bluuebunny/crossref_metadata_2025 huggingface dataset:
The Teichmüller spaces are distinct
Authors: Patterson David B.
Published: June 2010

The Teichmüller space

T
(
g
,
n
)

T(g,n)

of a compact Riemann surface of genus g with n punctures is a complex manifold of

dim
=
3
g
−
3
+
n

\dim = 3g - 3 + n

. In any given dimension, there are a finite number of these Teichmüller spaces and it is natural to ask if all of these are distinct (up to biholomorphic equivalence). We have shown here that with the exception of two special cases in dimensions 1 and 3 all of these spaces are distinct, that is,

T
(
g
,
n
)

T(g,n)

is not biholomorphically equivalent to

T
(

g
′

,

n
′

)

T(g’,n’)

unless

g
′

=
g

g’ = g

and

n
′

=
n

n’ = n

.
Applications of Laplace transforms and their inverses
Authors: Fox Charles
Published: June 2010

By means of Laplace transforms and their inverses we first solve the Varma transform, considered as an integral equation for an unknown function in the integrand. We then express two operators of fractional integration in terms of Laplace and inverse Laplace transforms.
Quotient and pseudo-open images of separable metric spaces
Authors: Strong Paul L.
Published: June 2010

Ernest A. Michael has given a characterization of the regular quotient images of separable metric spaces. His result is generalized here to a characterization of the

T
1

{T_1}

quotient images of separable metric spaces (which are the same as the

T
1

{T_1}

quotient images of second countable spaces). This result is then used to characterize the Hausdorff pseudo-open images of separable metric spaces.
Automorphism of a finite group scalar on the cosets of a subgroup
Authors: Sidki Saïd
Published: June 2010

Let G be a finite group,

σ
\sigma

an automorphism of G, M a

σ
\sigma

-invariant subgroup of G, and n a fixed integer. If

σ
(
g
)
∈

g
n

M

\sigma (g) \in {g^n}M

for all

g
∈
G

g \in G

then there exists a

σ
\sigma

-invariant normal subgroup K of G, contained in M, with

σ
(
g
)
∈

g
n

K

\sigma (g) \in {g^n}K

for all

g
∈
G

g \in G

.
Maps between topological groups that are homotopic to homomorphisms
Authors: Scheffer Wladimiro
Published: June 2010

Let G be a compact connected group and let H be a locally compact abelian group. Denote by

C
e

(
G
,
H
)

{C_e}(G,H)

the space of all identity preserving continuous functions from G to H with the compact-open topology, and denote by Hom(G, H) the space of all homomorphisms in

C
e

(
G
,
H
)

{C_e}(G,H)

. We prove that

C
e

(
G
,
H
)

{C_e}(G,H)

is isomorphic to

V
×

Hom

(
G
,
H
)

V \times {\text {Hom}}(G,H)

, where V is a topological vector space. This is used to prove that every element of

C
e

(
G
,
H
)

{C_e}(G,H)

is homotopic to precisely one element of Hom(G, H). We also prove that the fundamental group of H is isomorphic to Hom(K, H), K being the circle group, that

π
n

(
H
)
=
0

{\pi _n}(H) = 0

for

n
≧
2

n \geqq 2

, and that a compact connected abelian group admits essentially only one H-space structure.
On convex subsets of a polytope
Authors: Hare W. R. , Smith C. R.
Published: June 2010

A. J. Hoffman conjectured the following: Given a d-polytope P and a collection,

C
1

,
⋯
,

C
k

{C_1}, \cdots ,{C_k}

, of closed convex subsets of P with the property that each t-flat,

0
≦
t
≦
d
−
1

0 \leqq t \leqq d - 1

, which meets P also meets some

C
i

{C_i}

, then there exist polytopes

D
j

⊂

C
j

{D_j} \subset {C_j}

such that every t-flat which meets P also meets some

D
j

{D_j}

. In this note it is shown that the above is true for

k
=
2

k = 2

.
The epimorphic images of a Dedekind domain
Authors: Cheatham T. , Enochs E.
Published: June 2010

We prove that the epimorphic image of a Dedekind domain A is characterized (up to A-isomorphisms) by its torsion submodule (as an A-module) and the torsion-free quotient by its torsion submodule. Necessary and sufficient conditions are given on a torsion and torsion-free A-module in order that they be the corresponding parts of an epimorphic image of A.
A characterization of exchange rings
Authors: Monk G. S.
Published: June 2010

A necessary and sufficient condition on the endomorphism ring of a module for the module to have the finite exchange property is given. This condition is shown to be strictly weaker than a sufficient condition given by Warfield. The class of rings having these properties is equationally definable and is a natural generalization of the class of regular rings. Finally, it is observed that in the commutative case the category of such rings is equivalent with the category of ringed spaces

(
X
,

R

)

(X,\mathcal {R})

with X a Boolean space and

R

\mathcal {R}

a sheaf of commutative (not necessarily Noetherian) local rings.
A note on Kaplun limits and double asymptotics
Authors: Freund D. D.
Published: June 2010

The foundation of “inner-outer” expansions and allied methods is examined. Two limit definitions (both yielding Kaplun’s extension theorem) are compared in regard to double limit asymptotics.
An algebraic characterization of dimension
Authors: Canfell M. J.
Published: June 2010

The purpose of this paper is to translate the condition defining Lebesgue covering dimension of a topological space X into a condition on

C
(
X
)

C(X)

, the ring of continuous real-valued functions on X.
A cobordism
Authors: Stong R. E.
Published: June 2010

A cobordism of complex projective n-space and the square of real projective n-space is exhibited.
Implicative homomorphisms with finite ranges
Authors: Nemitz William C.
Published: June 2010

In this note, it is shown that every implicative homomorphism with a finite range is a factor of a projection.
On the isomorphisms between certain congruence groups
Authors: Solazzi Robert E.
Published: June 2010

In this paper we study the possible isomorphisms between the congruence subgroups of the classical groups over integral domains by applying the involution-free techniques previously used by O’Meara and the author. We prove, in dimensions at least 6 and characteristic not 2, that a linear congruence group is never isomorphic to a symplectic congruence group nor to an isotropic unitary congruence group whose associated hermitian space has Witt index at least 3.
Generalized overrelaxation and Gauss-Seidel convergence on Hilbert space
Authors: Hanna Michael P.
Published: June 2010

We present a generalized result on Gauss-Seidel convergence for bounded linear operators on Hilbert space

H

\mathcal {H}

. From this result, we obtain overrelaxation theorems of Petryshyn [4], [5], de Pillis [1], Ostrowski [3] and Reich [6].
Ordinal sum-sets
Authors: Zuckerman Martin M.
Published: June 2010

A finite set, B, of ordinals will be called a sum-set if there are nonzero ordinals

α
1

,

α
2

,
⋯
,

α
n

{\alpha _1},{\alpha _2}, \cdots ,{\alpha _n}

such that the set of sums of

α
1

,

α
2

,
⋯
,

α
n

{\alpha _1},{\alpha _2}, \cdots ,{\alpha _n}

, in all n! permutations of the summands, is B. Let

B
k

{B_k}

denote an arbitrary k-element sum-set; we consider various matters related to the set of numbers n for which there are n summands for

B
k

{B_k}

.
Immersions and embeddings of projective spaces
Authors: Feder S. , Segal D. M.
Published: June 2010

The topic is embedding and immersions of complex and quaternionic projective spaces. The results are obtained using spin representations and relating these with the various K-theories in which they occur. A numerical result on nonembeddings and and nonimmersions is obtained.
An exact sequence calculation for the second homotopy of a knot
Authors: Gutiérrez M. A.
Published: June 2010

This paper deals with the computation of the second homotopy group of a knot, cancelling the action of the commutator subgroup of the fundamental group.
Hereditary ball-covers for some Banach manifolds
Authors: West James E.
Published: June 2010

At a problem seminar in Ithaca, New York, during January 1969, James Eells raised the question (numbered 33 on the circulated list) of whether a paracompact Fréchet manifold admits a locally finite cover by open sets, all of whose intersections are contractible. This had been established in the separable case by David Henderson, who obtained star-finite covers. This note settles the case that the model space is a Banach space homeomorphic to its countably infinite Cartesian power. The cover elements and all nonempty intersections are homeomorphic to the model. A short proof that the nerve of the cover has the homotopy type of the manifold is also included.
Sets of multiplicity and differentiable functions
Authors: Kaufman R.
Published: June 2010

The paper contains two theorems relating the fine structure of differentiable functions, in one or more dimensions, to the behavior of Fourier-Stieltjes transforms on sets that are small in various ways.
Inverting sets for function algebras
Authors: Eifler Larry Q.
Published: June 2010

If A is a function algebra on X, then we say that X is an inverting set for A if

f
∈
A

f \in A

and f does not vanish on X implies f is invertible in A. We obtain results on inverting sets for tensor products and for extensions of

R
(
X
)

R(X)

by real valued functions.
A theorem on injectivity of the cup product
Authors: Wood John C.
Published: June 2010

We prove that if a space X has abelian or sufficiently abelian fundamental group, then the cup product

H
1

(
X
)
∧

H
1

(
X
)
→

H
2

(
X
)

{H^1}(X) \wedge {H^1}(X) \to {H^2}(X)

is injective, giving an inequality between the associated Betti numbers. This generalises to a theorem of injectivity of the k-fold cup product on

H
n

(
X
)

{H^n}(X)

, given that the kth order Whitehead product on

π
n

(
X
)

{\pi _n}(X)

is trivial or torsion.
Commuting analytic functions without fixed points
Authors: Behan Donald F.
Published: June 2010

Let A be the set of nonidentity analytic functions which map the open unit disk into itself. Wolff has shown that the iterates of

f
∈
A

f \in A

converge uniformly on compact sets to a constant

T
(
f
)

T(f)

, unless f is an elliptic conformal automorphism of the disk. This paper presents a proof that if f and g are in A and commute under composition, and if f is not a hyperbolic conformal automorphism of the disk, then

T
(
f
)
=
T
(
g
)

T(f) = T(g)

. This extends, in a sense, a result of Shields. The proof involves the so-called angular derivative of a function in A at a boundary point of the disk.
On M. Hall’s continued fraction theorem
Authors: Cusick T. W.
Published: June 2010

For each integer

k
≧
2

k \geqq 2

, let

F
(
k
)

F(k)

denote the set of real numbers

α
\alpha

such that

0
≦
α
≦
1

0 \leqq \alpha \leqq 1

and

α
\alpha

has a continued fraction containing no partial quotient greater than

k
k

. A well-known theorem of Marshall Hall, Jr. states that (with the usual definition of a sum of point sets)

F
(
4
)
+
F
(
4
)

F(4) + F(4)

contains an interval of length

≧
1

\geqq 1

; it follows immediately that every real number is representable as a sum of two real numbers each of which has fractional part in

F
(
4
)

F(4)

. In this paper it is shown that every real number is representable as a sum of real numbers each of which has fractional part in

F
(
3
)

F(3)

or

F
(
2
)

F(2)

, the number of summands required being 3 or 4, respectively.
A note on intersections of valuation ideals
Authors: Brase Charles H.
Published: June 2010

In this note it is proved that if

R
R

is an integral domain the set of valuation ideals of

R
R

is closed under intersection if and only if the integral closure of

R
R

is a valuation ring. Let

S
S

be a domain which is integrally dependent on

R
R

and contains the integral closure of

R
R

. Then the set of valuation ideals of

R
R

is the same as the set of ideals of

R
R

which contract from ideals of

S
S

if and only if the set of valuation ideals of

R
R

is closed under intersection.
A hyponormal operator whose spectrum is not a spectral set
Authors: Wadhwa Bhushan L.
Published: June 2010

Clancey has given an example of a hyponormal, nonnormal operator whose spectrum is thin and hence not a spectral set. In this note, using fairly simple techniques, we give an example of a hyponormal operator whose spectrum contains a disc and is not a spectral set.
A minimal partial degree ≤𝑂^{’}
Authors: Sasso Leonard P.
Published: June 2010

We construct, recursively in 0’, a minimal element in the upper semilattice, excluding least element, of Turing degrees of partial functions.
On the Hasse principle for quadratic forms
Authors: Hsia J. S.
Published: June 2010

Examples are given for rational function fields that do not satisfy the strong Hasse principle for quadratic forms.
Certain determinants related to the Vandermonde
Authors: Fink A. M.
Published: June 2010

We find a formula for determinants similar to the Vandermonde. These determinants arise from a problem in differential equations.
A van Kampen theorem for separable algebras
Authors: Magid Andy R.
Published: June 2010

If the commutative ring

S
S

is the fibre product of

R
1

{R_1}

and

R
2

{R_2}

over

R
R

, and if

R
2

{R_2}

maps onto

R
R

, then the fundamental group of

S
S

is the profinite free product of the fundamental groups of

R
1

{R_1}

and

R
2

{R_2}

with the fundamental group of

R
R

amalgamated.
On the structure of semiprime rings
Authors: Ortiz Augusto H.
Published: June 2010

The structure of prime rings has recently been studied by A. W. Goldie, R. E. Johnson, L. Lesieur and R. Croisot. In their main results some sort of finiteness assumption is invariably made. It is shown in this paper that certain semiprime rings are subdirect sums of full rings of linear transformations of a right vector space over a division ring. No finiteness assumption is made about the ring. An apparently new radical property is defined and some of its properties are established; e.g., the radical of a matrix ring

R
n

{R_n}

is the matrix ring of the radical of

R
R

.
Strict radical classes of associative rings
Authors: Stewart Patrick N.
Published: June 2010

A class of rings is strongly hereditary if it is closed under taking subrings. Strict radical classes (that is, radical classes for which the class of semisimple rings is strongly hereditary) are studied, strongly hereditary strict radical classes are classified, and it is shown that the category of associative rings has no proper localizing subcategories in the sense of Šul’geĭfer.
Semigroups with invariant Radon measures
Authors: Gowrisankaran Chandra
Published: June 2010

Let

S
S

be a commutative semigroup which is a topological space such that the translations are both continuous and open maps. The main result states that if (1) either

S
S

is Suslin such that there is at least one point of continuity for the semigroup mapping

S
×
S
→
S

S \times S \to S

or

S
S

is polish and (2)

∃
\exists

a nontrivial Radon measure on

S
S

such that

μ
(
V
)
=
μ
(
x
+
V
)

\mu (V) = \mu (x + V)

for

V
V

open

⊂
S

\subset S

and

x
∈
S

x \in S

, then

S
S

can be embedded as an open subsemigroup of a locally compact group. It is also shown that if

S
S

is polish and a cancellation semigroup then

S
S

can be embedded as an open subsemigroup of a group.
The critical points of a typically-real function
Authors: Goodman A. W.
Published: June 2010

The critical points of a typically-real function cannot lie too close to the real axis. By adding a mild restriction, we determine

D
k

{D_k}

the domain of variability of a

k
k

th order critical point. Similar results are obtained for a

k
k

th order branch point. We determine the domain of univalence for typically-real functions and propose a reasonable conjecture for the domain of

k
k

-valence.
Application of Liapunov theory to boundary value problems. II
Authors: George J. H. , York R. J.
Published: June 2010

The second order vector differential equation

x
=
f
(
t
,
x
,

x
′

)

x = f(t,x,x’)

is considered. Liapunov conditions for existence of solutions to boundary value problems are obtained strictly in terms of the function f, extending the results of George and Sutton [1].
The Fourier transform is onto only when the group is finite
Authors: Graham Colin C.
Published: June 2010

A very simple proof of the result of the title is given. Unlike previous proofs, the one presented here uses no results of harmonic analysis beyond the Pontryagin duality theorem.
Additions and corrections to: “On the ideal structure of the algebra of radial functions”
Authors: Schwartz Alan L.
Published: June 2010

The corrections and additions are made in the context of Hankel transforms which generalize the Fourier transforms of radial functions. The following question is studied: given two closed ideals

I
1

{I_1}

and

I
2

{I_2}

in the algebra of Hankel transforms such that both have the same spectrum and

I
1

⊂

I
2

{I_1} \subset {I_2}

, when is there a closed ideal

I
I

such that

I
1

⊂
I
⊂

I
2

{I_1} \subset I \subset {I_2}

?
On fixed points of nonexpansive mappings in nonconvex sets
Authors: Dotson W. G.
Published: June 2010

Two theorems are proved concerning the existence of fixed points of nonexpansive mappings on a certain class of nonconvex sets. This work extends the author’s previous work on star-shaped sets.
A metric characterizing Čech dimension zero
Authors: Broughan K. A.
Published: June 2010

In this paper we prove the following: a metrizable space

(
X
,
τ
)

(X,\tau )

has (Čech) dimension zero if and only if there is a metric for

X
X

, generating the topology

τ
\tau

, taking values in some subset of the nonnegative real numbers with 0 as its only cluster point.
Splitting fields and separability
Authors: Ramras Mark
Published: June 2010

It is a classical result that if

(
R
,

M

)

(R,\mathfrak {M})

is a complete discrete valuation ring with quotient field

K
K

, and if

R

/

M

R/\mathfrak {M}

is perfect, then any finite dimensional central simple

K
K

-algebra

Σ
\Sigma

can be split by a field

L
L

which is an unramified extension of

K
K

. Here we prove that if

(
R
,

M

)

(R,\mathfrak {M})

is any regular local ring, and if

Σ
\Sigma

contains an

R
R

-order

Λ
\Lambda

whose global dimension is finite and such that

Λ

/

Rad
⁡
Λ

\Lambda /\operatorname {Rad} \Lambda

is central simple over

R

/

M

R/\mathfrak {M}

, then the existence of an “

R
R

-unramified” splitting field

L
L

for

Σ
\Sigma

implies that

Λ
\Lambda

is

R
R

-separable. Using this theorem we construct an example which shows that if

R
R

is a regular local ring of dimension greater than one, and if its characteristic is not 2, then there is a central division algebra over

K
K

which has no

R
R

-unramified splitting field.
A new simple Lie algebra of characteristic three
Authors: Frank Marguerite
Published: June 2010

We define a restricted simple algebra

T
T

of dimension 18 over an arbitrary field of characteristic 3. From a certain property of its Cartan decomposition, we show

T
T

to be nonisomorphic to any known algebra of identical dimension.
Some inequalities for the multiplicator of a finite group
Authors: Jones Michael R.
Published: June 2010

The paper is devoted to the derivation of certain upper and lower bounds for the multiplicator of a finite group. The lower bounds enable us to give a sufficient condition for a finite group to have nontrivial multiplicator.
Commutators as products of squares
Authors: Lyndon Roger C. , Newman Morris
Published: June 2010

It is shown that if

G
G

is the free group of rank 2 freely generated by

x
x

and

y
y

, then

x
y

x

−
1

y

−
1

xy{x^{ - 1}}{y^{ - 1}}

is never the product of two squares in

G
G

, although it is always the product of three squares in

G
G

. It is also shown that if

G
G

is the free group of rank

n
n

freely generated by

x
1

,

x
2

,
⋯
,

x
n

{x_1},{x_2}, \cdots ,{x_n}

, then

x
1
2

x
2
2

⋯

x
n
2

x_1^2x_2^2 \cdots x_n^2

is never the product of fewer than

n
n

squares in

G
G

.
Indecomposable continua in Stone-Čech compactifications
Authors: Bellamy David P. , Rubin Leonard R.
Published: June 2010

We show that if

Y
Y

is a continuum irreducible from

a
a

to

b
b

, which is connected im Kleinen and first countable at

b
b

, and if

X
=
Y
−
{
b
}

X = Y - \{ b\}

, then

β
X
−
X

\beta X - X

is an indecomposable continuum. Examples are given showing that both first countability and connectedness im Kleinen are needed here. We also show that

β
[
0
,
1
)
−
[
0
,
1
)

\beta [0,1) - [0,1)

has a strong near-homogeneity property.
Some relations between semigroups of polyhedra
Authors: Kozma Ilan
Published: June 2010

All spaces are CW-complexes of finite type. The notation “=” means homotopy equivalence. The following theorems are proved: (1) If

X
∨
A
=
Y
∨
A

X \vee A = Y \vee A

then there exists

T
T

such that

Ω
X
×
T
=
Ω
Y
×
T

\Omega X \times T = \Omega Y \times T

, (2)

X
×
A
=
Y
×
A

X \times A = Y \times A

implies that there is a

T
T

such that

Σ
X
∨
T
=
Σ
Y
∨
T

\Sigma X \vee T = \Sigma Y \vee T

. A partial converse is also proved. As a corollary we get that if

X
∨
A
=
Y
∨
A

X \vee A = Y \vee A

then

π
∗

(
X
)
=

π
∗

(
Y
)

{\pi _ \ast }(X) = {\pi _ \ast }(Y)

and if

X
×
A
=
Y
×
A

X \times A = Y \times A

then

h
∗

(
X
)
=

h
∗

(
Y
)

{h_ \ast }(X) = {h_ \ast }(Y)

for many homology theories.
Model companions for ℵ₀-categorical theories
Authors: Saracino D.
Published: June 2010

We show that any countable

ℵ
0

{\aleph _0}

-categorical theory without finite models has a model companion (which is also

ℵ
0

{\aleph _0}

-categorical). We find the model companions for all

ℵ
0

{\aleph _0}

-categorical abelian groups, and conclude with some remarks on the

ℵ
1

{\aleph _1}

-categorical case.
A theorem on the restriction of type I representations of a group to certain of its subgroups
Authors: Kallman Robert R.
Published: June 2010

Theorem. Let

G
G

be a separable locally compact group and

H
H

a closed subgroup such that

G

/

H

G/H

is finite. Let

π
\pi

be a Type I representation of

G
G

. Then

π

|

H

\pi |H

is Type I.
An extremal problem for the geometric mean of polynomials
Authors: Beller E. , Newman D. J.
Published: June 2010

Let

M

0
,
n

{M_{0,n}}

be the maximum of the geometric mean of all

n
n

th degree polynomials

∑
n

a
k

e

i
k
t

{\sum ^n}{a_k}{e^{ikt}}

which satisfy

|

a
k

|

=
1
,
k
=
0
,
1
,
⋯
,
n

|{a_k}| = 1,k = 0,1, \cdots ,n

. We show the existence of certain polynomials

R
n

{R_n}

whose geometric mean is asymptotic to

√
n

\surd n

, thus proving that

M

0
,
n

{M_{0,n}}

is itself asymptotic to

√
n

\surd n

.
Commutative extensions by canonical modules are Gorenstein rings
Authors: Fossum Robert
Published: June 2010

Reiten has demonstrated that the trivial Hochschild extension of a Cohen-Macaulay local ring by a canonical module is a Gorenstein local ring. Here it is proved that any commutative extension of a Cohen-Macaulay local ring by a canonical module is a Gorenstein ring. Also Gorenstein extensions of a local Cohen-Macaulay ring by a module are studied.
The growth of hypoelliptic polynomials and Gevrey classes
Authors: Newberger E. , Zieleźny Z.
Published: June 2010

For given hypoelliptic polynomials

P
P

and

Q
Q

, classes

Γ
P
ρ

(
Ω
)

\Gamma _P^\rho (\Omega )

and

Γ
Q
ρ

(
Ω
)

\Gamma _Q^\rho (\Omega )

involving Gevrey type estimates on the successive iterates of the corresponding differential operators are defined. The equivalence of the inequality
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue upper Q left-parenthesis xi right-parenthesis EndAbsoluteValue squared less-than-over-equals upper C left-parenthesis 1 plus StartAbsoluteValue upper P left-parenthesis xi right-parenthesis EndAbsoluteValue squared right-parenthesis Superscript h Baseline comma xi element-of upper R Superscript n">

|

Q
(
ξ
)

|

2

≦
C

(
1
+

|

P
(
ξ
)

|

2

)
h

,
ξ
∈

R
n

|Q(\xi ){|^2} \leqq C{(1 + |P(\xi ){|^2})^h},\xi \in {R^n}

, and the inclusion
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Gamma Subscript upper P Superscript rho Baseline left-parenthesis normal upper Omega right-parenthesis subset-of normal upper Gamma Subscript upper Q Superscript rho h Baseline left-parenthesis normal upper Omega right-parenthesis">

Γ
P
ρ

(
Ω
)
⊂

Γ
Q

ρ
h

(
Ω
)

\Gamma _P^\rho (\Omega ) \subset \Gamma _Q^{\rho h}(\Omega )

is proved.
Physical states on a 𝐶*-algebra
Authors: Akemann Charles A. , Newberger Stuart M.
Published: June 2010

When a locally compact Hausdorff space

X
X

is totally disconnected, any doubly generated subalgebra of (real)

C
0

(
X
)

{C_0}(X)

is singly generated.
An example in the space of bounded operators from 𝐶(𝑋) to 𝐶(𝑌)
Authors: Kaplan Samuel
Published: June 2010

Let

X
,
Y

X,Y

be compact spaces, and

C
(
X
)
,
C
(
Y
)

C(X),C(Y)

the corresponding Banach lattices of real continuous functions. It is shown that the partially ordered space of bounded operators from

C
(
X
)

C(X)

to

C
(
Y
)

C(Y)

need not be generated by its positive cone.
Metric inequalities and convexity
Authors: Wolfe Dorothy
Published: June 2010

Conditions that a given point of a normed linear space is (or is not) a convex combination of

n
n

fixed points are given in terms of the metric. The point is said to be metrically dependent if the conditions hold.
On characteristic classes of groups and bundles of 𝐾(Π,1)’s
Authors: Hill R. O.
Published: June 2010

If

F
→
E
→
B

F \to E \to B

is a fibration with

F
=
K
(
G
,
1
)

F = K(G,1)

,

G
G

Abelian, and

B
=
K
(
∏
,
1
)

B = K(\prod ,1)

, then it is shown that the action and characteristic class of the fibration correspond to those of the induced group extension.
Permanent groups. II
Authors: Beasley Leroy B. , Cummings Larry
Published: June 2010

A permanent group is a group of nonsingular matrices on which the permanent function is multiplicative. We consider only permanent groups which contain the group of nonsingular diagonal matrices. If the underlying field is infinite of characteristic zero or greater than

n
n

, then each such permanent group consists only of matrices in which exactly one diagonal has all nonzero entries.
Free topological groups and the projective dimension of a locally compact abelian group
Authors: Mack John , Morris Sidney A. , Ordman Edward T.
Published: June 2010

It is shown that a free topological group on a

k
ω

{k_\omega }

-space is a

k
ω

{k_\omega }

-space. Using this it is proved that if

X
X

is a

k
ω

{k_\omega }

-group then it is a quotient of a free topological group by a free topological group. A corollary to this is that the projective dimension of any

k
ω

{k_\omega }

-group, relative to the class of all continuous epimorphisms admitting sections, is either zero or one. In particular the projective dimension of a connected locally compact abelian group or a compact abelian group is exactly one.
Semigroups with positive definite structure
Authors: Saworotnow Parfeny P.
Published: June 2010

Let

G
G

be a semigroup with the identity 1 and an involution

x
→

x
∗

x \to {x^ \ast }

. One can define a complex-valued and an

H
∗

{H^ \ast }

-algebra valued positive definite function on

G
G

in the obvious way. Assume that for each

x
∈
G

x \in G

there exists a positive number

L
x

{L_x}

such that

q
(

x
∗

x
)
≦

L
x

q
(
1
)

q({x^ \ast }x) \leqq {L_x}q(1)

for each complex positive definite function on

G
G

. It is shown that each

H
∗

{H^ \ast }

-algebra valued positive definite function on

G
G

is of the form

p
(
x
)
=
(
f
,

T
x

f
)

p(x) = (f,{T_x}f)

for some representation

T
T

of

G
G

on a Hilbert module

H
H

and

f
∈
H

f \in H

. Also there is an analogue of Bochner theorem for

G
G

.
A bounded Hilbertian basis in 𝐶[0,1]
Authors: Samn Sherwood
Published: June 2010

The existence of a bounded Hilbertian basis in

C
[
0
,
1
]

C[0,1]

is established.
A characterization of convex surfaces which are 𝐿-sets
Authors: Buchman E. O. , Valentine F. A.
Published: June 2010

If the surface of a bounded three dimensional convex body has the property that each pair of its points can see some third point via the surface, then with a single exception the body must be a finite cone with a convex base. The exceptional shape is that of a solid hexahedron with six triangular plane faces formed as the union of two tetrahedra having a congruent face in common.
Bounded holomorphic functions in Siegel domains
Authors: Chen Su Shing
Published: June 2010

A Siegel domain

D
D

of the second kind (not necessarily affine homogeneous) is shown to be complete with respect to the Carathéodory distance. Thus

D
D

is convex with respect to the bounded holomorphic functions, hence is a domain of holomorphy. A Phragmén-Lindelöf theorem for

D
D

is also given. That is, if a holomorphic function

f
f

in

D
D

is continuous in

D
¯

\bar D

, bounded on the distinguished boundary

S
S

of

D
D

and not of exponential growth, then

f
f

is bounded in

D
¯

\bar D

.
Negligibility in nonlocally convex spaces
Authors: Riley Charles A.
Published: June 2010

A negligibility theorem is established in a linear topological space without assuming the existence of a convex body or linearly bounded open set.
On classical quotients of polynomial identity rings with involution
Authors: Rowen Louis Halle
Published: June 2010

Let

(
R
,
∗
)

(R, \ast )

denote a ring

R
R

with involution

(
∗
)

( \ast )

, where “involution” means “

anti - automorphism of order

≦

 two

{\text {anti - automorphism of order}} \leqq {\text { two}}

". We can specialize many ring-theoretical concepts to rings with involution; in particular an ideal of

(
R
,
∗
)

(R, \ast )

is an ideal of

R
R

stable under

(
∗
)

( \ast )

, and the center of

(
R
,
∗
)

(R, \ast )

is the set of central elements of

R
R

which are fixed under

(
∗
)

( \ast )

. Then we say

(
R
,
∗
)

(R, \ast )

is prime when the product of any two nonzero ideals of

(
R
,
∗
)

(R, \ast )

is nonzero; similarly

(
R
,
∗
)

(R, \ast )

is semiprime when any power of a nonzero ideal of

(
R
,
∗
)

(R, \ast )

is nonzero. The main result of this paper is a strong analogue to Posner’s theorem [5], namely that any prime

(
R
,
∗
)

(R, \ast )

with polynomial identity has a ring of quotients

R
T

{R_T}

, formed merely by adjoining inverses of nonzero elements of the center of

(
R
,
∗
)

(R, \ast )

. This quotient ring

(

R
T

,
∗
)

({R_T}, \ast )

is simple and finite dimensional over its center. An extension of these results to semiprime Goldie rings with polynomial identity is given.
Flat and FP-injectivity
Authors: Jain Saroj
Published: June 2010

One of the main results of this paper is the characterization of left FP-injective rings as rings over which every finitely presented right module is torsionless. The necessity of the torsionless condition (in fact reflexivity) previously has been observed for special classes of FP-injective rings (e.g., self-injective rings (Kato and McRae), right and left coherent and self FP-injective rings (Stenström)). Furthermore, if the ring is left coherent, it is equivalent to say that every finitely presented right module is reflexive. We investigate the condition (called IF) that every injective right module is flat and characterize this via FP-injectivity. IF-rings generalize regular rings and QF-rings, and under certain chain or homological conditions coincide with regular or QF-rings (e.g.,

w
g
l
dim
⁡
R
≦
1
⇒

regular

wgl\dim R \leqq 1 \Rightarrow {\text {regular}}

, noetherian, or

right perfect

⇒

QF)

{\text {right perfect}} \Rightarrow {\text {QF)}}

.
The projective class group of the fundamental group of a surface is trivial
Authors: Choo Koo Guan
Published: June 2010

Let

D
=

F
1

×

F
2

×
⋯
×

F
n

D = {F_1} \times {F_2} \times \cdots \times {F_n}

be a direct product of

n
n

free groups

F
1

,

F
2

,
⋯
,

F
n

,
α

{F_1},{F_2}, \cdots ,{F_n},\alpha

an automorphism of

D
D

which leaves all but one of the noncyclic factors in

D
D

pointwise fixed and

T
T

an infinite cyclic group. Let

D

×
α

T

D{ \times _\alpha }T

be the semidirect product of

D
D

and

T
T

with respect to

α
\alpha

. We prove that the Whitehead group of

D

×
α

T

D{ \times _\alpha }T

and the projective class group of the integral group ring

Z
(
D

×
α

T
)

Z(D{ \times _\alpha }T)

are trivial. The second result implies that the projective class group of the integral group ring over the fundamental group of a surface is trivial.
Asymptotic values and Baire category
Authors: Mida Chaim
Published: June 2010

Let

f
f

be meromorphic in the unit disc, and let

α
\alpha

be a complex number. Given

ε
>
0

\varepsilon > 0

, let

T
ε

(
α
)

{T_\varepsilon }(\alpha )

denote the set of points

e

i
θ

{e^{i\theta }}

for which the cluster set

C

L

(
f
,

e

i
θ

)

{C_\mathcal {L}}(f,{e^{i\theta }})

lies in the

ε
\varepsilon

-neighbourhood of

α
\alpha

for some arc

L

→

e

i
θ

\mathcal {L} \to {e^{i\theta }}

. Then a sufficient condition that the set of points on the unit circle at which

f
f

possesses point-asymptotic value

α
\alpha

be of first category is that

T
ε

(
α
)

{T_\varepsilon }(\alpha )

contains no arc for some

ε
>
0

\varepsilon > 0

.
Nonlinear oscillation of a sublinear delay equation of arbitrary order
Authors: Kusano Takaŝi , Onose Hiroshi
Published: June 2010

The equations considered generalize
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x Superscript left-parenthesis n right-parenthesis Baseline left-parenthesis t right-parenthesis plus p left-parenthesis t right-parenthesis StartAbsoluteValue x left-parenthesis g left-parenthesis t right-parenthesis right-parenthesis EndAbsoluteValue Superscript alpha Baseline s g n x left-parenthesis g left-parenthesis t right-parenthesis right-parenthesis equals 0 comma 0 greater-than alpha greater-than 1 period">

x

(
n
)

(
t
)
+
p
(
t
)

|

x
(
g
(
t
)
)

|

α

sgn
⁡
x
(
g
(
t
)
)
=
0
,

0
>
α
>
1.

{x^{(n)}}(t) + p(t)|x(g(t)){|^\alpha }\operatorname {sgn} x(g(t)) = 0,\quad 0 > \alpha > 1.

\]
A necessary and sufficient condition is established that all solutions are oscillatory when

n
n

is even and are either oscillatory or strongly monotone when

n
n

is odd. The result makes clear a difference in oscillatory property between sublinear delay equations and the corresponding ordinary differential equations.
A tauberian group algebra
Authors: Mueller-Roemer Peter R.
Published: June 2010

Let G be the group of real matrices
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis x comma y right-parenthesis equals Start 2 By 2 Matrix 1st Row 1st Column e Superscript x Baseline 2nd Column a m p semicolon 0 2nd Row 1st Column y 2nd Column a m p semicolon 1 EndMatrix left-parenthesis x comma y element-of upper R right-parenthesis period">

(
x
,
y
)
=

(

e
x

a
m
p
;
0

y

a
m
p
;
1

)

(
x
,
y
∈
R
)
.

(x,y) = \left ( {\begin {array}{*{20}{c}} {{e^x}} & 0 \\ y & 1 \\ \end {array} } \right )\quad (x,y \in R).

\]
Every proper closed two-sided ideal of

L
1

(
G
)

{L^1}(G)

is contained in a maximal modular two-sided ideal. The strong radical of

L
1

(
G
)

{L^1}(G)

is the set of all

f
∈

L
1

(
G
)

f \in {L^1}(G)

with

∫
f
(
x
,
y
)

d
y
=
0

\smallint f(x,y)\;dy = 0

for almost all

x
∈
R

x \in R

. The strong structure spaces of

L
1

(
G
)

{L^1}(G)

and

L
1

(
R
)

{L^1}(R)

are homeomorphic.
Continuity of linear fractional transformations on an operator algebra
Authors: Helton J. William
Published: June 2010

An operator coefficient linear fractional automorphism

F

\mathcal {F}

on the unit ball of operators is continuous in the weak operator topology if and only if

F

(
0
)

\mathcal {F}(0)

is compact.
Subalgebras of 𝐵[𝑐]
Authors: Brown H. I. , Cho Tae Geun
Published: June 2010

Two classes of subalgebras of the bounded operators on the Banach space of convergent sequences are studied. One class contains the well-known algebra of conservative matrices and the other contains the algebra of almost matrices. It is shown that the nontrivial members within each class are isomorphic to each other.
A counterexample to the two-thirds conjecture
Authors: Barnard Roger W. , Lewis John L.
Published: June 2010

Let

w
=
f
(
z
)
=
z
+

a
2

z
2

+
⋯

w = f(z) = z + {a_2}{z^2} + \cdots

be regular and univalent for

|

z

|

>
1

|z| > 1

, and

map
⁡

|

z

|

>
1

\operatorname {map} |z| > 1

onto a region which is starlike with respect to

w
=
0

w = 0

. If

r
0

{r_0}

denotes the radius of convexity of

f
(
z
)
,

d
∗

=
min

|

f
(
z
)

|

f(z),{d^\ast } = \min |f(z)|

for

|

z

|

=

r
0

|z| = {r_0}

and

d
=
inf

|

β

|

d = \inf |\beta |

for which

f
(
z
)
≠
β

f(z) \ne \beta

, then it has been conjectured by A. Schild in 1953 that

d
∗

/

d
≧

2
3

{d^\ast }/d \geqq \tfrac {2}{3}

. It is shown here that this conjecture is false by giving two counter-examples.
Harmonic measure and domains bounded by quasiconformal circles
Authors: Blevins Donald K.
Published: June 2010

We index the class of quasiconformal circles by

k
k

between zero and one such that

k
=
0

k = 0

corresponds to arbitrary Jordan curves and

k
=
1

k = 1

to circles. We establish an estimate depending on

k
k

for harmonic measure in a domain bounded by a quasiconformal circle. Applications of this estimate are made to boundary correspondence under conformal maps, Hardy class of certain functions and a Phragmén-Lindelöf theorem.
Chebyshev approximation with a null space
Authors: Dunham Charles B.
Published: June 2010

Chebyshev approximation involving continuous functions vanishing on a closed set

V
V

is considered. The approximating families studied have the betweenness property. Examples are given of such families. A necessary and sufficient condition for uniqueness of best approximations is obtained.
Degrees of nonrecursive presentability
Authors: Feiner Lawrence
Published: June 2010

We prove that every

0
′

0’

’-recursive binary relation of natural numbers is isomorphic to a recursive relation restricted to a co-r.e. subset of its domain. We use this result to define and discuss “degrees of nonrecursive presentability."
Chebyshev subspaces and convergence of positive linear operators
Authors: Micchelli C. A.
Published: June 2010

A theorem of Korovkin states that a sequence of positive linear operators on

C
[
a
,
b
]

C[a,b]

converges strongly to the identity if and only if convergence holds on a three-dimensional Chebyshev subspace of

C
[
a
,
b
]

C[a,b]

. We extend this theorem to include Chebyshev subspaces of arbitrary dimension and convergence to other positive linear operators.
Concave solutions of a Dirichlet problem
Authors: Guggenheimer H.
Published: June 2010

We define a function that may serve as the measure of the deviation of a plane convex domain from circular shape. Then we show that the Dirichlet problem of

Δ
u
+
λ
p
(
x
,
y
)
u
=
0

\Delta u + \lambda p(x,y)u = 0

and vanishing boundary values on a plane, convex domain can have a concave solution only if an integral condition involving the deviation from circular shape is satisfied. A weak form of the condition is generalized to

n
n

dimensions.
A class of 𝐶*-algebras
Authors: Behncke Horst , Bös Wolfgang
Published: June 2010

In this paper we present a construction of

C
∗

{C^ \ast }

-algebras based on a countable system of subsets of a countable set. The properties of such algebras are described in terms of this system of sets.
Locally contractible spaces that are absolute neighborhood retracts
Authors: Haver William E.
Published: June 2010

It is shown that every locally contractible metric space that is the countable union of finite dimensional compacta is an absolute neighborhood retract.
Compact subsets of 𝑅ⁿ and dimension of their projections
Authors: Mardešić Sibe
Published: June 2010

In this paper it is proved that a

k
k

-dimensional closed subset

X
⊂

R
n

X \subset {R^n}

admits a projection

p
p

into one of the coordinate

k
k

-planes such that

dim
⁡
p
(
X
)
=
k

\dim p(X) = k

.
Certain elements in quotients of measure algebras
Authors: Saeki Sadahiro
Published: June 2010

Let

G
G

be a locally compact group, and

M
(
G
)

M(G)

the convolution algebra with unit

δ
\delta

of all bounded Radon measures on

G
G

. Let

I
I

be a left ideal in

M
(
G
)

M(G)

and let

C
∩

I
⊥

C \cap {I^ \bot }

be the space of all bounded continuous functions

P
P

on

G
G

with

∫
G

P
d
μ
=
0

\int _GPd\mu = 0

for all

μ
\mu

in

I
I

. Suppose that there exists a function

P
0

{P_0}

in

C
∩

I
⊥

C \cap {I^ \bot }

such that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue EndAbsoluteValue upper P 0 StartAbsoluteValue EndAbsoluteValue Subscript normal infinity Baseline greater-than limit sup Underscript x right-arrow normal infinity Endscripts StartAbsoluteValue upper P 0 left-parenthesis x right-parenthesis EndAbsoluteValue">

|

|

P
0

|

|

∞

>
lim

sup

x
→
∞

|

P
0

(
x
)

|

||{P_0}|{|_\infty } > \lim {\sup _{x \to \infty }}|{P_0}(x)|

. Let also

λ
\lambda

and

μ
\mu

be two measures in

M
(
G
)

M(G)

such that

|

|

λ
+
I

|

|

=

|

|

μ
+
I

|

|

=
1

||\lambda + I|| = ||\mu + I|| = 1

, and

(
λ
+
I
)
∗
μ
⊂
δ
+
1

(\lambda + I) \ast \mu \subset \delta + 1

. In this paper we prove under these conditions that there exist a complex number

c
c

of modulus one and a point

x
0

{x_0}

in

G
G

such that

∫
G

P
d
μ
=
c
P
(

x
0

)

\int _G Pd\mu = cP({x_0})

for all functions

P
P

in

C
∩

I
⊥

C \cap {I^ \bot }

with

|

|

P

|

|

∞

≦

|

∫
G

P
d
μ

|

=
1

||P|{|_\infty } \leqq |\int _G Pd\mu | = 1

. This generalizes a theorem of K. deLeeuw and Y. Katznelson.
Effective matchmaking and 𝑘-chromatic graphs
Authors: Manaster Alfred B. , Rosenstein Joseph G.
Published: June 2010

In an earlier paper we showed that there is a recursive society, in which each person knows exactly two other people, whose marriage problem is solvable but not recursively solvable. We generalize this result, using a different construction, to the case where each person knows exactly

k
k

other people. From this we deduce that for each

k
≧
2

k \geqq 2

there is a recursive

2
(
k
−
1
)

2(k - 1)

-regular graph, whose chromatic number is

k
k

but which is not recursively

k
k

chromatic.
Some remarks concerning the number theoretic functions 𝜔(𝑛) and Ω(𝑛)
Authors: Dressler Robert E. , van de Lune Jan
Published: June 2010

In this paper we establish a duality relation between the number theoretic functions

ω
(
n
)

\omega (n)

and

Ω
(
n
)

\Omega (n)

, and we investigate some of its consequences, one of which concerns the Riemann zeta function.
A characterization of thin operators in a von Neumann algebra
Authors: Olsen Catherine L.
Published: June 2010

Let

A

\mathcal {A}

be a von Neumann algebra,

J

\mathcal {J}

a uniformly closed, weakly dense, two-sided ideal in

A

,

L

\mathcal {A},\mathcal {L}

the center of

A

\mathcal {A}

, and

P

\mathcal {P}

the lattice of projections in

J

\mathcal {J}

. An operator

A
∈

A

A \in \mathcal {A}

is thin relative to

J

\mathcal {J}

if

A
=
Z
+
K

A = Z + K

, for some

Z
∈

L

,
K
∈

J

Z \in \mathcal {L},K \in \mathcal {J}

. The thin operators relative to

J

\mathcal {J}

are characterized as those

A
∈

A

A \in \mathcal {A}

satisfying

lim

P
∈

P

|

|

A
P
−
P
A

|

|

=
0

{\lim _{P \in \mathcal {P}}}||AP - PA|| = 0

. It is also shown that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="limit sup Underscript upper P element-of script upper P Endscripts StartAbsoluteValue EndAbsoluteValue upper P upper A upper P minus upper A upper P StartAbsoluteValue EndAbsoluteValue equals limit sup Underscript upper P element-of script upper P Endscripts StartAbsoluteValue EndAbsoluteValue upper P upper A upper P minus upper P upper A StartAbsoluteValue EndAbsoluteValue period">

lim

sup

P
∈

P

|

|

P
A
P
−
A
P

|

|

=
lim

sup

P
∈

P

|

|

P
A
P
−
P
A

|

|

.

\lim \sup \limits _{P \in \mathcal {P}} ||PAP - AP|| = \lim \sup \limits _{P \in \mathcal {P}} ||PAP - PA||.

\]
Scalar curvature, inequality and submanifold
Authors: Chen Bang-yen , Okumura Masafumi
Published: June 2010

Using an inequality relation between scalar curvature and length of second fundamental form, we may conclude that a submanifold must have nonnegative (or positive) sectional curvatures. An application to compact submanifolds in obtained.
Embedding of categories
Authors: Barr Michael
Published: June 2010

In this paper we generalize the notion of exact functor to an arbitrary category and show that every small category has a full embedding into a category of all set-valued functors on some small category. The notion of exact is such that this result generalizes the author’s exact embedding of regular categories and, indeed, Mitchell’s embedding of abelian categories. An example is given of the type of diagram-chasing argument that can be given with this embedding.
Torsion theory and associated primes
Authors: Cahen Paul-Jean
Published: June 2010

A torsion theory partitions the spectrum of the base ring into two sets. Over a Noetherian ring, every suitable partition of the spectrum gives rise to one and only one torsion theory. It is possible to know whether a module is torsion or torsion-free by looking at its associated primes. The example of the polynomial torsion theory is developed.
Direct decomposition of tensor products into subtensor products
Authors: Chung I. Y.
Published: June 2010

A subtensor product of a family of modules is defined by using a subdirect product of the family of modules considered as sets. A tensor product of modules can be decomposed into a direct sum of subtensor products of the modules. Subtensor products of graded modules and graded algebras are also studied. As an application of these, a certain subtensor product of a family (not necessarily finite) of anticommutative algebras is shown to be a coproduct of this family in the category of unitary anticommutative algebras, and it can be imbedded as a direct summand into a tensor product of the family as modules.
Principal congruences of pseudocomplemented distributive lattices
Authors: Lakser Harry
Published: June 2010

Principal congruences of pseudocomplemented distributive lattices are characterized. This characterization is used to give a new proof of the congruence extension property and to show that the meet of two principal congruences is always principal in an equational class of pseudocomplemented distributive lattices if and only if the class is a subclass of the class of Stone algebras.
Groups with central 2-Sylow intersections of rank at most one
Authors: Herzog Marcel , Shult Ernest
Published: June 2010

An involution in a finite group is called central if it lies in the center of a

2
2

-Sylow subgroup of

G
G

. A

2
2

-Sylow intersection is called central if it is either trivial or contains a central involution. Suppose

G
G

is a finite simple group all of whose central

2
2

-Sylow intersections are trivial or rank one

2
2

-groups. It is proved that

G
G

is a known simple group.
Shocks violating Lax’s condition are unstable
Authors: Conway E. D. , Smoller J. A.
Published: June 2010

For a system of two conservation laws, we prove that solutions violating Lax’s condition across shocks are unstable relative to smoothing of the initial data.
A lifting theorem for formal power series
Authors: Bender Edward A.
Published: June 2010

We define a class of operations on formal power series that includes practically all operations of interest. The class is closed under composition. We prove that an operation in this class vanishes for complex numbers if and only if it vanishes for functions analytic at the origin. A variety of applications of this “lifting theorem” are discussed.
On the Marx conjecture for the convex hulls of families of starlike and convex mappings
Authors: Hallenbeck David J.
Published: June 2010

We prove a Marx conjecture for the closed convex hull of the family of functions which are starlike of order

α
\alpha

and k-fold symmetric. We obtain precise results for the functions which are starlike, starlike of order

1
2

\tfrac {1}{2}

, and starlike with 2-fold symmetry in their power series expansions.
Nonlinear integral equations in a measure space
Authors: Das P. C.
Published: June 2010

An abstract nonlinear integral equation is formulated in a measure space and existence, uniqueness of its solution is proved. It is shown that it includes as particular cases certain classes of integral equations and also differential equations containing measures.