bluuebunny/crossref_metadata_2025 huggingface dataset:
Every finite abelian group is the Brauer group of a ring
Authors: Ford T. J.
Published: July 2010

Given an arbitrary finite abelian group

G
G

a ring

R
R

is constructed using cohomological techniques from algebraic geometry whose Brauer group is

G
G

. If

G
G

is a cyclic group, then

R
R

can be taken to be a three-dimensional noetherian integral domain. If

G
G

is not a cyclic group the ring

R
R

is a three-dimensional noetherian ring. At the expense of raising the dimension of

R
R

,

R
R

can be chosen to be a domain. We also calculate

B
(
R
[
x
,
1

/

x
]
)

B(R[x,1/x])

for

R
R

a commutative noetherian regular ring containing a field of characteristic zero.
A note on matrices with positive definite real part
Authors: London David
Published: July 2010

A lemma characterizing complex matrices with positive definite real part is given. It is shown that many results concerning such matrices are straightforward consequences of this lemma.
On centralizers of 𝑝-elements in indecomposable modules
Authors: Landrock Peter
Published: July 2010

For

M
M

any liftable module of a group algebra of a finite group

G
G

over a field of characteristic

p
p

and

x
∈
G

x \in G

any

p
p

-element, we discuss connections between the restriction of

M
M

to

⟨
x
⟩

\left \langle x \right \rangle

and that of

χ
\chi

to

⟨
x
⟩

\left \langle x \right \rangle

, where

χ
\chi

is the character of

M
M

. In particular we get a lower bound for the number of Jordan components of this restriction of

M
M

in terms of

χ
\chi

restriction. For

M
M

a permutation module, this bound is trivially an equality, and we derive several results by L. Scott, which hitherto have been considered relatively deep, in a very elementary and straightforward manner.
From a 3-local plus 3-fusion to the centralizer of an involution
Authors: Frohardt Daniel
Published: July 2010

It is shown that much of the structure of the centralizer of a central involution in a group of characteristic 2 type with a standard

3
3

-component of type

G
L
(
n
,
2
)

GL(n,2)

,

n
⩾
6

n \geqslant 6

, is easily determined from the

3
3

-fusion. Consequently, one can shorten the previous treatment of such groups by Finkelstein and the author.
On the ubiquity of herringbones in finitely generated lattices
Authors: Rival I. , Ruckelshausen W. , Sands B.
Published: July 2010

Every finitely generated infinite lattice of finite width contains a subset isomorphic to the "herringbone" or its dual.
The third axiom of countability for abelian groups
Authors: Hill Paul
Published: July 2010

Three different definitions of the third axiom of countability for abelian

p
p

-groups are shown to be equivalent. The main interest in this stems from the fact that the third axiom of countability characterizes one of the most important classes of abelian groups. Moreover, the equivalence of two of these definitions validates the proof of Theorem 67 in P. Griffith’s Infinite abelian group theory. As a further application of our method of proof, we show that every torsionfree abelian group satisfies the third axiom of countability with respect to purity.
Maximal separable intermediate fields of large codegree
Authors: Heerema Nickolas
Published: July 2010

Let

k
k

be a function field in

n
(
n
>
0
)

n(n > 0)

variables over

k
0

{k_0}

a field having characteristic

p
≠
0

p \ne 0

. An intermediate field

s
s

is maximal separable if

s

/

k
0

s/{k_0}

is separable and

s
s

is not properly contained in any subfield of

k
k

separable over

k
0

{k_0}

. The following result is proved. If

n
=
1

n = 1

the set

Δ
=
{
[
k
:
s
]

|

s

\Delta = \{ [k:s]|s

maximal separable} is bounded if and only if the algebraic closure

k
¯

0

{\bar k_0}

of

k
0

{k_0}

in

k
k

is separable over

k
0

{k_0}

. If

n
⩾
1

n \geqslant 1

and

Δ
\Delta

is bounded then

k
¯

0

/

k
0

{\bar k_0}/{k_0}

is separable. An upper bound for

Δ
\Delta

is obtained for the case

n
=
1

n = 1

and

k
¯

0

/

k
0

{\bar k_0}/{k_0}

separable.
The Bruhat order of the symmetric group is lexicographically shellable
Authors: Edelman Paul H.
Published: July 2010

The title theorem is proven. It then follows from a theorem of Björner that the simplicial complex of chains of this Bruhat order is shellable and thus Cohen-Macaulay. It is further established that this complex is a double cone over a triangulation of a sphere.
Decomposability of completely Suslin-additive families
Authors: Frolík Zdeněk , Holický Petr
Published: July 2010

It is proved that every point-finite completely Suslin-additive family in the product of a complete metric space by a compact space is

σ
\sigma

-discretely decomposable. Several applications are indicated.
Equivalence of certain representing measures
Authors: Glicksberg I.
Published: July 2010

If an interior component

Ω
\Omega

of a compact

K
⊂

C

K \subset {\mathbf {C}}

is a part for

R
(
K
)

R(K)

, then given

z
1

{z_1}

,

z
2

{z_2}

in

Ω
\Omega

and a representing measure

λ
1

{\lambda _1}

for

z
1

{z_1}

there is a representing measure for

z
2

{z_2}

equivalent to

λ
1

{\lambda _1}

.
On subsequential limit points of a sequence of iterates
Authors: Maiti M. , Babu A. C.
Published: July 2010

In this note we study the properties of the subsequential limit points of a sequence of iterates of mappings which are contractive over two consecutive elements of an orbit.
On the Dini test and divergence of Fourier series
Authors: Calderón Calixto P.
Published: July 2010

In this note we prove that no condition weaker than the Dini assures the pointwise convergence of a Fourier series in a set of positive measure.
A problem on a geometric property of lemniscates
Authors: Hwang J. S.
Published: July 2010

Let

R
3

{R^3}

be the Eulcidean space and let

p
n

{p_n}

be the product defined by
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p Subscript n Baseline left-parenthesis upper W comma upper W Subscript k Baseline right-parenthesis equals normal upper Pi Subscript k equals 1 Superscript n Baseline StartAbsoluteValue upper W minus upper W Subscript k Baseline EndAbsoluteValue">

p
n

(
W
,

W
k

)
=

Π

k
=
1

n

|

W
−

W
k

|

{p_n}(W,{W_k}) = \Pi _{k = 1}^n\left | {W - {W_k}} \right |

,

W
W

,

W
k

∈

R
3

{W_k} \in {R^3}

, where

|

W
−

W
k

|

\left | {W - {W_k}} \right |

is the distance between

W
W

and

W
k

{W_k}

. Let

C
(
n
)

C(n)

be the class of all such products with the same degree

n
n

. For any product

p
p

, we call

E
(
p
)
=
{
W
:
p
(
W
)
⩽
1
}

E(p) = \{ W:p(W) \leqslant 1\}

the lemniscate of

p
p

. We recently proved that if

p
n

(
W
,

W
k

)

{p_n}(W,{W_k})

and

p
n
∗

(
W
,

W
k
∗

)

p_n^*(W,W_k^*)

are two products in

C
(
n
)

C(n)

such that

E
(

p
n

)
⊆
E
(

p
n
∗

)

E({p_n}) \subseteq E(p_n^*)

, and if all zeros

W
k

{W_k}

of

p
n

{p_n}

lie on the same plane, then

p
n

≡

p
n
∗

{p_n} \equiv p_n^*

. We then asked whether this result is sharp. In this note, we answer this question in the affirmative sense.
Fixed points and boundaries
Authors: Chandler Eric
Published: July 2010

A lemma of Ludvik Janos is used to show that if a nonexpansive self-map

T
T

of a compact set

X
X

is contractive on

Δ
′

X

\Delta ’X

, the boundary of

X
X

in

co

¯

X

\overline {{\text {co}}} X

, then

T
T

has a fixed point in

X
X

. It is further proven that if

T
(

Δ
′

X
)
∩

Δ
′

X
=
∅

T(\Delta ’X) \cap \Delta ’X = \emptyset

, or if

T
T

maps any point

y
y

of

X
X

away from

Δ
′

X

\Delta ’X

, then

T
T

has a fixed point in

X
X

.
On the compactification of strongly pseudoconvex surfaces
Authors: Tan Vo Van
Published: July 2010

In this paper, we shall prove that the compactification of a strongly pseudoconvex surface is either a projective algebraic or an Inoue surface. Furthermore, we shall construct an example of a strongly pseudoconvex surface

X
X

which admits two distinct compactifications: One

M
′

M’

projective algebraic and the other one

M
M

(highly) nonalgebraic.
A fixed point free nonexpansive map
Authors: Alspach Dale E.
Published: July 2010

In this note we give an example of a weakly compact convex subset of

L
1

[
0
,
1
]

{L_1}[0,1]

that fails to have the fixed point property for nonexpansive maps. This answers a long-standing question which was recently raised again by S. Reich [7].
Differentiability of weak solutions to an abstract inhomogeneous differential equation
Authors: Travis C. C.
Published: July 2010

A characterization is given of those strongly continuous semigroups

T
(
t
)

T(t)

for which the function

∫
0
t

T
(
t
−
s
)
f
(
s
)
d
s

\int _0^tT(t - s)f(s)ds

is continuously differentiable on

t
>
0

t > 0

for each continuous

f
:
[
0
,
∞
)
→
X

f:[0,\infty ) \to X

.
The separation principle for impulse control problems
Authors: Menaldi José-Luis
Published: July 2010

In this paper, one shows that the combined problem of optimal impulse control and filtering, for a stochastic linear dynamic system observed via a noisy linear channel, can be reduced to two independent problems of impulse control and filtering, respectively.
A generalization of Laplace’s method
Authors: Hwang Chii Ruey
Published: July 2010

Let

Q
Q

be Gaussian with mean 0 and covariance

B
B

in a separable Hilbert space. Analogous to Laplace’s method, the weak limit (as

θ
↓
0

\theta \downarrow 0

)

P
P

of

{

P
θ

|

θ
>
0
}

\{ {P_\theta }|\theta > 0\}

, with
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis d upper P Subscript theta Baseline slash d upper Q right-parenthesis left-parenthesis x right-parenthesis equals upper C Subscript theta Baseline exp left-parenthesis minus upper H left-parenthesis x right-parenthesis slash theta right-parenthesis">

(
d

P
θ

/

d
Q
)
(
x
)
=

C
θ

exp
⁡
(
−
H
(
x
)

/

θ
)

(d{P_\theta }/dQ)(x) = {C_\theta }\exp ( - H(x)/\theta )

, is considered, where
\[

H
(
x
)
=

1
2

⟨
F
x
,
x
⟩
−
2
⟨
F
m
,
x
⟩
)
,

H(x) = \frac {1} {2}\langle Fx,x\rangle - 2\langle Fm,x\rangle ),

\]

F
F

is s.a. nonnegative definite and bounded. If

m
∈
ℜ
(

B

1

/

2

)

m \in \Re ({B^{1/2}})

, then

P
P

is Gaussian with mean

m
−

B

1

/

2

π

B

−
1

/

2

m

m - {B^{1/2}}\pi {B^{ - 1/2}}m

and covariance

B

1

/

2

π

B

1

/

2

{B^{1/2}}\pi {B^{1/2}}

, where

π
\pi

is the projection onto

N

(

B

1

/

2

F

B

1

/

2

)

\mathfrak {N}({B^{1/2}}F{B^{1/2}})

. Moreover

P
P

is the fiber measure of

Q
Q

on

m
+

N

(
F
)

m + \mathfrak {N}(F)

. Under stronger conditions,

P
P

is induced by an affine transformation.
Dimension of subsets of product spaces
Authors: Sternfeld Y.
Published: July 2010

It is proved that under a certain condition on a separable metric space

X
X

, each compact subset

W
W

of

X
×
Y

X \times Y

with

dim
⁡
W
=
dim
⁡
X
+
dim
⁡
Y

\dim W = \dim X + \dim Y

contains a product

X
′

×

Y
′

⊂
W

X’ \times Y’ \subset W

with

dim
⁡

X
′

=
dim
⁡
X

\dim X’ = \dim X

and

dim
⁡

Y
′

=
dim
⁡
Y

\dim Y’ = \dim Y

. This condition is satisfied when

X
X

is a Euclidean space.
Nontoral pinched Anosov maps
Authors: Fried David
Published: July 2010

We show Anosov maps satisfying a certain spectral property can arise on nilmanifolds of any nilpotent degree, settling a conjecture of Brin.
The existence of a coadjoint equivariant momentum mapping for a semidirect product
Authors: Mikami Kentaro
Published: July 2010

We consider a symplectic action of a group

G
G

on a symplectic manifold

P
P

, which admits a momentum mapping. Assume that

G
G

is a semidirect product of

G
1

{G_1}

by

G
2

{G_2}

. We prove that if the symplectic action of

G
1

{G_1}

has a coadjoint equivariant momentum mapping, and if

H
1

(
u
n

k
1

:

R

)
=

H
2

(
u
n

k
2

:

R

)
=
0

{H^1}(un{k_1}:{\mathbf {R}}) = {H^2}(un{k_2}:{\mathbf {R}}) = 0

, then the symplectic action of

G
G

has a coadjoint equivariant momentum mapping, where

u
n

k
1

un{k_1}

and

u
n

k
2

un{k_2}

are the Lie algebras of

G
1

{G_1}

and

G
2

{G_2}

respectively.
Homogeneous treelike continua
Authors: Lewis Wayne
Published: July 2010

We prove that every

k
k

-junctioned homogeneous tree-like continuum is chainable, and hence a pseudo-arc. Possible extensions of this result are briefly discussed.
Exponential growth and the spectrum of the Laplacian
Authors: Brooks Robert
Published: July 2010

Conditions are given on a noncompact manifold which allow one to conclude that 0 is in the spectrum of the Laplacian on

M
M

.
On Stokes’ theorem for noncompact manifolds
Authors: Karp Leon
Published: July 2010

Stokes’ theorem was first extended to noncompact manifolds by Gaffney. This paper presents a version of this theorem that includes Gaffney’s result (and neither covers nor is covered by Yau’s extension of Gaffney’s theorem). Some applications of the main result to the study of subharmonic functions on noncompact manifolds are also given.
Flat bundles with solvable holonomy
Authors: Goldman William M. , Hirsch Morris W.
Published: July 2010

Let

G
G

be a solvable linear Lie group. We show that for every flat principal

G
G

-bundle

ξ
\xi

over a CW-complex

M
M

, there is a finite-sheeted covering space

p
:

M
^

→
M

p:\hat M \to M

such that

p
∗

ξ

{p^ * }\xi

is trivial as a principal

G
G

-bundle. This result is used to show that every affine manifold with solvable fundamental group has a finite covering which is parallelizable.
A note on 4/𝑛=1/𝑥+1/𝑦+1/𝑧
Authors: Yang Xun Qian
Published: July 2010

Denoting by

S
(
N
)

S(N)

the number of natural numbers

n
n

less than

N
N

for which
\[

4
n

=

1
x

+

1
y

+

1
z

\frac {4} {n} = \frac {1} {x} + \frac {1} {y} + \frac {1} {z}

\]
has no solutions in positive integers, we show that

S
(
N
)
≪
N

/

log
2

N

S(N) \ll N/{\log ^2}N

.
On 𝑈ₘ-numbers
Authors: Alniaçik K.
Published: July 2010

In this paper we shall give some examples of

U
m

{U_m}

-numbers by using the continued fraction expansions of algebraic numbers of degree

m
>
1

m > 1

.
The unit groups of affine algebraic monoids
Authors: Waterhouse William C.
Published: July 2010

An affine algebraic group can be embedded as a proper dense subgroup of an affine algebraic monoid iff it has a homomorphism onto the multiplicative group.
Minimizing setups for cycle-free ordered sets
Authors: Duffus D. , Rival I. , Winkler P.
Published: July 2010

A machine performs a set of jobs one at a time subject to a set of precedence constraints. We consider the problem of scheduling the jobs to minimize the number of "setups".
Schur indices in finite quaternion-free groups
Authors: Oh A. D.
Published: July 2010

Let

G
G

be a finite, quaternion-free group with exponent

e
e

, let

F
F

be a field of characteristic zero and let

χ
\chi

be an absolutely irreducible character of

G
G

. Suppose that a Sylow

2
2

-subgroup of the Galois group of

F

(
e

1

)

F{(^e}\sqrt 1 )

over

F
F

is cyclic. It is shown that if

χ
\chi

is not real valued, then the Schur index of

χ
\chi

over

F
F

is odd.
A note on topological ℎ𝑜𝑚-functors
Authors: Harvey J. M.
Published: July 2010

This note establishes internal criteria on a category

C
C

and a separator

Σ
\Sigma

in

C
C

which characterize the condition that the

Σ
\Sigma

-induced covariant hom-functor

h
Σ

:
C
→

{h_\Sigma }:C \to

Set is (epi, mono-source)-topological.
A criterion for finite module type
Authors: Bessenrodt Christine
Published: July 2010

The following result is proved: If a

p
p

-block of a finite group has only finitely many indecomposable liftable modules with the defect group of the block as a vertex or if it has only finitely many indecomposable periodic modules, then the block is of finite module type.
A note on preprojective partitions over hereditary Artin algebras
Authors: Todorov Gordana
Published: July 2010

If

Λ
\Lambda

is an artin algebra there is a partition of

ind
⁡
Λ

\operatorname {ind} \Lambda

, the category of indecomposable finitely generated

Λ
\Lambda

-modules,

ind
⁡
Λ
=

∪

i
⩾
0

P
_

_

i

\operatorname {ind} \Lambda = { \cup _{i \geqslant 0}}{\underline {\underline {P}}_i}

, called the preprojective partition. We show that

P
_

_

i

\underline {\underline {P}}_i

can be easily constructed for hereditary artin algebras, if

P
_

_

i
−
1

\underline {\underline {P}}_{i - 1}

is known:

A
A

is in

P
_

_

i

\underline {\underline {P}}_i

if and only if

A
A

is not in

P
_

_

i
−
1

\underline {\underline {P}}_{i - 1}

and there is an irreducible map

B
→
A

B \to A

, where

B
B

is in

P
_

_

i
−
1

\underline {\underline {P}}_{i - 1}

.
Conull hypersurfaces in Minkowski space
Authors: Goldstein Norman
Published: July 2010

A submanifold of

M

=

Gr(2,

C

4

)

{\mathbf {M}} = {\text {Gr(2,}}{{\mathbf {C}}^4}{\text {)}}

is conull when its conormal space is in the kernel of the dualized conformal metric of

M
M

. We show that there are no conull compact complex

3
3

-dimensional submanifolds of

M
M

.
On the uniform asymptotic stability in functional-differential equations
Authors: Wen L. Z.
Published: July 2010

We consider a system of functional differential equations

x
′

(
t
)
=
F
(
t
,

x
t

)

x’(t) = F(t,{x_t})

and obtain conditions on a Liapunov functional to insure the uniform asymptotic stability of the zero solution.
On the oscillation and nonoscillation of second order sublinear equations
Authors: Kwong Man Kam , Wong James S. W.
Published: July 2010

An oscillation criterion and a nonoscillation criterion are given for the sublinear equation

y
+
a
(
t
)

|

y

|

γ

sgn
⁡
y
=
0

y + a(t)|y{|^\gamma }\operatorname {sgn} y = 0

,

0
>
γ
>
1
,
t
∈
[
0
,
∞
)

0 > \gamma > 1,t \in [0,\infty )

, where

a
(
t
)

a(t)

is allowed to change sign. When applied to the special case

a
(
t
)
=

t
λ

sin
⁡
t

a(t) = {t^\lambda }\sin t

, we deduce oscillation for

λ
>
−
γ

\lambda > - \gamma

and nonoscillation for

λ
>
−
γ

\lambda > - \gamma

.
Another characterization of BLO
Authors: Bennett Colin
Published: July 2010

It is shown that a locally integrable function

f
f

on

R

n

{{\mathbf {R}}^n}

has bounded lower oscillation

(
f
∈

BLO

)

(f \in {\text {BLO}})

if and only if

f
=
M
F
+
h

f = MF + h

, where

F
F

has bounded mean oscillation

(
F
∈

BMO

)

(F \in {\text {BMO}})

and

M
F
>
∞

MF > \infty

a.e., and

h
h

is bounded. Here,

M
F

MF

is a variant of the familiar Hardy-Littlewood maximal function:

M
F
=

sup

Q
∍
x

Q
(
F
)

MF = {\text {sup}_{Q\backepsilon x}}Q(F)

(no absolute values), where

Q
(
F
)

Q(F)

is the mean value of

F
F

over the cube

Q
Q

.
Lipschitz constants and moduli of continuity for the Chebyshev projection
Authors: Bridges Douglas S.
Published: July 2010

It is shown how to construct Lipschitz constants and moduli of continuity for the Chebyshev projection of

C
[
0
,
1
]

C[0,1]

onto the finite-dimensional subspace spanned by a Chebyshev system.
A radial uniqueness theorem for meromorphic functions
Authors: Rippon P. J.
Published: July 2010

A classical theorem of Lusin and Privalov states that a meromorphic function in the unit disc, which has radial limit zero on a set which is both of second category and metrically dense in some boundary arc, must vanish identically. We prove below a radial uniqueness theorem which includes the Lusin-Privalov theorem as a special case and which also generalises the Barth-Schneider-Tse asymptotic analogue of the F. and M. Riesz radial uniqueness theorem. The part of the proof relating to Baire category is disposed of by using the Collingwood maximality theorem.
A remark on expanding maps
Authors: Chang Kung Ching , Li Shu Jie
Published: July 2010

In this paper we discuss the following problem stated by L. Nirenberg: Let

T
T

be an expanding map

H
→
H

H \to H

(

H
H

is a Hilbert space) with

T
(
0
)
=
0

T(0) = 0

. Suppose

T
T

maps a neighborhood of the origin onto a neighborhood of the origin. Does

T
T

map

H
H

onto

H
H

? We answer positively the problem when

T
T

is differentiable.
A note on the irreducibility of Lebesgue measure with applications to random walks on the unit circle
Authors: Chiang Tzuu Shuh
Published: July 2010

Let

μ
\mu

be a probability measure on

R
R

. We say that a

σ
\sigma

-finite measure

λ
\lambda

is irreducible with respect to

μ
\mu

if there does not exist a Borel set

A
A

with

μ
(
A
)

\mu (A)

,

μ
(

A
c

)
>
0

\mu ({A^c}) > 0

such that

∫
A

μ
(

A
c

−
x
)

λ
(
d
x
)
=
0

\int _A {\mu ({A^c} - x)} \lambda (dx) = 0

. It is well known that the Lebesgue measure

m
(
d
x
)

m(dx)

is irreducible with respect to any discrete measure whose support is

R
R

. We prove that every absolutely continuous measure is irreducible with respect to any probability measure whose support is

R
R

and give an application of this fact to random walks on the unit circle.
Solution of the 𝛾-space problem
Authors: Fox Ralph
Published: July 2010

This paper disproves the classic conjecture that every

γ
\gamma

-space is quasi-metrizable.
Perfect images of 𝑝-spaces
Authors: Chaber Józef
Published: July 2010

We give a new proof of the fact that paracompact

p
p

-spaces are preserved by perfect mappings. This proof gives more information about the image space than the preceding proofs. We construct some examples showing that the information we get is complete in a way, and an example showing that a perfect image of a

σ
\sigma

-paralindelöf and screenable

p
p

-space need not be a

p
p

-space.
Homotopy idempotents on finite-dimensional complexes split
Authors: Hastings Harold M. , Heller Alex
Published: July 2010

We prove that (unpointed) homotopy idempotents on finite-dimensional complexes split, and describe some geometric consequences.
Graded algebras having a unique rational homotopy type
Authors: Shiga Hiroo , Yagita Nobuaki
Published: July 2010

We consider the problem for which graded algebra

A
∗

{A^* }

complexes such that

H
∗

(
K
,
Q
)
≃

A
∗

{H^*}(K,Q) \simeq {A^*}

is unique up to homotopy type. A necessary and sufficient condition is given using formal minimal model of

A
∗

{A^*}

.
The only genus zero 𝑛-manifold is 𝑆ⁿ
Authors: Ferri Massimo , Gagliardi Carlo
Published: July 2010

All

n
n

-manifolds of regular genus zero, i.e. admitting a crystallization which regularly imbeds into

S

2

{{\mathbf {S}}^2}

, are proved to be homeomorphic to

S

n

{{\mathbf {S}}^n}

. A conjecture implying the Poincaré Conjecture in dimension four is also formulated. Si dimostra che tutte le

n
n

-varietà di genere regolare zero, cioè aventi una cristallizzazione che si immerge regularmente in

S

2

{{\mathbf {S}}^2}

, sono omeomorfe a

S

n

{{\mathbf {S}}^n}

. Si formula anche una congettura che implica quella di Poincaré in dimensione quattro.
Sigma-compact locally convex metric linear spaces universal for compacta are homeomorphic
Authors: Dobrowolski T. , Mogilski J.
Published: July 2010

It is proved that every

σ
\sigma

-compact locally convex metric linear space containing a topological copy of the Hilbert cube

Q
Q

is homeomorphic to

Σ
\Sigma

the linear span of the Hilbert cube

Q
Q

, in the Hilbert space

l
2

{l_2}

.
The spaces which contain an 𝑆-space
Authors: Pfeffer W. F.
Published: July 2010

Under the continuum hypothesis, we show that a

T
1

{T_1}

-space

X
X

contains an

S
S

-space if and only if there is an uncountable locally countable set

E
⊂
X

E \subset X

containing no Borel subset of

X
X

.
Homeomorphism groups of some direct limit spaces
Authors: Hale Margie
Published: July 2010

Let

F
F

be either of the spaces

R
∞

=

R
n

{R^\infty } = {R^n}

or

Q
∞

=

Q
n

{Q^\infty } = {Q^n}

where

R
R

denotes the reals and

Q
Q

the Hilbert cube. Let

H

(
M
)

\mathcal {H}(M)

be the homeomorphism group of a connected

F
F

-manifold

M
M

with the compact-open topology. We prove that

H

(
M
)

\mathcal {H}(M)

is separable, Lindelöf, paracompact, non-first-countable, and not a

k
k

-space.
The conjugacy problem for graph products with cyclic edge groups
Authors: Horadam K. J.
Published: July 2010

A graph product is the fundamental group of a graph of groups. Amongst the simplest examples are HNN groups and free products with amalgamation. The conjugacy problem is solvable for recursively presented graph products with cyclic edge groups over finite graphs if the vertex groups have solvable conjugacy problem and the sets of cyclic generators in them are semicritical. For graph products over infinite graphs these conditions are insufficient: a further condition ensures that graph products over infinite graphs of bounded path length have solvable conjugacy problem. These results generalise the known ones for HNN groups and free products with amalgamation.
The center of the quotient division ring of the universal envelope of a Lie algebra
Authors: Ooms Alfons I.
Published: July 2010

Let

L
L

be a finite dimensional Lie algebra over a field

k
k

of characteristic zero,

D
(
L
)

D(L)

the quotient division ring of

U
(
L
)

U(L)

. We compare the center

Z
(
D
(
L
)
)

Z(D(L))

with

Z
(
D
(
H
)
)

Z(D(H))

where

H
H

is an ideal of

L
L

of codimension one.
Varieties of rings with definable principal congruences
Authors: Simons G. E.
Published: July 2010

A variety

V

\mathcal {V}

of rings has definable principal congruences (DPC) if there is a first order sentence defining principal two-sided ideals for all rings in

V

\mathcal {V}

. The key result is that for any ring

R
R

,

V
(

M
n

(
R
)
)

V({M_n}(R))

does not have DPC if

n
⩾
2

n \geqslant 2

. This allows us to show that if

V
(
R
)

V(R)

has DPC, then

R
R

is a polynomial identity ring. Results from the theory of PI rings are used to prove that for a semiprime ring

R
R

,

V
(
R
)

V(R)

has DPC if and only if

R
R

is commutative. An example of a finite, local, noncommutative ring

R
R

with

V
(
R
)

V(R)

having DPC is given.
Hyperplanarity of the equimultiple locus
Authors: Narasimhan R.
Published: July 2010

It is known that the (local) equimultiple locus of a hypersurface defined over a field of characteristic zero is contained in a hyperplane (for example, the one given by the Tchirnhausen transformation: see Abhyankar’s paper [A] for details). In this note (a) we show that this theorem is no longer true for varieties of dimension bigger than two in char

p
>
0

p > 0

, and (b) we give proofs of this statement in the cases of (i) ’purely inseparable’ surfaces, (ii) double points of surfaces in char 2.
Distributively generated centralizer near-rings
Authors: Maxson C. J. , Smith K. C.
Published: July 2010

Let

G
G

be a finite group.

A

\mathcal {A}

a group of automorphisms of

G
G

and

C

(

A

;
G

)

\mathcal {C}\left ( {\mathcal {A};G} \right )

the centralizer near-ring determined by the pair

(

A

,
G
)

(\mathcal {A},G)

. In this paper we investigate the structure of those centralizer near-rings

C

(

A

;
G

)

\mathcal {C}\left ( {\mathcal {A};G} \right )

which are distributively generated. Particular attention is given to the situation in which

G
G

is a solvable group.
A note on asymptotic prime sequences
Authors: Katz Daniel
Published: July 2010

The lengths of all maximal asymptotic prime sequences over an ideal in a local ring are shown to be the same. This number can be calculated in terms of analytic spread and depths of minimal primes in the completion.
The determination of all varieties consisting of absolutely closed semigroups
Authors: Higgins P. M.
Published: July 2010

An example is given of a right normal band that is not absolutely closed. This enables us to determine all varieties of semigroups that consist entirely of absolutely closed semigroups.
An extrapolation theorem in the theory of 𝐴_{𝑝} weights
Authors: García-Cuerva José
Published: July 2010

A new proof is given of the extrapolation theorem of J. L. Rubio de Francia [7]. Unlike the proof in [7], the proof presented here is independent of the theory of vector valued inequalities.
Walsh-Fourier coefficients and locally constant functions
Authors: Wade William R.
Published: July 2010

A condition on the Walsh-Fourier coefficients of a continuous function

f
f

sufficient to conclude that

f
f

is locally constant is obtained. The condition contains certain conditions identified earlier by Bočkarev, Coury, Skvorcov and Wade, and Powell and Wade.
On extreme points of subordination families
Authors: Abu-Muhanna Yusuf
Published: July 2010

Let

F
F

be the set of analytic functions in

U
=
{
z
:

|

z

|

>
1
}

U = \{ z:|z| > 1\}

subordinate to a univalent function

f
f

. Let

D
=
f
(
U
)

D = f(U)

. For

g
(
z
)
=
f
(
ϕ
(
z
)
)
∈
F

g(z) = f(\phi (z)) \in F

, let

λ
(
θ
)

\lambda (\theta )

denote the distance between

g
(

e

i
θ

)

g({e^{i\theta }})

and

∂
D

\partial D

(boundary of

D
D

). We obtain the following results. (1) If

f
′

f’

is Nevanlinna then

∫
0

2
π

log
⁡
λ
(
θ
)
d
θ
=
−
∞

\int _0^{2\pi } {\log \lambda (\theta )d\theta = - \infty }

if and only if
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Subscript 0 Superscript 2 pi Baseline log left-parenthesis 1 minus StartAbsoluteValue phi left-parenthesis e Superscript i theta Baseline right-parenthesis EndAbsoluteValue right-parenthesis d theta equals negative normal infinity period">

∫
0

2
π

log
⁡

(

1
−

|

ϕ
(

e

i
θ

)

|

)

d
θ
=
−
∞

.

\int _0^{2\pi } {\log \left ( {1 - |\phi ({e^{i\theta }})|} \right )d\theta = - \infty } .

\]
(2) If

g
g

is an extreme point of the closed convex hull of

F
F

then
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Subscript 0 Superscript 2 pi Baseline log left-parenthesis 1 minus StartAbsoluteValue phi left-parenthesis e Superscript i theta Baseline right-parenthesis EndAbsoluteValue right-parenthesis d theta equals negative normal infinity comma">

∫
0

2
π

log
⁡

(

1
−

|

ϕ
(

e

i
θ

)

|

)

d
θ
=
−
∞

,

\int _0^{2\pi } {\log \left ( {1 - |\phi ({e^{i\theta }})|} \right )d\theta = - \infty } ,

\]
for the case when

D
D

is a Jordan domain subset to a half-plane and

f
′

f’

is Nevanlinna.
A note on weighted norm inequalities for the Hardy-Littlewood maximal operator
Authors: Christ Michael , Fefferman Robert
Published: July 2010

In this note we give an extremely simple proof of the weight norm inequalities for the Hardy-Littlewood maximal operator in

R

n

{{\mathbf {R}}^n}

.
On the order and lower order of entire functions with radially distributed zeros
Authors: Steinmetz Norbert
Published: July 2010

It is shown that the order and lower order of an entire function with zeros restricted to

k
k

distinct rays differ at most by

k
k

, if either

k
⩽
2

k \leqslant 2

or if the zeros or the rays are regularly distributed.
Essential spectra of operators in the class ℬ_{𝓃}(Ω)
Authors: Seddighi Karim
Published: July 2010

For a connected open subset

Ω
\Omega

of the plane and

n
n

a positive integer, let

B

n

(
Ω
)

{\mathcal {B}_n}(\Omega )

be the space introduced by Cowen and Douglas in their paper Complex Geometry and Operator Theory. Our paper deals with characterizing the essential spectrum of an operator

T
T

in

B

n

(
Ω
)

{\mathcal {B}_n}(\Omega )

for which

σ
(
T
)
=

Ω
¯

\sigma (T) = \bar \Omega

and the point spectrum of

T
∗

{T^ * }

is empty. This class of operators forms an important part of

B

n

(
Ω
)

{\mathcal {B}_n}(\Omega )

denoted by

B

n
′

(
Ω
)

{\mathcal {B}’_n}(\Omega )

. We use this characterization to give another proof of the result of Axler, Conway and McDonald on determining the essential spectrum of the Bergman operator. Let
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A Subscript n Baseline left-parenthesis upper G right-parenthesis equals StartSet upper S colon upper T equals upper S Superscript asterisk Baseline is in script upper B prime Subscript n Baseline left-parenthesis upper G Superscript asterisk Baseline right-parenthesis EndSet">

A
n

(
G
)
=

{

S
:
T
=

S
∗

is

in

B

′

n

(

G
∗

)

}

{A_n}(G) = \left \{ {S:T = {S^ * }{\text {is}}\;{\text {in}}{{\mathcal {B}’}_n}({G^ * })} \right \}

. We also characterize the weighted shifts in

A
1

(
G
)

{A_1}(G)

.
Divergent Jacobi polynomial series
Authors: Meaney Christopher
Published: July 2010

Fix real numbers

α
⩾
β
⩾
−

1
2

\alpha \geqslant \beta \geqslant - \tfrac {1}{2}

, with

α
>
−

1
2

\alpha > - \tfrac {1}{2}

, and equip

[
−
1
,
1
]

[ - 1,1]

with the measure

d
μ
(
x
)
=

(
1
−
x

)
α

(
1
+
x

)
β

d
x

d\mu (x) = {(1 - x)^\alpha }{(1 + x)^\beta }dx

. For

p
=
4
(
α
+
1
)

/

(
2
α
+
3
)

p = 4(\alpha + 1)/(2\alpha + 3)

there exists

f
∈

L
p

(
μ
)

f \in {L^p}(\mu )

such that

f
(
x
)
=
0

f(x) = 0

a.e. on

[
−
1
,
0
]

[ - 1,0]

and the appropriate Jacobi polynomial series for

f
f

diverges a.e. on

[
−
1
,
1
]

[ - 1,1]

. This implies failure of localization for spherical harmonic expansions of elements of

L

2
d

/

(
d
+
1
)

(
X
)

{L^{2d/(d + 1)}}(X)

, where

X
X

is a sphere or projective space of dimension

d
>
1

d > 1

.
On Gronwall and Wendroff type inequalities
Authors: Abramowich J.
Published: July 2010

It is shown how Gronwall’s Lemma and the extension to many variables given by W. Walter may be derived using the simple method of recursion. This same method is used to extend this result and to derive a more general Wendroff type inequality. Upper and lower bounds for the Neumann series in the case of two independent variables are given.
Recoverability of some classes of analytic functions from their boundary values
Authors: Zayed Ahmed I.
Published: July 2010

The technique devised by D. J. Patil to recover the functions of the Hardy space

H
p

(
1
⩽
p
⩽
∞
)

{H^p}(1 \leqslant p \leqslant \infty )

from the restrictions of their boundary values to a set of positive measure on the unit circle was modified by S. E. Zarantonello in order to extend the result to

H
p

(
0
>
p
>
1
)

{H^p}(0 > p > 1)

. In this paper, we show that Zarantonello’s technique can be slightly modified to extend the result to a larger class of analytic functions in the unit disc. In particular, if

f
(
z
)

f(z)

is analytic in the unit disc and satisfies
\[

lim

r
→
1

(
1
−
r

)
β

log
⁡
M
(
r
,
f
)
=
0

for

some

β
⩾
1
,

\lim \limits _{r \to 1} {(1 - r)^\beta }\log M(r,f) = 0\quad {\text {for}}\;{\text {some}}\;\beta \geqslant 1,

\]
then

f
(
z
)

f(z)

can be recovered from the restriction of its boundary value to an open arc.
Jeux topologiques et espaces de Namioka
Authors: Saint-Raymond Jean
Published: July 2010

The aim of this paper is to improve certain recent results of J. P. R. Christensen, by using and extending the methods of topological games introduced by him. We study the relationship between Baire spaces and Namioka spaces, proving that these two notions agree in the case of metrizable spaces.
𝑞-probability distributions via an extension of the Bernoulli process
Authors: Feinsilver Philip
Published: July 2010

One-parameter extensions of the Binomial, Negative Binomial, Poisson, Geometric and Gamma distributions are derived via an extension of the standard Bernoulli counting scheme. The method is to examine the elementary "potential theory" for the basic process. Some interesting extensions to continuous time are mentioned also.
Periodic points and topological entropy of maps of the circle
Authors: Bernhardt Chris
Published: July 2010

Let

f
f

be a continuous map from the circle to itself, let

P
(
f
)

P(f)

denote the set of integers

n
n

for which

f
f

has a periodic point of period

n
n

. In this paper it is shown that the two smallest numbers in

P
(
f
)

P(f)

are either coprime or one is twice the other.
Totally analytic spaces under 𝑉=𝐿
Authors: Balogh Zoltán , Junnila Heikki
Published: July 2010

The following results obtain under the axiom of constructibility

(
V
=
L
)

(V = L)

: Assume that every subset of a topological space

X
X

is analytic. Then

X
X

is

σ
\sigma

-left-separatcd. Moreover, if the character of

X
X

is

⩽

ω
1

\leqslant {\omega _1}

, then

X
X

is

σ
\sigma

-discrete. Assume that

X
X

is a perfectly normal space of character

⩽

ω
1

\leqslant {\omega _1}

such that every subset of

X
X

belongs to the

σ
\sigma

-algebra generated by the analytic subsets of

X
X

. Then

X
X

is

σ
\sigma

-discrete.
The 𝐴̂-genus of complex hypersurfaces and complete intersections
Authors: Brooks Robert
Published: July 2010

In this note, we classify the even-dimensional complex hypersurfaces and complete intersections which carry a metric of positive scalar curvature. This is done by computing the

A
^

\hat A

-genus of these manifolds to eliminate all cases not known to carry such a metric.
Adjunction spaces of monotonically normal spaces and spaces dominated by monotonically normal subsets
Authors: Miwa Takuo
Published: July 2010

In this paper, we shall prove the following results: (1) the adjunction space of two monotonically normal spaces is also monotonically normal, (2) a topological space is monotonically normal if and only if it is dominated by a collection of monotonically normal subsets.
Lebesgue sets and insertion of a continuous function
Authors: Lane Ernest P.
Published: July 2010

Necessary and sufficient conditions in terms of Lebesgue sets are presented for the following two insertion properties for real-valued functions defined on a topological space: (1)

g
⩽
f

g \leqslant f

there is a continuous function

h
h

such that

g
⩽
h
⩽
f

g \leqslant h \leqslant f

, and for each

x
x

for which

g
(
x
)
>
f
(
x
)

g(x) > f(x)

then

g
(
x
)
>
h
(
x
)
>
f
(
x
)

g(x) > h(x) > f(x)

. (2)

g
>
f

g > f

there is a continuous function

h
h

such that

g
>
h
>
f

g > h > f

.
Locally 𝑃-closed spaces and rim 𝑃-closed spaces
Authors: Pettey Dix H.
Published: July 2010

It is shown in this paper that for

P
=

T
2

P = {T_2}

or

P
=

T
3

P = {T_3}

every locally

P
P

-closed space is a retract of a rim

P
P

-closed, locally

P
P

-closed space by an open, perfect retraction map. From this it follows that there exist noncompact, rim

H
H

-closed,

H
H

-closed spaces and noncompact, rim

R
R

-closed,

R
R

-closed spaces.
Triviality of simple fiber-preserving actions of tori on Hilbert-cube-fiber bundles
Authors: Liem Vo Thanh
Published: July 2010

Let

σ
\sigma

denote the standard based-free action of a torus

T
T

on the Hilbert cube

Q
Q

. It will be shown that every simple fiber-preserving action of

T
T

on

Q
×
B

Q \times B

, where

B
B

is a finite-dimensional, compact metric absolute retract, is fiber-preserving equivalent to the diagonal action

σ
×

i

d

B

\sigma \times {\text {i}}{{\text {d}}_B}

.
Stable homotopy types of stunted real projective spaces
Authors: Kobayashi Teiichi
Published: July 2010

The purpose of this note is to improve partly necessary conditions for two stunted real projective spaces to be of the same stable homotopy tvpe given in [4].
On supercomplete uniform spaces
Authors: Hohti Aarno
Published: July 2010

We show that a uniform space

μ
X

\mu X

is supercomplete if, and only if, the Ginsburg-Isbell locally fine coreflection of

μ
X
×

F

β
X

\mu X \times \mathcal {F}\beta X

is equinormal.
Pseudocomplete nilpotent groups
Authors: Fournelle Thomas A.
Published: July 2010

Semicomplete nilpotent groups, that is, nilpotent groups with no outer automorphisms, have been of interest for many years. In this paper pseudocomplete nilpotent groups, that is, nilpotent groups in which the automorphism group and the inner automorphism group are isomorphic (not equal), are constructed. When suitable conditions are placed on the pseudocomplete nilpotent group, the quotient of the automorphism group by the inner automorphism group is completely characterized.
A Hopf module characterization of Hopf algebras
Authors: Radford David E.
Published: July 2010

A bialgebra over a field is a Hopf algebra if and only if all (nonzero) right Hopf modules are free, as modules, on a set of invariants.
Maximal separable subfields of bounded codegree
Authors: Deveney James K. , Mordeson John N.
Published: July 2010

Let

L
L

be a function field in

n
>
0

n > 0

variables over a field

K
K

of characteristic

p
≠
0

p \ne 0

. An intermediate field

S
S

is maximal separable if

S
S

is separable over

K
K

and every subfield of

L
L

which properly contains

S
S

is inseparable over

K
K

. This paper examines when

[
L
:
S
]

|

S

[L:S]|S

is maximal separable is bounded. The main result states that this set is bounded if and only if there is an integer

c
c

such that any intermediate field

L
1

{L_1}

over which

L
L

is purely inseparable and

[
L
:

L
1

]
>

p
c

[L:{L_1}] > {p^c}

must be separable over

K
K

. Examples are also given where the above bound is

p

n
+
1

{p^{n + 1}}

for any

n
⩾
1

n \geqslant 1

.
Affine geometry: a lattice characterization
Authors: Bennett M. K.
Published: July 2010

Necessary and sufficient conditions are given for a lattice

L
L

to be the lattice of flats of an affine space of arbitrary (possibly infinite) dimension.
Length and area estimates of the derivatives of bounded holomorphic functions
Authors: Yamashita Shinji
Published: July 2010

MacGregor [1] and Yamashita [5] proved the estimates of the coefficient

a
n

{a_n}

of the Taylor expansion

f
(
z
)
=

a
0

+

a
n

z
n

+
⋯

f(z) = {a_0} + {a_n}{z^n} + \cdots

of

f
f

nonconstant and holomorphic in

|

z

|

>
1

|z| > 1

in terms of the area of the image of

|

z

|

>
r
>
1

|z| > r > 1

by

f
f

and the length of its outer or exact outer boundary. We shall consider some analogous estimates in terms of the non-Euclidean geometry for

f
f

bounded,

|

f

|

>
1

|f| > 1

, in

|

z

|

>
1

|z| > 1

. For example,

2
π

r
n

|

a
n

|

/

(
1
−

|

a
0

|

2

)

2\pi {r^n}|{a_n}|/(1 - |{a_0}{|^2})

is strictly less than the non-Euclidean length of the boundary of the image of

|

z

|

>
r

|z| > r

, the multiplicity not being counted.
Another proof of the existence of the ergodic Hilbert transform
Authors: Petersen Karl
Published: July 2010

We give a direct proof of the existence of the ergodic Hilbert transform

∑

k
=
−
∞

∞
′

f
(

T
k

x
)

/

k

\sum _{k = - \infty }^{\infty ’}f({T^k}x)/k

, where

T
:
X
→
X

T:X \to X

is a measure-preserving transformation and

f
f

is an integrable function.
The almost fixed point property for nonexpansive mappings
Authors: Reich Simeon
Published: July 2010

It is shown that a closed convex subset of a reflexive Banach space has the almost fixed point property for nonexpansive mappings if and only if it is linearly bounded.
On an elliptic boundary value problem not in divergence form
Authors: Các Nguyên Phuong
Published: July 2010

Let

G
G

be a bounded domain in

R
n

(
n
⩾
2
)

{R^n}(n \geqslant 2)

with smooth boundary

∂
G

\partial G

. We consider the boundary value problem

M
u
−
c
u
=
f

Mu - cu = f

on

G
G

,

u
=
0

u = 0

on

∂
G

\partial G

, where

M
M

is an elliptic differential operator not in divergence form. We discuss the characterization of the first eigenvalue

λ
0

{\lambda _0}

of

M
M

and the solvability of the boundary value problem in terms of the relationship between

c
(
⋅
)

c( \cdot )

and

λ
0

{\lambda _0}

.
Approximate identities and 𝐻¹(𝑅)
Authors: Uchiyama Akihito , Wilson J. Michael
Published: July 2010

Let
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi left-parenthesis x right-parenthesis element-of upper L Superscript 1 Baseline left-parenthesis bold upper R right-parenthesis intersection upper L Superscript normal infinity Baseline left-parenthesis bold upper R right-parenthesis">

φ
(
x
)
∈

L
1

(

R

)
∩

L
∞

(

R

)

\varphi (x) \in {L^1}({\mathbf {R}}) \cap {L^\infty }({\mathbf {R}})

be a real-valued function with

∫

R

φ
d
x
≠
0

\int \limits _{\mathbf {R}} {\varphi dx \ne 0}

. For

y
>
0

y > 0

, let

φ
y

(
x
)
=

y

−
1

φ
(
x

/

y
)

{\varphi _y}(x) = {y^{ - 1}}\varphi (x/y)

. For

f
(
x
)
∈

L
1

(

R

)

f(x) \in {L^1}({\mathbf {R}})

define
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f Subscript phi Superscript asterisk Baseline left-parenthesis x right-parenthesis equals sup Underscript y greater-than 0 comma t element-of bold upper R colon StartAbsoluteValue x minus t EndAbsoluteValue greater-than y Endscripts StartAbsoluteValue f asterisk phi Subscript y Baseline left-parenthesis t right-parenthesis EndAbsoluteValue period">

f
φ
∗

(
x
)
=

sup

y
>
0
,
t
∈

R

:

|

x
−
t

|

>
y

|

f
∗

φ
y

(
t
)

|

.

f_\varphi ^*(x) = \sup \limits _{y > 0,t \in {\mathbf {R}}:|x - t| > y} |f * {\varphi _y}(t)|.

\]
We investigate the space
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H Subscript phi Superscript 1 Baseline equals StartSet f element-of upper L Superscript 1 Baseline left-parenthesis bold upper R right-parenthesis colon f Subscript phi Superscript asterisk Baseline element-of upper L Superscript 1 Baseline left-parenthesis bold upper R right-parenthesis EndSet">

H
φ
1

=
{
f
∈

L
1

(

R

)
:

f
φ
∗

∈

L
1

(

R

)
}

H_\varphi ^1 = \{ f \in {L^1}({\mathbf {R}}):f_\varphi ^* \in {L^1}({\mathbf {R}})\}

.
Unbounded perturbations of forced harmonic oscillations at resonance
Authors: Ding Tung Ren
Published: July 2010

In 1969, A. C. Lazer and D. E. Leach proved an existence theorem for periodic solutions of Duffing’s equations with bounded perturbations at resonance. In the present note, with the use of a topological technique, the author extended some results of Lazer and Leach to an

n
n

-dimensional Duffing system with unbounded perturbations at resonance.
On Hardy’s inequality in weighted rearrangement invariant spaces and applications. I
Authors: Maligranda Lech
Published: July 2010

We give inequalities relating the norm of a function and the norm of its average operators

P
ψ

,

Q
ψ

{P_\psi },{Q_\psi }

and

S
ψ

,

T
ψ

{S_\psi },{T_\psi }

in weighted rearrangement invariant spaces

E

κ
,
δ

{E_{\kappa ,\delta }}

and

E
(
μ
)
,
d
μ
(
t
)
=

τ
′

(
t
)
d
t

E(\mu ),d\mu (t) = \tau ’(t)dt

. These average operators include, for example, the integral mean, the

P
p

,

Q
p

{P_p},{Q_p}

operators of Boyd [4] and Butzer and Fehér [6], the average operators

P
φ

,

Q
φ

{P_\varphi },{Q_\varphi }

and

S
E

,

T
E

{S_E},{T_E}

from [14,15,16]. In the particular case, for some

ψ
,
κ
,
δ
,
τ

\psi ,\kappa ,\delta ,\tau

and

E
E

these inequalities were obtained by many authors and applied to a study of interpolation operators and imbedding theorems for Sobolev weight spaces.
Strongly exposed points in Bochner 𝐿^{𝑝}-spaces
Authors: Greim Peter
Published: July 2010

We give necessary and sufficient conditions for vector-valued

L
p

{L^p}

functions to be strongly exposed in terms of their values

(
1
>
p
>
∞
)

(1 > p > \infty )

.
An analogue of the Schwarz lemma for bounded symmetric domains
Authors: Travaglini Giancarlo
Published: July 2010

We determine the best possible estimate for the determinant of the Jacobian of a holomorphic mapping of a bounded symmetric domain into a ball.
Ideals of regular operators on 𝑙²
Authors: Arendt W. , Sourour A. R.
Published: July 2010

Let

L

r

{\mathcal {L}^r}

be the Banach algebra (and Banach lattice) of all regular operators on

l

2

{l^{^2}}

, i.e. the algebra of all operators

A
A

on

l
2

{l^2}

which are given by a matrix

(

a

m
n

)

({a_{mn}})

such that

(

|

a

m
n

|

)

(\left | {{a_{mn}}} \right |)

defines a bounded operator

|
A
|

\left | A \right |

. We show that there exists exactly one nontrivial closed subspace of

L

r

{\mathcal {L}^r}

which is both a lattice-ideal and an algebra-ideal of

L

r

{\mathcal {L}^r}

, namely the space

K

r

=
{
A
∈

L

r

:

|
A
|

 is compact

}

{\mathcal {K}^r} = \{ A \in {\mathcal {L}^r}:\left | A \right |{\text { is compact}}\}

. We also show that every nontrivial ideal in

L

r

{\mathcal {L}^r}

is included in

K

r

{\mathcal {K}^r}

.
A note on two weight function conditions for a Fourier transform norm inequality
Authors: Muckenhoupt Benjamin
Published: July 2010

Recent papers have given two different conditions on pairs of nonnegative weight functions that insure that a Fourier transform norm inequality holds in

R

n

{{\mathbf {R}}^n}

. With additional assumptions these conditions were also shown to be implied by the norm inequality. A direct proof is given here that these conditions are equivalent; this can be used to simplify some of the proofs in those papers.