bluuebunny/crossref_metadata_2025 huggingface dataset:
Extension of holomorphic mappings from 𝐸 to 𝐸”
Authors: Moraes Luiza A.
Published: June 2010

Assuming that

E
E

is a distinguished locally convex space and

F
F

is a complete locally convex space, we prove that there exists an open subset

V
V

of

E
E

that contains

E
E

and such that every holomorphic mapping

f
:
E
→
F

f:E \to F

whose restriction

f

|

B

f|B

is

σ
(
E
,

E
′

)

\sigma (E,E’)

-uniformly continuous for every bounded subset

B
B

of

E
E

has a unique holomorphic extension

f
~

:
V
→
F

\tilde f:V \to F

such that

f
~

|

B

\tilde f|B

is

σ
(
E
,

E
′

)

\sigma (E,E’)

-uniformly continuous for every bounded subset

B
B

of

V
V

. We show that in many cases we can take

V
=
E

V = E

. This is the case when

E
E

is a locally convex space where every

G
G

-holomorphic mapping that is bounded in a neighbourhood of the origin is locally bounded.
A short note on the Schur-Jacobson theorem
Authors: Cowsik R. C.
Published: June 2010

An upper bound for the length of a commutative Artinian ring in terms of the length of a faithful module is given. This generalizes a theorem of Schur and Jacobson.
The second normal bordism group of a space pair
Authors: Li Gui Song
Published: June 2010

We determine the second normal bordism groups of space pairs in terms of their homology groups except for certain group extension problems.
Integer-valued polynomials, Prüfer domains, and localization
Authors: Chabert Jean-Luc
Published: June 2010

Let

A
A

be an integral domain with quotient field

K
K

and let

Int
⁡
(
A
)

\operatorname {Int} (A)

be the ring of integer-valued polynomials on

A
:
{
P
∈
K
[
X
]

|

P
(
A
)
⊂
A
}

A:\{ P \in K[X]|P(A) \subset A\}

. We study the rings

A
A

such that

Int
⁡
(
A
)

\operatorname {Int} (A)

is a Prüfer domain; we know that

A
A

must be an almost Dedekind domain with finite residue fields. First we state necessary conditions, which allow us to prove a negative answer to a question of Gilmer. On the other hand, it is enough that

Int
⁡
(
A
)

\operatorname {Int} (A)

behaves well under localization; i.e., for each maximal ideal

m

\mathfrak {m}

of

A
A

,

Int
⁡

(
A

)

m

\operatorname {Int} {(A)_\mathfrak {m}}

is the ring

Int
⁡
(

A

m

)

\operatorname {Int} ({A_\mathfrak {m}})

of integer-valued polynomials on

A

m

{A_\mathfrak {m}}

. Thus we characterize this latter condition: it is equivalent to an "immediate subextension property" of the domain

A
A

. Finally, by considering domains

A
A

with the immediate subextension property that are obtained as the integral closure of a Dedekind domain in an algebraic extension of its quotient field, we construct several examples such that

Int
⁡
(
A
)

\operatorname {Int} (A)

is Prüfer.
Some deformations of the Hopf foliation are also Kähler
Authors: Scofield Paul D.
Published: June 2010

Fix

α
=
(

α
0

,
…
,

α
n

)
∈

R

˚

n
+
1

\alpha = ({\alpha _0}, \ldots ,{\alpha _n}) \in \mathring {\mathbf {R}}^{n + 1}

. The trajectories of the flow on

S

2
n
+
1

⊂

C

n
+
1

{{\mathbf {S}}^{2n + 1}} \subset {{\mathbf {C}}^{n + 1}}

given by
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi Subscript t Baseline colon left-parenthesis z 0 comma ellipsis comma z Subscript n Baseline right-parenthesis right-arrow from bar left-parenthesis z 0 e Superscript i alpha 0 t Baseline comma ellipsis comma z Subscript n Baseline e Superscript i alpha Super Subscript n Superscript t Baseline right-parenthesis">

ϕ
t

:
(

z
0

,
…
,

z
n

)
↦
(

z
0

e

i

α
0

t

,
…
,

z
n

e

i

α
n

t

)

{\phi _t}:({z_0}, \ldots ,{z_n}) \mapsto ({z_0}{e^{i{\alpha _0}t}}, \ldots ,{z_n}{e^{i{\alpha _n}t}})

\]
constitute the leaves of a

2
n

2n

-codimensional (nonsingular) foliation of

S

2
n
+
1

{{\mathbf {S}}^{2n + 1}}

. We use (locally defined) branches of the logarithm to give this foliation a (global) transverse Kähler structure.
Local isogeny theorem for Drinfel′d modules with nonintegral invariants
Authors: Bae Sunghan , Kang Pyung-Lyun
Published: June 2010

An isogeny theorem for the Drinfeld modules of rank

2
2

over a local field analogous to that of elliptic curves is proved.
Unitary 𝑍^{𝑑}-actions with continuous spectrum
Authors: Bergelson Vitaly , Kornfeld Isaac , Mityagin Boris
Published: June 2010

For any unitary

Z

d

{\mathbb {Z}^d}

-action on a Hilbert space with continuous spectrum weakly wandering vectors are dense. This wandering can be forced to occur along

I
P

IP

-sets. This is a generalization and strengthening of a result due to Krengel. Our method is based on the contractive mapping fixed-point theorem.
The fat locus of Hilbert schemes of points
Authors: Coppens Marc
Published: June 2010

Let

X
X

be a smooth projective variety over an algebraically closed field

k
k

. Let

Hilb
d

(
X
)

{\operatorname {Hilb} ^d}(X)

be its Hilbert scheme of

0
0

-dimensional subschemes of

X
X

of degree

d
d

. Let

[

Hilb
d

(
X
)
]
(
k
)

[{\operatorname {Hilb} ^d}(X)](k)

be the set of

k
k

-rational points. We prove that the subset of points of

[

Hilb
d

(
X
)
]
(
k
)

[{\operatorname {Hilb} ^d}(X)](k)

corresponding to fat points on

X
X

is a locally closed subset with respect to the Zariski topology.
Symmetric functions, Lebesgue measurability, and the Baire property
Authors: Darji Udayan B.
Published: June 2010

In this paper, we generalize some results of Stein and Zygmund and of Evans and Larson concerning symmetric functions. In particular, we show that if

f
f

is Lebesgue measurable or has the Baire property in the wide sense, then the set of symmetric points of

f
f

is Lebesgue measurable or has the Baire property in the wide sense, respectively. We also give some examples that show that these results cannot be improved in a certain sense. Finally, we show that there are plenty of examples of functions that are both Lebesgue measurable and have the Baire property in the wide sense, yet the set of points where each of the functions is symmetric and discontinuous has the same cardinality as that of the continuum.
A characterization of harmonic Arakelyan sets
Authors: Goldstein M. , Ow W. H.
Published: June 2010

Given a closed subset

F
F

of either

R
N

,

N
⩾
3

{R^N},\;N \geqslant 3

, or a Riemann surface, necessary and sufficient conditions are given so that every function continuous on

F
F

and harmonic in the interior can be uniformly approximated on

F
F

by globally defined harmonic functions.
“Complete-simple” distributive lattices
Authors: Grätzer G. , Schmidt E. T.
Published: June 2010

It is well known that the only simple distributive lattice is the two-element chain. We can generalize the concept of a simple lattice to complete lattices as follows: a complete lattice is complete-simple if it has only the two trivial complete congruences. In this paper we show the existence of infinite complete-simple distributive lattices.
Some studies on Π-coherent rings
Authors: Wang Ming Yi
Published: June 2010

An internal description and a classification of

Π
\Pi

-coherent rings are obtained by using

W
W

-ideals and FGT-projective dimension, respectively, as defined in this paper.
A note on Hilbert’s Theorem 90
Authors: Jia Bao-Ping , Santoni Larry
Published: June 2010

In this paper we extend "up to powers" Hilbert’s Theorem 90 to arbitrary finite Galois extensions. In the case of algebraic number fields with class number equal to

1
1

, we completely determine the kernel and image of the norm map.
Entropy of random walks on groups and the Macaev norm
Authors: Voiculescu D.
Published: June 2010

We show that a discrete group on which there is a finitary random walk with positive entropy satisfies a certain condition involving the Macaev norm. This links the entropy of random walks on groups to the author’s work on quasicentral approximate units relative to normed ideals in perturbation theory. On the other hand, the condition we are considering is also an analogue for the Macaev norm of Yamasaki’s hyperbolicity condition.
The Poincaré inequality and entire functions
Authors: Pearson J. Michael
Published: June 2010

Inequalities for spaces of entire functions on

C

n

{{\mathbf {C}}^n}

, which generalize the Poincaré inequality for Gaussian measure, are obtained. The relationship between these inequalities and hypercontractive estimates for diffusion semigroups are discussed.
On closed subspaces of 𝜔*
Authors: Dow A. , Frankiewicz R. , Zbierski P.
Published: June 2010

It is consistent with the negation of the Continuum Hypothesis that closed subsets of the space

ω

∗

{\omega ^{\ast }}

are exactly compact

0
0

-dimensional F-spaces of weight

⩽
c

\leqslant c

.
An equivariant construction
Authors: Pergher Pedro L. Q.
Published: June 2010

In this paper we show how to construct the equivariant bordism class of a closed manifold with differentiable

(

Z
2

)
k

{({Z_2})^k}

-action from its fixed data.
Derivations with invertible values on a multilinear polynomial
Authors: Lee Tsiu Kwen
Published: June 2010

Let

R
R

be a semiprime

K
K

-algebra with unity,

d
d

a nonzero derivation of

R
R

, and

f
(

x
1

,
…
,

x
t

)

f({x_1}, \ldots ,{x_t})

a monic multilinear polynomial over

K
K

such that

d
(
f
(

a
1

,
…
,

a
t

)
)
≠
0

d(f({a_1}, \ldots ,{a_t})) \ne 0

for some

a
1

,
…
,

a
t

∈
R

{a_1}, \ldots ,{a_t} \in R

. It is shown that if for every

r
1

,
…
,

r
t

{r_1}, \ldots ,{r_t}

in

R
R

either

d
(
f
(

r
1

,
…
,

r
t

)
)
=
0

d(f({r_1}, \ldots ,{r_t})) = 0

or

d
(
f
(

r
1

,
…
,

r
t

)
)

d(f({r_1}, \ldots ,{r_t}))

is invertible in

R
R

, then

R
R

is either a division ring

D
D

or

M
2

(
D
)

{M_2}(D)

, the ring of

2
×
2

2 \times 2

matrices over

D
D

, unless

f
(

x
1

,
…
,

x
t

)

f({x_1}, \ldots ,{x_t})

is a central polynomial for

R
R

. Moreover, if

R
=

M
2

(
D
)

R = {M_2}(D)

, where

2
R
≠
0

2R \ne 0

and

f
(

x
1

,
…
,

x
t

)

f({x_1}, \ldots ,{x_t})

is not a central polynomial for

D
D

, then

d
d

is an inner derivation of

R
R

.
Is a semidirect product of groups necessarily a group?
Authors: Birkenmeier Gary F. , Davis C. Brad , Reeves Kevin J. , Xiao Sihai
Published: June 2010

The aim of this paper is to provide nonassociative commutative loops which are semidirect products of subgroups.
On algebras with Gel′fand-Kirillov dimension one
Authors: Kobayashi Shigeru , Kobayashi Yuji
Published: June 2010

We study the growth of finitely generated algebras by means of the Ufnarovskij graph. We improve a result of Bergman about the jumps of the growth function and give a characterization of algebras with

GKdim
=
1

\operatorname {GKdim} = 1

in terms of the Ufnarovskij graph. For monomial algebras the behavior of the growth functions is studied in more detail.
Operators with nilpotent 𝑝-curvature
Authors: Schmitt Hans
Published: June 2010

This article studies the variety of nilpotent

p
p

-curvature of linear differential operators on the sphere with

m
+
1

m + 1

singularities. We shall show that for a given set of exponents

∈

F

p

\in {{\mathbf {F}}_p}

satisfying Fuchs’s relation the associated variety of nilpotent

p
p

-curvature is a nonempty complete intersection of dimension, essentially,

m
−
2

m - 2

. The subject has previously been studied by Katz, Honda, and Dwork.
On homogeneous nilpotent groups and rings
Authors: Cherlin Gregory , Saracino Dan , Wood Carol
Published: June 2010

We give a new framework for the construction of homogeneous nilpotent groups and rings which goes a long way toward unifying the two cases, and enables us to extend previous constructions, producing a variety of new examples. In particular we find ingredients for the manufacture of

2

ℵ

0

2{}^\aleph 0

homogeneous nilpotent groups "in nature".
Complete minimal surfaces in 𝑅³ of genus one and four planar embedded ends
Authors: Costa Celso J.
Published: June 2010

By using elliptic functions and Weierstrass representation we construct a one-parameter family of complete minimal surfaces in

R

3

{{\mathbf {R}}^3}

with genus one and four planar embedded ends. These surfaces are critical points of the Willmore functional.
A finite capacity analogue of the Koebe one-quarter theorem
Authors: Cunningham Robin
Published: June 2010

A variational method is used to determine the largest disk about the origin covered by the image of every normalized univalent function that maps the unit disk onto a region of prescribed logarithmic capacity (transfinite diameter).
Fixed points of finite groups of free group automorphisms
Authors: White Tad
Published: June 2010

We construct an equivariant collection of contractions of the compactified Culler-Vogtmann outer space

X
¯

n

{\overline X _n}

. As a consequence, we prove that any finite subgroup of the outer automorphism group of a free group fixes a contractible subset of

X
¯

n

{\bar X_n}

.
The 𝛼-boundification of 𝛼
Authors: García-Ferreira Salvador , Tamariz-Mascarúa Angel
Published: June 2010

A space

X
X

is

>
α

> \alpha

-bounded if for all

A
⊆
X

A \subseteq X

with

|

A

|

>
α

|A| > \alpha

,

cl
X

A

{\operatorname {cl} _X}\;A

is compact. Let

B
(
α
)

B(\alpha )

be the smallest

>
α

> \alpha

-bounded subspace of

β
(
α
)

\beta (\alpha )

containing

α
\alpha

. It is shown that the following properties are equivalent: (a)

α
\alpha

is a singular cardinal; (b)

B
(
α
)

B(\alpha )

is not locally compact; (c)

B
(
α
)

B(\alpha )

is

α
\alpha

-pseudocompact; (d)

B
(
α
)

B(\alpha )

is initially

α
\alpha

-compact. Define

B
0

(
α
)
=
α

{B^0}(\alpha ) = \alpha

and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper B Superscript n Baseline left-parenthesis alpha right-parenthesis equals left-brace c l Subscript beta left-parenthesis alpha right-parenthesis Baseline upper A colon upper A subset-of-or-equal-to upper B Superscript n minus 1 Baseline left-parenthesis alpha right-parenthesis comma StartAbsoluteValue upper A EndAbsoluteValue greater-than alpha right-brace">

B
n

(
α
)
=
{

cl

β
(
α
)

A
:
A
⊆

B

n
−
1

(
α
)
,

|

A

|

>
α
}

{B^n}(\alpha ) = \{ {\operatorname {cl} _{\beta (\alpha )}}A:A \subseteq {B^{n - 1}}(\alpha ),|A| > \alpha \}

for

0
>
n
>
ω

0 > n > \omega

. We also prove that

B
2

(
α
)
≠

B
3

(
α
)

{B^2}(\alpha ) \ne {B^3}(\alpha )

when

ω
=
cf
⁡
(
α
)
>
α

\omega = \operatorname {cf} (\alpha ) > \alpha

. Finally, we calculate the cardinality of

B
(
α
)

B(\alpha )

and prove that, for every singular cardinal
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="alpha comma StartAbsoluteValue upper B left-parenthesis alpha right-parenthesis EndAbsoluteValue equals StartAbsoluteValue upper B left-parenthesis alpha right-parenthesis EndAbsoluteValue Superscript alpha Baseline equals StartAbsoluteValue upper N left-parenthesis alpha right-parenthesis EndAbsoluteValue Superscript c f left-parenthesis alpha right-parenthesis">

α
,

|

B
(
α
)

|

=

|

B
(
α
)

|

α

=

|

N
(
α
)

|

cf
⁡
(
α
)

\alpha ,\;|B(\alpha )| = |B(\alpha ){|^\alpha } = |N(\alpha ){|^{\operatorname {cf} (\alpha )}}

where

N
(
α
)
=
{
p
∈
β
(
α
)
:

there is

A
∈
p

with

|

A

|

>
α
}

N(\alpha ) = \{ p \in \beta (\alpha ):\;{\text {there is}}\;A \in p\;{\text {with}}\;|A| > \alpha \}

.
On 𝜙-extensions of developable spaces
Authors: Mizokami T.
Published: June 2010

We prove that the

φ
\varphi

-extension of Moore spaces is a developable space.
The characteristic exponent of second-order linear differential equations with two irregular singular points
Authors: Bühring Wolfgang
Published: June 2010

A second-order linear differential equation with two irregular singular points, of which one has unit rank, is investigated. A simple limit formula is obtained for the characteristic exponent of the multiplicative solutions as well as a more detailed asymptotic formula which is suitable for getting accurate numerical values. Only the recursively known coefficients of the formal power series solutions at the irregular singular point of unit rank enter our formulas.
On the exponents of ideal class groups of cyclotomic fields
Authors: Horie Kuniaki
Published: June 2010

It will be proved that the ideal class group of the cyclotomic field of 65th roots of unity is of type

(
4
,
4
,
2
,
2
)

(4,4,2,2)

, and remarks on the exponents of ideal class groups of cyclotomic fields will be made.
Projectively flat surfaces in 𝐴³
Authors: Podestà Fabio
Published: June 2010

We consider a nondegenerate immersion

f
:

M
2

→

A

3

f:{M^2} \to {\mathbb {A}^3}

of an orientable

2
2

-dimensional manifold

M
2

{M^2}

together with the Blaschke connection

∇
\nabla

induced on

M
2

{M^2}

; this work is aimed at studying locally convex surfaces whose Blaschke connection is projectively flat, reducing the problem of their classification to a system of PDE’s. In particular we can prove the existence of locally convex projectively flat surfaces which are not locally symmetric.
Homotopy, diffeomorphism, and deformation classifications of certain surfaces of class 𝑉𝐼𝐼
Authors: Qin Zhenbo
Published: June 2010

We study the homotopy, diffeomorphism, and deformation classifications of all known surfaces of class VII which are not Hopf surfaces.
On deterministic and random fixed points
Authors: Tan Kok-Keong , Yuan Xian-Zhi
Published: June 2010

Based on an extension of Aumann’s measurable selection theorem due to Leese, it is shown that each fixed point theorem for

F
(
ω
,
⋅
)

F(\omega , \cdot )

produces a random fixed point theorem for

F
F

provided the

σ
\sigma

-algebra

Σ
\Sigma

for

Ω
\Omega

is a Suslin family and

F
F

has a measurable graph (in particular, when

F
F

is random continuous with closed values and

X
X

is a separable metric space). As applications and illustrations, some random fixed points in the literature are obtained or extended.
Schatten class Hankel operators on the Bergman spaces of strongly pseudoconvex domains
Authors: Li Huiping
Published: June 2010

In this paper, we characterize holomorphic functions

f
f

such that the Hankel operators

H

f
¯

{H_{\bar f}}

are in the Schatten classes on bounded strongly pseudoconvex domains. It is proved that for

p
>
2
n
,

H

f
¯

p > 2n,\;{H_{\bar f}}

is in the Schatten class

S
p

{S_p}

if and only if

f
f

is in the Besov space

B
p

{B_p}

; for

p
⩽
2
n
,

H

f
¯

p \leqslant 2n,\;{H_{\bar f}}

is in the Schatten class

S
p

{S_p}

if and only if

f
=

constant

f = {\text {constant}}

.
Factorizations of generic mappings between surfaces
Authors: Luminati Domenico
Published: June 2010

Given a generic mapping

F
:

S

→

N

F:{\mathbf {S}} \to {\mathbf {N}}

of two smooth (i.e.,

C
∞

{C^\infty }

) real surfaces,

S

{\mathbf {S}}

compact, and a line bundle

π
:

E

→

N

\pi :{\mathbf {E}} \to {\mathbf {N}}

, we look for necessary and sufficient conditions to find an immersion

F
~

:

S

→

E

\tilde F:{\mathbf {S}} \to {\mathbf {E}}

such that

F
=
π
∘

F
~

F = \pi \circ \tilde F

.
Averages along uniformly distributed directions on a curve
Authors: Barrionuevo Jose
Published: June 2010

We obtain a sharp

L
2

{L^2}

estimate for the maximal operator associated with uniformly distributed directions on a curve of finite type in

R

n

{{\mathbf {R}}^n}

.
Generalized Hadwiger numbers for symmetric ovals
Authors: Boju Valentin , Funar Louis
Published: June 2010

Some estimations for the "juxtaposition function"

h
F

{h_F}

and an asymptotic formula for the function

h
F

/

h
G

{h_F}/{h_G}

, where

F
,

G

F,\;G

are central symmetric convex bodies, are given. Hadwiger and Grünbaum gave for

h
F

(
1
)

{h_F}(1)

the bounds

n
2

+
n
⩽

h
F

(
1
)
⩽

3
n

−
1

{n^2} + n \leqslant {h_F}(1) \leqslant {3^n} - 1

. Grünbaum conjectured (and proved for

n
=
2

n = 2

in Pacific J. Math. 11 (1961), 215-219) that for every even

r
r

between these bounds there exists in

E
n

{E^n}

an oval

F
F

such that

h
F

(
1
)
=
r

{h_F}(1) = r

. Lower bounds for

h
F

{h_F}

could be derived in the same way as in Theorems 1 and 2 from a good estimate of packing numbers on a Minkowski sphere, that is, from solutions to a Tammes-type problem in a Banch space.
The Hausdorff dimension of self-similar sets under a pinching condition
Authors: Gu Xiao Ping
Published: June 2010

We study self-similar sets in the case where the construction diffeomorphisms are not necessarily conformal. Using topological pressure we give an upper estimate of the Hausdorff dimension, when the construction diffeomorphisms are

C

1
+
κ

{C^{1 + \kappa }}

and satisfy a

κ
\kappa

-pinching condition for some

κ
⩽
1

\kappa \leqslant 1

. Moreover, if the construction diffeomorphisms also satisfy the disjoint open set condition we then give a lower bound for the Hausdorff dimension.
Complete minimal surfaces and the puncture number problem
Authors: Yang Kichoon
Published: June 2010

Given a nonnegative integer

g
g

, let

P

(
g
)

\mathcal {P}(g)

denote the set of integers

N
N

such that an arbitrary compact Riemann surface with genus

g
g

can be completely conformally and minimally immersed in

R

3

{\mathbb {R}^3}

(with finite total curvature) with exactly

N
N

punctures. We prove that the infimum of

P

(
g
)

\mathcal {P}(g)

is at most

4
g

4g

and that the set

P

(
g
)

\mathcal {P}(g)

may not miss any

3
g

3g

consecutive integers larger than the infimum of

P

(
g
)

\mathcal {P}(g)

.
An example of 𝑙_{𝑝}-equivalent spaces which are not 𝑙*_{𝑝}-equivalent
Authors: Baars Jan , de Groot Joost , van Mill Jan , Pelant Jan
Published: June 2010

We give an example of two locally compact countable metric spaces

X
X

and

Y
Y

which are

l
p

{l_p}

-equivalent but not

l
p

∗

l_p^{\ast }

-equivalent, i.e.,

C
p

(
X
)

{C_p}(X)

and

C
p

(
Y
)

{C_p}(Y)

are linearly homeomorphic but

C
p

∗

(
X
)

C_p^{\ast }(X)

and

C
p

∗

(
Y
)

C_p^{\ast }(Y)

are not linearly homeomorphic.
A note on compact ideal perturbations in semifinite von Neumann algebras
Authors: Pop Florin
Published: June 2010

Let

M
M

be a semifinite von Neumann algebra and denote by

J
(
M
)

J(M)

the closed two-sided ideal generated by the finite projections in

M
M

. A subspace

S
⊂
M

S \subset M

is called local if it is equal to the ultraweak closure of

S
∩
J
(
M
)

S \cap J(M)

. If

M
=
B
(
H
)

M = B(H)

and

J
(
M
)
=
K
(
H
)

J(M) = K(H)

, Fall, Arveson, and Muhly proved that

S
+
J
(
M
)

S + J(M)

is closed for every local subspace

S
S

. In this note we prove that if

M
M

is a type

I

I

∞

{\text {I}}{{\text {I}}_\infty }

, factor, then there exist local subspaces in

M
M

which fail to have closed compact ideal perturbations; thus answering in the negative a question of Kaftal, Larson, and Weiss.
Nilpotent groups acting on abelian groups
Authors: Cassidy Charles , Laberge Guy
Published: June 2010

In this paper, we study certain properties of the group ring of a nilpotent group which are related to commutativity and conjugation. We establish some relations involving conjugates of the elements of the group ring; these relations are then used to get a better understanding of torsion in abelian-by-nilpotent groups; we shall see notably that given any action of a nilpotent group

N
N

on an abelian group

A
A

, then the set of torsion elements of

A
A

with respect to the action of

N
N

is actually a subgroup of

A
A

.
A construction of a subspace in Euclidean space with designated values of dimension and metric dimension
Authors: Goto Tatsuo
Published: June 2010

For every integer

m
,
k

m,k

, and

n
n

such that

0
⩽
m
⩽
n
−
1

0 \leqslant m \leqslant n - 1

and

m
⩽
k
⩽
min
{
2
m
,
n
−
1
}

m \leqslant k \leqslant \min \{ 2m,n - 1\}

, we construct a subspace

S

m
,
k

n

S_{m,k}^n

in Euclidean

n
n

space

R

n

{{\mathbf {R}}^n}

satisfying the conditions that

μ
dim
⁡

S

m
,
k

n

=
m

\mu \dim S_{m,k}^n = m

and

dim
⁡

S

m
,
k

n

=
k

\dim S_{m,k}^n = k

, where

μ
dim

\mu \dim

denotes the metric dimension.
On isomorphisms between certain non-CSL algebras
Authors: Papadakis Manos
Published: June 2010

In this paper we characterize the existence of algebraic isomorphisms between certain reflexive algebras with two atom lattices. We also show by an example that these isomorphisms need not preserve certain geometric properties of their lattices.
On the Fredholm theory of multipliers
Authors: Aiena Pietro
Published: June 2010

Multipliers that are Fredholm operators on certain commutative semisimple Banach algebras may be characterized by means of a quotient algebra of multipliers. Some spectral properties of multipliers of these algebras are considered
On the dimensional properties of Stone-Čech remainder of 𝑃₀-spaces
Authors: Attia H.
Published: June 2010

A space X is called a

P
0

{P_0}

-space if there exists a perfect mapping f from X onto a metric space Y such that

dim
⁡
f
=
sup
{

f

−
1

(
y
)
:
y
∈
Y
}
=
0

\dim f = \sup \{ {f^{ - 1}}(y):y \in Y\} = 0

. We prove that the

P
0

{P_0}

-space X is almost weakly infinite dimensional iff the remainder

β
X
∖
X

\beta X\backslash X

of the Stone-Čech compactification

β
X

\beta X

of X is A-weakly infinite dimensional. Furthermore we prove that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Delta left-parenthesis beta upper X minus upper X equals ind left-parenthesis beta upper X minus upper X right-parenthesis equals Ind left-parenthesis beta upper X minus upper X right-parenthesis equals dimension left-parenthesis beta upper X minus upper X right-parenthesis">

Δ
(
β
X
∖
X
=

ind

(
β
X
∖
X
)
=

Ind

(
β
X
∖
X
)
=
dim
⁡
(
β
X
∖
X
)

\Delta (\beta X\backslash X = {\text {ind}}(\beta X\backslash X) = {\text {Ind}}(\beta X\backslash X) = \dim (\beta X\backslash X)

for the

P
0

{P_0}

-space X.
Unit groups of integral group rings
Authors: Bist Vikas
Published: June 2010

Let

U
(

Z

G
)

U(\mathbb {Z}G)

be the unit group of the integral group ring

Z

G

\mathbb {Z}G

. A group

G
G

satisfies

(

∗

)

({\ast })

if either the set

T
(
G
)

T(G)

of torsion elements of

G
G

is a central subgroup of

G
G

or, otherwise, if

x
∈
G

x \in G

does not centralize

T
(
G
)

T(G)

, then for every

t
∈
T
(
G
)
,

x

−
1

t
x
=

t

−
1

t \in T(G),\,{x^{ - 1}}tx = {t^{ - 1}}

. This property appears quite frequently while studying

U
(

Z

G
)

U(\mathbb {Z}G)

. In this paper we investigate why one encounters this property and we have also given a "unified proof" for some known results regarding this property. Further, some additional results have been obtained.
Integral matrices of fixed rank
Authors: Katznelson Yonatan R.
Published: June 2010

Asymptotic formulæare derived for the number of

n
×
m

n \times m

matrices of fixed rank

k
k

with rational integral coefficients that are contained in a Euclidean ball of radius

T
T

in

R

n
×
m

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

. It is assumed that

n
⩾
m
>
k
⩾
1

n \geqslant m > k \geqslant 1

are fixed, and the asymptotics are valid as

T
T

tends to infinity. The methods used are elementary.
On nonnegative cosine polynomials with nonnegative integral coefficients
Authors: Kolountzakis Mihail N.
Published: June 2010

We show that there exist

p
0

>
0

{p_0} > 0

and

p
1

,
…
,

p
N

{p_1}, \ldots ,{p_N}

nonnegative integers, such that
\[

0
⩽
p
(
x
)
=

p
0

+

p
1

cos
⁡
x
+
⋯
+

p
N

cos
⁡
N
x

0 \leqslant p(x) = {p_0} + {p_1}\cos x + \cdots + {p_N}\cos Nx

\]
and

p
0

≪

s

1

/

3

{p_0} \ll {s^{1/3}}

for

s
=

∑

j
=
0

N

p
j

s = \sum \nolimits _{j = 0}^N {{p_j}}

, improving on a result of Odlyzko who showed the existence of such a polynomial

p
p

that satisfies

p
0

≪

(
s
log
⁡
s

)

1

/

3

{p_0} \ll {(s\log s)^{1/3}}

. Our result implies an improvement of the best known estimate for a problem of Erdős and Szekeres. As our method is nonconstructive, we also give a method for constructing an infinite family of such polynomials, given one good "seed" polynomial.
A note on Borel equivalence relations
Authors: Louveau Alain , Veličković Boban
Published: June 2010

We prove that the class of Borel equivalence relations, under the order of Borel reducibility, is a very complicated structure, by embedding into it the partial order of inclusion modulo finite sets on

P

(
ω
)

\mathcal {P}(\omega )

.
(𝑀,𝜀,𝛿)-minimal curve regularity
Authors: Morgan Frank
Published: June 2010

(

M

,
c

r
α

,
δ
)

({\mathbf {M}},c{r^\alpha },\delta )

-minimal sets are embedded

C

1
,
α

/

2

{C^{1,\alpha /2}}

curves meeting in threes at

120
∘

120^\circ

angles.
Tight analytic immersions of highly connected manifolds
Authors: Niebergall Ross
Published: June 2010

An immersion of a manifold which minimizes total absolute curvature is called tight. In this paper we determine which

(
k
−
1
)

(k - 1)

-connected (but not

k
k

-connected) manifolds of dimension

2
k

2k

, with trivial

k
k

th Stiefel-Whitney class, admit codimension

2
2

tight analytic immersions.
Translation invariants for periodic Denjoy-Carleman classes
Authors: Gallagher P. X.
Published: June 2010

The Denjoy-Carleman classes in real

C
∞

(

R

/

Z

)

{C^\infty }(\mathbb {R}/\mathbb {Z})

on which the derivative sequence

f

(
n
)

(
x
)

{f^{(n)}}(x)

at any point is a complete set of invariants are exactly the ones on which the integrals of products of derivatives

f

(

n
1

)

⋯

f

(

n
r

)

{f^{({n_1})}} \cdots {f^{({n_r})}}

are a complete set of invariants up to translation.
Existence of periodic solutions for nonlinear evolution equations in Hilbert spaces
Authors: Hirano Norimichi
Published: June 2010

In this paper, we consider the existence and multiplicity of periodic solutions of the problem

u
′

+
A
u
∋
g
(
t
,
u
)

u’ + Au \ni g(t,u)

where

A
A

is a subdifferential of a convex function defined in a Hilbert space

H
H

and

g
:
R
×
H
→
H

g:R \times H \to H

is a Carathéodory function periodic with respect to the first variable.
On a functional equation connected with Rao’s quadratic entropy
Authors: Chung J. K. , Ebanks B. R. , Ng C. T. , Sahoo P. K.
Published: June 2010

We determine the general solution of the functional equation fxy,
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis StartFraction x plus y Over 2 EndFraction right-parenthesis plus f left-parenthesis StartFraction x minus y Over 2 EndFraction right-parenthesis equals 2 f left-parenthesis StartFraction x Over 2 EndFraction right-parenthesis plus 2 f left-parenthesis StartFraction y Over 2 EndFraction right-parenthesis plus lamda f left-parenthesis x right-parenthesis f left-parenthesis y right-parenthesis comma">

f

(

x
+
y

2

)

+
f

(

x
−
y

2

)

=
2
f

(

x
2

)

+
2
f

(

y
2

)

+
λ
f
(
x
)
f
(
y
)
,

f\left ( {\frac {{x + y}} {2}} \right ) + f\left ( {\frac {{x - y}} {2}} \right ) = 2f\left ( {\frac {x} {2}} \right ) + 2f\left ( {\frac {y} {2}} \right ) + \lambda f(x)f(y),

\]
/: [-

f
:
[
−
1
,
1
]
→

R

f:[ - 1,1] \to {\mathbf {R}}

. This equation was used by Lau in order to characterize Rao’s quadratic entropies. The general solution is obtained here as a special case of a more general result for

f
f

mapping a neighborhood of

0
0

in linear topological space into a field.
Isospectral convex domains in the hyperbolic plane
Authors: Gordon Carolyn S. , Webb David L.
Published: June 2010

We construct pairs of nonisometric convex polygons in the hyperbolic plane for which the Laplacians are both Dirichlet and Neumann isospectral. We also give examples of pairs of isospectral potentials for the Schrödinger operator on certain convex hyperbolic polygons.
Parabolicity of a class of higher order abstract differential equations
Authors: Xio Ti Jun , Liang Jin
Published: June 2010

Let

E
E

be a complex Banach space,

c
i

∈

C

(
1
⩽
i
⩽
n
−
1
)

{c_i} \in \mathbb {C}\;(1 \leqslant i \leqslant n - 1)

, and

A
A

be a nonnegative operator in

E
E

. We discuss the parabolicity of the higher-order abstract differential equations
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row with Label left-parenthesis asterisk right-parenthesis EndLabel u Superscript left-parenthesis n right-parenthesis Baseline left-parenthesis t right-parenthesis plus sigma-summation Underscript i equals 1 Overscript n minus 1 Endscripts c Subscript i Baseline upper A Superscript k Super Subscript i Baseline u Superscript left-parenthesis n minus i right-parenthesis Baseline left-parenthesis t right-parenthesis plus upper A u left-parenthesis t right-parenthesis equals 0 EndLayout">

(

∗

)

u

(
n
)

(
t
)
+

∑

i
=
1

n
−
1

c
i

A

k
i

u

(
n
−
i
)

(
t
)
+
A
u
(
t
)
=
0

\begin{equation} \tag {$\ast $} {u^{(n)}}(t) + \sum \limits _{i = 1}^{n - 1} {{c_i}{A^{{k_i}}}{u^{(n - i)}}(t) + Au(t) = 0} \end{equation}

and some perturbation cases of (

∗
\ast

). A sufficient and necessary condition for (

∗
\ast

) to be parabolic is obtained, provided
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k 1 greater-than k 2 minus k 1 greater-than midline-horizontal-ellipsis greater-than 1 minus k Subscript n minus 1 Baseline greater-than 0 comma c Subscript i Baseline not-equals 0 left-parenthesis 1 less-than-or-slanted-equals i less-than-or-slanted-equals n minus 1 right-parenthesis">

k
1

>

k
2

−

k
1

>
⋯
>
1
−

k

n
−
1

>
0
,

c
i

≠
0

(
1
⩽
i
⩽
n
−
1
)

{k_1} > {k_2} - {k_1} > \cdots > 1 - {k_{n - 1}} > 0,\;{c_i} \ne 0\;(1 \leqslant i \leqslant n - 1)

. For

A
A

strictly nonnegative (Definition 1.3),

n
=
3
,

c
1

,

c
2

⩾
0

n = 3,{c_1},{c_2} \geqslant 0

, a sharp criterion is given.
A characterization of positive constrictive operators
Authors: Du Hong Ke
Published: June 2010

In this note we prove that if T is a positive operator on a real Banach lattice, then T is constrictive if and only if that T has the operator matrix decomposition
\[

T
=

(

T
1

a
m
p
;
0

0

a
m
p
;

T
2

)

,

T = \left ( {\begin {array}{*{20}{c}} {{T_1}} & 0 \\ 0 & {{T_2}} \\ \end {array} } \right ),

\]
where

T
1

{T_1}

is a power-bounded generalized permutation matrix on a finite-dimensional space and

T
2
n

→
0

T_2^n \to 0

strongly.
On the cohomology of split extensions
Authors: Benson D. J. , Feshbach M.
Published: June 2010

We construct, for each value of n, a split extension of finite 2-groups, with complement isomorphic to Z/2 , for which the differential

d
n

{d_n}

is nonzero in the Lyndon-Hochschild-Serre spectral sequence.
Dimension functions for fractal sets associated to series
Authors: Morán Manuel
Published: June 2010

In this article we analyze suitable dimension functions for the measure of fractal sets associated to certain absolutely convergent series of vectors of

R

n

{\mathbb {R}^n}

. The complex binomial series provides an example of a family of fractals, all of them with the same Hausdorff dimension but with a totally ordered family of suitable dimension functions indexed by a parameter with range in a real interval. We also show a construction, based on sets associated to series, to obtain fractal sets with given dimension function.
The nonexistence of some noncompact constant mean curvature surfaces
Authors: Cheung Leung-Fu
Published: June 2010

Using isoperimetric inequality, we prove that there are no complete noncompact surfaces in

R

3

{\mathbb {R}^3}

with finite total curvature, odd Euler characteristic, and mean curvature bounded away from zero.
On a claim of Ramanujan about certain hypergeometric series
Authors: Bradley David
Published: June 2010

We state and prove a claim of Ramanujan. As a consequence, a large new class of Saalschützian hypergeometric series is summed in closed form.
Koszul complexes and hypersurface singularities
Authors: Choudary A. D. R. , Dimca A.
Published: June 2010

The behavior of Poincaré series and Betti numbers of complex projective hypersurfaces in terms of their singularities is compared.
On the factorization of 𝐴_{𝑝} weights
Authors: Li Xing Min
Published: June 2010

It is shown that if

(
u
,
v
)
∈

A
p

(u,v) \in {A_p}

then there exist

(

u
1

,

v
1

)
∈

A
1

({u_1},{v_1}) \in {A_1}

and

(

u
2

,

v
2

)
∈

A
1

({u_2},{v_2}) \in {A_1}

such that

u
=

u
1

p
′

v
2

−
p

,
v
=

v
1

p
′

u
2

−
p

u = u_1^{p’ }v_2^{ - p},v = v_1^{p’ }u_2^{ - p}

.
Finitely additive correspondences
Authors: Basile Achille
Published: June 2010

Let X be a locally convex space. Finitely additive X-valued correspondences are investigated, and exhaustive, weakly compact-valued ones are shown to be rich in selections. If, in addition, X is metrizable, then one of such selections is a control. The range of nonatomic correspondences is also studied.
Classification of Cohen-Macaulay modules of covariants for systems of binary forms
Authors: Broer Bram
Published: June 2010

For every module of covariants for a system of binary forms a formula is given, measuring to what extent Stanley’s functional equation fails to be satisfied. As an application a new proof is given for the classification of the Cohen-Macaulay modules of covariants for systems of binary forms.
The automorphism group of a free group is not a 𝐶𝐴𝑇(0) group
Authors: Gersten S. M.
Published: June 2010

If F is a finitely generated free group, then the group

Aut

(
F
)

{\operatorname {Aut}}(F)

, if

rank

(
F
)
≥
3

{\text {rank}}(F) \geq 3

, and

Out

(
F
)

{\text {Out}}(F)

, if

rank

(
F
)
≥
4

{\text {rank}}(F) \geq 4

, are not isomorphic to a subgroup of a group which acts properly discontinuously and cocompactly on a 1-connected geodesic metric space satisfying Gromov’s condition

CAT

(
0
)

{\text {CAT}}(0)

.
On the relationship between convergence in distribution and convergence of expected extremes
Authors: Hill Theodore P. , Spruill M. C.
Published: June 2010

It is well known that the expected values

{

M
k

(
X
)
}
,
k
≥
1

\{ {M_k}(X)\} , k \geq 1

, of the k-maximal order statistics of an integrable random variable X uniquely determine the distribution of X. The main result in this paper is that if

{

X
n

}
,
n
≥
1

\{ {X_n}\} , n \geq 1

, is a sequence of integrable random variables with

lim

n
→
∞

M
k

(

X
n

)
=

α
k

{\lim _{n \to \infty }}{M_k}({X_n}) = {\alpha _k}

for all

k
≥
1

k \geq 1

, then there exists a random variable X with

M
k

(
X
)
=

α
k

{M_k}(X) = {\alpha _k}

for all

k
≥
1

k \geq 1

and

X
n

→

L

X

{X_n}\xrightarrow {\mathcal {L}}X

if and only if

α
k

=
o
(
k
)

{\alpha _k} = o(k)

, in which case the collection

{

X
n

}

\{ {X_n}\}

is also uniformly integrable. In addition, it is shown using a theorem of Müntz that any subsequence

{

M

k
j

(
X
)
}
,
j
≥
1

\{ {M_{{k_j}}}(X)\} , j \geq 1

, satisfying

∑
1

/

k
j

=
∞

\sum 1/{k_j} = \infty

uniquely determines the law of X.
What strong monotonicity condition on Fourier coefficients can make the ratio ‖𝑓-𝑆_{𝑛}(𝑓)‖/𝐸_{𝑛}(𝑓) be bounded?
Authors: Zhou S. P.
Published: June 2010

Let

{

ϕ
n

}

n
=
1

∞

\{ {\phi _n}\} _{n = 1}^\infty

be a positive increasing sequence and

ϕ
n

f
^

(
n
)

{\phi _n}\hat f(n)

decrease. We ask what exact conditions on

{

ϕ
n

}

\{ {\phi _n}\}

make

‖

f
−

S
n

(
f
)

‖

/

E
n

(
f
)

\left \| {f - {S_n}(f)} \right \|/{E_n}(f)

bounded? The present paper will give a complete answer to it.
Nonexistence of weakly almost complex structures on Grassmannians
Authors: Tang Zi Zhou
Published: June 2010

In this paper we prove that, for

2
≤
k
≤
n

/

2

2 \leq k \leq n/2

, the unoriented Grassmann manifold

G
k

(

R

n

)

{G_k}({\mathbb {R}^n})

admits a weakly almost complex structure if and only if

n
=
2
k
=
4

or

6

n = 2k = 4 \; \text {or} \; 6

; for

3
≤
k
≤

n
2

3 \leq k \leq \frac {n}{2}

, none of the oriented Grassmann manifolds

G
~

k

(

R

n

)

{\tilde G_k}({\mathbb {R}^n})

—except

G
~

3

(

R

6

)

{\tilde G_3}({\mathbb {R}^6})

and a few as yet undecided ones—admits a weakly almost complex structure.
Invariant measures of symmetric Lévy processes
Authors: Ying Jiangang
Published: June 2010

If

π
=
{

π
t

:
t
>
0
}

\pi = \{ {\pi _t}:t > 0\}

is a symmetric convolution semigroup with the Lévy exponent

ϕ
\phi

, then supp

π
t

{\pi _t}

, is a group determined by

ϕ
\phi

, and

π
\pi

has a unique Radon invariant measure if and only if

ϕ
\phi

has a unique zero at

0
0

.
Auslander’s 𝛿-invariants of Gorenstein local rings
Authors: Ding Songqing
Published: June 2010

Let (R,

m

\mathfrak {m}

, k) be a Gorenstein local ring with associated graded ring

G
(
R
)

G(R)

. It is conjectured that for any integer

n
>
0

n > 0

, Auslander’s

δ
\delta

-invariant

δ
(
R

/

m

n

)

\delta (R/{\mathfrak {m}^n})

of

R

/

m

n

R/{\mathfrak {m}^n}

equals 1 if and only if

m

n

{\mathfrak {m}^n}

is contained in a parameter ideal of R. In an earlier paper we showed that the conjecture holds if

G
(
R
)

G(R)

is Cohen-Macaulay. In this paper we prove that the conjecture has an affirmative answer if depth

G
(
R
)
=
dim
⁡
R
−
1

G(R) = \dim R - 1

and R is gradable. We also prove that if R is not regular and depth

G
(
R
)
≥
dim
⁡
R
−
1

G(R) \geq \dim R - 1

, then

δ
(
R

/

m

2

)
=
1

\delta (R/{\mathfrak {m}^2}) = 1

if and only if R has minimal multiplicity.
Fixed point iteration processes for asymptotically nonexpansive mappings
Authors: Tan Kok-Keong , Xu Hong Kun
Published: June 2010

Let X be a uniformly convex Banach space which satisfies Opial’s condition or has a Fréchet differentiable norm, C a bounded closed convex subset of X, and

T
:
C
→
C

T:C \to C

an asymptotically nonexpansive mapping. It is then shown that the modified Mann and Ishikawa iteration processes defined by

x

n
+
1

=

t
n

T
n

x
n

+
(
1
−

t
n

)

x
n

{x_{n + 1}} = {t_n}{T^n}{x_n} + (1 - {t_n}){x_n}

and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x Subscript n plus 1 Baseline equals t Subscript n Baseline upper T Superscript n Baseline left-parenthesis s Subscript n Baseline upper T Superscript n Baseline x Subscript n Baseline plus left-parenthesis 1 minus s Subscript n Baseline right-parenthesis x Subscript n Baseline right-parenthesis plus left-parenthesis 1 minus t Subscript n Baseline right-parenthesis x Subscript n">

x

n
+
1

=

t
n

T
n

(

s
n

T
n

x
n

+
(
1
−

s
n

)

x
n

)
+
(
1
−

t
n

)

x
n

{x_{n + 1}} = {t_n}{T^n}({s_n}{T^n}{x_n} + (1 - {s_n}){x_n}) + (1 - {t_n}){x_n}

, respectively, converge weakly to a fixed point of T.
On the existence of positive solutions of ordinary differential equations
Authors: Erbe L. H. , Wang Haiyan
Published: June 2010

We study the existence of positive solutions of the equation

u

+
a
(
t
)
f
(
u
)
=
0

{u^{}} + a(t)f(u) = 0

with linear boundary conditions. We show the existence of at least one positive solution if

f
f

is either superlinear or sublinear by a simple application of a Fixed Point Theorem in cones.
On bivariate Gaussian cubature formulae
Authors: Schmid H. J. , Xu Yuan
Published: June 2010

It is shown that for two classes of integrals the results of Gaussian quadrature can be extended straightforwardly to the bivariate case. For these classes Gaussian formulae of an arbitrary degree are derived.
Prime factor algebras of the coordinate ring of quantum matrices
Authors: Goodearl K. R. , Letzter E. S.
Published: June 2010

It is proved that every prime factor algebra of the coordinate ring

O

q

(

M
n

(
k
)
)

{\mathcal {O}_q}({M_n}(k))

of quantum

n
×
n

n \times n

matrices over a field k is an integral domain (albeit not necessarily commutative) when q is not a root of unity. The same conclusion follows for the quantum groups

O

q

(

SL
n

(
k
)
)

{\mathcal {O}_q}({\text {SL}_n}(k))

and

O

q

(

GL
n

(
k
)
)

{\mathcal {O}_q}({\text {GL}_n}(k))

. The proof uses a q-analog of Sigurdsson’s theorem bounding the Goldie ranks of prime factors of differential operator rings; this q-analog in turn is based on results from the authors’ recent work on q-skew polynomial rings.
On the Hilbert function of determinantal rings and their canonical module
Authors: Conca Aldo , Herzog Jürgen
Published: June 2010

We determine the Hilbert function of a determinantal ring and of its canonical module using a combinatorial result of Krattenthaler. This gives a new proof of Abhyankar’s formula.
Countable paracompactness of Σ-products
Authors: Yang Le Cheng
Published: June 2010

It is known that

Σ
\Sigma

-products of compact spaces always are countably paracompact but not necessarily normal. In the present paper it is proved that a

Σ
\Sigma

-product of paracompact

σ
\sigma

-spaces is normal if and only if it is countably paracompact.
Scharlemann’s 4-manifolds and smooth 2-knots in 𝑆²×𝑆²
Authors: Sato Yoshihisa
Published: June 2010

Scharlemann gave an example of a 4-manifold admitting a fake homotopy structure on

S
3

×

S
1

♯

S
2

×

S
2

{S^3} \times {S^1}\sharp {S^2} \times {S^2}

, which is homeomorphic to

S
3

×

S
1

♯

S
2

×

S
2

{S^3} \times {S^1}\sharp {S^2} \times {S^2}

by a theorem of Freedman. We address the problem whether a Scharlemann’s manifold is diffeomorphic to

S
3

×

S
1

♯

S
2

×

S
2

{S^3} \times {S^1}\sharp {S^2} \times {S^2}

in terms of 2-knots in

S
2

×

S
2

{S^2} \times {S^2}

.
Nonparametric estimation of the singularities of a signal from noisy measurements
Authors: Katsevich A. I. , Ramm A. G.
Published: June 2010

We study a problem of locating and estimating singularities of a signal measured with noise on a discrete set of points (fixed-design model). The signal consists of a smooth part with bounded first derivative and of finite number of singularities of the type

(
x
−

t
i

)
±
p

d
i

,
0
≤
p
≤

1
2

(x - {t_i})_ \pm ^p{d_i},0 \leq p \leq \frac {1}{2}

. The case

p
=
0

p = 0

corresponds to a piecewise continuous function. The algorithm is based on convolving the data with a kernel having compact support. Optimal bandwidth of the kernel is calculated, the consistency of the algorithm is proved. The results of testing the proposed algorithm on model examples are presented.
Infinite cyclic normal subgroups of fundamental groups of noncompact 3-manifolds
Authors: Winters Bobby Neal
Published: June 2010

It is shown that an end-irreducible

3
3

-manifold each of whose boundary components is compact and whose fundamental group contains an infinite cyclic normal subgroup is Seifert fibered.
Strassen’s theorem for vector measures
Authors: Shortt R. M.
Published: June 2010

A type of Strassen’s Theorem for measures taking values in the positive cone of a Banach lattice is proved. An application is given to metrics for convergence of vector measures.
On the best constant for the Besicovitch covering theorem
Authors: Füredi Zoltán , Loeb Peter A.
Published: June 2010

This note shows that in terms of known proofs of the Besicovitch Covering Theorem, the best constant for that theorem is the maximum number of points that can be packed into a closed ball of radius 2 when the distance between pairs of points is at least 1 and one of the points is at the center of the ball. Exponential upper and lower bounds are also established.
Intermediate value theorems and fixed point theorems for semi-continuous functions in product spaces
Authors: Guillerme Jean
Published: June 2010

We prove an intermediate value theorem for noncontinuous functions; as consequences, we obtain coincidence and fixed points theorems for nonmonotone and noncontinuous functions defined and with values in a product space

R

I

{\mathbb {R}^I}

. Some of them, even when the index set I is a singleton, improve recent statements of S. Schmitd.
Metrics associated with extremal plurisubharmonic functions
Authors: Klimek Maciej
Published: June 2010

A natural metric is introduced on the family of all polynomially convex compactL-regular sets inCn{\mathbb {C}^n}, thus turning this family into a complete metric space. An application in complex dynamics is described.
On the derivatives of harmonic functions on the boundary
Authors: Kellogg Oliver D.
Published: June 2010

Let U be harmonic in a closed region R, whose boundary contains a regular surface element E, with a representation

z
=
ϕ
(
x
,
y
)

z = \phi (x,y)

. If E has bounded curvatures, and if

ϕ
(
x
,
y
)

\phi (x,y)

and the boundary values of U on E have continuous derivatives of order n which satisfy a Dini condition, then the partial derivatives of U of order n exist, as limits, on E, and are continuous in R at any interior point of E. Hölder conditions on the boundary values of U, or on their derivatives of order n, imply Hölder conditions on U, or the corresponding derivatives, in R, in the neighborhood of the interior points of E.