bluuebunny/crossref_metadata_2025 huggingface dataset:
Manifolds of almost half of the maximal volume
Authors: Durumeric Oguz C.
Published: June 2010

The Riemannian manifolds with sectional curvature

≥
1

\geq 1

and volume slightly less (in terms of the dimension and the upper bound of the sectional curvature) than

V
V

, the half of the volume of the standard sphere, are classified. The behavior of the critical points of the distance function on manifolds whose volume differ from

V
V

in terms of constructible constants in terms of the dimension is discussed.
Example of a 𝑇₁ topological space without a Noetherian base
Authors: Tamariz-Mascarúa Angel , Wilson Richard G.
Published: June 2010

A Noetherian base

B

\mathcal {B}

of a topological space

X
X

is a base for the topology of

X
X

which has the following property: If

B
1

⊂

B
2

⊂
⋯

{B_1} \subset {B_2} \subset \cdots

is a nondecreasing sequence of elements of

B

\mathcal {B}

, then

{

B
n

}

n
∈

N

{\left \{ {{B_n}} \right \}_{n \in {\mathbf {N}}}}

is finite. In this article we give an example of a

T
1

{T_1}

topological space without a Noetherian base.
The space of minimal prime ideals of 𝐶(𝑋) need not be basically disconnected
Authors: Dow A. , Henriksen M. , Kopperman Ralph , Vermeer J.
Published: June 2010

Problems posed twenty and twenty-five years ago by M. Henriksen and M. Jerison are solved by showing that the space of minimal prime ideals of the ring

C

(
X
)

C\left ( X \right )

of continuous real-valued functions on a compact (Hausdorff) space need not be basically disconnected—or even an

F
F

-space.
The inverse limit of the fundamental groups of branched cyclic coverings
Authors: Dellomo Michael
Published: June 2010

Cowsik and Swarup [CS] have shown that the homology groups of the infinite cyclic cover of a knot inject into the inverse limit of the homology groups of the branched cyclic covers. They also give conditions under which the injection is an isomorphism. We prove an analogous result for the fundamental group and generalize it to the case of links.
Almost Jordan rings
Authors: Hentzel Irvin Roy , Peresi Luiz Antonio
Published: June 2010

It is well known that any Jordan ring satisfies the identity:
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2 left-parenthesis left-parenthesis a x right-parenthesis x right-parenthesis x plus a left-parenthesis left-parenthesis x x right-parenthesis x right-parenthesis equals 3 left-parenthesis a left-parenthesis x x right-parenthesis right-parenthesis x">

2
(
(
a
x
)
x
)
x
+
a
(
(
x
x
)
x
)
=
3
(
a
(
x
x
)
)
x

2((ax)x)x + a((xx)x) = 3(a(xx))x

. We show that this identity along with commutativity implies the Jordan identity in any semiprime ring. The proof requires characteistic

≠
2
,
3

\ne 2,3

.
A nonlinear ergodic theorem for a reversible semigroup of Lipschitzian mappings in a Hilbert space
Authors: Ishihara Hajime , Takahashi Wataru
Published: June 2010

Let

C
C

be a nonempty closed convex subset of a Hilbert space,

S
S

a right reversible semitopological semigroup,

S

=
{

T
t

:
t
∈
S
}

\mathcal {S} = \{ {T_t}:t \in S\}

a continuous representation of

S
S

as Lipschitzian mappings on a closed convex subset

C
C

into

C
C

, and

F
(

S

)

F(\mathcal {S})

the set of common fixed points of mappings

T
t

,
t
∈
S

{T_t},t \in S

. Then we deal with the existence of a nonexpansive retraction

P
P

of

C
C

onto

F
(

S

)

F(\mathcal {S})

such that

P

T
t

=

T
t

P
=
P

P{T_t} = {T_t}P = P

for each

t
∈
S

t \in S

and

P
x

{P_x}

is contained in the closure of the convex hull of

{

T
t

x
:
t
∈
S

}

\left \{ {{T_t}x:t \in S} \right \}

for each

x
∈
C

x \in C

.
Subspaces of 𝐿_{𝑝,𝑞}
Authors: Carothers N. L. , Dilworth S. J.
Published: June 2010

We examine the subspace structure of the Lorentz function space

L

p
,
q

[
0
,
∞
)

{L_{p,q}}[0,\infty )

. Our main result is that a subspace of

L

p
,
q

[
0
,
∞
)
,
p
≠
2
,
q
>
∞

{L_{p,q}}[0,\infty ),p \ne 2,q > \infty

, must either strongly embed in

L
p

[
0
,
1
]

{L_p}[0,1]

or contain a complemented copy of

l
q

{l_q}

.
The visibility axiom on a Hadamard manifold whose geodesic flow is of Anosov type
Authors: Ukai Tetsuo
Published: June 2010

For a Hadamard manifold

M
M

, the set of points at infinity

M
(
∞
)

M(\infty )

is defined. If the geodesic flow on the unit tangent bundle of

M
M

is of Anosov type, then with a certain curvature condition

M
M

satisfies the Visibility Axiom. To prove this result, we use the Tits metric on

M
(
∞
)

M(\infty )

.
The isometry groups of compact manifolds with negative Ricci curvature
Authors: Katsuda Atsushi
Published: June 2010

We estimate the order of the isometry groups of compact manifolds with negative Ricci curvature in terms of geometric quantities: the sectional curvature, the Ricci curvature, the diameter, and the injectivity radius.
Independent statements about finite stretchable structures
Authors: McAloon K. , Ressayre J. P.
Published: June 2010

We consider several analogs of the theorem of Ehrenfeucht and Mostowski, in which the models generated by indiscernibles are finite; we show these analogs to be independent from strong axioms, ranging from Peano’s arithmetic to set theory with Mahlo cardinals.
Structure of generalized local rigid motion groups
Authors: Pantoja J. , Soto-Andrade J.
Published: June 2010

We consider the higher-order local field analogue of the real euclidean plane afforded by a Galois field extension of degree

n
n

, and we describe the structure of its corresponding "rigid motion" group

G
G

.
A characterization of complete intersection curves in 𝑃³
Authors: Strano Rosario
Published: June 2010

We prove the following theorem. Let

C
⊂

P

3

C \subset {{\mathbf {P}}^3}

be a reduced and irreducible curve not lying on a quadric. If the generic plane section

Γ
\Gamma

of

C
C

is a complete intersection then

C
C

is a complete intersection.
Karp’s theorem in electromagnetic scattering theory
Authors: Colton David , Kress Rainer
Published: June 2010

Karp’s Theorem for acoustic waves states that if the far field pattern of the scattered wave corresponding to a plane wave incident upon an obstacle is only a function of the scalar product of the directions of incidence and observation then the obstacle is a ball. In this paper we shall give the analogue of Karp’s Theorem for the scattering of electromagnetic waves by a perfect conductor.
On the nonsingular quadratic differential equations in the plane
Authors: Gasull A. , Llibre J.
Published: June 2010

We point out that the maximum number of inseparable leaves of nonsingular polynomial differential equations of degree two is 3, and we present an example with exactly 3 inseparable leaves.
Weakly compact cardinals and nonspecial Aronszajn trees
Authors: Shelah Saharon , Stanley Lee
Published: June 2010

Lemma 1. If

λ
\lambda

is a cardinal with cf

λ
>
ω

\lambda > \omega

, then

◻

λ

{\square _\lambda }

implies that there is a

λ
+

{\lambda ^ + }

-Aronszajn tree with an

ω
\omega

-ascent path, i.e. a sequence

(

x
¯

α

:
α
>

λ
+

)

\left ( {{{\bar x}^\alpha }:\alpha > {\lambda ^ + }} \right )

with each

x
¯

α

=

(

x
n
α

:
n
>
ω

)

{\bar x^\alpha } = \left ( {x_n^\alpha :n > \omega } \right )

a one-to-one sequence from

T
α

{T_\alpha }

, such that for all

α
>
β
>

λ
+

,

x
n
α

\alpha > \beta > {\lambda ^ + },x_n^\alpha

precedes

x
n
β

x_n^\beta

in the tree order for sufficiently large

n
n

. Lemma 2. If

λ
\lambda

is a cardinal with

cf
⁡
λ
=
ω
>
λ

\operatorname {cf} \lambda = \omega > \lambda

, then

◻

λ

{\square _\lambda }

implies that there is a

λ
+

{\lambda ^ + }

-Aronszajn tree with an

ω
1

{\omega _1}

-ascent path (replace

ω
\omega

by

ω
1

{\omega _1}

, above). Lemma 3. If

λ
\lambda

is an uncountable cardinal,

κ
\kappa

is regular,

κ
>
λ
,
cf
⁡
λ
≠
κ
,
T

\kappa > \lambda ,\operatorname {cf} \lambda \ne \kappa ,T

is a

λ
+

{\lambda ^ + }

-Aronszajn tree, and

(

x
i
α

:
i
>
κ

)

\left ( {x_i^\alpha :i > \kappa } \right )

is a one-to-one sequence from

T

ζ

(
α
)

{T_{\zeta \left ( \alpha \right )}}

with the property of ascent paths, where

ζ
:

λ
+

→

λ
+

\zeta :{\lambda ^ + } \to {\lambda ^ + }

is a monotone increasing function of

α
\alpha

, then

T
T

is nonspecial. Theorem 4. If

λ
\lambda

is uncountable, then

◻

λ

{\square _\lambda }

implies that there is a nonspecial

λ
+

{\lambda ^ + }

-Aronszajn tree. Theorem 5. If

λ
\lambda

is an uncountable cardinal,

κ
=

λ
+

\kappa = {\lambda ^ + }

, and

κ
\kappa

is not

(
w
e
a
k
l
y

c
o
m
p
a
c
t

)
L

{(weakly\;compact)^L}

, then there is a nonspecial

κ
\kappa

-Aronszajn tree.
Eventual extensions of finite codes
Authors: Boyle Mike
Published: June 2010

Suppose

S
S

and

T
T

are shift equivalent mixing shifts of finite type, and

f
f

is a conjugacy from a subsystem of

S
S

to a subsystem of

T
T

. Then for any sufficiently large

n
n

,

f
f

extends to a conjugacy of

S
n

{S^n}

and

T
n

{T^n}

. A consequence of the proof is a fortified version of Wagoner’s Stable FOG Theorem.
Characterizing Ω-stability for flows in the plane
Authors: Peixoto Maria Lúcia Alvarenga
Published: June 2010

In this paper, the

C
r

Ω

{C^r}\Omega

-stability for flows in the plane is characterized using the notion called "generalized recurrence" by J. Auslander [1].
Mathias forcing which does not add dominating reals
Authors: Canjar R. Michael
Published: June 2010

Assume that there is no dominating family of reals of cardinality

>
c

> c

. We show that there then exists an ultrafilter on the set of natural numbers such that its associated Mathias forcing does not adjoin any real which dominates all ground model reals. Such ultrafilters are necessarily

P
P

-points with no

Q
Q

-points below them in the Rudin-Keisler order.
Products and remote points: examples and counterexamples
Authors: Dow A. , Peters T. J.
Published: June 2010

Examples of products with remote points and counterexamples of products without remote points are given. The paradoxical behavior of remote points with respect to products is exhibited. Also, an example is given of spaces

X
X

and

Y
Y

, where neither

X
X

nor

Y
Y

has a

σ
\sigma

-locally finite

π
\pi

-base, but

X
×
Y

X \times Y

does.
On compact Hausdorff spaces of countable tightness
Authors: Balogh Zoltán T.
Published: June 2010

A general combinatorial theorem for countably compact, noncompact spaces is given under the Proper Forcing Axiom. It follows that compact Hausdorff spaces of countable tightness are sequential under PFA, solving the Moore-Mrowka Problem. Other applications are also given.
Completely bounded linear extensions of operator-valued functions on *-semigroups
Authors: Suen Ching Yun
Published: June 2010

Let

G
G

be a unital

∗
*

-semigroup [7, p. 1] in a unital (complex)

C
∗

{C^*}

-algebra such that the linear span of

G
G

is norm dense in it. Extending the results of [6], we have completely bounded linear extension theorems of operatorvalued functions on

G
G

. Applying extension theorems, we have that each regular bounded operator measure has the form

V
1
∗

F
(
)

V
2

V_1^*F(){V_2}

, where

V
1

{V_1}

and

V
2

{V_2}

are linear operators and

F
F

is a selfadjoint spectral operator measure.
Some special 2-generator Kleinian groups
Authors: Maskit Bernard
Published: June 2010

We explore the following question. Let

G
G

be the subgroup of

PSL

(
2
,

C

)

{\text {PSL}}(2,{\mathbf {C}})

generated by the elements

A
A

and

B
B

, where

A
A

has two fixed points, and

B
B

maps one fixed point of

A
A

onto the other; when is

G
G

discrete?
The conjugate property for Diophantine approximation of continued fractions
Authors: Tong Jing Cheng
Published: June 2010

Let

ξ
\xi

be an irrational number with simple continued fraction expansion

ξ
=
[

a
0

;

a
1

,
…
,

a
i

,
…
]

\xi = [{a_0};{a_1}, \ldots ,{a_i}, \ldots ]

, and

p
i

/

q
i

{p_i}/{q_i}

be its

i
i

th convergent. In this paper we first prove the duality of some inequalities, and then prove the following conjugate properties for symmetric and asymmetric Diophantine approximations. (i) Among any three consecutive convergents

p
i

/

q
i

(
i
=
n
−
1
,
n
,
n
+
1
)

{p_i}/{q_i}(i = n - 1,n,n + 1)

, at least one satisfies
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="xi minus p Subscript i Baseline slash q Subscript i Baseline vertical-bar greater-than 1 slash left-parenthesis StartRoot a Sub Superscript n plus 1 Subscript Superscript 2 Baseline plus 4 q Subscript i Superscript 2 Baseline EndRoot right-parenthesis comma">

ξ
−

p
i

/

q
i

|

>
1

/

(

a

n
+
1

2

+
4

q
i
2

)

,

\xi - {p_i}/{q_i}| > 1/\left ( {\sqrt {a_{^{n + 1}}^2 + 4q_i^2} } \right ),

\]
and at least one does not satisfy this inequality. (ii) Let

τ
\tau

be a positive real number. Among any four consecutive convergents

p
i

/

q
i

(
i
=
n
−
1
,
n
,
n
+
1
,
n
+
2
)

{p_i}/{q_i}(i = n - 1,n,n + 1,n + 2)

, at least one satisfies
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="negative 1 slash left-parenthesis StartRoot c Sub Superscript n Subscript Superscript 2 Baseline plus 4 tau q Subscript i Superscript 2 Baseline EndRoot right-parenthesis greater-than xi minus p Subscript i Baseline slash q Subscript i Baseline greater-than tau slash left-parenthesis StartRoot c Subscript n Superscript 2 Baseline plus 4 tau q Subscript i Superscript 2 Baseline EndRoot right-parenthesis comma">

−
1

/

(

c

n

2

+
4
τ

q
i
2

)

>
ξ
−

p
i

/

q
i

>
τ

/

(

c
n
2

+
4
τ

q
i
2

)

,

- 1/\left ( {\sqrt {c_{^n}^2 + 4\tau q_i^2} } \right ) > \xi - {p_i}/{q_i} > \tau /\left ( {\sqrt {c_n^2 + 4\tau q_i^2} } \right ),

\]
and at least one does not satisfy this inequality, where

c
n

=

a

n
+
1

{c_n} = {a_{n + 1}}

if

n
n

is odd,

c
n

=

a

n
+
2

{c_n} = {a_{n + 2}}

if

n
n

is even.
Closure properties of families of Cauchy-Stieltjes transforms
Authors: Hibschweiler R. A. , MacGregor T. H.
Published: June 2010

For

α
>
0

\alpha > 0

let

F

α

{\mathcal {F}_\alpha }

denote the class of functions defined for

|
z
|

>
1

\left | z \right | > 1

by integrating

1

/

(
1
−
x
z

)
α

1/{(1 - xz)^\alpha }

against a complex measure on

|
x
|

=
1

\left | x \right | = 1

. The main results in this paper assert that

F

α

{\mathcal {F}_\alpha }

is closed under multiplication by a function holomorphic for

|
z
|

≤
1

\left | z \right | \leq 1

and under composition with a function

φ
\varphi

holomorphic and satisfying

|

φ
(
z
)

|

>
1

\left | {\varphi (z)} \right | > 1

for

|
z
|

>
1

\left | z \right | > 1

when

α
≥
1

\alpha \geq 1

. The last result is shown to be false when

0
>
α
>
1

0 > \alpha > 1

.
Artinian duo rings and self-duality
Authors: Xue Wei Min
Published: June 2010

We show that the endomorphism ring of the minimal cogenerator over an Artinian duo ring is still an Artinian duo ring, and that an Artinian duo ring has self-duality if its Jacobson radical is a direct sum of colocal ideals.
The Cauchy functional equations in distributions
Authors: Koh E. L.
Published: June 2010

The Pompeiu functional equation is defined by Neagu for Schwartz distributions. His method is extended to the four Cauchy functional equations by means of two new operators

Q
∗

{Q^*}

and

R
∗

{R^*}

on

D

′

(
I
)

\mathcal {D}’(I)

. The Cauchy equations in distributions reduce to the classical equations when the solutions are regular distributions, i.e. locally integrable functions.
A recurrence related to trees
Authors: Knuth Donald E. , Pittel Boris
Published: June 2010

The asymptotic behavior of the solutions to an interesting class of recurrence relations, which arise in the study of trees and random graphs, is derived by making uniform estimates on the elements of a basis of the solution space. We also investigate a family of polynomials with integer coefficients, which may be called the "tree polynomials."
Finitely nonreflexive Banach spaces
Authors: Wójtowicz Marek
Published: June 2010

A Banach space

X
X

is said to be finitely nonreflexive if for some

n
≥
1

n \geq 1

the space

H
n

(
X
)

{H_n}(X)

is reflexive with

dim
⁡

H
n

(
X
)
≥
1

\dim {H_n}(X) \geq 1

, where

H
0

(
X
)
=
X

{H_0}(X) = X

, and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H Subscript n plus 1 Baseline left-parenthesis upper X right-parenthesis equals upper H Subscript n Baseline left-parenthesis upper X right-parenthesis Superscript asterisk asterisk Baseline slash upper H Subscript n Baseline left-parenthesis upper X right-parenthesis">

H

n
+
1

(
X
)
=

H
n

(
X

)

∗
∗

/

H
n

(
X
)

{H_{n + 1}}(X) = {H_n}{(X)^{**}}/{H_n}(X)

. A simple construction of (pairwise nonisomorphic) finitely nonreflexive separable Banach spaces which are both nonisomorphic to their Cartesian squares and isomorphic to their biduals is presented.
The normal index of a maximal subgroup of a finite group
Authors: Mukherjee N. P. , Bhattacharya Prabir
Published: June 2010

For a maximal subgroup

M
M

of a finite group

G
G

, the normal index

η
(
G
:
M
)

\eta (G:M)

is defined to be the order of a chief factor

H

/

K

H/K

where

H
H

is minimal in the set of supplements of

M
M

in

G
G

. We obtain several results on the normal index of maximal subgroups

M
M

of composite index in

G
G

with

[
G
:
M

]
p

=
1

{[G:M]_p} = 1

which imply

G
G

to be solvable, supersolvable.
The coefficients of Nevanlinna’s parametrization are not in 𝐻^{𝑝}
Authors: Nicolau A.
Published: June 2010

We construct an example of a Pick-Nevanlinna interpolation problem such that the coefficients of its Nevanlinna’s parametrization are not in

H
p

{H^p}

, for

p
>
0

p > 0

.
Meromorphic functions on a compact Riemann surface and associated complete minimal surfaces
Authors: Yang Kichoon
Published: June 2010

We prove that given any meromorphic function

f
f

on a compact Riemann surface

M
′

M’

there exists another meromorphic function

g
g

on

M
′

M’

such that

{

d
f
,
g

}

\left \{ {df,g} \right \}

is the Weierstrass pair defining a complete conformal minimal immersion of finite total curvature into Euclidean

3
3

-space defined on

M
′

M’

punctured at a finite set of points. As corollaries we obtain i) any compact Riemann surface can be immersed in Euclidean

3
3

-space as in the above with at most

4
p
+
1

4p + 1

punctures, where

p
p

is the genus of the Riemann surface; ii) any hyperelliptic Riemann surface of genus

p
p

can be so immersed with at most

3
p
+
4

3p + 4

punctures.
𝐿²-boundedness of spherical maximal operators with multidimensional parameter sets
Authors: Ha Young-Hwa
Published: June 2010

For

s
>
0

s > 0

, let
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M Subscript s Baseline f left-parenthesis x right-parenthesis equals integral Underscript StartAbsoluteValue y EndAbsoluteValue equals 1 Endscripts f left-parenthesis x minus s y right-parenthesis d sigma left-parenthesis y right-parenthesis">

M
s

f
(
x
)
=

∫

|

y

|

=
1

f
(
x
−
s
y
)
d
σ
(
y
)

{M_s}f(x) = \int _{|y| = 1} {f(x - sy)d\sigma (y)}

be the spherical mean operator on

R
n

{R^n}

. For a certain class of surfaces

S
S

in

R
+

n
+
1

R_ + ^{n + 1}

with

dim
⁡
S
=
n
−
2

\dim S = n - 2

or

dim
⁡
S
=
n
−
1

\dim S = n - 1

with an additional condition, the maximal operator
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper M f left-parenthesis x right-parenthesis equals sup Underscript left-parenthesis u comma s right-parenthesis element-of upper S Endscripts StartAbsoluteValue upper M Subscript s Baseline f left-parenthesis x minus u right-parenthesis EndAbsoluteValue">

M

f
(
x
)
=

sup

(
u
,
s
)
∈
S

|

M
s

f
(
x
−
u
)

|

\mathcal {M}f(x) = \sup \limits _{(u,s) \in S} |{M_s}f(x - u)|

\]
is shown to be bounded on

L
2

(

R
n

)

{L^2}({R^n})

. This extends (on

L
2

(

R
n

)

{L^2}({R^n})

) the theorem of Stein [7], where

S
=
{
(
0
,
s
)
:
s
>
0
}

S = \{ (0,s):s > 0\}

, and its generalizations to

dim
⁡
S
=
1

\dim S = 1

in Greenleaf [2] and Sogge and Stein [6].
Graded rings and Krull orders
Authors: Jespers Eric , Wauters Paul
Published: June 2010

Let

R
R

be a faithfully

S
S

-graded ring, where

S
S

is a submoniod of a torsion-free commutative group and

S
S

has no nontrivial units. In case

R
R

is a prime Krull order we give necessary and sufficient conditions for

R
R

to be a crossed product (respectively a polynomial ring).
A dichromatic polynomial for weighted graphs and link polynomials
Authors: Traldi Lorenzo
Published: June 2010

A dichromatic polynomial for weighted graphs is presented. The Kauffman bracket of a signed graph, an invariant inspired by the Jones polynomial of a link in three-space, is shown to be essentially an evaluation of this dichromatic polynomial, as are the homfly polynomials of certain particular types of links.
Conditional Yeh-Wiener integrals with vector-valued conditioning functions
Authors: Park Chull , Skoug David
Published: June 2010

In this paper we establish various results involving conditional Yeh-Wiener integrals with vector-valued conditioning functions. We first develop a very simple formula for converting conditional Yeh-Wiener integrals into ordinary (i.e., nonconditional) Yeh-Wiener integrals. We then use this simple formula to evaluate the conditional Yeh-Wiener integral of various functionals, including functionals in which the sectional average of an

L
2

{L_2}

-function occurs naturally. Finally, we use these results to obtain a general Cameron-Martin type translation theorem for conditional Yeh-Wiener integrals.
Strong homology and the proper forcing axiom
Authors: Dow Alan , Simon Petr , Vaughan Jerry E.
Published: June 2010

This paper concerns applications of set theory to the problem of calculating the strong homology of certain subsets of Euclidean spaces. We prove the set theoretic result that it is consistent that every almost coinciding family indexed by

ω

ω

^\omega \omega

is trivial (e.g., the proper forcing axiom implies this). This result, combined with results of S. Mardešić and A. Prasalov, show that the statement "the

k
k

-dimensional strong homology of

Y

(
k
+
1
)

{Y^{(k + 1)}}

(the discrete sum of countably many copies of the

(
k
+
1
)

(k + 1)

-dimensional Hawaiian earring) is trivial" is consistent with and independent of the usual axioms of set theory.
Characterizations of the conjugacy of Sylow 𝑝-subgroups of CC-groups
Authors: Otal J. , Peña J. M.
Published: June 2010

A group

G
G

is said to be a CC-group (group with Černikov conjugacy classes) if

G

/

C
G

(

x
G

)

G/{C_G}({x^G})

is a Černikov group for all

x
x

in

G
G

. In this paper we show the characterization of the conjugacy of the Sylow

p
p

-subgroups of such a group

G
G

in terms of the number of them and of the inner structure of

G
G

.
Refinable maps and 𝜃_{𝑛}-continua
Authors: Grace E. E. , Vought Eldon J.
Published: June 2010

Many properties of continua, e.g., irreducibility, span zero, and various kinds of aposyndesis and unicoherence, are preserved by refinable maps or their inverses. The purpose of this paper is to consider the extent to which the property of being a

θ
n
′

{\theta ’_n}

-continuum is preserved by refinable maps or by inverses of refinable maps. One consequence of this study is to generalize results of the first author where the domain or range is a graph. Several of his results are corollaries of ours.
A dynamical system on 𝑅³ with uniformly bounded trajectories and no compact trajectories
Authors: Kuperberg K. M. , Reed Coke S.
Published: June 2010

This paper contains an example of a rest point free dynamical system on

R
3

{R^3}

with uniformly bounded trajectories, and with no circular trajectories. The construction is based on an example of a dynamical system described by P. A. Schweitzer, and on an example of a dynamical system on

R
3

{R^3}

constructed previously by the authors.
A note on the Diophantine equation 𝑥^{2𝑝}-𝐷𝑦²=1
Authors: Le Mao Hua
Published: June 2010

Let

D
D

be a positive integer which is square free, and let

p
p

be a prime. In this note we prove that if

p
=
2

p = 2

and

D
>
exp
⁡
64

D > \exp 64

, then the equation

x

2
p

−
D

y
2

=
1

{x^{2p}} - D{y^2} = 1

has at most one positive integer solution

(

x
,
y

)

\left ( {x,y} \right )

; if

p
>
2

p > 2

and

D
>
exp
⁡
exp
⁡
exp
⁡
exp
⁡
10

D > \exp \exp \exp \exp 10

, then every positive integer solution

(

x
,
y

)

\left ( {x,y} \right )

can be expressed as

x
p

+
y

D

=

ε
1
m

{x^p} + y\sqrt D = \varepsilon _1^m

, where

m
m

is a positive integer with

2
∤
m
,

ε
1

2\nmid m,{\varepsilon _1}

is the fundamental solution of Pell’s equation

u
2

−
D

v
2

=
1

{u^2} - D{v^2} = 1

.
Graphs with parallel mean curvature
Authors: Salavessa Isabel Maria da Costa
Published: June 2010

We prove that if the graph

Γ
f

=

{

(

x
,
f

(
x
)

)

:
x
∈
M

}

{\Gamma _f} = \left \{ {\left ( {x,f\left ( x \right )} \right ):x \in M} \right \}

of a map

f
:

(

M
,
g

)

→

(

N
,
h

)

f:\left ( {M,g} \right ) \to \left ( {N,h} \right )

between Riemannian manifolds is a submanifold of

(

M
×
N
,
g
×
h

)

\left ( {M \times N,g \times h} \right )

with parallel mean curvature

H
H

, then on a compact domain

D
⊂
M

D \subset M

,

‖
H
‖

\left \| H \right \|

is bounded from above by

1
m

A

(

∂
D

)

V

(
D
)

\frac {1}{m}\frac {{A\left ( {\partial D} \right )}}{{V\left ( D \right )}}

. In particular,

Γ
f

{\Gamma _f}

is minimal provided

M
M

is compact, or noncompact with zero Cheeger constant. Moreover, if

M
M

is the

m
m

-hyperbolic space—thus with nonzero Cheeger constant—then there exist real-valued functions the graphs of which are nonminimal submanifolds of

M
×

R

M \times \mathbb {R}

with parallel mean curvature.
A result on nearness of functions and their regular 𝐶-fraction expansions
Authors: Jacobsen Lisa , Waadeland Haakon
Published: June 2010

We shall prove a "nearness"-result of the following type. If

f
(
w
)

f(w)

is a holomorphic function in

Ω
=
{
w
∈

C

;

|

arg
⁡
(
1
+
4
w
)

|

>
π
}

\Omega = \{ w \in {\mathbf {C}};\left | {\arg (1 + 4w)} \right | > \pi \}

and "sufficiently near" the function

(

1
+
4
w

−
1
)

/

2

(\sqrt {1 + 4w} - 1)/2

, then

f
(
w
)

f(w)

has a regular C-fraction expansion

K
(

a
n

w

/

1
)

K({a_n}w/1)

where

a
n

→
1

{a_n} \to 1

.
Remarks on the rigidity and stability of minimal submanifolds
Authors: Sakaki Makoto
Published: June 2010

We improve the pinching theorem of Simons and the stability theorem of Barbosa and do Carmo with an elementary method.
The number hides game
Authors: Baston V. J. , Bostock F. A. , Ferguson T. S.
Published: June 2010

We solve the following two-person zero-sum game, introduced by Ruckle. Players I and II simultaneously choose sequences of

m
m

and

n
n

consecutive integers respectively from the integers 1 to

p
p

inclusive. The payoff to I is the number of integers in the intersection of the two sequences. A continuous version of this game is also solved as well as the variations in which one of the players need not choose his integers consecutively.
An integrally closed ring which is not the intersection of valuation rings
Authors: Gräter Joachim
Published: June 2010

Each commutative ring

R
R

which is integrally closed in its total quotient ring

T
(
R
)

T(R)

is the intersection of all paravaluation rings of

T
(
R
)

T(R)

containing

R
R

. In this note an example is given that shows that this statement is not true with "valuation rings" instead of "paravaluation rings". This is an answer of a question asked by J. A. Huckaba in [3].
Each hyperinvariant subspace for a multiplication operator is spectral
Authors: Huang Sen Zhong
Published: June 2010

We consider multiplication operators on general separable complex

L
p

{L^p}

-spaces, for

1
≤
p
>
+
∞

1 \leq p > + \infty

, and obtain the result announced in the title. Moreover, a result of Douglas and Pearcy on normal operators is given an alternate proof.
Positive semidefinite forms over ordered skew fields
Authors: Leung Ka Hin
Published: June 2010

In any ordered field

K
K

, the inequality

x
2

+

y
2

≥
2
x
y

{x^2} + {y^2} \geq 2xy

obviously holds for any

x
,
y
∈
K

x,y \in K

. Naturally, we may ask if the same inequality holds in every ordered skew field. Surprisingly, it can be proved that in an ordered domain

R
R

, the above inequality holds for any elements

x
,
y

x,y

in

R
R

iff

R
R

is commutative. In this paper, we formulate a generalization of the above observation and prove that if a "positive semidefinite form" over an ordered skew field admits a "nontrivial" solution, then the skew field is actually a field.
Solvability of noninvariant differential operators on homogeneous spaces
Authors: Lipsman Ronald L.
Published: June 2010

We consider the solvability of non-invariant differential operators on homogeneous spaces. Such operators cannot be expected to have solutions in smooth functions (an illustrative example is provided). However, Lion has shown that, under suitable growth conditions on the infinitesimal components of the operators in a representation-theoretic decomposition, one can deduce solvability in a space of distributions. In this paper we prove that Lion’s result can be improved to yield solvability in square-integrable functions.
On the homotopy type of the spectrum representing elliptic cohomology
Authors: Baker Andrew
Published: June 2010

In this paper we analyse the homotopy type at primes

p
>
3

p > 3

of the ring spectrum

E
ℓ
ℓ

E\ell \ell

representing a version of elliptic cohomology whose coefficient ring

E
ℓ

ℓ
∗

E\ell {\ell _ * }

agrees with the ring of modular forms for

S

L
2

(

Z

)

S{L_2}(\mathbb {Z})

. For any prime (=maximal) graded ideal

P

◃
E
ℓ

ℓ
∗

\mathcal {P} \triangleleft E\ell {\ell _*}

containing the Eisenstein function

E

p
−
1

{E_{p - 1}}

as well as

p
p

, we show that there is a morphism of ring spectra
\[

E
(
2
)

^

→
(
E
ℓ
ℓ

)

P

^

\widehat {E(2)} \to (E\ell \ell )_{\hat {\mathcal {P}}}

\]
and a corresponding splitting
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper E script l script l right-parenthesis Subscript ModifyingAbove script upper P With caret Baseline asymptotically-equals logical-or Underscript i Endscripts normal upper Sigma Superscript 2 theta left-parenthesis i right-parenthesis Baseline ModifyingAbove upper E left-parenthesis 2 right-parenthesis With caret">

(
E
ℓ
ℓ

)

P

^

≃

⋁
i

Σ

2
θ
(
i
)

E
(
2
)

^

(E\ell \ell )_{\hat {\mathcal {P}}} \simeq \bigvee \limits _i {\Sigma ^{2\theta (i)}}\widehat {E(2)}

\]
of algebra spectra over

E
(
2
)

^

\widehat {E(2)}

(the

I
2

{I_2}

-adic completion of

E
(
2
)

E(2)

); here

(

)

P

^

(\;)_{\hat {\mathcal {P}}}

denotes the

P

\mathcal {P}

-adic completion of the spectrum

E
ℓ
ℓ

E\ell \ell

. Moreover, there is a multiplicative reduction

(
E
ℓ
ℓ

/

P

)
∗

(

)

{(E\ell \ell /\mathcal {P})^ * }(\;)

and we similarly show that there is a splitting of

K
(
2
)

K(2)

algebra spectra
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E script l script l slash script upper P asymptotically-equals logical-or Underscript i Endscripts normal upper Sigma Superscript 2 theta prime left-parenthesis i right-parenthesis Baseline upper K left-parenthesis 2 right-parenthesis period">

E
ℓ
ℓ

/

P

≃

⋁
i

Σ

2

θ
′

(
i
)

K
(
2
)
.

E\ell \ell /\mathcal {P} \simeq \bigvee \limits _i {\Sigma ^{2\theta ’(i)}}K(2).

\]
In each case the indexing

i
i

ranges over a finite set.
Fourier transforms and the Hermite-Biehler theorem
Authors: Csordas G. , Varga R. S.
Published: June 2010

A new necessary and sufficient condition for real entire functions, represented by Fourier transforms, to have only real zeros is proved. An application of this result to the Riemann

ξ
\xi

-function is also given.
Prime ideals in two-dimensional polynomial rings
Authors: Heinzer William , Wiegand Sylvia
Published: June 2010

We show that for every nonzero prime ideal

P
P

in a Noetherian domain

R
R

there are either just one or infinitely many prime ideals of the absolute integral closure of

R
R

lying over

P
P

. Using this result we show that if

R
R

is a semilocal countable one-dimensional Noetherian domain, then there exist just two possibilities for the prime ideal spectrum of

R
[
y
]

R[y]

, depending on whether or not

R
R

is Henselian.
On the preservation of Baire category under preimages
Authors: Noll Dominikus
Published: June 2010

We discuss the problem of preservation of Baire category under continuous and feebly open preimages. We obtain a solution by imposing a completeness condition on the fibres

f

−
1

(
y
)

{f^{ - 1}}(y)

of the function

f
f

under consideration. Based on a theorem on the invariance of residuality under continuous and nearly feebly open images, we also derive a result concerning the preservation of category under continuous and nearly feebly open preimages. We end up with an open mapping theorem for functions

f
f

of this kind defined on a Čech complete space.
A generalized Hölder inequality and a generalized Szegő theorem
Authors: Avram Florin , Brown Lawrence
Published: June 2010

We prove a limit theorem connected to graphs, which when the graph is a cycle reduces to Szego’s theorem for the trace of a product of Toeplitz matrices. The main tool used is a Holder type inequality for multiple integrals of functions which are applied to variables satisfying linear dependency relations.
Products of perfectly meager sets and Lusin’s function
Authors: Pawlikowski Janusz
Published: June 2010

In [R] Recław solved an old problem of Marczewski by constructing two perfectly meager sets with a non-perfectly meager cartesian product. We show another method for getting such sets.
Uniform persistence and repellors for maps
Authors: Hofbauer Josef , So Joseph W.-H.
Published: June 2010

We establish conditions for an isolated invariant set

M
M

of a map to be a repellor. The conditions are first formulated in terms of the stable set of

M
M

. They are then refined in two ways by considering (i) a Morse decomposition for

M
M

, and (ii) the invariantly connected components of the chain recurrent set of

M
M

. These results generalize and unify earlier persistence results.
Metrization of the one-point compactification
Authors: Mandelkern Mark
Published: June 2010

A new, more widely applicable, constructive definition of locally compact metric space is given, and a metric one-point compactification is constructed. Classically, this provides a simpler, more direct, construction of a metric on the one-point compactification of a separable locally compact metric space.
Weakly compact homomorphisms from 𝐶*-algebras are of finite rank
Authors: Mathieu Martin
Published: June 2010

We give a straightforward proof of the fact that every weakly compact homomorphism from a

C

∗

{{\text {C}}^ * }

-algebra is a finite rank operator.
The image of 𝐻_{∗}(𝐵𝑆𝑂;𝑍₂) in 𝐻_{∗}(𝐵𝑂;𝑍₂)
Authors: Papastavridis Stavros
Published: June 2010

We construct explicit polynomial generators of the image of

H
∗

(
B
S
O
;

Z
2

)

{H_ * }(BSO;{Z_2})

in

H
∗

(
B
O
;

Z
2

)

{H_ * }(BO;{Z_2})

.
Sums and products of Hilbert spaces
Authors: Castillo Jesús M. F.
Published: June 2010

Let

H
H

be a Hilbert space. We prove that the locally convex sum

⊕
I

H

{ \oplus _I}H

is a subspace of the product

H
J

{H^J}

if and only if

I
I

is countable,

H
H

is infinite dimensional, and card

J
≥

2

ℵ
0

J \geq {2^{{\aleph _0}}}

.
Covers of Dehn fillings on once-punctured torus bundles. II
Authors: Baker Mark D.
Published: June 2010

Let

M
M

be a compact, orientable

3
3

-manifold that fibers over

S
1

{S^1}

with fiber a once-punctured torus. We prove that infinitely many Dehn fillings on

M
M

yield manifolds with virtually

Z

\mathbb {Z}

-representable fundamental groups.
On a Lipschitz invariant of normed spaces
Authors: Benyamini Yoav
Published: June 2010

C. Bessaga introduced an invariant

η
(
X
)

\eta (X)

for

σ
\sigma

-compact normed linear spaces. He showed that

η
(
X
)
=
η
(
Y
)

\eta (X) = \eta (Y)

whenever

X
X

and

Y
Y

are Lipschitz homeomorphic. In this note we construct two

σ
\sigma

-compact normed spaces with

η
(
X
)
=
η
(
Y
)

\eta (X) = \eta (Y)

which are not Lipschitz homeomorphic. Moreover, there are no compact convex sets

K
K

and

L
L

generating

X
X

and

Y
Y

, respectively, which are Lipschitz homeomorphic. This answers two problems posed by Bessaga.
A nullset for normal functions in several variables
Authors: Riihentaus Juhani
Published: June 2010

Suppose that

Ω
\Omega

is a domain in

C
n

,
E
⊂
Ω

{C^n},E \subset \Omega

is closed in

Ω
\Omega

, and

f
:
Ω
∖
E
→

C
∗

f:\Omega \backslash E \to {C^ * }

is a meromorphic function. We show that if

f
f

is normal and

E
E

is an analytic subvariety or, more generally, of locally finite

(
2
n
−
2
)

(2n - 2)

-dimensional Hausdorff measure in

Ω
\Omega

satisfying a certain geometric condition, then

f
f

can be extended to a meromorphic function (= holomorphic mapping)

f
∗

:
Ω
→

C
∗

{f^ * }:\Omega \to {C^ * }

. In the case of a subvariety sufficient, but not necessary, for the geometric condition is that the singularities of

E
E

are normal crossings. As a digression, we give a new proof for the following result, due to Parreau in the case

n
=
1

n = 1

: if

f
f

is in the Nevanlinna class and

E
E

is polar (in

R

2
n

{R^{2n}}

), then

f
f

has a meromorphic extension

f
∗

{f^ * }

to

Ω
\Omega

.
The Cesàro means and strong laws of large numbers for orthogonal sequences in von Neumann algebras
Authors: Hensz Ewa
Published: June 2010

The extension of Moricz’s strong law of large numbers to the von Neumann algebras context is given.
A short solution of Markov’s problem on connected group topologies
Authors: Remus Dieter
Published: June 2010

In 1945 A. A. Markov posed a problem concerning the existence of connected group topologies that was recently solved by V. G. Pestov. In this note, a short and independent solution is given.
Index and total curvature of surfaces with constant mean curvature
Authors: do Carmo Manfredo P. , Da Silveira Alexandre M.
Published: June 2010

We prove an analogue, for surfaces with constant mean curvature in hyperbolic space, of a theorem of Fischer-Colbrie and Gulliver about minimal surfaces in Euclidean space. That is, for a complete surface

M
2

{M^2}

in hyperbolic

3
3

-space with constant mean curvature 1, the (Morse) index of the operator

L
=
Δ
−
2
K

L = \Delta - 2K

is finite if and only if the total Gaussian curvature is finite.
Characteristics of index one orbits of Morse-Smale diffeomorphisms
Authors: Holmgren Richard A.
Published: June 2010

We use Lyapunov functions to find restrictions on the periodic data of index one orbits of Morse-Smale diffeomorphisms. The resulting structure is then used to find connections between index one orbits.
Lower 2-estimates for sequences in Banach lattices
Authors: Räbiger Frank
Published: June 2010

We characterize Banach lattices in which every bounded sequence contains a subsequence which either converges in norm or satisfies a lower

2
2

-estimate. As a consequence we obtain, for the class of all Banach lattices, a positive answer to a question of D.J. Aldous and D.H. Fremlin whether a Banach space of cotype 2 satisfies the above-mentioned property.
The range of a vector measure determines its total variation
Authors: Rodríguez-Piazza Luis
Published: June 2010

We prove that if the ranges of two finitely additive measures with values in a normed space have the same closed convex hull, then the measures have the same total variation. We also study the monotonicity of this variation with respect to the range, proving that a normed space

X
X

is

C
C

-isomorphic to a subspace of an

L
1

{L^1}

space if and only if, for every pair

μ
,
ν

\mu ,\nu

of

X
X

-valued measures such that the range of

μ
\mu

lies inside the closed convex hull of the range of

ν
\nu

, the total variation of

μ
\mu

is less than or equal to

C
C

times the total variation of

ν
\nu

. This allows us to answer two questions raised by R. Anantharaman and J. Diestel.
Exponential sums and Goppa codes. I
Authors: Moreno Carlos J. , Moreno Oscar
Published: June 2010

A bound is obtained which generalizes the Carlitz-Uchiyama result, based on a theorem of Bombieri and Weil about exponential sums. This new bound is used to estimate the covering radius of long binary Goppa codes. A new lower bound is also derived on the minimum distance of the dual of a binary Goppa code, similar to that for BCH codes. This is an example of the use of a number-theory bound for the problem of the estimation of minimum distance of codes, as posed in research problem 9.9 of Mac Williams and Sloane, The Theory of Error Correcting Codes.
Ultraseparating function spaces and operating functions for the real part of a function algebra
Authors: Briem Eggert
Published: June 2010

We show how a local version of a result due to A. Bernard on ultraseparating Banach function spaces can be used to give a short proof of the theorem stating that only affine functions operate on the real part of a function algebra.
Stability in interpolation of families of Banach spaces
Authors: Cao Wei , Sagher Yoram
Published: June 2010

Let

D
D

be a simply connected domain in the complex plane whose boundary

Γ
\Gamma

is a rectifiable simple closed curve. Let

{

A
(
γ
)

/

γ
∈
Γ

}

\left \{ {A(\gamma )/\gamma \in \Gamma } \right \}

and

{

B
(
γ
)

/

γ
∈
Γ

}

\left \{ {B(\gamma )/\gamma \in \Gamma } \right \}

be interpolation families of Banach spaces. Let

T
T

be a linear operator mapping

A
(
γ
)

A(\gamma )

continuously into

B
(
γ
)

B(\gamma )

. For

z
∈
D

z \in D

let

T
z

{T_z}

be the restriction of

T
T

to the interpolation space

A
z

{A_z}

. Then

{
z
∈
D

/

cod
⁡
(

T
z

)
=
d
>
∞

\{ z \in D/\operatorname {cod}(T_z) = d > \infty

and

dim
⁡
Ker
⁡
(

T
z

)
=
0
}

\dim \operatorname {Ker}({T_z}) = 0 \}

and

{
z
∈
D

/

dim
⁡
Ker
⁡
(

T
z

)
=
d
>
∞

\{ z \in D/\dim \operatorname {Ker}(T_z) = d > \infty

and

T
z

T_z

is onto

B
z

}

B_z\}

are open sets.
Representations of 𝑆𝑂(𝑘,𝐶) on harmonic polynomials on a null cone
Authors: Debarre Olivier , Ton-That Tuong
Published: June 2010

The linear action of the group

S
O
(
k
,

C

)

SO(k,{\mathbf {C}})

on the vector space

C

n
×
k

{{\mathbf {C}}^{n \times k}}

extends to an action on the algebra of polynomials on

C

n
×
k

{{\mathbf {C}}^{n \times k}}

. The polynomials that are fixed under this action are called

S
O
(
k
,

C

)

SO(k,{\mathbf {C}})

-invariant. The

S
O
(
k
,

C

)

SO(k,{\mathbf {C}})

-harmonic polynomials are common solutions of the

S
O
(
k
,

C

)

SO(k,{\mathbf {C}})

-invariant differential operators. The ideal of all

S
O
(
k
,

C

)

SO(k,{\mathbf {C}})

-invariants without constant terms, the null cone of this ideal, and the orbits of

S
O
(
k
,

C

)

SO(k,{\mathbf {C}})

on this null cone are studied in great detail. All irreducible holomorphic representations of

S
O
(
k
,

C

)

SO(k,{\mathbf {C}})

are concretely realized on the space of

S
O
(
k
,

C

)

SO(k,{\mathbf {C}})

-harmonic polynomials.
The neat embedding problem and the number of variables required in proofs
Authors: Maddux Roger D.
Published: June 2010

By constructing special relation algebras we show that if

3
>
α
>
ω

3 > \alpha > \omega

, then
\[

S

N

r

3

C

A
α

≠

S

N

r

3

C

A

3
α
−
7

{\mathbf {S}}N{{\text {r}}_3}C{A_\alpha } \ne {\mathbf {S}}N{{\text {r}}_3}C{A_{3\alpha - 7}}

\]
and there is a logically valid first-order sentence containing at most three variables with a proof in which every sentence has at most

3
α
−
7

3\alpha - 7

variables, but no proof in which every sentence has at most a variables.
Index of faithful normal conditional expectations
Authors: Tsui Sze-Kai
Published: June 2010

Let

E
E

be a faithful normal conditional expectation of a factor

M
M

onto its subfactor

N
N

, and the index of

E
E

be denoted by

IND
E

{\operatorname {IND}_E}

. We investigate the question: For two such faithful normal conditional expectations

E
1

,

E
2

{E_1},{E_2}

of

M
M

onto

N
N

, when does

IND

E
1

=

IND

E
2

{\operatorname {IND}}_{{E_1}} = {\operatorname {IND}}_{{E_2}}

hold? In this paper we answer this question completely for type

I
I

factor

M
M

. We also derive a tensor product formula for index, i.e.,
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper I upper N upper D Subscript upper E 1 circled-times upper E 2 Baseline equals left-parenthesis upper I upper N upper D Subscript upper E 1 Baseline right-parenthesis left-parenthesis upper I upper N upper D Subscript upper E 2 Baseline right-parenthesis">

IND

E
1

⊗

E
2

=
(

IND

E
1

)
(

IND

E
2

)

{\operatorname {IND}}_{{E_1} \otimes {E_2}} = ({\operatorname {IND}}_{{E_1}})({\operatorname {IND}}_{{E_2}})

. For any

α
>
9

\alpha > 9

we construct uncountable nonisomorphic faithful normal conditional expectations

E
E

of a factor

M
M

onto its subfactor

N
N

with

IND
E

=
α

{\operatorname {IND}_E} = \alpha

such that both of

M
M

and

N
N

, are of type

I
I

or

I
I

II

or

I
I

I
λ

,
0
≤
λ
≤
1

II{I_\lambda },0 \leq \lambda \leq 1

. For each

β
∈
{
4

cos
2

π

/

n
,

|

n
≥
3
}
∪
[
4
,
∞
)

\beta \in \{ 4{\cos ^2}\pi /n,|n \geq 3\} \cup [4,\infty )

we exhibit a type

I
I

I
λ

II{I_\lambda }

factor

M
M

and its subfactor

N
N

and a faithful normal conditional expectation

E
E

such that

IND

E

=
β

{\operatorname {IND}}_E = \beta

.
On the clustering conjecture for Bernoulli factors of Bernoulli shifts
Authors: Keller G.
Published: June 2010

We give sufficient algebraic conditions on the probabilities

p
i

{p_i}

of a Bernoulli shift

B
(

p

)

 = 

B
(

p
1

,
…
,

p
M

)

B({\mathbf {p}}){\text { = }}B({p_1}, \ldots ,{p_M})

which imply that if

B
(

q

)
=
B
(

q
1

,
…
,

q
N

)

B({\mathbf {q}}) = B({q_1}, \ldots ,{q_N})

is a continuous factor of

B
(

p

)

B({\mathbf {p}})

, then

q

{\mathbf {q}}

is a clustering of

p

{\mathbf {p}}

.
Self-similar sets. V. Integer matrices and fractal tilings of 𝑅ⁿ
Authors: Bandt Christoph
Published: June 2010

Tilings with self-similar tiles and "just-touching fractals" are constructed from matrices of integers, extending work by Levy, Mandelbrot, Dekking, Bedford, and others.
Bernstein-type inequalities for the derivatives of constrained polynomials
Authors: Erdélyi Tamás
Published: June 2010

Generalizing a number of earlier results, P. Borwein established a sharp Markov-type inequality on

[
−
1
,
1
]

[ - 1,1]

for the derivatives of polynomials

p
∈

π
n

p \in {\pi _n}

having at most

k
(
0
≤
k
≤
n
)

k(0 \leq k \leq n)

zeros in the complex unit disk. Using Lorentz representation and a Markov-type inequality for the derivative of Müntz polynomials due to D. Newman, we give a surprisingly short proof of Borwein’s Theorem. The new result of this paper is to obtain a sharp Bernstein-type analogue of Borwein’s Theorem. By the same method we prove a sharp Bernstein-type inequality for another wide family of classes of constrained polynomials.
Radon-Nikodým theorems for multimeasures and transition multimeasures
Authors: Papageorgiou Nikolaos S.
Published: June 2010

In this paper we prove two set valued Radon-Nikodym theorems. One for simple multimeasures and the other for transition multimeasures. In the process of proving the second theorem, we obtain a result concerning transition selectors of transition multimeasures, which is of independent interest.
Criteria for the extremality of the Koebe mapping
Authors: Bshouty D. , Hengartner W.
Published: June 2010

A criterion is developed which gives a necessary condition on a real functional in order that the Koebe Mapping be extremal for this functional in the well known class

S
S

of normalized univalent functions. This is applied to the coefficient problem of

[
f
(
z
)

]
λ

,
0
>
λ
>
1

{[f(z)]^\lambda },0 > \lambda > 1

as well as to the problem of univalence of sections of the power series expansion of

f
(
z
)

f(z)

.
The span and semispan of some simple closed curves
Authors: Tkaczyńska Katarzyna
Published: June 2010

The spans of simple closed curves that are boundaries of convex regions are determined. The following question of Lelek is answered affirmatively for these curves: Are the span and the semispan of a simple closed curve equal? The same answer is obtained in the case of nonconvex quadrilaterals.