bluuebunny/crossref_metadata_2025 huggingface dataset:
Some maximal topologies which are QHC
Authors: Cameron Douglas E.
Published: June 2010

In this paper we characterize maximal C-compact spaces, maximal QHC spaces, and maximal nearly compact spaces. We also discuss a covering property which turns out to be equivalent to S-closed and extremally disconnected.
A theorem on extending representations
Authors: Fabec Raymond C.
Published: June 2010

We obtain sufficient conditions for a unitary representation of a closed subgroup M of a separable locally compact group G to have a unique unitary extension to G. The conditions depend on the behavior of the representation on a closed normal subgroup N of G contained in M. We then discuss an application of the theorem in particle physics.
The real Brauer group of a finite CW-complex
Authors: Strickland Elisabetta
Published: June 2010

In this paper a complete description in homological terms of the real Brauer group

Br
R

(
X
)

{\text {Br}_R}(X)

of a finite CW-complex X is obtained, in analogy with Jean Pierre Serre’s result on the complex Brauer group

Br
C

(
X
)

{\text {Br}_C}(X)

and the author’s one for the orthogonal case. Precisely it is shown that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="Br Subscript upper R Baseline left-parenthesis upper X right-parenthesis approximately-equals upper H squared left-parenthesis upper X comma upper Z 2 right-parenthesis circled-plus upper H Superscript 0 Baseline left-parenthesis upper X comma upper Z 2 right-parenthesis period">

Br
R

(
X
)
≅

H
2

(
X
,

Z
2

)
⊕

H
0

(
X
,

Z
2

)
.

{\text {Br}_R}(X) \cong {H^2}(X,{Z_2}) \oplus {H^0}(X,{Z_2}).

\]
An intersection result for tensor products of 𝐶*-algebras
Authors: Huruya Tadasi
Published: June 2010

There exists a

C
∗

{C^\ast }

-tensor product

A
⊗
B

A \otimes B

with

C
∗

{C^\ast }

-subalgebras

A
1

⊗

B
1

{A_1} \otimes {B_1}

and

A
2

⊗

B
2

{A_2} \otimes {B_2}

such that

(

A
1

⊗

B
1

)
∩
(

A
2

⊗

B
2

)

({A_1} \otimes {B_1}) \cap ({A_2} \otimes {B_2})

strictly contains

(

A
1

∩

A
2

)
⊗
(

B
1

∩

B
2

)

({A_1} \cap {A_2}) \otimes ({B_1} \cap {B_2})

.
The essential closure of 𝐶(𝑋)
Authors: Anderson Marlow
Published: June 2010

Each archimedean l-group admits a unique essential closure, which is the l-group of continuous almost finite real-valued functions on some Stonean space; thus the l-group

C
(
X
)

C(X)

of real-valued continuous functions on a topological space X admits such an essential closure. In this note we will construct a natural embedding of

C
(
X
)

C(X)

into its essential closure, making explicit the topological relationship between X and the appropriate Stonean space.
The étale homotopy type of varieties over 𝑅
Authors: Cox David A.
Published: June 2010

For a variety X over

Spec

(

R

)

{\text {Spec}}({\mathbf {R}})

, the étale homotopy type of X is computed in terms of the action of complex conjugation on the complex points

X
(

C

)

X({\mathbf {C}})

. This enables one to show that

X
(

R

)
≠
∅

X({\mathbf {R}}) \ne \emptyset

is equivalent to various conditions on the étale cohomology of X, and, when X is a smooth, geometrically connected, proper curve over

Spec

(

R

)

{\text {Spec}}({\mathbf {R}})

, to compute the étale cohomology. Finally, there is a negative result, showing that étale cohomology cannot be used to compute the topological degree of a mapping germ

f
:
(

R

n

,
0
)
→
(

R

n

,
0
)

f:({{\mathbf {R}}^n},0) \to ({{\mathbf {R}}^n},0)

.
A realization of the additive Witt group
Authors: Newman Kenneth , Sweedler Moss E.
Published: June 2010

For each prime p we construct in several ways a canonical sequence of divided powers and give an elementary proof that its coefficients lie

Z

(
p
)

{{\mathbf {Z}}_{(p)}}

.
Constructive solution of the 1918 problem of Lord Rayleigh
Authors: McAllister M. N. , Rohde S. M. , McAllister G. T.
Published: June 2010

In 1918 Lord Rayleigh posed the problem of finding the profile (shape) of a one dimensional slider bearing which will support the greatest weight. In this paper we give, in closed form, the solution of this problem.
Robertson’s conjecture on the coefficients of close-to-convex functions
Authors: Leung Y.
Published: June 2010

We use an inequality due to Lebedev and Milin to prove a conjecture made by M.S. Robertson on the coefficients of close-to-convex functions.
Compact operators with root vectors that span
Authors: Deckard D. , Foiaş C. , Pearcy C.
Published: June 2010

A concrete example is given of a bounded, linear, compact, quasiaffinity T acting on a separable, infinite dimensional, Hilbert space

H

\mathcal {H}

with the property that the eigenvectors of T span

H

\mathcal {H}

but the root vectors of

T
∗

{T^ \ast }

span a subspace of

H

\mathcal {H}

with infinite dimensional orthocomplement.
Some characterizations of Hermitian operators and related classes of operators. I
Authors: Fong Che Kao , Istrăţescu Vasile I.
Published: June 2010

It is shown that, among other things, an operator T is hermitian if and only if

|

T

|

2

⩽

(
Re
⁡
T

)
2

|T{|^2} \leqslant {(\operatorname {Re} T)^2}

. Also, the class of those operators T satisfying

|

T

|

2

⩾

(
Re
⁡
T

)
2

|T{|^2} \geqslant {(\operatorname {Re} T)^2}

is investigated.
Inner limit derivations
Authors: Herman Richard H.
Published: June 2010

We give a condition involving the approximating derivations and a faithful state which, in conjunction with the “core condition", guarantees that the derivation gives rise to an automorphism group of the von Neumann algebra coming from the state via the GNS procedure.
Near derivations and information functions
Authors: Lawrence John , Mess Geoff , Zorzitto Frank
Published: June 2010

Near-derivations

γ
\gamma

satisfy the conditions

γ
(
x
y
)
=
x
γ
(
y
)
+
y
γ
(
x
)

\gamma (xy) = x\gamma (y) + y\gamma (x)

for

x
,
y
∈
R
,
γ
(
x
+
y
)
⩾
γ
(
x
)
+
γ
(
y
)

x,y \in R,\gamma (x + y) \geqslant \gamma (x) + \gamma (y)

for

x
,
y
⩾
0
,
γ
(
x
)
=
0

x,y \geqslant 0,\gamma (x) = 0

for

x
∈
Q

x \in Q

. Existence of near-derivations other than derivations is tied in with that of nonnegative information functions and an example of Daróczy and Maksa. Conditions for near-derivations to be derivations are discussed.
A Schröder-Bernstein theorem in Baer*-rings with lattice-theoretic proof
Authors: Hakeda Jôsuke
Published: June 2010

The Schröder-Bernstein theorem (SB-theorem) for

∗
*

-equivalence of projections of a

B
a
e
r

∗

\mathrm {Baer}^*

-ring is known. Here, we will prove an SB-theorem for algebraic equivalence (Theorem A) as a consequence of a lattice-theoretic SB-theorem (Theorem B). Theorem A and the known result about

∗
*

-equivalence will be derived from Theorem B.
Poincaré duality and fibrations
Authors: Gottlieb Daniel Henry
Published: June 2010

Let

F
→
E
→
B

F \to E \to B

be a fibration such that F, E, and B are homotopy equivalent to finite complexes. Then the following fact is proved. E is a Poincaré duality space if and only if B and F are Poincaré duality spaces.
A surjective characterization of Dugundji spaces
Authors: Hoffmann Burkhard
Published: June 2010

It is shown that the class of Dugundji spaces coincides with the class of continuous images of the generalized Cantor set by maps satisfying the zero-dimensional lifting property. It follows that each point in a Dugundji space has a neighbourhood base of Dugundji spaces.
The Schur index of the 𝑝-regular characters of the Borel subgroup
Authors: Lehrer G. I.
Published: June 2010

Let B be the group of

F

q

{{\mathbf {F}}_q}

-rational points of the Borel subgroup of a connected reductive group defined over the finite field

F

q

{{\mathbf {F}}_q}

. It is shown that under appropriate conditions, all irreducible characters of B which have degree prime to q have Schur index one.
Majorization on a partially ordered set
Authors: Hwang F. K.
Published: June 2010

We extend the classical concept of set majorization to the case where the set is partially ordered. We give a useful property which characterizes majorization on a partially ordered set. Quite unexpectedly, the proof of this property relies on a theorem of Shapley on convex games. We also give a theorem which is parallel to the Schur-Ostrowski theorem in comparing two sets of parameters in a function.
Periodic modules with large periods
Authors: Carlson Jon F.
Published: June 2010

Let G be a nonabelian group of order

p
3

{p^3}

and exponent p, where p is an odd prime. Let K be a field of characteristic p. In this paper it is proved that there exist periodic KG-modules whose periods are 2p. Some examples of such modules are constructed.
Dynamical systems whose orbit spaces are nearly Hausdorff
Authors: McCann Roger C.
Published: June 2010

Consider a continuous flow on a locally compact, separable, metric space. If the set of nonperiodic recurrent points is nowhere dense, then there is an open, dense, invariant subset of the phase space which has a Hausdorff orbit space. A separatrix is defined to be a trajectory which is in the closure of the set of trajectories at which the orbit space is not Hausdorff. If the flow is completely unstable, then the set of points which lie on separatrices is nowhere dense in the phase space.
A note on transforms of subspaces of Hilbert space
Authors: Longstaff W. E.
Published: June 2010

The transform of a family

F

\mathcal {F}

of (closed linear) subspaces of a Hilbert space H by an invertible (bounded, linear) operator S on H is the family of subspaces

{
S
M
:
M
∈

F

}

\{ SM:M \in \mathcal {F}\}

. It is shown that the set of projections

{

P

S
M

:
M
∈

F

}

\{ {P_{SM}}:M \in \mathcal {F}\}

is closed in the uniform (respectively, strong, weak) operator topology if and only if the set of projections

{

P
M

:
M
∈

F

}

\{ {P_M}:M \in \mathcal {F}\}

is uniformly (respectively, strongly, weakly) closed. This answers affirmatively a question raised by K. J. Harrison.
Dissection of the hypercube into simplexes
Authors: Mead D. G.
Published: June 2010

A generalization of Sperner’s Lemma is proved and, using extensions of p-adic valuations to the real numbers, it is shown that the unit hypercube in n dimensions can be divided into m simplexes all of equal hypervolume if and only if m is a multiple of n!. This extends the corresponding result for

n
=
2

n = 2

of Paul Monsky.
A complete bounded complex submanifold of 𝐶³
Authors: Jones Peter W.
Published: June 2010

We produce an example of a bounded complete complex submanifold of

C

3

{{\mathbf {C}}^3}

. This is accomplished by using the duality between

H
1

(

T

)

{H^1}({\mathbf {T}})

and

BMO

(

T

)

{\text {BMO}}({\mathbf {T}})

.
On the dimension of product spaces and an example of M. Wage
Authors: Przymusiński Teodor C.
Published: June 2010

Modifying a recent example obtained under the assumption of the Continuum Hypothesis by Michael Wage, we prove, without any set-theoretic assumptions beyond ZFC, that for every natural number n there exists a separable and first countable space X such that: (a)

X
n

{X^n}

is Lindelöf and

dim
⁡

X
n

=
0

\dim {X^n} = 0

; (b)

X

n
+
1

{X^{n + 1}}

is normal but

dim
⁡

X

n
+
1

>
0

\dim {X^{n + 1}} > 0

. We obtain from this the following corollary. There exists a separable and first countable Lindelöf space X such that: (a)

dim
⁡
X
=
0

\dim X = 0

; (b)

X
2

{X^2}

is normal but

dim
⁡

X
2

>
0

\dim {X^2} > 0

. The space X instead of being Lindelöf can be made locally compact and locally countable.
Periodic and fixed points, and commuting mappings
Authors: Jungck Gerald
Published: June 2010

We employ commuting mappings to produce generalizations of locally contractive and locally expansive maps, and obtain criteria for the existence of fixed and periodic points of arbitrary maps on compacta.
There is no universal separable Moore space
Authors: van Douwen Eric K.
Published: June 2010

There is no Hausdorff space of cardinality

c

\mathfrak {c}

(in particular, there is no separable Moore space) which includes a homeomorph of every separable Moore space.
Trivial extension of a ring with balanced condition
Authors: Sekiyama Hideaki
Published: June 2010

A ring R is called QF-1 if every faithful R-module is balanced. In this paper we study commutative QF-1 rings. It is shown that a commutative QF-1 ring is local if and only if it is uniform. It is well known that commutative artinian QF-1 rings are QF, but Osofsky has constructed a nonartinian nonnoetherian commutative injective cogenerator, so QF-1, ring which is a trivial extension of a valuation ring. It is shown that if a trivial extension of a valuation ring is QF-1, then it has a nonzero socle. Furthermore such rings become injective cogenerator rings under certain conditions.
A right PCI ring is right Noetherian
Authors: Damiano Robert F.
Published: June 2010

C. Faith and J. Cozzens have shown that a ring, whose right proper cyclic modules are injective, is either semisimple or a simple, right semihereditary, right Ore V-domain. They have posed a question as to whether such a ring is right noetherian. In this paper, an affirmative answer is given to that question. Moreover, necessary and sufficient conditions are given as to when a right PCI ring is left PCI.
The Lyndon-Hochschild-Serre spectral sequences for sheaves with operators
Authors: Suwa Tatsuo
Published: June 2010

Two spectral sequences associated with a G-sheaf and a normal subgroup of G are given together with an application.
Graphical evaluation of sparse determinants
Authors: Drucker Daniel , Goldschmidt David M.
Published: June 2010

In this paper, we show that the determinant of a matrix with entries in a commutative ring can be recursively computed by use of an associated directed graph whose circuits are assigned weights in the ring. This result provides an efficient means of calculating the determinants of sparse matrices. As an application, we compute the determinants of the Cartan matrices associated to the simple complex Lie algebras.
La semicontinuité et la propriété de Baire
Authors: Grande Z. , Stawikowska S.
Published: June 2010

Let X, Y be two metric separable and complete spaces and R be a set of all reals numbers. If all sections

f
x

(
y
)
=
f
(
x
,
y
)

(
x
∈
X

{f_x}(y) = f(x,y)\;(x \in X

and

y
∈
Y
)

y \in Y)

of a function

f
:
X
×
Y
→
R

f:X \times Y \to R

are almost qualitative upper semiequicontinuous and upper semicontinuous [upper semiequicontinuous] and if all sections

f
y

(
x
)
=
f
(
x
,
y
)

{f^y}(x) = f(x,y)

have the Baire property [are borelien], then the function f has the Baire property [is borelien].
Unbounded uniformly absolutely continuous sets of measures
Authors: Bell Wayne C.
Published: June 2010

It is shown that a uniformly absolutely continuous set of finitely additive measures can be decomposed into bounded and finite dimensional parts.
𝐶₁₁ contractions are reflexive
Authors: Wu Pei Yuan
Published: June 2010

It is shown that a completely nonunitary

C

11

{C_{11}}

contraction defined on a separable Hilbert space with finite defect indices is reflexive.
d’Alembert’s functional equation on groups
Authors: Penney R. C. , Rukhin A. L.
Published: June 2010

Group representation theory is used to solve a functional equation of the D’Alembert type on groups.
New explicit formulas for the coefficients of 𝑝-symmetric functions
Authors: Todorov Pavel G.
Published: June 2010

In comparison with Goodman’s well-known method and results, we use an alternate method by which we obtain more tractable formulas for the coefficients of p-symmetric univalent functions of classes

S
p

{S^p}

and

Σ
p

{\Sigma ^p}

in terms of the coefficients of their associated functions in the class s. Our method and results are simple and convenient and they make it easier to compute the coefficients for functions in the classes

S
p

{S^p}

and

Σ
p

{\Sigma ^p}

, because we obtain a new recursion formula for them.
Stiffness of harmonic functions
Authors: Wang Cecilia Y.
Published: June 2010

Harmonic functions cannot change rapidly. For example, if K is a compact subset of a Riemann surface R and {u} a family of harmonic functions u on R of nonconstant sign on K, then it is known that there exists a constant

q
∈
(
0
,
1
)

q \in (0,1)

independent of u such that

max
K

|

u

|

⩽
q

sup
R

|

u

|

{\max _K}|u| \leqslant q{\sup _R}|u|

for all

u
∈
{
u
}

u \in \{ u\}

. In the present note we shall show that relations expressing such “stiffness” of harmonic functions can also be given for the Dirichlet norm and for the partial derivative with respect to the Green’s function.
A maximal inequality for 𝐻¹-functions on a generalized Walsh-Paley group
Authors: Fujii Nobuhiko
Published: June 2010

Let

G
=

∏

i
=
0

∞

Z
(

p
i

)

G = \prod _{i = 0}^\infty Z({p_i})

be the countable product of discrete cyclic groups of order

p
i

{p_i}

. We assume that

sup

i
⩾
0

p
i

>
∞

{\sup _{i \geqslant 0}}{p_i} > \infty

. We consider Walsh-Fourier series on G and define

H
1

{H^1}

-functions on G by the Coifman-Weiss atoms. Let

K
n

(
x
)

{K_n}(x)

be the nth (C, 1)-kernel. We prove that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Underscript upper G Endscripts sup Underscript n greater-than-or-slanted-equals 1 Endscripts StartAbsoluteValue left-parenthesis upper K Subscript n Baseline asterisk f right-parenthesis left-parenthesis x right-parenthesis EndAbsoluteValue d mu less-than-or-slanted-equals upper C double-vertical-bar f double-vertical-bar Subscript upper H Sub Superscript 1 Baseline">

∫
G

sup

n
⩾
1

|

(

K
n

∗
f
)
(
x
)

|

d
μ
⩽
C

‖
f
‖

H
1

{\smallint _G {{{\sup }_{n \geqslant 1}}|({K_n} \ast f)(x)|d\mu \leqslant C\left \| f \right \|} _{{H^1}}}

. Here

d
μ

d\mu

is the normalized Haar measure,

‖
‖

H
1

{\left \| \right \|_{{H^1}}}

is the

H
1

{H^1}

-norm and C is a constant independent of f.
On a theorem of P. S. Muhly
Authors: Tanaka Jun-ichi
Published: June 2010

The purpose of this paper is to show that if

M

A

{\mathfrak {M}_\mathfrak {A}}

is the maximal ideal space of the function algebra induced by a strictly ergodic flow, then almost every point in

M

A

{\mathfrak {M}_\mathfrak {A}}

has a unique representing measure which is concentrated on an orbit. This result enables us to extend some theorems of Muhly to a more general setting.
Construction of a rigid Aronszajn tree
Authors: Avraham Uri
Published: June 2010

We construct in ZFC an Aronszajn tree with no automorphism.
Nontrivially pseudocomplemented lattices are complemented
Authors: Lambrou M. S.
Published: June 2010

Nontrivially pseudocomplemented lattices are complemented.
Rings whose right modules are direct sums of indecomposable modules
Authors: Zimmermann-Huisgen Birge
Published: June 2010

It is shown that, given a module M over a ring with 1, every direct product of copies of M is a direct sum of modules with local endomorphism rings if and only if every direct sum of copies of M is algebraically compact. As a consequence, the rings whose right modules are direct sums of indecomposable modules coincide with those whose right modules are direct sums of finitely generated modules.
Modified Poisson kernels on rank one symmetric spaces
Authors: Mantero Anna Maria
Published: June 2010

An extension is obtained to the case of a real rank one noncompact symmetric space G/K of the solution of the following problem on half-spaces: given an arbitrary continuous function

f
(
x
)

f(x)

on

R

n

{{\mathbf {R}}^n}

, is it possible to find a function F on

R

n

×

R

+

{{\mathbf {R}}^n} \times {{\mathbf {R}}^ + }

such that

F
(
x
,
y
)

F(x,y)

is continuous for

y
>
0

y > 0

, harmonic for

y
>
0

y > 0

and such that

F
(
x
,
0
)
=
f
(
x
)

F(x,0) = f(x)

?
The very well poised ₆𝜓₆
Authors: Askey Richard , Ismail Mourad E. H.
Published: June 2010

A simple proof is given for Bailey’s sum of the very well poised

6

ψ
6

_6{\psi _6}

and then this is shown to contain a q-extension of the partial fraction decomposition of

csc
⁡
π
x

\csc \pi x

.
Eigenvalues and eigenfunctions of Riemannian manifolds
Authors: Lange Frieder-Jens , Simon Udo
Published: June 2010

S.-Y. Cheng [Proc. Amer. Soc. 55 (1976), 379-381] investigated closed two-dimensional Riemannian manifolds of genus zero which admit m first eigenfunctions with constant square sum,

m
>
1

m > 1

. In this note, we will investigate n-dimensional Riemannian manifolds with m eigenfunctions, corresponding to the eigenvalue

λ
\lambda

, and with constant square sum. Examples of such manifolds are minimal submanifolds of spheres. While Cheng investigated closed manifolds, most of our results have local character. We give lower bounds for

λ
\lambda

by curvature functions (scalar curvature, sectional curvature) and apply these results in two cases: (i) to characterize manifolds which are locally isometric to spheres; (ii) to the investigation of minimal submanifolds of spheres. These results extend earlier results of Lange and Simon.
New decidable fields of algebraic numbers
Authors: van den Dries L.
Published: June 2010

A formally real field of algebraic numbers is constructed which has decidable elementary theory and does not have a real closed or p-adically closed subfield.
On two results of J. Dugundji about extensions of maps and retractions
Authors: Steinlein H.
Published: June 2010

We give a short proof of Dugundji’s result that spheres in infinite-dimensional normed spaces are absolute retracts.
Pseudolattice properties of the star-orthogonal partial ordering for star-regular rings
Authors: Hartwig Robert E.
Published: June 2010

It is shown that a star-regular ring R forms a pseudo upper semilattice under the star-orthogonal partial ordering. That is, for every a, b in R, the set

{
c

|

c
⩾
a
,
c
⩾
b
}

\{ c|c \geqslant a,c \geqslant b\}

is nonempty if and only if

a
∨
b

a \vee b

exists in R, in which case
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a logical-or b equals a plus left-parenthesis 1 minus a a Superscript dagger Baseline right-parenthesis b b Superscript asterisk Baseline left-bracket left-parenthesis 1 minus a Superscript dagger Baseline a right-parenthesis b Superscript asterisk Baseline right-bracket Superscript dagger Baseline period">

a
∨
b
=
a
+
(
1
−
a

a
†

)
b

b
∗

[
(
1
−

a
†

a
)

b
∗

]
†

.

a \vee b = a + (1 - a{a^\dagger })b{b^ \ast }{[(1 - {a^\dagger }a){b^ \ast }]^\dagger }.

\]
On the classification of finite simple groups by the number of involutions
Authors: Herzog Marcel
Published: June 2010

Simple groups with k involutions, where

k
≡
1

k \equiv 1

(modulo 4), are completely determined.
Generic properties of contraction semigroups and fixed points on nonexpansive operators
Authors: De Blasi F. S. , Myjak J.
Published: June 2010

Let

Ω
\Omega

be a nonempty, closed, bounded and starshaped subset of a Banach space X. It is shown that most (in the Baire category sense) differential equations

u
′

+
A
u
=
0

u’ + Au = 0

do have a unique asymptotic equilibrium point. Here

A
:
Ω
→
X

A:\Omega \to X

is supposed to be a nonlinear, continuous, bounded and accretive operator satisfying the Nagumo boundary condition. An application to the fixed point theory of nonexpansive operators

F
:
Ω
→
X

F:\Omega \to X

satisfying

F
(
∂
Ω
)
⊂
Ω

F(\partial \Omega ) \subset \Omega

is given.
Ultra-strong Ditkin sets in hypergroups
Authors: Chilana Ajit Kaur , Kumar Ajay
Published: June 2010

We introduce compactly separating sets for hypergroups which under certain conditions turn out to be ultra-strong Ditkin for the hypergroup algebra whenever their boundary is. We also characterize such sets for the hypergroup related to p-adic numbers.
A Cohen type inequality for compact Lie groups
Authors: Giulini Saverio , Soardi Paolo M. , Travaglini Giancarlo
Published: June 2010

The following theorem is proved: let G denote a compact connected semisimple Lie group. There exists

θ
=
θ
(
G
)
(
3
⩽
θ
>
4
)

\theta = \theta (G)(3 \leqslant \theta > 4)

such that, if

χ
1

,
…
,

χ
N

{\chi _1}, \ldots ,{\chi _N}

are N distinct characters of G,

d
1

,
…
,

d
N

{d_1}, \ldots ,{d_N}

their dimensions,

c
1

,
…
,

c
N

{c_1}, \ldots ,{c_N}

complex numbers of modulus greater than or equal to one, then, for all
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p greater-than theta comma StartAbsoluteValue EndAbsoluteValue StartAbsoluteValue normal upper Sigma Subscript j equals 1 Superscript upper N Baseline c Subscript j Baseline d Subscript j Baseline chi Subscript j Baseline EndAbsoluteValue StartAbsoluteValue EndAbsoluteValue Subscript p Baseline greater-than-or-slanted-equals const Subscript p Baseline upper N Superscript alpha Super Subscript p Superscript">

p
>
θ
,

|

|

|

Σ

j
=
1

N

c
j

d
j

χ
j

|

|

|

p

⩾

const
p

N

α
p

p > \theta ,|||\Sigma _{j = 1}^N{c_j}{d_j}{\chi _j}||{|_p} \geqslant \text {const}_p N^{\alpha _p}

where

|

|

|

⋅

|

|

|

p

||| \cdot ||{|_p}

denotes the

L
p

(
G
)

{L^p}(G)

convolutor norm and

const
p

\text {const}_p

and

α
p

=

α
p

(
G
)

{\alpha _p} = {\alpha _p}(G)

are positive constants. Results on divergence of Fourier series on compact Lie groups are deduced.
Common fixed points and partial orders
Authors: Brøndsted Arne
Published: June 2010

It is observed that certain theorems on common fixed points may be derived from a theorem on partially ordered sets.
Common fixed-point theorems for commuting maps on a metric space
Authors: Das K. M. , Naik K. Viswanatha
Published: June 2010

Results generalizing and unifying fixed point theorems of Jungck and Ciric are established.
𝐿² harmonic forms on rotationally symmetric Riemannian manifolds
Authors: Dodziuk Jozef
Published: June 2010

The paper contains a vanishing theorem for

L
2

{L^2}

harmonic forms on complete rotationally symmetric Riemannian manifolds. This theorem requires no assumptions on curvature.
The generation of nonlinear equivariant differential operators
Authors: Delver Robert
Published: June 2010

Finite generation results are given for the set of smooth nonlinear differential operators:

C
∞

(
M
,
N
)
→

C
∞

(
M
,

R

)

{C^\infty }(M,N) \to {C^\infty }(M,{\mathbf {R}})

of order

⩽
k

\leqslant k

which are equivariant with respect to the action of a Lie group on the base manifold M.
An axiomatic proof of Stiefel’s conjecture
Authors: Blanton John D. , McCrory Clint
Published: June 2010

Stiefel’s combinatorial formula for the Stiefel-Whitney homology classes of a smooth manifold is proved, by verifying that the classes defined by his formula satisfy axioms which characterize the Stiefel-Whitney classes.
The Hahn-Banach theorem implies Sine’s mean ergodic theorem
Authors: Satō Ryōtarō
Published: June 2010

Using the Hahn-Banach theorem, a simple proof of Sine’s mean ergodic theorem is given.
On system of parameters, local intersection multiplicity and Bezout’s theorem
Authors: Bod’a Eduard , Vogel Wolfgang
Published: June 2010

This paper provides effective methods for computing the local intersection multiplicity as the length of a well-defined ideal (see Theorem and Proposition 1). There are other ways of obtaining such an ideal (see [2], [9], [12], [18]) but ours is simpler because of our use of reducing systems of parameters. Applying these ideal theoretic methods we will give a new and simple proof of Bezout’s Theorem (see §4). Hence this proof again provides the connection between the different viewpoints which are treated in the work of Lasker-Macaulay-Gröbner and Severi-van der Waerden-Weil concerning the multiplicity theory.
The residual finiteness of certain one-relator groups
Authors: Allenby R. B. J. T. , Moser L. E. , Tang C. Y.
Published: June 2010

We prove that the groups

⟨
a
,
b
;

(

a

−
1

b
l

a

b
m

)
t

⟩

\langle a,b;{({a^{ - 1}}{b^l}a{b^m})^t}\rangle

, where

l
,
m
,
t
∈
Z

l,m,t \in Z

and

t
⩾
2

t \geqslant 2

are residually finite

(
R

F
)

{(_R}F)

, thus establishing a conjecture of G. Baumslag [Bull. Amer. Math. Soc. 73 (1967), 618-620].
Reflexive lattices of subspaces
Authors: Kim K. H. , Roush F. W.
Published: June 2010

A lattice of subspaces of a vector space is called reflexive if no other subspace is invariant under all linear mappings which leave invariant all subspaces of the lattice. We characterize finite reflexive lattices of subspaces of a finite dimensional vector space over an infinite field.
Subharmonic functions and uniform algebras
Authors: Kumagai Donna
Published: June 2010

Recently Aupetit and Wermer [J. Functional Anal. 28 (1978), 386-400] have shown conditions under which analytic structure exists in the spectrum space of a uniform algebra. Their work makes critical use of subharmonicity properties of certain classes of functions. In this paper, we develop a technique which offers an alternate and unified proof for subharmonicity of the functions in their paper assuming Basener’s generalized Shilov boundary conjecture. Our technique uses the Oka-Wermer method applied to the n-fold tensor product of the algebra. We exhibit further applications of our main result including a special case which holds for all uniform algebras.
On a boundedness condition for operators with a singleton spectrum
Authors: Williams J. P.
Published: June 2010

For a bounded invertible linear operator A let

B

A

{\mathcal {B}_A}

consist of those operators X for which

sup
{

‖

A
n

X

A

−
n

‖

:
n
⩾
0
}
>
∞

\sup \{ \left \| {{A^n}X{A^{ - n}}} \right \|:n \geqslant 0\} > \infty

. It is shown that

B

A

{\mathcal {B}_A}

contains the ideal of compact operators if and only if A is similar to a scalar multiple of a unitary operator. Also, if A is invertible and either has a one-point spectrum or is positive definite then

B

A

∩

B

A

−
1

{\mathcal {B}_A} \cap {\mathcal {B}_{{A^{ - 1}}}}

is the commutant of A.
A separable Banach space with the Radon-Nikodým property that is not isomorphic to a subspace of a separable dual
Authors: McCartney Philip W. , O’Brien Richard C.
Published: June 2010

In this paper an example is given of a separable Banach space with the Radon-Nikodým property that is not isomorphic to a subspace of a separable dual space.
The weak behavior of spherical means
Authors: Kenig Carlos E. , Tomas Peter A.
Published: June 2010

C. Fefferman has shown that the disc multiplier is not bounded on

L
p

(

R

n

)
,
n
>
1
,
p
≠
2

{L^p}({{\mathbf {R}}^n}),n > 1,p \ne 2

. In contrast, C. Herz showed that, when restricted to

L
p

{L^p}

radial functions, it is bounded on

L
p

(

R

n

)

{L^p}({{\mathbf {R}}^n})

if and only if

2
n

/

(
n
+
1
)
>
p
>
2
n

/

(
n
−
1
)

2n/(n + 1) > p > 2n/(n - 1)

. We show that it is not weakly bounded for

p
=
2
n

/

(
n
+
1
)

p = 2n/(n + 1)

or

p
=
2
n

/

(
n
−
1
)

p = 2n/(n - 1)

.
Radius of starlikeness of convex combinations of univalent starlike functions
Authors: Hamilton D. H. , Tuan P. D.
Published: June 2010

The radius of starlikeness of the convex combination
\[

t
f
(
z
)
+
(
1
−
t
)
g
(
z
)
,

0
>
t
>
1
,

tf(z) + (1 - t)g(z),\quad 0 > t > 1,

\]
where

f
(
z
)

f(z)

and

g
(
z
)

g(z)

are normalized univalent starlike functions, is

r
u

=
0.4035
…

{r_u} = 0.4035 \ldots

, the positive root of the equation

r
6

+
5

r
4

+
79

r
2

−
13
=
0

{r^6} + 5{r^4} + 79{r^2} - 13 = 0

.
Sumsets of measurable sets
Authors: Nathanson Melvyn B.
Published: June 2010

Let

A

1

,

A

2

,
…
,

A

n

{\mathcal {A}_1},{\mathcal {A}_2}, \ldots ,{\mathcal {A}_n}

be Lebesgue measurable sets of positive real numbers such that

inf

A

i

=
0

{\inf \mathcal {A}_i} = 0

for all i. Let

μ
\mu

denote Lebesgue measure and let

μ
∗

{\mu _ \ast }

denote inner Lebesgue measure. If

∑

i
=
1

n

μ
(

A

i

∩
[
0
,
t
]
)
⩾
γ
t

\sum \nolimits _{i = 1}^n \mu ({\mathcal {A}_i} \cap [0,t]) \geqslant \gamma t

for some

γ
⩽
1

\gamma \leqslant 1

and all

t
⩽
x

t \leqslant x

, then
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="mu Subscript asterisk Baseline left-parenthesis left-parenthesis script upper A 1 plus script upper A 2 plus midline-horizontal-ellipsis plus script upper A Subscript n Baseline right-parenthesis intersection left-bracket 0 comma x right-bracket right-parenthesis greater-than-or-slanted-equals gamma x period">

μ
∗

(
(

A

1

+

A

2

+
⋯
+

A

n

)
∩
[
0
,
x
]
)
⩾
γ
x
.

{\mu _ \ast }(({\mathcal {A}_1} + {\mathcal {A}_2} + \cdots + {\mathcal {A}_n}) \cap [0,x]) \geqslant \gamma x.

\]
This generalizes results of Dyson and Macbeath.
Oscillation of first-order nonlinear differential equations with deviating arguments
Authors: Kitamura Yuichi , Kusano Takaŝi
Published: June 2010

This paper is devoted to the study of the oscillatory behavior of solutions of the first-order nonlinear functional differential equations
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row with Label left-parenthesis upper A right-parenthesis EndLabel StartLayout 1st Row x prime left-parenthesis t right-parenthesis equals sigma-summation Underscript i equals 1 Overscript upper N Endscripts q Subscript i Baseline left-parenthesis t right-parenthesis f Subscript i Baseline left-parenthesis x left-parenthesis g Subscript i Baseline left-parenthesis t right-parenthesis right-parenthesis right-parenthesis 2nd Row plus upper F left-parenthesis t comma x left-parenthesis t right-parenthesis comma x left-parenthesis g 1 left-parenthesis t right-parenthesis right-parenthesis comma ellipsis comma x left-parenthesis g Subscript upper N Baseline left-parenthesis t right-parenthesis right-parenthesis right-parenthesis comma EndLayout EndLayout">

(

A

)

x
′

(
t
)
=

∑

i
=
1

N

q
i

(
t
)

f
i

(
x
(

g
i

(
t
)
)
)

+
F
(
t
,
x
(
t
)
,
x
(

g
1

(
t
)
)
,
…
,
x
(

g
N

(
t
)
)
)
,

\begin {array}{*{20}{c}} x’(t) = \sum \limits _{i = 1}^N {{q_i}(t){f_i}(x({g_i}(t)))} \\ + F(t,x(t),x({g_1}(t)), \ldots ,x({g_N}(t))),\tag {$A$} \\ \end {array}

\]

\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row with Label left-parenthesis upper B right-parenthesis EndLabel StartLayout 1st Row x prime left-parenthesis t right-parenthesis plus sigma-summation Underscript i equals 1 Overscript upper N Endscripts q Subscript i Baseline left-parenthesis t right-parenthesis f Subscript i Baseline left-parenthesis x left-parenthesis g Subscript i Baseline left-parenthesis t right-parenthesis right-parenthesis right-parenthesis 2nd Row plus upper F left-parenthesis t comma x left-parenthesis t right-parenthesis comma x left-parenthesis g 1 left-parenthesis t right-parenthesis right-parenthesis comma ellipsis comma x left-parenthesis g Subscript upper N Baseline left-parenthesis t right-parenthesis right-parenthesis right-parenthesis equals 0 period EndLayout EndLayout">

(

B

)

x
′

(
t
)
+

∑

i
=
1

N

q
i

(
t
)

f
i

(
x
(

g
i

(
t
)
)
)

+
F
(
t
,
x
(
t
)
,
x
(

g
1

(
t
)
)
,
…
,
x
(

g
N

(
t
)
)
)
=
0.

\begin {array}{*{20}{c}} x’(t) + \sum \limits _{i = 1}^N {{q_i}(t){f_i}(x({g_i}(t)))} \\ + F(t,x(t),x({g_1}(t)), \ldots ,x({g_N}(t))) = 0.\tag {$B$} \\ \end {array}

\]
First, without assuming that the deviating arguments

g
i

(
t
)
,
1
⩽
i
⩽
N

{g_i}(t),1 \leqslant i \leqslant N

, are retarded or advanced, sufficient conditions are established for all solutions of (A) and (B) to be oscillatory. Secondly, a characterization of oscillation of all solutions is obtained for equation (A) with

F
≡
0

F \equiv 0

and

g
i

(
t
)
>
t
,
1
⩽
i
⩽
N

{g_i}(t) > t,1 \leqslant i \leqslant N

, as well as for equation (B) with

F
≡
0

F \equiv 0

and

g
i

(
t
)
>
t
,
1
⩽
i
⩽
N

{g_i}(t) > t,1 \leqslant i \leqslant N

.
Noncompact unimodular groups with purely atomic Plancherel measures
Authors: Mauceri Giancarlo , Picardello Massimo A.
Published: June 2010

A noncompact unimodular group whose regular representation decomposes as a direct sum of irreducible subrepresentations was constructed by J. M. G. Fell. In the present paper, groups of this kind are studied, and several new examples are provided to settle open structure problems.
There are no 𝑄-points in Laver’s model for the Borel conjecture
Authors: Miller Arnold W.
Published: June 2010

It is shown that it is consistent with ZFC that no nonprincipal ultrafilter on

ω
\omega

is a Q-point (also called a rare ultrafilter).
On submetrizability and 𝐺_{𝛿}-diagonals
Authors: Mizokami Takemi
Published: June 2010

Open perfect maps and open compact maps with the property that the collection of all nontrivial fibers is discrete are shown to preserve submetrizability and if

f
:
X
→
Y

f:X \to Y

is an open compact or perfect map with the above property such that the union of all nontrivial fibers is

G
δ

{G_\delta }

and if X has a

G
δ

(
1
)

¯

\overline {{G_\delta }(1)}

-diagonal, then Y is shown to have a

G
δ

{G_\delta }

-diagonal.
Fixed points for confluent maps onto disks
Authors: Nadler Sam B.
Published: June 2010

Let M be a compact subset of a disk D such that

H
1

(
M
)
≈
0

{H^1}(M) \approx 0

. It is shown that if f is a confluent mapping from M onto D and if g is any mapping from M into D, then

f
(
p
)
=
g
(
p
)

f(p) = g(p)

for some

p
∈
M

p \in M

.
Compactifications with countable remainder
Authors: Charalambous M. G.
Published: June 2010

In this paper, we deal with the problem of characterizing those spaces that have a compactification with countable remainder.
A conjecture on the 𝑝-regularity of an 𝐻-space
Authors: Hubbuck J. R.
Published: June 2010

It is shown that a compact, simply connected, Lie group G is p-regular if and only if

K
o

(
Ω
G
,
Z

/

p
Z
)

{K_o}(\Omega G,Z/pZ)

is a primitively generated polynomial algebra. It is conjectured that this remains true for G a finite, simply connected, associative, H-space.
A proof of the principle of local reflexivity
Authors: Stegall Charles
Published: June 2010

A quite elementary proof of the principle of local reflexivity is given.
Incidence rings with self-duality
Authors: Haack Joel K.
Published: June 2010

An artinian ring R is said to have self-duality if there is a Morita duality between the categories of left and right finitely generated R-modules. Here it is shown that the incidence ring of a finite preordered set over a division ring has self-duality. This is accomplished in part by calculating their injective modules.
Algebraic automorphism groups of pro-affine algebraic groups
Authors: Lee Dong Hoon
Published: June 2010

We study the maximum connected algebraic subgroup of automorphisms of certain pro-affine algebraic groups.
An application of the Moore-Penrose inverse to antisymmetric relations
Authors: Hartwig Robert E.
Published: June 2010

Let R be a star-ring and let

R
†

{R_\dagger }

denote the set of star-regular elements in R. It is shown that the relation

a
Δ
b

a\Delta b

, defined by

a

a
∗

a
=
a

b
∗

a

a{a^\ast }a = a{b^\ast }a

, is antisymmetric on

R
†

{R_\dagger }

provided that the two-term star-cancellation law and the positive-semidefinite axiom hold in R. This includes the star-regular elements of all

C
∗

{C^\ast }

-algebras, and in particular those elements in

C

n
×
n

{{\mathbf {C}}_{n \times n}}

and

B
(
H
)

B(H)

, the bounded linear transformations on Hilbert space H.
A characterization of positive linear functionals and oscillation criteria for matrix differential equations
Authors: Walters Terry
Published: June 2010

Etgen and Pawlowski have recently given criteria for oscillation of matrix differential equations which involve the value of positive linear functionals on the matrices appearing in a matrix differential equation. We characterize these functionals and indicate relationships to eigenvalue criteria for oscillation. Our results are also useful for the detection of the oscillation of particular matrix differential equations.
Derivative measures
Authors: Goffman Casper , Liu Fon Che
Published: June 2010

A characterization of those measures which are distribution derivatives is undertaken. For functions of n variables in BVC, the derivative measures are absolutely continuous with respect to Hausdorff

n
−
1

n - 1

measure. For functions in

W
1
1

W_1^1

they are absolutely continuous with respect to n measure. For linearly continuous functions the derivative measures are zero for sets whose Hausdorff

n
−
1

n - 1

measure is finite. For

n
=
1

n = 1

, since

n
−
1
=
0

n - 1 = 0

, this reduces to the standard facts.
A Bloch function in all 𝐻^{𝑝} classes, but not in BMOA
Authors: Campbell Douglas , Cima Joseph , Stephenson Kenneth
Published: June 2010

All BMOA functions are Bloch and in

∩

p
>
∞

H
p

{ \cap _{p > \infty }}{H^p}

. A technique is given that creates a Bloch function in all

H
p

{H^p}

classes but which is not in BMOA.
Bounded extension property and 𝑝-sets
Authors: Hag Per
Published: June 2010

The main result of this paper is a theorem which asserts that a closed subset of the compact Hausdorff space X is a p-set for a uniform algebra A on X if and only if

S
=
{
f
∈
A
;
Re
⁡
f
⩾
0
}

S = \{ f \in A;\operatorname {Re} f \geqslant 0\}

has the so-called bounded extension property with respect to F. Similar results have been obtained by Bishop, Gamelin, Semadeni and the author.
Systems of partial differential operators with fundamental solutions supported by a cone
Authors: Lancaster Kirk E. , Petersen Bent E.
Published: June 2010

Necessary and sufficient conditions are given for a system of partial differential operators to have a fundamental solution supported by a convex salient cone. As a simple application an overdetermined Cauchy problem is solved.
Interpolating functions associated with second-order differential equations
Authors: Trench William F.
Published: June 2010

Functions are exhibited which interpolate the magnitude of a solution y of a linear, homogeneous, second-order differential equation at its critical points,

|

y
′

|

|y’|

at the zeros of y, and

|

∫

x
0

x

y
(
t
)
h
(
t
)

d
t

|

|\smallint _{{x_0}}^xy(t)h(t)\;dt|

at the zeros of y. Except for a normalization condition, the interpolating functions are independent of the specific solution y. A theorem similar in its conclusions to the Sonin-Pólya-Butlewski theorem is presented and examples are given.
Mapping surfaces harmonically into 𝐸ⁿ
Authors: Milnor Tilla Klotz
Published: June 2010

A Weierstrass representation is given for harmonic maps from simply connected surfaces into

E
3

{E^3}

. The main result implies that the normals to a complete, harmonically immersed surface in

E
n

{E^n}

cannot omit a neighborhood of an (unoriented) direction if the mean curvature vector never vanishes, and the map from given to induced conformal structure is quasiconformal. In particular, the closure of the Gauss map to the complete graph of a harmonic function must be a hemisphere if the mean curvature never vanishes, and vertical projection is quasiconformal.
On 𝑄 sets
Authors: Fleissner William G. , Miller Arnold W.
Published: June 2010

A Q set is an uncountable set X of the real line such that every subset of X is an

F
σ

{F_\sigma }

relative to X. It is known that the existence of a Q set is independent of and consistent with the usual axioms of set theory. We show that one cannot prove, using the usual axioms of set theory: 1. If X is a Q set then any set of reals of cardinality less than the cardinality of X is a Q set. 2. The union of a Q set and a countable set is a Q set.
Boundary preserving maps of 3-manifolds
Authors: Swarup G. A.
Published: June 2010

We prove an extension of Waldhausen’s theorem [5] conjectured by Hempel in [3].
The radical of the center of a group algebra
Authors: Passman D. S.
Published: June 2010

Let

K
[
G
]

K[G]

denote the group algebra of a finite group G over a field K of characteristic

p
>
0

p > 0

and let

Z

=

Z

(
K
[
G
]
)

\mathcal {Z} = {\mathbf {Z}}(K[G])

. In this paper, we offer a bound for the nilpotence degree of the Jacobson radical

J

Z

J\mathcal {Z}

in terms of the order of a Sylow p-subgroup of G.
On boundedness of integrable automorphic forms in 𝐶ⁿ
Authors: Chen Su Shing
Published: June 2010

We give a necessary and sufficient condition for an integrable automorphic form on a bounded symmetric domain D in

C

n

{{\mathbf {C}}^n}

to be bounded.
Periodic solutions for a class of ordinary differential equations
Authors: Ward James R.
Published: June 2010

A T-periodic solution to the differential equation

x
+
c

x
′

+
g
(
x
)
=
f
(
t
)
≡
f
(
t
+
T
)

x + cx’ + g(x) = f(t) \equiv f(t + T)

is shown to exist whenever a simple condition on g holds, provided

c
≠
0

c \ne 0

. No assumption is made concerning the growth of g. The condition on g is necessary if g is either an increasing or a decreasing function.
Some relations between nonexpansive and order preserving mappings
Authors: Crandall Michael G. , Tartar Luc
Published: June 2010

It is shown that nonlinear operators which preserve the integral are order preserving if and only if they are nonexpansive in

L
1

{L^1}

and that those which commute with translation by a constant are order preserving if and only if they are nonexpansive in

L
∞

{L^\infty }

. Examples are presented involving partial differential equations, difference approximations and rearrangements.
A simplicity theorem for amoebas over random reals
Authors: Abramson Fred G.
Published: June 2010

Let M be a countable standard transitive model of ZFC,

A

\mathcal {A}

be an amoeba over M, and r be a random real over M. Theorem. (a) There is no infinite set of reals X contained in the complement of

A

\mathcal {A}

with
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X element-of upper M left-bracket r right-bracket semicolon left-parenthesis b right-parenthesis upper I f left-brace x Subscript n Baseline vertical-bar n greater-than omega right-brace element-of upper M left-bracket r right-bracket">

X
∈
M
[
r
]
;
(
b
)

I
f

{

x
n

|

n
>
ω
}
∈
M
[
r
]

X \in M[r];(b)\;If\;\{ {x_n}|n > \omega \} \in M[r]

is a sequence of distinct reals, then for all large enough n,

{

x
i

|

2
n

⩽
i
>

2

n
+
1

}
∩

A

≠
∅

\{ {x_i}|{2^n} \leqslant i > {2^{n + 1}}\} \cap \mathcal {A} \ne \emptyset

.
A divergent, two-parameter, bounded martingale
Authors: Dubins Lester E. , Pitman Jim
Published: June 2010

An example is given of a divergent, uniformly bounded martingale

X
=
{

X
t

:
t
∈
T
}

X = \{ {X_t}:t \in T\}

where the index t ranges over the set T of pairs of positive integers with the usual coordinatewise ordering.
A provisional solution to the normal Moore space problem
Authors: Nyikos Peter J.
Published: June 2010

The Product Measure Extension Axiom (PMEA), whose consistency would follow from the existence of a strongly compact cardinal, implies that every normalized collection of sets in a space of character less than the continuum is well separated. Consistency of PMEA would thus solve many well-known problems of general topology, including that of whether every first countable normal space is collectionwise normal, as well as the normal Moore space problem.
Weakly confluent mappings and finitely-generated cohomology
Authors: Rogers James T.
Published: June 2010

In this paper we answer a question of Wayne Lewis by proving that if X is a one-dimensional, hereditarily indecomposable continuum and if

H
1

(
X
)

{H^1}(X)

is finitely generated, then

C
(
X
)

C(X)

, the hyperspace of subcontinua of X, has dimension 2.
Proof of a theorem of Burke and Hodel on the cardinality of topological spaces
Authors: Blair Robert L.
Published: June 2010

Techniques of Pol are used to give a direct proof of Burke and Hodel’s inequality

|

X

|

⩽

2

Δ
(
X
)
⋅

psw

(
X
)

|X| \leqslant {2^{\Delta (X) \cdot {\text {psw}}(X)}}

, where

Δ
(
X
)

\Delta (X)

is the discreteness character of the

T
1

{T_1}

space X and

psw

(
X
)

{\text {psw}}(X)

is the point separating weight of X.
Reducing the codimension of Kähler immersions
Authors: Jacobowitz H.
Published: June 2010

The codimension of an immersion of a Kähler manifold may be reduced if there is a holomorphic vector field normal to the manifold.
On semihereditary noncommutative polynomial rings
Authors: Pillay P.
Published: June 2010

McCarthy [4] showed that a polynomial ring over a commutative von Neumann regular ring is semihereditary. Camillo [1] proved the converse. In this paper we examine polynomial rings over von Neumann regular rings which are not necessarily commutative.