bluuebunny/crossref_metadata_2025 huggingface dataset:
HIV-1 Antigen–specific and –nonspecific B Cell Responses Are Sensitive to Combination Antiretroviral Therapy
Authors: Morris Lynn , Binley James M. , Clas Brian A. , Bonhoeffer Sebastian , Astill Thomas P. , Kost Rhonda , Hurley Arlene , Cao Yunzhen , Markowitz Martin , Ho David D. , Moore John P.
Published: July 2002

We studied how combination antiviral therapy affects B cell abnormalities associated with HIV-1 infection, namely elevated circulating immunoglobulin (Ig)G antibody-secreting cell (ASC) frequencies and hypergammaglobulinemia. Within a few weeks of starting antiviral therapy, there is a marked decline in IgG-ASC frequency in both acutely and chronically infected people, whereas the hypergammaglobulinemia often present during chronic infection is more gradually resolved. These reductions are sustained while HIV-1 replication is suppressed. HIV-1 antigen–specific B cell responses are also affected by therapy, manifested by a rapid decline in circulating gp120-specific ASCs. Anti-gp120 titers slowly decrease in chronically infected individuals and usually fail to mature in acutely infected individuals who were promptly treated with antiretroviral therapy. Long-term nonprogressors have high titer antibody responses to HIV-1 antigens, but no detectable gp120-specific IgG-ASC, and normal (or subnormal) levels of total circulating IgG-ASC. Overall, we conclude that HIV-1 infection drives B cell hyperactivity, and that this polyclonal activation is rapidly responsive to decreases in viral replication caused by combination antiviral therapy.
The Role of Macrophages in T Cell–mediated Autoimmune Diabetes in Nonobese Diabetic Mice
Authors: Jun Hee-Sook , Yoon Chang-Soon , Zbytnuik Lori , van Rooijen Nico , Yoon Ji-Won
Published: July 2002

We have shown previously that the inactivation of macrophages in nonobese diabetic (NOD) mice results in the prevention of diabetes; however, the mechanisms involved remain unknown. In this study, we found that T cells in a macrophage-depleted environment lost their ability to differentiate into β cell–cytotoxic T cells, resulting in the prevention of autoimmune diabetes, but these T cells regained their β cell–cytotoxic potential when returned to a macrophage-containing environment. To learn why T cells in a macrophage-depleted environment lose their ability to kill β cells, we examined the islet antigen–specific immune response and T cell activation in macrophage-depleted NOD mice. There was a shift in the immune balance, a decrease in the T helper cell type 1 (Th1) immune response, and an increase in the Th2 immune response, due to the reduced expression of the macrophage-derived cytokine IL-12. As well, there was a deficit in T cell activation, evidenced by significant decreases in the expression of Fas ligand and perforin. The administration of IL-12 substantially reversed the prevention of diabetes in NOD mice conferred by macrophage depletion. We conclude that macrophages play an essential role in the development and activation of β cell–cytotoxic T cells that cause β cell destruction, resulting in autoimmune diabetes in NOD mice.
A type of Strassen’s theorem for positive vector measures with values in dual spaces
Authors: Kawabe Jun
Published: July 2002

In this paper, we extend a type of Strassen’s theorem for the existence of probability measures with given marginals to positive vector measures with values in the dual of a barreled locally convex space which has certain order conditions. In this process of the extension we also give some useful properties for vector measures with values in dual spaces.
Quadratic division algebras revisited (Remarks on an article by J. M. Osborn)
Authors: Dieterich Ernst
Published: July 2002

In his remarkable article “Quadratic division algebras” (Trans. Amer. Math. Soc. 105 (1962), 202–221), J. M. Osborn claims to solve ‘the problem of determining all quadratic division algebras of order 4 over an arbitrary field

F
F

of characteristic not two

…
\ldots

modulo the theory of quadratic forms over

F
F

’ (cf. p. 206). While we shall explain in which respect he has not achieved this goal, we shall on the other hand complete Osborn’s basic results (by a reasoning which is finer than his) to derive in the real ground field case a classification of all 4-dimensional quadratic division algebras and the construction of a 49-parameter family of pairwise nonisomorphic 8-dimensional quadratic division algebras. To make these points clear, we begin by reformulating Osborn’s fundamental observations on quadratic algebras in categorical terms.
Purely infinite, simple 𝐶*-algebras arising from free product constructions. III
Authors: Choda Marie , Dykema Kenneth
Published: July 2002

In the reduced free product of C

∗

^{*}

–algebras,

(
A
,
ϕ
)
=
(

A

1

,

ϕ

1

)
∗
(

A

2

,

ϕ

2

)

(A,\phi )=(A_{1},\phi _{1})*(A_{2},\phi _{2})

with respect to faithful states

ϕ

1

\phi _{1}

and

ϕ

2

\phi _{2}

,

A
A

is purely infinite and simple if

A

1

A_{1}

is a reduced crossed product

B

⋊

α
,
r

G

B\rtimes _{\alpha ,r}G

for

G
G

an infinite group, if

ϕ

1

\phi _{1}

is well behaved with respect to this crossed product decomposition, if

A

2

≠

C

A_{2}\ne \mathbf {C}

and if

ϕ
\phi

is not a trace.
Convergence of paths for pseudo-contractive mappings in Banach spaces
Authors: Morales Claudio , Jung Jong
Published: July 2002

Let

X
X

be a real Banach space, let

K
K

be a closed convex subset of

X
X

, and let

T
T

, from

K
K

into

X
X

, be a pseudo-contractive mapping (i.e.

(
λ
−
1
)

(\lambda -1)

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar u minus v double-vertical-bar less-than-or-equal-to double-vertical-bar left-parenthesis lamda upper I minus upper T right-parenthesis left-parenthesis u right-parenthesis minus left-parenthesis lamda upper I minus upper T right-parenthesis left-parenthesis v right-parenthesis double-vertical-bar">

‖
u
−
v
‖
≤
‖
(
λ
I
−
T
)
(
u
)
−
(
λ
I
−
T
)
(
v
)
‖

\|u-v\|\le \|(\lambda I-T)(u)-(\lambda I-T)(v)\|

for all

u
,
v
∈
K

u,v\in K

and

λ
>
1
)

\lambda >1)

. Suppose the space

X
X

has a uniformly Gâteaux differentiable norm, such that every closed bounded convex subset of

K
K

enjoys the Fixed Point Property for nonexpansive self-mappings. Then the path

t
→

x
t

∈
K

t\to x_t\in K

,

t
∈
[
0
,
1
)

t\in [0,1)

, defined by the equation

x
t

=
t
T

x
t

+
(
1
−
t
)

x
0

x_t=tTx_t+(1-t)x_0

is continuous and strongly converges to a fixed point of

T
T

as

t
→

1
−

t\to 1^-

, provided that

T
T

satisfies the weakly inward condition.
Solvability of a finite or infinite system of discontinuous quasimonotone differential equations
Authors: Biles Daniel , Schechter Eric
Published: July 2002

This paper proves the existence of solutions to the initial value problem
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis normal upper I normal upper V normal upper P right-parenthesis StartLayout Enlarged left-brace 1st Row x prime left-parenthesis t right-parenthesis equals f left-parenthesis t comma x left-parenthesis t right-parenthesis right-parenthesis left-parenthesis 0 less-than-or-equal-to t less-than-or-equal-to 1 right-parenthesis comma x left-parenthesis 0 right-parenthesis equals 0 comma EndLayout">

(

I
V
P

)

{

x
′

(
t
)
=
f
(
t
,
x
(
t
)
)

(
0
≤
t
≤
1
)
,
x
(
0
)
=
0
,

(\mathrm {IVP})\qquad \qquad \left \{\begin {array}{l} x’(t)=f(t,x(t))\qquad \quad (0\le t\le 1), x(0)=0,\end {array} \right .

\]
where

f
:
[
0
,
1
]
×

R

M

→

R

M

f:[0,1]\times \mathbb {R}^M\to \mathbb {R}^M

may be discontinuous but is assumed to satisfy conditions of superposition-measurability, quasimonotonicity, quasisemicontinuity, and integrability. The set

M
M

can be arbitrarily large (finite or infinite); our theorem is new even for

card

(
M
)
=
2

\mbox {card}(M)=2

. The proof is based partly on measure-theoretic techniques used in one dimension under slightly stronger hypotheses by Rzymowski and Walachowski. Further generalizations are mentioned at the end of the paper.
On Euler products associated with noncuspidal metaplectic forms
Authors: Dutta Gupta Shamita , She Xiaotie
Published: July 2002

In this paper, we obtain an Euler product with functional equation associated to a noncuspidal metaplectic form

f
f

on the double cover of

G
L
(
2
)

GL(2)

. Zagier’s idea of Rankin-Selberg method is used to define the convolution of

f
f

and the

θ
\theta

-function.
A result about a selection problem of Michael
Authors: Jordan Francis , Nadler Sam
Published: July 2002

It is shown that a continuum that is an

S
4

S_4

space in the sense of Michael must be hereditarily decomposable. This improves known results, thereby providing more evidence that such continua must be dendrites.
On the simplicial volumes of fiber bundles
Authors: Hoster M. , Kotschick D.
Published: July 2002

We show that surface bundles over surfaces with base and fiber of genus at least

2
2

have non-vanishing simplicial volume.
Torus actions on symplectic orbi-spaces
Authors: Schmah Tanya
Published: July 2002

Which2n2n-dimensional orbi-spaces have effective symplectickk- torus actions? As shown by Lerman and Tolman (1997) and Watson (1997), this question reduces to that of characterizing the finite subgroups of centralizers of tori in the real symplectic groupSp(2n,R)Sp(2n, \mathbb {R}). We resolve this question, and generalize our method to a calculation of the centralizers of all tori inSp(2n,R)Sp(2n,\mathbb {R}).
Stability of 𝑛-vortices in the Ginzburg-Landau equation
Authors: Coleman James
Published: July 2002

We consider the class of

n
n

-vortex solutions to the time-independent Ginzburg-Landau equation on

R

2

\mathbf {R}^2

. We prove an inequality governing the solutions of a particular boundary value problem. This inequality is crucial for an elementary proof by Ovchinnikov and Sigal that such

n
n

-vortices are unstable in the case

|
n
|
≥
2

\vert n \vert \ge 2

.
Existence and uniqueness of steady-state solutions for an electrochemistry model
Authors: Fang Weifu , Ito Kazufumi
Published: July 2002

We present a simple proof for the existence and uniqueness of steady-state solutions to an electrochemistry model with multiple species.
A topological property of integrable systems
Authors: Álvarez Paiva J.
Published: July 2002

If we are given

n
n

real-valued smooth functions on

R

2
n

\mathbb {R}^{2n}

which are in involution, then, under some mild hypotheses, the subset of

R

2
n

\mathbb {R}^{2n}

where these functions are linearly independent is not simply connected.
Lipschitz functions with maximal Clarke subdifferentials are generic
Authors: Borwein Jonathan , Wang Xianfu
Published: July 2002

We show that on a separable Banach space most Lipschitz functions have maximal Clarke subdifferential mappings. In particular, the generic nonexpansive function has the dual unit ball as its Clarke subdifferential at every point. Diverse corollaries are given.
Sufficient conditions for a linear functional to be multiplicative
Authors: Seddighi K. , Haghighi M. H.
Published: July 2002

A commutative Banach algebra

A

\mathcal {A}

is said to have the

P
(
k
,
n
)

P(k,n)

property if the following holds: Let

M

{{M}}

be a closed subspace of finite codimension

n
n

such that, for every

x
∈

M

x\in {{M}}

, the Gelfand transform

x
^

\hat {x}

has at least

k
k

distinct zeros in

Δ
(

A

)

\Delta (\mathcal {A})

, the maximal ideal space of

A

\mathcal {A}

. Then there exists a subset

Z
Z

of

Δ
(

A

)

\Delta (\mathcal {A})

of cardinality

k
k

such that

M

^

\hat {{M}}

vanishes on

Z
Z

, the set of common zeros of

M

{{M}}

. In this paper we show that if

X
⊂

C

X\subset \mathbf {C}

is compact and nowhere dense, then

R
(
X
)

R(X)

, the uniform closure of the space of rational functions with poles off

X
X

, has the

P
(
k
,
n
)

P(k,n)

property for all

k
,
n
∈

N

k,n\in \mathbf {N}

. We also investigate the

P
(
k
,
n
)

P(k,n)

property for the algebra of real continuous functions on a compact Hausdorff space.
Borel complexity of the space of probability measures
Authors: Dasgupta Abhijit
Published: July 2002

Using a technique developed by Louveau and Saint Raymond, we find the complexity of the space of probability measures in the Borel hierarchy: if

X
X

is any non-Polish Borel subspace of a Polish space, then

P
(
X
)

P(X)

, the space of probability Borel measures on

X
X

with the weak topology, is always true

Π

ξ

0

{\boldsymbol {\Pi }^{\boldsymbol {0}}_{\boldsymbol {\xi }}}

, where

ξ
\xi

is the least ordinal such that

X
X

is

Π

ξ

0

{\boldsymbol {\Pi }^{\boldsymbol {0}}_{\boldsymbol {\xi }}}

.
Shape aspherical compacta–applications of a theorem of Kan and Thurston to cohomological dimension and shape theories
Authors: Miyata Takahisa
Published: July 2002

Dydak and Yokoi introduced the notion of shape aspherical compactum. In this paper, we use this notion to obtain a generalization of Kan and Thurston theorem for compacta and pro-homology. As an application, we obtain a characterization of cohomological dimension with coefficients in

Z

\mathbb {Z}

and

Z

/

p

\mathbb {Z}/p

(

p
p

prime) in terms of acyclic maps from a shape aspherical compactum, which improves the theorems of Edwards and Dranishnikov. Furthermore, we obtain the shape version of the theorem and as a consequence we show that every compactum has the stable shape type of a shape aspherical compactum.
A proof of the homotopy push-out and pull-back lemma
Authors: Sakai Michihiro
Published: July 2002

The homotopy push-out and pull-back lemma of Iwase (1998) is a generalized version of Theorem 1.1 of Ganea (1965) and the Theorem of Rutter (1971) whose proofs were given under the simply-connectivity condition. The purpose of this paper is to give a proof in the general case.
Low-dimensional unitary representations of 𝐵₃
Authors: Tuba Imre
Published: July 2002

We characterize all simple unitarizable representations of the braid group

B
3

B_3

on complex vector spaces of dimension

d
≤
5

d \leq 5

. In particular, we prove that if

σ
1

\sigma _1

and

σ
2

\sigma _2

denote the two generating twists of

B
3

B_3

, then a simple representation

ρ
:

B
3

→
GL
⁡
(
V
)

\rho :B_3 \to \operatorname {GL} (V)

(for

dim
⁡
V
≤
5

\dim V \leq 5

) is unitarizable if and only if the eigenvalues

λ
1

,

λ
2

,
…
,

λ
d

\lambda _1, \lambda _2, \ldots , \lambda _d

of

ρ
(

σ
1

)

\rho (\sigma _1)

are distinct, satisfy

|

λ
i

|

=
1

|\lambda _i|=1

and

μ

1
i

(
d
)

>
0

\mu ^{(d)}_{1i} > 0

for

2
≤
i
≤
d

2 \leq i \leq d

, where the

μ

1
i

(
d
)

\mu ^{(d)}_{1i}

are functions of the eigenvalues, explicitly described in this paper.
Analytic sets and the boundary regularity of CR mappings
Authors: Pinchuk Sergey , Verma Kaushal
Published: July 2002

It is shown that if a continuous CR mapping between smooth real analytic hypersurfaces of finite type in

C

n

{\mathbf C}^n

extends as an analytic set, then it extends as a holomorphic mapping.
The Fefferman-Stein type inequality for the Kakeya maximal operator
Authors: Tanaka Hitoshi
Published: July 2002

LetKδK_\delta,0>δ>>10>\delta >>1, be the Kakeya maximal operator defined as the supremum of averages over tubes of the eccentricityδ\delta. We shall prove the so-called Fefferman-Stein type inequality forKδK_\delta,\[<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar upper K Subscript delta Baseline f double-vertical-bar Subscript upper L Sub Superscript p Subscript left-parenthesis bold upper R Sub Superscript d Subscript comma w right-parenthesis Baseline less-than-or-equal-to upper C Subscript d comma p Baseline left-parenthesis StartFraction 1 Over delta EndFraction right-parenthesis Superscript d slash p minus 1 Baseline left-parenthesis log left-parenthesis StartFraction 1 Over delta EndFraction right-parenthesis right-parenthesis Superscript alpha left-parenthesis d right-parenthesis Baseline double-vertical-bar f double-vertical-bar Subscript upper L Sub Superscript p Subscript left-parenthesis bold upper R Sub Superscript d Subscript comma upper K Sub Subscript delta Subscript w right-parenthesis Baseline comma">‖Kδf‖Lp(Rd,w)≤Cd,p(1δ)d/p−1(log⁡(1δ))α(d)‖f‖Lp(Rd,Kδw),\|K_\delta f\|_{L^p(\mathbf R^d,w)} \le C_{d,p} (\frac {1}{\delta })^{d/p-1} (\log (\frac {1}{\delta }))^{\alpha (d)} \|f\|_{L^p(\mathbf R^d,K_\delta w)},\]in the range(1>p≤(d2−2)/(2d−3)(1>p\le (d^2-2)/(2d-3),d≥3d\ge 3, with some constantsCd,pC_{d,p}andα(d)\alpha (d)independent offfand the weightww.
Iterative approximation of fixed points of Lipschitz pseudocontractive maps
Authors: Chidume C.
Published: July 2002

Let

E
E

be a

q
q

-uniformly smooth Banach space possessing a weakly sequentially continuous duality map (e.g.,

ℓ
p

,
 
1
>
p
>
∞

\ell _p, \ 1>p>\infty

). Let

T
T

be a Lipschitzian pseudocontractive selfmapping of a nonempty closed convex and bounded subset

K
K

of

E
E

and let

ω
∈
K

\omega \in K

be arbitrary. Then the iteration sequence

{

z
n

}

\{z_n\}

defined by
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="z 0 element-of upper K comma z Subscript n plus 1 Baseline equals left-parenthesis 1 minus mu Subscript n plus 1 Baseline right-parenthesis omega plus mu Subscript n plus 1 Baseline y Subscript n Baseline semicolon y Subscript n Baseline equals left-parenthesis 1 minus alpha Subscript n Baseline right-parenthesis z Subscript n Baseline plus alpha Subscript n Baseline upper T z Subscript n Baseline">

z
0

∈
K
,
 
 

z

n
+
1

=
(
1
−

μ

n
+
1

)
ω
+

μ

n
+
1

y
n

;
 
 

y
n

=
(
1
−

α
n

)

z
n

+

α
n

T

z
n

z_0\in K, \ \ z_{n+1}=(1-\mu _{n+ 1})\omega + \mu _{n+1}y_n; \ \ y_n = (1-\alpha _n)z_n+\alpha _nTz_n

, converges strongly to a fixed point of

T
T

, provided that

{

μ
n

}

\{\mu _n\}

and

{

α
n

}

\{\alpha _n\}

have certain properties. If

E
E

is a Hilbert space, then

{

z
n

}

\{z_n\}

converges strongly to the unique fixed point of

T
T

closest to

ω
\omega

.
Epimorphism sequences between hyperbolic 3-manifold groups
Authors: Soma Teruhiko
Published: July 2002

We will show that any infinite sequence of epimorphisms between finitely generated hyperbolic 3-manifold groups eventually consists of isomorphisms.
An application of Ramsey’s Theorem to the Banach Contraction Principle
Authors: Merryfield James , Rothschild Bruce , Stein James
Published: July 2002

One of the most fundamental fixed-point theorems is Banach’s Contraction Principle, of which the following conjecture is a generalization. Generalized Banach Contraction Conjecture (GBCC). Let

T
T

be a self-map of a complete metric space

(
X
,
d
)

(X,d)

, and let

0
>
M
>
1

0>M>1

. Let

J
J

be a positive integer. Assume that for each pair

x
,
y
∈
X

x,y\in X

,
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="min left-brace right-brace colon of dd left-parenthesis right-parenthesis comma times times Tkx comma times times Tky colon less-than-or-equal-to less-than-or-equal-to less-than-or-equal-to 1 kJ less-than-or-equal-to upper M d left-parenthesis x comma y right-parenthesis">

min
{
d
(

T
k

x
,

T
k

y
)
:
1
≤
k
≤
J
}
≤
M

d
(
x
,
y
)

\min \{d(T^kx, T^ky):1\le k\le J\}\le M\,d(x,y)

. Then

T
T

has a fixed point. Unlike Banach’s original theorem (the case

J
=
1

J=1

), the above hypothesis does not compel

T
T

to be continuous. In this paper we use Ramsey’s Theorem from combinatorics to establish the GBCC for arbitrary

J
J

in the case when

T
T

is assumed to be continuous, and also derive a result which enables us to prove the GBCC when

J
=
3

J=3

without the assumption of continuity; it is known that the case

J
=
3

J=3

includes instances where

T
T

is not continuous.
Strongly meager sets of real numbers and tree forcing notions
Authors: Nowik Andrzej , Weiss Tomasz
Published: July 2002

We show that every strongly meager set has the

l
0

l_0

- and the

m
0

m_0

- property.
Classification of torsion-free genus zero congruence groups
Authors: Sebbar Abdellah
Published: July 2002

We study and classify all torsion-free genus zero congruence subgroups of the modular group.
Triangular derivations related to problems on affine 𝑛-space
Authors: van den Essen Arno , van Rossum Peter
Published: July 2002

This paper studies the Cancellation Problem, the Embedding Problem, and the Linearization Problem. It shows how these problems can be related to a special class of locally nilpotent derivations.
Minimal Lagrangian submanifolds with constant sectional curvature in indefinite complex space forms
Authors: Vrancken Luc
Published: July 2002

We study minimal Lagrangian immersions from an indefinite real space form

M
s
n

(
c
)

M^n_s(c)

into an indefinite complex space form

M

~

s
n

(
4

c
~

)

{\tilde {\mathbb {M}}}^n_s(4\tilde c)

. Provided that

c
≠

c
~

c \ne \tilde c

, we show that

M
s
n

(
c
)

M^n_s(c)

has to be flat and we obtain an explicit description of the immersion. In the case when the metric is positive definite or Lorentzian, this result was respectively obtained by Ejiri (1982) and by Kriele and the author (1999). In the case that

c
=

c
~

c = \tilde c

, this theorem is no longer true; see for instance the examples discovered by Chen and the author (accepted for publication in the Tôhoku Mathematical Journal).
Evaluations of initial ideals and Castelnuovo-Mumford regularity
Authors: Trung Ngô
Published: July 2002

This paper characterizes the Castelnuovo-Mumford regularity by evaluating the initial ideal with respect to the reverse lexicographic order.
Simple algebras of Weyl type, II
Authors: Zhao Kaiming
Published: July 2002

Over a field

F

\mathbb {F}

of any characteristic, for a commutative associative algebra

A
A

, and for a commutative subalgebra

D
D

of

Der

F

⁡
(
A
)

\operatorname {Der}_{\mathbb {F}}(A)

, the vector space

A
[
D
]

A[D]

which consists of polynomials of elements in

D
D

with coefficients in

A
A

and which is regarded as operators on

A
A

forms naturally an associative algebra. It is proved that, as an associative algebra,

A
[
D
]

A[D]

is simple if and only if

A
A

is

D
D

-simple. Suppose

A
A

is

D
D

-simple. Then, (a)

A
[
D
]

A[D]

is a free left

A
A

-module; (b) as a Lie algebra, the subquotient
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-bracket upper A left-bracket upper D right-bracket comma upper A left-bracket upper D right-bracket right-bracket slash left-parenthesis upper Z left-parenthesis upper A left-bracket upper D right-bracket right-parenthesis intersection left-bracket upper A left-bracket upper D right-bracket comma upper A left-bracket upper D right-bracket right-bracket right-parenthesis">

[
A
[
D
]
,

A
[
D
]

]

/

(
Z
(
A
[
D
]
)
∩
[
A
[
D
]
,

A
[
D
]

]
)

[A[D],{A[D]}]/(Z(A[D])\cap [A[D], {A[D]}])

is simple (except for one case), where

Z
(
A
[
D
]
)

Z(A[D])

is the center of

A
[
D
]

A[D]

. The structure of this subquotient is explicitly described. This extends the results obtained by Su and Zhao.
Specker’s theorem for Nöbeling’s group
Authors: Blass Andreas
Published: July 2002

Specker proved that the group

Z

ℵ
0

\mathbb {Z}^{\aleph _0}

of integer-valued sequences is far from free; all its homomorphisms to

Z

\mathbb {Z}

factor through finite subproducts. Nöbeling proved that the subgroup

B

\mathcal {B}

consisting of the bounded sequences is free and therefore has many homomorphisms to

Z

\mathbb {Z}

. We prove that all “reasonable” homomorphisms

B

→

Z

\mathcal {B}\to \mathbb {Z}

factor through finite subproducts. Among the reasonable homomorphisms are all those that are Borel with respect to a natural topology on

B

\mathcal {B}

. In the absence of the axiom of choice, it is consistent that all homomorphisms are reasonable and therefore that Specker’s theorem applies to

B

\mathcal {B}

as well as to

Z

ℵ
0

\mathbb {Z}^{\aleph _0}

.
Existence of multiwavelets in ℝⁿ
Authors: Cabrelli Carlos , Gordillo María
Published: July 2002

For a

q
q

-regular Multiresolution Analysis of multiplicity

r
r

with arbitrary dilation matrix

A
A

for a general lattice

Γ
\Gamma

in

R

n

\mathbb {R}^n

, we give necessary and sufficient conditions in terms of the mask and the symbol of the vector scaling function in order that an associated wavelet basis exists. We also show that if

2
r
(
m
−
1
)
≥
n

2r(m-1) \geq n

where

m
m

is the absolute value of the determinant of

A
A

, then these conditions are always met, and therefore an associated wavelet basis of

q
q

-regular functions always exists. This extends known results to the case of multiwavelets in several variables with an arbitrary dilation matrix

A
A

for a lattice

Γ
\Gamma

.
On the continuity of biconjugate convex functions
Authors: Borwein J. , Vanderwerff J.
Published: July 2002

We show that a Banach space is a Grothendieck space if and only if every continuous convex function on

X
X

has a continuous biconjugate function on

X

∗
∗

X^{**}

, thus also answering a question raised by S. Simons. Related characterizations and examples are given.
ACL homeomorphisms and linear dilatation
Authors: Kallunki S. , Martio O.
Published: July 2002

We establish an integrability condition on the linear dilatation to guarantee ACL.
Hölder estimates of solutions to a degenerate diffusion equation
Authors: Lu Yunguang
Published: July 2002

This paper is concerned with the Hölder estimates of weak solutions of the Cauchy problem for the general degenerate parabolic equations
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u Subscript t Baseline equals normal upper Delta upper G left-parenthesis u right-parenthesis plus sigma-summation Underscript j equals 1 Overscript upper N Endscripts f Subscript j Baseline left-parenthesis u right-parenthesis Subscript x Sub Subscript j Subscript Baseline plus h left-parenthesis u right-parenthesis comma">

u

t

=
Δ
G
(
u
)
+

∑

j
=
1

N

f

j

(
u

)

x

j

+
h
(
u
)
,

\begin{equation*} u_{t}= \Delta G(u)+ \sum \limits _{j=1}^{N}f_{j}(u)_{x_{j}}+h(u), \end{equation*}

with the initial data

u
(
x
,
0
)
=

u

0

(

x
1

,

x
2

,
…
,

x
N

)

u(x,0)=u_{0}(x_1,x_2,\dots ,x_N)

, where the diffusion function

G
(
u
)

G(u)

can be a constant on a nonzero measure set, such as the equations of two-phase Stefan type. Some explicit Hölder exponents of the composition function

G
(
u
)

G(u)

with respect to the space variables are obtained by using the maximum principle.
A note on idempotents in finite AW*-factors
Authors: Nagy Gabriel
Published: July 2002

We prove that the value of the quasi-trace on an idempotent element in an AW*-factor of type

II
1

\text {II}_1

is the same as the dimension of its left (or right) support.
Invariant ideals of abelian group algebras under the multiplicative action of a field. II
Authors: Osterburg J. , Passman D. , Zalesskiĭ A.
Published: July 2002

Let

D
D

be a division ring and let

V
=

D
n

V=D^n

be a finite-dimensional right

D
D

-vector space, viewed multiplicatively. If

G
=

D
∙

G=D^\bullet

is the multiplicative group of

D
D

, then

G
G

acts on

V
V

and hence on any group algebra

K
[
V
]

K[V]

. In this paper, we completely describe the semiprime

G
G

-stable ideals of

K
[
V
]

K[V]

, and conclude that these ideals satisfy the ascending chain condition. As it turns out, this result follows fairly easily from the corresponding results for the field of rational numbers (due to Brookes and Evans) and for infinite locally-finite fields (handled in Part I).
Rigidity of proper holomorphic mappings between equidimensional bounded symmetric domains
Authors: Tu Zhen-Han
Published: July 2002

We prove that any proper holomorphic mapping between two equidimensional irreducible bounded symmetric domains with rank

≥
2

\geq 2

is a biholomorphism. The proof of the main result in this paper will be achieved by a differential-geometric study of a special class of complex geodesic curves on the bounded symmetric domains with respect to their Bergman metrics.
On an adjoint functor to the Thom functor
Authors: Rudyak Yuli
Published: July 2002

We construct a right adjoint functor to the Thom functor, i.e., to the functor which assigns the Thom space

T
ξ

T\xi

to a vector bundle

ξ
\xi

.
The fundamental groups of one-dimensional wild spaces and the Hawaiian earring
Authors: Eda Katsuya
Published: July 2002

Let

X
X

be a one-dimensional space which contains a copy

C
C

of a circle and let it not be semi-locally simply connected at any point on

C
.

C.

Then the fundamental group of

X
X

cannot be embeddable into a free

σ
\sigma

-product of n-slender groups, for instance, the fundamental group of the Hawaiian earring. Consequently, any one of the fundamental groups of the Sierpinski gasket, the Sierpinski curve, and the Menger curve is not embeddable into the fundamental group of the Hawaiian earring.
A Bernstein type theorem for minimal volume preserving maps
Authors: Ni Lei
Published: July 2002

We show that any minimal volume preserving map from the Euclidean plane into itself is a linear diffeomorphism. We derive this from a similar result on minimal diffeomorphisms. We also show that the classical Bernstein theorem on minimal graphs is a corollary of our result.
Parallel tangent hyperplanes
Authors: Schwartzman Sol
Published: July 2002

Let

Σ

2
n

\Sigma ^{2n}

be a smooth strictly convex closed hypersurface in

R

2
n
+
1

R^{2n+1}

and let

M

2
n

M^{2n}

be any oriented smooth connected manifold immersed in

R

2
n
+
1

.

R^{2n+1}.

Suppose that

f
f

is a continuous function from

Σ

2
n

\Sigma ^{2n}

to

M

2
n

.

M^{2n}.

Then there is at least one point

p
∈

Σ

2
n

p \in \Sigma ^{2n}

such that the hyperplane tangent to

Σ

2
n

\Sigma ^{2n}

at

p
p

is parallel to the hyperplane tangent to the immersed manifold

M

2
n

M^{2n}

at the point corresponding to

f
(
p
)
.

f(p).

If there did not exist at least two such points,

M

2
n

M^{2n}

would have to be compact and the Hurewicz homomorphism of

π

2
n

(

M

2
n

)

\pi _{2n}(M^{2n})

into

H

2
n

(

M

2
n

)

\mbox {H}_{2n}(M^{2n})

would have to be surjective. If in addition our immersion was an embedding, the Euler characteristic of

M

2
n

M^{2n}

would have to be equal to

±
2.

\pm 2.

For any

Σ

2
n

\Sigma ^{2n}

and any immersed

M

2
n

M^{2n}

we could always get maps

f
f

for which the number of points

p
p

satisfying the conditions of our theorem exactly equaled two. An example can be given in which both

Σ

2
n

\Sigma ^{2n}

and

M

2
n

M^{2n}

are the unit sphere about the origin in

R

2
n
+
1

R^{2n+1}

and there is only one such point

p
p

.
Explicit continued fractions with expected partial quotient growth
Authors: Okano Takeshi
Published: July 2002

For

0
>
x
>
1

0>x>1

let

[
0
,

a
1

(
x
)
,

a
2

(
x
)
,
…
]

[0,a_1(x),a_2(x),\dots ]

be the continued fraction expansion of

x
x

. Write
\[

L
N

(
x
)
=

max

1
≤
n
≤
N

a
n

(
x
)
.

L_N(x)=\max _{1\le n\le N}a_n(x).

\]
We construct some numbers

x
x

’s with
\[

lim

N
→
∞

inf

N

−
1

L
N

(
x
)
log
⁡
log
⁡
N
=
1

/

log
⁡
2.

\lim _{N\to \infty }\inf N^{-1}L_N(x)\log \log N=1/\log 2.

\]
A ZFC example (of minimum weight) of a Lindelöf space and a completely metrizable space with a nonnormal product
Authors: Lawrence L.
Published: July 2002

We give an example as indicated in the title where the weight (i.e., the minimum cardinality of a base for the topology) of the product is the smallest uncountable cardinal.
Limits of differentiable functions
Authors: Darji Udayan
Published: July 2002

Suppose that

{

f
n

}

\{f_n\}

is a sequence of differentiable functions defined on [0,1] which converges uniformly to some differentiable function

f
f

, and

{

f
n
′

}

\{f’_n\}

converges pointwise to some function

g
g

. Let

M
=
{
x
:

f
′

(
x
)
≠
g
(
x
)
}

M = \{x: f’(x) \neq g(x)\}

. In this paper we characterize such sets

M
M

under various hypotheses. It follows from one of our characterizations that

M
M

can be the entire interval [0,1].
A note on the kernel of a locally nilpotent derivation
Authors: Freudenburg Gene
Published: July 2002

This note concerns locally nilpotent derivations

D
D

of the polynomial ring

C

[

X
1

,
…
,

X
n

]

\mathbf C[X_1,\dots , X_n]

. It is shown that if

D
D

annihilates a polynomial in two variables, then

D
D

annihilates a variable.
A Banach subspace of 𝐿_{1/2} which does not embed in 𝐿₁ (isometric version)
Authors: Koldobsky Alexander
Published: July 2002

For everyn≥3,n\geq 3,we construct annn-dimensional Banach space which is isometric to a subspace ofL1/2L_{1/2}but is not isometric to a subspace ofL1.L_1.The isomorphic version of this problem (posed by S. Kwapien in 1969) is still open. Another example gives a Banach subspace ofL1/4L_{1/4}which does not embed isometrically inL1/2.L_{1/2}.Note that, from the isomorphic point of view, all the spacesLqL_qwithq>1q>1have the same Banach subspaces.
On a question of Makar-Limanov
Authors: Reichstein Zinovy
Published: July 2002

Let

K
K

be an uncountable field, let

K
⊂
F

K \subset F

be a field extension, and let

A
A

be an associative

K
K

-algebra. We show that if

F

⊗
K

A

F \otimes _K A

contains a non-commutative free algebra, then so does

A
A

.
Seminormality of operators from their tensor product
Authors: Stochel Jan
Published: July 2002

The question of seminormality of tensor products of nonzero bounded linear operators on Hilbert spaces is investigated. It is shown that

A
⊗
B

A \otimes B

is subnormal if and only if so are

A
A

and

B
B

.
A Farey tree organization of locking regions for simple circle maps
Authors: Brucks K. , Tresser C.
Published: July 2002

Let

f
f

be a

C
3

C^3

circle endomorphism of degree one with exactly two critical points and negative Schwarzian derivative. Assume that there is no real number

a
a

such that

f
+
a

f + a

has a unique rotation number equal to

p
q

\frac {p}{q}

. Then the same holds true for any

p
′

q
′

\frac {p’}{q’}

such that

p
q

\frac {p}{q}

stands above

p
′

q
′

\frac {p’}{q’}

in the Farey tree and can be related to it by a path on the tree.
Extension of orderings on *-fields
Authors: Craven Thomas
Published: July 2002

An analysis is made of the ways in which a total ordering of the set of symmetric elements of a skew field with involution can be extended to an ordering of a larger set of elements. This is done for several different types of orderings found in the literature.
On a measure-theoretic problem of Arveson
Authors: Haydon Richard , Shulman Victor
Published: July 2002

A probability measure

ν
\nu

on a product space

X
×
Y

X\times Y

is said to be bistochastic with respect to measures

λ
\lambda

on

X
X

and

μ
\mu

on

Y
Y

if the marginals

π
1

(
ν
)

\pi _1(\nu )

and

π
2

(
μ
)

\pi _2(\mu )

are exactly

λ
\lambda

and

μ
\mu

. A solution is presented to a problem of Arveson about sets which are of measure zero for all such

ν
\nu

.
The classification of two-component Cuntz-Krieger algebras
Authors: Huang Danrun
Published: July 2002

Cuntz-Krieger algebras with exactly one nontrivial closed ideal are classified up to stable isomorphism by the Cuntz invariant. The proof relies on Rørdam’s classification of simple Cuntz-Krieger algebras up to stable isomorphism and the author’s classification of two-component reducible topological Markov chains up to flow equivalence.
Infinite covering systems of congruences which don’t exist
Authors: Lewis Ethan
Published: July 2002

We prove there is no infinite set of congruences with: every integer satisfying exactly one congruence, distinct moduli, the sum of the reciprocals of the moduli equal to 1, the lcm of the moduli divisible by only finitely many primes, and a prime greater than 3 dividing any of the moduli.
A boundary value problem for Hermitian harmonic maps and applications
Authors: Chen Jingyi
Published: July 2002

We study the existence and uniqueness problems for Hermitian harmonic maps from Hermitian manifolds with boundary to Riemannian manifolds of nonpositive sectional curvature and with convex boundary. The complex analyticity of such maps and the related rigidity problems are also investigated.
Boundary value estimates for harmonic forms
Authors: Iwaniec T. , Mitrea M. , Scott C.
Published: July 2002

We prove a bound for the

L
2

L^2

-norm of harmonic forms in terms of certain

L
p

L^p

-norms of their normal and tangential components. In turn, this is used to show the

L
2

L^2

-norm equivalence of the normal and tangential components of harmonic forms on manifolds.
The Weyl calculus for hermitian matrices
Authors: Jefferies Brian
Published: July 2002

The Weyl calculus is a means of constructing functions of a system of hermitian operators which do not necessarily commute with each other. This note gives a new proof of a formula, due to E. Nelson, for the Weyl calculus associated with a system of hermitian matrices.
Harmonic maps with finite total energy
Authors: Cheng Shiu-Yuen , Tam Luen-Fai , Wan Tom
Published: July 2002

We will give a criteria for a nonnegative subharmonic function with finite energy on a complete manifold to be bounded. Using this we will prove that if on a complete noncompact Riemannian manifold

M
M

, every harmonic function with finite energy is bounded, then every harmonic map with finite total energy from

M
M

into a Cartan-Hadamard manifold must also have bounded image. No assumption on the curvature of

M
M

is required. As a consequence, we will generalize some of the uniqueness results on homotopic harmonic maps by Schoen and Yau.
A 𝑑-dimensional extension of a lemma of Huneke’s and formulas for the Hilbert coefficients
Authors: Huckaba Sam
Published: July 2002

A

d
d

-dimensional version is given of a

2
2

-dimensional result due to C. Huneke. His result produced a formula relating the length

λ
(

I

n
+
1

/

J

I

n

)

\lambda (I^{n+1}/JI^{n})

to the difference

P

I

(
n
+
1
)
−

H

I

(
n
+
1
)

P_{I}(n+1)-H_{I}(n+1)

, where

I
I

is primary for the maximal ideal of a

2
2

-dimensional Cohen-Macaulay local ring

R
R

,

J
J

is a minimal reduction of

I
I

,

H

I

(
n
)
=
λ
(
R

/

I

n

)

H_{I}(n)=\lambda (R/I^{n})

, and

P

I

(
n
)

P_{I}(n)

is the Hilbert-Samuel polynomial of

I
I

. We produce a formula that is valid for arbitrary dimension, and then use it to establish some formulas for the Hilbert coefficients of

I
I

. We also include a characterization, in terms of the Hilbert coefficients of

I
I

, of the condition

d
e
p
t
h
(
G
(
I
)
)
≥
d
−
1

depth(G(I))\geq d-1

.
𝑆¹-quotients of quaternion-Kähler manifolds
Authors: Battaglia Fiammetta
Published: July 2002

The notion of symplectic reduction has been generalized to manifolds endowed with other structures, in particular to quaternion-Kähler manifolds, namely Riemannian manifolds with holonomy in

S
p
(
n
)
S
p
(
1
)

Sp(n)Sp(1)

. In this work we prove that the only complete quaternion-Kähler manifold with positive scalar curvature obtainable as a quaternion-Kähler quotient by a circle action is the complex Grassmannian

G

r
2

(

C

n

)

Gr_2(\mathbb {C}^n)

.
The largeness of sets of points with non-dense orbit in basic sets on surfaces
Authors: Chung Yong
Published: July 2002

We show that if

f
f

is a diffeomorphism of a closed surface and

Λ
\varLambda

is a basic set for

f
f

, then

H
D
(
{
x
∈
Λ
:
t
h
e

o
r
b
i
t

o
f

x

b
y

f

i
s

n
o
t

d
e
n
s
e

i
n

Λ
}
)
=
H
D
(
Λ
)

HD(\{x\in \varLambda :the \enspace orbit \enspace of \enspace x \enspace by \enspace f \enspace is \enspace not \enspace dense \enspace in \enspace \varLambda \} )=HD(\varLambda )

.
Comparison of perturbed Dirac operators
Authors: Fox Jeffrey , Haskell Peter
Published: July 2002

This paper extends the index theory of perturbed Dirac operators to a collection of noncompact even-dimensional manifolds that includes both complete and incomplete examples. The index formulas are topological in nature. They can involve a compactly supported standard index form as well as a form associated with a Toeplitz pairing on a hypersurface.
Fixed points of contractive multivalued maps
Authors: Górniewicz L. , Marano S. , Slosarski M.
Published: July 2002

For a class of contractive multivalued maps defined on a complete absolute retract and with closed bounded values, the set of fixed points is proved to be an absolute retract. This result unifies and extends to arbitrary absolute retracts both Theorem 1 by Ricceri [Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 81 (1987), 283–286] and Theorem 1 by Bressan, Cellina, and Fryszkowski [Proc. Amer. Math. Soc. 112 (1991), 413–418].
Integral conditions on the asymptotic stability for the damped linear oscillator with small damping
Authors: Hatvani L.
Published: July 2002

The equation

x
+
h
(
t
)

x
′

+

k
2

x
=
0

x+h(t)x’+k^2x=0

is considered under the assumption

0
≤
h
(
t
)
≤

h
¯

>
∞

0\le h(t)\le \overline {h}>\infty

(
t
≥
0
)

(t\ge 0)

. It is proved that

lim sup

t
→
∞

(

t

−
2

/

3

∫
0
t

h
)

>
0

\limsup _{t \to \infty }\left (t^{-2/3}\int _0 ^t h\right )>0

is sufficient for the asymptotic stability of

x
=

x
′

=
0

x=x’=0

, and

2

/

3

2/3

is best possible here. This will be a consequence of a general result on the intermittent damping, which means that

h
h

is controlled only on a sequence of non-overlapping intervals.
When is a 𝑝-adic power series an endomorphism of a formal group?
Authors: Li Hua-Chieh
Published: July 2002

If

f
(
x
)

f(x)

is a noninvertible endomorphism of a formal group, then we have that

f
(
x
)

f(x)

commutes with an invertible series and

O

¯

[
[
x
]
]

\overline {\mathcal {O}}[[x]]

is Galois over

O

¯

[
[

f
n

(
x
)
]
]

\overline {\mathcal {O}}[[f^n(x)]]

for all

n
∈

N

n\in \mathbf {N}

. We shall prove that the converse of this statement is also true.
On the prime model property
Authors: Newelski Ludomir
Published: July 2002

Assume

T
T

is superstable,

Φ
(
x
)

\Phi (x)

is a formula over

∅
\emptyset

,

Q
=
Φ
(

M
∗

)

Q=\Phi (M^*)

is countable and

K
Q

=
{
M
:
M

K_Q=\{M: M

is countable and

Φ
(
M
)
=
Q
}

\Phi (M)=Q\}

. We investigate models in

K
Q

K_Q

assuming

K
Q

K_Q

has the prime model property. We prove some corollaries on the number of models in

K
Q

K_Q

. We show an example of an

ω
\omega

-stable

T
T

and

Q
Q

with

K
Q

K_Q

having exactly 3 models.
The local cohomology modules of Matlis reflexive modules are almost cofinite
Authors: Belshoff Richard , Slattery Susan , Wickham Cameron
Published: July 2002

We show that if

M
M

and

N
N

are Matlis reflexive modules over a complete Gorenstein local domain

R
R

and

I
I

is an ideal of

R
R

such that the dimension of

R

/

I

R/I

is one, then the modules

E
x
t

R

i

(
N
,

H

I

j

(
M
)
)

\mathrm {Ext}^{i}_{R}(N,\mathrm {H}^{j}_{I}(M))

are Matlis reflexive for all

i
i

and

j
j

if

S
u
p
p

(
N
)
⊆
V
(
I
)

\mathrm {Supp}(N) \subseteq V(I)

. It follows that the Bass numbers of

H

I

j

(
M
)

\mathrm {H}^{j}_{I}(M)

are finite. If

R
R

is not a domain, then the same results hold for

M
=
R

M=R

.
On Ramanujan congruences for modular forms of integral and half-integral weights
Authors: Datskovsky B. , Guerzhoy P.
Published: July 2002

In 1916 Ramanujan observed a remarkable congruence:

τ
(
n
)
≡

σ

11

(
n
)

mod

691

\tau (n)\equiv \sigma _{11}(n) \quad \bmod \, 691

. The modern point of view is to interpret the Ramanujan congruence as a congruence between the Fourier coefficients of the unique normalized cusp form of weight

12
12

and the Eisenstein series of the same weight modulo the numerator of the Bernoulli number

B

12

B_{12}

. In this paper we give a simple proof of the Ramanujan congruence and its generalizations to forms of higher integral and half-integral weights.
Extremal problems in Minkowski space related to minimal networks
Authors: Swanepoel K.
Published: July 2002

We solve the following problem of Z. Füredi, J. C. Lagarias and F. Morgan (1991): Is there an upper-bound polynomial in

n
n

for the largest cardinality of a set

S
S

of unit vectors in an

n
n

-dimensional Minkowski space (or Banach space) such that the sum of any subset has norm less than 1? We prove that

|

S

|

≤
2
n

|S|\leq 2n

and that equality holds iff the space is linearly isometric to

ℓ

∞

n

\ell ^{n}_{\infty }

, the space with an

n
n

-cube as unit ball. We also remark on similar questions they raised that arose out of the study of singularities in length-minimizing networks in Minkowski spaces.
Gaps in (𝒫(𝜔),⊂*) and (𝜔^{𝜔},≤*)
Authors: Spasojević Zoran
Published: July 2002

For a partial order

(
P
,

≤
P

)

(P,\le _P)

, let

Γ
(
P
,

≤
P

)

\Gamma (P,\le _P)

denote the statement that for every

≤
P

\le _P

-increasing

ω
1

\omega _1

-sequence

a
⊆
P

a\subseteq P

there is a

≤
P

\le _P

-decreasing

ω
1

\omega _1

-sequence

b
⊆
P

b\subseteq P

on top of

a
a

such that

(
a
,
b
)

(a,b)

is an

(

ω
1

,

ω
1

)

(\omega _1,\omega _1)

-gap in

P
P

. The main result of this paper is that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German t greater-than omega 1 left-right-arrow normal upper Gamma left-parenthesis script upper P left-parenthesis omega right-parenthesis comma subset-of Superscript asterisk Baseline right-parenthesis left-right-arrow normal upper Gamma left-parenthesis omega Superscript omega Baseline comma less-than-or-equal-to Superscript asterisk Baseline right-parenthesis">

t

>

ω
1

↔
Γ
(

P

(
ω
)
,

⊂
∗

)
↔
Γ
(

ω
ω

,

≤
∗

)

\mathfrak t>\omega _1\leftrightarrow \Gamma (\mathcal P(\omega ),\subset ^*)\leftrightarrow \Gamma (\omega ^\omega ,\le ^*)

. It is also shown, as a corollary, that

Γ
(

ω
ω

,

≤
∗

)
→

b

>

ω
1

\Gamma (\omega ^\omega ,\le ^*)\to \mathfrak b>\omega _1

but

b

>

ω
1

↛
Γ
(

ω
ω

,

≤
∗

)

\mathfrak b>\omega _1\not \to \Gamma (\omega ^\omega ,\le ^*)

.
On separation properties of finite dimensional compact convex sets
Authors: Queiró João , Sà Eduardo
Published: July 2002

In a real finite-dimensional vector space, we study families of sets such that every compact convex set in the space is the intersection of all members of the family that contains it.
Properties of the normset relating to the class group
Authors: Coykendall Jim
Published: July 2002

In a recent paper by the author the normset and its multiplicative structure was studied. In that paper it was shown that under certain conditions (including Galois) that a normset has unique factorization if and only if its corresponding ring of integers has unique factorization. In this paper we shall examine some of the properties of a normset and describe what it says about the class group of the corresponding ring of integers.
On weak compactness and countable weak compactness in fixed point theory
Authors: Kulesza John , Lim Teck-Cheong
Published: July 2002

We prove that weak compactness and countable weak compactness in metric spaces are not equivalent. However, if the metric space has normal structure, they are equivalent. It follows that some fixed point theorems proved recently are consequences of a classical theorem of Kirk.
Continuous singular measures with absolutely continuous convolution squares
Authors: Dooley Anthony , Gupta Sanjiv
Published: July 2002

We prove for every non-abelian compact connected group

G
G

there is a continuous, singular, central measure

μ
\mu

with

μ
∗
μ

\mu *\mu

in

L

p

L^{p}

for all

p
,
1
≤
p
>
∞

p, 1 \leq p > \infty

. We also construct such measures on some families of non-abelian compact totally disconnected groups. These results settle an open question of Ragozin.
Non-simple links with tunnel number one
Authors: Eudave-Muñoz Mario , Uchida Yoshiaki
Published: July 2002

We determine all non-simple links which admit an unknotting tunnel, i.e. links which contain an essential annulus or torus in its exterior and have tunnel number one.
Rings of weak dimension one and syzygetic ideals
Authors: Planas-Vilanova Francesc
Published: July 2002

We prove that rings of weak dimension one are the rings with all (three-generated) ideals syzygetic. This leads to a characterization of these rings in terms of the André-Quillen homology.
Spectrally determined growth is generic
Authors: Renardy Michael
Published: July 2002

Let

A
A

be the infinitesimal generator of a

C
0

C_0

-semigroup of operators in a Hilbert space. We consider the class of operators

A
+
B

A+B

, where

B
B

is bounded. It is proved that the spectrum of

A
+
B

A+B

determines the growth of the associated semigroup for “most" operators

B
B

(in the sense of Baire category).