bluuebunny/crossref_metadata_2025 huggingface dataset:
Singularly continuous measures in Nevai’s class 𝑀
Authors: Lubinsky D. S.
Published: June 2010

Letdνd\nube a nonnegative Borel measure on[−π,π][ - \pi ,\pi ], with0>∫−ππdν>∞0 > \smallint _{ - \pi }^\pi d\nu > \inftyand with support of Lebesgue measure zero. We show that there exist{ηj}j=1∞⊂(0,∞)\{ {\eta _j}\} _{j = 1}^\infty \subset (0,\infty )and{tj}j=1∞⊂(−π,π)\{ {t_j}\} _{j = 1}^\infty \subset ( - \pi ,\pi )such that if\[<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="d mu left-parenthesis theta right-parenthesis colon equals sigma-summation Underscript j equals 1 Overscript normal infinity Endscripts eta Subscript j Baseline d nu left-parenthesis theta plus t Subscript j Baseline right-parenthesis comma theta element-of left-bracket negative pi comma pi right-bracket comma">dμ(θ):=∑j=1∞ηjdν(θ+tj),θ∈[−π,π],d\mu (\theta ): = \sum \limits _{j = 1}^\infty {{\eta _j}d\nu (\theta + {t_j}),\quad \theta \in [ - \pi ,\pi ],}\](with the usual periodic extensiondν(θ±2π)=dν(θ)d\nu (\theta \pm 2\pi ) = d\nu (\theta )), then the leading coefficients{κn(dμ)}n=0∞\{ {\kappa _n}(d\mu )\} _{n = 0}^\inftyof the orthonormal polynomials fordμd\musatisfy\[limn→∞κn(dμ)/κn+1(dμ)=1.\lim \limits _{n \to \infty } {\kappa _n}(d\mu )/{\kappa _{n + 1}}(d\mu ) = 1.\]As a consequence, we obtain pure singularly continuous measuresdαd\alphaon[−1,1][ - 1,1]lying in Nevai’s classMM.
On a differential equation for Koornwinder’s generalized Laguerre polynomials
Authors: Koekoek J. , Koekoek R.
Published: June 2010

Koornwinder’s generalized Laguerre polynomials

{

L
n

α
,
N

(
x
)

}

n
=
0

∞

\left \{ {L_n^{\alpha ,N}(x)} \right \}_{n = 0}^\infty

are orthogonal on the interval

[
0
,
∞
)

[0,\infty )

with respect to the weight function
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartFraction 1 Over normal upper Gamma left-parenthesis alpha plus 1 right-parenthesis EndFraction x Superscript alpha Baseline e Superscript negative x Baseline plus upper N delta left-parenthesis x right-parenthesis comma alpha greater-than negative 1 comma upper N greater-than-or-equal-to 0">

1

Γ
(
α
+
1
)

x
α

e

−
x

+
N
δ
(
x
)
,
α
>
−
1
,
N
≥
0

\frac {1}{{\Gamma (\alpha + 1)}}{x^\alpha }{e^{ - x}} + N\delta (x),\alpha > - 1,N \geq 0

. We show that these polynomials for

N
>
0

N > 0

satisfy a unique differential equation of the form
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N sigma-summation Underscript i equals 0 Overscript normal infinity Endscripts a Subscript i Baseline left-parenthesis x right-parenthesis y Superscript left-parenthesis i right-parenthesis Baseline left-parenthesis x right-parenthesis plus x y left-parenthesis x right-parenthesis plus left-parenthesis alpha plus 1 minus x right-parenthesis y prime left-parenthesis x right-parenthesis plus n y left-parenthesis x right-parenthesis equals 0 comma">

N

∑

i
=
0

∞

a
i

(
x
)

y

(
i
)

(
x
)
+
x
y
(
x
)
+
(
α
+
1
−
x
)

y
′

(
x
)
+
n
y
(
x
)

=
0
,

N\sum \limits _{i = 0}^\infty {{a_i}(x){y^{(i)}}(x) + xy(x) + (\alpha + 1 - x)y’(x) + ny(x)} = 0,

\]
where

{

a
i

(
x
)

}

i
=
0

∞

\left \{ {{a_i}(x)} \right \}_{i = 0}^\infty

are continuous functions on the real line and

{

a
i

(
x
)

}

i
=
1

∞

\left \{ {{a_i}(x)} \right \}_{i = 1}^\infty

are independent of the degree

n
n

. If

N
>
0

N > 0

, only in the case of nonnegative integer values of

α
\alpha

this differential equation is of finite order.
A note on the quenching rate
Authors: Fila Marek , Hulshof Josephus
Published: June 2010

We examine the quenching rate near a quenching point of a solution of a semilinear heat equation with singular powerlike absorption. A selfcontained result on similarity profiles allows us to improve a previous quenching theorem by Guo.
An operator-valued moment problem
Authors: Lemnete Luminiţa
Published: June 2010

We link Carey’s exponential representation of the determining function of a perturbation pair with the moment problem. We prove that an operator sequence represents the moments of a phase operator if and only if there is another positively defined sequence of operators satisfying a boundedness condition.
Permutation groups in Euclidean Ramsey theory
Authors: Kříž Igor
Published: June 2010

A finite subset of a Euclidean space is called Ramsey if for each

k
k

and each

k
k

-coloring of a sufficiently dimensional Euclidean space

E
E

there is a monochromatic isometrical embedding from

F
F

to

E
E

. We show that if

F
F

has a transitive solvable group of isometries then it is Ramsey. In particular, regular polygons are Ramsey. We also show that regular polyhedra in

R

3

{{\mathbf {R}}^3}

are Ramsey.
On the behavior of mappings which do not satisfy Hyers-Ulam stability
Authors: Rassias Themistocles M. , Šemrl Peter
Published: June 2010

We find an example to show when the Hyers-Ulam stability does not occur for approximately linear mappings. We also investigate the behavior of such mappings.
On the ideal structure of the Nevanlinna class
Authors: Martin Reiner
Published: June 2010

Let

N
N

denote the Nevanlinna class, i.e. the algebra of holomorphic functions of bounded characteristic in the open unit disc. We study analytic conditions for a finitely generated ideal to be equal to the whole algebra

N
N

. Then we characterize the finitely generated prime ideals containing a nontangential interpolating Blaschke product. Further, we give an example of an ideal of

N
N

whose closure in the natural metric on

N
N

is not an ideal.
Composition operators on potential spaces
Authors: Adams David R. , Frazier Michael
Published: June 2010

By a result of B. Dahlberg, the composition operators

T
H

f
=
H
∘
f

{T_H}f = H \circ f

need not be bounded on some of the Sobolev spaces (or spaces of Bessel potentials) even for very smooth functions

H
=
H

(
t
)

,
H

(
0
)

=
0

H = H\left ( t \right ),H\left ( 0 \right ) = 0

, unless of course,

H

(
t
)

=
c
t

H\left ( t \right ) = ct

. In this note a natural domain is found for

T
H

{T_H}

that is, in a sense, maximal and on which the

{

T
H

}

\left \{ {{T_H}} \right \}

form an algebra of bounded operators. Here the functions

H

(
t
)

H\left ( t \right )

need not be bounded though they are required to have a sufficient number of bounded derivatives.
Inverses généralisés d’opérateurs non bornés
Authors: Labrousse J.-Ph.
Published: June 2010

This paper is devoted to the definition and the study of the generalized inverses of unbounded densely defined closed operators in Banach and Hubert spaces. In this latter case an identity is established that links the orthogonal projection on the graph of an operator to the orthogonal projection on the graph of its Moore-Penrose inverse.
Required redundancy in the representation of reals
Authors: Starbird Michael , Starbird Thomas
Published: June 2010

Redundancy in decimal-like representations of reals cannot be avoided. It is proved here that if

{

A
i

}

i
=
0
,
1
,
2
,
…

{\{ {A_i}\} _{i = 0,1,2, \ldots }}

is a countable collection of countable (or finite) sets of reals such that for each real

x
x

there are

a
i

∈

A
i

{a_i} \in {A_i}

with
\[

x
=

∑

i
=
0

∞

a
i

,

x = \sum \limits _{i = 0}^\infty {{a_i},}

\]
then there is a dense subset of reals with redundant representations; that is, there is a dense set

C
C

of

R

\mathbb {R}

such that for each

x
x

in

C
,

x
=

∑

i
=
0

∞

a
i

C,\quad x = \sum \nolimits _{i = 0}^\infty {{a_i}}

and

x
=

∑

i
=
0

∞

b
i

x = \sum \nolimits _{i = 0}^\infty {{b_i}}

with

a
i

,

b
i

{a_i}\,,\quad {b_i}

in

A
i

{A_i}

, but

a
i

≠

b
i

{a_i} \ne {b_i}

for some

i
i

. Petkovsek [1] proved a similar result under the added assumption that every sum of the form

∑

i
=
0

∞

a
i

\sum \nolimits _{i = 0}^\infty {{a_i}}

with

a
i

∈

A
i

{a_i} \in {A_i}

converges.
Koszul homology of Cohen-Macaulay rings with linear resolutions
Authors: Rentería Carlos , Villarreal Rafael H.
Published: June 2010

The first Koszul homology module of a Cohen-Macaulay ideal with a linear resolution is studied and some new examples of rings of minimal multiplicity are presented.
An estimate on the Ricci curvature of a submanifold and some applications
Authors: Leung Pui Fai
Published: June 2010

We prove a best possible lower bound on the Ricci curvature of an immersed submanifold in a Euclidean space and apply it to study the size of the Gauss image of a complete noncompact hypersurface with constant positive mean curvature in a Euclidean space.
The Hausdorff mean of a Fourier-Stieltjes transform
Authors: Georgakis Constantine
Published: June 2010

It is shown that the integral Hausdorff mean

T

μ
^

T\hat \mu

of the Fourier-Stieltjes transform of a measure on the real line is the Fourier transform of an

L
1

{L^1}

function if and only if

T

μ
^

T\hat \mu

vanishes at infinity or the kernel of

T
T

has mean value zero. Also a sufficient condition on the kernel of

T
T

and a necessary and sufficient condition on the measure is established in order for

−
i
sign
⁡
(
x
)
T

μ
^

(
x
)

- i\operatorname {sign}(x)T\hat \mu (x)

to be the Fourier transform of an

L
1

{L^1}

-function. These results yield an improvement of Fejer’s and Wiener’s formulas for the inversion of Fourier-Stieltjes transforms, the uniqueness property of certain generalized Fourier transforms, and a generalization of the mean ergodic theorem for unitary operators.
A note on the commutants of CSL algebras modulo bimodules
Authors: Han De Guang
Published: June 2010

In this note, we show that for any

σ
\sigma

-weakly closed bimodule

M
M

of a CSL algebra

A
A

satisfying

M
⊇
A

M \supseteq A

, the commutant of

A
A

modulo

M
M

is equal to

M
M

itself. Theorem 6 provided a result on the cohomology groups of CSL subalgebras of Von Neumann algebras.
Noether normalizations for local rings of algebraic varieties
Authors: Kurano Kazuhiko
Published: June 2010

When

D
D

is a regular subring of

A
A

such that the inclusion map is finite,

D
D

is called a Noether normalization of

A
A

. We will prove the existence of Noether normalizations of

A
A

, when

A
A

is a local ring of a one-dimensional algebraic variety. Furthermore we will give a criterion for the existence and interesting examples.
Every 𝐺-module is a submodule of a direct sum of cyclics
Authors: Magid Andy R.
Published: June 2010

Let

G
G

be a group and

V
V

a finite-dimensional complex

G
G

-module. It is shown that

G
G

is (isomorphic to) a submodule of a direct sum

W
1

⊕
⋯
⊕

W
S

{W_1} \oplus \cdots \oplus {W_S}

where each

W
i

{W_i}

is a cyclic finite-dimensional complex

G
G

-module. If

G
G

is an analytic (respectively algebraic) group and

V
V

is an analytic (respectively rational) module then the

W
i

{W_i}

can be taken to be analytic (respectively rational).
Two questions on scalar-reflexive rings
Authors: Snashall Nicole
Published: June 2010

A module

M
M

over a commutative ring

R
R

with unity is reflexive if the only

R
R

-endomorphisms of

M
M

leaving invariant every submodule of

M
M

are the scalar multiplications by elements of

R
R

. A commutative ring

R
R

is scalar-reflexive if every finitely generated

R
R

-module is reflexive. A local version of scalar-reflexivity is introduced, and it is shown that every locally scalar-reflexive ring is scalar-reflexive. An example is given of a scalar-reflexive domain that is not

h
h

-local. This answers a question posed by Hadwin and Kerr. Theorem 7 gives eight equivalent conditions on an

h
h

-local domain for it to be scalar-reflexive, thus classifying the scalar-reflexive

h
h

-local domains.
The Cesàro operator is bounded on 𝐻^{𝑝} for 0<𝑝<1
Authors: Miao Jie
Published: June 2010

In this note the boundedness of the Cesàro operator on

H
p

,
0
>
p
>
1

{H^p},0 > p > 1

, is proved.
The space of Pettis integrable functions is barrelled
Authors: Drewnowski Lech , Florencio Miguel , Paúl Pedro J.
Published: June 2010

It is well known that the normed space of Pettis integrable functions from a finite measure space to a Banach space is not complete in general. Here we prove that this space is always barrelled; this tells us that we may apply two important results to this space, namely, the Banach-Steinhaus uniform boundedness principle and the closed graph theorem. The proof is based on a theorem stating that a quasi-barrelled space having a convenient Boolean algebra of projections is barrelled. We also use this theorem to give similar results for the spaces of Bochner integrable functions.
The characterization of the almost periodic ultradistributions of Beurling type
Authors: Cioranescu Ioana
Published: June 2010

We introduce and study the space of almost periodic ultradistributions of Beurling type and characterize it in terms of classical Bohr almost periodicity. To this aim we establish a structure theorem for the bounded ultradistributions. Application is made to the Dirichlet Problem for the half plane with almost periodic untradistributional boundary values.
Construction of compactifications using essential semilattice homomorphisms
Authors: Caterino A. , Faulkner G. D. , Vipera M. C.
Published: June 2010

In this paper we introduce a new method for constructing compactifications of a locally compact space. The method generalizes the notion of a singular compactification to a much larger collection of compactifications, which we call ESH-compactifications. In particular, if

X
X

is paracompact, or realcompact, then

β
X

\beta X

is of this form. We also establish conditions that ensure an ESH-compactification is a singular or weakly singular compactification.
On the maximum modulus of polynomials
Authors: Qazi M. A.
Published: June 2010

The maximum modulus on

|

z

|

r
>
1

|z|r > 1

of a polynomial of degree

n
n

not vanishing in

|

z

|

>
1

|z| > 1

is estimated in terms of its maximum modulus on

|

z

|

=
1

|z| = 1

and certain of its coefficients. Some other related problems are also considered.
Ramified primes in the field of definition for the Mordell-Weil group of an elliptic surface
Authors: Kuwata Masato
Published: June 2010

Let

π
:
X
→
C

\pi :X \to C

be an elliptic surface defined over a number field

k
k

. We consider the field

K
K

in which all the sections are defined. Assuming that the

j
j

-invariant is nonconstant,

K
K

is again a number field. We describe the primes of possible ramification of the extension

K

/

k

K/k

in terms of the configuration of the points of bad fibers in

C
C

. Aside from few possible exceptions,

K

/

k

K/k

is unramified outside of the primes of bad reduction of

C
C

and the primes

p

\mathfrak {p}

for which two or more points of bad fibers become identical modulo

p

\mathfrak {p}

.
Cogrowth of regular graphs
Authors: Northshield S.
Published: June 2010

Let

G

\mathcal {G}

be a

d
d

-regular graph and

T
T

the covering tree of

G

\mathcal {G}

. We define a cogrowth constant of

G

\mathcal {G}

in

T
T

and express it in terms of the first eigenvalue of the Laplacian on

G

\mathcal {G}

. As a corollary, we show that the cogrowth constant is as large as possible if and only if the first eigenvalue of the Laplacian on

G

\mathcal {G}

is zero. Grigorchuk’s criterion for amenability of finitely generated groups follows.
A full characterization of stable unit balls in Orlicz spaces
Authors: Granero Antonio S.
Published: June 2010

We give a full characterization of stable unit balls in Orlicz spaces, with Luxemburg norm, completing the partial results given by the author in Stable unit balls in Orlicz spaces, Proc. Amer. Math. Soc. 109 (1990), 97-104 and by M. Wisla in Extreme points and stable unit balls in Orlicz sequence spaces, Arch. Math. 56 (1991), 482-490.
A characterization of finitely junctioned continua
Authors: Duda Edwin , Krupski Paweł
Published: June 2010

Metric continua which are

k
k

-junctioned are defined and characterized. Furthermore such continua are shown to be invariant under open or monotone mappings.
Regular sets of sampling and interpolation for weighted Bergman spaces
Authors: Seip Kristian
Published: June 2010

Let

z

m
n

=

a
m

(
b
n
+
i
)
,

a
>
1
,

b
>
0
,

m
,

n

{z_{mn}} = {a^m}(bn + i),\;a > 1,\;b > 0,\;m,\;n

integers. For each weighted Bergman space on the upper half-plane there exists a constant

c
>
0

c > 0

such that

{

z

m
n

}

\{ {z_{mn}}\}

is a set of sampling if and only if

b

ln

a
>
c

b\,\ln \,a > c

and a set of interpolation if and only if

b

ln

a
>
c

b\,\ln \,a > c

. When

b

ln

a
=
c

b\,\ln \,a = c

,

{

z

m
n

}

\{ {z_{mn}}\}

is a set of uniqueness.
Hitting time bounds for Brownian motion on a fractal
Authors: Krebs William B.
Published: June 2010

We calculate a bound on hitting times for Brownian motion defined on any nested fractal. We apply this bound to show that any such process is point recurrent. We then show that any diffusion on a nested fractal must have a transition density with respect to Hausdorff measure on the underlying fractal. We also prove that any Brownian motion on a nested fractal has a jointly continuous local time with a simple modulus of space-time continuity.
Free subgroups of quaternion algebras
Authors: Alperin Roger C.
Published: June 2010

Using the theory of group actions on trees, we shall prove that if a quaternion algebra over Laurant polynomials is not split then a certain congruence subgroup of the group of norm one elements is a free group. This generalizes and gives an easy, conceptually simpler proof than that given by Pollen for the field of real numbers.
The equivariant Serre spectral sequence
Authors: Moerdijk I. , Svensson J.-A.
Published: June 2010

For spaces with a group action, we introduce Bredon cohomology with local (or twisted) coefficients and show that it is invariant under weak equivariant homotopy equivalence. We use this new cohomology to construct a Serre spectral sequence for equivariant fibrations.
Boundary values of holomorphic semigroups
Authors: Boyadzhiev Khristo , deLaubenfels Ralph
Published: June 2010

Suppose

A
A

generates a bounded strongly continuous holomorphic semigroup of angle

π

/

2

\pi /2

. We show that

i
A

iA

generates a

(
1
−
A

)

−
r

{(1 - A)^{ - r}}

regularized group, which is

O
(
1
+

|

s

|

r

)

∀
r
>
γ
⩾
0

O(1 + |s{|^r})\;\forall r > \gamma \geqslant 0

, if and only if

|

|

e

z
A

|

|

||{e^{zA}}||

is
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper O left-parenthesis left-parenthesis left-parenthesis 1 plus StartAbsoluteValue z EndAbsoluteValue right-parenthesis slash upper R e left-parenthesis z right-parenthesis right-parenthesis Superscript r Baseline right-parenthesis for-all r greater-than gamma">

O
(

(
(
1
+

|

z

|

)

/

Re
⁡
(
z
)

)
r

)
∀
r
>
γ

O({((1 + |z|)/\operatorname {Re} (z))^r})\forall r > \gamma

and

i
A

iA

generates a bounded

(
1
−
A

)

−
r

{(1 - A)^{ - r}}

regularized group

∀
r
>
γ
⩾
0

\forall r > \gamma \geqslant 0

if and only if

|

|

e

z
A

|

|

||{e^{zA}}||

is

O
(

(
1

/

Re
⁡
(
z
)

)
r

)

∀
r
>
γ

O({(1/\operatorname {Re} (z))^r})\;\forall r > \gamma

. We apply this to the Schrödinger operator

i
(
Δ
−
V
)

i(\Delta - V)

.
Cyclic inequalities
Authors: Yamagami Shigeru
Published: June 2010

We prove a class of cyclic inequalities including the ones that are related with the positivity of Choi’s maps in matrix algebras.
Simplicity of crossed products of 𝐶*-algebras
Authors: Jang Sun Young , Lee Sa Ge
Published: June 2010

Let

(
A
,
G
,
α
)

(A,G,\alpha )

be a

C

∗

{C^{\ast }}

-dynamical system and let

G
G

be a discrete group. When

G
G

is a cental shift in

(
A
,
G
,
α
)

(A,G,\alpha )

, we show that

A
A

is

G
G

-simple (resp.

G
G

-prime) if and only if the

C

∗

{C^{\ast }}

-crossed product

A
×

α

G

A \times {}_\alpha G

is simple (resp. prime).
An invariant of links in a handlebody associated with the spin 𝑗 representation of 𝑈_{𝑞}(𝔰𝔩(2,𝐂))
Authors: Nakabo Shigekazu
Published: June 2010

We construct an invariant of framed links in a handlebody by means of the spin

j
j

representation of

U
q

(

s

l

(
2
,

C

)
)

{U_q}(\mathfrak {s}\mathfrak {l}(2,\mathbb {C}))

. We can see this invariant is an extension of the Jones polynomial and Kauffman’s Dubrovnik polynomial. Moreover, we can obtain a linear representation of the generalized braid group associated with the Lie algebras of types

B
B

and

C
C

by applying the operators used in constructing an invariant to tangles in a solid torus.
Inequalities in the most simple Sobolev space and convolutions of 𝐿₂ functions with weights
Authors: Saitoh Saburou
Published: June 2010

For the most simple Sobolev space on

R

\mathbb {R}

composed of real-valued and absolutely continuous functions

f
(
x
)

f(x)

on

R

\mathbb {R}

with finite norms
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace integral Subscript negative normal infinity Superscript normal infinity Baseline left-parenthesis a squared f prime left-parenthesis x right-parenthesis squared plus b squared f left-parenthesis x right-parenthesis squared right-parenthesis d x right-brace Superscript 1 slash 2 Baseline left-parenthesis a comma b greater-than 0 right-parenthesis comma">

{

∫

−
∞

∞

(

a
2

f
′

(
x
)

2

+

b
2

f

(
x
)

2

)

d
x

}

1

/

2

(
a
,
b
>
0
)
,

{\left \{ {\int _{ - \infty }^\infty {({a^2}{f’}{{(x)}^2} + {b^2}f{{(x)}^2})\,dx} } \right \}^{1/2}}\qquad (a,b > 0),

\]
we shall apply the theory of reproducing kernels, and derive natural norm inequalities in the space and the related inequalities for convolutions of

L
2

{L_2}

functions with weights.
Shore points and dendrites
Authors: Neumann Lara Víctor , Puga-Espinosa Isabel
Published: June 2010

A point

x
x

in a dendroid

X

{\mathbf {X}}

is called a shore point if there is a sequence of subdendroids of

X

{\mathbf {X}}

not containing

x
x

and converging to

X

{\mathbf {X}}

in the Hausdorff metric. We give necessary and sufficient conditions for a dendroid to be a dendrite, in terms of shore points and Kelley’s property.
Constructibility of the set of points where a complex analytic morphism is open
Authors: Parusiński Adam
Published: June 2010

Using the local flattening theorem we prove that the set of points where a complex analytic morphism is open (or universally open) is constructible. A similar result is obtained for a morphism of complex algebraic varieties.
Topological ergodic theory and mean rotation
Authors: Alpern Steve , Prasad V. S.
Published: June 2010

Let

H

0

(

M
n

,
μ
)

{\mathcal {H}_0}({M^n},\mu )

denote the set of all homeomorphisms of a compact manifold

M
n

{M^n}

that preserve a locally positive nonatomic Borel probability measure

μ
\mu

and are isotopic to the identity. The notion of the mean rotation vector for a torus homeomorphism has been extended by Fathi to a continuous map

θ
\theta

on

H

0

(

M
n

,
μ
)

{\mathcal {H}_0}({M^n},\mu )

. We show that any abstract ergodic behavior typical for automorphisms of

(

M
n

,
μ
)

({M^n},\mu )

as a Lebesgue space is also typical not only in

H

0

(

M
n

,
μ

{\mathcal {H}_0}({M^n},\mu

but also in each closed subset of constant

θ
\theta

. By typical we mean dense

G
δ

{G_\delta }

in the appropriate space. Weak mixing is an example of such a typical abstract ergodic behavior. This contrasts sharply with a deep result of the KAM theory that for some rotation vectors

v
→

\overrightarrow v

, there is an open neighborhood of rotation by

v
→

\overrightarrow v

, in the space of smooth volume preserving

n
n

-torus diffeomorphisms with

θ
=

v
→

\theta = \overrightarrow v

, where each diffeomorphism in the open set is conjugate to rotation by

v
→

\overrightarrow v

(and hence cannot be weak mixing).
Convex real projective structures on closed surfaces are closed
Authors: Choi Suhyoung , Goldman William M.
Published: June 2010

The deformation space

C

(
Σ
)

\mathfrak {C}(\Sigma )

of convex

R

P

2

\mathbb {R}{{\mathbf {P}}^2}

-structures on a closed surface

Σ
\Sigma

with

χ
(
Σ
)
>
0

\chi (\Sigma ) > 0

is closed in the space

Hom
⁡
(
π
,
SL
⁡
(
3
,

R

)
)

/

SL
⁡
(
3
,

R

)

\operatorname {Hom} (\pi ,\operatorname {SL} (3,\mathbb {R}))/\operatorname {SL} (3,\mathbb {R})

of equivalence classes of representations

π
1

(
Σ
)
→
SL
⁡
(
3
,

R

)

{\pi _1}(\Sigma ) \to \operatorname {SL} (3,\mathbb {R})

. Using this fact, we prove Hitchin’s conjecture that the contractible "Teichmüller component" (Lie groups and Teichmüller space, preprint) of

Hom
⁡
(
π
,
SL
⁡
(
3
,

R

)
)

/

SL
⁡
(
3
,

R

)

\operatorname {Hom} (\pi ,\operatorname {SL} (3,\mathbb {R}))/\operatorname {SL} (3,\mathbb {R})

precisely equals

C

(
Σ
)

\mathfrak {C}(\Sigma )

.
On the divergence of Lagrange interpolation with equidistant nodes
Authors: Li X. , Mohapatra R. N.
Published: June 2010

This paper is concerned with the optimal rate of divergence of Lagrange interpolation of

f
(
x
)
=

|

x

|

f(x) = |x|

at equidistant nodes.
The Hankel transformation of Banach-space-valued generalized functions
Authors: Koh E. L. , Li C. K.
Published: June 2010

The object of this paper is to study Banach-space-valued generalized functions belonging to

[

H
μ

(
A
)
;
B
]

[{H_\mu }(A);B]

for which the Hankel transformation may be defined. In Realizability theory for continuous linear systems (Academic Press, New York, 1972), Zemanian considered certain

ρ
\rho

-type testing function spaces for which the Laplace transformation is defined. Tiwari (Banach space valued distributional Mellin transform and form invariant linear filtering, Indian J. Pure Appl. Math. 20 (1989), 493-504) follows Zemanian in extending the Mellin transform. Their works are based on the denseness of the Schwartz space

D
m

(
A
)

{D^m}(A)

in the testing function spaces of interest. This method is not possible here since the space

D
m

(
A
)

{D^m}(A)

is not dense in

H
μ

(
A
)

{H_\mu }(A)

, and the structure of

H
μ

(
A
)

{H_\mu }(A)

is quite different from that of

D
m

(
A
)

{D^m}(A)

, which has an inductive-limit topology. Thus, it is necessary to introduce a dense subspace

μ

D
I

(
A
)

{}_\mu {D_I}(A)

of

H
μ

(
A
)

{H_\mu }(A)

to derive some properties of

H
μ

(
A
)

{H_\mu }(A)

. We then define the Hankel transformation on

[

H
μ

(
A
)
;
B
]

[{H_\mu }(A);B]

. We end this paper with some operational formulas, which are analogous with those given by the first author in SIAM J. Math. Anal. 1 (1970), 322-327.
The Hayman-Wu constant
Authors: Øyma Knut
Published: June 2010

The Hayman-Wu constant is at least

π
2

{\pi ^2}

.
Certain games, category, and measure
Authors: Solecki Sławomir
Published: June 2010

For

A
⊂

2
ω

A \subset {2^\omega }

and

X
⊂
ω

X \subset \omega

consider an infinite game

Γ
(
A
,
X
)

\Gamma (A,X)

in which two players I and II choose

c
n

∈
{
0
,
1
}

{c_n} \in \{ 0,1\}

.

c
n

{c_n}

is chosen by I if

n
∈
X

n \in X

and by II if

n
∈
ω
∖
X

n \in \omega \backslash X

. I wins if

(

c
0

,

c
1

,

c
2

,
…
)
∈
A

({c_0},{c_1},{c_2}, \ldots ) \in A

. We analyze connections between

A
A

and the family of all sets

X
⊂
ω

X \subset \omega

for which I has a winning strategy in

Γ
(
A
,
X
)

\Gamma (A,X)

. Certain similarities and differences appear if one formulates these connections in the language of category and of Lebesgue measure.
Strong Boehmians
Authors: Dill Ellen R. , Mikusiński Piotr
Published: June 2010

A new class of generalized functions is introduced. The objects are defined as convolution quotients. The space is larger than the space of Schwartz distributions but smaller than the space of Boehmians.
On Volterra equations associated with a linear operator
Authors: Lizama Carlos
Published: June 2010

In this work we define the Hille-Yosida space, in the sense of S. Kantorovitz, for a Volterra equation of convolution type.
The Steenrod algebra action on generators of rings of invariants of subgroups of 𝐺𝐿_{𝑛}(𝑍/𝑝𝑍)
Authors: Kechagias Nondas E.
Published: June 2010

We compute the action of the Steenrod algebra on rings of invariants of certain subgroups of

GL
n

(

Z

/

p

Z

)

{\operatorname {GL} _n}({\mathbf {Z}}/p{\mathbf {Z}})

, namely, the upper triangular and parabolic subgroups. As a consequence we get the action on the Dickson algebra for any prime

p
p

. The methods we use are elementary.
The evolution operator approach to functional-differential equations with delay
Authors: Ruess Wolfgang M.
Published: June 2010

The nonlinear nonautonomous functional differential equation
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove x With dot left-parenthesis t right-parenthesis element-of upper B left-parenthesis t right-parenthesis x left-parenthesis t right-parenthesis plus upper F left-parenthesis t comma x Subscript t Baseline right-parenthesis comma t greater-than-or-slanted-equals s comma x Subscript s Baseline equals phi">

x
˙

(
t
)
∈
B
(
t
)

x
(
t
)
+
F
(
t
,

x
t

)
,

t
⩾
s
,

x
s

=
φ

\dot x(t) \in B(t)\,x(t) + F(t,{x_t}),\;t \geqslant s,\,{x_s} = \varphi

, is considered. The representation of the solution to this equation via the associated evolution operator is extended from the single-valued case to the general case of multivalued operators

B
(
t
)

B(t)

.
On generators of 𝐿/𝑅² Lie algebras
Authors: Shpilrain Vladimir
Published: June 2010

Let

L
L

be a free Lie algebra of finite rank

n
n

and

R
R

its arbitrary ideal. A necessary and sufficient condition for

n
n

elements of the Lie algebra

L

/

R
2

L/{R^2}

to be a generating set is given. In particular, we have a criterion for

n
n

elements of a free Lie algebra of rank

n
n

to be a generating set which is similar to the corresponding group-theoretic result due to Birman (An inverse function theorem for free groups, Proc. Amer. Math. Soc. 41 (1973), 634-638).
Zero entropy factors of topological flows
Authors: Blanchard F. , Lacroix Y.
Published: June 2010

The maximal zero entropy factor of a topological flow is defined using entropy pairs and explicitly given for some simple cartesian products. As a consequence, it is proved that only the trivial flow is disjoint from all flows whose maximal zero entropy factor is trivial.
A structure theorem for a pair of quadratic forms
Authors: Hsia J. S. , Jöchner M. , Shao Y. Y.
Published: June 2010

For any two lattices

L
L

and

K
K

in the same genus there exist isometric primitive sublattices

L
′

,

K
′

{L’},{K’}

of codimension

1
1

. This result not only proves Friedland’s conjecture but also extends it to lattices in an arbitrary genus and defined over any algebraic number field.
Quasi-isomorphism invariants for two classes of finite rank Butler groups
Authors: Arnold D. , Vinsonhaler C.
Published: June 2010

A complete set of numerical quasi-isomorphism invariants is given for a class of torsion-free abelian groups containing all groups of the form

G

[

A

]

\mathcal {G}[\mathcal {A}]

, where

A

=
(

A
1

,
…
,

A
n

)

\mathcal {A} = ({A_1}, \ldots ,{A_n})

is an

n
n

-tuple of subgroups of the additive rationals and

G

[

A

]

\mathcal {G}[\mathcal {A}]

is the cokernel of the diagonal embedding

⋂

A
i

→
⊕

A
i

\bigcap {{A_i} \to \oplus {A_i}}

. This classification and its dual include, as special cases, earlier classifications of strongly indecomposable groups of the form

G

[

A

]

\mathcal {G}[\mathcal {A}]

and their duals.
On the solution of the Dirichlet problem for the two-dimensional Laplace equation
Authors: Constanda Christian
Published: June 2010

The solution of the Dirichlet problem for the two-dimensional Laplace equation is obtained as a modified single layer potential by a method applicable even when the logarithmic capacity of the boundary curve is equal to

1
1

.
On Burkholder’s biconvex-function characterization of Hilbert spaces
Authors: Lee Jinsik Mok
Published: June 2010

Suppose that

X

{\mathbf {X}}

is a real or complex Banach space with norm

|

⋅

|

| \cdot |

. Then

X

{\mathbf {X}}

is a Hilbert space if and only if
\[

E

|

x
+
Y

|

⩾
1

E|x + Y| \geqslant 1

\]
for all

x
∈

X

x \in {\mathbf {X}}

and all

X

{\mathbf {X}}

-valued Bochner integrable functions

Y
Y

on the Lebesgue unit interval satisfying

E
Y
=
0

EY = 0

and

|

Y

|

⩾
1

|Y| \geqslant 1

a.e. This leads to a simple proof of the biconvex-function characterization due to Burkholder.
A Henrici theorem for joint spectra of commuting matrices
Authors: Bhatia Rajendra , Bhattacharyya Tirthankar
Published: June 2010

A version of Henrici’s classical perturbation theorem for eigenvalues of matrices is obtained for joint spectra of commuting tuples of matrices. The approach involves Clifford algebra techniques introduced by McIntosh and Pryde.
Approximate continuity and linear approximate continuity
Authors: Goffman Casper
Published: June 2010

A contrast between approximated continuity and continuity is obtained similar to the classical one for derivatives.
Equivalence of the defining sequences for ultradistributions
Authors: Chung Soon-Yeong , Kim Dohan
Published: June 2010

We prove that

M
p

∗

p
!
∼

M
p

M_p^{\ast }p! \sim {M_p}

. This result is a stronger version of the conjecture

M
p

∗

p
!
⊃

M
p

M_p^{\ast }p! \supset {M_p}

which has been given by Komatsu in Ultradistributions I, Structure theorems and a characterization (J. Fac. Sci. Univ. Tokyo Sect. IA 20 (1973), 25-105).
On compositions of conformal immersions
Authors: Dajczer Marcos , Vergasta Enaldo
Published: June 2010

We consider conformal immersions of a manifold

M
n

,

n
⩾
6

{M^n},\;n \geqslant 6

, into conformally flat manifolds. If the principal curvatures of

f
:

M
n

→

N

c
f

n
+
1

f:{M^n} \to N_{cf}^{n + 1}

have multiplicities at most

n
−
4

n - 4

, we show that any

g
:

M
n

→

N
~

c
f

n
+
2

g:{M^n} \to \tilde N_{cf}^{n + 2}

can locally be written as

g
=
ρ
∘
f

g = \rho \circ f

, where

ρ
:

N

c
f

n
+
1

→

N
~

c
f

n
+
2

\rho :N_{cf}^{n + 1} \to \tilde N_{cf}^{n + 2}

is a conformal immersion.
The chromatic convergence theorem and a tower in algebraic 𝐾-theory
Authors: McClure J. E. , Staffeldt R. E.
Published: June 2010

In this note we show how the chromatic convergence theorem of Hopkins and Ravenel implies that a tower of relative algebraic

K
K

-theories constructed by Waldhausen converges to the

p
p

-local part of the algebraic

K
K

-theory of the one-point space relative to the

K
K

-theory of the integers. The notion of convergence used here is made precise using the language of pro-homotopy theory.
On the homology of Postnikov fibres
Authors: Félix Y. , Thomas J. C.
Published: June 2010

Let

k
k

be a field of positive characteristic and

X
X

be a simply connected space of the homotopy type of a finite type CW complex. The Postnikov fibre

X

[
n
]

{X_{[n]}}

of

X
X

is defined as the homotopy fibre of the

n
n

-equivalence

f
n

:
X
→

X
n

{f_n}:X \to {X_n}

coming from the Postnikov tower

{

X
n

}

\{ {X_n}\}

of

X
X

. We prove that if the Lusternik-Schnirelmann category of

X
X

is finite, then

H

∗

(

X

[
n
]

;
k
)

{H_{\ast }}({X_{[n]}};k)

contains a free module on a subalgebra

K
K

of

H

∗

(
Ω

X
n

;
k
)

{H_{\ast }}(\Omega {X_n};k)

such that

H

∗

(
Ω

X
n

;
k
)

{H_{\ast }}(\Omega {X_n};k)

is a finite-dimensional free

K
K

-module.
Ortho-bases and monotonic properties
Authors: Junnila Heikki J. K. , Künzi Hans-Peter A.
Published: June 2010

We study monotonic properties in the sense of Gartside and Moody. Among other things we show that each space with an ortho-base admits a monotonic quasi-uniformity and that the fine quasi-uniformity of a topological space which admits a monotonic quasi-uniformity need not be monotonic. Furthermore we give an example of a countable space that does not admit any monotonic quasi-uniformity. As a byproduct of our investigations we obtain a new characterization of the topological spaces having an ortho-base.
On approximate antigradients
Authors: Gan Xiao-Xiong , Stromberg Karl R.
Published: June 2010

For

n
∈

N

n \in \mathbb {N}

and

I
=
[
0
,
1
]

I = [0,1]

, let

I
n

{I^n}

be the unit cube and

λ
n

{\lambda ^n}

the Lebesgue measure in

R

n

{\mathbb {R}^n}

. It is proved that if

f
:

I
n

→

R

n

f:{I^n} \to {\mathbb {R}^n}

and

F
0

:

I
n

→

R

{F_0}:{I^n} \to \mathbb {R}

are continuous and

ε
>
0

\varepsilon > 0

, then there exist a continuous

F
:

I
n

→

R

F:{I^n} \to \mathbb {R}

and an open set

W
⊂

(

I
n

)
∘

W \subset {({I^n})^ \circ }

with

λ
n

(
W
)
=
1

{\lambda ^n}(W) = 1

such that (i)

∇
F

\nabla F

exists and is continuous on

W
W

, (ii)

|

|

∇
F
(
x
)
−
f
(
x
)

|

|

>
ε

∀
x
∈
W

||\nabla F(x) - f(x)|| > \varepsilon \;\forall x \in W

, and (iii)

|

F
(
x
)
−

F
0

(
x
)

|

>
ε

∀
x
∈

I
n

|F(x) - {F_0}(x)| > \varepsilon \;\forall x \in {I^n}

, where
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue EndAbsoluteValue y StartAbsoluteValue EndAbsoluteValue equals left-parenthesis sigma-summation Underscript j equals 1 Overscript n Endscripts y Subscript j Superscript 2 Baseline right-parenthesis Superscript 1 slash 2 Baseline for-all y element-of double-struck upper R Superscript n">

|

|

y

|

|

=

(

∑

j
=
1

n

y
j
2

)

1

/

2

∀
y
∈

R

n

||y|| = {\left ( {\sum \nolimits _{j = 1}^n {y_j^2} } \right )^{1/2}}\;\forall y \in {\mathbb {R}^n}

.
On weakly chainable inverse limits with simplicial bonding maps
Authors: Minc Piotr
Published: June 2010

In this paper we prove that if an atriodic and weakly chainable continuum is the inverse limit of trees with simplicial bonding maps, then it is chainable.
A lower bound for sectional genera of ample and spanned vector bundles on algebraic surfaces
Authors: Lanteri Antonio , Russo Francesco
Published: June 2010

Let

E
E

be an ample and spanned vector bundle of rank

r
r

over a complex projective surface

S
S

. It is shown that the sectional genus

g
(
S
,
det
E
)

g(S,\det E)

is bounded from below by the number

b
=
max
{
q
(
S
)
,
2
−
r
χ
(

O

S

)
}

b = \max \{ q(S),2 - r\chi ({\mathcal {O}_S})\}

and pairs

(
S
,
E
)

(S,E)

satisfying

b
⩽
g
(
S
,
det
E
)
⩽
b
+
1

b \leqslant g(S,\det E) \leqslant b + 1

are characterized.
Pages from the computer files of R. William Gosper
Authors: Ismail Mourad E. H. , Takeuchi Yu , Zhang Ruiming
Published: June 2010

We give proofs of summation theorems and continued fraction evaluations conjectured by R. W. Gosper. We also give two new elementary proofs of a theorem of Gosper whose original proof uses matrix methods. One proof uses iteration of two term recurrence relation. The latter proof is also used to give elementary proofs of three other identities due to Gosper.
Linear operators that preserve column rank of Boolean matrices
Authors: Song Seok-Zun
Published: June 2010

We study the extent to which certain theorems on rank preservers of Boolean matrices carry over to column rank preservers. We characterize the linear operators that preserve the column rank of Boolean matrices.
An inequality for sections and projections of a convex set
Authors: Spingarn Jonathan E.
Published: June 2010

Let

K
⊂

R

d

K \subset {{\mathbf {R}}^d}

be a convex body,

γ
\gamma

its center of mass. For

Λ
⊂

R

d

\Lambda \subset {{\mathbf {R}}^d}

a subspace of dimension

d
−
k

d - k

, we establish the inequality
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper V o l Subscript d Baseline left-parenthesis upper K right-parenthesis less-than-or-slanted-equals upper V o l Subscript d minus k Baseline left-parenthesis upper K vertical-bar normal upper Lamda right-parenthesis upper V o l Subscript k Baseline left-parenthesis left-parenthesis upper K minus gamma right-parenthesis intersection normal upper Lamda Superscript up-tack Baseline right-parenthesis">

Vol
d

(
K
)
⩽

Vol

d
−
k

(
K

|

Λ
)

Vol
k

(
(
K
−
γ
)
∩

Λ
⊥

)

{\operatorname {Vol} _d}(K) \leqslant {\operatorname {Vol} _{d - k}}(K|\Lambda ){\operatorname {Vol} _k}((K - \gamma ) \cap {\Lambda ^ \bot })

\]
(where

K

|

Λ

K|\Lambda

denotes orthogonal projection of

K
K

onto

Λ
\Lambda

). Equality holds only if each

k
k

-dimensional section of

K
K

parallel to

Λ
⊥

{\Lambda ^ \bot }

is a translate of

(
K
−
γ
)
∩

Λ
⊥

(K - \gamma ) \cap {\Lambda ^ \bot }

.
A cyclic monotonically normal space which is not 𝐾₀
Authors: Rudin Mary Ellen
Published: June 2010

We construct a space as in the title, thus answering a variety of questions.
Canonical system on elliptic curves
Authors: Piovan Luis A.
Published: June 2010

We deduce a canonical algebraic complete integrable system using the representation of the Heisenberg group. This system is shown to have solutions equivalent to those of the rigid body motion on SO(3) (Euler Top).
Regular Auslander-Reiten components containing directing modules
Authors: Skowroński Andrzej
Published: June 2010

We describe completely all regular Auslander-Reiten components of artin algebras containing directing modules. We prove also that the Auslander-Reiten quiver of an artin algebra admits at most finitely many DTr-orbits containing directing modules.
Invariant theory of the dual pairs (𝑆𝑂*(2𝑛),𝑆𝑝(2𝑘,𝐂)) and (𝐒𝐩(2𝐧,ℜ),𝔒(𝔑))
Authors: Leung Eric Y. , Ton-That Tuong
Published: June 2010

Let

G
≡

Sp

(
2
k
,

C

)

G \equiv {\text {Sp}}(2k,{\mathbf {C}})

or

O

(
N
)

{\text {O}}(N)

and

G
′

≡

S

O

∗

(
2
n
)

G’ \equiv {\text {S}}{{\text {O}}^{\ast }}(2n)

or

Sp

(
2
n
,
ℜ
)

{\text {Sp}}(2n,\Re )

. The adjoint representation of

G
′

G’

on its Lie algebra

G

′

\mathcal {G}’

gives rise to the coadjoint representation of

G
′

G’

on the symmetric algebra of all polynomial functions on

G

′

\mathcal {G}’

. The polynomials that are fixed by the restriction of the coadjoint representation to a block diagonal subgroup

K
′

K’

of

G
′

G’

form a subalgebra called the algebra of

K
′

K’

-invariants. Using the theory of invariants of Procesi for the "dual pair"

(

G
′

,
G
)

(G’,G)

, a finite set of generators of this algebra is explicitly determined.
An improved Poincaré inequality
Authors: Hurri-Syrjänen Ritva
Published: June 2010

We show that a large class of domains

D
D

in

R

n

{\mathbb {R}^n}

including John domains satisfies the improved Poincaré inequality
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue EndAbsoluteValue u left-parenthesis x right-parenthesis minus u Subscript upper D Baseline StartAbsoluteValue EndAbsoluteValue Subscript upper L Sub Superscript q Subscript left-parenthesis upper D right-parenthesis Baseline less-than-or-slanted-equals c StartAbsoluteValue EndAbsoluteValue nabla u left-parenthesis x right-parenthesis d left-parenthesis x comma partial-differential upper D right-parenthesis Superscript delta Baseline StartAbsoluteValue EndAbsoluteValue Subscript upper L Sub Superscript p Subscript left-parenthesis upper D right-parenthesis">

|

|

u
(
x
)
−

u
D

|

|

L
q

(
D
)

⩽
c

|

|

∇
u
(
x
)
d

(
x
,
∂
D

)
δ

|

|

L
p

(
D
)

||u(x) - {u_D}|{|_{{L^q}(D)}} \leqslant c||\nabla u(x)d{(x,\partial D)^\delta }|{|_{{L^p}(D)}}

\]
where
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p less-than-or-slanted-equals q less-than-or-slanted-equals StartFraction n p Over n minus p left-parenthesis 1 minus delta right-parenthesis EndFraction comma p left-parenthesis 1 minus delta right-parenthesis greater-than n comma delta element-of left-bracket 0 comma 1 right-bracket comma c equals c left-parenthesis p comma q comma delta comma upper D right-parenthesis greater-than normal infinity">

p
⩽
q
⩽

n
p

n
−
p
(
1
−
δ
)

,

p
(
1
−
δ
)
>
n
,

δ
∈
[
0
,
1
]
,

c
=
c
(
p
,
q
,
δ
,
D
)
>
∞

p \leqslant q \leqslant \tfrac {{np}} {{n - p(1 - \delta )}},\;p(1 - \delta ) > n,\;\delta \in [0,1],\;c = c(p,q,\delta ,D) > \infty

, and

u
u

is in an appropriate Sobolev class.
Solvability of systems of linear operator equations
Authors: Jia Rong Qing , Riemenschneider Sherman , Shen Zuowei
Published: June 2010

Let

G
G

be a semigroup of commuting linear operators on a linear space

S
S

with the group operation of composition. The solvability of the system of equations

l
i

f
=

ϕ
i

,

i
=
1
,

…

,

r

{l_i}f = {\phi _i},\;i = 1,\, \ldots \,,\,r

, where

l
i

∈
G

{l_i} \in G

and

ϕ
i

∈
S

{\phi _i} \in S

, was considered by Dahmen and Micchelli in their studies of the dimension of the kernel space of certain linear operators. The compatibility conditions

l
j

ϕ
i

=

l
i

ϕ
j

,
i
≠
j

{l_j}{\phi _i} = {l_i}{\phi _j},i \ne j

, are necessary for the system to have a solution in

S
S

. However, in general, they do not provide sufficient conditions. We discuss what kinds of conditions on operators will make the compatibility sufficient for such systems to be solvable in

S
S

.
A characterization of a special ordering in a root system
Authors: Papi Paolo
Published: June 2010

We give necessary and sufficient conditions for an ordering of a set of positive roots in a root system

R
R

to be associated to a reduced expression of an element of the Weyl group of

R
R

. Finally we characterize the sets of positive roots which can be given such an ordering.
Generating ideals up to projective equivalence
Authors: Katz D.
Published: June 2010

It is shown that every ideal in a commutative Noetherian ring of dimension

d
d

is projectively equivalent to an ideal having

d
+
1

d + 1

generators.
A 𝑞-analogue of the Wronskian and a second solution of the Hahn-Exton 𝑞-Bessel difference equation
Authors: Swarttouw R. F. , Meijer H. G.
Published: June 2010

A second solution of the

q
q

-difference equation of the Hahn-Exton

q
q

-Bessel function, corresponding to the classical

Y
ν

(
x
)

{Y_\nu }(x)

, is found. We introduce a

q
q

-extension of the Wronskian to determine that the two solutions form a fundamental set.
On certain pairs of functions of semiprime rings
Authors: Brešar Matej
Published: June 2010

Let

f
f

and

g
g

be functions of a set

S
S

into a semiprime ring

R
R

. A necessary and sufficient condition for

f
f

and

g
g

to satisfy

f
(
s
)
x
g
(
t
)
=
g
(
s
)
x
f
(
t
)

f(s)xg(t) = g(s)xf(t)

for all

s
,
t
∈
S
,
x
∈
R

s,t \in S,x \in R

is given. As an application, biderivations and commuting additive mappings of semiprime rings are characterized.
An intrinsic characterization for zero-diagonal operators
Authors: Fan Peng , Fong Che Kao
Published: June 2010

The purpose of this paper is to present the following intrinsic characterization for zero-diagonal operators. Theorem. An operator T has a zero diagonal if and only if

tr

Re
⁡
(

e

i
θ

)
+
=

tr

Re
⁡

(

e

i
θ

T

)
−

{\text {tr}}\operatorname {Re} ({e^{i\theta }}) + = {\text {tr}}\operatorname {Re} {({e^{i\theta }}T)_ - }

for all

θ
,
0
≤
θ
>
2
π

\theta ,0 \leq \theta > 2\pi

.
Finite dimensionality of irreducible unitary representations of compact quantum groups
Authors: Quan Xiu Chi
Published: June 2010

In this paper, we study the representations of Hopf

C
∗

{C^ \ast }

-algebras; the main result is that every irreducible left unitary representation of a Hopf

C
∗

{C^\ast }

-algebra with a Haar measure is finite dimensional. To prove this result, we first study the comodule structure of the space of Hilbert-Schmidt operators; then we use this comodule structure to show that every irreducible left unitary representation of a Hopf

C
∗

{C^\ast }

-algebra with a Haar measure is finite dimensional.
Functions with a unique mean value and amenability
Authors: Takahashi Yuji
Published: June 2010

It is shown that there exist many amenable locally compact groups for which the sets of functions with unique left invariant mean values are not closed under addition. This resolves negatively a problem raised by T. Miao.
On the Szegő kernel of an annulus
Authors: McCullough Scott , Shen Li-Chien
Published: June 2010

In this paper we introduce a class of reproducing kernels of an annulus. Using the properties of the theta functions, we obtain a set of functional equations involving these kernels. We discuss some extremal problems associated with the functional equations.
On constructing Banach spaces with no unconditional basis
Authors: Komorowski Ryszard
Published: June 2010

There exists a weak Hilbert space with no unconditional basis.
Automorphisms of 𝑃(𝑉)_{𝐺}
Authors: Sperlich Thomas
Published: June 2010

This paper gives a proof of the theorem that for Coxeter groups the algebra of coinvariants is isomorphic to the normalizer of the Coxeter group in the linear group of a vector space over

R

\mathbb {R}

. I have tried to give a relatively elementary proof which requires only elementary algebra and a little knowledge of the theory of invariants.