = 4, then G need not be solvable (e.g., G = PSL(2, 2n))\ however [5], if G is solvable then dl(G) ≦4.
On Isomorphisms of Abelian Group Algebras
Authors: Spiegel Eugene
Published: December 2010

For F a field and G a group, let FG = F(G) be the group algebra of G over F. It is a class of finite abelian groups, F induces an equivalence relation on by are equivalent if and only if FG ⋍ FH. We will call two fields F and K equivalent on if they induce the same equivalence relation on We will say F is equivalent to isomorphism on if FG ⋍ FH if and only if G ⋍ H for any two elements .
Norm Convergence of Riesz-Bochner Means For Radial Functions
Authors: Welland G. V.
Published: December 2010

It is well known now that certain spherical methods in k (≧2) dimensions are rather poor for reconstructing a function from its Fourier transform. Consider a function f in L1(Rk), k ≧ 2,

and

where both integrals are integrals in Rk, the first over the whole space the second over the ball of radius R; x • y is the usual Euclidean inner product of x and y in Rk and \z\2 = z • z.
On Finite Line Transitive Affine Planes Whose Collineation Groups Contain no Baer Involutions
Authors: Czerwinski Terry
Published: December 2010

A finite line transitive affine planeAis a finite plane which admits a collineation groupGacting transitively on the set of all lines ofA. Wagner [11] has shown thatAis a translation plane and Hering [9] recently investigated the structure ofAunder the assumption thatGhas a composition factor isomorphic to a given nonabelian simple group. The purpose of this paper is to show that if the number of points on a line ofAis odd, and ifGcontains no Baer involutions, then the hypothesis of Hering's Main Theorem holds.
Induced Representations of Rings
Authors: Rieffel Marc A.
Published: December 2010

At the beginning of the chapter on induced representations in the treatise of Curtis and Reiner [8] on representation theory, they write “Most of the results have not yet found suitable generalization to rings with minimum condition or finite dimensional algebras, …”. The purpose of this paper is to indicate how some of the more basic theorems concerning induced representations can, in fact, be generalized to rings and algebras. In most cases we can do this by bringing together known results, so that in this sense this paper does not contain substantially new results.
Rice Theorems For D.R.E. Sets
Authors: Hay Louise
Published: December 2010

Two of the basic theorems in the classification of index sets of classes of recursively enumerable (r.e.) sets are the following:

(i) The index set of a class C of r.e. sets is recursive if and only if C is empty or contains all r.e. sets; and

(ii) the index set of a class C or r.e. sets is recursively enumerable if and only if C is empty or consists of all r.e. sets which extend some element of a canonically enumerable class of finite sets.

The first theorem is due to Rice [7, p. 364, Corollary B]. The second was conjectured by Rice [7, p. 361] and proved independently by McNaughton, Shapiro, and Myhill [6].
Partially Bounded Solutions of Linear Ordinary Differential Equations
Authors: Lovelady David Lowell
Published: December 2010

Let R, R+, and R- be the intervals (-∞, ∞), [0, ∞), and ( — ∞, 0] respectively. Let m be a positive integer, and let be the algebra of all m X m matrices. Let A be a locally integrable function from R to We propose to study the problems

(NH) u‘(t) = f(t) + A﹛t)u﹛t)

and

(H) v‘(t) =A(t)v(t)

in Rm. (H) and (NH) will denote whole-line problems, whereas (H)+, (NH)+, (H)-, and (NH)- will denote corresponding semi-axis problems.

In [1] (see also [2, Theorem 1, p. 131]), W. A. Coppel obtained necessary and sufficient conditions for each bounded Continuous/ on R+ to yield at least one bounded solution u of (NH)+. The present author [3] has determined that an analogous result holds for (NH).
Center Points Of Nets
Authors: Anderson C. L. , Hyams W. H. , McKnight C. K.
Published: December 2010

Suppose x = (x∝) is a net with values in a metric space X having metric ρ. If a point z in X can be found to minimize

then z is called a center point (c.p.) of x. The space X is (netwise) c.p. complete if every bounded net has at least one c.p.; it is sequentially c.p. complete if every bounded sequence has a c.p. Netwise c.p. completeness implies sequential c.p. completeness, and the latter implies completeness since any c.p. of a Cauchy sequence will necessarily be a limit point of that sequence.

These notions are related to the set centers of Calder et al. [2].
Holomorphic Mappings of the Hyperbolic Space into the Complex Euclidean Space and the Bloch Theorem
Authors: Hahn Kyong T.
Published: December 2010

This paper is to study various properties of holomorphic mappings defined on the unit ball B in the complex euclidean space Cn with ranges in the space Cm. Furnishing B with the standard invariant Kähler metric and Cm with the ordinary euclidean metric, we define, for each holomorphic mapping f : B → Cm, a pair of non-negative continuous functions qf and Qf on B ; see § 2 for the definition.

Let (Ω), Ω > 0, be the family of holomorphic mappings f : B → Cn such that Qf(z) ≦ Ω for all z ∈ B. (Ω) contains the family (M) of bounded holomorphic mappings as a proper subfamily for a suitable M > 0.
Certain Submodules of Simple Rings with Involution, II
Authors: Herstein I. N.
Published: December 2010

Let R be a simple ring, of characteristic not 2, having an involution *. Let 5 = ﹛x G R|x* = x﹜ and K = ﹛x £ R|x* = — x﹜ be the set of symmetric and skew elements, respectively, of R.

In [1] we discuss the structure of S as a Jordan ring and K as a Lie ring. In [2] we considered cross-over submodules, namely additive subgroups U ⊂ K, V ⊂ S such that
H-Equivalence Classes of Multiplications on Certain Fiber Spaces
Authors: Cheng Chao-Kun
Published: December 2010

The enumeration of the H-equivalence classes of multiplications on a space is a topic of current interest. In this paper we try to study the H-equivalence classes of multiplications on a CW complex X with finitely many non-vanishing homotopy groups, by using the Postnikov decomposition of X and multiplier arguments [1; 4], This paper presents a way to compute the set of H-equivalence classes of multiplications on X from the knowledge of certain quotient sets of H*(B Λ B, ∑) and some homotopy equivalences of B, where B represents the spaces in the Postnikov decomposition of X, and ∑ denotes abelian groups corresponding to the homotopy groups of X.
Prefrattini Subgroups and Cover-Avoidance Properties in 𝔘-Groups
Authors: Tomkinson M. J.
Published: December 2010

W. Gaschutz [5] introduced a conjugacy class of subgroups of a finite soluble group called the prefrattini subgroups. These subgroups have the property that they avoid the complemented chief factors of G and cover the rest. Subsequently, these results were generalized by Hawkes [12], Makan [14; 15] and Chambers [2]. Hawkes [12] and Makan [14] obtained conjugacy classes of subgroups which avoid certain complemented chief factors associated with a saturated formation or a Fischer class. Makan [15] and Chambers [2] showed that if W, D and V are the prefrattini subgroup, 𝔍-normalizer and a strongly pronormal subgroup associated with a Sylow basis S, then any two of W, D and V permute and the products and intersections of these subgroups have an explicit cover-avoidance property.
On the Triple Characterization for Stone Algebras
Authors: Balbes Raymond
Published: December 2010

In [1], C. C. Chen and G. Grâtzer developed a method for studying Stone algebras by associating with each Stone algebra L, a uniquely determined triple (C(L), D(L), ɸ (L)), consisting of a Boolean algebra C(L), a distributive lattice D(L), and a connecting map ɸ(L). This approach has been successfully exploited by various investigators to determine properties of Stone algebras (e.g. H. Lakser [9] characterized the injective hulls of Stone algebras by means of this technique). The present paper is a continuation of this program.
Convergence Formulas for Sequences of Sets
Authors: Chimenti Frank A.
Published: December 2010

This paper is concerned with the convergence of sequences of subsets of a topological space, as defined by F. Hausdorff [6]. Such a sequence converges if and only if its limit inferior equals its limit superior, where its limit inferior (respectively, superior) is that set each of whose elements satisfies the condition that each of its neighborhoods has nonempty intersection with all but finitely (respectively, with infinitely) many terms of the sequence.
Cartan Subalgebras of Zassenhaus Algebras
Authors: Brown Gordon
Published: December 2010

Cartan subalgebras play a very important role in the classification of the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic zero. It is well-known [5, 273] that any two Cartan subalgebras of such an algebra are conjugate, i.e. images of one another under some automorphism of the algebra. On the other hand, there exist finitedimensional simple Lie algebras over fields of finite characteristic p possessing non-conjugate Cartan subalgebras [2; 3; 4]. The simple Lie algebras discovered by Zassenhaus [6] also possess non-conjugate Cartan subalgebras, and we shall give a complete classification of Cartan subalgebras of these algebras in this paper.
Equality of Decomposable Symmetrized Tensors
Authors: Merris Russell
Published: December 2010

Let V be an n-dimensional vector space over the field F. Let ꕕm V be the rath tensor power of V. If ᓂ ∈ Sm, the symmetric group, there exists a linear operator P (ᓂ1) on ꕕm V such that

for all x1, … , xm ∈ V. (Here, x1 ꕕ … ꕕ xm denotes the decomposable tensor product of the indicated vectors.) If c is any function of Sm taking its values in F, we define
Sharp Transferability and Finite Sublattices of Free Lattices
Authors: Gaskill H. S. , Platt C. R.
Published: December 2010

Transferable and sharply transferable lattices were defined and characterized in [1]. Finite sublattices of free lattices were studied in [2] and a characterization of them given in [3]. In this paper, we will show that the class of finite sharply transferable lattices coincides with the class of finite sublattices of free lattices.
Coefficient Behavior of a Class of Meromorphic Functions
Authors: Noonan J. W.
Published: December 2010

With , denote by Λk the class of functions ƒ of the form

which are analytic in and which map y onto the complement of a domain with boundary rotation at most . It is known [2] that ƒ ∈ Λk if and only if there exist regular starlike functions s1 and s2, with

such that
Sharply Transferable Lattices
Authors: Gaskill H. , Grätzer G. , Platt C. R.
Published: December 2010

In a lecture in 1966 (see [6]), the second author considered briefly those first order properties which hold for a lattice if and only if they hold for the lattice of all ideals of . The best known examples of such properties are those given by identities. The well-known connection between the modular identity ϵ and the five-element nonmodular lattice transforms the above result for ϵ into the following statement: is a sublattice of a lattice if and only if is a sublattice of .
Products of Commutators as Products of Squares
Authors: Edmunds Charles C.
Published: December 2010

In any group G, the commutator subgroup G' is contained in G2, the subgroup of G generated by the squares in G. Thus any product of commutators can be written as a product of squares in G. For instance, the commutator [x, y] ( = xyx-1y-1) can be expressed as the product of three squares: [x, y] = x2(x-1y)2(y-1)2. Roger Lyndon and Morris Newman have made the interesting observation [4, Theorem 1] that, in this case, the number three is minimal in the sense that there are groups which contain commutators not expressible as the product of fewer than three squares.
Intersections of m-Convex Sets
Authors: Breen Marilyn
Published: December 2010

Let S be a subset of some linear topological space. The set S is said to be m-convex, m ≧ 2, if and only if for every m-member subset of line segments determined by these points lies in S. A point x in S is called a point of local convexity of S if and only if there is some neighborhood N of x such that if y, z ∈ N⋂ S, then [y, z] ⊆ S. If S fails to be locally convex at some point q in S, then q is called a point of local nonconvexity (lnc point) of S.
Einstein-Kaehler Manifolds Immersed in a Complex Projective Space
Authors: Nakaga Hisao
Published: December 2010

A Kaehler manifold of constant holomorphic curvature is called a complex space form. By a Kaehler submanifold we mean a complex submanifold with the induced Kaehler metric. B. Smyth [5] has studied a complete Einstein- Kaehler hypersurface in a complete and simply connected complex space form and classified completely the hypersurface. The local version of this result has been shown to be true by S. S. Chern [1], and partially by T. Takahashi [6] independently.
On a Theorem of Kuiper
Authors: Wells Robert , Favaro Luiz A.
Published: December 2010

Let be the standard (n + 1) simplex with its standard triangulation. By the Generalized Poincare Conjecture, if n ≧ 5 and is a smooth homotopy w-sphere, then there exists a smooth triangulation , where K is a suitable subdivision of . On the other hand, in [3], N. Kuiper proves the following theorem.
Factor Representations and Factor States on a C*-Algebra
Authors: Schoen James A.
Published: December 2010

Let A be a C*-algebra and H a Hilbert space of large enough (infinite at least) dimension so that every πƒ, where ƒ is a factor state on A, can be unitarily represented on H. Let Fac (A, H) denote the set of all factor representations of A on H. If π is in Fac (A, H) we call its essential subspace the smallest, closed, vector subspace KoiH such that π (A ) is null on H Θ K. We define Fac∞(A, H) to be the set of elements in Fac (A, H) whose essential subspace is H.
Weakly Regular Algebras, Boolean Orthogonalities and Direct Products of Integral Domains
Authors: Cornish William H. , Stewart Patrick N.
Published: December 2010

In this paper we consider representations of weakly regular algebras with permutable congruences and a Boolean orthogonality as direct products of orthoprime algebras. Our theorems generalize results of Abian [2; 3] and Speed [24] which characterize direct products of integral domains, and results of Abian [1] and Chacron [7] which characterize direct products of division rings.
On a Theorem of Goldschmidt Applied to Groups with a Coprime Automorphism
Authors: Pettet Martin R.
Published: December 2010

In a recent important paper of Goldschmidt [3], all finite simple groups were determined in which a non-trivial abelian 2-subgroup controls 2-fusion. Our purpose here is to present a straightforward application of this deep result to the following general question: If p is a prime and G is a finite group of order not divisible by p which admits an automorphism σ of order pn, what conditions on the fixed point subgroup CG(σ) will ensure that G is solvable?
Orthogonal Designs with Zero Diagonal
Authors: Geramita A. V. , Verner J. H.
Published: December 2010

Definition 1. An orthogonal design of order n and type (si, … , si) (st positive integers) on the commuting variables x1, … , xl is an n X n matrix X with entries chosen from ﹛0, ±x1, … , ±xl﹜ such that
Cardinal Interpolation and Generalized Exponential Euler Splines
Authors: Sharma A. , Tzimbalario J.
Published: December 2010

Let denote the class of cardinal splines S(x) of degree n (n ≧ 1) having their knots at the integer points of the real axis. We assume that the knots are simple so that . Recently Schoenberg [3] has studied cardinal splines such that S(x) interpolates the exponential function tx at the integers and
Isometries of Hp Spaces of Bounded Symmetric Domains
Authors: Korányi Adam , Vági Stephen
Published: December 2010

The isometries of the Hardy spaces Hv (0 < p < ∞, p ≠ 2) of the unit disc were determined by Forelli in 1964 [3]. For p = 1 the result had been found earlier by deLeeuw, Rudin and Wermer [2]. For several variables the state of affairs at present is this: For the polydisc the isometries of Hp onto itself have been characterized by Schneider [13]. For the unit ball the same result was proved in the case p > 2 by Forelli [4]. Finally in [12] Rudin removed the restriction p > 2 and also established some results about isometries of Hp of the ball and the polydisc into itself.
Continuous Finite Apollonius Sets in Metric Spaces
Authors: Loveland L. D.
Published: December 2010

The set of all points in the Euclidean plane E2, the ratio of whose distances from two fixed points is a constant ƛ, is known as the circle of Apollonius [7, p. 62]. This ‘'Apollonius” set is a circle except for the degenerate cases where ƛ = 1 or ƛ = 0. In more general metric spaces the same definition applies to select certain Apollonius sets (or “ ƛ-sets” in our terminology), but of course these sets are not always circles. For example, all ƛ-sets (ƛ > 0) relative to a circle in E2 are two-point sets, and all ƛ-sets relative to E1 are either singletons or two-point sets. This paper deals with the topological structure of a metric space when certain cardinality conditions have been imposed on its ƛ-sets.
On a Class of Archimedean Integral Domains
Authors: Beauregard Raymond A. , Dobbs David E.
Published: December 2010

Our starting point is an observation in elementary number theory [10, Exercise 26, p. 17]: if a and b are positive integers such that each number in the sequence a, b2, a3, b4, … divides the next, then a = b. Its proof depends only on Z being a unique factorization domain (UFD) whose units are 1, —1. Accordingly, we abstract and say that a (commutative integral) domain R satisfies (*) in case, whenever nonzero elements a and b in R are such that each element in the sequence a, b2, a3, b4, … divides the next, then a and b are associates in R (that is, a = bu for some unit u of R). The main objective of this paper is the study of the class of domains satisfying (*).
Determining the Frattini Subgroup from the Character Table
Authors: Garrison Sidney
Published: December 2010

Brauer [1, p. 141] has discussed the question of which subgroups of a group can be determined from its character table. He mentions, referring to p-groups, that the Frattini subgroup can be determined. We show that for an arbitrary finite solvable group, the Frattini subgroup can be determined from the character table. Then we exhibit an infinite set of pairs of non-solvable groups such that both members of a given pair have the same character table but Frattini subgroups of different orders. All groups to be considered are finite.
Almost-Riemannian Structures on Banach Manifolds: The Morse Lemma and the Darboux Theorem
Authors: Tromba A. J.
Published: December 2010

In this paper we introduce the notion of an almost Riemannian manifold. Briefly speaking, an almost-Riemannian structure on a Banach manifold is a generalization of the notion of a Riemannian structure on a Hilbert manifold, common examples would be manifolds of maps modelled on the Sobolev spaces Lkp. The successful use of weak Riemannian structures in hard problems has been given by Ebin [2] and Ebin and Marsden [10].
A Generalization of a Construction Due to Robinson
Authors: Thomas Glânffrwd P.
Published: December 2010

A method for constructing the product of two Schur functions was stated, but not proved in the most general case, by Littlewood and Richardson [1] in 1934. This method, which came to be known as the Littlewood-Richardson rule, was later proved completely by Robinson [2] in 1938. In this proof, Robinson describes an operation on a finite sequence of positive integers. It is this operation, set in a more general context, that is the subject of this paper.
Weak Separation Lattices of Graphs
Authors: Sabidussi Gert
Published: December 2010

In an interesting, but apparently largely unknown, paper [1] Halin has introduced the concept of a primitive set of vertices of a graph. This concept, or rather a slight modification of it, seems to provide the key to a new approach to the wrell-known and important class of graph-theoretical problems centering on the notion of separation. As is well known, if A, B, C are sets of vertices of a (non-oriented) graph X, C is said to separate A and B if and only if every AB-path in X contains a vertex of C.
Treillis de Séparation des Graphes
Authors: Polat Norbert
Published: December 2010

L'objet de cet article est essentiellement de poursuivre la généralisation entreprise par Sabidussi [4] du concept d'ensemble primitif de sommets d'un graphe, introduit par Halin [1].
Localizations of Hi and Di Rings
Authors: Houston Evan G.
Published: December 2010

In this paper we study conditions under which certain localizations of semilocal Hi and Di rings satisfy the second chain condition. Two of these results are as follows.

1) If P is a prime in a semilocal Hi ring with depth P > i ≧ height P — 1, then RP satisfies the second chain condition.

2) If P is a prime in a semilocal Dt ring with depth P ≧ i, then RP satisfies the second chain condition.
The Ordering of Spec R
Authors: Lewis William J. , Ohm Jack
Published: December 2010

Let Specie denote the set of prime ideals of a commutative ring with identity R, ordered by inclusion; and call a partially ordered set spectral if it is order isomorphic to Spec R for some R. What are some conditions, necessary or sufficient, for a partially ordered set X to be spectral? The most desirable answer would be the type of result that would allow one to stare at the diagram of a given X and then be able to say whether or not X is spectral. For example, it is known that finite partially ordered sets are spectral (see [2] or [5]).
Permutation Problems and Special Functions
Authors: Askey Richard , Ismail Mourad E. H.
Published: December 2010

Suppose we have n events Ai, … , An and let p(Aj1 … , Ajk) be the probability that the events Ah, . . . , Ajk occur jointly. The probability P0 that none of Ai, . . . , An occur is given by Poincaré's formula, the probabilistic version of the principle of inclusion and exclusion:
Holomorphic Functionals on Open Riemann Surfaces
Authors: Gauthier P. M. , Rubel L. A.
Published: December 2010

Let denote the space of functions holomorphic on an open Riemann surface R, where has the topology of uniform convergence on compact sets. In this note, we characterize the dual space *. The result is not new, for it is implicitly contained in the more general results of Tillmann [5] and, in case R is planar, in those of Köthe [4]. However, the paper of Gunning and Narasimhan [3], which appeared subsequently, allows us to give a short proof of this important result. Actually, our characterization is a natural one in terms of differentials, while the Köthe-Tillmann characterization is in terms of functions, but we show that these two characterizations are isomorphic. We end our paper by using our characterization to prove an interpolation result. The second author gratefully acknowledges a helpful discussion with Professor George Szekeres.
More About the Mathieu Group M22
Authors: Jónsson W. , McKay J.
Published: December 2010

We assume familiarity with the notation and contents of Conway [2] and Edge [3]. That the Mathieu group is a subgroup of the simple group PSU (6, 22) appears to have been first recognized by Conway and is consequent upon his identification of ·222 with PSU (6, 22). Although we know of no proof of this identification in the literature, several proofs exist in the folklore of the subject: for example, N. Patterson showed one of the authors a proof that depends on ·222 being a Fischer group, hence on consideration of order, isomorphic to PSU (6, 22). There is another proof which relies on McLaughlin's work on rank three groups.