bluuebunny/crossref_metadata_2025 huggingface dataset:
On the semigroups of fully invariant ideals of the free group algebra and the free associative algebra
Authors: Vovsi Samuel M.
Published: June 2010

Let

R
R

be an integral domain,

K
K

its field of fractions,

F
F

a free group. Let

I
I

and

J
J

be fully invariant (=verbal) ideals of the group algebra

K
F

KF

. We prove that over certain domains the equality

I
J
∩
R
F
=
(
I
∩
R
F
)
×
(
J
∩
R
F
)

IJ \cap RF = (I \cap RF) \times (J \cap RF)

need not be true. A similar result is valid for fully invariant ideals of the free associative algebra. This implies that the product of pure varieties of group representations over an integral domain need not be pure, that there exist pure nonprojective varieties of group representations and of associative algebras, and also answers some other questions raised in the literature.
Homological invariants of powers of an ideal
Authors: Kodiyalam Vijay
Published: June 2010

For any fixed nonnegative integer

i
i

and all sufficiently large

n
n

, the following are shown to be polynomials in

n
n

: (1) The

i
i

th Betti number,

β
i

R

0

(

M

n

)

\beta _i^{{\mathcal {R}_0}}({\mathcal {M}_n})

, and the

i
i

th Bass number,

μ

R

0

i

(

M

n

)

\mu _{{\mathcal {R}_0}}^i({\mathcal {M}_n})

, where

M

=

⊕

n
⩾
0

M

n

\mathcal {M} = { \oplus _{n \geqslant 0}}{\mathcal {M}_n}

is a finitely generated graded module over a Noetherian graded ring

R

=

R

0

[

R

1

]

\mathcal {R} = {\mathcal {R}_0}[{\mathcal {R}_1}]

with

R

0

{\mathcal {R}_0}

local. (2) The lengths,

λ
R

(

Tor
i
R

⁡
(
M

/

I
n

M
,
Q
)
)

{\lambda _R}(\operatorname {Tor} _i^R(M/{I^n}M,Q))

and

λ
R

(

Ext
R
i

⁡
(
Q
,
M

/

I
n

M
)
)

{\lambda _R}(\operatorname {Ext} _R^i(Q,M/{I^n}M))

, for an ideal

I
I

of a Noetherian ring

R
R

and finitely generated

R
R

-modules

M
,

Q

M,\;Q

with

M

⊗
R

Q

M{ \otimes _R}Q

of finite length. (3) The minimal number of generators,

ν
R

(

Tor
i
R

⁡
(
M

/

I
n

M
,
Q
)
)

{\nu _R}(\operatorname {Tor} _i^R(M/{I^n}M,Q))

and

ν
R

(

Ext
R
i

⁡
(
Q
,
M

/

I
n

M
)
)

{\nu _R}(\operatorname {Ext} _R^i(Q,M/{I^n}M))

, where

I
I

is an ideal of a Noetherian local ring

R
R

and

M
,

Q

M,\;Q

are finitely generated

R
R

-modules. It is also shown that the degrees of these polynomials are bounded by constants independent of

i
i

.
On sets nonmeasurable with respect to invariant measures
Authors: Solecki Sławomir
Published: June 2010

A group

G
G

acts on a set

X
X

, and

μ
\mu

is a

G
G

-invariant measure on

X
X

. Under certain assumptions on the action of

G
G

and on

μ
\mu

(e.g.,

G
G

acts freely and is uncountable, and

μ
\mu

is

σ
\sigma

-finite), we prove that each set of positive

μ
\mu

-measure contains a subset nonmeasurable with respect to any invariant extensions of

μ
\mu

. We study the case of ergodic measures in greater detail.
Relations on some summability methods
Authors: Sulaiman W. T.
Published: June 2010

In this paper we prove a new result connecting the summability methods

|

N
¯

,

p
n

|

k

|\overline N ,{p_n}{|_k}

with either

|

N
,

q
n

|

k

|N,{q_n}{|_k}

or

|

N
,

¯

w
n

|

k

|\overline {N,} {w_n}{|_k}

for given sequences

{

p
n

}
,

{

q
n

}

\{ {p_n}\} ,\,\{ {q_n}\}

, and

{

w
n

}

\{ {w_n}\}

of positive real constants. Several results, some of them known, are deduced.
Continua as positive Whitney levels
Authors: Charatonik Włodzimierz J.
Published: June 2010

It is shown that every continuum is a positive Whitney level of some continuum.
Jacobson radicals of nest algebras in factors
Authors: Dai Xing De
Published: June 2010

Definition. Let

β
\beta

be a nest in a separably acting type

I

I

∞

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

factor

M

\mathcal {M}

. An element

P
∈
β
∖
{
0
,
I
}

P \in \beta \backslash \{ 0,I\}

is said to be a singular point of

β
\beta

if it satisfies either of the following conditions: (1) There is a strictly increasing sequence

{

Q
n

}
⊆
β
,

lim

n
→
∞

Q
n

=
P

\{ {Q_n}\} \subseteq \beta ,\;{\lim _{n \to \infty }}{Q_n} = P

, and

P
−

Q
n

P - {Q_n}

is infinite for each

n
∈

N

n \in \mathbb {N}

. Also, there is a projection

Q
∈
β

Q \in \beta

such that

Q
>
P

Q > P

and

Q
−
P

Q - P

is finite. (2) There is a strictly decreasing sequence

{

Q
n

}
⊆
β
,

lim

n
→
∞

Q
n

=
P

\{ {Q_n}\} \subseteq \beta ,\;{\lim _{n \to \infty }}{Q_n} = P

, and

Q
n

−
P

{Q_n} - P

is infinite for each

n
∈

N

n \in \mathbb {N}

. Also, there is a projection

Q
∈
β

Q \in \beta

such that

Q
>
P

Q > P

and

P
−
Q

P - Q

is finite. Main Theorem. Let

β
\beta

be a nest in a separably acting factor

M

\mathcal {M}

. (1) If

M

\mathcal {M}

is of type

I

I

∞

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

, then a necessary and sufficient condition for the Jacobson radical

R

β

{\mathcal {R}_\beta }

of

alg
⁡
β

\operatorname {alg} \beta

to be a norm-closed singly generated ideal of

alg
⁡
β

\operatorname {alg} \beta

is that the nest

β
\beta

is countable and it does not contain a singular point. (2) If

M

\mathcal {M}

is of type

I

I

1

{\text {I}}{{\text {I}}_1}

or type

III

{\text {III}}

, then a necessary and sufficient condition for the Jacobson radical

R

β

{\mathcal {R}_\beta }

of

alg
⁡
β

\operatorname {alg} \beta

to be a norm-closed singly generated ideal of

alg
⁡
β

\operatorname {alg} \beta

is that the nest

β
\beta

is countable. (3) In (1) and (2) the single generation is equivalent to countable generation.
Some estimates for harmonic measures. III
Authors: Jenkins James A.
Published: June 2010

A simple determination is given for continua in the closed unit disc having minimal harmonic measure at the centre.
Vanishing theorems for singular varieties
Authors: Oh Kyungho
Published: June 2010

We give generalizations of Ramanujam’s version of the Kodaira Vanishing Theorem to singular varieties.
On the infimum of the Hausdorff and Vietoris topologies
Authors: Levi S. , Lucchetti R. , Pelant J.
Published: June 2010

We study the infimum of the Hausdorff and Vietoris topologies on the hyperspace of a metric space. We show that this topology coincides with the supremum of the upper Hausdorff and lower Vietoris topologies if and only if the underlying metric space is either totally bounded or is a UC space.
Construction of convex sets in negatively curved manifolds
Authors: Borbély Albert
Published: June 2010

It was proved by Choi that one can solve the Dirichlet problem at infinity for simply connected negatively curved manifolds by constructing appropriate convex sets. All the known constructions, it seems, inherently need some kind of growth condition on the curvature; therefore, it is interesting to find new ways to construct convex sets in negatively curved manifolds. In this paper we give a new way to construct convex sets from sets we call

ε
\varepsilon

-almost-convex. From the point of view of this problem this can be considered as a natural generalization of convexity.
On Poincaré type integral inequalities
Authors: Cheung Wing Sum
Published: June 2010

In this paper some new integral inequalities of the Poincaré type, on a region of rectangular dimensions, involving many functions in many variables are obtained. These in turn can be used to serve as generators of other integral inequalities.
Regularity for operator algebras on a Hilbert space
Authors: Froelich John
Published: June 2010

Four notions of regularity for operator algebras are introduced. An algebra

A
A

is called

1
1

-regular if for any two linearly independent vectors

x
,
y
∈
H

x,y \in H

there is an

a
∈
A

a \in A

such that

a
x
=
0

ax = 0

and

a
y
≠
0

ay \ne 0

. We show that the only weakly closed transitive

1
1

-regular algebra is

B
(
H
)

B(H)

, thus providing a natural generalization of the Rickart-Yood density theorem. We construct an example of a

1
1

-regular algebra which contains no nonzero compact operators. This example is related to the "thin set" phenomena of classical harmonic analysis.
Lifting Gottlieb sets and duality
Authors: Yoon Yeon Soo
Published: June 2010

Let

p
:

E
f

→
X

p:{E_f} \to X

be a fibration induced by a map

f
:
X
→
Y

f:X \to Y

from the path space fibration

ε
:
P
Y
→
Y

\varepsilon :PY \to Y

. Let

g
:
A
→
X

g:A \to X

be cyclic. When does

g
g

lift to a map

A
→

E
f

A \to {E_f}

which is cyclic? We give an answer of this question for arbitrary

A
A

and

Y
Y

. Also, we give an answer in the dual situation.
A note on a transplantation theorem of Kanjin and multiple Laguerre expansions
Authors: Thangavelu S.
Published: June 2010

By applying a transplantation theorem of Kanjin, a multiplier theorem and a Cesáro summability result are proved for multiple Laguerre expansions. In the one-dimensional case an improved version of the multiplier theorem is obtained.
Topological orbifolds
Authors: Farsi Carla
Published: June 2010

We show that two topologically homeomorphic orbifolds are also Lipshitz homeomorphic. We then prove that the

L
L

-class of a good orbifold with finite fundamental group depends only on the topological structure.
Best approximations in 𝐿¹ are near best in 𝐿^{𝑝},𝑝<1
Authors: Brown Lawrence G. , Lucier Bradley J.
Published: June 2010

We show that any best

L
1

{L^1}

polynomial approximation to a function

f
f

in

L
p

,

0
>
p
>
1

{L^p},\,0 > p > 1

, is near best in

L
p

{L^p}

.
Killing Luzin and Sierpiński sets
Authors: Judah H. , Shelah S.
Published: June 2010

We will kill the old Luzin and Sierpinski sets in order to build a model where

U
(

M

)
=
U
(

N

)
=

ℵ
1

U(\mathcal {M}) = U(\mathcal {N}) = {\aleph _1}

and there are neither Luzin nor Sierpinski sets. Thus we answer a question of J. Steprans, communicated by S. Todorcevic on route from Evans to MSRI.
On singular 𝐻-closed extensions
Authors: Srivastava Kavita
Published: June 2010

Introducing the notion of singular

H
H

-closed extensions of a locally

H
H

-closed space, we obtain a necessary and sufficient condition for a semiregular

H
H

-closed extension to be singular.
On numerically Gorenstein quasi-simple elliptic singularities with 𝐶*-action
Authors: Tomaru Tadashi
Published: June 2010

Let

(
X
,
x
)

(X,x)

be a numerically Gorenstein elliptic singularity with

C

∗

{\mathbb {C}^{\ast }}

-action and

π
:
(

X
~

,
A
)
→
(
X
,
x
)

\pi :(\tilde X,A) \to (X,x)

the minimal good resolution. Assume that the central curve of

π
\pi

is an elliptic curve. We will determine the configuration of the w.d. graph (weighted dual graph) of

A
A

and obtain a condition for

(
X
,
x
)

(X,x)

to be a maximally elliptic singularity in the sense of Yau.
Numerical integration of vector fields over curves with zero area
Authors: Harrison Jenny C.
Published: June 2010

The boundary of a Jordan domain A may be a nonsmooth curve

γ
\gamma

. If F is a smooth vector field defined near

γ
\gamma

, then F is integrable over

γ
\gamma

provided

γ
\gamma

has two-dimensional Lebesgue measure zero and F is sufficiently smooth. When actually computing the integral

∫
γ

F
∙
d
s

{\smallint _\gamma }F \bullet ds

, one might hope that

lim

k
→
∞

∫

γ
k

F
∙
d
s
=

∫
γ

F
∙
d
s

{\lim _{k \to \infty }}{\smallint _{{\gamma _k}}}F \bullet ds = {\smallint _\gamma }F \bullet ds

for PL or smooth approximators

γ
k

{\gamma _k}

of

γ
\gamma

. Several examples show that this is not the case. However, there are algorithms for choosing

γ
k

{\gamma _k}

so that

∫

γ
k

F
∙
d
s

{\smallint _{{\gamma _k}}}F \bullet ds

converges to

∫
γ

F
∙
d
s

{\smallint _\gamma }F \bullet ds

exponentially quickly.
Perturbation of spectrums of 2×2 operator matrices
Authors: Du Hong Ke , Jin Pan
Published: June 2010

In this paper, we study the perturbation of spectrums of

2
×
2

2 \times 2

operator matrices such as

M
C

=

[

A

a
m
p
;
C

0

a
m
p
;
B

]

{M_C} = \left [ {\begin {array}{*{20}{c}} A & C \\ 0 & B \\ \end {array} } \right ]

on the Hilbert space

H
⊕
K

H \oplus K

. For given A and B, we prove that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="intersection Underscript upper C element-of upper B left-parenthesis upper K comma upper H right-parenthesis Endscripts sigma left-parenthesis upper M Subscript upper C Baseline right-parenthesis equals sigma Subscript pi Baseline left-parenthesis upper A right-parenthesis union sigma Subscript delta Baseline left-parenthesis upper B right-parenthesis union left-brace lamda element-of upper C colon n left-parenthesis upper B minus lamda right-parenthesis not-equals d left-parenthesis upper A minus lamda right-parenthesis right-brace comma">

⋂

C
∈
B
(
K
,
H
)

σ
(

M
C

)
=

σ
π

(
A
)
∪

σ
δ

(
B
)
∪
{
λ
∈
C
:
n
(
B
−
λ
)
≠
d
(
A
−

λ
)
}
,

\bigcap \limits _{C \in B(K,H)} {\sigma ({M_C}) = {\sigma _\pi }(A) \cup {\sigma _\delta }(B) \cup \{ \lambda \in C:n(B - \lambda ) \ne d(A - } \lambda )\} ,

\]
where
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma left-parenthesis upper T right-parenthesis comma sigma Subscript pi Baseline left-parenthesis upper T right-parenthesis comma sigma Subscript delta Baseline left-parenthesis upper T right-parenthesis comma n left-parenthesis upper T right-parenthesis">

σ
(
T
)
,

σ
π

(
T
)
,

σ
δ

(
T
)
,
n
(
T
)

\sigma (T),{\sigma _\pi }(T),{\sigma _\delta }(T),n(T)

, and

d
(
T
)

d(T)

denote the spectrum of T, approximation point spectrum, defect spectrum, nullity, and deficiency, respectively. Some related results are obtained.
𝑊^{𝑝}-spaces and Fourier transform
Authors: Pathak R. S. , Upadhyay S. K.
Published: June 2010

The spaces
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper W Subscript upper M Superscript p Baseline comma upper W Subscript upper M comma a Superscript p Baseline comma upper W Superscript normal upper Omega comma p Baseline comma upper W Superscript normal upper Omega comma b comma p Baseline comma upper W Subscript upper M Superscript normal upper Omega comma p Baseline comma upper W Subscript upper M comma a Superscript normal upper Omega comma b comma p">

W
M
p

,

W

M
,
a

p

,

W

Ω
,
p

,

W

Ω
,
b
,
p

,

W
M

Ω
,
p

,

W

M
,
a

Ω
,
b
,
p

W_M^p,W_{M,a}^p,{W^{\Omega ,p}},{W^{\Omega ,b,p}},W_M^{\Omega ,p},W_{M,a}^{\Omega ,b,p}

generalizing the spaces of type W due to Gurevich (also given by Friedman, and Gelfand and Shilov) are investigated. Here M,

Ω
\Omega

are certain continuous increasing convex functions, a, b are positive constants and

1
≤
p
>
∞

1 \leq p > \infty

. The Fourier transformation F is shown to be a continuous linear mapping as follows:
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F colon upper W Subscript upper M comma a Superscript p Baseline right-arrow upper W Superscript normal upper Omega comma 1 slash a comma r Baseline comma upper F colon upper W Superscript normal upper Omega comma b comma p Baseline right-arrow upper W Subscript upper M comma 1 slash b Superscript r Baseline comma upper F colon upper W Subscript upper M comma a Superscript normal upper Omega comma b comma p Baseline right-arrow upper W Subscript upper M comma 1 slash b Superscript normal upper Omega comma 1 slash a comma r">

F
:

W

M
,
a

p

→

W

Ω
,
1

/

a
,
r

,
F
:

W

Ω
,
b
,
p

→

W

M
,
1

/

b

r

,
F
:

W

M
,
a

Ω
,
b
,
p

→

W

M
,
1

/

b

Ω
,
1

/

a
,
r

F:W_{M,a}^p \to {W^{\Omega ,1/a,r}},F:{W^{\Omega ,b,p}} \to W_{M,1/b}^r,F:W_{M,a}^{\Omega ,b,p} \to W_{M,1/b}^{\Omega ,1/a,r}

. These results will be used in investigating uniqueness classes of certain Cauchy problems in future work.
The Hausdorff dimension of elliptic and elliptic-caloric measure in 𝑅^{𝑁},𝑁≥3
Authors: Sweezy Caroline
Published: June 2010

The existence of an L-caloric measure with parabolic Hausdorff dimension

4
−
ε

4 - \varepsilon

in

R

2

×

R

1

{{\mathbf {R}}^2} \times {{\mathbf {R}}^1}

is demonstrated. The method is to use a specially constructed quasi-disk Q whose boundary has Hausdorff

dim
=
2
−
ε

\dim = 2 - \varepsilon

. There is an elliptic measure supported on the entire boundary of Q. Then the L-caloric measure on

∂
p

Q
×
[
0
,
T
]

{\partial _p}Q \times [0,T]

is compared with the corresponding elliptic measure. The same method gives the existence of an elliptic measure in

R

n

{{\mathbf {R}}^n}

whose support has Hausdorff

dim
⁡
n
−
ε

\dim n - \varepsilon

for

n
≥
3

n \geq 3

, and an L-caloric measure in

R

n

×

R

1

{{\mathbf {R}}^n} \times {{\mathbf {R}}^1}

supported on a set of parabolic Hausdorff dimension

n
+
2
−
ε

n + 2 - \varepsilon

.
Absolute conjugate Fourier effective methods and functions
Authors: Kumar A. , Peyerimhoff A.
Published: June 2010

We consider matrix transformation of the conjugate series of a Fourier series. Necessary and sufficient conditions on the function, generating the Fourier series, as well as on the method of the transformation have been obtained for absolute summability of the transformed series.
Mesures dominées par une capacité alternée d’ordre 2
Authors: El Kaabouchi A.
Published: June 2010

Let C be an alternating capacity of order 2 on a metrizable compact space, and let

P

C

{\mathcal {P}_C}

be the convex set of all measures dominated by C. We find a quite simple set of extreme elements of

P

C

{\mathcal {P}_C}

such that the closed convex hull of this set is

P

C

{\mathcal {P}_C}

. We also give other properties, including a generalization of one of Anger’s results.
A remark on the moment map
Authors: Azad H.
Published: June 2010

Following S. Lie, it is proposed that moment maps be constructed for degenerate forms and the utility of such maps is illustrated by computing the moment maps for torus actions on

C

n

{{\mathbf {C}}^n}

and

U
(
n
)

U(n)

actions on

P

n

(

C

)

{{\mathbf {P}}^n}({\mathbf {C}})

.
A norm-preserving 𝐻^{∞} extension problem
Authors: Yan Zhi Min
Published: June 2010

First we establish a Schwarz lemma for holomorphic mappings between bounded symmetric domains. Then, as an application, we solve a norm-preserving extension problem.
Pre-frame operators, Besselian frames, and near-Riesz bases in Hilbert spaces
Authors: Holub James R.
Published: June 2010

A problem of enduring interest in connection with the study of frames in Hubert space is that of characterizing those frames which can essentially be regarded as Riesz bases for computational purposes or which have certain desirable properties of Riesz bases. In this paper we study several aspects of this problem using the notion of a pre-frame operator and a model theory for frames derived from this notion. In particular, we show that the deletion of a finite set of vectors from a frame

{

x
n

}

n
=
1

∞

\{ {x_n}\} _{n = 1}^\infty

leaves a Riesz basis if and only if the frame is Besselian (i.e.,

∑

n
=
1

∞

a
n

x
n

{\sum } _{n = 1}^\infty \,{a_n}{x_n}

converges

⇔
(

a
n

)
∈

l
2

\Leftrightarrow ({a_n}) \in {l^2}

).
Closures of direct sums of classes of operators
Authors: Hadwin Don
Published: June 2010

We prove that certain classes of Hilbert space operators that are direct sums of operators in specified classes are closed under sequential

∗
\ast

-strong limits. One such example is the class of operators that are direct sums of operators that are either subnormal or have imaginary parts with spectrum contained in

[
0
,
1
]
∪
[
2
,
3
]

[0,1] \cup [2,3]

.
Fast spectrally-accurate solution of variable-coefficient elliptic problems
Authors: Strain John
Published: June 2010

A simple, efficient, spectrally-accurate numerical method for solving variable-coefficient elliptic partial differential equations in periodic geometry is described. Numerical results show that the method is efficient and accurate even for difficult problems including convection-diffusion equations. Generalizations and applications to phase field models of crystal growth are discussed.
The dynamics of the Sierpiński curve
Authors: Aarts Jan M. , Oversteegen Lex G.
Published: June 2010

The Sierpiński curve

X
X

admits a homeomorphism with a dense orbit. However,

X
X

is not minimal and does not admit an expansive homeomorphism.
Electromagnetic scattering for dielectrics: iterative methods for solving boundary integral equations
Authors: Bielefeld B. , Deng Y. , Glimm J. , Tangerman F. , Asvestas J. S.
Published: June 2010

We consider multigrid iterative methods for the solution of electromagnetic scattering for dielectric materials. We show convergence of the iteration using coarse grids which are two to four times coarser in each dimension than the fine grid. These results allow a significant increase in problem size and solution speed, for a given hardware configuration. We report in particular on the solution of scattering problems which require the solution of 31,000 equations on the fine grid, using the direct solution of 3,500 double precision equations on the coarse grid, and project the ability to solve significantly larger systems using larger machines or an out-of-core capability.
The prevalence of continuous nowhere differentiable functions
Authors: Hunt Brian R.
Published: June 2010

In the space of continuous functions of a real variable, the set of nowhere differentiable functions has long been known to be topologically "generic". In this paper it is shown further that in a measure theoretic sense (which is different from Wiener measure), "almost every" continuous function is nowhere differentiable. Similar results concerning other types of regularity, such as Hölder continuity, are discussed.
On compactness of composition operators in Hardy spaces of several variables
Authors: Li Song-Ying , Russo Bernard
Published: June 2010

Characterizations of compactness are given for holomorphic composition operators on Hardy spaces of a strongly pseudoconvex domain.
Nonlinear demi-regular approximation solvability of equations involving strongly accretive operators
Authors: Verma Ram U.
Published: June 2010

Based on the demiregular convergence theory of the operator equations involving strongly monotone operators by Anselone and Lei (1986), we study approximation solvability of the nonlinear equations involving strongly accretive operators.
Cut points in Čech-Stone remainders
Authors: Dow Alan , Hart Klaas Pieter
Published: June 2010

We investigate cut points of subcontinua of

β

R

∖

R

\beta \mathbb {R}\backslash \mathbb {R}

. We find, under CH, the topologically smallest type of subset of

R

\mathbb {R}

that can support such a cut point. On the other hand we answer Question 66 of Hart and van Mill’s Open problems on

β
ω

\beta \omega

[Open Problems in Topology (J. van Mill and G. M. Reed, eds.), North-Holland, Amsterdam, 1990, pp. 97-125] by showing that it is consistent that all cut points are trivial (in a sense to be made precise in the paper).
Nonisomorphic algebraic models of a smooth manifold with group action
Authors: Dovermann Karl Heinz , Masuda Mikiya , Suh Dong Youp
Published: June 2010

Let G be a finite group and M a closed smooth G manifold. If M has any equivariant algebraic model, then we show that it has uncountable many birationally inequivalent such models. This generalizes a non-equivariant result of Bochnak and Kucharz.
The finite fibre problem and an index formula for elementary operators
Authors: Eschmeier Jörg , Putinar Mihai
Published: June 2010

Let

J
⊂
L
(
K
,
H
)

J \subset L(K,H)

be an operator ideal between Hilbert spaces, and let

S
∈
L

(
H

)
n

,
T
∈
L

(
K

)
n

S \in L{(H)^n},T \in L{(K)^n}

be commuting tuples of continuous linear operators. It is shown that the elementary operator

R
:
J
→
J
,
A
→

∑

i
=
1

n

S
i

A

T
i

R:J \to J,A \to \sum \nolimits _{i = 1}^n {{S_i}A{T_i}}

determined by S and T satisfies the finite fibre property. As a consequence it follows that an index formula proved by L. Fialkow for elementary operators under the additional assumption of the finite fibre property holds true in general.
The Riccati flow and singularities of Schubert varieties
Authors: Wolper James S.
Published: June 2010

Let

Gr
⁡
(
m
,
n
)

\operatorname {Gr}(m,n)

be the Grassmannian of m-dimensional subspaces of an n-dimensional k-vector space, with

k
=

R

k = {\mathbf {R}}

or C. Fix an

n
×
n

n \times n

matrix R with coefficients in k. The Riccati Flow

Φ
\Phi

on

Gr
⁡
(
m
,
n
)

\operatorname {Gr}(m,n)

is the action of a one-parameter subgroup of

GL
n

(
k
)

{\text {GL}_n}(k)

, given by

Φ
t

(
Λ
)
=

e

R
t

Λ

{\Phi _t}(\Lambda ) = {e^{Rt}}\Lambda

. We prove: Theorem. Let X be a Schubert variety in

Gr
⁡
(
m
,
n
)

\operatorname {Gr}(m,n)

. Then there exists a Riccati flow

Φ
\Phi

on X and a stable manifold W for

Φ
\Phi

such that W is the smooth locus of X. Corollary (over C). X as above is smooth if and only if the cohomology of X satisfies Poincaré Duality.
Best approximation in 𝐿¹(𝐼,𝑋)
Authors: Khalil R. , Saidi F.
Published: June 2010

Let X be a Banach space and G a closed subspace of X. The subspace G is called proximinal in X if for every

x
∈
X

x \in X

there exists at least one

y
∈
G

y \in G

such that

‖

x
−
y

‖

=
d
(
x
,
G
)
=
inf
{

‖

x
−
z

‖

:
z
∈
G
}

\left \| {x - y} \right \| = d(x,G) = \inf \{ \left \| {x - z} \right \|:z \in G\}

. It is an open problem whether

L
1

(
I
,
G
)

{L^1}(I,G)

is proximinal in

L
1

(
I
,
X
)

{L^1}(I,X)

if G is proximinal in X, where I is the unit interval with the Lebesgue measure. In this paper, we prove the proximinality of

L
1

(
I
,
G
)

{L^1}(I,G)

in

L
1

(
I
,
X
)

{L^1}(I,X)

for a class of proximinal subspaces G in X.
A note on the Dirichlet problem for the Stokes system in Lipschitz domains
Authors: Shen Zhong Wei
Published: June 2010

We study the

L
p

{L^p}

Dirichlet problem for the Stokes system in Lipschitz domains. Optimal estimates are obtained when the dimension

n
=
3

n = 3

. In the case of

n
≥
4

n \geq 4

, we establish a weak estimate of solutions for certain range of p.
Topology of factored arrangements of lines
Authors: Paris Luis
Published: June 2010

A real arrangement of affine lines is a finite family

A

\mathcal {A}

of lines in

R

2

{{\mathbf {R}}^2}

. A real arrangement

A

\mathcal {A}

of lines is said to be factored if there exists a partition

Π
=
(

Π
1

,

Π
2

)

\Pi = ({\Pi _1},{\Pi _2})

of

A

\mathcal {A}

into two disjoint subsets such that the Orlik-Solomon algebra of

A

\mathcal {A}

factors according to this partition. We prove that the complement of the complexification of a factored real arrangement of lines is a

K
(
π
,
1
)

K(\pi ,1)

space.
Singular Kobayashi metrics and finite type conditions
Authors: Yu Ji Ye
Published: June 2010

We introduce a family of invariants associated with the higher order Kobayashi metrics and study their relations with the regular type in the sense of Kohn and the variety type in the sense of D’Angelo.
Descriptions of conditional expectations induced by non-measure preserving transformations
Authors: Lambert Alan , Weinstock Barnet M.
Published: June 2010

Given a measure-preserving transformation T acting on a

σ
\sigma

-finite measure space

(
X
,

A

,
m
)

(X,\mathcal {A},m)

and a

σ
\sigma

-finite sigma algebra

B

⊂

A

\mathcal {B} \subset \mathcal {A}

, the conditional expectations

E
(
⋅

|

B

)

E( \cdot |\mathcal {B})

acting on

L
∞

(

A

)

{L^\infty }(\mathcal {A})

and

E
(
⋅

|

T

−
1

B

)

E( \cdot |{T^{ - 1}}\mathcal {B})

acting on

L
∞

(

T

−
1

A

)

{L^\infty }({T^{ - 1}}\mathcal {A})

are known to be related by the formula
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-bracket upper E left-parenthesis f vertical-bar script upper B right-parenthesis right-bracket ring upper T equals upper E left-parenthesis f ring upper T vertical-bar upper T Superscript negative 1 Baseline script upper B right-parenthesis">

[
E
(
f

|

B

)
]
∘
T
=
E
(
f
∘
T

|

T

−
1

B

)

[E(f|\mathcal {B})] \circ T = E(f \circ T|{T^{ - 1}}\mathcal {B})

. In this note the conditional expectation

E
(
⋅

|

T

−
1

B

)

E( \cdot |{T^{ - 1}}\mathcal {B})

is investigated in the non-measure-preserving case, and those transformations for which the above equation holds are characterized in terms of measurability conditions for

d
(
m
∘

T

−
1

)

/

d
m

d(m \circ {T^{ - 1}})/dm

. It is precisely in the non-measure-preserving case that the measurability of

d
(
m
∘

T

−
1

)

/

d
m

d(m \circ {T^{ - 1}})/dm

plays an important role. Relatedly, it is shown that if composition by T intertwines

E
(
⋅

|

B

)

E( \cdot |\mathcal {B})

and any mapping

Λ
\Lambda

, then

Λ
\Lambda

is a conditional expectation induced by a measure equivalent to m. These results were motivated by a result concerning induced conditional expectation operators on

C
∗

{C^ \ast }

-algebras, and the paper concludes with a brief description of this

C
∗

{C^\ast }

-algebra setting.
Some inequalities of algebraic polynomials
Authors: Varma A. K.
Published: June 2010

Erdös and Lorentz showed that by considering the special kind of the polynomials better bounds for the derivative are possible. Let us denote by

H
n

{H_n}

the set of all polynomials whose degree is n and whose zeros are real and lie inside

[
−
1
,
1
)

[ - 1,1)

. Let

P
n

∈

H
n

{P_n} \in {H_n}

and

P
n

(
1
)
=
1

{P_n}(1) = 1

; then the object of Theorem 1 is to obtain the best lower bound of the expression

∫

−
1

1

|

P
n
′

(
x
)

|

p

d
x

\smallint _{ - 1}^1|P_n’(x){|^p}\,dx

for

p
≥
1

p \geq 1

and characterize the polynomial which achieves this lower bound. Next, we say that

P
n

∈

S
n

[
0
,
∞
)

{P_n} \in {S_n}[0,\infty )

if

P
n

{P_n}

is a polynomial whose degree is n and whose roots are all real and do not lie inside

[
0
,
∞
)

[0,\infty )

. In Theorem 2, we shall prove Markov-type inequality for such a class of polynomials belonging to

S
n

[
0
,
∞
)

{S_n}[0,\infty )

in the weighted

L
p

{L_p}

norm (p integer). Here
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar upper P Subscript n Baseline double-vertical-bar Subscript upper L Sub Subscript p Baseline equals left-parenthesis integral Subscript 0 Superscript normal infinity Baseline StartAbsoluteValue upper P Subscript n Baseline left-parenthesis x right-parenthesis EndAbsoluteValue Superscript p Baseline e Superscript negative x Baseline d x right-parenthesis Superscript 1 slash p">

‖

P
n

‖

L
p

=

(

∫
0
∞

|

P
n

(
x
)

|

p

e

−
x

d
x

)

1

/

p

{\left \| {{P_n}} \right \|_{{L_p}}} = {(\smallint _0^\infty |{P_n}(x){|^p}{e^{ - x}}\,dx)^{1/p}}

. In Theorem 3 we shall consider another analogous problem as in Theorem 2.
Preference relations and measures in the context of fair division
Authors: Barbanel Julius B. , Taylor Alan D.
Published: June 2010

One of the most well-known metaphors in the mathematical theory of fair division concerns the problem of dividing a cake among n people in such a way that each person is satisfied with the piece he or she receives, even though different people value different parts of the cake differently. Our concern here is with how an individual’s preferences are formalized. David Gale has pointed out that although most of the deeper results in the field assume that preferences are given by an additive measure, the fundamental algorithms in the field require only that preferences be given by a binary relation satisfying a few natural properties. We introduce here one additional condition—an Archimedean property that obviously holds if the relation is induced by a measure—and we show that a preference relation satisfying Gale’s conditions is induced by a finitely additive measure if and only if it satisfies this Archimedean property.
Universally first return continuous functions
Authors: Darji Udayan B. , Evans Michael J. , O’Malley Richard J.
Published: June 2010

It is known that the first return continuous functions are precisely the Darboux functions in Baire class 1, and that every such function can be changed via a homeomorphism into an approximately continuous function. Here we give two characterizations of the smaller class of universally first return continuous functions, one of which is the capacity of changing such a function via a homeomorphism into an approximately continuous function which is continuous almost everywhere.
Positive unstable periodic solutions for superlinear parabolic equations
Authors: Hirano Norimichi , Mizoguchi Noriko
Published: June 2010

In this paper, we are concerned with a superlinear parabolic equation
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout Enlarged left-brace 1st Row 1st Column StartFraction partial-differential u Over partial-differential t EndFraction minus normal upper Delta u equals u Superscript p Baseline plus h left-parenthesis t comma x right-parenthesis comma 2nd Column a m p semicolon left-parenthesis t comma x right-parenthesis element-of bold upper R Subscript plus Baseline times normal upper Omega comma 2nd Row 1st Column u equals 0 comma 2nd Column a m p semicolon left-parenthesis t comma x right-parenthesis element-of bold upper R Subscript plus Baseline times partial-differential normal upper Omega comma 3rd Row 1st Column u greater-than 0 comma 2nd Column a m p semicolon left-parenthesis t comma x right-parenthesis element-of bold upper R Subscript plus Baseline times partial-differential normal upper Omega comma EndLayout">

{

∂
u

∂
t

−
Δ
u
=

u
p

+
h
(
t
,
x
)
,

a
m
p
;

(
t
,
x
)
∈

R

+

×
Ω
,

u
=
0
,

a
m
p
;

(
t
,
x
)
∈

R

+

×
∂
Ω
,

u
>
0
,

a
m
p
;

(
t
,
x
)
∈

R

+

×
∂
Ω
,

\left \{ {\begin {array}{*{20}{c}} {\frac {{\partial u}}{{\partial t}} - \Delta u = {u^p} + h(t,x),} \hfill & {(t,x) \in {{\mathbf {R}}_ + } \times \Omega ,} \hfill \\ {{u = 0,}} \hfill & {(t,x) \in {{\mathbf {R}}_ + } \times \partial \Omega ,} \hfill \\ {{u > 0,}} \hfill & {(t,x) \in {{\mathbf {R}}_ + } \times \partial \Omega ,} \hfill \\ \end {array} } \right .

\]
where

Ω
⊂

R

N

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

is a bounded domain with smooth boundary

∂
Ω

\partial \Omega

, h is T-periodic with respect to the first variable, and

1
>
p
>

N
+
2

N
−
2

1 > p > \frac {{N + 2}}{{N - 2}}

if

N
≥
3

N \geq 3

and

1
>
p
>
+
∞

1 > p > + \infty

if

N
≤
2

N \leq 2

. It is shown that there exist a stable and an unstable positive T-periodic solution for this problem if h is sufficiently small in

L
∞

{L^\infty }

.
Asymptotic behaviour of firmly nonexpansive sequences
Authors: Djafari Rouhani Behzad
Published: June 2010

We introduce the notion of firmly nonexpansive sequences in a Banach space and present several results concerning their asymptotic behaviour extending previous results and giving an affirmative answer to an open question raised by S. Reich and I. Shafrir [Proc. Amer. Math. Soc. 101 (1987), 246-250]. Applications to averaged mappings are also given.
Invariant subspaces for positive operators acting on a Banach space with basis
Authors: Abramovich Y. A. , Aliprantis C. D. , Burkinshaw O.
Published: June 2010

Recently we established several invariant subspace theorems for operators acting on an

l
p

{l_p}

-space. In this note we extend these results from operators acting on an

l
p

{l_p}

-space to operators acting on any Banach space with a (not necessarily unconditional) Schauder basis. For instance, it is shown that if a continuous quasinilpotent operator on a Banach space is positive with respect to the closed cone generated by a basis, then the operator has a nontrivial closed invariant subspace.
The composition of operator-valued measurable functions is measurable
Authors: Badrikian A. , Johnson G. W. , Yoo Il
Published: June 2010

Given separable Frechet spaces, E, F, and G, let

L

(
E
,
F
)
,

L

(
F
,
G
)

\mathcal {L}(E,F),\mathcal {L}(F,G)

, and

L

(
E
,
G
)

\mathcal {L}(E,G)

denote the space of continuous linear operators from E to F , F to G, and E to G, respectively. We topologize these spaces of operators by any one of a family of topologies including the topology of pointwise convergence and the topology of compact convergence. We will show that if

(
X
,

F

)

(X,\mathcal {F})

is any measurable space and both

A
:
X
→

L

(
E
,
F
)

A:X \to \mathcal {L}(E,F)

and

B
:
X
→

L

(
F
,
G
)

B:X \to \mathcal {L}(F,G)

are Borelian, then the operator composition

B
A
:
X
→

L

(
E
,
G
)

BA:X \to \mathcal {L}(E,G)

is also Borelian. Further, we will give several consequences of this result.
Antipodal coincidence for maps of spheres into complexes
Authors: Izydorek Marek , Jaworowski Jan
Published: June 2010

This paper gives a partial answer to the question of whether there exists a Borsuk-Ulam type theorem for maps of

S
n

{S^n}

into lower-dimensional spaces, which are not necessarily manifolds. It is shown that for each k and

n
≤
2
k
−
1

n \leq 2k - 1

, there exists a map f of

S
n

{S^n}

into a contractible k-dimensional complex Y such that

f
x
≠
f
(
−
x
)

fx \ne f( - x)

, for all

x
∈

S
n

x \in {S^n}

. In particular, there exists a map of

S
3

{S^3}

into a 2-dimensional complex Y without an antipodal coincidence. This answers a question raised by Conner and Floyd in 1964. The complex Y provides also an example of a countractible k-dimensional complex whose deleted product has the Yang-index equal to

2
k
−
1

2k - 1

.
Fractional powers of momentum of a spectral distribution
Authors: Jazar M.
Published: June 2010

In this paper we construct fractional and imaginary powers for the positive momentum B of a spectral distribution and prove the basic properties. The main result is that for any

α
>
0
,
−

B
α

\alpha > 0, - {B^\alpha }

generates a bounded strongly continuous holomorphic semigroup of angle

π
2

\frac {\pi }{2}

. In particular for

α
=
1

\alpha = 1

, using Stone’s generalized theorem, if iB generates a k-times integrated group of type

O
(

|

t

|

k

)

O(|t{|^k})

with

σ
(
B
)
⊂
[
0
,
+
∞
[

\sigma (B) \subset [0, + \infty [

, then -B generates a strongly continuous holomorphic semigroup of angle

π
2

\frac {\pi }{2}

. A similar corollary is given in the regularized group situation.
Almost periodic solutions of periodic systems governed by subdifferential operators
Authors: Ôtani Mitsuharu
Published: June 2010

We construct an example of the periodic evolution system governed by the time-dependent subdifferential operators admitting almost periodic orbits which are not quasiperiodic.
Quadratic descent of involutions in degree 2 and 4
Authors: Dherte Hélène
Published: June 2010

If K/F is a quadratic extension, we give necessary and sufficient conditions in terms of the discriminant (resp. the Clifford algebra) for a quadratic form of dimension 2 (resp. 4) over K to be similar to a form over F. We give similar criteria for an orthogonal involution over a central simple algebra A of degree 2 (resp. 4) over K to be such that

A
=

A
′

⊗
F

K

A = A’ { \otimes _F}K

, where

A
′

A’

is invariant under the involution. This leads us to an example of a quadratic form over K which is not similar to a form over F but such that the corresponding involution comes from an involution defined over F.
Index theory for perturbed Dirac operators on manifolds with conical singularities
Authors: Fox Jeffrey , Haskell Peter
Published: June 2010

On an odd-dimensional manifold with isolated conical singularities, we perturb a Dirac operator by a vector bundle endomorphism whose pointwise norm grows in inverse proportion to the distance from the singular set. We give two proofs of an index formula for the resulting Fredholm operator. We mention an application to the index theory of transversally elliptic operators.
On polynomially bounded operators with rich spectrum
Authors: Gadidov Radu
Published: June 2010

D. Westood (J. Funct. Anal. 66 (1986), 96-104) proved that

C

00

{C_{00}}

-contractions with dominating spectrum are in

A

ℵ
0

{\mathbb {A}_{{\aleph _0}}}

. We generalize this result to polynomially bounded operators.
An estimation of singular values of convolution operators
Authors: Dostonic Milutin R.
Published: June 2010

In this paper we determine the asymptotic order of singular values of convolution operators

∫
0
x

k
(
x
−
y
)
∙
d
y

\smallint _0^xk(x - y) \bullet dy

, where

k
(
x
)
=

x

α
−
1

L
(
1

/

x
)
(
0
>
α
>
1

/

2
)

k(x) = {x^{\alpha - 1}}L(1/x)(0 > \alpha > 1/2)

and L is a slowly varying function from some class.
Uniqueness of maximal entropy odd orbit types
Authors: Geller William , Weiss Benjamin
Published: June 2010

We prove that the maximal entropy orbit types of odd period for interval maps are unique. In fact we prove that they are uniquely maximal among all (not necessarily cyclic) permutations.
Mayer-Vietoris formula for the determinant of a Laplace operator on an even-dimensional manifold
Authors: Lee Yoonweon
Published: June 2010

Let

Δ
\Delta

be a Laplace operator acting on differential p-forms on an even-dimensional manifold M. Let

Γ
\Gamma

be a submanifold of codimension 1. We show that if B is a Dirichlet boundary condition and R is a Dirichlet-Neumann operator on

Γ
\Gamma

, then
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper D e t left-parenthesis normal upper Delta plus lamda right-parenthesis equals upper D e t left-parenthesis normal upper Delta plus lamda comma upper B right-parenthesis upper D e t left-parenthesis upper R plus lamda right-parenthesis">

Det

(
Δ
+
λ
)
=

Det

(
Δ
+
λ
,
B
)

Det

(
R
+
λ
)

{\operatorname {Det}}(\Delta + \lambda ) = {\operatorname {Det}}(\Delta + \lambda ,B){\operatorname {Det}}(R + \lambda )

and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper D e t Superscript asterisk Baseline normal upper Delta equals StartFraction 1 Over left-parenthesis det upper A right-parenthesis squared EndFraction upper D e t left-parenthesis normal upper Delta comma upper B right-parenthesis upper D e t Superscript asterisk Baseline upper R">

Det
∗

Δ
=

1

(
det
A
)

2

Det

(
Δ
,
B
)

Det
∗

R

{\operatorname {Det}^ \ast }\Delta = \frac {1}{{{{(\det A)}^2}}}{\operatorname {Det}}(\Delta ,B){\operatorname {Det}^ \ast }R

. This result was established in 1992 by Burghelea, Friedlander, and Rappeler for a 2-dimensional manifold with

p
=
0

p = 0

.
Provable Π¹₂-singletons
Authors: Friedman S. D.
Published: June 2010

In this note we describe a subtheory T of

Z
F
C
+

0
#

ZFC + {0^\# }

exists such that T is consistent with

V
=
L

V = L

and there is a T-provable

Π
2
1

\Pi _2^1

-singleton

R
,
0

>
L

R

>
L

0
#

R,0{ > _L}R{ > _L}{0^\# }

.
Some inequalities for entire functions of exponential type
Authors: Gardner Robert B. , Govil N. K.
Published: June 2010

If

f
(
z
)

f(z)

is an asymmetric entire function of exponential type

τ
\tau

,
\[

‖
f
‖

=

sup

−
∞
>
x
>
∞

|

f
(
x
)

|

,

\left \| f \right \| = \sup \limits _{ - \infty > x > \infty } |f(x)|,

\]
then according to a well-known result of R. P. Boas,
\[

‖

f
′

‖

≤

τ
2

‖
f
‖

\left \| {f’} \right \| \leq \frac {\tau }{2}\left \| f \right \|

\]
and
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue f left-parenthesis x plus i y right-parenthesis EndAbsoluteValue less-than-or-equal-to StartFraction left-parenthesis e Superscript tau StartAbsoluteValue y EndAbsoluteValue Baseline plus 1 right-parenthesis Over 2 EndFraction double-vertical-bar f double-vertical-bar comma negative normal infinity greater-than x greater-than normal infinity comma negative normal infinity greater-than y less-than-or-equal-to 0 period">

|

f
(
x
+
i
y
)

|

≤

(

e

τ

|

y

|

+
1
)

2

‖
f
‖

,

−
∞
>
x
>
∞
,
−
∞
>
y
≤
0.

|f(x + iy)| \leq \frac {{({e^{\tau |y|}} + 1)}}{2}\left \| f \right \|,\quad - \infty > x > \infty , - \infty > y \leq 0.

\]
Both of these inequalities are sharp. In this paper we generalize the above two inequalities of Boas by proving a sharp inequality which, besides giving as special cases the above two inequalities of Boas, yields some other results as well.
Triangular truncation and normal limits of nilpotent operators
Authors: Hadwin Don
Published: June 2010

We show that, as

n
→
∞

n \to \infty

, the product of the norm of the triangular truncation map on the

n
×
n

n \times n

complex matrices with the distance from the norm-one hermitian

n
×
n

n \times n

matrices to the nilpotents converges to 1/2. We also include an elementary proof of D. Herrero’s characterization of the normal operators that are norm limits of nilpotents.
Two-dimensional representations of uniform algebras
Authors: Nakazi Takahiko , Takahashi Katsutoshi
Published: June 2010

It is shown that every two-dimensional representation of a uniform algebra has a dilation, which extends the result by Paulsen. We also prove some dilation result for a representation of the disk algebra.
On ℳ-harmonic Bloch space
Authors: Jevtić Miroljub , Pavlović Miroslav
Published: June 2010

We show that many of the characterizations of analytic Bloch functions also characterize

M

\mathcal {M}

-harmonic Bloch functions.
On the Betti number of the image of a codimension-𝑘 immersion with normal crossings
Authors: Biasi Carlos , Saeki Osamu
Published: June 2010

Let

f
:
M
→
N

f:M \to N

be a codimension-k immersion with normal crossings of a closed m-dimensional manifold. We show that f is an embedding if and only if the

(
m
−
k
+
1
)

(m - k + 1)

-th Betti numbers of M and

f
(
M
)

f(M)

coincide, under a certain condition on the normal bundle of f.
A right inverse of the Askey-Wilson operator
Authors: Brown B. Malcolm , Ismail Mourad E. H.
Published: June 2010

We establish an integral representation of a right inverse of the Askey-Wilson finite difference operator on

L
2

{L^2}

with weight

(
1
−

x
2

)

−
1

/

2

{(1 - {x^2})^{ - 1/2}}

. The kernel of this integral operator is

ϑ
4
′

/

ϑ
4

\vartheta _4’/\vartheta _4

and is the Riemann mapping function that maps the interior of an ellipse conformally onto the open unit disc.
Projections algebraically generate the bounded operators on real or quaternionic Hilbert space
Authors: Holland Samuel S.
Published: June 2010

We prove the theorem of the title.
A nonhomogeneity property of 𝜎-ideals
Authors: Prikry Karel
Published: June 2010

The object of this note is to prove a theorem of P. Chernoff and R. Solovay concerning a structural property of

ω
1

{\omega _1}

-saturated ideals. Their proof used Boolean-valued models; the present proof does not use any specialized tools of mathematical logic.
A direct proof of a theorem of Telgársky
Authors: Scheepers Marion
Published: June 2010

We give a direct proof of the fact that if player TWO of a certain infinite game on a metric space has a winning strategy, then the space is a union of countably many of its compact subsets.
A full extension of the Rogers-Ramanujan continued fraction
Authors: Andrews George E. , Bowman Douglas
Published: June 2010

In this paper, we present the natural extension of the Rogers-Ramanujan continued fraction to the nonterminating very well-poised basic hypergeometric function

8

ϕ
7

_8{\phi _7}

. In a letter to Hardy, Ramanujan indicated that he possessed a four variable generalization. Our generalization has seven variables and is, perhaps, all one can expect from this method.
A counter-example on a quasi-variational inequality without lower semicontinuity assumption
Authors: Cubiotti Paolo
Published: June 2010

In this note we show that a recent result on quasi-variational inequalities, which seems to improve deeply some well-known results, is not correct.
A note on a theorem of Chiswell
Authors: Jackson Stephen , Zamboni Luca Q.
Published: June 2010

In this note we give an alternative proof of a theorem of I. M. Chiswell which states that every finitely generated group which acts non-trivially on a

Λ
−

\Lambda -

tree admits a non-trivial action on an

R

−

\mathbb {R} -

tree.
A note on the Thue inequality
Authors: Bean Michael A.
Published: June 2010

We show that for an arbitrary binary form

F
(
X
,
Y
)

F(X,Y)

, there is no non-trivial lower bound for the area of the region

|

F
(
x
,
y
)

|

≤
1

|F(x,y)| \leq 1

which depends only on the discriminant of F.
On the area distortion by quasiconformal mappings
Authors: Erëmenko A. , Hamilton D. H.
Published: June 2010

We give the sharp constants in the area distortion inequality for quasiconformal mappings in the plane.
A topological equivalence of the singular cardinals hypothesis
Authors: Ismail M. , Szymanski A.
Published: June 2010

We show, in particular, that the Singular Cardinals Hypothesis is equivalent to the following statement: for each metric space X of cardinality greater than the continuum and of weigh of uncountable cofinality, the cardinality of X equals the weight of X.