bluuebunny/crossref_metadata_2025 huggingface dataset:
On Some Results in Morse Theory
Authors: Kalmbach Gudrun
Published: December 2010

The /z-cobordism theorem in [8], the generalized Poincaré conjecture in higher dimensions in [20] and several other results in differential topology are proved by using the following theorems of Morse theory:

(1) the elimination of critical points;

(2) the existence of nondegenerate functions for which the descending and ascending bowls have normal intersection;

(3) the alteration of function values at critical points. (For the details see below.)

We shall give short and elementary pr∞fs of these theorems together with some stronger statements than the ones given in [8-13] or [19].

The theorems are proved for noncompact manifolds rather than for compact manifolds since, by a trivial modification of the manifold (deleting the boundary or one point) the case of compact manifolds is included.
Strongly Oscillatory and Nonoscillatory Subspaces of Linear Equations
Authors: Michael Dolan J. , Klaasen Gene A.
Published: December 2010

Consider the nth order linear equation

and particularly the third order equation

A nontrivial solution of (1)n is said to be oscillatory or nonoscillatory depending on whether it has infinitely many or finitely many zeros on [a, ∞). Let denote respectively the set of all solutions, oscillatory solutions, nonoscillatory solutions of (1)n. is an n-dimensional linear space. A subspace is said to be nonoscillatory or strongly oscillatory respectively if every nontrivial solution of is nonoscillatory or oscillatory. If contains both oscillatory and nonoscillatory solutions then is said to be weakly oscillatory.
Deficiencies of Certain Real Uniform Algebras
Authors: Limaye B. V. , Simha R. R.
Published: December 2010

Let U be a complex uniform algebra, Z and dZ its maximal ideal space and its Šilov boundary, respectively. The Dirichlet (respectively Arens-Singer) deficiency of U is the codimension in CR(∂Z) of the closure of Re U (respectively of the real linear span of log|U-1|). Algebras with finite Dirichlet deficiency have many interesting properties, especially when the Arens-Singer deficiency is zero. (See, e.g. [5].) By a real uniform algebra we mean a real commutative Banach algebra A with identity 1, and norm ‖ ‖ such that ‖f2‖ = ‖f‖2 for each fin A
The Characterization of a Lattice Homomorphism
Authors: Kim Jongsik
Published: December 2010

We shall give a simple characterization of a lattice homomorphism from a linear lattice E to a linear lattice F. This paper is motivated by the following two theorems in Kaplan [2] :

If ϕ is a lattice homomorphism, then ϕt(Fb) is an ideal in Eb.

(2) If ϕ is a lattice homomorphism, then ϕtt is a lattice homomorphism from ϕbb into ϕbb.

The main theorem is stated and proved in section 3. In section 1, we shall give notations and in section 2, we shall prove a main lemma. For details, we refer to Vulikh [3].
Multivalent and Meromorphic Functions of Bounded Boundary Rotation
Authors: Leach Ronald J.
Published: December 2010

The classVk(p). We generalize the class Vk of analytic functions of bounded boundary rotation [8] by allowing critical points in the unit disc U.

Definition. Let f(z) = aqzq + . . . (q 1) be analytic in U. Then f(z) belongs to the class Vk(p) if for r sufficiently close to 1,

and

We note that (1.1) implies that / has precisely p — 1 critical points in U.
Boundary and Interior Control for Partial Differential Equations
Authors: Delver Robert
Published: December 2010

From the time that the basic existence and regularity problems for partial differential equations have been solved many interesting new variational and control problems could be studied. In general a differential equation or boundary value problem is used to define a class of admissible functions, and then the problem is that of finding the extrema of a given functional defined on that class of functions.
Non-Free Groups Generated by Two 2 X 2 Matrices
Authors: Brenner J. L. , Macleod R. A. , Olesky D. D.
Published: December 2010

Let m be any real or complex number, and let Gm be the group generated by the 2 X 2 matrices A = (1, m\ 0, 1) and B = (1, 0; m, 1), where we use the notation (C11, C12; c21, C22) to denote (by rows) the elements of a 2 X 2 matrix C. Thus, Gm is the set of all finite products (or words) of the form

… Ah(3)Bh(2)Ah(1)

where the h(i) are nonzero integers with h﹛\) possibly zero. If a non-trivial word of this form equals the identity / = (1, 0; 0, 1), then Gm is non-free; otherwise, Gm is free.
Free Decompositions of a Lattice
Authors: Grätzer G. , Sichler J.
Published: December 2010

Two basic questions have been raised for free products of lattices:

1. Do any two free products have a common refinement?

2. Can every lattice be decomposed into a free product of freely indecomposable lattices?

Both questions have been around for some time and attempts at solving them were made especially after the Structure Theorem for Free Products was discovered (see G. Grâtzer, H. Lasker, and C. R. Piatt [3]). Partial answer to question one was supplied in A. Kostinsky [7].

In this paper we answer both questions. Our basic observation is that the proper framework for these results is the theory of free K-products, that is, free products in an arbitrary equational class K of lattices.
Ultrafunctor
Authors: Magid Andy R.
Published: December 2010

Let G be a functor from commutative rings to abelian groups and let ﹛Rt : i ∈ S﹜ be a family of commutative rings indexed by the set S. Let be an ultrafilter on S, and let denote the ultraproduct of the Rt with respect to . This paper studies the problem of computing from the G(Rj) via the map

The functors studied are Pic = Picard group, Br = Brauer group, U = units, and the functors K0, K1, SK1, K2 of Algebraic K-Theory. For G = Pic, U, K1 and SK1, (*) is always a monomorphism. An example is given to show that even if all the Rt are finite fields the map (*) has a kernel for G = K2.
The Gibbs Phenomenon for Generalized Taylor and Euler Transforms
Authors: Powell Robert E. , Shoop Richard A.
Published: December 2010

Let f be a real-valued function satisfying the Dirichlet conditions in a neighborhood of x = x0, at which point f has a jump discontinuity. If {Sn(x)} is the sequence of partial sums of the Fourier series of f at x, then ﹛Sn(x)﹜ cannot converge uniformly at x — x0. Moreover, for any number , there exists a sequence ﹛tn﹜, where tn → x0 and
Solution Space Decompositions for nth Order Linear Differential Equations
Authors: Gustafson G. B. , Sedziwy S.
Published: December 2010

Consider the wth order scalar ordinary differential equation

with pr ∈ C([0, ∞) → R ) . The purpose of this paper is to establish the following:

DECOMPOSITION THEOREM. The solution space X of (1.1) has a direct sum Decomposition

where M1 and M2 are subspaces of X such that

(1) each solution in M1\﹛0﹜ is nonzero for sufficiently large t ﹛nono sdilatory) ;

(2) each solution in M2 has infinitely many zeros ﹛oscillatory).
Criteria for Groups with Representations of the Second Kind and for Simple Phase Groups
Authors: Van Zanten A. J. , De Vries E.
Published: December 2010

In this paper we consider matrix representations of compact groups over the field of the complex numbers. We shall deal mainly with finite groups.

The Kronecker product of two irreducible representations σ1and σ2of a groupis in general a reducible representation of. The explicit reduction of such a product to irreducible representations σ3can be performed by means of a unitary matrix, the elements of which are called Wigner coefficients or Clebsch-Gordan coefficients [1; 25; 27].
Structure of Rings with Involution Applied to Generalized Polynomial Identities
Authors: Halle Rowen Louis
Published: December 2010

In [14, §4], some theorems were obtained about generalized polynomial identities in rings with involution, but the statements had to be weakened somewhat because a structure theory of rings with involution had not yet been developed sufficiently to permit proofs to utilize enough properties of rings with involution. In this paper, such a theory is developed. The key concept is that of the central closure of a ring with involution, given in § 1, shown to have properties analogous to the central closure of a ring without involution. In § 2, the theory of primitive rings with involution, first set forth by Baxter-Martindale [5], is pushed forward, to enable a setting of generalized identities in rings with involution which can parallel the non-involutory situation.
Immersions with Semi-Definite Second Fundamental Forms
Authors: Jonker Leo B.
Published: December 2010

Let M be a. complete connected Riemannian manifold of dimension n and let £:M → Rn+k be an isometric immersion into the Euclidean space Rn+k. Let ∇ be the connection on Mn and let be the Euclidean connection on Rn+k. Also let

denote the second fundamental form B(X, Y) = (xY)→. Here TP(M) denotes the tangent space at p, NP(M) the normal space and (…)→ the normal component.
Planar Lattices
Authors: Kelly David , Rival Ivan
Published: December 2010

A finite partially ordered set (poset) P is customarily represented by drawing a small circle for each point, with a lower than b whenever a < b in P, and drawing a straight line segment from a to b whenever a is covered by b in P (see, for example, G. Birkhoff [2, p. 4]). A poset P is planar if such a diagram can be drawn for P in which none of the straight line segments intersect.
Maximal Pre-Primal Clusters
Authors: Froemke Jon
Published: December 2010

A number of unsolved problems of primal algebra theory concern the existence of certain collections of dependent primal algebras. In [3] E. S. O'Keefe showed that any collection of pairwise non-isomorphic primal algebras of type {n} with n > 1 forms a primal cluster. Recently the author has discovered that if τ is any type containing at least two elements, one of which is > 1, then there are at least two non-isomorphic dependent primal algebras of type τ, except possibly in the case = {2, 0}; this result will appear later.
Homeomorphisms on the Solid Double Torus
Authors: Myers Donald
Published: December 2010

A finite set of generators for the isotopy classes of selfhomeomorphisms of closed surfaces was given by Lickorish in three papers [2; 3; 4]. In [5] the group of isotopy classes for a particular, well-known cube with holes was presented. There the structure was “tight” enough to allow the computation of the relators as well as the generators. In this paper we give a finite set of generators for the group of isotopy classes of self-homeomorphisms on the solid double torus, the cube with two handles. Let us remark that the group of isotopy classes for the solid torus is well-known.
Racine Minimum D'un Groupe Elementaire Abelien
Authors: Dez Mikhail
Published: December 2010

Soit L un groupe abélien élémentaire d'ordre pn (p est un premier, n est un entier positif). Soient (a) le groupe cyclique d'élément a ∈ L, \A\\e nombre des éléments de l'ensemble A ᑕ L. Nous appellerons l'ensemble B ᑕ L racine du groupe L si pour tout a, {0} 9 ≠ a ∈ L, il existe b1, b2 ∈ B (b1 ≠ b2) tels que b 1 b2 ∈ (a). (A ce propos, il est évident que si B est une racine de L, l'ensemble Bst* = {bi* = sbi + t/bi ∈ B}, où sont donnés s, t ∈ L, (s) ≠ (0), (c'est-à-dire Bst* est le résultat de l'affinité de B) est également racine de L.) Nous appellerons la racine B minimum et désignerons |B| par β (L) si tout autre racine contient au minimum |B| éléments. Voici les exemples de racines minimum du L pour L = F2n, n = 1, 2, 3, 4, 5 et pour L = F33:
Some Explicit Generators for SL(3, 3n), SU(3, 3n), Sp(4,3n) and SL(4, 3n)
Authors: Ho C. Y.
Published: December 2010

This is a generalization of the results in [3, § 5]. Some of the proofs presented here are actually the original proofs presented in [3]. Although we can find alternate proofs in the case p = 3, since [3] will not be published for a while yet, we feel that it is worthwhile to present the proof in [3] whenever it carries over in the case p = 3. The results in this paper will be used in the investigation of the quadratic pairs for the prime 3.
A Pointwise Ergodic Theorem in Lp-Spaces
Authors: Akcoglu M. A.
Published: December 2010

Let be a measure space and the usual Banach spaces. A linear operator T : Lp → Lpis called a positive contraction if it transforms non-negative functions into non-negative functions and if its norm is not more than one. The purpose of this note is to show that if 1 < p < ∞ and if T : Lp → Lp is a positive contraction then
Interpolation in Separable Frechet Spaces with Applications to Spaces of Analytic Functions
Authors: Gauthier Paul M. , Rubel Lee A.
Published: December 2010

Let E be a separable Fréchet space, and let E* be its topological dual space. We recall that a Fréchet space is, by definition, a complete metrizable locally convex topological vector space. A sequence {Ln} of continuous linear functional is said to be interpolating if for every sequence {An} of complex numbers, there exists an ƒ ∈ E such that Ln(ƒ) = An for n = 1, 2, 3, … . In this paper, we give necessary and sufficient conditions that {Ln} be an interpolating sequence. They are different from the conditions in [2] and don't seem to be easily interderivable with them.
Structure of a Certain Class of Rings with Involution
Authors: Chacron M. , Herstein I. N. , Montgomery S.
Published: December 2010

Let R be a ring with involution *, and let Z denote the center of R. In R let S = {x ∈ R|x* = x} be the set of symmetric elements of R. We shall study rings which are conditioned in the following way: given s ∈ S, then for some integer and some polynomial p(t), with integer coefficients which depend on . What can one hope to say about such rings? Certainly all rings in which every symmetric element is nilpotent fall into this class.
Subregular Spreads and Indicator Sets
Authors: Bruen A.
Published: December 2010

In a previous paper [3] we introduced indicator sets in order to facilitate the study of partial spreads and spreads in ∑ = PG(3, q). The idea enabled us to disprove a conjecture in the literature by constructing a spread that contained no regulus. More recently there have been some notable advances in the theory of spreads. One such advance is Denniston's theorem that packings of spreads always exist in ∑. This result can be very nicely interpreted in terms of indicator sets [1], Another notable advance is the result on subregular spreads due to W. F. Orr [4; 5] which is discussed below. In this note we develop further some ideas on indicator sets in [3] and then use these results to give an alternative proof of this result of Orr.
Equidistribution Des Valeurs Dune Application Holomorphe Generique a Valeurs Dans L'Espace Projectif
Authors: Gauthier P. M.
Published: December 2010

Un exemple de Fatou-Bieberbach [1, p. 45] montre qu'il existe des applications holomorphes

h:Cn → Cn

à Jacobien J(h) partout non nul, mais dont le complémentaire de l'image Cn\h(Cn) est un fermé à intérieur non vide. Néanmoins on a montré récemment [3; 5] qu'une application holomorphe générique de Cn dans Cn est surjective. Nous voulons montrer qu'il en est de même pour les applications prennant leurs valeurs dans l'espace projectif Pn.
Faithful Representations of Finitely Generated Metabelian Groups
Authors: Wehrfritz B. A. F.
Published: December 2010

In [3] Remeslennikov proves that a finitely generated metabelian group G has a faithful representation of finite degree over some field F of characteristic zero (respectively, p > 0) if its derived group G’ is torsion-free (respectively, of exponent p). By the Lie-Kolchin-Mal'cev theorem any metabelian subgroup of GL(n, F) has a subgroup of finite index whose derived group is torsion-free if char F = 0 and is a p-group of finite exponent if char F = p > 0. Moreover every finite extension of a group with a faithful representation (of finite degree) has a faithful representation over the same field. Thus Remeslennikov's results have a gap which we propose here to fill.
Uniform And Tangential Approximations By Meromorphic Functions on Closed Sets
Authors: Roth Alice
Published: December 2010

Let G be an (open) domain in the finite complex plane and F a relatively closed proper subset of G. We denote by M(G) the set of functions meromorphic on G and as usual by R(K) (for a compact set K) the set of uniform limits of rational functions without poles on K.
On Translation Planes with Affine Central Collineations, II
Authors: Johnson Norman L. , Kallaher Michael J.
Published: December 2010

This article, as the name implies, is a continuation of [9]. In that article the second author investigates finite translation planes containing both affine dations and affine homologies. (See the beginning of Section 2 for definitions.) Such translation planes are called Ei7-planes. In [9] the author restricted himself to translation planes of characteristic p ≧ 5. The main reasons for this were that Ostrom's and Hering's theorem [13;4] on affine dations excluded the case p = 3 and the conclusions were easier to interpret geometrically when p ≧ 5 (as opposed to the case p = 2). Since then Ostrom [17] has settled the case p = 3.
An Induction Theorem for Rearrangements
Authors: Chong Kong-Ming
Published: December 2010

In this paper, an induction theorem for rearrangements involving w-tuples in Rn is proved, showing that a certain proposition regarding a pair of w-tuples related by the weak spectral order ≪ is true for any integer n ≧ 2 if and only if it is true for n = 2. This theorem contains as particular cases a well-known theorem of Hardy-Littlewood-Pólya [4, Lemma 2, p. 47], a theorem of Pólya [8], a theorem of Rado [9, pp. 1-2], two theorems of Mirsky [6, Theorem 2, p. 232; 7, Theorem 4, p. 90], a result given in [1, Corollary 2.4, p. 1333] and also [2, Proposition 2.1, p. 439].
Classification of Restricted Linear Spaces
Authors: Totte Jim
Published: December 2010

The material in this paper is taken from the author's doctoral dissertation [2]. We will use the terminology and notation of [3]. Let us recall those terms which will be needed here.

We define a restricted linear space (RLS) as a finite set of p elements, called points, of which q subsets, called lines, are distinguished so that the following axioms hold:

(RLS-1) Any two distinct points u, v belong to exactly one common line uv.
Characterizations of the Generalized Hughes Planes
Authors: Lüneburg Heinz
Published: December 2010

Let be a projective plane and a subplane of . If l is a line of , we let denote the group of all elations in that have as axis and leave Q invariant. In [12, p. 921], Ostrom asked for a description of all finite planes that have a Baer subplane with the property that for all lines l of . Here denotes the order of G. Both the desarguesian planes of square order and the generalized Hughes planes have this property (Hughes [10], Ostrom [14], Dembowski [6]). One of the aims of this paper is to show that these are the only planes having such a Baer subplane.
Canonically Isomorphic Spaces of Bounded Solutions of △u = Pu
Authors: Glasner Moses
Published: December 2010

Let R be a hyperbolic Riemann surface and P, Q nonnegative C1 2-forms on R. The space of bounded solutions of △u = Pu (△u = Qu, respectively) on R is denoted by PB(R) (QB(R), respectively). A vector space isomorphism S between PB(R) and QB(R) is called canonical if for each u ϵ PB(R), there is a potential pu on R with \u — Su\ ≦ pu. The canonical isomorphism theme in the study of the equation △u = Pu was introduced in H. Royden's paper [9] on the order comparison condition.
A Generalization of Lyndon's Theorem on the Cohomology of One-Relator Groups
Authors: Gildenhuys D.
Published: December 2010

In this paper we generalize a theorem of Lyndon's [7], which states that a one-relator group G = F/(r) (F is free and r Ç F) has cohomological dimension cd (F/(r)) ≧ 2 if and only if the relator r is not a proper power in F. His proof relies on the Identity Theorem and recently he has shown [8] how a generalized version of this theorem and a generalized version of the Freiheitsatz can be simultaneously obtained by the methods of combinatorial geometry. These generalizations refer to a situation where the free group F is replaced by a free product of subgroups of the additive group of real numbers.
Fuchsian Subgroups of the Picard Group
Authors: Fine Benjamin
Published: December 2010

The Picard group Γ = PSL2 (Z(i)) is the group of linear transformations

with a, b, c, d Gaussian integers.

Γ is of interest both as an abstract group and in automorphic function theory [10]. In [10] Waldinger constructed a subgroup H of finite index which is a generalized free product, while in [1] Fine showed that T is a semidirect product with the subgroup H, contained as a subgroup of finite index in the normal factor.
Continuous Boundary Values of Holomorphic Functions on Kähler Domains
Authors: Weinstock Barnet M.
Published: December 2010

LetMbe a complex manifold of dimensionnwhich admits a Kähler metric, and letDbe a relatively compact domain onMwhose boundaryBis a C ∞ submanifold ofMof real codimension one. The object of this paper is to use the potential theory associated with the Laplace-Beltrami operator onMto characterize the continuous functions onBwhich have holomorphic extensions toD.
On the Groups of Britton's Theorem A
Authors: Sacerdote George S.
Published: December 2010

In his simple proof of the unsolvability of the word problem for groups [1], J. L. Britton proved a normal form theorem (Britton's Lemma) for groups obtained by the HNN construction. In the appendix to that paper he described a generalization of the HNN construction and sketched the proof of a generalization of Britton's Lemma for this new construction, Britton's Theorem A. In this note we demonstrate that all groups obtained by means of this generalized construction are in fact HNN groups; and it will follow that Theorem A is simply a restatement of Britton's Lemma. This argument makes it clear that while Theorem A can be (and has been) useful in various group theoretic situations, in practice, every application of this generalized construction can be replaced by a straightforward application of the HNN construction.
Systemes Faibles de Tchebycheff et Polynomes de Bernstein
Authors: Bastien Richard , Dubuc Serge
Published: December 2010

Nous allons montrer que tout système faible de Tchebycheff est voisin d'un système de Tchebycheff. Ce fait permet de prolonger aux systèmes faibles de Tchebycheff plusieurs résultats valides pour les systèmes de Tchebycheff, tels le théorème d'alternance et le théorème de de la Vallée- Poussin qui sont reliés au problème de la meilleure approximation uniforme par une fonction d'un système de Tchebycheff. Il arrive que certaines classes de fonctions splines forment un système faible de Tchebycheff. Pour ces classes, on pourra donc caractériser les meilleures approximations par des propriétés d'alternance de l'écart à la fonction à approcher.
Transitivity Properties of Fuchsian Groups
Authors: Nicholls Peter J.
Published: December 2010

A Fuchsian group G is a discrete group of fractional linear transforms each of which preserve a disc (or half plane). We consider only groups which preserve the unit disc Δ = {z: |z| < 1} and none of whose transforms, except the identity, fix infinity (any Fuchsian group is conjugate to such a group).
Transformations With Discrete Spectrum are Stacking Transformations
Authors: Del Junco Andrés
Published: December 2010

The stacking method (see [1] and [5, Section 6]) has been used with great success in ergodic theory to construct a wide variety of examples of ergodic transformations (see, for example, [1 ; 3 ; 4; 5; 7]). However very little is known in general about the class of transformations which can be constructed by the stacking method using single stacks. In particular there is no simple characterization of the class .
Purity And Copurity in Systems of Linear Transformations
Authors: Zorzitto Frank
Published: December 2010

Consider a system of N linear transformations A1, … , AN: V → W, where F and IF are complex vector spaces. Denote it for short by (F, W). A pair of subspaces X ⊂ V, Y ⊂ W such that determines a subsystem (X, Y) and a quotient system (V/X, W/Y) (with the induced transformations). The subsystem (X, Y) is of finite codimension in (V, W) if and only if V/X and W / Y are finite-dimensional. It is a direct summand of (V, W) in case there exist supplementary subspaces P of X in F and Q of F in IF such that (P, Q) is a subsystem.
Some Fixed Point Theorems for Partially Ordered Sets
Authors: Höft Hartmut , Höft Margret
Published: December 2010

A partially ordered set P has the fixed point property if every order-preserving map f : P → P has a fixed point, i.e. there exists x ∊ P such that f(x) = x. A. Tarski's classical result (see [4]), that every complete lattice has the fixed point property, is based on the following two properties of a complete lattice P:

(A)

For every order-preserving map f : P → P there exists x ∊ P such that x ≦ f(x).

(B)

Suprema of subsets of P exist; in particular, the supremum of the set {x|x ≦ f(x)} ⊂ P exists.
On Jordan Structure in Semiprime Rings
Authors: Awtar Ram
Published: December 2010

A remarkable theorem of Herstein [1, Theorem 2] of which we have made several uses states: If R is a semiprime ring of characteristic different from 2 and if U is both a Lie ideal and a subring of R then either U ⊂ Z (the centre of R) or U contains a nonzero ideal of R. In a recent paper [3] Herstein extends the above mentioned result significantly and has proved that if R is a semiprime ring of characteristic different from 2 and V is an additive subgroup of R such that [V, U] ⊂ V, where U is a Lie ideal of R, then either [V, U] = 0 or V ⊃ [M, R] ≠ 0 where M is an ideal of R. In this paper our object is to prove the following.
A Simple Proof of the Maximal Ergodic Theorem
Authors: La Torre Alberto De
Published: December 2010

Let X be a σ-finite measure space and let Tk, k any integer, be a group of positive linear transformations in Lp(X) such that

with C independent of / and k. From now on / will be a positive function in Lp(X) and we will use the following notation:
Compatible Tight Riesz Orders on the Group of Automorphisms of an 0-2-Homogeneous Set
Authors: Davis Gary , Fox Colin D.
Published: December 2010

Davis and Bolz (1974) considered, and to some extent classified, compatible tight Riesz order on the group of all order-preserving permutations of a totally ordered field. Glass (1976) carried out a more general study of compatible tight Riesz orders on ordered permutation groups and, in particular, showed the importance of determining compatible tight Riesz orders on O-primitive ordered permutation groups. However, the general problems of existence and classification of compatible tight Riesz orders on O-primitive ordered permutation groups remained open.
Finite Dimensional Perturbations of Differential Expressions
Authors: Kemp R. R. D. , Lee S. J.
Published: December 2010

Operators in L2, or more generally, Lp spaces, which are generated by differential expressions, have had extensive study. More recently some authors, in particular Krall [3; 4; 5; 6; 7], Kim [2], and Krall and Brown [8], have studied operators which are generated by a differential expression plus an additional term. This additional term is of the nature of a perturbation of the differential expression by an operator with finite dimensional range. However even if the basic operator is specifically of the form of a finite dimensional perturbation of a differential operator, this is not true of the adjoint, since the boundary conditions which arise on the adjoint are not appropriate to the adjoint of the differential operator alone.
Semiregular Modules and Rings
Authors: Nicholson W. K.
Published: December 2010

Mares [9] has called a projective module semiperfect if every homomorphic image has a projective cover and has shown that many of the properties of semiperfect rings can be extended to these modules. More recently Zelmanowitz [16] has called a module regular if every finitely generated submodule is a projective direct summand. In the present paper a class of semiregular modules is introduced which contains all regular and all semiperfect modules. Several characterizations of these modules are given and a structure theorem is proved. In addition several theorems about regular and semiperfect modules are extended.
Fixed Point Theorem for Positive Operators on KB Spaces
Authors: Fai Lam Ling
Published: December 2010

The existence of nonzero fixed points of positive contractions inL1spaces has received considerable attention in recent years. In 1966, Dean and Sucheston [1] and independently, Neveu [5] showed that a positive contraction has a strictly positive invariant function if and only iffor any measurable subsetAwith positive measure, where 1 is the constant function of value one.
Systems of Magic Latin k-Cubes
Authors: Arkin Joseph , Hoggatt Verner E. , Straus E. G.
Published: December 2010

A Latin K-cube A of order n is a k-dimensional array where

runs through the distinct elements 0, 1, …, n — 1 as j runs from 0 to n — 1.
Weak Sequential Compactness and Completeness in Riesz Spaces
Authors: Burkinshaw Owen , Dodds Peter
Published: December 2010

If L is an Archimedean Riesz space and M an ideal in the order dual of L, the subset A of L is called M-equicontinuous if and only if each monotone decreasing sequence of positive elements of M is uniformly Cauchy on A.
Quasigraphs
Authors: Lane Norman D. , Scherk Peter , Turgeon Jean M.
Published: December 2010

In the study of direct differential geometry, families of oriented arcs and curves have been employed extensively to define the differentiability of an arc at a point in various kinds of planes; cf. [2]. In [6], P. Scherk used lines in the projective plane; in [3] and [4], N. D. Lane and P. Scherk used circles in the conformai plane; conic-sections in the projective plane were employed in [5] and [7] by N. D. Lane and K. D. Singh; in [1], M. Gupta and N. D. Lane used the graphs of polynomials of degree at most n in the affine plane.
Sur Les Groupes Quasi-Purs-Projectifs Torsions
Authors: Benabdallah Khalid , Bradley Robert
Published: December 2010

Dans ce travail, nous établissons une caractérisation complète des groupes quasi-purs-projectifs torsions résolvant ainsi le problème 17 de L. Fuchs dans le cas important des groupes torsions. Les groupes quasi-purs-injectifs ont été caractérisés dans le cas torsion par K. Benabdallah et A. Laroche dans [1].
Indicator Sets, Reguli, and a New Class of Spreads
Authors: Sherk F. A. , Pabst Günther
Published: December 2010

Let Σ be the projective 3-space over the field GF(q) where q = pe, p an odd prime. A spread W in ∑ is a set of q2 + 1 lines in ∑ which are such that each point of Σ lies on exactly one line of W. Thus the lines of W are all mutually skew. The notion of a spread extends to higher dimensions and also applies for arbitrary fields [1; 3; 6, p. 29; 7, p. 5]. Our concern, however, will be within the narrower but still extensive bounds indicated.
On Rational Approximation on the Positive Real Axis
Authors: Rahman Q. I. , Schmeisser G.
Published: December 2010

In their study of the uniform approximation of the reciprocal of e2 by reciprocals of polynomials on the positive real axis, Cody, Meinardus, and Varga [3] showed that if denotes the class of all polynomials of degree at most n and

then
On the Calkin Algebra and the Covering Homotopy Property, II
Authors: Conway John B.
Published: December 2010

For a separable Hilbert space is the algebra of bounded linear operators on is the ideal of compact operators, and Π is the natural map of onto the Calkin algebra .
Strict Topology on Paracompact Locally Compact Spaces
Authors: Singh Khurana Surjit
Published: December 2010

In this paper, X denotes a Hausdorff paracompact locally compact space, E a Hausdorff locally convex space over K, the field of real or complex numbers (we call the elements of K scalars), a filtering upwards family of semi-norms on E generating the topology of E, Cb(X) the space of all continuous scalar-valued funcions on X, and Cb(X, E) the space of all continuous, bounded E-valued functions.
Some New Replaceable Translation Nets
Authors: Bruen A. A.
Published: December 2010

We discuss partial spreads (translation nets) U, V of ∑ = PG(3, q) where U, V cover the same points of ∑ and have no lines in common. Write t = |U| = |V|. It has been shown in a previous paper [4] that t ≧ 2(g — 1) provided q + 4.
Automorphism Groups of Denumerable Boolean Algebras
Authors: Mckenzie Ralph
Published: December 2010

We are concerned with the extent to which the structure of a Boolean algebra (or BA, for brevity) is reflected in its group of automorphisms, Aut . In particular, for which algebras can one conclude that if Aut Aut , then Monk has conjectured [3] that this implication holds for denumerable BA's with at least one atom. We shall refute his conjecture, but show that the implication does hold if and are denumerable, if each has at least one atom, and if the sum of the atoms exists in . In fact, under those assumptions the algebra 21 can be rather neatly recovered from its abstract automorphism group.
Quasi-P-Pure-Injective Groups
Authors: Benabdallah Khalid , Laroche Adele
Published: December 2010

Recently, a great deal of attention has been paid to the concept of quasipure injectivity introduced by L. Fuchs as Problem 17 in [5]. An abelian group G is said to be quasi-pure-injective (q.p.i.) if every homomorphism from a pure subgroup of G to G can be lifted to an endomorphism of G. D. M. Arnold, B. O'Brien and J. D. Reid have succeeded in [1] to characterize torsion free q.p.i. of finite rank, whereas in [2] we solved the torsion case and in [3] we studied certain classes of infinite rank torsion free q.p.i. groups.
Homomorphisms from S(X) into S(Y)
Authors: Magill Kenneth D.
Published: December 2010

S(X) is the semigroup under composition of all continuous selfmaps of the topological space X. For certain spaces X and Y we classify completely the homomorphisms from S(X) into S(Y). An application of the main result to S(I) the semigroup of all continuous selfmaps of the closed unit interval I results in the solution of a problem which was suggested in the closing paragraph of [6].
Compatible Tight Riesz Orders on the Group of Automorphisms of an 0-2-Homogeneous Set: Addendum
Authors: Davis Gary , Fox Colin D.
Published: December 2010

The purpose of this note is to show that Theorem 8 of Davis and Fox [1] is sharp. That is, we show that the following result is valid.

THEOREM. Let Ω be an 0-2-homogeneous ordered set. Then Tρ(respectively, Tƛ ) is a maximal compatible tight Riesz order if and only if Ω has a countable cofinal(respectively, coinitial) subset.
A Characterization of Starshaped Sets
Authors: Chan Stanek Jean
Published: December 2010

In 1946 Krasnoselskii proved that if every n + 1 points of a compact connected set S in a Euclidean space En can see at least one point of S via S then S is starshaped [1]. This result was expanded by Robkin in 1965 [2]. In this paper, we characterize starshaped sets in En by a local arcwise convexity property relative to a point p.
Rice Theorems for ∑n-1 Sets
Authors: Johnson Nancy
Published: December 2010

In [3] Hay proves generalizations of Rice's Theorem and the Rice-Shapiro Theorem for differences of recursively enumerable sets (d.r.e. sets). The original Rice Theorem [5, p. 3G4, Corollary B] says that the index set of a class C of r.e. sets is recursive if and only if C is empty or C contains all r.e. sets. The Rice-Shapiro Theorem conjectured by Rice [5] and proved independently by McNaughton, Shapiro, and Myhill [4] says that the index set of a class C of r.e. sets is r.e. if and only if C is empty or C consists of all r.e. sets which extend some element of a canonically enumerable class of finite sets. Since a d.r.e. set is a difference of r.e. sets, a d.r.e. set has an index associated with it, namely, the pair of indices of the r.e. sets of which it is the difference.
On the Distribution Modulo 1 of the Sequence αn2 + βn
Authors: Schmidt Wolfgang M.
Published: December 2010

Dirichlet's Theorem says that for any real α and for N ≧ 1, there exists a natural n ≦ N with

where || || denotes the distance to the nearest integer. Heilbronn [2], improving estimates of Vinogradov [3], showed that for α, N as above and for ϵ ≧ 0, there exists an n ≦ N with
On Some Classes of Primary Banach Spaces
Authors: Casazza P. G. , Kottman C. A. , Lin Bor-Luh
Published: December 2010

A Banach spaceXis calledprimary(respectively,prime)if for every (bounded linear) projectionPonXeitherPXor (I—P)X(respectively,PXwith dimPX =∞ ) is isomorphic toX.It is well-known that C0andlp, 1 ≦p≦ ∞ [8;14] are prime. However, it is unknown whether there are other prime Banach spaces. For a discussion on prime and primary Banach spaces, we refer the reader to [9].
Witts Theorem for Quadratic Forms Over Non-Dyadic Discrete Valuation Rings
Authors: Mordecai Cohen David
Published: December 2010

Let R be a discrete valuation ring, with maximal ideal pR, such that ½ ϵ R. Let L be a finitely generated R-module and B : L × L → R a non-degenerate symmetric bilinear form. The module L is called a quadratic module. For notational convenience we shall write xy = B(x, y). Let O(L) be the group of isometries, i.e. all R-linear isomorphisms φ : L → L such that B((φ(x), (φ(y)) = B(x, y).
Decomposition Based Generating Functions for Sequences
Authors: Jackson D. M. , Aleliunas R.
Published: December 2010

Numerous combinatorial enumeration problems may be reduced to equivalent problems of enumerating sequences with prescribed restrictions. For example, the expression, given by Tutte [38], for the number of planar maps may be derived (see Cori and Richard [12]) by essentially a sequence enumeration technique. The correspondence between a set of configurations which are to be enumerated and an appropriate set of sequences is often complicated. Indeed, the existence of such a correspondence has occasionally only been discovered fortuitously by observing the equality of two counting series (see, for example, Klarner [25]).
On Characterizing Injective Sheaves
Authors: Dobbs David E.
Published: December 2010

LetTbe a Grothendieck topology, Ab the category of abelian groups, and. the category of Ab-valued sheaves onT.It is known that is an abelianA B5category with a set of generators [2, Theorem 1.6(i), p. 30] and, hence, has injective envelopes [10, Theorem 3.2, p. 89]. Consider an objectFof.
Simple Proofs of Some Theorems on High Degrees of Unsolvability
Authors: Jockusch Carl G.
Published: December 2010

If a is a degree of unsolvability, a is called high if a ≦ 0’ and a’ = 0”. In [1], S. B. Cooper showed that if a is high, then (i) a is not a minimal degree, and (ii) there is a minimal degree b < a. We give new proofs of these results which avoid the intricate priority and recursive approximation arguments of [1] in favor of “oracle” constructions using the recursion theorem. Also our constructions apply to degrees a which are not below 0'. Call a degree ageneralized high if a’ = (a U 0')' . Among the degrees ≦ 0', the generalized high degrees obviously coincide with the high degrees.
A Note on a Comparison Result for Elliptic Equations
Authors: Allegretto W.
Published: December 2010

In a recent paper [2], Bushard established and applied a comparison theorem for positive solutions to the equation:

in an arbitrary bounded domain D of Euclidean w-space Rn. The proof of these results depended on the absence of mixed derivatives of u in the equation considered.
Monocoreflective Subcategories in General Topology
Authors: Grant Woods R.
Published: December 2010

Let be a full subcategory of a category is said to be coreflective in if for each object X in there exists an object X in and a morphism such that for each object P in and each morphism f : P ⟶ X there exists a unique morphism such that .
Filter Adjunction of Spaces and Compactifications
Authors: Harris Douglas
Published: December 2010

The problem of describing the T1 compactifications of a given T1 space arises quite naturally in many contexts, and has been approached from a number of directions. One characteristic of all approaches has been the exclusive consideration of strict topological extensions. There are obvious advantages to this approach. Points of the compactification may be distinguished by their trace filters, and the topology of the compactification is readily described in a natural manner. Moreover every T2 compactification is strict, so the method loses no generality in this most important special case.
Some Good Sequences of Interpolatory Polynomials: Addendum
Authors: Freud G. , Sharma A.
Published: December 2010

In 1974 [2] we used the n + 2 zeros of (1 - x2)Pn(α, β)(x), α, β > — 1, where Pn(α, β)(x) denotes Jacobi polynomials, to construct a sequence of linear operators {An(α, β)(f, x)} which has the following properties:

(i) An(α, β)(f, x) is a linear polynomial operator mapping C[— 1, 1] into polynomials of degree ≦ n(1 + c), (c > 0 fixed but arbitrary)
Integral Representations and Complete Monotonicity of Various Quotients of Bessel Functions
Authors: Ismail Mourad E. H.
Published: December 2010

Complete monotonicity of functions, Definition 3.1, is often proved by showing that their inverse Laplace transforms are nonnegative. There are relatively few simple functions whose inverse Laplace transforms can be expressed in terms of standard higher transcendental functions. Inverting a Laplace transform involves integrating a complex-valued function over a vertical line, and establishing the positivity of the resulting integral can be tricky. Sometimes asymptotic methods are helpful, see for example Fields and Ismail [6].
Quasicyclic Subnormal Semigroups
Authors: Frankfurt Richard
Published: December 2010

Let T(s), s ≧ 0, be a strongly continuous semigroup of bounded operators on a separable Hilbert space . T(s) is said to be quasicyclic if there is a continuum of vectors such that T(s)xt = xs+t for all s, t > 0 and
Shimura Varieties and the Selberg Trace Formula
Authors: Langlands R. P.
Published: December 2010

This paper is a report on work in progress rather than a description of theorems which have attained their final form. The results I shall describe are part of an attempt to continue to higher dimensions the study of the relation between the Hasse-Weil zeta-functions of Shimura varieties and the Euler products associated to automorphic forms, which was initiated by Eichler, and extensively developed by Shimura for the varieties of dimension one bearing his name. The method used has its origins in an idea of Sato, which was exploited by Ihara for the Shimura varieties associated to GL(2).
Covering Linkage Invariants
Authors: Hartley Richard , Murasugi Kunio
Published: December 2010

Let K be a knot in a manifold M. Corresponding to a representation of Π1(M — K) into a transitive group of permutations there is a branched covering space of M. K is covered by which may be a link of several components. The set of linking numbers between the various components of has long been recognised as a useful knot invariant. Bankwitz and Schumann used this invariant in considering dihedral coverings of Viergeflechte.
Invariant Subrings in Rings with Involution
Authors: Lanski Charles
Published: December 2010

The purpose of this paper is to consider, in rings with involution, the
structure of those subrings which are invariant under Lie commutation with
[K, K]. Our goal is to find conditions which force
such subrings to contain a noncentral ideal of the ring. Of course, the subring
itself may lie in the center. Orders in 4 × 4 matrix rings over fields are known
to provide examples of invariant subrings which are not central and contain no
ideal (see [1, 40] or
[5]). Except for subdirect products of these two kinds
of “counter-examples”, we show that in semi-prime rings, invariant subrings do
contain noncentral ideals. This generalizes work of Herstein
[4] in two directions by considering semi-prime rings
rather than simple rings, and by using [K, K] instead
of K.
A Note on Subnormal Subgroups of Division Algebras
Authors: Greenfield Gary R.
Published: December 2010

Let D be a division algebra and let
D* denote the multiplicative group of nonzero
elements of D. In [3] Herstein
and Scott asked whether any subnormal subgroup of D*
must be normal in D*. Our purpose here is to show that
division algebras over certain p-local fields do not
satisfy such a “subnormal property”.
Real Interpolation of Sobolev Spaces on Subdomains of Rn
Authors: Adams R. A. , Fournier J. J. F.
Published: December 2010

The real interpolation method is a very convenient tool in the study of
imbedding relationships among Sobolev spaces and some of their fractional order
generalizations, (Besov spaces, Nikolskii spaces etc.) Central to the application
of these methods is the a priori determination that a
given Sobolev space
Wk'p(Ω)
belongs to an appropriate class of spaces intermediate between two other “extreme”
spaces.
Countably Compact Spaces and Martin's Axiom
Authors: Weiss William
Published: December 2010

The relationship between compact and countably compact topological spaces has
been studied by many topologists. In particular an important question is: “What
conditions will make a countably compact space compact?” Conditions which are
“covering axioms” have been extensively studied. The best results of this type
appear in [19]. We wish to examine countably compact spaces
which are separable or perfectly normal. Recall that a space is
perfect if and only if every closed subset is a
Gδ, and that a space is
perfectly normal if and only if it is both perfect
and normal. We show that the following statement follows from MA +┐ CH and thus is
consistent with the usual axioms of set theory: Every countably compact perfectly
normal space is compact. This result is Theorem 3 and can be understood without
reading much of what goes before.
Dimension of Null Spaces with Applications to Group Rings
Authors: Promislow David
Published: December 2010

In this paper we investigate methods for estimating the dimension of the null
space of operators in a finite W* algebra, the
dimension being measured by the trace τ. For the most part we are concerned with
operators A which are a finite linear combination of
orthogonal unitaries. We give various results which show how certain information
about the unitaries and the coefficients can be utilized to derive an upper bound
for τ(N

A
) where NA
is the null space of A.
On Some Classes of Univalent Polynomials
Authors: Rahman Q. I. , Szynal J.
Published: December 2010

It was in the year 1931 that Dieudonné [4] proved the
following necessary and sufficient condition for a polynomial to be univalent in
the unit disk.

THEOREM A (Dieudonné criterion). The polynomial

is univalent in |z| < 1 if and only if for every θ in [0, π/2] the
associated polynomial

does not vanish in |z| < 1. For θ = 0, ϕ(z, θ) is to be interpreted as
Pn'(z).
Structure Results for Function Lattices
Authors: Duffus D. , Jónsson B. , Rival I.
Published: December 2010

For partially ordered sets X and F let
Yx
denote the set of all order-preserving maps of
X to Y partially ordered
by f ≦ g if and only if
f(x)≦ g (x) for each
x ∈ X
[1; 4; 6].
If X is unordered then
Yx
is the usual direct product of partially ordered sets, while if
both X and Y are finite
unordered sets then Yx
is the commonplace exponent of cardinal numbers. This generalized
exponentiation has an important vindication especially for those partially ordered
sets that are lattices.
Cosine Representations of Abelian *-Semigroups and Generalized Cosine Operator
Functions
Authors: Faulkner G. D. , Shonkwiler R. W.
Published: December 2010

In the following R will denote the real numbers, for a
Hilbert space H, B(H) and
L(H) will denote the
collections of bounded linear operators on H and
linear, but not necessarily bounded, operators on H
respectively. Cosine Operator Functions, namely functions
C:R ⟶
B(H) which satisfy D'Alembert's functional
equation

(1)

and

(2)