bluuebunny/crossref_metadata_2025 huggingface dataset:
An extension of Skorohod’s almost sure representation theorem
Authors: Blackwell David , Dubins Lester E.
Published: June 2010

Skorohod discovered that if a sequence

Q
n

{Q_n}

of countably additive probabilities on a Polish space converges in the weak star topology, then, on a standard probability space, there are

Q
n

{Q_n}

-distributed

f
n

{f_n}

which converge almost surely. This note strengthens Skorohod’s result by associating, with each probability

Q
Q

on a Polish space, a random variable

f
Q

{f_Q}

on a fixed standard probability space so that for each

Q
Q

, (a)

f
Q

{f_Q}

has distribution

Q
Q

and (b) with probability 1,

f
P

{f_P}

is continuous at

P
=
Q

P = Q

.
Foliations with nonorientable leaves
Authors: Dwyer W. G. , Ellis D. B. , Szczarba R. H.
Published: June 2010

We prove that a codimension one foliation of an orientable paracompact manifold has at most a countable number of nonorientable leaves. We also give an example of a codimension one foliation of a compact orientable manifold with an infinite number of nonorientable leaves.
Terminal quotient singularities in dimensions three and four
Authors: Morrison David R. , Stevens Glenn
Published: June 2010

We classify isolated terminal cyclic quotient singularities in dimension three, and isolated Gorenstein terminal cyclic quotient singularities in dimension four. In addition, we give a new proof of a combinatorial lemma of G. K. White using Bernoulli functions.
On the derivation of 𝑥ⁿ in a ring
Authors: Bridges Douglas , Bergen Jeffrey
Published: June 2010

The main result of this paper gives conditions which ensure that an additive map of a ring

R
R

into itself which satisfies a generalisation of the rule

d

x
n

/

d
x
=
n

x

n
−
1

d{x^n}/dx = n{x^{n - 1}}

is a derivation on

R
R

.
Minimax theorems for ANRs
Authors: McClendon J. F.
Published: June 2010

Some minimax theorems for real valued functions on a product space are proved. The functions considered are lower semicontinuous or continuous. Also, some related results on the intersection of subsets of a product space are proved.
On a theorem of P. L. Uljanov
Authors: Stanojevic Vera B.
Published: June 2010

It is shown that if

c

(
n
)

=
o

(
1
)

c\left ( n \right ) = o\left ( 1 \right )

,

|
n
|

→
∞

\left | n \right | \to \infty

, and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript StartAbsoluteValue n EndAbsoluteValue Endscripts Underscript greater-than normal infinity Endscripts StartAbsoluteValue normal upper Delta Superscript m Baseline c left-parenthesis n right-parenthesis EndAbsoluteValue greater-than normal infinity">

∑

|
n
|

>
∞

|

Δ
m

c

(
n
)

|

>
∞

{\sum _{\left | n \right |}}_{ > \infty }\left | {{\Delta ^m}c\left ( n \right )} \right | > \infty

, for some integer

m
⩾
1

m \geqslant 1

, then the series

∑

|
n
|

>
∞

c

(
n
)

e

int

{\sum _{\left | n \right |}}_{ > \infty }c\left ( n \right ){e^{\operatorname {int} }}

converges to some

f
∈

L
p

(

T

)

f \in {L^p}\left ( {\mathbf {T}} \right )

for any

0
>
p
>
1

/

m

0 > p > 1 / m

.
A general isepiphanic inequality
Authors: Lutwak Erwin
Published: June 2010

An inequality of Petty regarding the volume of a convex body and that of the polar of its projection body is shown to lead to an inequality between the volume of a convex body and the power means of its brightness function. A special case of this power-mean inequality is the classical isepiphanic (isoperimetric) inequality. The power-mean inequality can also be used to obtain strengthened forms and extensions of some known and conjectured geometric inequalities. Affine projection measures (Quermassintegrale) are introduced.
The jump inversion theorem for 𝑄_{2𝑛+1}-degrees
Authors: Kastanas Ilias G.
Published: June 2010

Assuming projective determinacy we extend Friedberg’s Jump Inversion theorem to

Q

2
n
+
1

{Q_{2n + 1}}

-degrees, after noticing that it fails for

Δ

2
n
+
1

1

\Delta _{2n + 1}^1

-degrees.
Group actions on aspherical 𝐴_{𝑘}(𝑁)-manifolds with nonzero Euler characteristics
Authors: Ku Hsü Tung
Published: June 2010

By an aspherical

A
k

(
N
)

{A_k}(N)

-manifold, we mean a compact manifold

M
M

together with a map

f
f

from

M
M

into an aspherical complex

N
N

such that

f
∗

{f^*}

:

H
k

(
N
;
Q
)
→

H
k

(
M
;
Q
)

{H^k}(N;Q) \to {H^k}(M;Q)

is nontrivial. In this paper we study the fixed point set, degree of symmetry, semisimple degree of symmetry and torus degree of symmetry of

M
M

with the Euler characteristic of

M
M

nonzero.
A note on quasi-Buchsbaum rings
Authors: Goto Shiro
Published: June 2010

In this paper the ubiquity of non-Buchsbaum but quasi-Buchsbaum rings is established. The result is stated as follows: Let

d
≥
3

d \ge 3

and

h
1

,

h
2

,
…
,

h

d
−
1

≥
0

{h_1},{h_2}, \ldots ,{h_{d - 1}} \ge 0

be integers and assume that at least two of

h
i

{h_i}

’s are positive. Then there exists a non-Buchsbaum but quasi-Buchsbaum local integral domain

A
A

of

dim
⁡
A
=
d

\dim A = d

and such that

l
A

(

H
m
i

(
A
)
)
=

h
i

{l_A}(H_m^i(A)) = {h_i}

for all

1
≤
i
≤
d
−
1

1 \le i \le d - 1

. Moreover if

h
1

=
0

{h_1} = 0

the ring

A
A

can be chosen to be normal.
Transfer in generalized sheaf cohomology
Authors: Piacenza Robert
Published: June 2010

The aim of this note is to define the transfer in generalized sheaf cohomology and state its most important properties. Under appropriate conditions the transfer defined here agrees with the transfer defined using different methods by Roush, Kahn, and Priddy.
A complement theorem for shape concordant compacta
Authors: Sher R. B.
Published: June 2010

Let

X
X

and

Y
Y

be compacta of polyhedral shape lying in the manifold

M
M

. Under suitable conditions, it is shown that if

X
X

and

Y
Y

are shape concordant, then

M
−
X

M - X

is homeomorphic to

M
−
Y

M - Y

.
Most maps of the pseudo-arc are homeomorphisms
Authors: Lewis Wayne
Published: June 2010

We prove the following results. (1) If

M
(
P
)

M(P)

is the space of maps of the pseudo-arc into itself with the sup metric, then the subset

H
^

(
P
)

\hat H(P)

of maps of the pseudo-arc into itself which are homeomorphisms onto their images is a dense

G
δ

{G_\delta }

in

M
(
P
)

M(P)

. (2) Every homeomorphism of the pseudo-arc onto itself is a product of

∈
\in

-homeomorphisms. (3) There exists a nonidentity homeomorphism of the pseudo-arc with an infinite sequence of

p
p

th roots. (4) Every map between chainable continua can be lifted to a homeomorphism of pseudo-arcs.
Applications of the joint angular field of values
Authors: Barker George Phillip
Published: June 2010

Let

A
1

,
…
,

A
m

{A_1}, \ldots ,{A_m}

be

n
×
n

n \times n

hermitian matrices and let

H

n

{\mathcal {H}_n}

be the real space of

n
×
n

n \times n

hermitian matrices. If

span

{

A
1

,
…
,

A
m

}

=

H

n

{\operatorname {span}}\left \{ {{A_1}, \ldots ,{A_m}} \right \} = {\mathcal {H}_n}

, then the extreme rays of the joint angular field of values of

{

A
1

,
…
,

A
m

}

\left \{ {{A_1}, \ldots ,{A_m}} \right \}

are determined. Then this cone is used to give necessary and sufficient conditions for the existence of hermitian matrices

B
1

,
…
,

B
m

{B_1}, \ldots ,{B_m}

such that

A
1

⊗

B
1

+
⋯
+

A
m

⊗

B
m

{A_1} \otimes {B_1} + \cdots + {A_m} \otimes {B_m}

preserves the cone of the positive semidefinite matrices where

A
⊗
B

A \otimes B

is the dyad product

A
⊗
B

(
H
)

=

(

tr

B
H

)

A

A \otimes B\left ( H \right ) = \left ( {{\text {tr}}BH} \right )A

.
A result concerning additive functions in Hermitian Banach *-algebras and an application
Authors: Vukman J.
Published: June 2010

Let

A

\mathcal {A}

be a complex hermitian Banach

∗
*

-algebra with an identity element

e
e

. Suppose there exists an additive function

f
:

A

→

A

f:\mathcal {A} \to \mathcal {A}

such that

f

(
a
)

=
−

a
∗

a
f

(

a

−
1

)

f\left ( a \right ) = - {a^ * }af\left ( {{a^{ - 1}}} \right )

holds for all normal invertible elements

a
∈

A

a \in \mathcal {A}

. We prove that in this case

f
f

is of the form

f

(
a
)

=
f

(

i
e

)

k

f\left ( a \right ) = f\left ( {ie} \right )k

, where

a
=
h
+
i
k

a = h + ik

. Using this result we generalize S. Kurepa’s extension of Jordan-Neumann characterization of pre-Hilbert space.
Topological minimax theorems
Authors: Geraghty Michael A. , Lin Bor-Luh
Published: June 2010

Mimimax theorems are given using only topological conditions.
Restriction of spherical representations of 𝑃𝐺𝐿₂(𝑄_{𝑝}) to a discrete subgroup
Authors: Figà-Talamanca Alessandro , Picardello Massimo A.
Published: June 2010

We study the action on the homogeneous tree associated with

PG

L

2

(

Q

p

)

{\text {PG}}{{\text {L}}_2}({{\mathbf {Q}}_p})

, of a suitably chosen discrete subgroup which is isomorphic to

Z

2

∗
⋯
∗

Z

2

{{\mathbf {Z}}_2} * \cdots * {{\mathbf {Z}}_2}

and is cocompact. We prove that the spherical representations of

PG

L

2

(

Q

p

)

{\text {PG}}{{\text {L}}_2}({{\mathbf {Q}}_p})

remain irreducible when restricted to this subgroup.
A new class of orthogonal polynomials
Authors: Nevai Paul
Published: June 2010

A new class of orthogonal polynomials is introduced which generalizes the Bernstein-Szegö polynomials and includes the associated polynomials as well.
Elementary proof of a formula of Ramanujan
Authors: Lamphere Robert L.
Published: June 2010

In this paper we use only elementary calculus to prove Ramanujan’s integral formula
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Subscript 0 Superscript normal infinity Baseline x Superscript m minus 1 Baseline ContinuedFraction left-parenthesis 1 plus a b x right-parenthesis left-parenthesis 1 plus a b squared x right-parenthesis midline-horizontal-ellipsis left-parenthesis 1 plus a b Superscript n Baseline x right-parenthesis midline-horizontal-ellipsis Over left-parenthesis 1 plus x right-parenthesis left-parenthesis 1 plus b x right-parenthesis left-parenthesis 1 plus b squared x right-parenthesis midline-horizontal-ellipsis left-parenthesis 1 plus b Superscript n Baseline x right-parenthesis midline-horizontal-ellipsis d x equals StartFraction pi Over upper S i n left-parenthesis m pi right-parenthesis EndFraction product Underscript k equals 1 Overscript normal infinity Endscripts StartFraction left-parenthesis 1 minus b Superscript k minus m Baseline right-parenthesis left-parenthesis 1 minus a b Superscript k Baseline right-parenthesis Over left-parenthesis 1 minus b Superscript k Baseline right-parenthesis left-parenthesis 1 minus a b Superscript k minus m Baseline right-parenthesis EndFraction">

∫
0
∞

x

m
−
1

(
1
+
a
b
x
)
(
1
+
a

b
2

x
)
⋯
(
1
+
a

b
n

x
)
⋯

(
1
+
x
)
(
1
+
b
x
)
(
1
+

b
2

x
)
⋯
(
1
+

b
n

x
)
⋯

d
x
=

π

Sin

(
m
π
)

∏

k
=
1

∞

(
1
−

b

k
−
m

)
(
1
−
a

b
k

)

(
1
−

b
k

)
(
1
−
a

b

k
−
m

)

\int _0^\infty {{x^{m - 1}}} \frac {{(1 + abx)(1 + a{b^2}x) \cdots (1 + a{b^n}x) \cdots }}{{(1 + x)(1 + bx)(1 + {b^2}x) \cdots (1 + {b^n}x) \cdots }}dx = \frac {\pi }{{{\operatorname {Sin}}(m\pi )}}\prod \limits _{k = 1}^\infty {\frac {{(1 - {b^{k - m}})(1 - a{b^k})}}{{(1 - {b^k})(1 - a{b^{k - m}})}}}

\]
where

m
m

,

a
a

and

b
b

are positive with

b
>
1

b > 1

and

a
>

b

m
−
1

a > {b^{m - 1}}

.
Spectra of constructs of a system of operators
Authors: Carrillo Angel , Hernández Carlos
Published: June 2010

This paper describes the spectrum and the upper and lower Fredholm spectra of

(
n
+
m
)

(n + m)

-tuples
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper F left-parenthesis upper A 1 right-parenthesis comma midline-horizontal-ellipsis comma upper F left-parenthesis upper A Subscript n Baseline right-parenthesis comma upper G left-parenthesis upper B 1 right-parenthesis comma midline-horizontal-ellipsis comma upper G left-parenthesis upper B Subscript m Baseline right-parenthesis right-parenthesis">

(
F
(

A
1

)
,
⋯
,
F
(

A
n

)
,
G
(

B
1

)
,
⋯
,
G
(

B
m

)
)

(F({A_1}), \cdots ,F({A_n}),G({B_1}), \cdots ,G({B_m}))

of operators, where

(

A
i

)

({A_i})

and

(

B
j

)

({B_j})

are systems of operators in two Hilbert spaces

H

1

{\mathcal {H}_1}

and

H

2

{\mathcal {H}_2}

, and

F
F

and

G
G

are certain linear operators defined on

L

(

H

i

)

\mathcal {L}({\mathcal {H}_i})

. Using spectral mapping theorems the spectra of operators constructed by the action of a polynomial on a system
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper F left-parenthesis upper A 1 right-parenthesis comma midline-horizontal-ellipsis comma upper F left-parenthesis upper A Subscript n Baseline right-parenthesis comma upper G left-parenthesis upper B 1 right-parenthesis comma midline-horizontal-ellipsis comma upper G left-parenthesis upper B Subscript m Baseline right-parenthesis right-parenthesis">

(
F
(

A
1

)
,
⋯
,
F
(

A
n

)
,
G
(

B
1

)
,
⋯
,
G
(

B
m

)
)

(F({A_1}), \cdots ,F({A_n}),G({B_1}), \cdots ,G({B_m}))

is obtained. In particular, the spectra of the elementary operator and tensor products of operators is determined.
On partially conservative sentences and interpretability
Authors: Lindström Per
Published: June 2010

A sentence

φ
\varphi

is

Γ
\Gamma

-conservative over

T
T

if

T
+
φ
⊢
ψ

T + \varphi \vdash \psi

implies

T
⊢
ψ

T \vdash \psi

for every

ψ
∈
Γ

\psi \in \Gamma

. In §1 this concept for

Γ
=

∑

n
+
1

0

\Gamma = \sum _{n + 1}^0

and

∏

n
+
1

0

\prod _{n + 1}^0

is investigated. In §2 results from §1 are applied to interpretability in theories containing arithmetic.
Remark on the divisibility of the class numbers of certain quartic number fields by 5
Authors: Endô Akira
Published: June 2010

The congruence relation modulo 5 between the class numbers of the real and imaginary quartic subfields of the extension of a quadratic number field obtained by adjoining a fifth root of unity is studied.
Differentiation of real-valued functions and continuity of metric projections
Authors: Fitzpatrick Simon
Published: June 2010

We characterize the Fréchet differentiability of real-valued functions on certain real Banach spaces in terms of a directional derivative being equal to a modified version of the local Lipschitz constant. This yields the continuity of metric projections onto closed sets whose distance functions have directional derivatives equal to 1, provided the Banach space and its dual have Fréchet differentiable norms.
𝜔-connected continua and Jones’ 𝐾 function
Authors: Vought Eldon J.
Published: June 2010

A continuum

X
X

is

ω
\omega

-connected if for every pair of points

x
x

,

y
y

of

X
X

, there exists an irreducible subcontinuum of

X
X

from

x
x

to

y
y

that is decomposable. If

A
⊂
X

A \subset X

then

K

(
A
)

K\left ( A \right )

is the intersection of all subcontinua of

X
X

that contain

A
A

in their interiors. The main theorem shows that if

X
X

is an

ω
\omega

-connected continuum and

H
H

is a connected nowhere dense subset of

X
X

, then

K

(
H
)

K\left ( H \right )

has a void interior. Several corollaries are established for continua with certain separation properties and a final theorem shows the equivalence of

ω
\omega

-connectedness and

δ
\delta

-connectedness for plane continua.
A note on maximal operators and reversible weak type inequalities
Authors: Leckband M. A.
Published: June 2010

A class of maximal operators is shown to satisfy a weak type inequality and a corresponding converse inequality. The results are applicable to a fractionally iterated Hardy-Littlewood maximal operator.
𝒞_{𝓅}-perturbations of nest algebras
Authors: Knowles Gareth J.
Published: June 2010

Given the ideal

C

p

{{\mathcal C}_p}

and a nest algebra

A

{\mathcal A}

in

L

(
H
)

{\mathcal L}(H)

there are two corresponding subalgebras of

L

(
H
)

{\mathcal L}(H)

. The first consists of all

C

p

{{\mathcal C}_p}

-perturbations of

A

{\mathcal A}

. The second, a natural generalization of the quasitriangular algebra corresponding to

A

{\mathcal A}

, consists of all

T
T

in

L

(
H
)

{\mathcal L}(H)

with

E
→
(
I
−
E
)
T
E

E \to (I - E)TE

continuous from Lat

A

{\mathcal A}

into

C

p

{{\mathcal C}_p}

. Necessary and sufficient conditions are given for these algebras to be identical.
A chaotic function with a scrambled set of positive Lebesgue measure
Authors: Smítal J.
Published: June 2010

There is a continuous map of the unit intervalIIwhich is chaotic in the sense of Li and Yorke and which has a scrambled set of Lebesgue measure arbitrarily close to 1.
Remarks on the parametrized symbol calculus
Authors: Kinoshita Michio
Published: June 2010

In his paper, L. Hörmander has used the Weyl calculus to study the Fourier integral operator theory. In the present paper, the author considers the correspondences

W
τ

{W_\tau }

,

τ
∈
R

\tau \in R

(

R
R

is the set of the real numbers), which mean the standard correspondence of symbol and operator if

τ
=
0

\tau = 0

, and the correspondence of Weyl type if

τ
=
1

/

2

\tau = 1/2

, and shows the explicit asymptotic formula which describes the deviation of

W
σ

(

W
τ

)

−
1

{W_\sigma }{\left ( {{W_\tau }} \right )^{ - 1}}

from the automorphisms as Lie algebra, and makes some remarks on the above formula.
On the injectivity of the attenuated Radon transform
Authors: Hertle Alexander
Published: June 2010

We show that the attenuated (exponential) Radon transform

R
μ

{R_\mu }

, where

μ
\mu

is assumed to be linear in the space variable, is injective on compactly supported distributions. Moreover, a limited angle reconstruction is possible and a hole theorem holds. We review the well-known special case of constant attenuation.
Counterexamples to several problems on the factorization of bounded linear operators
Authors: Ghoussoub N. , Johnson W. B.
Published: June 2010

For every

1
⩽
p
>
∞

1 \leqslant p > \infty

, there exist a Banach lattice

X
p

{X_p}

and a lattice homomorphism

T
p

{T_p}

from

X
p

{X_p}

onto

c
0

{c_0}

which satisfy: (1)

T
p

{T_p}

does not preserve an isomorphic copy of

c
0

{c_0}

. (2)

T
p

{T_p}

is a Radon-Nikodym operator. (3)

T
1

{T_1}

maps weakly Cauchy sequences into norm convergent sequences. (4) If

T
p

{T_p}

is written as the product of two operators, then one of them preserves a copy of

c
0

{c_0}

.
On the second dual of the Lorentz space
Authors: Ghatage Pratibha G. , Scott Brian M.
Published: June 2010

If

ϕ
(
t
)
=

t

1

/

p

(
p
>
1
)

\phi (t) = {t^{1/p}}(p > 1)

and

(
X
,

S

,
μ
)

(X,\mathcal {S},\mu )

is a completely nonatomic finite measure space, then the dual of the Lorentz space

N
ϕ

{N_\phi }

is denoted by

M
ϕ

{M_\phi }

and the closure of the simple functions in

M
ϕ

{M_\phi }

by

M
ϕ
0

M_\phi ^0

. It is known that

(

M
ϕ
0

)
∗

=

N
ϕ

{(M_\phi ^0)^ * } = {N_\phi }

. In this note we show that given a positive number

β
>
1

\beta > 1

it is possible to construct a set of contractive embeddings of

(

l
∞

/

c
0

)

({l_\infty }/{c_0})

into

(

M
ϕ

/

M
ϕ
0

)
∗

{({M_\phi }/M_\phi ^0)^ * }

, each of which is bounded below by

M
=
M
(
β
)
→
1

as

β
→

0

+

M = M(\beta ) \to 1\;{\text {as}}\;\beta \to {{\text {0}}^ + }

. The union of the ranges of these embeddings is a total set in

(

M
ϕ

/

M
ϕ
0

)
∗

{({M_\phi }/M_\phi ^0)^ * }

.
Excess linear series on an algebraic curve
Authors: Fulton William , Harris Joe , Lazarsfeld Robert
Published: June 2010

We prove that the dimensions of the varieties

W
d
r

W_d^r

of complete linear series of degree

d
d

and dimension at least

r
r

on a curve satisfy the inequalities

dim
⁡

W

d
−
1

r

⩾
dim
⁡

W
d
r

−
(
r
−
1
)

\dim W_{d - 1}^r \geqslant \dim W_d^r - (r - 1)

. In particular, a curve with

∞
2

g
d
1

{\infty ^2}g_d^1

’s must have a

g

d
−
1

1

g_{d - 1}^1

.
Properties of the Fourier algebra that are equivalent to amenability
Authors: Losert Viktor
Published: June 2010

It is shown that a locally compact group

G
G

is amenable iff each multiplier on the Fourier algebra

A

(
G
)

A\left ( G \right )

is given by a function from the Fourier-Stieltjes algebra

B

(
G
)

B\left ( G \right )

. Another condition is that the norm of

A

(
G
)

A\left ( G \right )

is equivalent to that induced by the regular representation of

A

(
G
)

A\left ( G \right )

.
The Vitali-Hahn-Saks theorem for Boolean algebras with the subsequential interpolation property
Authors: Freniche Francisco José
Published: June 2010

It is shown that the Vitali-Hahn-Saks theorem holds for a new class of Boolean algebras which are defined by a separation property of its disjoint sequences: the Subsequential Interpolation Property. It is also proved that this property is strictly weaker than the Interpolation Property, the

(
f
)

\left ( f \right )

-Property and the Subsequential Completeness Property.
An integral inequality for the disc multiplier
Authors: Córdoba A.
Published: June 2010

In this paper an integral inequality is proved for the Bochner-Riesz operators in dimension two. This inequality expresses how those operators are controlled by maximal functions associated to families of rectangles with an appropriate number of directions.
Arrangements of lines with a large number of triangles
Authors: Füredi Z. , Palásti I.
Published: June 2010

An arrangement of lines is constructed by choosing

n
n

diagonals of the regular

2
n

2n

-gon. This arrangement is proved to form at least

n
(
n
−
3
)

/

3

n(n - 3)/3

triangular cells.
2-sphere bundles over compact surfaces
Authors: Melvin Paul
Published: June 2010

Closed

4
4

-manifolds which fiber over a compact surface with fiber a sphere are classified, and the fibration is shown to be unique (up to diffeomorphism).
A note on strong extreme and strongly exposed points in Bochner 𝐿^{𝑝}-spaces
Authors: Greim Peter
Published: June 2010

A strongly exposed (strongly extreme) vector-valued

L
p

{L^p}

-function takes only strongly exposed (strongly extreme) values almost everywhere on its support. We remove the restrictions, concerning the range space and the measure, in previous papers of the author and M. A. Smith.
Iterates of holomorphic self-maps of the unit ball in Hilbert space
Authors: Stachura Adam
Published: June 2010

An example is given of a biholomorphic self-mapping

T
T

of the unit ball in infinite-dimensional Hilbert space satisfying
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="0 equals limit inf Underscript n Endscripts double-vertical-bar upper T Superscript n Baseline left-parenthesis 0 right-parenthesis double-vertical-bar greater-than limit sup Underscript n Endscripts StartAbsoluteValue EndAbsoluteValue upper T Superscript n Baseline left-parenthesis 0 right-parenthesis StartAbsoluteValue EndAbsoluteValue equals 1">

0
=
lim

inf
n

‖

T
n

(
0
)

‖

>
lim

sup
n

|

|

T
n

(
0
)

|

|

=
1

0 = \lim {\inf _n}\left \| {{T^n}\left ( 0 \right )} \right \| > \lim {\sup _n}||{T^n}(0)|| = 1

.
A note on the set of periods for continuous maps of the circle which have degree one
Authors: Alsedà Lluís , Llibre Jaume
Published: June 2010

The main result of this paper is to complete Misiurewicz’s characterization of the set of periods of a continuous map

f
f

of the circle with degree one (which depends on the rotation interval of

f
f

). As a corollary we obtain a kind of perturbation theorem for maps of the circle of degree one, and a new algorithm to compute the set of periods when the rotation interval is known. Also, for maps of degree one which have a fixed point, we describe the relationship between the characterizations of the set of periods of Misiurewicz and Block.
ℵ₀-point compactifications of locally compact spaces and product spaces
Authors: Kimura Takashi
Published: June 2010

We give necessary and sufficient conditions for a locally compact space to have a compactification with countably infinite remainder. We also characterize the product space of two locally compact spaces having such a compactification.
On the intrinsic topology and some related ideals of 𝐶(𝑋)
Authors: Karamzadeh O. A. S. , Rostami M.
Published: June 2010

The above topology is defined and studied on

C
(
X
)

C(X)

, the ring of real-valued continuous functions on a completely regular Hausdorff space

X
X

. The minimal ideals and the socle of

C
(
X
)

C(X)

are characterized via their corresponding

z
z

-filters. We observe that these ideals are

z
z

-ideals and

X
X

is discrete if and only if the socle of

C
(
X
)

C(X)

is a free ideal. It is also shown that for a class of topological spaces, containing all

P
P

-spaces, the family

C
k

(
X
)

{C_k}(X)

of functions with compact support is identical with the intersection of the free maximal ideals of

C
(
X
)

C(X)

.
Two proofs in combinatorial number theory
Authors: Nešetřil Jaroslav , Rödl Vojtěch
Published: June 2010

The aim of this paper is to present a short combinatorial proof of a theorem of P. Erdős on multiplicative bases of integers. A solution of a problem of P. Erdős and D. J. Newman is also presented.
Self-dual lattices for maximal orders in group algebras
Authors: Gluck David
Published: June 2010

LetGGbe a finite group andVVan irreducibleQ[G]{\mathbf {Q}}[G]-module. LetRRbe a Dedekind domain with quotient fieldQ{\mathbf {Q}}such that|G|\left | G \right |is a unit inRR. For applications to topology it is of interest to know ifVVcontains a full self-dualR[G]R[G]-lattice. We show that such lattices always exist for some major classes of finite groups.
Random polytopes on the torus
Authors: Buchta C. , Tichy R. F.
Published: June 2010

The expected volume of the convex hull of

n
n

random points chosen independently and uniformly on the

d
d

-dimensional torus is determined.
Words periodic over the center of a division ring
Authors: Makar-Limanov Leonid , Malcolmson Peter
Published: June 2010

In generalization of a result of Herstein, the authors prove that, in a division ring with uncountable center, if any given nontrivial group word takes only values periodic over the center, then the division ring is commutative. Techniques include use of the result that a noncommutative division ring finite-dimensional over its center includes a nonabelian free group in its multiplicative group.
Isometries of the disc algebra
Authors: El-Gebeily Mohamad , Wolfe John
Published: June 2010

The linear isometries

u
:
A
→
A

u:A \to A

of the disc algebra

A
A

into itself are completely described. Such isometries

u
u

must be one of two distinct types. The first type is

u
f
=
ψ
⋅
f
(
ϕ
)

uf = \psi \cdot f(\phi )

, where

ψ
∈
A

\psi \in A

and

ϕ
∈

H
∞

\phi \in {H^\infty }

satisfy certain described conditions. The second type is

u
f
=
E
(
ψ
⋅
f
(
ϕ
)
)

uf = E(\psi \cdot f(\phi ))

, where

ϕ
:
Q
→
T

\phi :Q \to T

is any continuous function from a closed zero measure subset

Q
Q

of the unit circle

T
T

onto itself,

ψ
∈
C
(
Q
)

\psi \in C(Q)

is unimodular, and

E
:
Y
→
A

E:Y \to A

is a norm 1 extension operator, where

Y
=

{

ψ
⋅
f
(
ϕ
)
:
f
∈
A

}

⊂
C
(
Q
)

Y = \left \{ {\psi \cdot f(\phi ):f \in A} \right \} \subset C(Q)

. Isometries of

C
(
K
)

C(K)

spaces into the disc algebra are also described.
A note on a weighted Sobolev inequality
Authors: Chiarenza Filippo , Frasca Michele
Published: June 2010

We give a simple proof of a weighted imebedding theorem whose proof was originally given in [3].
Strong limit theorems for orthogonal sequences in von Neumann algebras
Authors: Jajte R.
Published: June 2010

Let

A
A

be a von Neumann algebra with a faithful normal state

ϕ
\phi

. It is shown that if a sequence

(

x
n

)

({x_n})

in

A
A

is orthogonal relative to

ϕ
\phi

and satisfies the condition
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript k Endscripts phi left-parenthesis StartAbsoluteValue x Subscript k Baseline EndAbsoluteValue squared right-parenthesis left-parenthesis StartFraction log k Over k EndFraction right-parenthesis squared greater-than normal infinity comma">

∑

k

ϕ
(

|

x
k

|

2

)

(

log
⁡
k

k

)

2

>
∞
,

\sum \limits _{k} {\phi (|{x_k}{|^2}){{\left ( {\frac {{\log k}}{k}} \right )}^2} > \infty ,}

\]
then

n
1

∑

k
=
1

n

x
k

→
0

{}_n^1\sum \nolimits _{k = 1}^n {{x_k} \to 0}

almost uniformly in

A
A

. Some other results related to this theorem are also discussed.
Typical continuous functions are virtually nonmonotone
Authors: Humke P. , Laczkovich M.
Published: June 2010

For every porosity premeasure

ϕ
\phi

, a typical continuous function meets every monotone function in a bilaterally strongly

ϕ
\phi

-porous set. The statement does not remain valid if we replace the class of monotone functions by the class of absolutely continuous functions.
Minimal solutions of the heat equation and uniqueness of the positive Cauchy problem on homogeneous spaces
Authors: Korányi A. , Taylor J. C.
Published: June 2010

The minimal positive solutions of the heat equation on

X
×
(
−
∞
,
T
)

X \times ( - \infty ,T)

are determined for

X
X

a homogeneous Riemannian space. A simple proof of uniqueness for the positive Cauchy problem on a homogeneous space is given using Choquet’s theorem and the explicit form of these solutions.
Existence of solutions in a cone for nonlinear alternative problems
Authors: Nieto Juan J.
Published: June 2010

Using the alternative method we present sufficient conditions for the existence of positive solutions to nonlinear equations at resonance and extend a well-known result of Cesari and Kannan.
On surfaces in 𝑅⁴
Authors: Seaman Walter
Published: June 2010

We provide answers (Theorem C) to some questions concerning surfaces in

R

4

{{\mathbf {R}}^4}

and maps into the quadric

Q
2

{Q_2}

raised by D. Hoffman and R. Osserman.
Bounded cohomology of certain groups of homeomorphisms
Authors: Matsumoto Shigenori , Morita Shigeyuki
Published: June 2010

We consider the condition when bounded cohomology injects into ordinary cohomology and prove the vanishing of bounded cohomology of the group of all compactly supported homeomorphisms of

R

n

{{\mathbf {R}}^n}

.
Left absolutely flat generalized inverse semigroups
Authors: Bulman-Fleming Sydney , McDowell Kenneth
Published: June 2010

A semigroup

S
S

is called (left, right) absolutely flat if all of its (left, right)

S
S

-sets are flat.

S
S

is a (left, right) generalized inverse semigroup if

S
S

is regular and its set of idempotents

E
(
S
)

E(S)

is a (left, right) normal band (i.e. a strong semilattice of (left zero, right zero) rectangular bands). In this paper it is proved that a generalized inverse semigroup

S
S

is left absolutely flat if and only if

S
S

is a right generalized inverse semigroup and the (nonidentity) structure maps of

E
(
S
)

E(S)

are constant. In particular all inverse semigroups are left (and right) absolutely flat (see [1]). Other consequences are derived.
Hermitian forms and the fibration of spheres
Authors: Binding Paul
Published: June 2010

We identify the real

(
2
n
−
1
)

(2n - 1)

-dimensional sphere

S

2
n
−
1

{S^{2n - 1}}

with the unit sphere of

F

2

{{\mathbf {F}}^2}

, where

F

=

reals

{\mathbf {F}} = {\text {reals}}

, complexes or quaternions and

n
=
1
,
2

n = 1,2

or 4, respectively. It is shown how any Hermitian form over

F

2

{{\mathbf {F}}^2}

, restricted to

S

2
n
−
1

{S^{2n - 1}}

, is related to the (double covering for

n
=
1

n = 1

, Hopf for

n
=
2
,
4

n = 2,4

) fibration
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis x 1 comma x 2 right-parenthesis right-arrow left-parenthesis StartAbsoluteValue x 1 EndAbsoluteValue squared minus StartAbsoluteValue x 2 EndAbsoluteValue squared comma 2 x 1 x overbar Subscript 2 Baseline right-parenthesis colon upper S Superscript 2 n minus 1 Baseline right-arrow upper S Superscript n Baseline period">

(

x
1

,

x
2

)
→
(

|

x
1

|

2

−

|

x
2

|

2

,
2

x
1

x
¯

2

)
:

S

2
n
−
1

→

S
n

.

({x_1},{x_2}) \to ({\left | {{x_1}} \right |^2} - {\left | {{x_2}} \right |^2},2{x_1}{\bar x_2}):{S^{2n - 1}} \to {S^n}.

\]
Convexity of the joint range of several Hermitian forms over the unit sphere of an arbitrary normed vector space

V
V

over

F

{\mathbf {F}}

, with

dim
⁡
V
>
2

\dim V > 2

, is deduced as a corollary.
On integral inequalities of Gronwall-Bellman type
Authors: Young Eutiquio C.
Published: June 2010

A sharp bound is given for solutions of an integral inequality of the Gronwall-Bellman type. The bound which is the exact solution of the corresponding integral equation is obtained by reducing the equation to a system of differential equations.
Convex functions and Fourier coefficients
Authors: Wang Hann Tzong
Published: June 2010

Let

f
f

be a continuous function defined on the interval

(
0
,
1
)

(0,1)

. For

n
=
1
,
2
,
…

n = 1,2, \ldots

and

0
>
s
>
t
>
1

0 > s > t > 1

, denote by

a
n

(
f
;
s
,
t
)
,

b
n

(
f
;
s
,
t
)

{a_n}(f;s,t),{b_n}(f;s,t)

the

n
n

th Fourier coefficients of

f

|

(
s
,
t
)

f|(s,t)

. It is shown that the following statements are equivalent: (i)

f
f

is strictly convex on

(
0
,
1
)

(0,1)

. (ii)
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="b Subscript n Baseline left-parenthesis f semicolon s comma t right-parenthesis greater-than left-parenthesis 2 slash n pi right-parenthesis left-bracket f left-parenthesis s right-parenthesis minus f left-parenthesis left-parenthesis s plus t right-parenthesis right-parenthesis slash 2 right-bracket">

b
n

(
f
;
s
,
t
)
>
(
2

/

n
π
)
[
f
(
s
)
−
f
(
(
s
+
t
)
)

/

2
]

{b_n}(f;s,t) > (2/n\pi )[f(s) - f((s + t))/2]

for all

n
=
1
,
2
,
…

n = 1,2, \ldots

and whenever

0
>
s
>
t
>
1

0 > s > t > 1

. (iii)
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="b Subscript n Baseline left-parenthesis f semicolon s comma t right-parenthesis greater-than left-parenthesis 2 slash n pi right-parenthesis left-bracket f left-parenthesis left-parenthesis s plus t right-parenthesis slash 2 right-parenthesis minus f left-parenthesis t right-parenthesis right-bracket">

b
n

(
f
;
s
,
t
)
>
(
2

/

n
π
)
[
f
(
(
s
+
t
)

/

2
)
−
f
(
t
)
]

{b_n}(f;s,t) > (2/n\pi )[f((s + t)/2) - f(t)]

for all

n
=
1
,
2
,
…

n = 1,2, \ldots

and whenever

0
>
s
>
t
>
1

0 > s > t > 1

. If, in addition,

f
f

is twice differentiable, then (i) and the following statement are also equivalent: (iv)

a
n

(
f
;
s
,
t
)
>
0

{a_n}(f;s,t) > 0

for all

n
=
1
,
2
,
…

n = 1,2, \ldots

and whenever

0
>
s
>
t
>
1

0 > s > t > 1

.
A differentially algebraic elimination theorem with application to analog computability in the calculus of variations
Authors: Rubel Lee A. , Singer Michael F.
Published: June 2010

An elimination theorem is proved in differential algebra, from which it follows that an analytic solution of virtually any ordinary differential equation that you can "write down" must actually solve an algebraic differential equation. As a corollary, it follows that the solutions of a large class of variational problems can be produced by an analog computer.
A characterization theorem for bounded starshaped sets in the plane
Authors: Breen Marilyn
Published: June 2010

Let

S
S

be a nonempty bounded set in

R
2

{R^2}

. Then

S
S

is starshaped if and only if every 3 or fewer boundary points of

S
S

are clearly visible via

S
S

from a common point of

S
S

. The number 3 is best possible.
Dense periodicity on the interval
Authors: Barge Marcy , Martin Joe
Published: June 2010

We give a description of those continuous functions on the interval for which the set of periodic points is dense.
A characterization of potential spaces
Authors: Dorronsoro José R.
Published: June 2010

A mean oscillation characterization, valid for all

α
>
0

\alpha > 0

, of the spaces

L
α
p

L_\alpha ^p

of Bessel potentials of

L
p

{L^p}

functions is given and is used to relate the known characterizations for

0
>
α
>
2

0 > \alpha > 2

via Marcinkiewicz integrals, due to E. M. Stein, and via vector-valued means of differences, due to R. S. Strichartz.
Some examples of cyclic vectors in the Dirichlet space
Authors: Brown Leon , Cohn William
Published: June 2010

We consider the Hilbert space of analytic functions in the open unit disc that have a finite Dirichlet integral. For

E
E

, a closed subset of the unit circle with logarithmic capacity zero, we construct a function in this space which is uniformly continuous, vanishes on

E
E

, and is cyclic with respect to the shift operator.
On an interpolation inequality and its applications to nonlinear elliptic equations
Authors: Trudinger Neil S.
Published: June 2010

We discuss the application of a nonlinear interpolation inequality involving Hölder norms to the estimation of derivatives of solutions of second order nonlinear elliptic equations.
Dense embeddings of sigma-compact, nowhere locally compact metric spaces
Authors: Bowers Philip L.
Published: June 2010

It is proved that a connected complete separable ANR

Z
Z

that satisfies the discrete

n
n

-cells property admits dense embeddings of every

n
n

-dimensional

σ
\sigma

-compact, nowhere locally compact metric space

X
(
n
∈
N
∪
{
0
,
∞
}
)

X(n \in N \cup \{ 0,\infty \} )

. More generally, the collection of dense embeddings forms a dense

G
δ

{G_\delta }

-subset of the collection of dense maps of

X
X

into

Z
Z

. In particular, the collection of dense embeddings of an arbitrary

σ
\sigma

-compact, nowhere locally compact metric space into Hilbert space forms such a dense

G
δ

{G_\delta }

-subset. This generalizes and extends a result of Curtis [Cu

1

_{1}

].
The automorphism tower problem
Authors: Thomas Simon
Published: June 2010

It is shown that the automorphism tower of an infinite centerless group terminates. For each ordinal

α
\alpha

, a group is constructed whose automorphism tower terminates in exactly

α
\alpha

steps.
On unimodular rows
Authors: Roitman Moshe
Published: June 2010

We prove here, among other results, that if

(

x
0

,
…
,

x
n

)

({x_0}, \ldots ,{x_n})

is a unimodular row over a commutative ring

A
A

,

n
⩾
2

n \geqslant 2

,

x
∈
A

x \in A

and
\[

x
≡

x
n

mod

J
(
A

x
0

+
⋯
+
A

x

n
−
2

)

x \equiv {x_n}\quad \mod J(A{x_0} + \cdots + A{x_{n - 2}})

\]
then
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis x 0 comma ellipsis comma x Subscript n minus 1 Baseline comma x Subscript n Baseline right-parenthesis tilde Subscript upper E Baseline left-parenthesis x 0 comma ellipsis comma x Subscript n minus 1 Baseline comma x right-parenthesis">

(

x
0

,
…
,

x

n
−
1

,

x
n

)

∼
E

(

x
0

,
…
,

x

n
−
1

,
x
)

({x_0}, \ldots ,{x_{n - 1}},{x_n}){ \sim _E}({x_0}, \ldots ,{x_{n - 1}},x)

.
Class number relation between certain sextic number fields
Authors: Endô Akira
Published: June 2010

The congruence relation modulo 7 between the class numbers of the real and imaginary sextic subfields of the extension of a quadratic number field obtained by adjoining a seventh root of unity is studied.
A 𝑝-local splitting of 𝐵𝑈(𝑛)
Authors: Ishiguro Kenshi
Published: June 2010

Let

p
p

be a prime and let

n
>
1

n > 1

. A necessary and sufficient condition that the classifying space

B
U
(
n
)

BU(n)

is

p
p

-equivalent to the product of nontrivial spaces is that

p
p

does not divide

n
n

.
Controlled approximation and a characterization of the local approximation order
Authors: de Boor C. , Jia R.-Q.
Published: June 2010

The local approximation order from a scale

(

S
h

)

({S_h})

of approximating functions on

R

m

{{\mathbf {R}}^m}

is characterized in terms of the linear span (and its Fourier transform) of the finitely many compactly supported functions

φ
\varphi

whose integer translates

φ
(
⋅
−
j
)
,
j
∈

z
m

\varphi ( \cdot - j),j \in {z^m}

, span the space

S
=

S
1

S = {S_1}

from which the scale is derived. This provides a correction of similar results stated and proved, in part, by Strang and Fix.
A problem on the Bloch norm of functions in Doob’s class
Authors: Hwang J. S.
Published: June 2010

Let

Δ
\Delta

denote the unit disc and

∂
Δ

\partial \Delta

denote the unit circle both in the complex plane. Define the Doob’s class

D
(
ρ
)

D(\rho )

,

0
>
ρ
>
2
π

0 > \rho > 2\pi

, as all holomorphic functions on

Δ
\Delta

satisfying (1)

f
(
0
)
=
0

f(0) = 0

, and (2) for some arc

Γ
f

⊆
∂
Δ

{\Gamma _f} \subseteq \partial \Delta

with arclength

ρ
\rho

, for all

p
∈
Γ

p \in \Gamma

,

lim
_

z
→
p

|

f
(
z
)

|

≥
1

{\underline {\lim } _{z \to p}}|f(z)| \geq 1

. Recently the author and Rung [6] proved a conjecture of Doob made in 1935 by showing that the norm
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue EndAbsoluteValue f StartAbsoluteValue EndAbsoluteValue equals sup Underscript z element-of normal upper Delta Endscripts left-parenthesis 1 minus StartAbsoluteValue z EndAbsoluteValue squared right-parenthesis StartAbsoluteValue f prime left-parenthesis z right-parenthesis EndAbsoluteValue greater-than-or-equal-to StartFraction 2 sine theta left-parenthesis rho right-parenthesis Over e theta left-parenthesis rho right-parenthesis EndFraction comma 0 less-than-or-equal-to theta left-parenthesis rho right-parenthesis less-than-or-equal-to pi minus rho slash 2 period">

|

|

f

|

|

=

sup

z
∈
Δ

(
1
−

|

z

|

2

)

|

f
′

(
z
)

|

≥

2
sin
⁡
θ
(
ρ
)

e
θ
(
ρ
)

,

0
≤
θ
(
ρ
)
≤
π
−
ρ

/

2.

||f|| = {\sup _{z \in \Delta }}(1 - |z{|^2})|f’(z)| \geq \frac {{2\sin \theta (\rho )}}{{e\theta (\rho )}},\quad 0 \leq \theta (\rho ) \leq \pi - \rho /2.

\]
We then conjecture that the result should be true if the arc

Γ
f

{\Gamma _f}

is replaced by a finite union of arcs whose total length is at least

ρ
\rho

. In this paper, we answer this problem. It turns out to be surprising that the answer depends on the connectivity of the union, namely, the answer is no for the disconnected case, but yes for the connected one.
Steiner minimal tree for points on a circle
Authors: Du D. Z. , Hwang F. K. , Chao S. C.
Published: June 2010

We show that the Steiner minimal tree for a set of points on a circle is the shortest path connecting them if at most one distance between two consecutive points is "large". We prove this by making an interesting use of the Steiner ratio

ρ
\rho

which has been well studied in the literature.
Mixed Hadamard’s theorems
Authors: Furuta Takayuki
Published: June 2010

An operator

T
T

means a bounded linear operator on a complex Hilbert space

H
H

. We give two types of mixed Hadamard’s theorems containing the terms

T
,

|
T
|

T,\left | T \right |

and

|

T
∗

|

\left | {{T^ * }} \right |

as extensions of Hadamard’s theorem and mixed Schwarz’s inequality
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue left-parenthesis upper T x comma y right-parenthesis EndAbsoluteValue squared less-than-or-equal-to left-parenthesis StartAbsoluteValue upper T EndAbsoluteValue x comma x right-parenthesis left-parenthesis StartAbsoluteValue upper T Superscript asterisk Baseline EndAbsoluteValue y comma y right-parenthesis">

|

(
T
x
,
y
)

|

2

≤
(

|
T
|

x
,
x
)
(

|

T
∗

|

y
,
y
)

{\left | {(Tx,y)} \right |^2} \leq (\left | T \right |x,x)(\left | {{T^ * }} \right |y,y)

for any

T
T

and for any

x
x

and

y
y

in

H
H

. Also we scrutinize the cases when the equalities in these mixed Hadamard’s theorems hold.
Real isomorphic complex Banach spaces need not be complex isomorphic
Authors: Bourgain J.
Published: June 2010

It is shown that complex Banach spaces may be isomorphic as real spaces and not as complex spaces. If

X
X

is a complex Banach space, denote

X
¯

\overline X

the Banach space with same elements and norm as

X
X

but scalar multiplication defined by

z
⋅
x
=

z
¯

⋅
x

z \cdot x = \bar z \cdot x

for

z
∈

C

,
x
∈
X

z \in {\mathbf {C}},x \in X

. If

X
X

is a space of complex sequences,

X
¯

\overline X

identifies with the space of coordinate-wise conjugate sequences and its norm is given by

‖
x
‖

X
¯

=

‖

x
¯

‖

X

{\left \| x \right \|_{\overline X }} = {\left \| {\bar x} \right \|_X}

, where

x
¯

=
(

z
¯

1

,

z
¯

2

,
…
)

\bar x = ({\bar z_1},{\bar z_2}, \ldots )

for

x
=
(

z
1

,

z
2

,
…
)

x = ({z_1},{z_2}, \ldots )

. Obviously

X
X

and

X
¯

\overline X

are isometric as real spaces. In this note, we prove that

X
X

and

X
¯

\overline X

may not be linearly isomorphic (in the complex sense). The method consists in constructing certain finite dimensional spaces by random techniques.
Regularity of Riesz measures
Authors: Prinz P.
Published: June 2010

It is shown that Riesz measures are inner regular, i.e., each Borel set may be approximated from inside by closed sets, if the basic space is metacompact or para-Lindelöf. On the other hand, an example is given to show that local compactness is not sufficient to ensure inner regularity of Riesz measures.
Essentially triangular algebras
Authors: Erdos J. A. , Hopenwasser A.
Published: June 2010

If

N

\mathcal {N}

is a nest, then the set of all bounded linear operators

T
T

such that

T
P
−
P
T
P

TP - PTP

is compact for all

P
P

in

N

\mathcal {N}

is the essentially triangular algebra associated with

N

\mathcal {N}

. Put another way, essentially triangular algebras are the inverse images under the Calkin map of nest-subalgebras of the Calkin algebra. J. Deddens has characterized nest algebras in terms of operators whose half-orbits under similarity by a positive invertible operator are bounded in norm. This paper, by substituting essential norms for norms, provides a related characterization of essentially triangular algebras.
A note on minimal modular symbols
Authors: Ash Avner
Published: June 2010

For any arithmetic group, a set of geometrically-defined cohomology classes is constructed which spans the cohomology of the group with rational coefficients in the highest nonvanishing dimension thereof.
Lower bounds for class numbers of real quadratic fields
Authors: Mollin R. A.
Published: June 2010

Based on the fundamental units of real quadratic fields we provide lower bounds for their class numbers. These results extend work of H. Hasse [2] and generalize and correct results of H. Yokoi [8, 9]. Moreover, for certain real quadratic fields we provide criteria for their class numbers to be divisible by a specific integer.
A covering lemma for product spaces
Authors: Journé Jean-Lin
Published: June 2010

We give a substitute for the Whitney decomposition of an arbitrary open set in

R

2

{{\mathbf {R}}^2}

where squares are replaced by rectangles. Then we deduce the

L
∞

{L^\infty }

-BMO boundedness of certain singular integral operators defined on product spaces.
Homogeneous Borel sets
Authors: van Engelen Fons
Published: June 2010

Topological characterizations of all zero-dimensional homogeneous absolute Borel sets are obtained; it turns out that there are

ω
1

{\omega _1}

such spaces. We use results from game theory—particularly, about Wadge classes.
Maps which preserve ANRs
Authors: Yagasaki Tatsuhiko
Published: June 2010

It is shown that maps preserve ANR’s and

L

C

n

{\text {L}}{{\text {C}}^n}

-property if they satisfy a certain movability condition in the fiber shape theory. This generalizes the known results of hereditary shape equivalences to a non cell-like case.
Finitely presented modules over semiperfect rings
Authors: Rowen Louis H.
Published: June 2010

Results of Bjork and Sabbagh are extended and generalized to provide a Krull-Schmidt theory over a general class of semiperfect rings which includes left perfect rings, right perfect rings, and semiperfect PI-rings whose Jacobson radicals are nil.
On certain groups of central type
Authors: Espuelas Alberto
Published: June 2010

A finite group

G
G

is a group of central type if there exists

χ
∈

Irr

(
G
)

\chi \in {\text {Irr}}\left ( G \right )

with

χ

(
1
)

2

=

|

G
:
Z

(
G
)

|

\chi {\left ( 1 \right )^2} = \left | {G:Z\left ( G \right )} \right |

. It is known that, in such conditions,

G
G

is solvable. Here some conditions assuring the nilpotence of groups of central type are given.
Boundary continuity of holomorphic functions in the ball
Authors: Beatrous Frank
Published: June 2010

It is shown that any holomorphic function on the unit ball of

C

n

{{\mathbf {C}}^n}

with

n
n

th partial derivatives in the Hardy class

H
1

{H^1}

has a continuous extension to the closed unit ball, and that the restriction to any real analytic curve in the boundary which is nowhere complex tangential is absolutely continuous.