bluuebunny/crossref_metadata_2025_split huggingface dataset:
Taming Wild Simple Closed Curves with Monotone
Maps
Authors: Boyd W. S. , Wright A. H. 
Published: December 2010

Hempel [6, Theorem 2] proved that if S is a
tame 2-sphere in E3 and f is a map of E3 onto itself such that f|S is a homeomorphism and
f(E3 - S) =
E3- f(S), then f(S) is
tame. Boyd [4] has shown that the converse is false; in fact,
if S is any 2-sphere in E3, then there is a monotone map f of
E3 onto itself such that f |S is a homeomorphism,
f(E3 — S) = E3 — f(S), and
f(S) is tame.It is the purpose of this paper to prove that the corresponding converse for
simple closed curves in E3 is also false. We show in Theorem 4 that if J is
any simple closed curve in a closed orientable 3-manifold
M3, then there is a monotone map f : M3 → S3 such that f |J is a homeomorphism,
f(J) is tame and unknotted, and
f(M3 - J) = S3 -
f(J).In Theorem 1 of § 2, we construct a cube-with-handles neighbourhood of a
simple closed curve in an orientable 3-manifold.
On Conformally Flat Spaces with Commuting Curvature and Ricci
Transformations
Authors: Bishop R. L. , Goldberg S.I. 
Published: December 2010

Let (M, g) be a C∞ Riemannian manifold and
A be the field of symmetric endomorphisms corresponding
to the Ricci tensor S; that is,We consider a condition weaker than the requirement that A
be parallel (▽ A = 0), namely, that the “second exterior
covariant derivative” vanish ( ▽x▽YA — ▽Y ▽XA — ▽[X,Y]A
= 0), which by the classical interchange formula reduces to the
propertywhere R(X, Y) is the curvature transformation determined by
the vector fields X and Y.The property (P) is equivalent toTo see this we observe first that a skew symmetric and a symmetric
endomorphism commute if and only if their product is skew symmetric.
The Strict Topology in a Completely Regular Setting: Relations
to Topological Measure Theory
Authors: Mosiman Steven E. , Wheeler Robert F. 
Published: December 2010

Let X be a locally compact Hausdorff space, and let
C*(X) denote the space of real-valued bounded
continuous functions on X. An interesting and important
property of the strict topology β on C*(X) was proved by Buck [2]: the dual
space of (C*(X), β) has a natural
representation as the space of bounded regular Borel measures on
X.Now suppose that X is completely regular (all topological
spaces are assumed to be Hausdorff in this paper). Again it seems natural to
seek locally convex topologies on the space C*(X) whose dual spaces are (via
the integration pairing) significant classes of measures.
Graphical Regular Representations of Non-Abelian Groups, I
Authors: Nowitz Lewis A. , Watkins Mark E. 
Published: December 2010

In this paper, all groups and graphs considered are finite and all graphs are simple (in the sense of Tutte [8, p. 50]). IfXis such a graph with vertex setV(X)and automorphism groupA(X),we say thatXis agraphical regular representation(GRR) of a given abstract groupGif(I) G ≅ A(X) , and(II)A(X)acts onV(X) as a regular permutation group; that is, givenu, v∈V(X), there exists a uniqueφ∈A(X)for whichφ(u) =v.That for any abstract groupGthere exists a graphXsatisfying (I) is well-known (cf. [3]).
Extension Closed and Cluster Closed Subspaces
Authors: Harris Douglas 
Published: December 2010

One of the most useful properties of a compact Hausdorff space is that such a space is closed whenever embedded into a Hausdorff space. This property does not extend to compact spaces with respect to embeddings into arbitrary spaces. Thus, an interesting topological problem is to characterize the types of absolute “closure” properties that are possessed by compact spaces. This is the problem that is solved in the present paper.The following notation and terminology will be used below. We shall consider a fixed space X and subspace A, representing arbitrary nonempty open subsets of X (respectively A ) by W (respectively V).
On the Ranges of Certain Fractional Integrals
Authors: Rooney P. G. 
Published: December 2010

Suppose 1 ≦ P < ∞, μ is real, and denote by Lμ,p the collection of functions f, measurable on (0, ∞ ), and which satisfy1.1Also denote by [X] the collection of bounded operators from a Banach space X to itself. For v > 0, Re α > 0, Re β > 0, let1.2and1.3where ξ and η are complex numbers. Iv,α,ξ and Jv,β,η, are generalizations of the Riemann-Liouville and Weyl fractional integrals respectively, and consequently we shall refer to them as fractional integrals.
Uniqueness Theorems for a Singular Partial Differential Equation
Authors: Ramankutty P. 
Published: December 2010

A singular partial differential equation which occurs frequently in mathematical physics is given bywhere is the Laplacian operator on Rn of which the generic point is denoted by x = (x1, … , xn) and s and k are real numbers. The study of solutions of this equation for the case k = 0 was initiated by A. Weinstein [5], who named it ‘Generalized Axially Symmetric Potential Theory'. Numerous references to the literature on this equation can be found in [1; 3; 6]. The analytic theory of equations of the type mentioned above has extensively been treated in [2].
Edge Partition Properties of Graphs
Authors: Henson C. Ward 
Published: December 2010

Erdös and Hajnal [1] have introduced an edge partition relation for graphs(1)which means that whenever the edges of G are separated into two sets, E1 and E2, there exists a subgraph G’ of G such that G’ is isomorphic to Hi and the edges of G’ are all in Ei. for i = 1 or 2. A class of graphs has the G-R (Galvin-Ramsey) property [2] if for each H in there exists a G in which satisfies G→(H,H).
Integral Extensions of Commutative Banach Algebras
Authors: Lindberg John A. 
Published: December 2010

In this paper, we continue the study of integral extensions begun in [7]. Whereas in the previous paper, we dealt exclusively with the extension A[x]/(α(x)), α(x) a monic polynomial over A, we now deal with arbitrary integral extensions. Applications of the results presented herein will be made in subsequent papers.To simplify our presentation, we make the following conventions. By an algebra, we will always mean a commutative complex algebra with an identity element, usually denoted by e
Subgroups of One-Relator Fuchsian Groups
Authors: Best L. A. 
Published: December 2010

Let Γ be the Fuchsian group with canonical presentation:Generators:Relations:where . The genus g, the period partition {m1, m2, … , mr} and the number s are invariants of Γ. The symbol (g|m1, m2, … , mr|s) is called the signature of Γ and it determines Γ up to isomorphism.
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 aswhereSnis 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 setwhose 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).
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 = 11.1where γ ≧ 1, a > 0, and the quantity in brackets is a power series in 1 — z with positive radius of convergence.
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 formSuch 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 normThe 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).
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 ∊ Kwhere {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].)
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 by1.1and 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.
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.
The Oscillation of Fourth Order Linear Differential Operators
Authors: Lewis Roger T. 
Published: December 2010

Define the self-adjoint operatorwhere 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 followingTHEOREM. 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.
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 Byγo = 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 followingTHEOREM 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).
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 Diagramwhere 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
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 definewhere [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.
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 bywhere
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 satisfyingwhere ||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]).
The Existence of Continuable Solutions of a Second Order Differential Equation
Authors: Butler G. J. 
Published: December 2010

A much-studied equation in recent years has been the second order nonlinear ordinary differential equationwhere q and f are continuous on the real line and, in addition, f is monotone increasing with yf(y) > 0 for y ≠ 0. Although the original interest in (1) lay largely with the case that q﹛t) ≧ 0 for all large values of t, a number of papers have recently appeared in which this sign restriction is removed.
Some Orbital Integrals and a Technique for Counting Representations of GL
2(F)
Authors: Callahan T. 
Published: December 2010

Let F be a local field of characteristic zero,
with q elements in its residue field, ring of integers
uniformizer
ωF and maximal ideal . Let
GF
= GL2(F). We fix
Haar measures dg
and dz
on GF
and ZF, the centre
of GF, so that
meas(K) = meas

where K = GL2() is a maximal
compact subgroup of GF. If T is a
torus in GF we take dt to be the
Haar measure on T such that
means(TM)=1
where TM denotes the maximal compact subgroup of
T.
Perturbation of Direct Sum Differential Operators
Authors: Lee S. J. 
Published: December 2010

Let I be an interval, and let for 1 ≦
j ≦ I &lt; ∞ be
abutted subintervals such that . Let τ
j
be a linear differential expression defined on I
j
. In this paper we study densely defined
operators associated with
(0.1)
Harmonic Mappings of Negatively Curved Manifolds
Authors: Har'el Zvi 
Published: December 2010

Volume decreasing properties of harmonic mappings of space forms were
investigated by S. S. Chern and S. I. Goldberg [3] and the
author. In a previous paper [6], a step toward
generalization of the results was made proving the following theorem:
Theorem. Let ƒ: M —&gt;
N be a harmonic mapping of
n-dimensional Riemannian manifolds, with C ≦ 0.
Suppose the scalar curvature of M is not less than — S, and the Ricci curvature of
N is not greater than —S/n, where S ≧ 0 and S
&gt; 0 are constants. Then, if u has a maximum on
M,

i.e. ƒ is volume decreasing up to a constant.
Ergodic Properties of Lamperti Operators
Authors: Kan Charn-Huen 
Published: December 2010

We shall assume throughout this paper, unless otherwise specified, that p is a fixed number, 1 < p < ∞.It is well known that to prove the poin.twise ergodic convergence of a contraction T on an Lp-space it is enough to prove a Dominated Ergodic Estimate (DEE) for T (see e.g. [11]).
Some Extreme Rays of the Positive Pluriharmonic Functions
Authors: Forelli Frank 
Published: December 2010

1.1. We will denote by B the open unit ball in Cn, and we will denote by H(B) the class of all holomorphic functions on B. LetThus N(B) is convex (and compact in the compact open topology). We think that the structure of N(B) is of interest and importance. Thus we proved in [1] that if(1.1)if(1.2)and if n≧ 2, then g is an extreme point of N(B). We will denote by E(B) the class of all extreme points of N(B). If n = 1 and if (1.2) holds, then as is well known g ∈ E(B) if and only if(1.3)
The Asymptotic Behaviour of Equidistant Permutation Arrays
Authors: Vanstone S. A. 
Published: December 2010

An equidistant permutation array (EPA) A(r λ v) is a v × r array defined on a set V of r symbols such that every row is a permutation of V and any two distinct rows have precisely λ common column entries. Define R(r, λ) to be the largest value of v for which there exists an A (r, λ; v). Deza [2] has shown thatwhere n = r – λ. Bolton [1] has shown that(*)In this paper, we show that equality holds in (*) for λ > ┌n/3┐(n2 + n). In order to do this we require several more definitions.
Labeled Bipartite Blocks
Authors: Harary F. , Robinson R. W. 
Published: December 2010

Graphs which are 2-connected have been called blocks in the graph theoretic literature [3] and stars in the parlance of statistical mechanics [1]. They are also called nonseparable graphs, and in this paper include the complete graph K2 on p = 2 points. The standard terminology of graphical enumeration can be found in [3].When its points are colored using two distinct colors in such a way that adjacent points receive different colors, a graph is called 2-colored. If the colors are considered interchangeable, such a graph is called bicolored. A graph which can be bicolored is called bicolorable. It is obvious that a connected bicolorable graph has a unique bicoloring, and so one can speak of the sizes of its color classes.