bluuebunny/crossref_metadata_2025 huggingface dataset:
Lower estimate in Littlewood’s conjecture on the mean spherical derivative of a polynomial and iteration theory
Authors: Erëmenko A. È.
Published: June 2010

Lewis and Wu have proved J. E. Littlewood’s conjecture of the growth of the spherical derivative of polynomials. We apply the theory of complex iteration to show that this conjecture is sharp in a qualitative sense.
A counterexample for Kobayashi completeness of balanced domains
Authors: Jarnicki Marek , Pflug Peter
Published: June 2010

The aim of this paper is to present an example of a bounded balanced domain of holomorphy in

C

n

(
n
≥
3
)

{\mathbb {C}^n}(n \geq 3)

with continuous Minkowski function that is not Kobayashi-finitely-compact.
A homogeneous continuum that is non-Effros
Authors: Bellamy David P. , Porter Kathryn F.
Published: June 2010

Using a very geometric, intuitive construction, an example is given of a homogeneous, compact, connected Hausdorff space

(
X
,
T
)

(X,T)

that does not satisfy the conclusion of the Effros Theorem. In particular, there is a point

p
p

and a neighborhood

V
V

, of the identity in the group of self-homeomorphisms on

X
X

, with the compact-open topology such that

V
p

=
{
h
(
p
)
:
h
∈
V
}

{V_p} = \{ h(p):h \in V\}

is nowhere dense in

X
X

.
There is a 𝑄-set space in ZFC
Authors: Balogh Zoltán T.
Published: June 2010

It is shown that there is a regular

T
1

{T_1}

-space whose every subset is a

G
δ

{G_\delta }

-set and yet the space is not

σ
\sigma

-discrete.
On the subgroup separability of generalized free products of nilpotent groups
Authors: Tang C. Y.
Published: June 2010

We prove that generalized free products of finitely generated nilpotent groups with cyclic amalgamation are subgroup separable
A comparison result for the oscillation of delay differential equations
Authors: Ladas G. , Qian C. , Yan J.
Published: June 2010

We obtain a comparison result for the oscillation of all solutions of the equation\[<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove y With dot left-parenthesis t right-parenthesis plus sigma-summation Underscript i equals 1 Overscript n Endscripts q Subscript i Baseline left-parenthesis t right-parenthesis y left-parenthesis t minus sigma Subscript i Baseline left-parenthesis t right-parenthesis right-parenthesis equals 0">y˙(t)+∑i=1nqi(t)y(t−σi(t))=0\dot y(t) + \sum \limits _{i = 1}^n {{q_i}(t)y(t - {\sigma _i}(t)) = 0}\]in terms of the oscillation of all solutions of the equation\[<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove x With dot left-parenthesis t right-parenthesis plus sigma-summation Underscript i equals 1 Overscript n Endscripts p Subscript i Baseline left-parenthesis t right-parenthesis x left-parenthesis t minus tau Subscript i Baseline left-parenthesis t right-parenthesis right-parenthesis equals 0">x˙(t)+∑i=1npi(t)x(t−τi(t))=0\dot x(t) + \sum \limits _{i = 1}^n {{p_i}(t)x(t - {\tau _i}(t)) = 0}\]under appropriate hypotheses on the asymptotic behavior of the quotientspi(t)/qi(t){p_i}(t)/{q_i}(t)andτi(t)/σi(t){\tau _i}(t)/{\sigma _i}(t)fori=1,2,…,ni = 1,2, \ldots ,n. An application to the oscillation of the nonautonomous delay-logistic equation is given.
Generic heat diffusion is scalar controllable
Authors: Markus Lawrence
Published: June 2010

The partial differential equation for heat diffusion on a closed manifold

M
M

is approximately controllable by a single distributed controller, under generic conditions. But we also give examples, where

M
M

is a torus surface, for which no finite number of scalar controllers suffice.
The nonlocal nature of the summability of Fourier series by certain absolute Riesz methods
Authors: Borwein David
Published: June 2010

It is proved that for a large class of sequences

{

λ
n

}

\{ {{\lambda _n}} \}

the summability at a point of a Fourier series

Σ

A
n

(
t
)

\Sigma A_n ( t )

by the absolute Riesz method

|

R
,

λ
n

,
1

|

| {R,{\lambda _n},1} |

is not a local property of the generating function. It is also proved, inter alia, that, for every

ε
>
0

\varepsilon > 0

, the

|

R
,

λ
n

,
1

|

| {R,{\lambda _n},1} |

summability of the factored series

Σ

A
n

(
t
)

λ
n

−
ε

\Sigma A_n ( t )\lambda _n^{ - \varepsilon }

at any point is always a local property of the generating function.
Orthogonal polynomials with ratio asymptotics
Authors: Totik Vilmos
Published: June 2010

A general construction is given for measures for which the corresponding orthogonal polynomials have ratio asymptotics.
Making a hole in the space
Authors: Goebel Kazimierz , Wośko Jacek
Published: June 2010

The paper provides a simple recipe for a construction of homeomorphisms "removing" convex bodies from nonreflexive Banach spaces.
An inequality of Araki-Lieb-Thirring (von Neumann algebra case)
Authors: Kosaki Hideki
Published: June 2010

For a trace

τ
\tau

on a semifinite von Neumann algebra we will prove
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="tau left-parenthesis left-parenthesis b Superscript 1 slash 2 Baseline a b Superscript 1 slash 2 Baseline right-parenthesis Superscript r p Baseline right-parenthesis less-than-or-equal-to tau left-parenthesis left-parenthesis b Superscript r slash 2 Baseline a Superscript r Baseline b Superscript r slash 2 Baseline right-parenthesis Superscript p Baseline right-parenthesis">

τ
(

(

b

1

/

2

a

b

1

/

2

)

r
p

)
≤
τ
(

(

b

r

/

2

a
r

b

r

/

2

)
p

)

\tau ({({b^{1/2}}a{b^{1/2}})^{rp}}) \leq \tau ({({b^{r/2}}{a^r}{b^{r/2}})^p})

. Here,

r
≥
1
,
p
>
0

r \geq 1,p > 0

, and

a
,
b

a,b

are positive operators.
A note on the Dirichlet problem at infinity for manifolds of negative curvature
Authors: Borbély Albert
Published: June 2010

M. T. Anderson and D. Sullivan showed that the Dirichlet problem at infinity for simply connected manifolds is solvable if the curvature satisfies

−

a
2

>
K
>
−

b
2

- {a^2} > K > - {b^2}

. Using M. T. Anderson’s method we generalize this statement to manifolds satisfying the weaker bounds

−
g
(
r
)
>
K
>
−

b
2

- g(r) > K > - {b^2}

, where

g
(
r
)
≈

e

λ
r

g(r) \approx {e^{\lambda r}}

, with

λ
>
1

/

3

\lambda > 1/3

.
On the minimum modulus of trigonometric polynomials
Authors: Benke George
Published: June 2010

For all even integers

N
N

greater than 2, a trigonometric polynomial

f
N

(
x
)
=

∑

k
=
−
N

N
2

a
k

e

i
k
x

{f_N}(x) = \sum \nolimits _{k = - N}^{{N^2}} {{a_k}{e^{ikx}}}

satisfying

|

a
k

|

≤

1

|{a_k}|\; \leq \;1

and

0.47
N
≤

|

f
N

(
x
)

|

≤
N

0.47N \leq |{f_N}(x)| \leq N

is constructed.
Boundedness of solutions to functional integro-differential equations
Authors: Hu Zuo Sheng
Published: June 2010

In this paper we discuss the boundedness of the solutions of a class of functional integro-differential equations. We give an example to answer a question posed by S. M. Kuen and K. P. Rybakowski, and we establish a sufficient condition, which is more general than the condition they obtained.
Domination and ergodicity for positive semigroups
Authors: Arendt W. , Batty C. J. K.
Published: June 2010

In this note we study the conditions under which ergodicity is preserved by domination. As an application, the criterion for almost periodicity given by Ljubich-Phong [9] (see also Batty-Phong [4]) can be simplified for positive semigroups.
Rationality of representations of linear Lie groups
Authors: Lee Dong Hoon , Wu Ta Sun
Published: June 2010

We are concerned with real linear Lie groups

G
G

having the property that every finite-dimensional continuous representation of

G
G

is rational.
A character sum for root system 𝐺₂
Authors: Evans Ronald
Published: June 2010

A character sum analog of the Macdonald-Morris constant term identity for the root system

G
2

{G_2}

is proved. The proof is based on recent evaluations of Selberg character sums and on a character sum analog of Dixon’s summation formula. A conjectural evaluation is presented for a related sum.
A transfer theorem for nonstandard uniserials
Authors: Eklof Paul C.
Published: June 2010

A general theorem is described and proved which allows the transfer of results about the existence of nonstandard uniserial modules over a valuation domain from models of

ZFC
+
♢

\operatorname {ZFC} + \diamondsuit

to all models of ZFC.
An AR-map whose range is more infinite-dimensional than its domain
Authors: Dijkstra J. J. , van Mill J. , Mogilski J.
Published: June 2010

We construct an example of an AR-map

f
:
X
→
Y

f:X \to Y

, where

X
X

is a strongly countable dimensional compact AR and

Y
Y

is a countable dimensional AR which is not strongly countable dimensional. Using this map we find a shrinkable decomposition of the pre-Hilbert space

l
f
2

l_f^2

whose quotient map does not stabilize to a near homeomorphism. We also present a partial result concerning the question whether cell-like maps preserve countable dimensionality.
The self-joinings of rank two mixing transformations
Authors: Ullman Daniel
Published: June 2010

The class of rank one mixing transformations has been known for some time to have certain so-called "exotic" properties. Specifically, any rank one mixing

T
T

has only the two trivial factors, and nothing can commute with

T
T

but powers of

T
T

itself. This much was known to Ornstein in 1969 [3]. In 1983 J. King showed that rank one mixing transformations possess an even stronger property known as minimal self-joinings (MSJ). In this note we investigate how these results can be extended to the case of rank two mixing transformations. In this class, it is possible for there to exist nontrivial factors and commuting transformations: the square of a rank one mixing transformation and certain two point extensions of a rank one mixing transformation are rank two mixing [2]. What we prove is that, other than those two kinds of rank two mixing transformations, this class also has MSJ.
Presentations for 3-dimensional special linear groups over integer rings
Authors: Conder Marston , Robertson Edmund , Williams Peter
Published: June 2010

The following

2
2

-generator

6
6

-relator presentation is obtained for the

3
3

-dimensional special linear group

SL
⁡
(
3
,

Z

k

)

\operatorname {SL}(3,{\mathbb {Z}_k})

for each odd integer

k
>
1

k > 1

:
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S upper L left-parenthesis 3 comma double-struck upper Z Subscript k Baseline right-parenthesis equals mathematical left-angle x comma y vertical-bar x cubed equals y cubed equals left-parenthesis x y right-parenthesis Superscript 6 Baseline equals left-parenthesis x Superscript negative 1 Baseline y x Superscript negative 1 Baseline y Superscript negative 1 Baseline x y right-parenthesis squared equals left-parenthesis x y Superscript negative 1 Baseline x y x y Superscript negative 1 Baseline x Superscript negative 1 Baseline y Superscript negative 1 Baseline right-parenthesis Superscript k Baseline equals left-parenthesis left-parenthesis x y Superscript negative 1 Baseline x y x y Superscript negative 1 Baseline x Superscript negative 1 Baseline y Superscript negative 1 Baseline right-parenthesis Superscript left-parenthesis k minus 1 right-parenthesis slash 2 Baseline x y right-parenthesis Superscript 4 Baseline equals 1 mathematical right-angle period">

SL
⁡
(
3
,

Z

k

)
=
⟨
x
,
y

|

x
3

=

y
3

=

(
x
y

)
6

=

(

x

−
1

y

x

−
1

y

−
1

x
y

)
2

=

(
x

y

−
1

x
y
x

y

−
1

x

−
1

y

−
1

)
k

=

(

(
x

y

−
1

x
y
x

y

−
1

x

−
1

y

−
1

)

(
k
−
1
)

/

2

x
y

)
4

=
1
⟩
.

\operatorname {SL}(3,{\mathbb {Z}_k}) = \langle x,y|{x^3} = {y^3} = {(xy)^6} = {({x^{ - 1}}y{x^{ - 1}}{y^{ - 1}}xy)^2} = {(x{y^{ - 1}}xyx{y^{ - 1}}{x^{ - 1}}{y^{ - 1}})^k} = {({(x{y^{ - 1}}xyx{y^{ - 1}}{x^{ - 1}}{y^{ - 1}})^{(k - 1)/2}}xy)^4} = 1\rangle .

\]
Alternative presentations for these groups and other groups associated with them are also given.
An extension of a theorem of D. Khavinson: “The Cauchy-Green formula and rational approximation on the sets with a finite perimeter in the complex plane” [J. Funct. Anal. 64 (1985), no. 1, 112–123; MR0808271 (87a:30062)]
Authors: Ferry John
Published: June 2010

We extend a generalization of the Cauchy-Green formula, which in turn extends results in rational approximation.
Representations of Chevalley groups arising from admissible lattices
Authors: Lin Zong Zhu
Published: June 2010

The modules for a Chevalley group arising from admissible lattices in an irreducible module for the associated complex semisimple Lie algebra are studied. It is proved that the transpose of such a module is still in this collection and generically the cohomology modules of line bundles on the flag varieties are in this collection also. In the rank 1 case, all modules in this collection are indecomposable and we hope this is true in general.
A consistency result on thin-tall superatomic Boolean algebras
Authors: Martínez Juan Carlos
Published: June 2010

We prove that if

[
u
n
k
]

[unk]

is an infinite cardinal with

[
u
n
k

]

>
[
u
n
k
]

=
[
u
n
k
]

{[unk]^{ > [unk]}} = [unk]

, then there is a cardinal-preserving notion of forcing that forces the existence of a

[
u
n
k
]

[unk]

-thin-tall superatomic Boolean algebra. Consistency for specific

[
u
n
k
]

[unk]

, like

ω
1

{\omega _1}

, then follows as a corollary.
Regularity and 𝜎-additivity of states on quantum logics
Authors: Navara Mirko
Published: June 2010

In 1977, Béaver and Cook [1] introduced the notion of regularity of states on quantum logics. They presented a generalization of Alexandroff theorem: each regular finitely additive state on a quantum logic is countably additive. Recently, Dvurečenskij, Neubrunn, and Pulmannová [2] observed an incorrectness in the original proof and doubted thus the validity of the result. We construct here a counterexample.
Dimensionally nilpotent Jordan algebras
Authors: Osborn J. Marshall
Published: June 2010

An algebra

A
A

of dimension

n
n

is called dimensionally nilpotent if it has a nilpotent derivation

∂
\partial

with the property that

∂

n
−
1

≠
0

{\partial ^{n - 1}} \ne 0

. Here we show that a dimensionally nilpotent Jordan algebra

A
A

over a perfect field of characteristic not 2 or 3 is either (i) nilpotent, or (ii) one-dimensional modulo its maximal nilpotent ideal. This result is also extended to noncommutative Jordan algebras.
Pointwise kernels of Schwartz distributions
Authors: Todorov Todor
Published: June 2010

We show that Schwartz distributions have kernels in the class of the pointwise nonstandard functions.
Exponential asymptotics for an eigenvalue of a problem involving parabolic cylinder functions
Authors: Brazel Neal , Lawless Fiona , Wood Alastair
Published: June 2010

We obtain the leading asymptotic behaviour asε→0+\varepsilon \to 0 +of the exponentially small imaginary part of the "eigenvalue" of the perturbed nonself-adjoint problem comprisingy(x)+(λ+εx2)y(x)=0y(x) + (\lambda + \varepsilon {x^2})y(x) = 0with a linear homogeneous boundary condition atx=0x = 0and an "outgoing wave" condition asx→+∞x \to + \infty. The problem is a generalization of a model equation for optical tunnelling considered by Paris and Wood [10]. We show that this "eigenvalue" corresponds to a pole in the Titchmarsh-Weyl functionm(λ)m(\lambda )for the corresponding formally self-adjoint problem withL2(0,∞){L^2}(0,\infty )boundary condition.
Quadrature formulas for monotone functions
Authors: Novak Erich
Published: June 2010

We prove that adaptive quadrature formulas for the class of monotone functions are much better than nonadaptive ones if the average error is considered. Up to now it was only known that adaptive methods are not better in the worst case (for this and many other classes of functions) or in various average case settings. We also prove that adaptive Monte Carlo methods are much better than nonadaptive ones. This also contrasts with analogous results for other classes (Sobolev classes, Hölder classes) where adaptive methods are only slightly better than nonadaptive ones.
On convexity of level curves of harmonic functions in the hyperbolic plane
Authors: Papadimitrakis M.
Published: June 2010

We prove that if two level curves of a harmonic function are convex in the hyperbolic disc then all intermediate level curves are also convex.
On the porosity of the set of 𝜔-nonexpansive mappings without fixed points
Authors: Myjak J. , Sampalmieri R.
Published: June 2010

Let

C
C

be a nonempty closed convex bounded subset of a Banach space

E
E

. Let

M

\mathcal {M}

denote the family of all multivalued mappings from

C
C

into

E
E

which are nonempty weakly compact convex valued,

ω
\omega

-nonexpansive and weakly-weakly u.s.c., endowed with the metric of uniform convergence. Let

M

0

{\mathcal {M}_0}

be the set of all

F
∈

M

F \in \mathcal {M}

for which the fixed point problem is well posed. It is proved that the set

M

∖

M

0

\mathcal {M}\backslash {\mathcal {M}_0}

is

σ
\sigma

-porous (in particular meager). A similar result is given for weak properness.
On the extension of multimeasures and integration with respect to a multimeasure
Authors: Kandilakis Dimitrios A.
Published: June 2010

We present a Caratheodory-Hahn-Kluvanek-type theorem for multimeasures whose values are weakly compact and convex subsets of a Banach space. Set functions obtained by integrating a bounded measurable function with respect to a multimeasure are also studied.
An extension of Rourke’s proof that Ω₃=0 to nonorientable manifolds
Authors: Ancel Fredric D. , Guilbault Craig R.
Published: June 2010

A classical result in manifold theory states that every closed

3
3

-manifold bounds a compact

4
4

-manifold. In 1985 C. Rourke discovered a strikingly short and elementary proof of the orientable case of this theorem

(

Ω
3

=
0
)

({\Omega _3} = 0)

. In this note we show that Rourke’s approach can be extended to include nonorientable

3
3

-manifolds.
An orientation reversing homeomorphism of the plane with invariant pseudo-arc
Authors: Bellamy David P. , Lewis Wayne
Published: June 2010

Using the universal cover of the Möbius band, we construct an example as described in the title which answers a question of K. Kuperberg.
A test theorem on coherent GCD domains
Authors: Zhao Yi Cai
Published: June 2010

Let

R
R

be a commutative indecomposable coherent ring. Then the following statements are equivalent: (i)

R
R

is a GCD domain; (ii)

R
M

{R_M}

is a GCD domain for every maximal ideal of

M
M

of

R
R

, and every finitely generated projective ideal in

R
R

is principal; (iii) every two-generated ideal in

R
R

has finite projective dimension, and every finitely generated projective ideal in

R
R

is principal. Auslander-Buchsbaum’s Theorem, etc. can be obtained from the result above.
On the cup product for groups
Authors: Dyer M. N. , Leahy J. V. , Mooney L. J.
Published: June 2010

For

G
G

any group and trivial coefficients in

R
R

, a commutative ring, the authors analyze the kernel of the cup product
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="union colon upper H Superscript 1 Baseline left-parenthesis upper G comma upper R right-parenthesis circled-times upper H Superscript 1 Baseline left-parenthesis upper G comma upper R right-parenthesis right-arrow upper H squared left-parenthesis upper G comma upper R right-parenthesis">

∪
:

H
1

(

G
,
R

)

⊗

H
1

(

G
,
R

)

→

H
2

(

G
,
R

)

\cup :{H^1}\left ( {G,R} \right ) \otimes {H^1}\left ( {G,R} \right ) \to {H^2}\left ( {G,R} \right )

by splicing it together with part of the six-term Hom-Ext exact sequence obtained from

0
→

I
2

/

I
3

→
I

/

I
3

→
I

/

I
2

→
0

0 \to {I^2}/{I^3} \to I/{I^3} \to I/{I^2} \to 0

.
Layers of components of 𝛽([0,1]×𝑁) are indecomposable
Authors: Smith Michel
Published: June 2010

We examine the structure of certain subcontinua of the Stone-Čech compactification of the reals. Let

N
N

denote the integers, let

X
=
[
0
,
1
]
×
N

X = [0,1] \times N

, and let

C
C

be a component of

X
∗

=
β
X
−
X

{X^*} = \beta X - X

. It is known that

C
C

admits an upper semicontinuous decomposition

G
G

into maximal nowhere dense subcontinua of

C
C

so that

C

/

G

C/G

is a Hausdorff arc. The elements of

G
G

are called layers. It has been shown that the layers of

C
C

that contain limit points of a countable increasing or decreasing sequence of cut points of

C
C

are nondegenerate indecomposable continua (various forms of this fact have been proven by Bellamy and Rubin, Mioduszewski, and Smith). We show that all the layers of

C
C

are indecomposable.*
Prescribing a Ricci tensor in a conformal class of Riemannian metrics
Authors: Xu Xingwang
Published: June 2010

We show that two pointwise conformal metrics that have the same Ricci tensor must be homothetic.
On Opial’s inequality for 𝑓⁽ⁿ⁾
Authors: Fink A. M.
Published: June 2010

We prove inequalities of the type
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Subscript 0 Superscript h Baseline StartAbsoluteValue f Superscript left-parenthesis i right-parenthesis Baseline left-parenthesis x right-parenthesis f Superscript left-parenthesis j right-parenthesis Baseline left-parenthesis x right-parenthesis EndAbsoluteValue d x less-than-or-equal-to upper C left-parenthesis n comma i comma j comma p right-parenthesis h Superscript 2 n minus i minus j plus 1 minus 2 slash p Baseline left-parenthesis integral Subscript 0 Superscript h Baseline StartAbsoluteValue f Superscript left-parenthesis n right-parenthesis Baseline left-parenthesis x right-parenthesis EndAbsoluteValue Superscript p Baseline d x right-parenthesis Superscript 2 slash p Baseline">

∫
0
h

|

f

(
i
)

(
x
)

f

(
j
)

(
x
)

|

d
x
≤
C
(
n
,
i
,
j
,
p
)

h

2
n
−
i
−
j
+
1
−
2

/

p

(

∫
0
h

|

f

(
n
)

(
x
)

|

p

d
x

)

2

/

p

{\int _0^h {|{f^{(i)}}(x){f^{(j)}}(x)|dx \leq C(n,i,j,p){h^{2n - i - j + 1 - 2/p}}\left ( {\int _0^h {|{f^{(n)}}(x){|^p}dx} } \right )} ^{2/p}}

\]
when
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis 0 right-parenthesis equals f prime left-parenthesis 0 right-parenthesis equals midline-horizontal-ellipsis equals f Superscript left-parenthesis n minus 1 right-parenthesis Baseline left-parenthesis 0 right-parenthesis equals 0">

f
(
0
)
=

f
′

(
0
)
=
⋯
=

f

(
n
−
1
)

(
0
)
=
0

f(0) = f’(0) = \cdots = {f^{(n - 1)}}(0) = 0

. We assume that

f

(
n
−
1
)

{f^{(n - 1)}}

is absolutely continuous and

f

(
n
)

∈

L
p

(
0
,
h
)

{f^{(n)}} \in {L_p}(0,h)

, with

p
≥
1
,
n
≥
2

p \geq 1,n \geq 2

, and

0
≤
i
≤
j
≤
n
−
1

0 \leq i \leq j \leq n - 1

.
Lattices with the Alexandrov properties
Authors: Gorelishvili Albert
Published: June 2010

By an Alexandrov lattice we mean a

δ
\delta

normal lattice

L

\mathcal {L}

of subsets of an abstract set

X
X

, such that the set of

L

\mathcal {L}

-regular countably additive bounded measures, denoted by

MR
⁡
(
σ
,

L

)

\operatorname {MR}(\sigma ,\mathcal {L})

, is sequentially closed in the set of

L

\mathcal {L}

-regular finitely additive bounded measures on the algebra generated by

L

\mathcal {L}

, i.e., if

μ
n

∈
MR
⁡
(
σ
,

L

)

{\mu _n} \in \operatorname {MR}(\sigma ,\mathcal {L})

and

μ
n

→
μ

{\mu _n} \to \mu

(weakly) then

μ
∈
MR
⁡
(
σ
,

L

)

\mu \in \operatorname {MR}(\sigma ,\mathcal {L})

. For a pair of lattices

L

1

⊂

L

2

{\mathcal {L}_1} \subset {\mathcal {L}_2}

in

X
X

sufficient conditions are indicated to determine when

L

1

{\mathcal {L}_1}

Alexandrov implies that

L

2

{\mathcal {L}_2}

is also Alexandrov and vice versa. The extension of this situation is given where

T
:
X
→
Y
,

L

1

T:X \to Y,{\mathcal {L}_1}

and

L

2

{\mathcal {L}_2}

are lattices of subsets of

X
X

of

Y
Y

respectively, and

T
T

is

L

1

−

L

2

{\mathcal {L}_1} - {\mathcal {L}_2}

continuous.
Boundaries of the spectra in ℒ(𝒳)
Authors: Lee Woo Young
Published: June 2010

Suppose

T
T

is a bounded linear operator on a complex Banach space

X
X

. If

T
T

is "regular" with some finite dimensional intersection property and if 0 is in the boundary of the spectrum of

T
T

then 0 is an isolated point of it.
An approximation connected with the exponential function
Authors: Soni K. , Soni R. P.
Published: June 2010

Some recent techniques in the uniform asymptotic expansions of integrals are used to obtain an expansion for a function related to the exponential function. This function is associated with Ramanujan, Watson, Copson, and Buckholtz. The results obtained complement those given by Buckholtz.
Multiplicative subgroups of finite index in a ring
Authors: Bergelson Vitaly , Shapiro Daniel B.
Published: June 2010

If

G
G

is a subgroup of finite index in the multiplicative group of an infinite field

K
K

then

G
−
G
=
K

G - G = K

. Similar results hold for various rings.
Some remarks of drop property
Authors: Lin Pei-Kee
Published: June 2010

Let

C
C

be a proper closed convex set.

C
C

is said to have the drop property if for any nonempty closed set

A
A

disjoint with

C
C

, there is

a
∈
A

a \in A

such that

co(

a
,
C

)

∩

A = 

{
a
}

{\text {co(}}a,C{\text {)}} \cap {\text {A = }}\left \{ a \right \}

. We show that if

X
X

contains a noncompact set with the drop property, then

X
X

is reflexive. Moreover, we prove that if

C
C

is a noncompact closed convex subset of a reflexive Banach space, then

C
C

has the drop property if and only if

C
C

satisfies the following conditions: (i) the interior of

C
C

is nonempty; (ii)

C
C

does not have any asymptote, and the boundary of

C
C

does not contain any ray; and (iii) every support point

x
x

of

C
C

is a point of continuity.
Two notes on convergence and divergence a.e. of Fourier series with respect to some orthogonal systems
Authors: Guadalupe J. J. , Pérez M. , Ruiz F. J. , Varona J. L.
Published: June 2010

We study some problems related to convergence and divergence a.e. for Fourier series in systems

{

ϕ
k

}

\{ {\phi _k}\}

, where

{

ϕ
k

}

\{ {\phi _k}\}

is either a system of orthonormal polynomials with respect to a measure

d
μ

d\mu

on

[
−
1
,
1
]

[-1,1]

or a Bessel system on

[
0
,
1
]

[0,1]

. We obtain boundedness in weighted

L
p

{L^p}

spaces for the maximal operators associated to Fourier-Jacobi and Fourier-Bessel series. On the other hand, we find general results about divergence a.e. of the Fourier series associated to Bessel systems and systems of orthonormal polynomials on

[
−
1
,
1
]

[-1,1]

.
Invariant subspaces for closed *-representations of *-algebras
Authors: Ikeda Itsuko , Inoue Atsushi
Published: June 2010

The first purpose of this paper is to investigate the selfadjointness of

∗
*

-subrepresentations of closed

∗
*

-representations. The second purpose is to define the notion of selfadjoint vectors for any closed

∗
*

-representation

π
\pi

of a

∗
*

-algebra

A

\mathcal {A}

and to show that

π
\pi

is decomposed into

π
=

π
1
S

⊕

π
2
S

\pi = \pi _1^S \oplus \pi _2^S

, where

π
1
S

\pi _1^S

is a direct sum of cyclic selfadjoint representations of

A

\mathcal {A}

and

π
2
S

\pi _2^S

is a closed

∗
*

-representation of

A

\mathcal {A}

that does not have any nonzero selfadjoint vector.
Sur la structure des composantes connexes semi-Fredholm de 𝐵(𝐻)
Authors: Mbekhta M.
Published: June 2010

Dans ce travail, nous montrons que dans

B
(
H
)

B(H)

les composantes connexes semi-Fredholm ont la même frontière et, d’autre part que

B
(
H
)

B(H)

s’écrit comme la réunion de cette frontière commune

(
Δ
)

(\Delta )

et de l’ensemble des opérateurs semi-Fredholm. Nous remarquons que

Δ
\Delta

est un ensemble de première catégorie, stable pour les perturbations compactes. Par ailleurs, nous montrons que l’intérieur de

[
u
n
k
]
(
H
)

[unk](H)

, l’ensemble des opérateurs "réguliers", est exactement l’ensemble des opérateurs semi-Fredholm et que la frontière de

[
u
n
k
]
(
H
)

[unk](H)

est également

Δ
\Delta

.
Compact weighted composition operators on 𝐿^{𝑝}
Authors: Takagi Hiroyuki
Published: June 2010

We characterize the compact weighted composition operators on

L
p

(
1
≤
p
>
∞
)

{L^p}(1 \leq p > \infty )

and determine their spectra. We also show that every weakly compact weighted composition operator on

L
1

{L^1}

is compact.
Principal eigenvalues for indefinite-weight elliptic problems in 𝑅ⁿ
Authors: Allegretto W.
Published: June 2010

We consider the problem

−
Δ
u
=
λ
g
u

- \Delta u = \lambda gu

in

R
n

{R^n}

,

u
→
0

u \to 0

at

∞
\infty

with

g
g

a function that changes sign. Under suitable growth conditions on

g
g

we show that this problem has an eigenvalue

λ
\lambda

with a positive solution

u
u

, as well as countably many other eigenvalues.
Density points and bi-Lipschitz functions in 𝑅^{𝑚}
Authors: Buczolich Zoltán
Published: June 2010

If

A
,
B
⊂

R

m

A,B \subset {{\mathbf {R}}^m}

and

f
f

is a bi-Lipschitz function mapping

A
A

onto

B
B

then density or dispersion points of

A
A

are mapped exactly onto density or dispersion points of

B
B

, respectively.
Representing knot groups into 𝑆𝐿(2,𝐶)
Authors: Cooper D. , Long D. D.
Published: June 2010

We show that if a knot in

S
3

{S^3}

has nontrivial Alexander polynomial then the fundamental group of its complement has a representation into

SL
⁡
(
2
,

C

)

\operatorname {SL}(2,{\mathbf {C}})

whose image contains a free group of rank two.
A counter example to a conjecture of Johns
Authors: Faith Carl , Menal Pere
Published: June 2010

In this paper, we construct a counter example to a conjecture of Johns to the effect that a right Noetherian ring in which every right ideal is an annihilator is right Artinian. Our example requires the existence of a right Noetherian domain

A
A

(not a field) with a unique simple right module

W
W

such that

W
A

{W_A}

is injective and

A
A

embeds in the endomorphism ring

End
⁡
(

W
A

)

\operatorname {End} ({W_A})

. Then the counter example is the trivial extension

R
=
A
⋉
W

R = A \ltimes W

of

A
A

and

W
W

. The ring

A
A

exists by a theorem of Resco using a theorem of Cohn. Specifically, if

D
D

is any countable existentially closed field with center

k
k

, then the right and left principal ideal domain defined by

A
=
D

⊗
k

k
(
x
)

A = D{ \otimes _k}k(x)

, where

k
(
x
)

k(x)

is the field of rational functions, has the desired properties, with

W
A

≈

D
A

{W_A} \approx {D_A}

.
A smooth holomorphically convex disc in 𝐶² that is not locally polynomially convex
Authors: Forstnerič Franc
Published: June 2010

We construct a smooth embedded disc in

C

2

{{\mathbf {C}}^2}

that is totally real except at one point

p
p

, is holomorphically convex, but fails to be locally polynomially or even rationally convex at

p
p

.
Complete conformal metrics with zero scalar curvature
Authors: Ma Xiaoyun , McOwen Robert C.
Published: June 2010

In this paper we consider the problem of when a noncompact Riemannian manifold

M
^

\widehat {M}

admits a complete conformal metric with zero scalar curvature. In particular, we show that this can be achieved if

M
^

\widehat {M}

is the noncompact manifold obtained by deleting a smooth submanifold

Γ
n

{\Gamma ^n}

from a compact Riemannian manifold

M
N

{M^N}

provided

n
≤
(
N
−
2
)

/

2

n \leq (N - 2)/2

and the Sobolev quotient is positive.
Linear transformations of Wiener integrals
Authors: Park Chull , Skoug David
Published: June 2010

In this paper we obtain a linear transformation theorem in which the Radon-Nikodym derivative is very closely related to the transformation. We also obtain a vector-valued conditional version of this linear transformation theorem.
Dirichlet polyhedra for cyclic groups in complex hyperbolic space
Authors: Phillips Mark B.
Published: June 2010

We prove that the Dirichlet fundamental polyhedron for a cyclic group generated by a unipotent or hyperbolic element

γ
\gamma

acting on complex hyperbolic

n
n

-space centered at an arbitrary point

w
w

is bounded by the two hypersurfaces equidistant from the pairs

w
,
γ
w

w,\gamma w

and

w
,

γ

−
1

w

w,{\gamma ^{ - 1}}w

respectively. The proof relies on a convexity property of the distance to an isometric flow containing

γ
\gamma

.
On the inverse of Mañé’s projection
Authors: Movahedi-Lankarani H.
Published: June 2010

We show that every compact ultrametric space is bi-Lipschitz embeddable in a Hilbert space. We also provide an example of a compact ultrametric space whose fractal (and hence Hausdorff) dimension is finite, but which cannot be bi-Lipschitz embedded in any finite dimensional Euclidean space. This example, in particular, establishes that the inverse of Mañé’s projection need not be Lipschitz even in the case of finite fractal dimension.
The differential equation 𝑄=0 in which 𝑄 is a quadratic form in 𝑦”,𝑦’,𝑦 having meromorphic coefficients
Authors: Chalkley Roger
Published: June 2010

A simple necessary and sufficient condition is given for the solutions of

Q
=
0

Q = 0

to be free of movable branch points. And, when the condition is satisfied, all the solutions of

Q
=
0

Q = 0

can be obtained by solving linear differential equations of order

≤
2

\leq 2

. There are four mutually exclusive cases. We shall relate Case 4 to less convenient conditions P. Appell had introduced. We shall also show how Cases 3 and 4 together motivated our discovery of an identity that is essential for a satisfactory theory of relative invariants for homogeneous linear differential equations.
Intrinsic chirality of complete graphs
Authors: Flapan Erica , Weaver Nikolai
Published: June 2010

A graph is said to be intrinsically chiral if no embedding of the graph in

3
3

-space is respected by any ambient orientation-reversing homeomorphism. In this note, we characterize those complete graphs that are intrinsically chiral.
Semigroup algebras of the full matrix semigroup over a finite field
Authors: Kovács L. G.
Published: June 2010

Let

M
M

denote the multiplicative semigroup of all

n
n

-by-

n
n

matrices over a finite field

F
F

and

K
K

a commutative ring with an identity element in which the characteristic of

F
F

is a unit. It is proved here that the semigroup algebra

K
[
M
]

K[M]

is the direct sum of

n
+
1

n + 1

algebras, namely, of one full matrix algebra over each of the group algebras

K
[
GL
⁡
(
r
,
F
)
]

K[\operatorname {GL}(r,F)]

with

r
=
0
,
1
,
…
,
n

r = 0,1, \ldots ,n

. The degree of the relevant matrix algebra over

K
[
GL
⁡
(
r
,
F
)
]

K[\operatorname {GL}(r,F)]

is the number of

r
r

-dimensional subspaces in an

n
n

-dimensional vector space over

F
F

. For

K
K

a field of characteristic different from that of

F
F

, this result was announced by Faddeev in 1976. He only published an incomplete sketch of his proof, which relied on details from the representation theory of finite general linear groups. The present proof is self-contained.
Characterizations of certain classes of hereditary 𝐶*-subalgebras
Authors: Kusuda Masaharu
Published: June 2010

This paper characterizes the class of full hereditary

C
∗

{C^ * }

-subalgebras and the class of hereditary

C
∗

{C^ * }

-subalgebras that generate essential ideals in a given

C
∗

{C^ * }

-algebra in terms of a certain projection of norm one from the enveloping von Neumann algebra of the

C
∗

{C^ * }

-algebra onto the enveloping von Neumann algebra of a hereditary

C
∗

{C^ * }

-subalgebra. For a

C
∗

{C^ * }

-dynamical system

(
A
,
G
,
α
)

(A,G,\alpha )

, it is also shown that an

α
\alpha

-invariant

C
∗

{C^ * }

-subalgebra

B
B

of

A
A

is a hereditary

C
∗

{C^ * }

-subalgebra belonging to either of the above classes if and only if the reduced

C
∗

{C^ * }

-crossed product

B

×

α
r

G

B{ \times _{\alpha r}}G

is a hereditary

C
∗

{C^ * }

-subalgebra, of the reduced

C
∗

{C^ * }

-crossed product

A

×

α
r

G

A{ \times _{\alpha r}}G

, belonging to the same class as

B
B

. Furthermore similar results for

C
∗

{C^ * }

-crossed products are also observed.
Attractors of iterated function systems
Authors: Duvall P. F. , Husch L. S.
Published: June 2010

In this paper, the question of which compact metric spaces can be attractors of hyperbolic iterated function systems on Euclidean space is studied. It is shown that given any finite-dimensional compact metric

X
X

, there is a Cantor set

C
C

such that the disjoint union of

C
C

and

X
X

is an attractor. In the process, it is proved that every such

X
X

is the Lipschitz image of a Cantor set.
Tricanonical system of a surface of general type in positive characteristic
Authors: Nakashima Tohru
Published: June 2010

Using vector bundle method, we study the tricanonical system on a minimal surface of general type defined over an algebraically closed field of positive characteristic. Under some conditions, it is proved that it has no fixed component.
Nonuniqueness for the Radon transform
Authors: Armitage D. H. , Goldstein M.
Published: June 2010

There exists a nonconstant harmonic function

h
h

on

R

N

{\mathbb {R}^N}

, where

N
⩾
2

N \geqslant 2

, such that

∫
P

|

h

|

>
+
∞

{\smallint _P}|h| > + \infty

and

∫
P

h
=
0

{\smallint _P}h = 0

for every

(
N
−
1
)

(N - 1)

-dimensional hyperplane

P
P

.
Reducible Yang-Mills connections on Kähler surfaces and moment maps
Authors: Mong Kai-Cheong
Published: June 2010

We determine the second-order approximation of the anti-self-duality equation around a reducible Yang-Mills connection on a compact

1
1

-connected Kähler surface.
On the Mazur-Ulam theorem and the Aleksandrov problem for unit distance preserving mappings
Authors: Rassias Themistocles M. , Šemrl Peter
Published: June 2010

Let

X
X

and

Y
Y

be two real normed vector spaces. A mapping

f
:
X
→
Y

f:X \to Y

preserves unit distance in both directions iff for all

x
,
y
∈
X

x,y \in X

with

|

|

x
−
y

|

|

=
1

||x - y|| = 1

it follows that

|

|

f
(
x
)
−
f
(
y
)

|

|

=
1

||f(x) - f(y)|| = 1

and conversely. In this paper we shall study, instead of isometries, mappings satisfying the weaker assumption that they preserve unit distance in both directions. We shall prove that such mappings are not very far from being isometries. This problem was asked by A. D. Aleksandrov. The first classical result that characterizes isometries between normed real vector spaces goes back to S. Mazur and S. Ulam in 1932. We also obtain an extension of the Mazur-Ulam theorem.
Complexity of winning strategies for Δ⁰₂ games
Authors: Barua Rana
Published: June 2010

For a

Δ
2
0

\Delta _2^0

game played on

ω
\omega

, we show that the winning player has a winning strategy that is recursive in

E

1

{\mathbb {E}_1}

, where

E

1

{\mathbb {E}_1}

is the total type-

2
2

object that embodies operation

A

\mathcal {A}

.
Faithful representations of crossed products by endomorphisms
Authors: Boyd Sarah , Keswani Navin , Raeburn Iain
Published: June 2010

Stacey has recently characterised the crossed product

A

×
α

N

A{ \times _\alpha }{\mathbf {N}}

of a

C

∗

{C^{\ast }}

-algebra

A
A

by an endomorphism

α
\alpha

as a

C

∗

{C^{\ast }}

-algebra whose representations are given by covariant representations of the system

(
A
,
α
)

(A,\alpha )

. Following work of O’Donovan for automorphisms, we give conditions on a covariant representation

(
π
,
S
)

(\pi ,S)

of

(
A
,
α
)

(A,\alpha )

which ensure that the corresponding representation

π
×
S

\pi \times S

of

A

×
α

N

A{ \times _\alpha }{\mathbf {N}}

is faithful. We then use this result to improve a theorem of Paschke on the simplicity of

A

×
α

N

A{ \times _\alpha }{\mathbf {N}}

.
The essential spectral radius of dominated positive operators
Authors: Martínez Josep
Published: June 2010

Let

E
E

be an

AL
p

{\operatorname {AL} _p}

-space with

1
⩽
p
⩽
∞

1 \leqslant p \leqslant \infty

. We prove that if a positive operator

S
∈

L

(
E
)

S \in \mathcal {L}(E)

satisfies the Doeblin conditions and

r
(
S
)
⩽
1

r(S) \leqslant 1

, then

S
S

is quasi-compact, i.e.,

r

ess

(
S
)
>
1

{r_{\operatorname {ess} }}(S) > 1

. We then deduce the following result about the monotonicity of the essential spectral radius: Let

S
,

T
∈

L

(
E
)

S,\;T \in \mathcal {L}(E)

be such that

0
⩽
S
⩽
T

0 \leqslant S \leqslant T

. If

r
(
S
)
⩽
1

r(S) \leqslant 1

and

r

ess

(
T
)
>
1

{r_{\operatorname {ess} }}(T) > 1

, then

r

ess

(
S
)
>
1

{r_{\operatorname {ess} }}(S) > 1

.
The even 𝐶* Clifford algebra
Authors: Robinson P. L.
Published: June 2010

We offer a new perspective on the theorem of Størmer demonstrating that the even and full CAR algebras are isomorphic.
Norm inequalities equivalent to Heinz inequality
Authors: Fujii Junichi , Fujii Masatoshi , Furuta Takayuki , Nakamoto Ritsuo
Published: June 2010

We investigate several norm inequalities equivalent to the Heinz inequality and discuss the equivalence relations among these norm inequalities. Here we shall show an elementary and simplified proof to the famous Heinz inequality.
A remark on O’Hara’s energy of knots
Authors: Nakauchi Nobumitsu
Published: June 2010

We show a relation between O’Hara’s energy of knots and the Douglas functional.
A fixed point theorem in non-Archimedean vector spaces
Authors: Petalas C. , Vidalis T.
Published: June 2010

A mapping

T
T

defined on a normed linear space

X
X

and taking values in

X
X

is said to be contractive (nonexpansive) if whenever

x
x

and

y
y

are distinct points in
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X comma StartAbsoluteValue EndAbsoluteValue upper T x minus upper T y StartAbsoluteValue EndAbsoluteValue greater-than StartAbsoluteValue EndAbsoluteValue x minus y StartAbsoluteValue EndAbsoluteValue left-parenthesis StartAbsoluteValue EndAbsoluteValue upper T x minus upper T y StartAbsoluteValue EndAbsoluteValue less-than-or-slanted-equals StartAbsoluteValue EndAbsoluteValue x minus y StartAbsoluteValue EndAbsoluteValue right-parenthesis">

X
,

|

|

T
x
−
T
y

|

|

>

|

|

x
−
y

|

|

(

|

|

T
x
−
T
y

|

|

⩽

|

|

x
−
y

|

|

)

X,\,||Tx - Ty|| > ||x - y||\;(||Tx - Ty|| \leqslant ||x - y||)

. In this paper we prove that every contractive mapping on a spherically complete non-Archimedean normed space has a unique fixed point.
Simple zeros of the Riemann zeta-function
Authors: Cheer A. Y. , Goldston D. A.
Published: June 2010

Assuming the Riemann Hypothesis, Montgomery and Taylor showed that at least 67.25
An Engel condition with derivation
Authors: Lanski Charles
Published: June 2010

Let

R
R

be a prime ring,

L
L

a noncommutative Lie ideal of

R
R

, and

D
D

a nonzero derivation of

R
R

. If for each

x
∈
L

x \in L

,
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-bracket upper D left-parenthesis x right-parenthesis comma x right-bracket Subscript k Baseline equals left-bracket left-bracket midline-horizontal-ellipsis left-bracket upper D left-parenthesis x right-parenthesis comma x right-bracket comma x right-bracket comma ellipsis comma x right-bracket equals 0">

[
D
(
x
)
,
x

]
k

=
[
[
⋯
[
D
(
x
)
,
x
]
,
x
]
,
…
,
x
]
=
0

{[D(x),x]_k} = [[ \cdots [D(x),x],x], \ldots ,x] = 0

with

k
k

fixed, then

char
⁡
(
R
)
=
2

\operatorname {char} (R) = 2

and

R
⊆

M
2

(
F
)

R \subseteq {M_2}(F)

for

F
F

a field.
The Banach-Mazur game and generic existence of solutions to optimization problems
Authors: Kenderov P. S. , Revalski J. P.
Published: June 2010

The existence of a winning strategy in the well-known Banach-Mazur game in a completely regular topological space

X
X

is proved to be equivalent to the generic existence of solutions of optimization problems generated by continuous functions in

X
X

.
A counterexample to a Vitali type theorem with respect to Hausdorff content
Authors: Melnikov Mark , Orobitg Joan
Published: June 2010

Mateu and Orobitg proved (in Lipschitz approximation by harmonic functions and some applications to spectral synthesis, Indiana Univ. Math. J. 39 (1990)) that given

λ
>
1

\lambda > 1

and

d
−
1
>
α
⩽
d

d - 1 > \alpha \leqslant d

there exist constants

C
C

and

N
N

(depending on

λ
\lambda

and

α
\alpha

) with the following property: For any compact set

K
K

in

R

d

{\mathbb {R}^d}

one can find a (finite) family of balls

{
B
(

x
i

,

r
i

)
}

\{ B({x_i},{r_i})\}

such that (i)

K
⊂
⋃

B
(

x
i

,

r
i

)

K \subset \bigcup {B({x_i},{r_i})}

, (ii)

∑

r
i
α

⩽
C

M
α

(
K
)

\sum {r_i^\alpha \leqslant C{M^\alpha }(K)}

,

M
α

{M^\alpha }

denoting the

α
\alpha

-dimensional Hausdorff content, and (iii) the dilated balls

{
B
(

x
i

,
λ

r
i

)
}

\{ B({x_i},\lambda {r_i})\}

are an almost disjoint family with constant

N
N

. In this paper we prove that such a result is false for

α
⩽
d
−
1

\alpha \leqslant d - 1

.
On the zeros of certain cosine polynomials
Authors: Mingarelli A. B. , Wang S.
Published: June 2010

In a recent paper [The first sign change of a cosine polynomial, Proc. Amer. Math. Soc. 111 (1991), 709-716], Zeng studies the location of the first sign change of a cosine polynomial and thereby improves on results by Nulton and Stolarsky [The first sign change of a cosine polynomial, Proc. Amer. Math. Soc. 84 (1982), 55-59]. In this article we present a proof for each one of the four conjectures announced in Zeng’s aforementioned paper and also discuss some extensions.
Large time behavior of the heat kernel: on a theorem of Chavel and Karp
Authors: Simon Barry
Published: June 2010

We show that a theorem of Chavel and Karp follows from the spectral theorem and elliptic regularity
The Morse index theorem in the degenerate endmanifold case
Authors: Hingston Nancy , Kalish Diane
Published: June 2010

We present a simple formulation and proof of the Morse index theorem for two endmanifolds in the degenerate case, that is, when each submanifold lies at a focal point of the other.
A module induced from a Whittaker module
Authors: McDowell Edward
Published: June 2010

In an earlier paper [On modules induced from Whittaker modules, J. Algebra 96 (1985)] we constructed a class of induced modules, over a finite-dimensional semisimple Lie algebra, which includes the Verma modules of Verma [Structure of certain induced representations of complex semisimple Lie algebras, Bull. Amer. Math. Soc. 74 (1968)] and the irreducible Whittaker modules of Kostant [On Whittaker vectors and representation theory, Invent. Math. 48 (1978)]. We proved that every module in this class has finite length and is irreducible most of the time. In this article we present a concrete example of this construction, over

sl
⁡
(
3
,
C
)

\operatorname {sl} (3,C)

, showing that proper submodules can exist when the induced module is not a Verma module.
Inversions of Hermite semigroup
Authors: Byun Du-Won
Published: June 2010

Let

{

e

−
c
H

|

c
⩾
0
}

\{ {e^{ - cH}}|c \geqslant 0\}

be the Hermite semigroup on the real line

R

\mathbb {R}

. Then a representation is constructed for inversions of the semigroup, and it gives a representation of

e

−
c
H

{e^{ - cH}}

for

c
>
0

c > 0

. Moreover, some characterizations of the domain in which, for

c
>
0
,

e

−
c
H

c > 0,\;{e^{ - cH}}

is well defined are examined.
Counterexamples for Brown-Pedersen’s conjecture in “𝐶*-algebras of real rank zero”
Authors: Osaka Hiroyuki
Published: June 2010

We give nonseparable

C

∗

{C^{\ast }}

-algebras which are counterexamples for Brown-Pedersen’s conjecture in "

C

∗

{C^{\ast }}

-algebras of real rank zero".
Integrability of reciprocals of the Green’s function for elliptic operators: counterexamples
Authors: Cerutti M. Cristina
Published: June 2010

We construct examples of elliptic operators for which the set of points where the reciprocal

1

/

g
(
x
,
⋅
)

1/g(x, \cdot )

of the Green’s function is not locally integrable in a dense set of points.
Invariant manifolds of hypercyclic vectors
Authors: Bourdon Paul S.
Published: June 2010

We show that any hypercyclic operator on Hilbert space has a dense, invariant linear manifold consisting, except for zero, entirely of hypercyclic vectors.
On infinite disjoint covering systems
Authors: Fraenkel Aviezri S. , Simpson R. Jamie
Published: June 2010

The structure of all infinite incongruent disjoint covering systems (IIDCS) whose moduli are divisible by no prime

>
3

> 3

is given. It is then shown that this structure characterizes the subset of IIDCS for which the greatest common factor of all the moduli is

1
1

, and the set of primes dividing the moduli is finite.