bluuebunny/crossref_metadata_2025 huggingface dataset:
Inner functions on the polydisc
Authors: Kon S. H.
Published: June 2010

It is shown that the inner functions on the polydisc, unlike the classical case of the unit disc, fail to separate the points of the maximal ideal space of

H
∞

(

U
n

)

{H^\infty }({U^n})

. From this we deduce that the inner functions generate a proper closed subalgebra of

H
∞

(

U
n

)

{H^\infty }({U^n})

.
Flat partial connections and holomorphic structures in 𝐶^{∞} vector bundles
Authors: Rawnsley J. H.
Published: June 2010

The notion of a flat partial connection D in a

C
∞

{C^\infty }

vector bundle E, defined on an integrable subbundle F of the complexified tangent bundle of a manifold X is defined. It is shown that E can be trivialized by local sections s satisfying

D
s
=
0

Ds = 0

. The sheaf of germs of sections s of E satisfying

D
s
=
0

Ds = 0

has a natural fine resolution, giving the de Rham and Dolbeault resolutions as special cases. If X is a complex manifold and F the tangents of type (0, 1), the flat partial connections in a

C
∞

{C^\infty }

vector bundle E are put in correspondence with the holomorphic structures in E. If X, E are homogeneous and F invariant, then invariant flat connections in E can be characterized as extensions of the representation of the isotropic subgroup to which E is associated, extending results of Tirao and Wolf in the holomorphic case.
Linear fractional maps and Jordan algebras
Authors: Watson Kym S.
Published: June 2010

Jordan algebras are characterized from amongst the finite dimensional commutative algebras without the use of identities. This is achieved by investigating the properties of the linear fractional transformations generated by the quasi-inversion and all translations.
An integral representation of holomorphic functions
Authors: Hilger R. W. , Michaliček J. F.
Published: June 2010

Let K be a compact set in the complex plane and let f be a function holomorphic on the complement

Ω
\Omega

of K and vanishing at infinity. We prove that there are finite complex-valued Borel measures

μ

m
,
n

(
m
,
n
=
0
,
1
,
2
,
…
;
m
+
n
⩾
1
)

{\mu _{m,n}}(m,n = 0,1,2, \ldots ;m + n \geqslant 1)

on

K
2

{K^2}

satisfying
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="limit Underscript k right-arrow normal infinity Endscripts left-parenthesis normal upper Sigma Subscript m plus n equals k Baseline double-vertical-bar mu Subscript m comma n Baseline double-vertical-bar right-parenthesis Superscript 1 slash k Baseline equals 0">

lim

k
→
∞

(

Σ

m
+
n
=
k

‖

μ

m
,
n

‖

)

1

/

k

=
0

{\lim _{k \to \infty }}{({\Sigma _{m + n = k}}\left \|{\mu _{m,n}}\right \|)^{1/k}} = 0

so that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis z right-parenthesis equals sigma-summation Underscript m comma n Endscripts integral Underscript upper K squared Endscripts left-parenthesis z minus w 1 right-parenthesis Superscript negative m Baseline left-parenthesis z minus w 2 right-parenthesis Superscript negative n Baseline d mu Subscript m comma n Baseline left-parenthesis w 1 comma w 2 right-parenthesis left-parenthesis z element-of normal upper Omega right-parenthesis period">

f
(
z
)
=

∑

m
,
n

∫

K
2

(
z
−

w
1

)

−
m

(
z
−

w
2

)

−
n

d

μ

m
,
n

(

w
1

,

w
2

)

(
z
∈
Ω
)
.

f(z) = \sum \limits _{m,n} {\int _{{K^2}} {{{(z - {w_1})}^{ - m}}{{(z - {w_2})}^{ - n}}d{\mu _{m,n}}({w_1},{w_2})\quad (z \in \Omega ).} }

\]
A necessary and sufficient condition for disfocality
Authors: Muldowney James S.
Published: June 2010

A criterion for the disfocality of a linear differential operator is given. The condition is analogous to a disconjugacy criterion of Pólya (1922).
Representing ergodic flows as flows built under functions with finite range
Authors: Fellgett Robin
Published: June 2010

It is shown, using a result of Rudolph, that any cross-section of an ergodic flow whose return-time function is bounded and bounded away from zero is isomorphic to a cross-section whose return-time function has finite range. A weaker result holds if the boundedness conditions are removed.
Pixley-Roy and the Souslin line
Authors: Rudin Mary Ellen
Published: June 2010

Necessary and sufficient conditions are given for normality and metricity of the Pixley-Roy space over a subset of the Souslin line.
Boolean algebras with few endomorphisms
Authors: Shelah Saharon
Published: June 2010

Using diamond for

ℵ
1

{\aleph _1}

we construct a Boolean algebra in

ℵ
1

{\aleph _1}

, whose only endomorphisms are those definable using finitely many elements and ultrafilters. We also generalize Rubin’s construction to higher cardinals.
Extending monotone decompositions of manifolds
Authors: Walsh John J.
Published: June 2010

Let

M
m

(
m
⩾
3
)

{M^m}\;(m \geqslant 3)

be a compact, connected PL manifold and let

X
⊆
M

X \subseteq M

be a proper, closed subset of the interior of M such that for each open, connected subset

U
⊆
M

U \subseteq M

either

U
−
(
X
∩
U
)

U - (X \cap U)

is connected or

X
∩

bd

(
U
)
≠
∅

X \cap {\text {bd}}(U) \ne \emptyset

. Let P be a connected and simply connected polyhedron with

dim
⁡
P
⩾
3

\dim P \geqslant 3

. There exists a monotone mapping f from M onto P with each component of X being a point-inverse of f. In the case with M oriented and P the m-sphere, there exists such a monotone mapping of each degree.
Generalized parabolic functions using the Perron-Wiener-Brelot method
Authors: Eklund Neil
Published: June 2010

Let L be a linear, second order parabolic operator in divergence form and let U be a bounded domain in

E

n
+
1

{E^{n + 1}}

. The Dirichlet problem for

L
u
=
0

Lu = 0

is solved in U using the Perron-Wiener-Brelot method.
On a superlinear elliptic boundary value problem at resonance
Authors: McKenna P. J.
Published: June 2010

Semilinear partial differential equations of the type

−
Δ
u
−

λ
2

u
+

e
u

=
h

- \Delta u - {\lambda _2}u + {e^u} = h

are studied and existence and multiplicity results obtained.
A note on singular integrals
Authors: Fefferman R.
Published: June 2010

In this article we discuss what happens when we consider a convolution operator whose kernel is a Calderón-Zygmund kernel multiplied by a bounded radial function. Some generalizations are obtained.
Dual 𝐴*-algebras of the first kind
Authors: Johnson David L. , Lahr Charles D.
Published: June 2010

Let A be an

A
∗

{A^\ast }

-algebra of the first kind. It is proved that A has property P2 of Máté if and only if

A
2

{A^2}

is dense in A if and only if A possesses an (operator-bounded) approximate identity. Further, it is shown that an

A
∗

{A^\ast }

-algebra of the first kind having property P2 is a dual algebra if and only if it is a modular annihilator algebra. As applications, these results are used to strengthen certain theorems about Hilbert algebras.
Multipliers of 𝐴*-algebras
Authors: Johnson David L. , Lahr Charles D.
Published: June 2010

Let A be an

A
∗

{A^\ast }

-algebra of the first kind with

C
∗

{C^\ast }

-algebra completion

A

\mathfrak {A}

. It is known that if A is dual then

A
2

{A^2}

is dense in A and the Banach algebras

M
L

(
A
)

{M_L}(A)

and

M
L

(

A

)

{M_L}(\mathfrak {A})

of left multipliers of A and

A

\mathfrak {A}

are algebra isomorphic. In this note it is proved that

M
L

(
A
)

{M_L}(A)

and

M
L

(

A

)

{M_L}(\mathfrak {A})

are topologically algebra isomorphic when A is an arbitrary

A
∗

{A^\ast }

-algebra of the first kind such that

A
2

{A^2}

is dense in A. As a consequence, it follows that every left multiplier of a replete Hilbert algebra A is automatically continuous.
Convergence of measurable random functions
Authors: Grinblat L. Š.
Published: June 2010

Using the theorem of Fréchet and Kolmogorov about compact subsets of the space

L
p

[
0
,
1
]

{L_p}[0,1]

and Prohorov’s theorem about the convergence of measures defined on a complete metric space we proved in [2] the following theorem: Let

ξ
1

(
t
)
,
…
,

ξ
n

(
t
)
,
…

{\xi _1}(t), \ldots ,{\xi _n}(t), \ldots

and

ξ
(
t
)

\xi (t)

be measurable random processes

(
0
⩽
t
⩽
1
)

(0 \leqslant t \leqslant 1)

and suppose that there exist numbers C and

p
⩾
1

p \geqslant 1

such that

E

|

ξ
n

(
t
)

|

p

⩽
C

E|{\xi _n}(t){|^p} \leqslant C

for all n and t. If
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E StartAbsoluteValue xi Subscript n Baseline left-parenthesis t right-parenthesis EndAbsoluteValue Superscript p Baseline right-arrow upper E StartAbsoluteValue xi left-parenthesis t right-parenthesis EndAbsoluteValue Superscript p">

E

|

ξ
n

(
t
)

|

p

→
E

|

ξ
(
t
)

|

p

E|{\xi _n}(t){|^p} \to E|\xi (t){|^p}

for all t and if for any finite set

{

t
1

,
…
,

t
k

}
⊂
[
0
,
1
]

\{ {t_1}, \ldots ,{t_k}\} \subset [0,1]

the joint distribution of

ξ
n

(

t
1

)
,
…
,

ξ
n

(

t
k

)

{\xi _n}({t_1}), \ldots ,{\xi _n}({t_k})

converges to the joint distribution of

ξ
(

t
1

)
,
…
,
ξ
(

t
k

)

\xi ({t_1}), \ldots ,\xi ({t_k})

, then the distribution of

f
(

ξ
n

)

f({\xi _n})

converges to the distribution of

f
(
ξ
)

f(\xi )

for any continuous functional f on

L
p

[
0
,
1
]

{L_p}[0,1]

. In this paper this theorem is generalized to random measurable functions. The results of the present paper are related to the results of [1], [3], [4].
A note on 𝑆-closed spaces
Authors: Mathur Asha
Published: June 2010

A topological space X is said to be S-closed if and only if for every semi-open cover of X there exists a finite subfamily such that the union of their closures cover X. For a Hausdorff space, the concept of S-closed is shown to be equivalent to the concept of extremally disconnected and nearly compact. Further it has been shown that EDH-closed spaces are precisely S-closed Hausdorff spaces.
Twisted Whitehead products
Authors: Marcum Howard J.
Published: June 2010

By combining the Hopf construction and the Whitehead product map construction we introduce twisted Whitehead products and then extend several well-known properties of Whitehead products to the twisted situation.
Hurewicz isomorphism theorem for Steenrod homology
Authors: Kodama Y. , Koyama A.
Published: June 2010

For a pointed compactum (X, x), a natural homomorphism

ξ
n

{\xi _n}

from the Quigley’s approaching group

π
_

_

n

(
X
,
x
)

{\underline {\underline \pi } _n}(X,x)

to the Steenrod homology group

s

H

n
+
1

(
X
)

^s{H_{n + 1}}(X)

is defined. A shape theoretical condition under which

ξ
n

{\xi _n}

is an isomorphism is obtained. For every pointed

S
n

{S^n}

-like continuum (X, x),

ξ
n

{\xi _n}

is an isomorphism for

n
≠
2

n \ne 2

and

ξ
2

{\xi _2}

is an isomorphism if and only if X is movable.
A characterization of compact groups
Authors: Johnson David L.
Published: June 2010

It is shown that the group algebra

L
1

(
G
)

{L^1}(G)

of a locally compact group G is an ideal in the bidual

L
1

(
G

)

∗
∗

{L^1}{(G)^{ \ast \ast }}

of

L
1

(
G
)

{L^1}(G)

(equipped with Arens product) if and only if G is compact.
Artinian skew group rings
Authors: Park Jae Keol
Published: June 2010

Let R be a ring with identity and let

θ
\theta

be a group homomorphism from a group G to

Aut

(
R
)

{\operatorname {Aut}}(R)

, the group of automorphisms of R. We prove that skew group ring

R

∗
θ

G

R{ \ast _\theta }G

is right Artinian (resp., semiprimary, right perfect) if and only if R is right Artinian (resp., semiprimary, right perfect) and the group G is finite. Also semilocal skew group rings over fields are characterized.
The Jacobson radical of the group algebra of a finite group
Authors: Bedi Surinder Singh
Published: June 2010

Let K be a field of characteristic

p
≠
0

p \ne 0

and G a finite group such that

p

|

o
(
G
)

p|o(G)

. Suppose G is a Frobenius group with a Sylow p-subgroup P as a complement. Then we have proved that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper J upper K left-parenthesis upper G right-parenthesis equals intersection Underscript x element-of upper G Endscripts upper J upper K left-parenthesis upper P Superscript x Baseline right-parenthesis upper K left-parenthesis upper G right-parenthesis period">

J
K
(
G
)
=

⋂

x
∈
G

J
K
(

P
x

)
K
(
G
)
.

JK(G) = \bigcap \limits _{x \in G} {JK({P^x})K(G).}

\]
We have given an example to show that equality does not hold in general.
Finite number of double cosets in a free product with amalgamation
Authors: Djoković Dragomir Ž.
Published: June 2010

If H is a finitely generated subgroup of a free group G such that every conjugate of H contains a cyclically reduced word then

(
G
:
H
)
>
∞

(G:H) > \infty

. This generalizes a well-known result of Karrass and Solitar. If H is a finitely generated subgroup of the free product with amalgamation

G
=
A

∗
U

B

G = A\;{ \ast _U}B

such that every conjugate of H meets A and B trivially and contains a cyclically reduced word then G has only finitely many (H, U)-double cosets. Both theorems are proved by defining an action of G on a tree such that H acts freely.
Monomial space curves in 𝐴³ as set-theoretic complete intersections
Authors: Bresinsky H.
Published: June 2010

It is shown constructively that all monomial space curves in affine 3-space are set-theoretic complete intersections.
Rotund complex normed linear spaces
Authors: Beesack P. R. , Hughes E. , Ortel M.
Published: June 2010

We show that rotundity in a complex normed linear space is equivalent to the property that for any distinct vectors x and y of unit norm, a complex number

α
\alpha

may be found for which

‖

α
x
+
(
1
−
α
)
y

‖

>
1

\left \| {\alpha x + (1 - \alpha )y} \right \| > 1

. This leads to a natural proof of a result due to Taylor and Foguel on the uniqueness of Hahn-Banach extensions.
An extremal property of the Bloch space
Authors: Rubel Lee A. , Timoney Richard M.
Published: June 2010

The Bloch space

B

\mathcal {B}

is the space of functions f analytic in the unit disc D such that

|

f
′

(
z
)

|

(
1
−

|

z

|

2

)

|f’(z)|(1 - |z{|^2})

is bounded. It is shown that

B

\mathcal {B}

is the largest Möbius-invariant linear space of analytic functions that can be equipped with a Möbius-invariant seminorm in such a way that there is at least one “decent” continuous linear functional on the space. The term “decent” has a simple and precise definition.
Measures whose integral transforms are pluriharmonic
Authors: Kolaski Clinton
Published: June 2010

Kolaski proved an F. and M. Riesz type theorem for the unit ball in

C

N

{{\mathbf {C}}^N}

. This paper generalizes those results.
On recurrent random walks on abelian semigroups
Authors: Högnäs Göran
Published: June 2010

We consider a random walk

Z
n

{Z_n}

on the locally compact second countable abelian semigroup S with unit e which is assumed to be a recurrent point for

Z
n

{Z_n}

. Then S is the disjoint union of a topologically simple abelian semigroup G and a null-set A of first category. Under some additional conditions G is a topological group.
Anosov does not imply infinitesimally ergodic
Authors: Swanson R. C. , Chicone Carmen
Published: June 2010

A class of hyperbolic toral automorphisms is exhibited which are not infinitesimally ergodic. These provide counterexamples to the conjecture that Anosov diffeomorphisms are infinitesimally ergodic.
An inequality for double tangents
Authors: Halpern Benjamin
Published: June 2010

For a regular closed curve on the plane it is known that

E
=
I
+
X
+

1
2

F

E = I + X + \tfrac {1}{2}F

where E, I, X and F are the numbers of external double tangents, internal double tangents, self-intersections, and inflexion points respectively. It is proven here that if

F
=
0

F = 0

then I is even and

I
⩽
(
2
X
+
1
)
(
X
−
1
)

I \leqslant (2X + 1)(X - 1)

. Furthermore, examples are given which show that if the four tuplet (E, I, X, F) of nonnegative integers satisfies (a) F even, (b)

E
=
I
+
X
+

1
2

F

E = I + X + \tfrac {1}{2}F

, and (c) if

F
=
0

F = 0

then I is even and

I
⩽
X
(
X
−
1
)

I \leqslant X(X - 1)

, then there is a regular closed plane curve which realizes these values.
Existence of closed timelike geodesics in Lorentz spaces
Authors: Tipler Frank J.
Published: June 2010

Certain classes of compact four-dimensional Lorentz spaces are shown to possess at least one closed timelike geodesic.
Demension and measure
Authors: Väisälä Jussi
Published: June 2010

We give a new characterization, based on Hausdorff measure, for the demension of a compact set in a euclidean space.
Rational surfaces with too many vector fields
Authors: Neuman Gerald
Published: June 2010

A method is given for constructing smooth rational surfaces with nonreduced automorphism groups, by a sequence of blow-ups of the projective plane. The technique works in all positive characteristics.
Group rings in which every left ideal is a right ideal
Authors: Menal P.
Published: June 2010

Let

K
[
G
]

K[G]

denote the group ring of G over the field K. In this note we characterize those group rings in which all left ideals are right ideals.
Lie algebra multiplicities
Authors: Berman S. , Moody R. V.
Published: June 2010

Exact formulas for root space multiplicities in Cartan matrix Lie algebras and their universal enveloping algebras are computed. We go on to determine the number of free generators of each degree of the radicals defining these algebras.
Spectral approximations of a normal operator
Authors: Bouldin Richard
Published: June 2010

If

Λ
\Lambda

is a closed convex set in the complex plane then

N

(
Λ
;
H
)

\mathfrak {N}(\Lambda ;H)

denotes all the normal (bounded linear) operators on the fixed separable Hilbert space H with spectrum contained in

Λ
\Lambda

. The fixed operator A has N as an

N

(
Λ
;
H
)

\mathfrak {N}(\Lambda ;H)

-approximant provided N belongs to

N

(
Λ
;
H
)

\mathfrak {N}(\Lambda ;H)

and the operator norm

‖

A
−
N

‖

\left \| {A - N} \right \|

equals

ρ
Λ

(
A
)

{\rho _\Lambda }(A)

, the distance from A to

N

(
Λ
;
H
)

\mathfrak {N}(\Lambda ;H)

. With some hypothesis on

Λ
\Lambda

, this note proves that the dimension of the convex set of all

N

(
Λ
;
H
)

\mathfrak {N}(\Lambda ;H)

-approximants of normal operator A is

(
dim
⁡

H
0

)
2

{(\dim {H_0})^2}

where

H
0

{H_0}

is the orthogonal complement of

ker
⁡
(

|

A
−
F
(
A
)

|

−

ρ
Λ

(
A
)
)

\ker (|A - F(A)| - {\rho _\Lambda }(A))

and

F
(
z
)

F(z)

is the unique distaince minimizing retract of the complex plane onto

Λ
\Lambda

.
Characterization of 𝑝-predictors
Authors: Landers D. , Rogge L.
Published: June 2010

Let

(
Ω
,

A

,
P
)

(\Omega ,\mathcal {A},P)

be a probability space and

1
>
p
>
∞

1 > p > \infty

. It is shown that each operator
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T colon upper L Subscript p Baseline left-parenthesis normal upper Omega comma script upper A comma upper P right-parenthesis right-arrow upper L Subscript p Baseline left-parenthesis normal upper Omega comma script upper A comma upper P right-parenthesis">

T
:

L
p

(
Ω
,

A

,
P
)
→

L
p

(
Ω
,

A

,
P
)

T:{L_p}(\Omega ,\mathcal {A},P) \to {L_p}(\Omega ,\mathcal {A},P)

which is homogeneous, constant preserving, positive, quasi-additive and fulfills Dykstra’s condition is an p-predictor with respect to a suitable

σ
\sigma

-field, i.e. a nearest point projection onto a closed subspace

L
p

(
Ω
,

B

,
P
)

{L_p}(\Omega ,\mathcal {B},P)

, where

B

⊂

A

\mathcal {B} \subset \mathcal {A}

is a

σ
\sigma

-field. None of the conditions for T can be dispensed without compensation.
The cohomology of the projective 𝑛-plane
Authors: Thedford William A.
Published: June 2010

An H-space is a topological space with a continuous multiplication and an identity element. In this paper X has the homotopy type of a countable CW-complex with integral cohomology of finite type and primitively generated k-cohomology, k a field. The projective n-plane of X is denoted

X
P
(
n
)

XP(n)

. The main results of this paper are: Theorem 1 which states that

H
∗

(
X
P
(
n
)
)
=
N
⊕
S

{H^\ast }(XP(n)) = N \oplus S

where N is a truncated polynomial algebra over k and S is a trivial k-ideal, and Theorem 2 which considers the case

k
=
Z
(
p
)

k = Z(p)

and states that

H
∗

(
X
P
(
n
)
)
=

N
^

⊕

S
^

{H^\ast }(XP(n)) = \hat N \oplus \hat S

where

N
^

\hat N

is a truncated polynomial algebra on generators in even dimensions and S is an A(p)-sub-algebra of

H
∗

(
X
P
(
n
)
)

{H^\ast }(XP(n))

so that an A(p)-algebra structure can be induced on

N
^

\hat N

. These theorems extend results by A. Borel, W. Browder, M. Rothenberg, N. E. Steenrod, and E. Thomas.
On a completeness theorem of Paley and Wiener
Authors: Young Robert M.
Published: June 2010

In this brief note we offer a simplified proof of a classical completeness theorem for systems of complex exponential functions

{

e

i

λ
n

t

}

\{ {e^{i{\lambda _n}t}}\}

.
Surfaces in the Grassmann variety 𝐺(1,3)
Authors: Papantonopoulou Aigli
Published: June 2010

Let G be the Grassmannian

G
(
1
,
3
)

G(1,3)

, Y a nonsingular subvariety of G and

N

Y

/

G

{N_{Y/G}}

the normal bundle of Y in G. Then

N

Y

/

G

{N_{Y/G}}

is not an ample bundle if and only if Y is a Schubert cycle.
Addendum to: “Residual linearity for certain nilpotent groups” (Proc. Amer. Math. Soc. 68 (1978), no. 1, 27–31)
Authors: Menal P.
Published: June 2010

In this note we offer an example of a residually Q-linear, but not residually finite, nilpotent group whose center is

Z

⊕

Z

{\mathbf {Z}} \oplus {\mathbf {Z}}

.
Function space flow invariance for functional-differential equations of retarded type
Authors: Lightbourne James H.
Published: June 2010

Let

C

\mathcal {C}

denote the Banach space of continuous functions

ϕ
:
[
−
r
,
0
]
→

R

n

\phi :[ - r,0] \to {{\mathbf {R}}^n}

, let

Ω
⊂

C

\Omega \subset \mathcal {C}

be closed, and let

f
:
[
0
,
∞
)
×
Ω
→

R

n

f:[0,\infty ) \times \Omega \to {{\mathbf {R}}^n}

be continuous. In this note we establish necessary and sufficient conditions for function space flow invariance for the functional differential equation:

x
′

(
t
)
=
f
(
t
,

x
t

)

x’(t) = f(t,{x_t})

for

t
⩾
0
,

x
0

=
ϕ
∈
Ω

t \geqslant 0,{x_0} = \phi \in \Omega

. That is, for each

ϕ
∈
Ω

\phi \in \Omega

there exist

b
>
0

b > 0

and a solution

x
:
[
−
r
,
b
]
→

R

n

x:[ - r,b] \to {{\mathbf {R}}^n}

such that

x
t

∈
Ω

{x_t} \in \Omega

for each

t
∈
[
0
,
b
]

t \in [0,b]

.
Operators commuting with positive operators
Authors: Radjabalipour Mehdi
Published: June 2010

Necessary and sufficient conditions are obtained for an operator to commute with a positive operator.
An extension of the Hardy-Littlewood inequality
Authors: Kwong M. K. , Zettl A.
Published: June 2010

The Hardy-Littlewood inequality is extended from

L
2

{L^2}

to

L
w
2

L_w^2

where w is any positive nondecreasing function.
Weak limits of measures and the standard part map
Authors: Loeb Peter A.
Published: June 2010

A construction is given, using the standard part map st, of the

weak
∗

{\text {weak}^\ast }

standard part of an internal Baire measure in the nonstandard extension of a compact Hausdorff space. It is shown that the inverse image with respect to st of a Borel set is universally measurable with respect to completions of the

σ
\sigma

-algebra generated by internal Baire sets. Applications and extensions of these results to noncompact spaces are given.
The minimal harmonic functions of sojourn processes of certain finite state Markov chains
Authors: Bolthausen E.
Published: June 2010

To a finite state, discrete time Markov chain a new chain is constructed which counts the number of sojourns in each state. This sojourn process is a transient Markov chain. The minimal harmonic functions of this chain are identified.
Simultaneous idempotents in 𝛽𝐍_{𝐍} and finite sums and products in 𝐍
Authors: Hindman Neil
Published: June 2010

The principal result is that there do not exist simultaneous multiplicative and additive idempotents in

β
N
∖
N

\beta N\backslash N

. Some consequences of the (already known) existence of multiplicative idempotents which are close to additive idempotents are also derived.
Regular sequences and powers of ideals
Authors: Vasconcelos Wolmer V.
Published: June 2010

Let I be an ideal of a Noetherian local ring. In this note we discuss how a power of I reflects that I is generated by a regular sequence.
On maximal nonparabolic normal subgroups of the modular group
Authors: Mason A. W. , Dickson N. K.
Published: June 2010

Let F be a free normal subgroup of finite index in the modular group

Γ
\Gamma

with

F
≠

Γ
′

.

F
′

F \ne \Gamma ’.F’

is known to be a nonparabolic normal subgroup of

Γ
\Gamma

. We show that, with two exceptions, there exists another nonparabolic normal subgroup of

Γ
\Gamma

properly containing

F
′

F’

.
Finitely presented lattices
Authors: Freese Ralph , Nation J. B.
Published: June 2010

It is shown that the generalized word problem for lattices is solvable. Moreover, one can recursively decide if two finitely presented lattices are isomorphic. It is also shown that the automorphism group of a finitely presented lattice is finite.
Isometries on 𝐿^{𝑝} spaces and copies of 𝑙^{𝑝} shifts
Authors: Campbell Stephen L. , Faulkner Gary D. , Gardner Marianne L.
Published: June 2010

Necessary and sufficient conditions are given on an isometry V in an

L
p

{L^p}

space so that there exists an invariant subspace M such that V restricted to M is isometrically equivalent to the unilateral shift on

l
p

{l^p}

.
An Abel-Tauber theorem on convolutions with the Möbius function
Authors: Geluk J. L.
Published: June 2010

Suppose

n
:

R
+

→

R
+

n:{R^ + } \to {R^ + }

and

n
(
x
)

/

x

n(x)/x

is integrable on

(
0
,
∞
)

(0,\infty )

. For

s
>
0

s > 0

we define
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove n With tilde left-parenthesis s right-parenthesis equals s integral Subscript 0 Superscript normal infinity Baseline StartFraction e Superscript minus u s Baseline Over 1 minus e Superscript minus u s Baseline EndFraction n left-parenthesis u right-parenthesis d u period">

n
~

(
s
)
=
s

∫
0
∞

e

−
u
s

1
−

e

−
u
s

n
(
u
)
d
u
.

\tilde n(s) = s\int _0^\infty {\frac {{{e^{ - us}}}}{{1 - {e^{ - us}}}}} n(u)du.

\]
In this paper an Abel-Tauber theorem is proved concerning this transform. Moreover the relation between

n
~

(
s
)

\tilde n(s)

and

Σ

m
⩽
s

n
(
s

/

m
)

/

m

{\Sigma _{m \leqslant s}}n(s/m)/m

is studied.
Coreflectors not preserving the interval and Baire partitions of uniform spaces
Authors: Tashjian G. , Vilímovský J.
Published: June 2010

Values of the compact interval and other spaces under coreflectors in the category of uniform spaces are studied. It is shown that any coreflector which changes the usual uniformity of the interval produces a new uniformity which contains all finite Baire partitions of the interval.
On generators of ideals
Authors: Moh T. T.
Published: June 2010

In our previous work we had constructed some space curves to illustrate the unboundedness of generators of prime ideals in analytic geometry. In this article we further study these space curves to establish the exact number of minimal generators for the corresponding ideals and to express them as determinant ideals.
Some decidable Diophantine problems: positive solution to a problem of Davis, Matijasevič and Robinson
Authors: Koppel Moshe
Published: June 2010

An algorithm is given for determining whether or not a finite system of conditions of the types

a

|

B
,
a
>
B

a|B,a > B

, a is a square, possess a simultaneous solution in positive integers. Various generalizations are also obtained.
On closed images of orthocompact spaces
Authors: Gruenhage Gary
Published: June 2010

An example is given which shows that orthocompactness is not preserved by closed maps. We also investigate a property, weaker than orthocompactness, which is preserved by closed maps.
A simple expression for the Casimir operator on a Lie group
Authors: Anderson Mary F.
Published: June 2010

The expression for the Casimir operator for a real semisimple Lie group G in terms of coordinates given by the Iwasawa decomposition

G
=
K
A
N

G = KAN

reduces on G/N to the difference of an elliptic operator with constant coefficients on A and an invariant operator on M. This result immediately identifies the principal series of induced representations with representations defined on the eigenspaces of the restriction of the Casimir operator to G/N.
An abstract Borel density theorem
Authors: Moskowitz Martin
Published: June 2010

In this paper an abstract form of the Borel density theorem and related results is given centering around the notion of the author’s of a (finite dimensional) “admissible” representation. A representation

ρ
\rho

is strongly admissible if each

Λ
r

ρ

{\Lambda ^r}\rho

is admissible. Although this notion is somewhat technical it is satisfied for certain pairs

(
G
,
ρ
)

(G,\rho )

; e.g., if G is minimally almost periodic and

ρ
\rho

arbitrary, if G is complex analytic and

ρ
\rho

holomorphic. If G is real analytic with radical R,

G

/

R

G/R

has no compact factors and R acts under

ρ
\rho

with real eigenvalues, then

ρ
\rho

is strongly admissible. If in addition G is algebraic/R, then each R-rational representation is admissible. The results are proven in three stages where V is defined either over R or C. If

ρ
\rho

is a strongly admissible representation of G on V, then each G-invariant measure

μ
\mu

on

G

(
V
)

\mathcal {G}(V)

, the Grassmann space of V, has support contained in the G-fixed point set. If

ρ
\rho

is a strongly admissible representation of G on V and

G

/

H

G/H

has finite volume, then each H-invariant subspace of V is G-invariant. If G is an algebraic subgroup of

Gl

(
V
)

{\text {Gl}}(V)

and each rational representation is admissible, then H is Zariski dense in G.
Dirichlet problem in Lipschitz domains with BMO data
Authors: Fabes Eugene B. , Neri Umberto
Published: June 2010

In any bounded starlike Lipschitz domain, the harmonic functions whose boundary values are in BMO (the class of functions with bounded mean oscillation) of the boundary are shown to be characterized by the property that their Littlewood-Paley measures are Carleson measures. This result extends the analogous characterization found by the authors when the domain in question is a half-space.
The infimum of small subharmonic functions
Authors: Fenton P. C.
Published: June 2010

Suppose that u is subharmonic in the plane and that, for some
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p greater-than 1 comma limit Underscript bar Endscripts Underscript r right-arrow normal infinity Endscripts upper B left-parenthesis r right-parenthesis slash left-parenthesis log r right-parenthesis Superscript p Baseline equals sigma greater-than normal infinity">

p
>
1
,

lim
_

r
→
∞

B
(
r
)

/

(
log
⁡
r

)
p

=
σ
>
∞

p > 1,{\underline {\lim } _{r \to \infty }}B(r)/{(\log r)^p} = \sigma > \infty

. It is shown that, given

ε
>
0

\varepsilon > 0

,
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A left-parenthesis r right-parenthesis greater-than upper B left-parenthesis r right-parenthesis minus left-parenthesis sigma plus epsilon right-parenthesis upper R e left-brace left-parenthesis log r right-parenthesis Superscript p Baseline minus left-parenthesis log r plus i pi right-parenthesis Superscript p Baseline right-brace">

A
(
r
)
>
B
(
r
)
−
(
σ
+
ε
)
Re
⁡
{

(
log
⁡
r

)
p

−

(
log
⁡
r
+
i
π

)
p

}

A(r) > B(r) - (\sigma + \varepsilon )\operatorname {Re} \{ {(\log r)^p} - {(\log r + i\pi )^p}\}

\]
for r outside an exceptional set E, where
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="limit Underscript bar Endscripts Underscript x right-arrow normal infinity Endscripts StartFraction 1 Over left-parenthesis log r right-parenthesis Superscript p minus 1 Baseline EndFraction integral Underscript upper E intersection left-bracket 1 comma r right-bracket Endscripts StartFraction left-parenthesis p minus 1 right-parenthesis left-parenthesis log t right-parenthesis Superscript p minus 2 Baseline Over t EndFraction d t less-than-or-slanted-equals StartFraction sigma Over sigma plus epsilon EndFraction period">

lim
_

x
→
∞

1

(
log
⁡
r
)

p
−
1

∫

E
∩
[
1
,
r
]

(
p
−
1
)

(
log
⁡
t
)

p
−
2

t

d
t

⩽

σ

σ
+
ε

.

\underline {\lim } \limits _{x \to \infty } \;\frac {1}{{{{(\log r)}^{p - 1}}}}\int _{E \cap [1,r]} {\frac {{(p - 1){{(\log t)}^{p - 2}}}}{t}\;dt\; \leqslant \frac {\sigma }{{\sigma + \varepsilon }}.}

\]
Weak sequential convergence in 𝐿_{𝐸}^{∞} and Dunford-Pettis property of 𝐿_{𝐸}¹
Authors: Khurana Surjit Singh
Published: June 2010

For a

σ
\sigma

-finite measure space

(
X
,

A

,
μ
)

(X,\mathfrak {A},\mu )

it is proved that weak sequential convergence in

L
E
∞

L_E^\infty

implies almost everywhere pointwise convergence, with the weak topology on the Banach space E. Also it is proved that if weak and norm sequential convergence coincide in

E
′

E’

, then

L
E
1

L_E^1

has the Dunford-Pettis property.
A note on 𝑀-ideals in 𝐵(𝑋)
Authors: Hennefeld Julien
Published: June 2010

In this paper we prove some properties of M-ideals and HB-subspaces in an arbitrary Banach space. We then apply these properties to prove a theorem which generalizes to other spaces Smith’s and Ward’s results in [8]: for

1
>
p
>
∞
,
B
(

l
p

)

1 > p > \infty ,B({l_p})

contains no nontrivial summands and that each nontrivial M-ideal in

B
(

l
p

)

B({l_p})

contains

K
(

l
p

)

K({l_p})

.
Monotone operator functions on arbitrary sets
Authors: Donoghue William F.
Published: June 2010

We give a new proof of a result of Chandler which shows that a monotone operator function defined on a set J admits an analytic continuation to the upper and lower half-planes, and that this continuation is a Pick function, real and regular on the convex hull of J.
A Morrey-Nikol′skiĭ inequality
Authors: Ross James
Published: June 2010

An inequality of Sobolev type is proved which unifies some work of Nikol’skiĭ on fractional derivatives and some work of Morrey which assumes that the growth rate of the

L
p

{L^p}

norm of the gradient of a function on balls is bounded by some power of the radius.
A nondevelopable Čech-complete space with a point-countable base
Authors: Davis S. W.
Published: June 2010

An example is presented which is a p-space, in fact a Cech-complete space, which has a point-countable base and is not developable. This answers questions raised by Burke in 1970 and by Burke and Tall in 1972.
On residual properties
Authors: Mekler Alan H.
Published: June 2010

It is shown that the class of structures residually in a universal class closed under elementary equivalence is definable by a sentence of

L

∞
ω

{L_{\infty \omega }}

.
𝑙^{∞}/𝑐₀ has no equivalent strictly convex norm
Authors: Bourgain J.
Published: June 2010

It is shown that the quotient space

l
∞

/

c
0

{l^\infty }/{c_0}

does not admit an equivalent strictly convex norm.
On 𝐿¹ isomorphisms
Authors: Cambern Michael
Published: June 2010

Let

(

X
1

,

Σ
1

,

μ
1

)

({X_1},{\Sigma _1},{\mu _1})

and

(

X
2

,

Σ
2

,

μ
2

)

({X_2},{\Sigma _2},{\mu _2})

be two

σ
\sigma

-finite measure spaces. We show that any isomorphism T of the Banach space

L
1

(

X
1

,

Σ
1

,

μ
1

)

{L^1}({X_1},{\Sigma _1},{\mu _1})

onto the Banach space

L
1

(

X
2

,

Σ
2

,

μ
2

)

{L^1}({X_2},{\Sigma _2},{\mu _2})

which satisfies

‖
T
‖

‖

T

−
1

‖

>
2

\left \| T \right \|\;\left \| {{T^{ - 1}}} \right \| > 2

induces a transformation of the underlying measure spaces.
Oscillation properties of 𝑦ⁿ+𝑝𝑦=0
Authors: Jones Gary D.
Published: June 2010

The purpose of this paper is to give necessary and sufficient conditions for

(
k
,
n
−
k
)

(k,n - k)

disconjugacy of

y
n

+
p
y
=
0

{y^n} + py = 0

. The results are then applied to give counterexamples to the following theorems of Nehari. If n is even and p is positive either all solutions of

y
n

+
p
y
=
0

{y^n} + py = 0

oscillate or none do. If n is even and p is negative and

y
n

+
p
y
=
0

{y^n} + py = 0

has an oscillatory solution then all positive nonoscillatory solutions are either strongly increasing or strongly decreasing.
Approximation by nonfundamental sequences of translates
Authors: Zalik R. A.
Published: June 2010

For functions

f
(
t
)

f(t)

satisfying certain growth conditions, we consider a sequence of the form

{
f
(

c
n

−
t
)
}

\{ f({c_n} - t)\}

, nonfundamental in

L
2

(
R
)

{L_2}(R)

, and find a representation for those functions which are in the closure of its linear span. Some theorems concerning degree of approximation are also proved.
A lemma on extensions of abelian groups
Authors: Mader Adolf
Published: June 2010

We prove: If H is a Fuchs 5 group, then for all groups G containing H it follows that

H
=

H
1

⊕

H
2

,
G
=

H
1

⊕

G
2

H = {H_1} \oplus {H_2},G = {H_1} \oplus {G_2}

such that

H
2

⊂

G
2

{H_2} \subset {G_2}

and

|

G
2

|

⩽

|

G

/

H

|

⋅

ℵ
0

|{G_2}| \leqslant |G/H| \cdot {\aleph _0}

. There are a variety of applications.
Frattini embeddings of normal subgroups
Authors: Wright C. R. B.
Published: June 2010

If N is a normal subgroup of the finite group G, there is a split extension X of an elementary abelian group by G such that

N
⊴
X

N \trianglelefteq X

and

N
∩
Φ
(
G
)
=
Φ
(
X
)

N \cap \Phi (G) = \Phi (X)

.
Dieudonné-Schwartz theorem on bounded sets in inductive limits
Authors: Kučera J. , McKennon K.
Published: June 2010

The Dieudonné-Schwartz Theorem for bounded sets in strict inductive limits does not hold for general inductive limits

E
=

ind

lim

E
n

E = {\text {ind}}\;\lim {E_n}

. It does if every closed convex set in

E
n

{E_n}

is closed in

E

n
+
1

{E_{n + 1}}

. This condition is not necessary. In case all spaces

E
n

{E_n}

are normed a necessary and sufficient condition for the validity of the Dieudonné-Schwartz Theorem is given.
Existence theorems for generalized Hammerstein equations
Authors: Srikanth P. N. , Joshi M. C.
Published: June 2010

In this paper we obtain existence theorems for generalized Hammerstein-type equations

K
(
u
)
N
u
+
u
=
0

K(u)Nu + u = 0

, where for each u in the dual

X
∗

{X^\ast }

of a real reflexive Banach space

X
,
K
(
u
)
:
X
→

X
∗

X,K(u):X \to {X^\ast }

is a bounded linear map and

N
:

X
∗

→
X

N:{X^\ast } \to X

is any map (possibly nonlinear). The method we adopt is totally different from the methods adopted so far in solving these equations. Our results in the reflexive space generalize corresponding results of Petry and Schillings.
Finiteness of isotopy classes of certain knots
Authors: Hausmann Jean-Claude
Published: June 2010

We prove finiteness results for the isotopy classes of certain high-dimensional knots whose complement satisfies some homology conditions. In some particular cases, the isotopy class of a knot is determined by the twisted homology of its complement.
The nonexistence of invariant universal measures of semigroups
Authors: Kannan V. , Raju S. Radhakrishneswara
Published: June 2010

We prove that if S is an uncountable subsemigroup of a group, then every (left or right)-translation invariant

σ
\sigma

-finite measure defined on all subsets of S must be trivial. This answers a question posed by Ryll-Nardzewski and Telgarsky.
An inequality concerning the smallest disc that contains the spectrum of an operator
Authors: Garske Gerhard
Published: June 2010

Any bounded linear operator T on a Hilbert space satisfies the inequality
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sup Underscript double-vertical-bar x double-vertical-bar equals 1 Endscripts left-brace double-vertical-bar upper T x double-vertical-bar squared minus StartAbsoluteValue left-parenthesis upper T x comma x right-parenthesis EndAbsoluteValue squared right-brace greater-than-or-slanted-equals upper R Subscript upper T Superscript 2">

sup

‖
x
‖

=
1

{

‖

T
x

‖

2

−

|

(
T
x
,
x
)

|

2

}
⩾

R
T
2

{\sup _{\left \| x \right \| = 1}}\{ {\left \| {Tx} \right \|^2} - |(Tx,x){|^2}\} \geqslant R_T^2

, where

R
T

{R_T}

is the radius of the smallest disc containing the spectrum of T. An example is given, which shows that we cannot expect equality for

G
1

{G_1}

operators in general, contrary to a conjecture of Istrǎţescu.
Monotone iteration and Green’s functions for boundary value problems
Authors: Eloe P. W. , Grimm L. J.
Published: June 2010

An iteration scheme is given for approximating solutions of boundary problems of the form

L
y
=
f
(
x
,
y
)
,
T
y
(
x
)
=
r

Ly = f(x,y),Ty(x) = r

, where L is an nth order linear differential operator, f is continuous and T is a continuous linear operator from

C

n
−
1

(
I
)

{C^{n - 1}}(I)

into

R

n

{{\mathbf {R}}^n}

. The scheme is based on the condition that the Green’s function

G
(
x
,
s
)

G(x,s)

for the associated linear problem

L
y
=
0
,
T
y
=
0

Ly = 0,Ty = 0

exists and has sign independent of s.
On closed starshaped sets and Baire category
Authors: Beer Gerald
Published: June 2010

Let C be a closed set of second category in a normed linear space, and let

C
∗

{C^\ast }

be the subset of C each point of which sees all points of C except a set of first category. If

C
∗

{C^\ast }

is nonempty, then

C
∗

{C^\ast }

is a closed convex set. Moreover,

C
=
K
∪
P

C = K \cup P

where K is a closed starshaped set with convex kernel

C
∗

{C^\ast }

and P is a set of first category.
Interpolation fails for the Souslin-Kleene closure of the open set quantifier logic
Authors: Sgro J. A.
Published: June 2010

In this paper we show that the Souslin-Kleene closure of the open set quantifier logic fails to have interpolation. We also show that the notion of a

T
0

{T_0}

-topological space is not definable in this logic. This gives a more natural proof that it is strictly weaker than the interior operator logic.
Unions of cells with applications to visibility
Authors: Loveland L. D.
Published: June 2010

A crumpled n-cell C in

E
n

{E^n}

is proven to be an n-cell

(
n
≠
4
)

(n \ne 4)

when it is known to contain two n-cells

C
1

{C_1}

and

C
2

{C_2}

, one of which is flat, such that

Bd

C
⊂
(

Bd

C
1

)
∪

(Bd

C
2

)

{\text {Bd}}\;C \subset ({\text {Bd}}\;{C_1}) \cup {\text {(Bd}}\;{C_2})

. This theorem is applied to show that C is an n-cell if its boundary is the union of two closed sets each of which is seen from some point of

Int
⁡
C

\operatorname {Int} C

. Examples are given to show that flatness of one of

C
1

{C_1}

and

C
2

{C_2}

is necessary in the first theorem and to show that two is the largest integer for which either theorem is true.
Topological entropy of block maps
Authors: Coven Ethan M.
Published: June 2010

We show that

h
(

f
∞

)
=
log
⁡
2

h({f_\infty }) = \log 2

where

f
∞

{f_\infty }

is the map on the space of sequences of zeros and ones induced by the block map
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis x 0 comma ellipsis comma x Subscript k Baseline right-parenthesis equals x 0 plus normal upper Pi Subscript i equals 1 Superscript k Baseline left-parenthesis x Subscript i Baseline plus b Subscript i Baseline right-parenthesis">

f
(

x
0

,
…
,

x
k

)
=

x
0

+

Π

i
=
1

k

(

x
i

+

b
i

)

f({x_0}, \ldots ,{x_k}) = {x_0} + \Pi _{i = 1}^k({x_i} + {b_i})

where

k
⩾
2

k \geqslant 2

and the k-block

b
1

…

b
k

{b_1} \ldots {b_k}

is aperiodic.
How to recognize a localized sphere
Authors: Aguadé J.
Published: June 2010

Two cohomological characterizations of the sphere localized at a prime are given.
An example concerning inverse limit sequences of normal spaces
Authors: Charalambous M. G.
Published: June 2010

Using techniques developed by Wage and Przymusiński, we construct an inverse limit sequence

(

X
n

,

f

n
m

)

({X_n},{f_{nm}})

with limit space X such that each

X
n

{X_n}

is Lindolöf with

dim
⁡

X
n

=
0

\dim {X_n} = 0

, where dim denotes covering dimension, while X is normal with

dim
⁡
X
>
0

\dim X > 0

. The space X is a counterexample to several conjectures in Topology.
Plane continua and transformation groups
Authors: Lau A.
Published: June 2010

If G is a compact transformation group acting on a nonseparating plane continuum, does G have a fixed point? This paper provides some partial answers to the question. In particular, it yields the corollary that a period homeomorphism on a nonseparating plane continuum has a fixed point.
A note on normal complements in mod 𝑝 envelopes
Authors: Ivory Lee R.
Published: June 2010

Let G be a finite p-group and let

Z
p

[
G
]

{Z_p}[G]

denote the group ring of G over the field of p elements. The

mod

p

\bmod \;p

envelope of G, denoted by

G
∗

{G^ \ast }

, is the set of elements of

Z
p

[
G
]

{Z_p}[G]

with coefficient-sum equal to 1. Many examples of p-groups that have a normal complement in

G
∗

{G^ \ast }

have been found, including ten of the fourteen different groups of order 16. This note proves that one of the remaining groups of order 16 has a normal complement. The remaining groups of order 16 are the dihedral, semidihedral, and generalized quaternion groups of order

2
n

,
n
=
4

{2^n},n = 4

. We will prove that these groups do not have a normal complement for any

n
⩾
4

n \geqslant 4

.
The Laskerian property, power series rings and Noetherian spectra
Authors: Gilmer Robert , Heinzer William
Published: June 2010

We show that if the power series ring

R
[
[
X
]
]

R[[X]]

in one indeterminate over a commutative ring R with identity is Laskerian, then R is Noetherian. On the other hand, if

R
[
[
X
]
]

R[[X]]

is a ZD-ring, then R has Noetherian spectrum, but R need not be Noetherian. We show that, in general, a Laskerian ring has Noetherian spectrum.
Differential criteria for flatness
Authors: Glaz Sarah
Published: June 2010

We introduce differential algebra methods to the study of flatness over Noetherian domains. The results concern the specific cases of ideals and attempt to use the underlying divisibility properties of the ring. They concern mostly regular (geometric) rings and one-dimensional rings.
Toral subgroups lying in the centralizer of the group of units
Authors: Hunter R. P.
Published: June 2010

Let S be a compact connected finite dimensional monoid whose group of units G is a compact connected Lie group. Then there is an open set W about the unit element such that any compact subgroup within W has dimension at most

dim
⁡
S
−
dim
⁡
G
−
1

\dim S - \dim G - 1

and if any toral subgroup achieves this dimension then that toral subgroup lies in the centralizer of G. Two applications are given, one to embeddings of irreducible monoids into S.
Self-homotopy-equivalences of a space with two nonvanishing homotopy groups
Authors: Tsukiyama Kouzou
Published: June 2010

The group

G
#

(
X
)

{G_\# }(X)

is isomorphic to

H
n

(

π
1

(
X
)
;

π
n

(
X
)
)

{H^n}({\pi _1}(X);{\pi _n}(X))

for the connected CW-complex X with two nonvanishing homotopy groups

π
1

(
X
)
,

π
n

(
X
)

{\pi _1}(X),{\pi _n}(X)

, where

π
1

(
X
)

{\pi _1}(X)

acts on

π
n

(
X
)

{\pi _n}(X)

usually.
The stationary set of a group action
Authors: Stowe Dennis
Published: June 2010

If a point is stationary for a differentiable group action, M. Hirsch suggested that the vanishing of the first group cohomology at that point might imply stability of the point under perturbations of the action. This is proved for compactly generated Lie groups. Further implications of the cohomology condition are also proved.
Zeros of successive derivatives and iterated operators on analytic functions
Authors: Shaw J. K. , Prather C. L.
Published: June 2010

For a function f analytic in the closed disc

|

z

|

⩽
1

|z| \leqslant 1

, we study the behavior of zeros of the successive iterates

(

θ
n

f
)
(
z
)
,
n
=
0
,
1
,
2
,
…

({\theta ^n}f)(z),n = 0,1,2, \ldots

, where

θ
=

(
z
+
α

)

p
+
1

d

/

d
z

\theta = {(z + \alpha )^{p + 1}}d/dz

. We find that such behavior closely parallels that for the ordinary derivative operator. Using change-of-variable methods, we obtain information on zeros of derivatives of functions analytic in half-planes.