bluuebunny/crossref_metadata_2025 huggingface dataset:
FK Spaces in Which the Sequence of Coordinate Vectors is Bounded
Authors: Ruckle William H.
Published: December 2010

The work presented in this paper was initially motivated by the following question of A. Wilansky: “Is there a smallest FK-space E in which is bounded?” Here FK-space means a complete linear metric space of real or complex sequences x = (xi) upon which the coordinate functional x → xt are continuous for each i (see [10, p. 202]), and An FK-space need not be locally convex, and therein lies the difficulty of the problem since it is easy to see that l1 is the smallest locally convex FK-space.
Strongly and Weakly Non-Poised H-B Interpolation Problems
Authors: Devore R. , Meir A. , Sharma A.
Published: December 2010

The problem of Hermite-Birkhoff interpolation is to determine: what n + 1 interpolatory conditions imposed on a polynomial P(x) of degree n and its derivatives determine the polynomial uniquely. It is customary now to indicate the imposed conditions by means of a matrix E = (eij) which is called the incidence matrix for the problem.
A Partition of Finite T0 Topologies
Authors: Das Shawpawn Kumar
Published: December 2010

The aim of this paper is to study a decomposition of finite T0 spaces into topological entities called chains and cells. These objects behave like complete units under homeomorphisms and they appear to be useful in investigating certain aspects of finite spaces. As an elementary illustration of how these entities can be used, the concept of an A2 space is introduced (in the next paragraph) and it is demonstrated that the order of the automorphism group of an A2 space is expressible as 2t, for some t ≧ 0.
On the Stable Homotopy Type of Thom Complexes
Authors: Held R. P. , Sjerve D.
Published: December 2010

Let α be a real vector bundle over a finite CW complex X and let T(α;X) be its associated Thorn complex. We propose to study the S-type (stable homotopy type) of Thorn complexes in the framework of the Atiyah-Adams J-Theory. Therefore we focus our attention on the group JR(X) which is defined to be the group of orthogonal sphere bundles over X modulo stable fiber homotopy equivalence.
Absolute Tauberian Constants for Hausdorff Transformations
Authors: Sherif Soraya
Published: December 2010

Let be a fixed sequence of real or complex numbers. The Hausdorff transform {tn} of a sequence \sn) by means of the fixed sequence (or, in short, the (H, μn) transform) is given by

where, for r, q ≧ 0,
An Intermediate Value Property for Operators with Applications to Integral and Differential Equations
Authors: Muldowney J. S. , Willett D.
Published: December 2010

It is well known that a real valued continuous function f on a closed interval S assumes every value between its maximum and minimum on S, i.e. if ξ is such that f(α) ≦ ξ ≦ f(β) then there exists γ between α and β such that f(γ) = ξ. The purpose of this paper is to develop the existence theory associated with differential and integral inequalities in the context of an intermediate value property for operators on partially ordered spaces. This has the advantage of allowing rather simple proofs of known results while in most cases giving slight improvements, and in some cases substantial improvements, in these results. Classical and recent results from different areas are unified under one principle.
A Generalization of Thom Classes and Characteristic Classes to Nonspherical Fibrations
Authors: Schultz Reinhard
Published: December 2010

Let X be a polyhedron, and let Fx denote the contravariant functor consisting of fiber homotopy types of Hurewicz fibrations over a given base whose fibers are homotopy equivalent to X. A fundamental theorem on fiber spaces states that Fx is a representable homotopy functor and a universal space for Fx is the classifying space for the topological monoid of self-equivalences of X [2; 5]. Frequently, algebraic topological information about the associated universal fibration yields information about arbitrary fibrations with fiber (homotopy equivalent to) X. However, present knowledge of the algebraic topological properties of the universal base space is extremely limited except in some special cases.
Improved Versions of Forms of Plessner's Theorem
Authors: Colwell Peter
Published: December 2010

With the aid of a theorem about the Julia points of a function meromorphic in the unit disk, this paper strengthens a theorem of K. Meier. As a consequence a stronger form of Plessner's Theorem is seen to hold which contains a theorem of E. F. Collingwood. An additional consequence is a stronger form of Meier's analogue to Plessner's Theorem.
A Note on Equicontinuous Families of Volumes With an Application to Vector
Measures
Authors: Oberle Richard Alan
Published: December 2010

Let V denote a ring of subsets of an abstract
space X, let R denote the
real numbers, and let N denote the positive integers.
Denote by a(V,
R) (respectively
ca(V,
R)) the space of real valued, finitely additive
(respectively countably additive) functions on the ring
V and denote by
ab(V,
R) the subspace consisting of those members of the
space a(V,
R) with finite variation on each set in the ring
V. Members of the space
a(V,
R) are referred to as charges and members of the
space ab(V,
R) are referred to as locally bounded charges. We
denote by cab(V,
R) the intersection of the spaces
ab(V,
R) and
ca(V,
R).
Highly Symmetric Homogeneous Spaces
Authors: Mann L. N.
Published: December 2010

We consider effective homogeneous spacesM=G/HwhereGis a compact connected Lie group,His a closed subgroup andGacts effectively onM(i.e.,Hcontains no non-trivial subgroup normal inG). It is known that dimG≦m2/2 +m/2 wherem= dimMand that if dimG=m2/2 +m/2, thenMis diffeomorphic to the standard sphereSmor the standard real projective spaceRPm[1]. In addition it has been shown that for fixedmthere are gaps in the possible dimensions forGbelow the maximal bound [4; 5].
Primitive Elements in Symmetric Algebras
Authors: Edwards Gordon
Published: December 2010

Let-R be a commutative ring with 1, and
let

be the symmetric algebra of an R-module
M. We regard the isomorphisms
S
0(M) ≅
R and S
1(M) ≅
M a s identifications. There is a unique
R-algebra homomorphism Δ :
S(M) →
S(M) ⊗
R

S(M) (called the
comultiplication) satisfying Δ(m) =
m ⊗ 1 + 1 ⊗ m for all
m ∊ M; any element
x ∊
S(M) for which
Δ(x) = x ⊗ 1 + 1 ⊗
x is said to be primitive. The set of all primitive
elements in S(M) is denoted
P(M).
The Family of Lodato Proximities Compatible With a Given Topological
Space
Authors: Thron W. J. , Warren R. H.
Published: December 2010

Let (X, ) be a topological
space. By we denote the
family of all Lodato proximities on X which induce
. We show that
is a complete
distributive lattice under set inclusion as ordering. Greatest lower bound and
least upper bound are characterized. A number of techniques for constructing
elements of are developed. By
means of one of these constructions, all covers of any member of
can be obtained.
Several examples are given which relate to the lattice
of all compatible
proximities of Čech and the family of all compatible
proximities of Efremovič. The paper concludes with a chart which summarizes many
of the structural properties of ,
and
.
Isomorphic Subgroups of Finite p-groups Revisited
Authors: Specht William
Published: December 2010

Several papers of George Glauberman have appeared which analyze the structure of a finite p-group which contains two isomorphic maximal subgroups. The usual setting for an application of these results is a finite group, a p-subgroup, and an isomorphism of this p-group induced by conjugation. In this paper we prove a stronger version of Glauberman's Theorem 8.1 [1].
A Note on Compactifying Artinian Rings
Authors: Haley David K.
Published: December 2010

In this note a number of compactifications are discussed within the class of artinian rings. In [1] the following was proved:

Theorem. For an artinian ring R the following are equivalent:

(1) R is equationally compact.

(2) R+ ≃ B ⊕ P, where B is a finite group, P is a finite direct sum of Prüfer groups, and R · P = P · R = {0}.

(3) R is a retract of a compact topological ring.
Permanents of Random Doubly Stochastic Matrices
Authors: Griffiths R. C.
Published: December 2010

The permanent of ann×nmatrixA= (aij) is defined as

whereSnis the symmetric group of ordern. For a survey article on permanents the reader is referred to [2]. An unresolved conjecture due to van der Waerden states that ifAis ann×ndoubly stochastic matrix; then per (A) ≧n!/nn, with equality if and only ifA=Jn= (1/n).
On Outer-Commutator Words
Authors: Wilson Jeremy
Published: December 2010

Let F be the group freely generated by the countably infinite set X = {x1, x2, . . . ,xi, . . . }. Let w(x1, x2, . . . , xn) be a reduced word representing an element of F and let G be an arbitrary group. Then V(w, G) will denote the set

whose elements will be called values of w in G. The subgroup of G generated by V(w, G) will be called the verbal subgroup of G with respect to w and be denoted by w(G).
A Generation Procedure for the Simple 3-Polytopes With Cyclically 5-Connected Graphs
Authors: Butler Jean W.
Published: December 2010

In this paper we derive a generation procedure for the simple (3-valent) 3-polytopes with cyclically 5-connected graphs. (A graph is called cyclically n-connected if it cannot be broken into two components, each containing a cycle, by the removal of fewer than n edges.) We define three new types of face splitting and we show, in Theorems 16 and 17, that the simple 3-polytopes with cyclically 5-connected graphs are exactly the polytopes obtained from the dodecahedron by these face splittings.
On the Classification of Biorthogonal Sequences
Authors: Ruckle William H.
Published: December 2010

The work of various authors (e.g. Frink [3] and Markushevitch [7]) suggests the possibility of studying complete biorthogonal sequences in Banach spaces as a generalization of orthogonal families of continuous functions. But except for the case where the complete biorthogonal sequence is a Schauder basis such studies have not led to a very rich theory. The main reason for this is that an arbitrary complete biorthogonal sequence is not likely to have many helpful properties. For instance, in every separable Banach space X one can find a complete biorthogonal sequence {ei, Ei} which is not one-summable.
A Purity Criterion for Pairs of Linear Transformations
Authors: Fixman Uri , Zorzitto Frank A.
Published: December 2010

In connection with the study of perturbation methods for differential eigenvalue problems, Aronszajn put forth a theory of systems (X, Y; A, B) consisting of a pair of linear transformations A, B:X → Y (see [1]; cf. also [2]). Here X and Y are complex vector spaces, possibly of infinite dimension. The algebraic aspects of this theory, where no restrictions of topological nature are imposed, where developed in [3] and [5]. We hasten to point out that the category of C2-systems (definition in § 1) in which this algebraic investigation takes place is equivalent to the category of all right modules over the ring of matrices of the form
On the Relation Between [f, g] and Aλ Summability
Authors: Bustoz Joaquin
Published: December 2010

First we will briefly define the [f, g] and Aλ summability methods. Let K = {w : |w| < 1}. T. H. Gronwall [3] introduced a general class of summability methods each of which involves a pair of functions f and g with the following properties. The function z = f (w) is analytic on \{1}, continuous and univalent on , with f (0) = 0, f (1) = 1, |f(w)| < 1 if w ∊ K. The inverse function w = f-1(z) is analytic on f (K)\{1}, and at z = 1

1.1

where γ ≧ 1, a > 0, and the quantity in brackets is a power series in 1 — z with positive radius of convergence.
Model-Completeness and Elementary Properties of Torsion Free Abelian Groups
Authors: Zakon Elias
Published: December 2010

The decidability of the elementary theory of abelian groups, and their complete classification by elementary properties (i.e. those formalizable in the lower predicate calculus (LPC) of formal logic), were established by W. Szmielew [13]. More general results were proved by Eklof and Fischer [2], and G. Sabbagh [12]. The rather formidable "high-power" techniques used in obtaining these remarkable results, and the length of the proofs (W. Szmielew's proof takes about 70 pages) triggered off several attempts at simplification. M. I. Kargapolov's proof [3] unfortunately turned out to be erroneous (cf. J. Mennicke's review in the Journal of Symbolic Logic, vol. 32, p. 535).
The Nakayama Map and Ramification for Maximally Complete Fields
Authors: Marshall Murray A.
Published: December 2010

Let K be a maximally complete valued field and let L be a totally ramified Galois extension of K with Galois group G. Assume (i) the value group quotient of L|K is cyclic and (ii) there exists an unramified cyclic extension of K of the same degree as L. Then there is an isomorphism of Ga onto a subgroup A/N(L×) of K×/N(L×) which maps the ramification group Gi onto AiN(L×)/N(L×) for all i > 0 where Ai = {x ∊ A|v(x ‒ 1) ≧ i}. This generalizes certain results of Local Class Field Theory.
Pseudo-Measure Energy and Spectral Synthesis
Authors: Benedetto John J.
Published: December 2010

In this paper we develop a natural notion of continuous pseudo-measure and study the Stieltjes integral with respect to a given pseudo-measure. The common feature to these two topics is the essential appearance in both of integrals having the form

Such integrals come about naturally when one defines the energy of distributions other than measures [6]. The reasons to study continuous pseudo-measures are to find properties analogous with those of continuous measures, and to discover more about the structure of pseudo-measures because of their importance in harmonic analysis, and particularly in spectral synthesis (e.g., [4;15]). The Stieltjes integral with respect to a pseudo-measure is studied because of its intimate relation with spectral synthesis (e.g., §5); the key observations on this matter were initially made by Beurling [6].
The Type I Part of the Regular Representation
Authors: Formanek Edward
Published: December 2010

Let G be a discrete group and let H = L2(G), with norm | |. Let B(H) be the ring of bounded operators on H with the norm

The right regular representation of G on H induces an injection ρ : C[G] → B(H), and W(G) is the closure of the image of ρ in the weak operator topology on B(H) (C = complex numbers). Using ρ, we identify C[G] with its image in W(G).
Quasi-Injective and Quasi-Projective Modules Over Hereditary Noetherian Prime Rings
Authors: Singh Surjeet
Published: December 2010

The structure theory of hereditary noetherian prime (hnp) rings—in particular of Dedekind prime rings—has been recently developed by many authors including Eisenbud, Griffith, Michler and Robson; this theory extends some of the well-known results concerning commutative Dedekind domains. In this paper we study quasi-injective modules and quasi-projective modules over those (hnp) rings which are not right primitive and establish some results which extend the corresponding well-known results concerning commutative Dedekind domains. LetRbe an (hnp) ring, which is not right primitive.
Right Invariant Right Hereditary Rings
Authors: Brungs H. H.
Published: December 2010

Let R be a right hereditary domain in which all right ideals are two-sided (i.e., R is right invariant). We show that R is the intersection of generalized discrete valuation rings and that every right ideal is the product of prime ideals. This class of rings seems comparable with (and contains) the class of commutative Dedekind domains, but the rings considered here are in general not maximal orders and not Dedekind rings in the terminology of Robson [9]. The left order of a right ideal of such a ring is a ring of the same kind and the class contains right principal ideal domains in which the maximal right ideals are two-sided [6].
Uniformly Lipschitzian Families of Transformations in Banach Spaces
Authors: Goebel K. , Kirk W. A. , Thele R. L.
Published: December 2010

The observations of this paper evolved from the concept of 'asymptotic nonexpansiveness' introduced by two of the writers in a previous paper [10]. Let X be a Banach space and K ⊆ X. A mapping T : K → K is called asymptotically nonexpansive if for each x, y ∊ K

where {ki} is a fixed sequence of real numbers such that ki→1 as i → ∞ . It is proved in [10] that if K is a bounded closed and convex subset of a uniformly convex space X then every asymptotically nonexpansive mapping T : K → K has a fixed point. This theorem generalizes the fixed point theorem of Browder-Göhde-Kirk [2 ; 12 ; 16] for nonexpansive mappings (mappings T for which ||T(x) — T(y)|| ≦ ||x — y||, x, y ∊ K) in a uniformly convex space. (A generalization along similar lines also has been obtained by Edelstein [4].)
Crowns, Fences, and Dismantlable Lattices
Authors: Kelly David , Rival Ivan
Published: December 2010

A finite lattice L of order n is dismantlable [6] if there is a chain L1 ⊂ L2 ⊂ . . . ⊂ Ln = L of sublattices of L such that |Li| = i for every i = 1, 2, . . . , n. In [1] it was shown that every finite planar lattice is dismantlable. Furthermore, every lattice L with |L| ≦ 7 is dismantlable [6]; in fact, every large enough lattice contains a dismantlable sublattice with precisely n elements [4]. As well, such lattices are closed under the formation of sublattices and homomorphic images [6].
The Double B-Dual Of An Inner Product Module Over a C*-Algebra B
Authors: Paschke William L.
Published: December 2010

The principal result of this paper states that if X is a pre-Hilbert B-module over an arbitrary C*-algebra B, then the B-valued inner product on X can be lifted to a B-valued inner product on X″ (the B-dual of the B-dual X′ of X). Appropriate identifications allow us to regard X as a submodule of X″ and the latter in turn as a submodule of X′. In this sense, the inner product on X″ is an extension of that on X. As an example (and application) of this result, we consider the special case in which X is a right ideal of B and give a topological description of X″ when in addition B is commutative.
On Conics Over a Finite Field
Authors: Jung Fuanglada R.
Published: December 2010

Let F denote a Galois field of order q and odd characteristic p, and F* = F\{0}. Let Sn denote an n-dimensional affine space with base field F. E. Cohen [1] had proved that if n ≧ 4, there is no hyperplane of Sn contained in the complement of the quadric Qn of Sn defined by

1.1

and in S3, there are q + 1 or 0 planes contained in the complement of Q3 according as — aα is not or is a square of F.
Some Criteria for Hermite Rings and Elementary Divisor Rings
Authors: Shores Thomas S. , Wiegand Roger
Published: December 2010

Recall that a ring R (all rings considered are commutative with unit) is an elementary divisor ring (respectively, a Hermite ring) provided every matrix over R is equivalent to a diagonal matrix (respectively, a triangular matrix). Thus, every elementary divisor ring is Hermite, and it is easily seen that a Hermite ring is Bezout, that is, finitely generated ideals are principal. Examples have been given [4] to show that neither implication is reversible.
Solving Linear Operator Equations
Authors: Davis Chandler , Rosenthal Peter
Published: December 2010

Let be a complex Banach space and the algebra of bounded operators on . M. Rosenblum's theorem [13; 12] (also discovered by M. G. Kreĭn, cf. [9]) states that (if A, B are fixed bounded operators) the spectrum of the operator on defined by = AX – XB is contained in σ (A) – σ(B) = {α – β : α∊σ(A), β∊σ(B)}. In particular, the condition σ(A) ∩ σ(B) = Ø implies that for each Y ∊ there is a unique X ∊ such that AX – XB = Y. This does not completely settle the question of solvability of the equation AX – XB = Y: for example, if A is the backward unilateral shift and B = 0, then the equation has a solution (for any Y) even though σ(B) ⊆ σ(A).
Large Matchings in Graphs
Authors: Weinstein J.
Published: December 2010

How large a matching must a graph have?

We consider graphs G (finite, undirected, with no loops or multiple edges), with order nG (always ≧ 1) and mG the maximum number of edges in a matching of G. The matchability μG of G is the fraction (2m/n) of nodes covered by a maximum matching.
Tensor Products of Jordan Algebras
Authors: Wulfsohn Aubrey
Published: December 2010

Let J1 and J2 be two Jordan algebras with unit elements. We define various tensor products of J1 and J2. The first, which we call the Kronecker product, is the most obvious and is based on the tensor product of the vector spaces. We find conditions sufficient for its existence and for its non-existence. Motivated by the universal mapping property for the tensor product of associative algebras we define, in Section 2, tensor products of J1 and J2 by means of a universal mapping property. The tensor products always exist for special Jordan algebras and need not coincide with the Kronecker product when the latter exists. In Section 3 we construct a more concrete tensor product for special Jordan algebras. Here the tensor product of a special Jordan algebra and an associative Jordan algebra coincides with the Kronecker product of these algebras. We show that this "special" tensor product is the natural tensor product for some Jordan matrix algebras.
The Oscillation of Fourth Order Linear Differential Operators
Authors: Lewis Roger T.
Published: December 2010

Define the self-adjoint operator

where r(x) > 0 on (0, ∞) and q and p are real-valued. The coefficient q is assumed to be differentiate on (0, ∞) and r is assumed to be twice differentia t e on (0, ∞).

The oscillatory behavior of L4 as well as the general even order operator has been considered by Leigh ton and Nehari [5], Glazman [2], Reid [7], Hinton [3], Barrett [1], Hunt and Namb∞diri [4], Schneider [8], and Lewis [6].
On a Generalization of the Catenoid
Authors: Blair David E.
Published: December 2010

It is a classical result that the only surface of revolution in Euclidean space E3 which is minimal is the catenoid. Of course the surface is conformally flat, but if Mn, n ≧ 4, is a conformally flat hypersurface of Euclidean space En+1, then Mn admits a distinguished direction [2] (“tangent to the meridians“). Thus we seek to characterize conformally flat hypersurfaces of En+1 which are minimal. Specifically we prove the following

THEOREM. Let Mn, n ≧ 4, be a conformally flat, minimal hypersurface immersed in En+1.
On Quasi-Ambivalent Groups
Authors: Sharp W. T. , Biedenharn L. C. , De Vries E. , Van Zanten A. J.
Published: December 2010

The prototype for applications of group theory to physics, and to mathematical physics, is the quantum theory of angular momentum [1] ; the use of such techniques is now almost universal, and familiarly (through somewhat imprecisely) known as “Racah algebra”. To categorize, group theoretically, those characteristics which underlay this applicability to physical problems, Wigner [30] isolated two significant conditions, and designated groups possessing these properties as simply reducible.

The two conditions for simple reducibility are:

(a)Every element is equivalent to its reciprocal, i.e., all classes are ambivalent.

(b) The Kronecker (or “direct“) product of any two irreducible representations of the group contains no representation more than once.
Construction of Large Sets of Almost Disjoint Steiner Triple Systems
Authors: Lindner C. C. , Rosa A.
Published: December 2010

A Steiner triple system (briefly STS) is a pair (S, t) where S is a set and t is a collection of 3-subsets of S (called triples) such that every 2-subset of S is contained in exactly one triple of t. The number |S| is called the order of the STS (S, t). It is well-known that there is an STS of order v if and only if v = 1 or 3 (mod 6). Therefore in saying that a certain property concerning STS is true for all v it is understood that v = 1 or 3 (mod 6).
Points of Local Nonconvexity and Finite Unions of Convex Sets
Authors: Breen Marilyn
Published: December 2010

Let 5 be a subset of Rd. A point x in 5 is a point of local convexity of S if and only if there is some neighborhood U of x such that, if y, z ϵ 5 ⌒ U, then [y, z] ⊆ S. If S fails to be locally convex at some point q in 5, then q is called a point of local nonconvexity (lnc point) of S.

Several interesting properties are known about sets whose lnc points Q may be decomposed into n convex sets. For S closed, connected, S ∼ Q connected, and Q having cardinality n, Guay and Kay [2] have proved that S is expressible as a union of n + 1 or fewer closed convex sets (and their result is valid in a locally convex topological vector space).
On the Lower Central Factors of a Free Associative Ring
Authors: Tyler Robert
Published: December 2010

Let R be a free associative ring with identity freely generated by r1, r2,. .. , rk. In analogy to group theory the lower central series for R is defined inductively By

γo = R and γn = [γn-1, R],

where γn is the ideal generated by the indicated ring commutators. Using P. Hall's collection process [2; 1, Chapter 11] γn/γn+1 will be shown to be free as a Z-module and as an R/R''-module for each non-negative integer n. In each case a basis will be exhibited.

Definition 1. Commutators of order zero are the free generators of R. A commutator, c, of order n (denoted by o(c) = n) is of the form [x, y], where x and y are commutators and o(x) + o(y) = n — 1.
The Coefficient Ring of a Primitive Group Ring
Authors: Lawrence John
Published: December 2010

All rings are associative with unity. A ring R is prime if xRy ≠ 0 whenever x and y are nonzero. A ring R is (left) primitive if there exists a faithful irreducible left R-module.

If the group ring R[G] is primitive, what can we say about R? First, since every primitive ring is prime, we know that R is prime, by the following

THEOREM 1 (Connell [1, 675]). The group ring R[G] is prime if and only if R is prime and G has no non-trivial finite normal subgroup.
When is Every Kernel Functor Idempotent?
Authors: Viola-Prioli Jorge E.
Published: December 2010

Introduction. All rings occurring are associative and possess a unity, which is preserved under subrings and ring homomorphisms. All modules are unitary right modules. We denote the category of rights-modules.

In recent years several authors have studied rings R by imposing restrictions on the torsion theories [4] of . (See for instance [2; 23; 24].) This paper offers another alternative to that trend, namely the study of rings R via their set of kernel functors K﹛R).
Skew-Hadamard Matrices of the Goethals-Seidel Type
Authors: Spence Edward
Published: December 2010

1. Introduction. We prove, using a theorem of M. Hall on cyclic projective planes, that if g is a prime power such that either 1 + q + q2 is a prime congruent to 3, 5 or 7 (mod 8) or 3 + 2q + 2q2 is a prime power, then there exists a skew-Hadamard matrix of the Goethals-Seidel type of order 4(1 + q + q2). (A Hadamard matrix H is said to be of skew type if one of H + I, H — lis skew symmetric. ) If 1 + q + q2 is a prime congruent to 1 (mod 8), then a Hadamard matrix, not necessarily of skew type, of order 4(1 + q + q2) is constructed. The smallest new Hadamard matrix obtained has order 292.
Linear Transformations Preserving the Real Orthogonal Group
Authors: Wei Albert
Published: December 2010

Let K be a field and Mn﹛K) denote the vector space of n X n matrices over K. Marcus [4] posed the following general problem: Let W be a subspace of Mn(K) and S a subset of W. Describe the set L(S, W) of all linear transformations T on W such that T(S) is contained in S.
Eulerian Graphs and Polynomial Identities for Skew-Symmetric Matrices
Authors: Hutchinson Joan P.
Published: December 2010

Let the standard identity of degree m be given by

Then we shall show that the set of all n X n skew-symmetric matrices over a field of characteristic 0 satisfies the standard identity of degree at least 2n — 2; specifically, we shall prove the following.
Linear Operators Preserving The Real Symplectic Group
Authors: Pierce Stephen
Published: December 2010

1. Introduction and s t a t e m e n t of results. Let F be a field and Mn(F) the n X n matrices over F. Set GL(n, F) to be t he units in Mn(F). Suppose H is a subgroup of GL(n, F) and L is an L-linear operator on Mn(F) mapping H into itself. Can L be neatly characterized?

Marcus [2] answered this question when F is the complex numbers C and H the unitary group. The set of such L is a group and L has the form L(A) = UAV or L(A) = UA'V where U, V are fixed unitary matrices and A’ is t he transpose of A.
On Decomposability of Compact Perturbations of Normal Operators
Authors: Radjabalipour M. , Radjavi H.
Published: December 2010

The main purpose of this paper is to show that a bounded Hilbert-space operator whose imaginary part is in the Schatten class Cp(1 ≦ p < ∞ ) is strongly decomposable. This answers affirmatively a question raised by Colojoara and Foias [6, Section 5(e), p. 218].

In case 0 ≦ T* — T ∈ C1, it was shown by B. Sz.-Nagy and C. Foias [2, p. 442; 25, p. 337] that T has many properties analogous to those of a decomposable operator and by A. Jafarian [11] that T is strongly decomposable. The authors of [11] and [24] employ the properties of the characteristic function of the contraction operator obtained from the Cayley transform of T;
The Map SJ → SF Does Not Deloop Mod 2
Authors: Clough Robert R.
Published: December 2010

It has been widely conjectured that there exists a homotopy commutative Diagram

where J is the stable Whitehead f-homomorphism and BSJ is the space constructed in [3]. In [4], Stasheff and the author proved that this conjecture is false. However, Quillen's proof of the Adams conjecture in [7] has as a corollary the existence of the homotopy commutative diagram
An Abstract Dauns-Hofmann-Kaplansky Multiplier Theorem
Authors: Elliott George A.
Published: December 2010

The present investigation was stimulated by a theorem of Alfsen and Effros (4.9 of [1]) concerning a real Banach space, its ikf-ideals, and its primitive M-ideals (these are denned in [1]). This theorem states that a real Banach space is in the natural way a module over the ring of bounded continuous real-valued functions on the space of primitive Jlf-ideals with the Jacobson topology.
Some Constructions in Abstract Measure Theory
Authors: Lutzer D. J.
Published: December 2010

In this paper we construct two examples which elucidate the relationships between several σ-algebras that arise in measure-theoretic constructions on locally compact spaces and groups. For any space X let (X) be the Borelσ-algebra on X, i.e., the smallest σ-algebra of subsets of X which contains the family of all closed subsets of X. Let δ (X) be the smallest δ-ring of subsets of X which contains every compact subset of X, where by a δ-ring we mean a collection of subsets of X which is closed under the formation of countable intersections, finite unions and relative complements. Let σ(X) be the smallest σ-ring of subsets of X which contains all compact subsets of X, where by a σ-ring we mean a collection of subsets of X which is closed under the formation of countable unions, finite intersections and relative complements.
Refinement Conditions on Operations in Sample Spaces
Authors: Weaver Robert J.
Published: December 2010

The recent study of operational statistics (see [2; 4; 5; 10 ; 11 ; 12 ; 13 ; 14 ; 15 ; 16]) describes a generalized sample space which represents the set of all possible outcomes of a collection of coherently related operations (experiments). This approach to probability generalizes the classical notion of a sample space due to A. N. Kolmogorov [8], and it gives the concept somewhat wider applicability. For instance in [4] and [14], D. J. Foulis and C. H. Randall set out the start of a program wherein a generalized sample space (hereafter called a GSS) and its affiliated partially ordered set of generalized propositions could be a framework within which a genuinely operational interpretation of the so called “logic” of quantum mechanical systems may be found.
The Second Conjugates of Certain Banach Algebras
Authors: Wong Pak-Ken
Published: December 2010

Let A be a Banach algebra and A** its second conjugate space. Arens has denned two natural extensions of the product on A to A**. Under either Arens product, A** becomes a Banach algebra. Let A be a semisimple Banach algebra which is a dense two-sided ideal of a B*-algebra B and R** the radical of (A**, o). We show that A** = Q ⊕ R**, where Q is a closed two-sided ideal of A**, o). This was inspired by Alexander's recent result for simple dual A*-algebras (see [1, p. 573, Theorem 5]). We also obtain that if A is commutative, then A is Arens regular.
Gottlieb Sets and Duality in Homotopy Theory
Authors: Halbhavi I. G. , Varadarajan K.
Published: December 2010

Evaluation subgroups of the homotopy groups have been objects of extensive study recently by Gottlieb, Haslam, Jerrold Siegel, G. E. Lang (Jr), etc. In [8] one of the authors has introduced the notions of ‘cyclic' and ‘cocyclic’ maps and studied generalizations of evaluation subgroups and their duals in the set up of Eckmann-Hilton duality. This paper continues the study of these generalized Gottlieb and dual Gottlieb subsets. All the spaces, except the function spaces, will be arc connected locally compact CW-complexes with base point at a vertex. For any X, Y the set of base point preserving homotopy classes of maps of X to Y is denoted by [X, Y].
A Characterization of Spaces Having Bases of Countable Order in Terms of Primitive Bases
Authors: Wicke H. H. , Worrell J. M.
Published: December 2010

The main theorem of this paper characterizes the class of essentially T1 spaces having bases of countable order as those spaces of the class of essentially T1 spaces having primitive bases in which closed sets are sets of interior condensation. In addition we deduce some corollaries of this theorem, derive some other characterizations, and prove a lemma concerning primitive sequences which is a key to the proof of the main theorem and has other applications.
On Splitting an Infinite Recursively Enumerable Class
Authors: Florence J. B.
Published: December 2010

By an RE (recursively enumerable) sequence we mean a sequence V(0), V(1), … of uniformly RE sets, denotes the class of all RE sets. If is an RE class if either for some RE sequence V(0), V(1) , … .
Steiner Triple Systems Having a Prescribed Number of Triples in Common
Authors: Lindner C. C. , Rosa A.
Published: December 2010

A Steiner triple system (briefly STS) is a pair where S is a finite set and is a collection of 3-subsets of S (called triples) such that every pair of distinct elements of S belongs to exactly one triple of . The number |S| is called the order of . It is well-known that there is an STS of order if and only if or 3 (mod 6). Therefore in saying that a certain property concerning STS is true for all it is understood that or 3 (mod 6). An STS of order v will sometimes be denoted by .
The Bott Suspension and the Intrinsic Join
Authors: Leise James A.
Published: December 2010

If (G ; U, V) is a triad with G a group we define

where [g, u] = gug-1u-1 is the commutator. CG(U, V) will be called the (left) center of U in G modulo V or in brief a (left) C-space. If G is a topological group it will be understood that the topology on CG(U, V) is the relative topology of G.
Sur Les Anneaux Reflexifs
Authors: Querre J.
Published: December 2010

Un anneau commutatif unitaire est dit réflexif si tous ses idéaux sont divisoriels [3; 6]. On dira qu'un anneau commutatif unitaire et intègre est un anneau de Mori, si ses idéaux divisoriels entiers vérifient la condition de chaîne ascendante [8]. Enfin, on appellera provisoirement, M-anneau, un anneau de Mori, tel que tout idéal engendré par deux éléments est divisoriel. Un anneau noethérien réflexif est un M -anneau; dans la première partie de cette note, nous établissons la réciproque. La troisième partie étudie la clôture intégrale de certains anneaux locaux réflexifs non noethériens.
Characterization of Certain Classes of Spaces With Gδ Points as Open Images of Metric Spaces
Authors: Abernethy Kenneth C.
Published: December 2010

The study of metrization has led to the development of a number of new topological spaces, called generalized metric spaces, within the past fifteen years. For a survey of results in metrization theory involving many of these spaces, the reader is referred to [13]. Quite a few of these generalized metric spaces have been studied extensively, somewhat independently of their role in metrization theorems. Specifically, we refer here to characterizations of these spaces by various workers as images of metric spaces. Results in this area have been obtained by Alexander [2], Arhangel'skii [3], Burke [5], Heath [10], Michael [15], Nagata [16], and the author [1], to mention a few. Later we will recall specifically some of these results.
Entropy and Kinetic Theory for a Confined Gas
Authors: Schnute Jon
Published: December 2010

A well-known theorem in the classical kinetic theory for a gas states that the entropy is an increasing function of time. However, in order to obtain this theorem for a confined gas, some assumption about molecular response to the container wall is required. For example, it is enough to suppose that the wall reflects the molecules specularly [4].
Restricting and Inducing on Inner Products of Representations of Finite Groups
Authors: de B. Robinson G.
Published: December 2010

Of recent years the author has been interested in developing a representation theory of the algebra of representations [5; 6] of a finite group G, and dually of its classes [7]. In this paper Frobenius’ Reciprocity Theorem provides a starting point for the introduction of the inverses R-1 and I-1 of the restricting and inducing operators R and I. The condition under which such inverse operations are available is that the classes of G do not splitin the subgroup Ĝ. When this condition is satisfied the application of these operations to inner products is of interest.
An n + 1 Member Decomposition for Sets Whose Lnc Points Form n Convex Sets
Authors: Breen Marilyn
Published: December 2010

Let S be a subset of Rd. A point x in 5 is a point of local convexity of S if and only if there is some neighborhood N of x such that, if y, z ∈ N ᑎ 5, 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.
Random Fourier Series on Compact Noncommutative Groups
Authors: Picardello Massimo A.
Published: December 2010

1. Let G be a compact group, let I b e a subset of its dual object 𝚪, which, without loss of generality, will be assumed to be a countable subset. Let Di, i ∈ I , be irreducible representations of G of degree di. The Fourier series of a function F in L1(G) is denned by

where
On the Endomorphisms of a Polynomial Ring
Authors: David John
Published: December 2010

This paper arises in the attempt to solve the following problem related to the Zariski Problem. Let A be a polynomial ring in three variables over a field, . Suppose there is a subring B of A such that k ⊆ B and there is variable t over B such that B[t] = A. Then is it true that B is a polynomial ring over k?
Boundaries For Real Banach Algebras
Authors: Limaye B. V.
Published: December 2010

Let A be a commutative real Banach algebra with unit, and MA its maximal ideal space. The existence of the Silov boundary SA for A was established in [5] by resorting to the complexification of A. We give here an intrinsic proof of this result which exhibits the close connection between the absolute values and the real parts of ‘functions’ in A (Theorem 1.3).
Pure Compactifications in Quasi-Primal Varieties
Authors: Taylor Walter
Published: December 2010

We prove that is quasi-primal, then every algebra in HSPhas a pure embedding into a product of finite algebras. For a general theory of varieties for which every can be purely embedded in an equationally compact algebra , and for all notions not explained here, the reader is referred to [38; 6; or 5]. This theorem was known for Boolean algebras simply as a corollary of the Stone representation theorem and the fact that in the variety of Boolean algebras, all embeddings are pure [2].
A Counterexample to a Classification Theorem of Linearly Stable Polytopes
Authors: Assaf David
Published: December 2010

We give an example of a centrally symmetric 5-polytope which is linearly stable though its vertices do not form a subset of the vertices of a 5-cube. This example contradicts the “only if” part of the classification theorem on linearly stable poly topes stated by P. McMullen [2]. Moreover the example gives a 5-polytope, the vertices of which form a subset of a 5-cube while its dual does not possess the same property.
Coding Ergodic Processes to Approximate Bernoulli Processes
Authors: Del Junco A.
Published: December 2010

In [1] Ornstein defined a metric on processes which, for processes (P, τ) and (Q, σ) with equal numbers of atoms, measures how closely the motions of P and Q under r and a, respectively, imitate each other. If we think of (P, τ) and (Q, σ) as stationary stochastic processes, and we assume (P, τ) and (Q, σ) are ergodic, then ((P, τ)(Q, σ)) < α says that with probability one a printout from (P, r) can be changed on a set of integers with density less than a to obtain a printout from (Q, σ).
On Nonstandard Hulls of Convex Spaces
Authors: Bellenot Steven F.
Published: December 2010

A nonstandard hull of a TVS (locally convex topological vector space) is a standard TVS constructed from a nonstandard model for [3]. If the nonstandard hulls of a TVS are independent of the non-standard model, we say that the TVS has invariant nonstandard hulls. This is (for complete spaces) the property that every finite element is inflnitesimally close to a standard point. We build on the work of Henson and Moore [4], to show that invariance of nonstandard hulls is a self dual property equivalent to bounded sets being precompact, for F and DF spaces, (see Theorem 4.4).
On the Fractional Parts of a Polynomial
Authors: Cook R. J.
Published: December 2010

Heilbronn [6] proved that for any ϵ > 0 there exists C(ϵ) such that for any real θ and N ≧ 1 there is an integer x satisfying

where ||α|| denotes the difference between α and the nearest integer, taken positively. Danicic [2] obtained an analogous result for the fractional parts of θxk and in 1967 Davenport [4] generalized Heilbronn's result to polynomials of degree with no constant term. The last condition is essential, for if there is a constant term then no analogous result can hold (see Koksma [7, Kap. 6 SatzlO]).
Divisibility of Direct Sums in Torsion Theories
Authors: Sarath B. , Varadarajan K.
Published: December 2010

Given a hereditary torsion theory on the category Mod R of right R-modules we obtain in this paper necessary and sufficient conditions for the direct sum of a given family of R-modules to be divisible for the torsion theory . Using this criterion we show that if is a family of R-modules having the property that is divisible for every countable subset K ol J then is itself divisible.
A New Approximation Operator Generalizing Meyer-König and Zellers Power Series
Authors: Levikson Benny
Published: December 2010

In this paper we introduce a new approximation operator of the Arato-Renyi type and study its properties. Special cases of our operator are the power-series, of W. Meyer-König and K. Zeller (see [9]) and the generalized Berenstein power series introduced by A. Jakimovski and D. Leviatan in [5] and analyzed by them in [6].
On Prime Immersions of S1 into R2
Authors: Martin John R.
Published: December 2010

A C1-mapping ƒ from the oriented circle S1 into the oriented plane R2 such that f f’ (t) ≠ 0 for all t is called a regular immersion. We call a point p in Im f a double point if f-1(p) is a two element set with the corresponding tangent vectors being linearly independent. A regular immersion which is one-to-one except at a finite number of points whose images are double points is called a normal immersion. The work of Whitney [7], Titus [3] and Verhey [6] shows that the normal immersions form a dense open subset in the space of regular immersions with the usual C1-topology, and can be characterized up to diffeomorphic equivalence by a combinatorial invariant called the intersection sequence.
A General Integral Inequality for the Derivative of an Equimeasurable Rearrangement
Authors: Duff G. F. D.
Published: December 2010

The theory of non-increasing (decreasing) equimeasurable rearrangements of functions was introduced by Hardy and Littlewood [6] in connection with their studies of fractional integrals and integral operators. Elementary properties of equimeasurable decreasing rearrangements are given in the monograph [7] of Hardy, Littlewood, and Polya on inequalities, while a more recent treatment is Okikiolu [9, § 5.4].
Integral Group Rings with Nilpotent Unit Groups
Authors: Polcino Milies César
Published: December 2010

Let R be a ring with unit element and G a finite group. We denote by RG the group ring of the group G over R and by U(RG) the group of units of this group ring.

The study of the nilpotency of U(RG) has been the subject of several papers.
The Algebraic Independence of Certain Exponential Functions
Authors: Dale Brownawell W.
Published: December 2010

In 1897 E. Borel proved a general theorem which implied as a special case the following result equivalent to his celebrated generalization of Picard's theorem [2]: If f1 … ,fm are entire functions such that for each, C then the functions exp f1, … , exp f/m are linearly independent over C. In 1929 R. Nevanlinna [6] extended Borel's theorem to consider arbitrary C-linearly independent meromorphic functions < ϕi, … , < ϕm satisfying < ϕ1 + … + ϕm = 1.
Free Ortholattices
Authors: Bruns Günter
Published: December 2010

It has been known for some time but does not seem to be anywhere in the literature that the variety of all ortholattices is generated by its finite members (see (4.2) of this paper). This is well known to imply that the word problem for free ortholattices is solvable. On the other hand, it is also known that the solution obtained this way is of no practical use. The main purpose of this paper is to present a workable solution.
A Commutativity Condition for Rings
Authors: Bell Howard E.
Published: December 2010

The object of this paper is to prove the following theorem, a special case of which was previously explored in [1].

THEOREM. Let R be any associative ring with the property that

(†) for each x,y ∊ R, there exist integers m,n ≧ I for which xy = ymxn.
A Decomposition Theorem for m-Convex Sets in Rd
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 S, at least one of the line segments determined by these points lies in S. A point x in S is said to be a point of local convexity of S if and only if there is some neighborhood N of x such that if y, z Є N ⌒ S, then [y, z] ⊆ S. If S fails to be locally convex at some point a in S, then q is called a point of local nonconvexity (lnc point) of S.
On Functional Cesàro And Hölder Methods of Summability
Authors: Borwein D. , Shawyer B. L. R.
Published: December 2010

Suppose that f(x) is integrable L in every finite interval [0, X], and that δ > 0. Define
Pure Subfields of Purely Inseparable Field Extensions
Authors: Deveney James K.
Published: December 2010

The notion of pure subgroups is due to Prufer [7]. It has proven extremely useful in establishing structural properties of abelian groups. In a recent paper [9], Waterhouse introduced the concept of a pure subfield of a purely inseparable extension. Let L be a purely inseparable modular extension of k, and let K be an intermediate field. K is called pure if K and k(Lpn) are linearly disjoint over k(Kpn) for all n. Waterhouse used this concept to establish the existence of basic subfields [9].
On the Number of Parity Sets in a Graph
Authors: Little Charles H. C.
Published: December 2010

The graphs considered in this paper are finite and have no loops or multiple edges. If G is such a graph, we denote its vertex set by VG and its edge set by EG. If X and Y are disjoint subsets of VG, we define δ (X, Y) to be the set of edges of G that join a vertex in X to one in Y.