bluuebunny/crossref_metadata_2025 huggingface dataset:
Solvable groups with 𝜋-isolators
Authors: Rhemtulla A. H. , Weiss A. , Yousif M.
Published: July 2010

Let

π
\pi

be any nonempty set of prime numbers. A natural number is a

π
\pi

-number precisely if all of its prime factors are in

π
\pi

. A group

G
G

is said to have the

π
\pi

-isolator property if for every subgroup

H
H

of

G
G

, the set

π

H

=
{
g
∈
G
;

g
n

∈
H

^\pi \sqrt H = \{ g \in G;{g^n} \in H

is a subgroup of

G
G

. It is well known that nilpotent groups have the

π
\pi

-isolator property for any nonempty set

π
\pi

of primes. Finitely generated solvable linear groups with finite Prüfer rank, and in particular polycyclic groups, have subgroups of finite index with the

π
\pi

-isolator property if

π
\pi

is the set of all primes. It is shown here that if

π
\pi

is any finite nonempty set of primes and

G
G

is a finitely generated solvable group, then

G
G

has a subgroup of finite index with the

π
\pi

-isolator property if and only if

G
G

is nilpotent-by-finite.
Equationally complete discriminator varieties of groupoids
Authors: Quackenbush Robert W.
Published: July 2010

J. Kalicki proved that there are continuum many equationally complete varieties of groupoids. In this note we give a constructive proof of this by defining a countable partial groupoid which has continuum many completions such that each completion generates an equationally complete variety, and no two distinct completions generate the same variety. Moreover, the variety generated by all the completions is a discriminator variety, and every nontrivial groupoid in this variety is cancellative but not a quasigroup; this answers a question of R. Padmanabhan. A. D. Bol’bot proved a similar result for loops, but his computations are more difficult since his varieties are not discriminator varieties.
On the number of locally bounded field topologies
Authors: Cohen Jo-Ann D.
Published: July 2010

Kiltinen has proven that there exist

2

|
F
|

{2^{\left | F \right |}}

first countable, locally bounded field topologies (the maximum number possible) on a field

F
F

of infinite transcendence degree over its prime subfield. We consider those fields

F
F

of countable transcendence degree over its prime subfield

E
E

. In particular it is shown that if the characteristic of

F
F

is zero and the transcendence degree of

F
F

over

E
E

is nonzero or if

F
F

is a field of prime characteristic and the transcendence degree of

F
F

over

E
E

is greater than one, then there exist

2

|
F
|

{2^{\left | F \right |}}

normable, locally bounded field topologies on

F
F

.
A representation theorem for semilattices
Authors: Bredikhin D. A.
Published: July 2010

We prove that every semilattice

(
L
,
∧
)

(L, \wedge )

admits an embedding

Q
Q

into the set

R
(
X
)

R(X)

of all partial orders on some set

X
X

such that for all

a
a

,

b
∈
L

b \in L

,

Q
(
a
∧
b
)
=
Q
(
a
)
∩
Q
(
b
)

Q(a \wedge b) = Q(a) \cap Q(b)

and if

a
∨
b

a \vee b

exists then also

Q
(
a
∨
b
)
=
Q
(
b
)
∘
Q
(
a
)

Q(a \vee b) = Q(b) \circ Q(a)

.
Approximately transitive diffeomorphisms of the circle
Authors: Hawkins J. , Woods E. J.
Published: July 2010

We prove that every

C
3

{C^3}

diffeomorphism of the circle with an irrational rotation number (and some

C
2

{C^2}

diffeomorphisms as well) are approximately transitive. This provides a class of examples of approximately transitive transformations which are smooth but non-measure-preserving.
Probability measure representation of norms associated with the notion of entropy
Authors: Dąbrowski Romuald
Published: July 2010

One of the applications of Banach spaces introduced by B. Korenblum [1,2] is a new convergence test [2] for Fourier series including both Dirichlet-Jordan and the Dini-Lipschitz tests [3], The norms of the spaces are given in terms of

κ
\kappa

-entropy where

κ

(
s
)

⩾
0

\kappa \left ( s \right ) \geqslant 0

,

0

 > 

s
⩽
1

0{\text { > }}s \leqslant 1

, is a nondecreasing concave function such that

κ

(
1
)

=
1

\kappa \left ( 1 \right ) = 1

. The

κ
\kappa

-norms fill the gap between the uniform and the variation norms. The original proof of the general properties of

κ
\kappa

-norms uses both combinatorial and approximation arguments which are rather complicated. We give a simple proof introducing a probabilistic representation of the norms so that the

κ
\kappa

-norm of a real function

f
f

on

T
=
R

/

2
π
Z

T = R / 2\pi Z

is the expectation of the mean oscillation of

f
f

on a subinterval of

T
T

, chosen in a suitable random process.
Reflexivity of a Banach space with a uniformly normal structure
Authors: Bae Jong Sook
Published: July 2010

In this note we prove that any Banach space with a uniformly normal structure is reflexive.
A note on an oscillation criterion for an equation with damped term
Authors: Yan Ju Rang
Published: July 2010

A new oscillation criterion is given for the equation

x

(
t
)

+
p

(
t
)

x
′

(
t
)

+
q

(
t
)

x

(
t
)

=
0

x\left ( t \right ) + p\left ( t \right )x’\left ( t \right ) + q\left ( t \right )x\left ( t \right ) = 0

,

t
∈
[

t
o

,
∞
)

t \in [{t_o},\infty )

, where

p

(
t
)

p\left ( t \right )

and

q

(
t
)

q\left ( t \right )

are allowed to change sign on

[

t
0

,
∞
)

[{t_0},\infty )

.
Continuity of measurable convex and biconvex operators
Authors: Thibault Lionel
Published: July 2010

We prove that a mapping from the product of two complete metrizable vector spaces into a topological vector space which is separately universally measurable and separately convex with respect to a convex cone is continuous.
Quand l’espace des mesures à variation bornée est-il faiblement séquentiellement complet?
Authors: Talagrand Michel
Published: July 2010

We construct a Banach lattice

E
E

which does not contain

c
0

{c_0}

(hence is weakly sequentially complete), but such that the lattice of

E
E

-valued measures of bounded variation contains

c
0

{c_0}

.
Stability of typical continuous functions with respect to some properties of their iterates
Authors: Smítal J. , Neubrunnová K.
Published: July 2010

Let

I
I

be a real compact interval, and let

C
C

be the space of continuous functions

I
→
I

I \to I

with the uniform metric. For

f
∈
C

f \in C

denote
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="nu left-parenthesis f right-parenthesis equals sup Underscript x element-of upper I Endscripts left-parenthesis limit sup Underscript n right-arrow x Endscripts f Superscript n Baseline left-parenthesis x right-parenthesis minus limit inf Underscript n right-arrow x Endscripts f Superscript n Baseline left-parenthesis x right-parenthesis right-parenthesis">

ν
(
f
)
=

sup

x
∈
I

(
lim

sup

n
→
x

f
n

(
x
)
−
lim

inf

n
→
x

f
n

(
x
)
)

\nu (f) = {\sup _{x \in I}}(\lim {\sup _{n \to x}}{f^n}(x) - \lim {\inf _{n \to x}}{f^n}(x))

, where

f
n

{f^n}

is the

n
n

th iterate of

f
f

. Then for each positive

d
d

there is an open set

C
∗

{C^*}

dense in

C
C

such that the oscillation of

v
v

at each point of

C
∗

{C^*}

is less than

d
d

. Consequently,

ν
\nu

is continuous in

C
C

except of the points of a first Baire category set.
A structure theorem for the polars of unitarily invariant norms
Authors: Mudholkar Govind S. , Freimer Marshall
Published: July 2010

The unitarily invariant norms of matrices, or operators, are essentially the symmetric norms of their singular values. A subclass of these norms depending upon only a few largest of the singular values is considered, and the polars of these norms are characterized. The result is then used to obtain generalizations of some well-known inequalities. The implications for operators on infinite-dimensional spaces are discussed.
On 𝐺-systems and 𝐺-graded rings
Authors: Grzeszczuk P.
Published: July 2010

Rings graded by finite groups and homomorphic images of such rings are studied. Obtained results concern finiteness conditions and radicals.
Positive definite bounded matrices and a characterization of amenable groups
Authors: Bożejko Marek
Published: July 2010

We show that a discrete group

G
G

is amenable iff the Herz-Schur multiplier algebra

B
2

(
G
)

{B_2}(G)

coincides with the Fourier-Stieltjes algebra

B
(
G
)

B(G)

.
The potential 𝒥-relation and amalgamation bases for finite semigroups
Authors: Hall T. E. , Putcha Mohan S.
Published: July 2010

Let

S
S

be a finite semigroup,

a
,
b
∈
S

a,b \in S

. When does there exist a finite semigroup

T
T

containing

S
S

such that

a

J

b

a\mathcal {J}b

in

T
T

? This problem was posed to the second named author by John Rhodes in 1974. We show here that if

a
a

,

b
b

are regular, then such a semigroup

T
T

exists if and only if either

a

J

b

a\mathcal {J}b

in

S
S

, or

a
∉
S
b
S

a \notin SbS

and

b
∉
S
a
S

b \notin SaS

. We use this result to show that analgamation bases for the class of finite semigroups have linearly ordered

J

\mathcal {J}

-classes.
On some properties of the Banach algebras 𝐴_{𝑝}(𝐺) for locally compact groups
Authors: Granirer Edmond E.
Published: July 2010

We strengthen and improve theorems of Choquet-Deny and of Foguel concerning convolution equations and iterates of convolution of a measure to all algebras

A
p

(
G
)

{A_p}(G)

and all locally compact groups. Furthermore, we improve results of H. P. Rosenthal on ideals of

A
(
G
)

A(G)

to the algebras

A
p

(
G
)

{A_p}(G)

and show that some hold for amenable groups but not for free nonabelian groups. Finally, we improve a (possibly) weak version of a theorem of Gilbert on projections onto some subspaces of

L
∞

(
G
)

{L^\infty }(G)

to all locally compact groups.
On the spectra of 𝐶₁₁-contractions
Authors: Bercovici H. , Kérchy L.
Published: July 2010

We give a complete characterization of the closed subsets of the complex plane that can serve as spectra of completely nonunitary contractions of class

C

11

{C_{11}}

.
A Hörmander type criterion for quasiradial Fourier multipliers
Authors: Dappa Henry , Luers Hajo
Published: July 2010

We state practicable sufficient conditions on quasi-radial functions

m
∘
ρ
(
ξ
)
=
m
(
ρ
(
ξ
)
)

m \circ \rho (\xi ) = m(\rho (\xi ))

to be Fourier multipliers in

L
p

(

R

n

)

{L^p}({{\mathbf {R}}^n})

. Here

m
m

is a bounded function and

ρ
\rho

is a homogeneous distance function. The conditions on

m
m

are given in terms of localized Bessel potentials and those on

ρ
\rho

reflect and generalize basic properties of the norm in

R

n

{{\mathbf {R}}^n}

. The results are related to those of Madych [7] and Fabes and Rivière [3] and improve their results (specialized to quasi-radial multipliers). The proof utilizes Madych’s approach [7] and interpolation properties of localized Bessel potential spaces [2].
Structure of the efficient point set
Authors: Lục Đinh The
Published: July 2010

Let

C
C

be a nontrivial cone and

X
X

be a set in the

n
n

-dimensional Euclidean space. Denote by

E

(
X

|

C
)

{\text {E}}(X|C)

the set of all efficient points of

X
X

with respect to

C
C

. It will be proven that under some adequate assumptions

E

(
X

|

C
)

{\text {E}}(X|C)

is homeomorphic to a simplex while

n
=
2

n = 2

, and for

n
>
2

n > 2

it is a contractible set. Furthermore, the set of all weak efficient points of

X
X

with respect to

C
C

is arcwise connected and its local contractibility is equivalent to being a retract of

X
X

. The results presented in this study cover all topological properties of the efficient point set which have been obtained by Peleg and Morozov for the case when

C
C

is the nonnegative orthant.
A nonlinear boundary problem
Authors: Hatcher John R.
Published: July 2010

A nonlinear Hilbert problem of power type is solved in closed form by representing a sectionally holomorphic function by means of an integral with power kernel. This technique transforms the problem to one of solving an integral equation of the generalized Abel type.
Minimal projections and absolute projection constants for regular polyhedral spaces
Authors: Chalmers Bruce L. , Shekhtman Boris
Published: July 2010

Let

V
=
[

v
1

,
…
,

v
n

]

V = [{v_1}, \ldots ,{v_n}]

be the

n
n

-dimensional space of coordinate functions on a set of points

v
~

⊂

R

n

\tilde v \subset {{\mathbf {R}}^n}

where

v
~

\tilde v

is the set of vertices of a regular convex polyhedron. In this paper the absolute projection constant of any

n
n

-dimensional Banach space

E
E

isometrically isomorphic to

V
⊂
C
(

v
~

)

V \subset C(\tilde v)

is computed, examples of which are the well-known cases

E
=

l
n
∞

,

l
n
1

E = l_n^\infty ,l_n^1

.
Weak convergence of the empirical characteristic function
Authors: Yukich J. E.
Published: July 2010

Let

P
P

be a probability measure on

R

{\mathbf {R}}

such that the density

f
(
x
)

f(x)

for

P
P

exists and there exists

x
0

>
0

{x_0} > 0

such that

f
(
x
)
+
f
(
−
x
)

f(x) + f( - x)

is decreasing for all

|
x
|

⩾

x
0

\left | x \right | \geqslant {x_0}

. Let

c
(
t
)

c(t)

be the characteristic function for

P
P

,

c
n

(
t
)

{c_n}(t)

the empirical characteristic function, and let
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Subscript n Baseline left-parenthesis t right-parenthesis colon equals n Superscript 1 slash 2 Baseline left-parenthesis c Subscript n Baseline left-parenthesis t right-parenthesis minus c left-parenthesis t right-parenthesis right-parenthesis">

C
n

(
t
)
:=

n

1

/

2

(

c
n

(
t
)
−
c
(
t
)
)

{C_n}(t): = {n^{1/2}}({c_n}(t) - c(t))

. New necessary and sufficient metric entropy conditions are obtained for the weak convergence of

C
n

(
t
)

{C_n}(t)

on the space of continuous complex valued functions on

[
−

1
2

,

1
2

]

[ - \tfrac {1}{2},\tfrac {1}{2}]

. The result is used to characterize the weak convergence of

C
n

(
t
)

{C_n}(t)

in terms of the tail behavior of

P
P

and it also provides the first step towards a generalization of the Borisov-Dudley-Durst theorem. It also provides a partial response to a challenge raised by Dudley.
Orbits of higher-dimensional hereditarily indecomposable continua
Authors: Rogers James T.
Published: July 2010

Let

X
X

be a continuum. The following theorems are proved. Theorem. If

dim
⁡
X
>
1

\dim X > 1

, then

X
X

contains uncountably many nonhomeomorphic continua. Theorem. If

dim
⁡
X
>
1

\dim X > 1

and

X
X

is hereditarily indecomposable, then

X
X

has uncountably many orbits under the action of its homeomorphism group.
Sets of recurrent points of continuous maps of the interval
Authors: Xiong Jin Cheng
Published: July 2010

For a continuous map of the interval the following conditions are equivalent: (1) the period of every periodic point is a power of 2, (2)

R
¯

(
+
)

∩

R
¯

(
−
)

−
R
=
ϕ

{\overline R ^{( + )}} \cap {\overline R ^{( - )}} - R = \phi

, and (3)

R
¯

−
R

\overline R - R

is countable, where

R
R

denotes the set of recurrent points.

R
¯

\overline R

is the closure of

R
R

, and

R
¯

(
+
)

{\overline R ^{( + )}}

(or

R
¯

(
−
)

{\bar R^{( - )}}

) is the right-side closure (left-side closure, respectively) of

R
R

.
Riemannian foliations of the rank one symmetric spaces
Authors: Escobales Richard H.
Published: July 2010

In this paper Riemannian folfiations of spheres by spheres and of projective spaces by projective spaces of the same kind are classified by using earlier results of the author and a theorem of Ucci.
The universality of words 𝑥^{𝑟}𝑦^{𝑠} in alternating groups
Authors: Brenner J. L. , Evans R. J. , Silberger D. M.
Published: July 2010

If

r
,
s

r,s

are nonzero integers and

m
m

is the largest squarefree divisor of

r
s

rs

, then for every element

z
z

in the alternating group

A
n

{A_n}

, the equation

z
=

x
r

y
s

z = {x^r}{y^s}

has a solution with

x
,
y
∈

A
n

x,y \in {A_n}

, provided that

n
⩾
5

n \geqslant 5

and

n
⩾
(
5

/

2
)
log
⁡
m

n \geqslant (5/2)\log m

. The bound

(
5

/

2
)
log
⁡
m

(5/2)\log m

improves the bound

4
m
+
1

4m + 1

of Droste. If

n
⩾
29

n \geqslant 29

, the coefficient

5

/

2

5/2

may be replaced by 2; however,

5

/

2

5/2

cannot be replaced by 1 even for all large

n
n

.
Semiprimeness of special Jordan algebras
Authors: McCrimmon Kevin
Published: July 2010

There are important connections between radicals of a special Jordan algebra

J
J

and its associative envelope

A
A

. For the locally nilpotent (Levitzki) radical

L

\mathcal {L}

, Skosyrskii proved

L

(
J
)
=
J
∩

L

(
A
)

\mathcal {L}(J) = J \cap \mathcal {L}(A)

. For the prime (Baer) radical

P

\mathcal {P}

, Erickson and Montgomery proved

P

(
J
)
=
J
∩

P

(
A
)

\mathcal {P}(J) = J \cap \mathcal {P}(A)

when

J
=
H
(
A
,
∗
)

J = H(A, * )

consists of all symmetric elements of an algebra

A
A

with involution

∗
*

. In his important work on prime Jordan algebras, Zelmanov proved

P

(
J
)
=
J
∩

P

(
A
)

\mathcal {P}(J) = J \cap \mathcal {P}(A)

for all linear

J
J

and all associative envelopes

A
A

. In the present paper we extend Zelmanov’s result to arbitrary quadratic Jordan algebras. In particular, we see that a special Jordan algebra is semiprime iff it has some semiprime associative envelope.
On weighted integrability of trigonometric series and 𝐿¹-convergence of Fourier series
Authors: Bray William O. , Stanojević Časlav V.
Published: July 2010

A result concerning integrability of

f
(
x
)
L
(
1

/

x
)
(
g
(
x
)
L
(
1

/

x
)
)

f(x)L(1/x)(g(x)L(1/x))

, where

f
(
x
)
(
g
(
x
)
)

f(x)(g(x))

is the pointwise limit of certain cosine (sine) series and

L
(
⋅
)

L( \cdot )

is slowly vary in the sense of Karamata [5] is proved. Our result is an excluded case in more classical results (see [4]) and also generalizes a result of G. A. Fomin [1]. Also a result of Fomin and Telyakovskii [6] concerning

L
1

{L^1}

-convergence of Fourier series is generalized. Both theorems make use of a generalized notion of quasi-monotone sequences.
Cyclic vectors for backward hyponormal weighted shifts
Authors: Walsh Shelley
Published: July 2010

A unilateral weighted shift

T
T

on a Hilbert space

H
H

is an operator such that

T

e
n

=

w
n

e

n
+
1

T{e_n} = {w_n}{e_{n + 1}}

for some orthonormal basis

{

e
n

}

n
=
0

∞

\left \{ {{e_n}} \right \}_{n = 0}^\infty

and weight sequence

{

w
n

}

n
=
0

∞

\left \{ {{w_n}} \right \}_{n = 0}^\infty

. If we assume

w
n

>
0

{w_n} > 0

, for all

n
n

, and let

β

(
n
)

=

w
0

⋯

w

n
−
1

\beta \left ( n \right ) = {w_0} \cdots {w_{n - 1}}

for

n
>
0

n > 0

and

β

(
0
)

=
1

\beta \left ( 0 \right ) = 1

, then

T
T

is unitarily equivalent to

f
↦
z
f

f \mapsto zf

on the weighted space

H
2

(
β
)

{H^2}\left ( \beta \right )

of formal power series

∑

n
=
0

∞

f
^

(
n
)

z
n

\sum \nolimits _{n = 0}^\infty {\hat f\left ( n \right ){z^n}}

such that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript n equals 0 Overscript normal infinity Endscripts StartAbsoluteValue ModifyingAbove f With caret left-parenthesis n right-parenthesis EndAbsoluteValue squared left-bracket beta left-parenthesis n right-parenthesis right-bracket squared greater-than normal infinity">

∑

n
=
0

∞

|

f
^

(
n
)

|

2

[

β

(
n
)

]

2

>
∞

\sum \nolimits _{n = 0}^\infty {{{\left | {\hat f\left ( n \right )} \right |}^2}{{\left [ {\beta \left ( n \right )} \right ]}^2} > \infty }

. Regarding

T
T

as multiplication for

z
z

on the space

H
2

(
β
)

{H^2}\left ( \beta \right )

, it is shown that, if

w
n

↑
1

{w_n} \uparrow 1

and

f
f

is analytic in a neighborhood of the unit disk, then either

f
f

is cyclic for

T
∗

{T^ * }

or

f
f

is contained in a finite-dimensional

T
∗

{T^ * }

-invariant subspace. This was shown—by different methods— for the unweighted shift operator by Douglas, Shields, and Shapiro [2]. It is also shown that every finite-dimensional

T
∗

{T^ * }

-invariant subspace is of the form
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis left-parenthesis z minus alpha 1 right-parenthesis Superscript n 1 Baseline midline-horizontal-ellipsis left-parenthesis z minus alpha Subscript k Baseline right-parenthesis Superscript n Super Subscript k Superscript Baseline upper H squared left-parenthesis beta right-parenthesis right-parenthesis Superscript up-tack Baseline comma">

(

(

z
−

α
1

)

n
1

⋯

(

z
−

α
k

)

n
k

H
2

(
β
)

)

⊥

,

{\left ( {{{\left ( {z - {\alpha _1}} \right )}^{{n_1}}} \cdots {{\left ( {z - {\alpha _k}} \right )}^{{n_k}}}{H^2}\left ( \beta \right )} \right )^ \bot },

\]
for some

α
1

,
…
,

α
k

{\alpha _1}, \ldots ,{\alpha _k}

in the unit disk and

n
1

,
…
,

n
k

{n_1}, \ldots ,{n_k}

positive integer.
Tightness in product spaces
Authors: Dissanayake U. N. B. , Willard S. W.
Published: July 2010

A product

∏

X
i

\prod {X_i}

of topological spaces

X
i

,
i
∈
I

{X_i},i \in I

will be said to preserve tightness if
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="partial-differential left-parenthesis product upper X Subscript i Baseline right-parenthesis less-than-or-equal-to StartAbsoluteValue upper I EndAbsoluteValue dot sup left-brace partial-differential left-parenthesis upper X Subscript i Baseline right-parenthesis vertical-bar i element-of upper I right-brace">

∂

(

∏

X
i

)

≤

|
I
|

⋅

sup

{

∂

(

X
i

)

|

i
∈
I

}

\partial \left ( {\prod {X_i}} \right ) \leq \left | I \right | \cdot {\text {sup}}\left \{ {\partial \left ( {{X_i}} \right )\left | {i \in I} \right .} \right \}

\]
where

∂

(
X
)

\partial \left ( X \right )

denotes the tightness of

X
X

. We show

∏

X
i

\prod {X_i}

preserves tightness whenever each finite subproduct does. It is further shown that this is the case whenever each

X
i

{X_i}

is a locally compact

T
2

{T_2}

-space, and whenever each

X
i

{X_i}

is a locally Lindelöf

T
3

{T_3}

P
P

-space, extending 5.9 in [J].
Baire spaces and graph theorems
Authors: Noll Dominik
Published: July 2010

We prove graph theorems and a variant of the Banach-Steinhaus theorem in a purely topological context. We obtain characterizations of Baire spaces in the class of metrizable spaces by means of graph theorems.
Note on compact sets of first Baire class functions
Authors: Pol Roman
Published: July 2010

We give an example of a separable compact subspace of the space of first Baire class functions on the irrationals which cannot be embedded in the space of first Baire class functions on the Cantor set, both of the function spaces being considered with the pointwise topology. This answers a question asked in [Ta, Problem 14-2-4].
Abstract Nash manifolds
Authors: Shiota M.
Published: July 2010

We prove that any abstract noncompact Nash manifold is

C
∞

{C^\infty }

diffeomorphic to the interior of some compact

C
∞

{C^\infty }

manifold with boundary, and conversely, that such an interior or a compact

C
∞

{C^\infty }

manifold admits infinitely many abstract Nash manifold structures. The last result is a generalization of [2], where the case of a torus is proved.
Examples in the theory of sufficiency of jets
Authors: Kucharz Wojciech
Published: July 2010

It is shown that for a given nonnegative integer

s
s

, there exist a positive integer

r
(
s
)

r(s)

and an

r
(
s
)

r(s)

-jet

υ
s

{\upsilon _s}

with source at

O
∈

R

3

O \in {{\mathbf {R}}^3}

which is not

V
V

-sufficient in the class of

C

r
(
s
)
+
s

{C^{r(s) + s}}

-realizations and is

C
0

{C^0}

-sufficient in the class of

C

r
(
s
)
+
s
+
1

{C^{r(s) + s + 1}}

-realizations. In the complex case, a jet with source at

O
∈

C

2

O \in {{\mathbf {C}}^2}

which is

V
V

-sufficient but not

C
0

{C^0}

-sufficient in the class of holomorphic realizations is constructed.
Coefficients of odd univalent functions
Authors: Hu Ke
Published: July 2010

Let
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S 2 equals left-brace f 2 left-parenthesis z right-parenthesis equals z plus sigma-summation Underscript n equals 1 Overscript normal infinity Endscripts b Subscript n Baseline z Superscript 2 n plus 1 Baseline element-of upper S right-brace period">

S
2

=

{

f
2

(
z
)
=
z
+

∑

n
=
1

∞

b
n

z

2
n
+
1

∈
S

}

.

{S_2} = \left \{ {{f_2}(z) = z + \sum \limits _{n = 1}^\infty {{b_n}{z^{2n + 1}}} \in S} \right \}.

\]
In this note we prove

|

b
n

|

>
1.1305

\left | {{b_n}} \right | > 1.1305

. This is an improvement of V. I. Milin’s result [1].
Nonexistence of some nonparametric surfaces of prescribed mean curvature
Authors: Lancaster Kirk E.
Published: July 2010

If

Ω
⊂

R

2

\Omega \subset {{\mathbf {R}}^2}

has a reentrant corner, the Dirichlet problem for the equation of prescribed mean curvature

H
H

with zero boundary value has no solution when

H
H

has constant nonzero sign.
Rings with a bounded number of generators for right ideals
Authors: Blair William D.
Published: July 2010

Let the ring

S
S

be a finitely generated module over a subring

R
R

of its center. Then it will be shown that

S
S

has the property that every right ideal can be generated by a bounded number of elements if and only if

R
R

has the property that every ideal can be generated by a bounded number of elements. As a corollary we show that a two-sided Noetherian affine ring satisfying a polynomial identity has the property that every right ideal can be generated by a bounded number of elements if and only if every left ideal can be generated by a bounded number of elements.
Growth of harmonic conjugates in the unit disc
Authors: Jevtić Miroljub
Published: July 2010

Assuming some mild regularity conditions on a positive nondecreasing function

ψ
(
x
)
=
O
(

x
a

)

\psi (x) = O({x^a})

(for some

a
>
0
,
x
→
∞

a > 0,x \to \infty

), we show that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M Subscript p Baseline left-parenthesis r comma u right-parenthesis equals upper O left-parenthesis psi left-parenthesis StartFraction 1 Over 1 minus r EndFraction right-parenthesis right-parenthesis left-parenthesis r right-arrow 1 comma 0 greater-than p greater-than 1 right-parenthesis">

M
p

(
r
,
u
)
=
O

(

ψ

(

1

1
−
r

)

)

(
r
→
1
,
0
>
p
>
1
)

{M_p}(r,u) = O\left ( {\psi \left ( {\frac {1} {{1 - r}}} \right )} \right )(r \to 1,0 > p > 1)

\]
implies
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M Subscript p Baseline left-parenthesis r comma v right-parenthesis equals upper O left-parenthesis psi overTilde Superscript p Baseline left-parenthesis 1 slash left-parenthesis 1 minus r right-parenthesis right-parenthesis right-parenthesis Superscript 1 slash p">

M
p

(
r
,
v
)
=
O

(

ψ
~

p

(
1

/

(
1
−
r
)
)

)

1

/

p

{M_p}(r,v) = O{({\tilde \psi ^p}(1/(1 - r)))^{1/p}}

, where

u
(
z
)
+
i
v
(
z
)

u(z) + iv(z)

is holomorphic in the open unit disc and
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove psi With tilde Superscript p Baseline left-parenthesis x right-parenthesis equals integral Subscript 1 slash 2 Superscript x Baseline StartFraction psi Superscript p Baseline left-parenthesis t right-parenthesis Over t EndFraction d t comma x greater-than-or-slanted-equals one half period">

ψ
~

p

(
x
)
=

∫

1

/

2

x

ψ
p

(
t
)

t

d
t
,

x
⩾

1
2

.

{\tilde \psi ^p}(x) = \int _{1/2}^x {\frac {{{\psi ^p}(t)}}{t}dt,\quad x \geqslant \frac {1}{2}.}

\]
Limit boundary value problems of retarded functional-differential equations
Authors: Chen Shao Zhu
Published: July 2010

We establish necessary and sufficient conditions assuring the existence and uniqueness of solutions of the limit boundary value problems on a half-line

[
a
,
∞
)

[a,\infty )

for the retarded functional equation
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove x With two-dots left-parenthesis t right-parenthesis plus f left-parenthesis t comma x left-parenthesis g 1 left-parenthesis t right-parenthesis right-parenthesis comma ellipsis comma x left-parenthesis g Subscript m Baseline left-parenthesis t right-parenthesis right-parenthesis right-parenthesis h left-parenthesis ModifyingAbove x With dot left-parenthesis t right-parenthesis right-parenthesis equals 0">

x
¨

(
t
)
+
f
(
t
,
x
(

g
1

(
t
)
)
,
…
,
x
(

g
m

(
t
)
)
)
h
(

x
˙

(
t
)
)
=
0

\ddot x(t) + f(t,x({g_1}(t)), \ldots ,x({g_m}(t)))h(\dot x(t)) = 0

\]
.
On functions whose derivative has positive real part
Authors: Thomas D. K.
Published: July 2010

Let

R
R

be the class of normalised analytic functions

f
f

, defined in the open disc

D
D

, such that Re

f
′

(
z
)
>
0

f’(z) > 0

for

z
∈
D

z \in D

. For

f
∈
R

f \in R

, a best possible growth estimate for

|

z

f
′

(
z
)

/

f
(
z
)

|

|zf’(z)/f(z)|

is obtained.
Algebra direct sum decomposition of 𝐶_{𝑅}(𝑋)
Authors: Mehta R. D. , Vasavada M. H.
Published: July 2010

Let

A
A

and

B
B

be closed subalgebras of

C
R

(
X
)

{C_R}(X)

with

1
∈
A

1 \in A

and

1
∉
B

1 \notin B

. We give necessary and sufficient conditions for

A
⊕
B
=

C
R

(
X
)

A \oplus B = {C_R}(X)

.
The exact cardinality of the set of topological left invariant means on an amenable locally compact group
Authors: Lau Anthony To Ming , Paterson Alan L. T.
Published: July 2010

The purpose of this note is to prove that if

G
G

is an amenable locally compact noncompact group, then the set of topological left invariant means on

L
∞

(
G
)

{L_\infty }(G)

has cardinality

2

2
d

{2^{{2^d}}}

, where

d
d

is the smallest cardinality of the covering of

G
G

by compact sets. We also prove that in this case the spectrum of the bounded left uniformly continuous complex-valued functions contains exactly

2

2
d

{2^{{2^d}}}

minimal closed invariant subsets (or left ideals)
Remark on: “Tridiagonal matrix representations of cyclic selfadjoint operators” [Pacific J. Math. 114 (1984), no. 2, 325–334; MR0757504 (85h:47033)] by J. Dombrowski
Authors: Fan Peng
Published: July 2010

In [2], Dombrowski used a "orthogonal polynomials" technique to obtain a sufficient condition (in terms of the weights) for the existence of an absolutely continuous subspace for real parts of unilateral weighted shifts. The purpose of this note is to present a "diagonal" technique that produces a trace criterion for the existence of an absolutely continuous subspace for real parts as well as unitary parts of (bounded) operators.
A note on asymptotic behavior of solutions to a heterogeneous nonlinear reaction-diffusion system
Authors: Zheng Si Ning
Published: July 2010

A result on asymptotic behavior of solutions to a heterogeneous nonlinear reaction-diffusion system with homogeneous Neumann boundary condition is obtained, which improves the results in [5].
An oscillation criterion for second order nonlinear differential equations
Authors: Wong James S. W.
Published: July 2010

An oscillation crierion is given for the second order nonlinear differential equation

x
+
a
(
t
)

|

x

|

γ

sgn
⁡
x

 = 0

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

,

γ
>
0

\gamma > 0

, where the coefficient

a
(
t
)

a(t)

is not assumed to be nonnegative for all large values of

t
t

. The result involves a condition obtained by Kamenev for the linear differential equation.
On isomorphic classical diffeomorphism groups. I
Authors: Banyaga Augustin
Published: July 2010

Let

(

M
i

,

α
i

)

({M_i},{\alpha _i})

,

i
=
1
,
2

i = 1,2

, be two smooth manifolds equipped with symplectic, contact or volume forms

α
i

{\alpha _i}

. We show that if a group isomorphism between the automorphism groups of

α
i

{\alpha _i}

is induced by a bijective map between

M
i

{M_i}

, then this map must be a

C
∞

{C^\infty }

diffeomorphism which exchanges the structures

α
i

{\alpha _i}

. This generalizes a theorem of Takens.
An extended Čencov characterization of the information metric
Authors: Campbell L. L.
Published: July 2010

Čencov has shown that Riemannian metrics which are derived from the Fisher information matrix are the only metrics which preserve inner products under certain probabilistically important mappings. In Čencov’s theorem, the underlying differentiable manifold is the probability simplex

Σ
1
n

x
i

=
1
,

x
i

>
0

\Sigma _1^n{x_i} = 1, x_i > 0

. For some purposes of using geometry to obtain insights about probability, it is more convenient to regard the simplex as a hypersurface in the positive cone. In the present paper Čencov’s result is extended to the positive cone. The proof uses standard techniques of differential geometry but does not use the language of category theory.
An example of a fake 𝑠-manifold with a nice locally contractible compactification
Authors: Bowers Philip L.
Published: July 2010

An example is constructed of a topologically complete separable AR

X
X

that satisfies the discrete

n
n

-cells property for each nonnegative integer

n
n

but fails to satisfy the discrete approximation property and be homeomorphic to

s
s

even though

X
X

arises as the complement of a

σ
\sigma

-

Z
Z

-set in a locally contractible compactum. Such examples are not possible in the setting of ANR compactifications.
A note on twist spun knots
Authors: Montesinos José María
Published: July 2010

A movie presentation for the twist spun knots of an arc is given.
Quotient rings of rings generated by faithful cyclic modules
Authors: Birkenmeier Gary F.
Published: July 2010

A ring

R
R

is said to be generated by faithful cyclics (right finitely pseudo-Frobenius), denoted by right GFC (FPF), if every faithful cyclic (finitely generated) right

R
R

-module generates the category of right

R
R

-modules. A fundamental result in FPF ring theory, due to S. Page, is that if

R
R

is a right nonsingular right FPF ring, then

Q
r

(
R
)

{Q_r}(R)

is FPF. In this paper we generalize this result by providing a necessary and sufficient condition for a right nonsingular right GFC ring to have an FPF maximal right quotient ring.
A note on pushing up
Authors: Fan Paul S.
Published: July 2010

The amalgam method is used to handle some so-called pushing-up problems in finite groups.
A simple proof of the theorem of Torelli based on Torelli’s approach
Authors: Collino Alberto
Published: July 2010

We give a simple proof of the classical theorem of Torelli, based on Torelli’s original approach and on the use of Poincaré’s formulas.
Embedding countable rings in 2-generator rings
Authors: O’Meara K. C.
Published: July 2010

A short elementary proof involving matrices is used to show that any countable ring can be embedded in a

2
2

-generator ring. Immediate corollaries are the known results that any countable (respectively finite) semigroup can be embedded in a

2
2

-generator (respectively finite

2
2

-generator) semigroup.
Boundedness properties in Volterra integro-differential systems
Authors: Mahfoud W. E.
Published: July 2010

Sufficient conditions are given to insure that all solutions of the integrodifferential system
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x prime equals upper A left-parenthesis t right-parenthesis x plus integral Subscript 0 Superscript t Baseline upper C left-parenthesis t comma s right-parenthesis x left-parenthesis s right-parenthesis d s plus f left-parenthesis t right-parenthesis">

x
′

=
A
(
t
)
x
+

∫
0
t

C
(
t
,
s
)
x
(
s
)
d
s
+
f
(
t
)

x’ = A(t)x + \int _0^t {C(t,s)x(s)ds + f(t)}

\]
are uniform bounded.
Convolution equations in spaces of distributions supported by cones
Authors: Meril Alex , Struppa Daniele C.
Published: July 2010

We describe some examples of surjective convolutors on

D

′

(
Γ
)

\mathcal {D}’(\Gamma )

, for

Γ
\Gamma

a closed convex cone in

R

n

{{\mathbf {R}}^n}

. We also give necessary and suffficient conditions on

S
1

,
…
,

S
m

{S_1}, \ldots ,{S_m}

in

S

′

(
Γ
)

\mathcal {S}’(\Gamma )

to be generators of the whole convolution algebra

S

′

(
Γ
)

\mathcal {S}’(\Gamma )

.
One expression for the solutions of second order difference equations
Authors: Popenda Jerzy
Published: July 2010

Explicit formulas for the general solutions of homogeneous and nonhomogeneous second order linear difference equations with arbitrarily varying coefficients are obtained.
On sequences without weak* convergent convex block subsequences
Authors: Haydon Richard , Levy Mireille , Odell Edward
Published: July 2010

Let

X
X

be a Banach space such that

X
∗

{X^ * }

contains a bounded sequence without a weak* convergent convex block subsequence. Then, subject to Martin’s Axiom and the negation of the Continuum Hypothesis,

X
X

contains

l
1

(

c

)

{l_1}(\mathfrak {c})

. With the same assumption, every nonreflexive Grothendieck space has

l
∞

{l_\infty }

as a quotient.
On the relation between the semigroup and its infinitesimal generator
Authors: Neubrander Frank
Published: July 2010

We prove that for a semigroup generator

A
A

the solutions of

u
′

(
t
)
=
A
u
(
t
)

u’(t) = Au(t)

and

u
(
0
)
=
x

u(0) = x

are completely determined by the resolvent of

A
A

along an equidistant sequence

(

s
0

+
n
r

)

n
∈

N

,
r
∈

R

,

s
0

∈

C

{({s_0} + nr)_{n \in {\mathbf {N}}}},r \in {\mathbf {R}},{s_0} \in {\mathbf {C}}

, of points in the resolvent set of

A
A

.
On the stability of exponential bases in 𝐿²(-𝜋,𝜋)
Authors: Young Robert M.
Published: July 2010

In this note we investigate the effects of small perturbations on an important class of exponential bases.
Algebra direct sum decomposition of 𝐶_{𝑅}(𝑋). II
Authors: Mehta R. D. , Vasavada M. H.
Published: July 2010

We give conditions under which the sets of constancy of a closed subalgebra of

C
R

(
X
)

{C_R}(X)

, which is complemented by a closed subalgebra, are retracts of

X
X

.
Restricted left invertible Toeplitz operators on multiply connected domains
Authors: Izuchi Keiji , Ohno Shûichi
Published: July 2010

A characterization of restricted left invertible Toeplitz operators on multiply connected domains is given. To prove this, some extension theorems are given.
Boolean reducts of relation and cylindric algebras and the cube problem
Authors: Andréka H.
Published: July 2010

It is shown that not every Boolean algebra is the Boolean part of a nondiscrete relation or cylindric algebra, but every nonatomless Boolean algebra is. Solutions of Tarski’s Cube Problem for nondiscrete relation and cylindric algebras are given.
The first eigenvalue of a scalene triangle
Authors: Brooks Robert , Waksman Peter
Published: July 2010

In this paper, we prove the lower bound
\[

λ
1

(
T
)
≥

(
L
+

4
π
A

)
2

16

A
2

{\lambda _1}(T) \geq \frac {{(L + \sqrt {4\pi A{)^2}} }}{{16{A^2}}}

\]
for a triangle

T
T

with area

A
A

and perimeter

L
L

, where

λ
1

{\lambda _1}

is the first eigenvalue for the Laplace operator with Dirichlet boundary conditions. We also present analogous estimates for an arbitrary convex polygon.
A continuum 𝑋 which is a retract of 𝐶(𝑋) but not of 2^{𝑋}
Authors: Illanes Alejandro
Published: July 2010

We give an example of a continuum

X
X

which is a retract of

C
(
X
)

C(X)

but not of

2
X

{2^X}

.
The intermediate prime divisors of integers
Authors: De Koninck J.-M. , Galambos J.
Published: July 2010

Let

p
1

>

p
2

>
⋯
>

p
ω

{p_1} > {p_2} > \cdots > {p_\omega }

be the distinct prime divisors of the integer

n
n

. If

ω
=
ω
(
n
)
→
+
∞

\omega = \omega (n) \to + \infty

with

n
n

, then

p
j

{p_j}

is called an intermediate prime divisor of

n
n

if both

j
j

and

ω
−
j

\omega - j

tend to infinity with

n
n

. We show that

log
⁡
log
⁡

p
j

\log \log {p_j}

, as

j
j

goes through the indices for which

p
j

{p_j}

is intermediate, forms a limiting Poisson process in the sense of natural density.
Dihedral algebras are cyclic
Authors: Mammone Pascal , Tignol Jean-Pierre
Published: July 2010

This note gives a simple proof of the following theorem of Rowen and Saltman: Every central simple algebra split by a Galois extension of rank

2
n

2n

(

n
n

odd) with dihedral Galois group is cyclic if the center contains a primitive

n
n

th root of unity.
Primes dividing character degrees and character orbit sizes
Authors: Gluck David
Published: July 2010

We consider an abelian group

A
A

which acts faithfully and coprimely on a solvable group

G
G

. We show that some

A
A

-orbit on

Irr
⁡
(
G
)

\operatorname {Irr}(G)

must have cardinality divisible by almost half the primes in

π
(
A
)

\pi (A)

. As a corollary, we improve a recent result of I. M. Isaacs concerning the maximum number of primes dividing any one character degree of a solvable group.
Dilations and subnormality
Authors: Szymański Wacław
Published: July 2010

A general view of subnormality via the dilation theory is presented.
Topologically trivial deformations of isolated quasihomogeneous hypersurface singularities are equimultiple
Authors: O’Shea Donal B.
Published: July 2010

It is shown that any topologically trivial (and, hence, any

μ
\mu

-constant) deformation of an isolated quasihomogeneous hypersurface singularity is equimultiple.
Mean value theorems for generalized Riemann derivatives
Authors: Ash J. M. , Jones R. L.
Published: July 2010

Let

x
,
e
⩾
0
,

u
0

>
⋯
>

u

d
+
e

x,e \geqslant 0,{u_0} > \cdots > {u_{d + e}}

and

h
>
0

h > 0

be real numbers. Let

f
f

be a real valued function and let

Δ
(
h
;
u
,
w
)
f
(
x
)

h

−
d

\Delta (h;u,w)f(x){h^{ - d}}

be a difference quotient associated with a generalized Riemann derivative. Set

I
=
(
x
+

u
0

h
,
x
+

u

d
+
e

h
)

I = (x + {u_0}h,x + {u_{d + e}}h)

and let

f
f

have its ordinary

(
d
−
1
)

(d - 1)

st derivative continuous on the closure of

I
I

and its

d
d

th ordinary derivative

f

(
d
)

{f^{(d)}}

existent on

I
I

. A necessary and sufficient condition that a difference quotient satisfy a mean value theorem (i.e., that there be a

ξ
∈
I

\xi \in I

such that the difference quotient is equal to

f

(
d
)

(
ξ
)
)

{f^{(d)}}(\xi ))

is given for

d
=
1

d = 1

and

d
=
2

d = 2

. The condition is sufficient for all

d
d

. It is used to show that many generalized Riemann derivatives that are "good" for numerical analysis do not satisfy this mean value theorem.
Closedness of index values for subfactors
Authors: Handelman David , Wenzl Hans
Published: July 2010

Let

{

A
i

⊂

B
i

}

\left \{ {{A_i} \subset {B_i}} \right \}

be a collection of inclusions of finite factors with the indices

{

[

B
i

:

A
i

]

}

\left \{ {\left [ {{B_i}:{A_i}} \right ]} \right \}

bounded and each with trivial relative commutant. Then any

W
∗

{W^ * }

ultraproduct yields an inclusion with trivial relative commutant whose index is the ultralimit of

{

[

B
i

:

A
i

]

}

\left \{ {\left [ {{B_i}:{A_i}} \right ]} \right \}

. In particular, the set of values of indices arising from pairs of factors with trivial relative commutant is a closed subset of

R

+

{{\mathbf {R}}^ + }

.
Exponential dichotomies for almost periodic equations
Authors: Palmer Kenneth J.
Published: July 2010

It is shown that if an almost periodic equation has an exponential dichotomy on a sufficiently long finite interval, then it has one on

(
−
∞
,
∞
)

( - \infty ,\infty )

.
Finite codimensional ideals in Banach algebras
Authors: Jarosz Krzysztof
Published: July 2010

Let

A
A

be a commutative, selfadjoint, point spectral Banach algebra and let

M
M

be a finite codimensional closed subspace of

A
A

such that for each

f
f

in

M
M

there are

n
n

distinct maximal ideals

I
1
f

,
…
,

I
n
f

I_1^f, \ldots ,I_n^f

of

A
A

with

f
∈

I
j
f

f \in I_j^f

. We prove that then there are distinct maximal ideals

I
1

,
…
,

I
n

{I_1}, \ldots ,{I_n}

of

A
A

such that

M
⊂

I
1

∩
⋯
∩

I
n

M \subset {I_1} \cap \cdots \cap {I_n}

; in particular if codim

(
M
)
=
n

(M) = n

, then

M
M

is an ideal.
On growth 𝑘-order of solutions of a complex homogeneous linear differential equation
Authors: Bernal Luis G.
Published: July 2010

In this paper, we give several results about growth

k
k

-order of solutions of a complex homogeneous linear differential equation with variable coefficients, provided that the coefficients are entire functions.
Spectral synthesis on the algebra of absolutely convergent Laguerre polynomial series
Authors: Kanjin Yūichi
Published: July 2010

Askey and Gasper

[
1
]

\left [ 1 \right ]

constructed the algebra with convolution structure for Laguerre polynomials. We will answer the question of spectral synthesis of the one point on this algebra.
Branched covers and contact structures
Authors: Gonzalo Jesús
Published: July 2010

The object of this paper is to prove the following Theorem. Every closed, orientable three-manifold has a parallelization by three contact forms.
Two-forms on four-manifolds
Authors: Seaman Walter
Published: July 2010

We study the eigenvalues of the Weitzenböck operator on a positively curved four-manifold, and give applications to its geometry and topology.
Uniqueness of the Dyer-Lashof operations
Authors: McClure James E.
Published: July 2010

It is well known that the Steenrod operations are uniquely determined by certain of their properties, namely stability, the Cartan formula, and the unstable property. In this note we give a similar characterization of Dyer-Lashof operations.
Cohomology morphisms from 𝐻*(𝐵𝑈;𝑍/𝑝) to 𝐻*(𝐵𝑍/𝑝;𝑍/𝑝)
Authors: Bisson Terrence Paul
Published: July 2010

In this paper we use Hopf algebra and generating function methods to determine the group of all cohomology morphisms from

H
∗

(

B
U
;
Z

/

p

)

{H^ * }\left ( {BU;Z/p} \right )

to

H
∗

(

B
Z

/

p
;
Z

/

p

)

{H^ * }\left ( {BZ/p;Z/p} \right )

that preserve the Steenrod operations, where

p
p

is an odd prime. The group

[

B
Z

/

p
,
B
U

]

\left [ {BZ/p,BU} \right ]

of homotopy classes of maps from

B
Z

/

p

BZ/p

to BU, which can be calculated directly, is seen to be naturally isomorphic to the group of cohomology morphisms. For

B
Z

/

2

BZ/2

and BO with coefficients in

Z

/

2

Z/2

there are precisely similar results.
The Schur subgroup of the Brauer group of cyclotomic rings of integers
Authors: Riehm C.
Published: July 2010

LetKKbe a finite abelian extension of the rational numbersQ\mathbb {Q}. LetS{\mathbf {S}}be a finite set of primes ofKKincluding the infinite ones, and leto\mathfrak {o}be the ring ofS{\mathbf {S}}-integers inKK. Then the Schur subgroupS(o)S(\mathfrak {o})of the Brauer groupB(o)B(\mathfrak {o})is defined, in analogy withS(K)S(K), via representations of finite groups on finitely generated projectiveo\mathfrak {o}-modules. It is easy to see thatS(o)⊆S(K)∩B(o)S(\mathfrak {o}) \subseteq S(K) \cap B(\mathfrak {o}). We shall show that there is equality in the case ofKKa purely cyclotomic extensionQ(εm)\mathbb {Q}({\varepsilon _m})ofQ\mathbb {Q}(whereεm{\varepsilon _m}is anmmth root of 1).
On the number of components of a graph related to character degrees
Authors: Manz O. , Staszewski R. , Willems W.
Published: July 2010

We connect two nonlinear irreducible character of a finite group

G
G

if their degrees have a common prime divisor. In this paper we show that the corresponding graph has at most three connected components.
Algebraic cycles and intersection homology
Authors: Yokura Shoji
Published: July 2010

We consider Dubson’s conjecture that the fundamental class in homology of an algebraic cycle on a complex algebraic variety is the image of a middle intersection homology class. In the case when the variety has only isolated singularities, we prove it for rational coefficients, and we give a counterexample to it for integral coefficients
The middle annihilator conjecture for embeddable rings
Authors: Dean C.
Published: July 2010

It is shown that any ring which can be embedded in an Artinian ring has just finitely many middle annihilator primes. In particular, this proves the middle annihilator conjecture for a large class of Noetherian rings.
Matrix representations of Artin groups
Authors: Squier Craig C.
Published: July 2010

We define matrix representations of Artin groups over a

2
2

-variable Laurent-polynomial ring and show that in the rank 2 case, the representations are faithful. In the special case of Artin’s braid group, our representation is a version of the Burau representation and our faithfulness theorem is a generalization of the well-known fact that the Burau representation of

B
3

{B_3}

is faithful.