bluuebunny/crossref_metadata_2025 huggingface dataset:
Control of Lytic Function by Mitogen-activated Protein Kinase/Extracellular Regulatory Kinase 2 (ERK2) in a Human Natural Killer Cell Line: Identification of Perforin and Granzyme B Mobilization by Functional ERK2
Authors: Wei Sheng , Gamero Ana M. , Liu Jin Hong , Daulton Angela A. , Valkov Nichola I. , Trapani Joseph A. , Larner Andrew C. , Weber Michael J. , Djeu Julie Y.
Published: July 2002

The signal pathways that control effector function in human natural killer (NK) cells are little known. In this study, we have identified the critical role of the mitogen-activated protein kinase (MAPK) pathway in NK lysis of tumor cells, and this pathway may involve the mobilization of granule components in NK cells upon interaction with sensitive tumor target cells. Evidence was provided by biological, biochemical, and gene transfection methods. NK cell binding to tumor cells for 5 min was sufficient to maximally activate MAPK/extracellular signal–regulatory kinase 2 (ERK2), demonstrated by its tyrosine phosphorylation and by its ability to function as an efficient kinase for myelin basic protein. MAPK activation was achieved in NK cells only after contact with NK-sensitive but not NK-resistant target cells. In immunocytochemical studies, cytoplasmic perforin and granzyme B were both maximally redirected towards the tumor contact zone within 5 min of NK cell contact with tumor cells. A specific MAPK pathway inhibitor, PD098059, could block not only MAPK activation but also redistribution of perforin/granzyme B in NK cells, which occur upon target ligation. PD098059 also interfered with NK lysis of tumor cells in a 5-h 51Cr-release assay, but had no ability to block NK cell proliferation. Transient transfection studies with wild-type and dominant-negative MAPK/ERK2 genes confirmed the importance of MAPK in NK cell lysis. These results document a pivotal role of MAPK in NK effector function, possibly by its control of movement of lytic granules, and clearly define MAPK involvement in a functional pathway unlinked to cell growth or differentiation.
M144, a Murine Cytomegalovirus (Mcmv)-Encoded Major Histocompatibility Complex Class I Homologue, Confers Tumor Resistance to Natural Killer Cell–Mediated Rejection
Authors: Cretney Erika , Degli-Esposti Mariapia A. , Densley Eloise H. , Farrell Helen E. , Davis-Poynter Nick J. , Smyth Mark J.
Published: July 2002

Until now, it has been unclear whether murine cytomegalovirus (MCMV)-encoded protein m144 directly regulates natural killer (NK) cell effector function and whether the effects of m144 are only strictly evident in the context of MCMV infection. We have generated clones of the transporter associated with antigen processing (TAP)-2–deficient RMA-S T lymphoma cell line and its parent cell line, RMA, that stably express significant and equivalent levels of m144. In vivo NK cell–mediated rejection of RMA-S-m144 lymphomas was reduced compared with rejection of parental or mock-transfected RMA-S clones, indicating the ability of m144 to regulate NK cell–mediated responses in vivo. Significantly, the accumulation of NK cells in the peritoneum was reduced in mice challenged with RMA-S-m144, as was the lytic activity of NK cells recovered from the peritoneum. Expression of m144 on RMA-S cells also conferred resistance to cytotoxicity mediated in vitro by interleukin 2–activated adherent spleen NK cells. In summary, the data demonstrate that m144 confers some protection from NK cell effector function mediated in the absence of target cell class I expression, but that in vivo the major effect of m144 is to regulate NK cell accumulation and activation at the site of immune challenge.
The Requirement of Membrane Lymphotoxin for the Presence of Dendritic Cells in Lymphoid Tissues
Authors: Wu Qiang , Wang Yang , Wang Jing , Hedgeman Elizabeth O. , Browning Jeffrey L. , Fu Yang-Xin
Published: July 2002

Although several cytokines, including tumor necrosis factor (TNF), can promote the growth of dendritic cells (DCs) in vitro, the cytokines that naturally regulate DC development and function in vivo have not been well defined. Here, we report that membrane lymphotoxin (LT), instead of TNF, regulates the migration of DCs in the spleen. LTα−/− mice, lacking membrane LTα/β and LTα3, show markedly reduced numbers of DCs in the spleen. Unlike wild-type mice and TNF−/− mice that have densely clustered DCs in the T cell zone and around the marginal zone, splenic DCs in LTα−/− mice are randomly distributed. The reduced number of DCs in lymphoid tissues of LTα−/− mice is associated with an increased number of DCs in nonlymphoid tissues. The number of splenic DCs in LTα−/− mice is restored when additional LT-expressing cells are provided. Blocking membrane LTα/β in wild-type mice markedly diminishes the accumulation of DCs in lymphoid tissues. These data suggest that membrane LT is an essential ligand for the presence of DCs in the spleen. Mice deficient in TNF receptor, which is the receptor for both soluble LTα3 and TNF-α3 trimers, have normal numbers of DCs. However, LTβR−/− mice show reduced numbers of DCs, similar to the mice lacking membrane LT α/β. Taken together, these results support the notion that the signaling via LTβR by membrane LTα/β is required for the presence of DCs in lymphoid tissues.
Specific Migratory Dendritic Cells Rapidly Transport Antigen from the Airways to the Thoracic Lymph Nodes
Authors: Vermaelen Karim Y. , Carro-Muino Ines , Lambrecht Bart N. , Pauwels Romain A.
Published: July 2002

Antigen transport from the airway mucosa to the thoracic lymph nodes (TLNs) was studied in vivo by intratracheal instillation of fluorescein isothiocyanate (FITC)-conjugated macromolecules. After instillation, FITC+ cells with stellate morphology were found deep in the TLN T cell area. Using flow cytometry, an FITC signal was exclusively detected in CD11cmed-hi/major histocompatibility complex class II (MHCII)hi cells, representing migratory airway-derived lymph node dendritic cells (AW-LNDCs). No FITC signal accumulated in lymphocytes and in a CD11chiMHCIImed DC group containing a CD8αhi subset (non–airway-derived [NAW]-LNDCs). Sorted AW-LNDCs showed long MHCIIbright cytoplasmic processes and intracytoplasmatic FITC+ granules. The fraction of FITC+ AW-LNDCs peaked after 24 h and had reached baseline by day 7. AW-LNDCs were depleted by 7 d of ganciclovir treatment in thymidine kinase transgenic mice, resulting in a strong reduction of FITC-macromolecule transport into the TLNs. Compared with intrapulmonary DCs, AW-LNDCs had a mature phenotype and upregulated levels of MHCII, B7-2, CD40, and intracellular adhesion molecule (ICAM)-1. In addition, sorted AW-LNDCs from FITC-ovalbumin (OVA)–instilled animals strongly presented OVA to OVA-TCR transgenic T cells. These results validate the unique sentinel role of airway DCs, picking up antigen in the airways and delivering it in an immunogenic form to the T cells in the TLNs.
Essential Role of the Prosurvival bcl-2 Homologue A1 in Mast Cell Survival After Allergic Activation
Authors: Xiang Zou , Ahmed Ahmed A. , Möller Christine , Nakayama Kei-ichi , Hatakeyama Shigetsugu , Nilsson Gunnar
Published: July 2002

Mast cells reside in tissues, where upon activation through the high-affinity-IgE-receptor (FcϵRI) they degranulate and orchestrate the allergic reaction. Mast cells survive this activation and can thus be reactivated. In this study we demonstrate that this process depends on the pro-survival gene A1. Activation of mast cells through FcϵRI resulted in degranulation, strong induction of A1 mRNA and protein, and cell survival. In contrast, A1-deficient mast cells released granule mediators similar to the wild-type control, but the cells did not survive an allergic activation. Furthermore, A1−/− mice that had been sensitized and provocated with allergen exhibited a lower number of mast cell compared with littermate controls. The induction of A1 was dependent on calcium, as EDTA prevented A1 expression. The calcium ionophore, ionomycin, induced A1 expression and mast cell survival, whereas compound 48/80, a well-known mast cell secretagogue, did not. This study uncovers the importance of A1 for mast cell survival in allergic reactions, and it proposes A1 as a potential target for the treatment of allergic diseases.
Induction of Cytotoxic T Lymphocyte Antigen 4 (Ctla-4)

Restricts

Clonal Expansion of Helper T Cells
Authors: Doyle Alden M. , Mullen Alan C. , Villarino Alejandro V. , Hutchins Anne S. , High Frances A. , Lee Hubert W. , Thompson Craig B. , Reiner Steven L.
Published: July 2002

Cytotoxic T lymphocyte antigen (CTLA)-4 plays an essential role in immunologic homeostasis. How this negative regulator of T cell activation executes its functions has remained controversial. We now provide evidence that CTLA-4 mediates a cell-intrinsic counterbalance to restrict the clonal expansion of proliferating CD4+ T cells. The regulation of CTLA-4 expression and function ensures that, after ∼3 cell divisions of expansion, most progeny will succumb to either proliferative arrest or death over the ensuing three cell divisions. The quantitative precision of the counterbalance hinges on the graded, time-independent induction of CTLA-4 expression during the first three cell divisions. In contrast to the limits imposed on unpolarized cells, T helper type 1 (Th1) and Th2 effector progeny may be rescued from proliferative arrest by interleukin (IL)-12 and IL-4 signaling, respectively, allowing appropriately stimulated progeny to proceed to the stage of tissue homing. These results suggest that the cell-autonomous regulation of CTLA-4 induction may be a central checkpoint of clonal expansion of CD4+ T cells, allowing temporally and spatially restricted growth of progeny to be dictated by the nature of the threat posed to the host.
Idiosyncratic Gating of HERG-like K+ Channels in Microglia
Authors: Pennefather Peter S. , Zhou Wei , DeCoursey Thomas E.
Published: July 2002

A simple kinetic model is presented to explain the gating of a HERG-like voltage-gated K+ conductance described in the accompanying paper (Zhou, W., F.S. Cayabyab, P.S. Pennefather, L.C. Schlichter, and T.E. DeCoursey. 1998. J. Gen. Physiol. 111:781–794). The model proposes two kinetically distinct closing pathways, a rapid one favored by depolarization (deactivation) and a slow one favored by hyperpolarization (inactivation). The overlap of these two processes leads to a window current between −50 and +20 mV with a peak at −36 mV of ∼12% maximal conductance. The near absence of depolarization-activated outward current in microglia, compared with HERG channels expressed in oocytes or cardiac myocytes, can be explained if activation is shifted negatively in microglia. As seen with experimental data, availability predicted by the model was more steeply voltage dependent, and the midpoint more positive when determined by making the holding potential progressively more positive at intervals of 20 s (starting at −120 mV), rather than progressively more negative (starting at 40 mV). In the model, this hysteresis was generated by postulating slow and ultra-slow components of inactivation. The ultra-slow component takes minutes to equilibrate at −40 mV but is steeply voltage dependent, leading to protocol-dependent modulation of the HERG-like current. The data suggest that “deactivation” and “inactivation” are coupled through the open state. This is particularly evident in isotonic Cs+, where a delayed and transient outward current develops on depolarization with a decay time constant more voltage dependent and slower than the deactivation process observed at the same potential after a brief hyperpolarization.
Role of Domain 4 in Sodium Channel Slow Inactivation
Authors: Mitrovic Nenad , George Alfred L. , Horn Richard
Published: July 2002

Depolarization of sodium channels initiates at least three gating pathways: activation, fast inactivation, and slow inactivation. Little is known about the voltage sensors for slow inactivation, a process believed to be separate from fast inactivation. Covalent modification of a cysteine substituted for the third arginine (R1454) in the S4 segment of the fourth domain (R3C) with negatively charged methanethiosulfonate-ethylsulfonate (MTSES) or with positively charged methanethiosulfonate-ethyltrimethylammonium (MTSET) produces a marked slowing of the rate of fast inactivation. However, only MTSES modification produces substantial effects on the kinetics of slow inactivation. Rapid trains of depolarizations (2–20 Hz) cause a reduction of the peak current of mutant channels modified by MTSES, an effect not observed for wild-type or unmodified R3C channels, or for mutant channels modified by MTSET. The data suggest that MTSES modification of R3C enhances entry into a slow-inactivated state, and also that the effects on slow inactivation are independent of alterations of either activation or fast inactivation. This effect of MTSES is observed only for cysteine mutants within the middle of this S4 segment, and the data support a helical secondary structure of S4 in this region. Mutation of R1454 to the negatively charged residues aspartate or glutamate cannot reproduce the effects of MTSES modification, indicating that charge alone cannot account for these results. A long-chained derivative of MTSES has similar effects as MTSES, and can produce these effects on a residue that does not show use-dependent current reduction after modification by MTSES, suggesting that the sulfonate moiety can reach a critical site affecting slow inactivation. The effects of MTSES on R3C are partially counteracted by a point mutation (W408A) that inhibits slow inactivation. Our data suggest that a region near the midpoint of the S4 segment of domain 4 plays an important role in slow inactivation.
Descent algebras, hyperplane arrangements, and shuffling cards
Authors: Fulman Jason
Published: July 2002

Two notions of riffle shuffling on finite Coxeter groups are given: one using Solomon’s descent algebra and another using random walk on chambers of hyperplane arrangements. These coincide for types

A
A

,

B
B

,

C
C

,

H
3

H_3

, and rank two groups but not always. Both notions have the same simple eigenvalues. The hyperplane definition is especially natural and satisfies a positivity property when

W
W

is crystallographic and the relevant parameter is a good prime. The hyperplane viewpoint suggests deep connections with Lie theory and leads to a notion of riffle shuffling for arbitrary real hyperplane arrangements and oriented matroids.
A modification of Louveau and Velickovic’s construction for 𝐹_{𝜎}-ideals
Authors: Mazur Krzysztof
Published: July 2002

We show that the construction of Louveau and Veličkovič can be modified to obtain an embedding of

(
[
ω

]
ω

,

⊂
∗

)

([\omega ]^\omega ,\subset ^*)

into the preorder

(

F
σ

-ideals

,
≤
)

(F_\sigma \textit {-ideals},\le )

where

≤
\le

is the relation of Borel reducibility.
Differentiable mappings with an infinite number of critical points
Authors: Pintea C.
Published: July 2002

In this paper we shall give some sufficient conditions in order that the so-called

φ
\varphi

-category of a pair

(
M
,
N
)

(M,N)

of differentiable manifolds be infinite.
Dehn surgeries on strongly invertible knots which yield lens spaces
Authors: Hirasawa Mikami , Shimokawa Koya
Published: July 2002

In this article we show no Dehn surgery on nontrivial strongly invertible knots can yield the lens space

L
(
2
p
,
1
)

L(2p,1)

for any integer

p
p

. In order to do that, we determine band attaches to

(
2
,
2
p
)

(2,2p)

-torus links producing the trivial knot.
An 𝑛-dimensional space that admits a Poincaré inequality but has no manifold points
Authors: Hanson Bruce , Heinonen Juha
Published: July 2002

For each integern≥2n\ge 2we construct a compact, geodesic metric spaceXXwhich has topological dimensionnn, is Ahlforsnn-regular, satisfies the Poincaré inequality, possessesRn\mathbb R^nas a unique tangent cone atHn\mathcal {H}_nalmost every point, but has no manifold points.
The Hochschild cohomology ring of a cyclic block
Authors: Siegel Stephen , Witherspoon Sarah
Published: July 2002

SupposeBBis a block of a group algebrakGkGwith cyclic defect group. We calculate the Hochschild cohomology ring ofBB, giving a complete set of generators and relations. We then show that ifBBis the principal block, the canonical map fromH∗(G,k)H^*(G,k)to the Hochschild cohomology ring ofBBinduces an isomorphism modulo radicals.
Decidability of the representation extension property for finite semigroups
Authors: Shoji Kunitaka
Published: July 2002

We prove that the decision problem of whether or not a finite semigroup has the representation extension property is decidable.
A criterion on weighted 𝐿^{𝑝} boundedness for rough multilinear oscillatory singular integrals
Authors: Ding Yong , Lu Shanzhen , Yang Dachun
Published: July 2002

In this paper the authors give a criterion on the weighted

L

p

L^{p}

boundedness of the multilinear oscillatory singular integral operators with rough kernels.
A bifurcation result for harmonic maps from an annulus to 𝑆² with not symmetric boundary data
Authors: Greco C.
Published: July 2002

We consider the problem of minimizing the energy of the maps

u
(
r
,
θ
)

u(r,\theta )

from the annulus

Ω
ρ

=

B
1

∖

B
¯

ρ

\Omega _\rho =B_1\backslash \bar B_\rho

to

S
2

S^2

such that

u
(
r
,
θ
)

u(r,\theta )

is equal to

(
cos
⁡
θ
,
sin
⁡
θ
,
0
)

(\cos \theta ,\sin \theta ,0)

for

r
=
ρ

r=\rho

, and to

(
cos
⁡
(
θ
+

θ
0

)

(\cos (\theta +\theta _0)

,

sin
⁡
(
θ
+

θ
0

)
,
0
)

\sin (\theta +\theta _0),0)

for

r
=
1

r=1

, where

θ
0

∈
[
0
,
π
]

\theta _0\in [0,\pi ]

is a fixed angle. We prove that the minimum is attained at a unique harmonic map

u
ρ

u_\rho

which is a planar map if

log
2

⁡
ρ
+
3

θ
0
2

≤

π
2

\log ^2\rho +3\theta _0^2\le \pi ^2

, while it is not planar in the case

log
2

⁡
ρ
+

θ
0
2

>

π
2

\log ^2\rho +\theta _0^2>\pi ^2

. Moreover, we show that

u
ρ

u_\rho

tends to

v
¯

\bar v

as

ρ
→
0

\rho \to 0

, where

v
¯

\bar v

minimizes the energy of the maps

v
(
r
,
θ
)

v(r,\theta )

from

B
1

B_1

to

S
2

S^2

, with the boundary condition

v
(
1
,
θ
)
=
(
cos
⁡
(
θ
+

θ
0

)

v(1,\theta )=(\cos (\theta +\theta _0)

,

sin
⁡
(
θ
+

θ
0

)
,
0
)

\sin (\theta +\theta _0),0)

.
The Dirichlet-Jordan test and multidimensional extensions
Authors: Taylor Michael
Published: July 2002

If

F

\mathcal {F}

is a foliation of an open set

Ω
⊂

R

n

\Omega \subset \mathbb {R}^n

by smooth

(
n
−
1
)

(n-1)

-dimensional surfaces, we define a class of functions

B

(
Ω
,

F

)

\mathcal {B}(\Omega ,\mathcal {F})

, supported in

Ω
\Omega

, that are, roughly speaking, smooth along

F

\mathcal {F}

and of bounded variation transverse to

F

\mathcal {F}

. We investigate geometrical conditions on

F

\mathcal {F}

that imply results on pointwise Fourier inversion for these functions. We also note similar results for functions on spheres, on compact 2-dimensional manifolds, and on the 3-dimensional torus. These results are multidimensional analogues of the classical Dirichlet-Jordan test of pointwise convergence of Fourier series in one variable.
Complete orthogonal decomposition homomorphisms between matrix ordered Hilbert spaces
Authors: Miura Yasuhide , Nishiyama Kiminao
Published: July 2002

The purpose of this paper is to show that a complete order homomorphism and a complete orthogonal decomposition homomorphism between the non-commutative

L

2

L^{2}

-spaces induce respectively an isomorphism and a

∗
*

-isomorphism between the associated reduced von Neumann algebras.
Fixed point and selection theorems in hyperconvex spaces
Authors: Khamsi M. , Kirk W. , Martinez Yañez Carlos
Published: July 2002

It is shown that a set-valued mappingT∗T^{\ast }of a hyperconvex metric spaceMMwhich takes values in the space of nonempty externally hyperconvex subsets ofMMalways has a lipschitzian single valued selectionTTwhich satisfies<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="d left-parenthesis upper T left-parenthesis x right-parenthesis comma upper T left-parenthesis y right-parenthesis right-parenthesis less-than-or-equal-to d Subscript upper H Baseline left-parenthesis upper T Superscript asterisk Baseline left-parenthesis x right-parenthesis comma upper T Superscript asterisk Baseline left-parenthesis y right-parenthesis right-parenthesis">d(T(x),T(y))≤dH(T∗(x),T∗(y))d(T(x),T(y))\leq d_{H}(T^{\ast }(x),T^{\ast }(y))for allx,y∈Mx,y\in M. (HeredHd_{H}denotes the usual Hausdorff distance.) This fact is used to show that the space of all boundedλ\lambda-lipschitzian self-mappings ofMMis itself hyperconvex. Several related results are also obtained.
On the number of maximal sum-free sets
Authors: Łuczak Tomasz , Schoen Tomasz
Published: July 2002

It is shown that the set

{
1
,
2
,
…
,
n
}

\{1,2,\dots ,n\}

contains at most

2

n

/

2
−

2

−
28

n

2^{n/2-2^{-28}n}

maximal sum-free subsets, provided

n
n

is large enough.
Isospectrality and 3-manifold groups
Authors: Ruberman Daniel
Published: July 2002

The Chern-Simons and

η
\eta

-invariants are closely related invariants of a Riemannian

3
3

-manifold. A difference in their behavior under taking a finite covering space is exploited to give an obstruction to a group being the fundamental group of a closed

3
3

-dimensional manifold.
Hypoelliptic random heat kernels: A case study
Authors: Sowers Richard
Published: July 2002

We consider the fundamental solution of a simple hypoelliptic stochastic partial differential equation in which the first-order term is modulated by white noise. We derive some short-time asymptotic formulæ. We discover that the form of the dominant short-time asymptotics depends nontrivially upon the interplay between the geometry of the noisy first-order term and the geometry defined by the hypoelliptic operator.
When products of selfadjoints are normal
Authors: Albrecht E. , Spain P.
Published: July 2002

Suppose that

h
,

k
∈

L

(

H

)

h, \, k \in \mathcal {L}(\mathcal {H})

are two selfadjoint bounded operators on a Hilbert space

H

\mathcal {H}

. It is elementary to show that

h
k

hk

is selfadjoint precisely when

h
k
=
k
h

hk = kh

. We answer the following question: Under what circumstances must

h
k

hk

be selfadjoint given that it is normal?
Splitting sets in integral domains
Authors: Anderson D. , Zafrullah Muhammad
Published: July 2002

Let

D
D

be an integral domain. A saturated multiplicatively closed subset

S
S

of

D
D

is a splitting set if each nonzero

d
∈
D

d\in D

may be written as

d
=
s
a

d=sa

where

s
∈
S

s\in S

and

s
′

D
∩
a
D
=

s
′

a
D

s’D\cap aD=s’aD

for all

s
′

∈
S

s’\in S

. We show that if

S
S

is a splitting set in

D
D

, then

S
U
(

D

N

)

SU(D_{N})

is a splitting set in

D

N

D_{N}

,

N
N

a multiplicatively closed subset of

D
D

, and that

S
⊆
D

S\subseteq D

is a splitting set in

D
[
X
]

⟺

S

D[X]\iff S

is an lcm splitting set of

D
D

, i.e.,

S
S

is a splitting set of

D
D

with the further property that

s
D
∩
d
D

sD\cap dD

is principal for all

s
∈
S

s\in S

and

d
∈
D

d\in D

. Several new characterizations and applications of splitting sets are given.
Real groups transitive on complex flag manifolds
Authors: Wolf Joseph
Published: July 2002

Let

Z
=
G

/

Q

Z = G/Q

be a complex flag manifold. The compact real form

G
u

G_u

of

G
G

is transitive on

Z
Z

. If

G
0

G_0

is a noncompact real form, such transitivity is rare but occasionally happens. Here we work out a complete list of Lie subgroups of

G
G

transitive on

Z
Z

and pick out the cases that are noncompact real forms of

G
G

.
On the regularity of 𝑝-Borel ideals
Authors: Herzog Jürgen , Popescu Dorin
Published: July 2002

In this paper we prove Pardue’s conjecture on the regularity of principal

p
p

-Borel ideals. As a consequence we obtain an upper bound for the regularity of general

p
p

-Borel ideals.
Vietoris continuous selections and disconnectedness-like properties
Authors: Gutev Valentin , Nogura Tsugunori
Published: July 2002

Suppose that

X
X

is a Hausdorff space such that its Vietoris hyperspace

(

F

(
X
)
,

τ

V

)

({\mathcal {F}}(X),\tau _{V})

has a continuous selection. Do disconnectedness-like properties of

X
X

depend on the variety of continuous selections for

(

F

(
X
)
,

τ

V

)

({\mathcal {F}}(X),\tau _{V})

and vice versa? In general, the answer is “yes” and, in some particular situations, we were also able to set proper characterizations.
On the commutant of operators of multiplication by univalent functions
Authors: Robati B. , Vaezpour S.
Published: July 2002

Let

B

\mathcal {B}

be a certain Banach space consisting of continuous functions defined on the open unit disk. Let

ϕ

∈

B

{\phi }\in \mathcal {B}

be a univalent function defined on

D

¯

\overline {\mathbf {D}}

, and assume that

M

ϕ

M_{\phi }

denotes the operator of multiplication by

ϕ

{\phi }

. We characterize the structure of the operator

T
T

such that

M

ϕ

T
=
T

M

ϕ

M_{\phi } T=T M_{\phi }

. We show that

T
=

M

φ

T=M_{\varphi }

for some function

φ

{\varphi }

in

B

\mathcal {B}

. We also characterize the commutant of

M

ϕ

2

M_{{\phi }^2}

under certain conditions.
A uniqueness theorem with moving targets without counting multiplicity
Authors: Ru Min
Published: July 2002

In this paper, we prove a uniqueness theorem for holomorphic curves with moving targets without counting multiplicity.
ℕ-compactness and weighted composition maps
Authors: Araujo Jesús
Published: July 2002

In this paper we study some conditions on (not necessarily continuous) linear maps

T
T

between spaces of real- or complex-valued continuous functions

C
(
X
)

C (X)

and

C
(
Y
)

C (Y)

which allow us to describe them as weighted composition maps. This description depends strongly on the topology in

X
X

; namely, it can be given when

X
X

is

N

\mathbb {N}

-compact, but cannot in general if some kind of connectedness on

X
X

is assumed. Finally we also give an infimum-preserving version of the Banach-Stone theorem. The results are also proved for spaces of bounded continuous functions when

K

\mathbb {K}

is a field endowed with a nonarchimedean valuation and it is not locally compact.
On a theorem of Jaworowski on locally equivariant contractible spaces
Authors: Ageev Sergei , Repovš Dušan
Published: July 2002

Ancel’s method of fiberwise trivial relations is applied to the problem of characterization of absolute equivariant extensors. We obtain a generalization of Jaworowski’s theorem on characterization of equivariant extensors lying in

R

n

\mathbb {R}^{n}

to the case when the space is infinite-dimensional, has infinitely many orbit types and the acting compact group

G
G

is not necessarily a Lie group.
Exactness of one relator groups
Authors: Guentner Erik
Published: July 2002

A discrete groupΓ{\Gamma }isC∗C^*-exact if the reduced crossed product withΓ{\Gamma }converts a short exact sequence ofΓ{\Gamma }-C∗C^*-algebras into a short exact sequence ofC∗C^*-algebras. A one relator group is a discrete groupΓ{\Gamma }admitting a presentationΓ=⟨X|R⟩{\Gamma }=\langle \; X \;|\; R \;\ranglewhereXXis a countable set andRRis a single word overXX. In this short paper we prove that all one relator discrete groups areC∗C^*-exact. Using the Bass-Serre theory we also prove that a countable discrete groupΓ\Gammaacting without inversion on a tree isC∗C^*-exact if the vertex stabilizers of the action areC∗C^*-exact.
L^{𝑝} estimates on functions of Markov operators
Authors: Marias Michel
Published: July 2002

We prove L

p

^{p}

estimates for functions of Markov operators on a discrete measure space of superpolynomial volume growth.
Characterizations of paracompact-like properties by means of set-valued semi-continuous selections
Authors: Miyazaki Kazumi
Published: July 2002

We give a characterization of countably paracompact and collectionwise normal spaces by means of set-valued semi-continuous selections. This provides a positive answer to a problem of V. Gutev.
A uniqueness result for harmonic functions
Authors: Bass Richard
Published: July 2002

Let

d
≥
2

d\geq 2

,

D
=

R

d

×
(
0
,
∞
)

D=\mathbb {R}^{d}\times (0,\infty )

, and suppose

u
u

is harmonic in

D
D

and

C

2

C^{2}

on the closure of

D
D

. If the gradient of

u
u

vanishes continuously on a subset of

∂
D

\partial D

of positive

d
d

-dimensional Lebesgue measure and

u
u

satisfies certain regularity conditions, then

u
u

must be identically constant.
Essential spectrum of a system of singular differential operators and the asymptotic Hain–Lüst operator
Authors: Mennicken Reinhard , Naboko Serguei , Tretter Christiane
Published: July 2002

We consider a matrix differential operator with singular entries which arises in magnetohydrodynamics. By means of the asymptotic Hain-Lüst operator and some pseudo-differential operator techniques, we determine the essential spectrum of this operator. Whereas in the regular case, the essential spectrum consists of two intervals, it turns out that in the singular case two additional intervals due to the singularity may arise. In addition, we establish criteria for the essential spectrum to lie in the left half-plane.
Finiteness theorems for submersions and souls
Authors: Tapp Kristopher
Published: July 2002

The first section of this paper provides an improvement upon known finiteness theorems for Riemannian submersions; that is, theorems which conclude that there are only finitely many isomorphism types of fiber bundles among Riemannian submersions whose total spaces and base spaces both satisfy certain geometric bounds. The second section of this paper provides a sharpening of some recent theorems which conclude that, for an open manifold of nonnegative curvature satisfying certain geometric bounds near its soul, there are only finitely many possibilities for the isomorphism class of a normal bundle of the soul. A common theme to both sections is a reliance on basic facts about Riemannian submersions whose

A
A

and

T
T

tensors are both bounded in norm.
A theorem on the 𝑘-adic representation of positive integers
Authors: Fang Yuguang
Published: July 2002

In this paper, a theorem on the asymptotic property of a summation of digits in a

k
k

-adic representation is presented.
A note on the distance set problem in the plane
Authors: Mitsis Themis
Published: July 2002

We use a simple geometric-combinatorial argument to establish a quantitative relation between the generalized Hausdorff measure of a set and its distance set, extending a result originally due to Falconer.
Games of length 𝜔⋅2
Authors: Löwe Benedikt , Rohde Philipp
Published: July 2002

This note combines an unpublished theorem of Woodin’s about

A
D

\mathsf {AD}

and Uniformisation with combinatorial arguments of Blass’ to get a startling consequence for games on

ω
\omega

of length

ω
⋅
2

\omega \cdot 2

: The determinacy of these games is equivalent to the Axiom of Real Determinacy.
A generalization of the non-triviality theorem of Serre
Authors: Klaus Stephan
Published: July 2002

We generalize the classical theorem of Serre on the non-triviality of infinitely many homotopy groups of

1
1

-connected finite CW-complexes to CW-complexes where the cohomology groups either grow too fast or do not grow faster than a certain rate given by connectivity. For example, this result can be applied to iterated suspensions of finite Postnikov systems and certain spaces with finitely generated cohomology ring. In particular, we obtain an independent, short proof of a theorem of R. Levi on the non-triviality of

k
k

-invariants associated to finite perfect groups. Another application concerns spaces where the cohomology grows like a polynomial algebra on generators in dimension

n
n

,

2
n

2n

,

3
n
,
…

3n, \ldots

for a fixed number

n
n

. We also consider spectra where we prove a non-triviality result in the case of fast growing cohomology groups.
𝐿^{𝑝} version of Hardy’s theorem on semisimple Lie groups
Authors: Narayanan E. , Ray S.
Published: July 2002

We prove an analogue of the

L
p

L^p

version of Hardy’s theorem on semisimple Lie groups. The theorem says that on a semisimple Lie group, a function and its Fourier transform cannot decay very rapidly on an average.
On a polynomial inequality of Kolmogoroff’s type
Authors: Bojanov B. , Varma A.
Published: July 2002

We prove an inequality of the form
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar f Superscript left-parenthesis j right-parenthesis Baseline double-vertical-bar squared less-than-or-equal-to upper A double-vertical-bar f Superscript left-parenthesis m right-parenthesis Baseline double-vertical-bar squared plus upper B double-vertical-bar f double-vertical-bar squared">

‖

f

(
j
)

‖
2

≤
A
‖

f

(
m
)

‖
2

+
B
‖
f

‖
2

\|f^{(j)}\|^2\leq A\|f^{(m)}\|^2+B\|f\|^2

\]
for polynomials of degree

n
n

and any fixed

0
>
j
>
m
≤
n

0>j>m\leq n

. Here

‖
⋅
‖

\|\cdot \|

is the

L
2

L_2

-norm on

(
−
∞
,
∞
)

(-\infty ,\infty )

with a weight

e

−

t
2

e^{-t^2}

. The coefficients

A
A

and

B
B

are given explicitly and depend on

j
,
m

j,m

and

n
n

only. The equality is attained for the Hermite orthogonal polynomials

H
n

(
t
)

H_n(t)

.
Radicals of algebras graded by cancellative linear semigroups
Authors: Kelarev A.
Published: July 2002

We consider algebras over a field of characteristic zero, and prove that the Jacobson radical is homogeneous in every algebra graded by a linear cancellative semigroup. It follows that the semigroup algebra of every linear cancellative semigroup is semisimple.
A note on generators of least degree in Gorenstein ideals
Authors: Miller Matthew , Villarreal Rafael
Published: July 2002

Assume

R
R

is a polynomial ring over a field and

I
I

is a homogeneous Gorenstein ideal of codimension

g
≥
3

g\ge 3

and initial degree

p
≥
2

p\ge 2

. We prove that the number of minimal generators

ν
(

I
p

)

\nu (I_p)

of

I
I

that are of degree

p
p

is bounded above by

ν
0

=

(

p
+
g
−
1

g
−
1

)

−

(

p
+
g
−
3

g
−
1

)

\nu _0=\binom {p+g-1}{g-1}-\binom {p+g-3}{g-1}

, which is the number of minimal generators of the defining ideal of the extremal Gorenstein algebra of codimension

g
g

and initial degree

p
p

. Further,

I
I

is itself extremal if

ν
(

I
p

)
=

ν
0

\nu (I_p)=\nu _0

.
Primeness of the enveloping algebra of a Cartan type Lie superalgebra
Authors: Wilson Mark
Published: July 2002

We show that a primeness criterion for enveloping algebras of Lie superalgebras discovered by Bell is applicable to the Cartan type Lie superalgebras

W
(
n
)

W(n)

,

n
n

even. Other algebras are considered but there are no definitive answers in these cases.
On Hankel operators not in the Toeplitz algebra
Authors: Barría José
Published: July 2002

In this paper we exhibit a class of Hankel operators, which is contained in the essential commutant of the unilateral shift, but disjoint from the Toeplitz algebra.
Representing the automorphism group of an almost crystallographic group
Authors: Igodt Paul , Malfait Wim
Published: July 2002

Let

E
E

be an almost crystallographic (AC-) group, corresponding to the simply connected, connected, nilpotent Lie group

L
L

and with holonomy group

F
F

. If

L
F

=
{
1
}

L^F = \{1\}

, there is a faithful representation

Aut
⁡

E

↪
Aff
⁡
(
L
)

\operatorname {Aut}{E} \hookrightarrow \operatorname {Aff}(L)

. In case

E
E

is crystallographic, this condition

L
F

=
{
1
}

L^F =\{1\}

is known to be equivalent to

Z
(
E
)
=
1

Z(E)=1

or

b
1

(
E
)
=
0

b_1(E)=0

. We will show (Example 2.2) that, for AC-groups

E
E

, this is no longer valid and should be adapted. A generalised equivalent algebraic (and easier to verify) condition is presented (Theorem 2.3). Corresponding to an AC-group

E
E

and by factoring out subsequent centers we construct a series of AC-groups, which becomes constant after a finite number of terms. Under suitable conditions, this opens a way to represent

Aut
⁡

E

\operatorname {Aut}{E}

faithfully in

G
l

(
k
,

Z

)
×
Aff
⁡
(

L
1

)

\mathrm {Gl}(k,\mathbb {Z}{}{}) \times \operatorname {Aff}(L_1)

(Theorem 4.1). We show how this can be used to calculate

Out
⁡

E

\operatorname {Out}{E}

. This is of importance, especially, when

E
E

is almost Bieberbach and, hence,

Out
⁡

E

\operatorname {Out}{E}

is known to have an interesting geometric meaning.
Integral equations in reflexive Banach spaces and weak topologies
Authors: O’Regan Donal
Published: July 2002

The Schauder Tychonoff theorem in a locally convex topological space is used to establish existence results for Volterra-Hammerstein and Hammerstein integral equations in a reflexive Banach space.
A characterization of integral curves with Gorenstein hyperplane sections
Authors: Yanagawa Kohji
Published: July 2002

We classify a reduced, irreducible and non-degenerate curve

C
⊂

P

r

C \subset \mathbb {P}^{r}

such that its general hyperplane section

C
∩
H

C \cap H

is arithmetically Gorenstein, but

C
C

itself is not. These curves are contained in surface scrolls and are closely related to Castelnuovo theory on curves in projective space.
A Cartan theorem for Banach algebras
Authors: Ransford Thomas
Published: July 2002

Let

A
A

be a semisimple Banach algebra, and let

Ω
A

\Omega _A

be its spectral unit ball. We show that every holomorphic map

G
:

Ω
A

→

Ω
A

G\colon \Omega _A\to \Omega _A

satisfying

G
(
0
)
=
0

G(0)=0

and

G
′

(
0
)
=
I

G’(0)=I

fixes those elements of

Ω
A

\Omega _A

which belong to the centre of

A
A

, but not necessarily any others. Using this, we deduce that the automorphisms of

Ω
A

\Omega _A

all leave the centre invariant. As a further application, we give a new proof of Nagasawa’s generalization of the Banach-Stone theorem.
The structure of measurable mappings with values in locally convex spaces
Authors: Kawabe Jun
Published: July 2002

The purpose of this paper is to show that a theorem of A. Wisniewski remains valid without the approximation property.
Representations of the Gupta-Sidki group
Authors: Passman D. , Temple W.
Published: July 2002

If

p
p

is an odd prime, then the Gupta-Sidki group

G

p

\mathcal {G}_p

is an infinite

2
2

-generated

p
p

-group. It is defined in a recursive manner as a particular subgroup of the automorphism group of a regular tree of degree

p
p

. In this note, we make two observations concerning the irreducible representations of the group algebra

K

G

p

K {\mathcal {G}_p }

with

K
K

an algebraically closed field. First, when

char
⁡
K
≠
p

\operatorname {char} K\neq p

, we obtain a lower bound for the number of irreducible representations of any finite degree

n
n

. Second, when

char
⁡
K
=
p

\operatorname {char} K=p

, we show that if

K

G

p

K {\mathcal {G}_p }

has one nonprincipal irreducible representation, then it has infinitely many. The proofs of these two results use similar techniques and eventually depend on the fact that the commutator subgroup

H

p

\mathcal {H}_p

of

G

p

\mathcal {G}_p

has a normal subgroup of finite index isomorphic to the direct product of

p
p

copies of

H

p

\mathcal {H}_p

.
Compact operators and the geometric structure of 𝐶*-algebras
Authors: Anoussis M. , Katsoulis E.
Published: July 2002

Given a

C
∗

C^\ast

-algebra

A

\mathcal {A}

and an element

A
∈

A

A\in \mathcal {A}

, we give necessary and sufficient geometric conditions equivalent to the existence of a representation

(
ϕ
,

H

)

(\phi ,\mathcal {H})

of

A

\mathcal {A}

so that

ϕ
(
A
)

\phi (A)

is a compact or a finite-rank operator. The implications of these criteria on the geometric structure of

C
∗

C^\ast

-algebras are also discussed.
Bases for vector spaces over the two-element field and the axiom of choice
Authors: Keremedis Kyriakos
Published: July 2002

It is shown that the axiom of choice follows in a weaker form than the Zermelo - Fraenkel set theory from the assertion: every set of generators G of a vector space V over the two element field includes a basis L for V. It is also shown that: for every family

A

=
{

A
i

:
i
∈
k
}

\mathcal {A}=\{A_i:i\in k\}

of non empty sets there exists a family

F
=

{

F
i

:
i
∈
k
}

\mathcal {F=}\{F_i:i\in k\}

of odd sized sets such that, for every

i
∈
k

i\in k

,

F
i

⊆
A

F_i\subseteq A

iff in every vector space

B
B

over the two-element field every subspace

V
⊆
B

V\subseteq B

has a complementary subspace

S
S

iff every quotient group of an abelian group each of whose elements has order 2 has a set of representatives.
Schottky’s form and the hyperelliptic locus
Authors: Poor Cris
Published: July 2002

We show that Schottky’s modular form,

J

g

J_{g}

, has in every genus an irreducible divisor which contains the hyperelliptic locus. We also improve a corollary of Igusa concerning Siegel modular forms that must necessarily vanish on the hyperelliptic locus.
On the spectral character of Toeplitz operators on planar regions
Authors: Estahbanati Gholamreza
Published: July 2002

Self-adjoint Toeplitz operators on multiply connected planar regions are investigated using theta functions on the double. An explicit resolvent form for self-adjoint Toeplitz operators on a Hardy space associated with any representing measure on a

g
g

-holed planar region is given via reproducing kernels in terms of theta functions on

C

g

\mathbb {C}^g

. This resolvent formula is a generalization of an analogous formula obtained by K. F. Clancey (1991) for the case of harmonic measure. Applications of this resolvent form to the spectral type of the self-adjoint Toeplitz operators are described.
Embedding of a Banach algebra 𝐴 into 𝐿(𝐴’)
Authors: Desquith Etienne
Published: July 2002

Given a Banach space

X
X

, we have shown in 1994 that a product can be defined on it in such a way that the resulting Banach algebra is isomorphic to a compact subalgebra of the algebra

L
(

X
′

)

L(X’)

of all bounded linear operators on the topological dual

X
′

X’

of

X
X

. Our purpose here is to prove that, more generally, any Banach algebra

A
A

admitting a left approximate identity, is isomorphic to a subalgebra of

L
(

A
′

)

L(A’)

, the isomorphism being isometric, provided the approximate identity is bounded by 1. As a consequence, we get a factorization through

L
(

A
′

)

L(A’)

, of the elements in

A
′

A’

.
Transformations conjugate to their inverses have even essential values
Authors: Goodson Geoffrey , Lemanczyk Mariusz
Published: July 2002

Let

T
T

be an ergodic automorphism defined on a standard Borel probability space for which

T
T

and

T

−
1

T^{-1}

are isomorphic. We study the structure of the conjugating automorphisms and attempt to gain information about the structure of

T
T

. It was shown in Ergodic transformations conjugate to their inverses by involutions by Goodson et al. (Ergodic Theory and Dynamical Systems 16 (1996), 97–124) that if

T
T

is ergodic having simple spectrum and isomorphic to its inverse, and if

S
S

is a conjugation between

T
T

and

T

−
1

T^{-1}

(i.e.

S
S

satisfies

T
S
=
S

T

−
1

TS=ST^{-1}

), then

S

2

=
I

S^{2}=I

, the identity automorphism. We give a new proof of this result which shows even more, namely that for such a conjugation

S
S

, the unitary operator induced by

T
T

on

L

2

(
X
,
μ
)

L^{2}(X,\mu )

must have a multiplicity function whose essential values on the ortho-complement of the subspace

{
f
∈

L

2

(
X
,
μ
)
:
f
(

S

2

)
=
f
}

\{ f\in L^{2}(X,\mu ): f(S^{2})=f \}

are always even. In particular, we see that

S
S

can be weakly mixing, so the corresponding

T
T

must have even maximal spectral multiplicity (regarding

∞
\infty

as an even number).
Linear independence of time-frequency translates
Authors: Heil Christopher , Ramanathan Jayakumar , Topiwala Pankaj
Published: July 2002

The refinement equation

φ
(
t
)
=

∑

k
=

N
1

N
2

c
k

φ
(
2
t
−
k
)

\varphi (t) = \sum _{k=N_1}^{N_2} c_k \, \varphi (2t-k)

plays a key role in wavelet theory and in subdivision schemes in approximation theory. Viewed as an expression of linear dependence among the time-scale translates

|

a

|

1

/

2

φ
(
a
t
−
b
)

|a|^{1/2} \varphi (at-b)

of

φ
∈

L
2

(

R

)

\varphi \in L^2(\mathbf {R})

, it is natural to ask if there exist similar dependencies among the time-frequency translates

e

2
π
i
b
t

f
(
t
+
a
)

e^{2 \pi i b t} f(t+a)

of

f
∈

L
2

(

R

)

f \in L^2(\mathbf {R})

. In other words, what is the effect of replacing the group representation of

L
2

(

R

)

L^2(\mathbf {R})

induced by the affine group with the corresponding representation induced by the Heisenberg group? This paper proves that there are no nonzero solutions to lattice-type generalizations of the refinement equation to the Heisenberg group. Moreover, it is proved that for each arbitrary finite collection

{
(

a
k

,

b
k

)

}

k
=
1

N

\{(a_k,b_k)\}_{k=1}^N

, the set of all functions

f
∈

L
2

(

R

)

f \in L^2(\mathbf {R})

such that

{

e

2
π
i

b
k

t

f
(
t
+

a
k

)

}

k
=
1

N

\{e^{2 \pi i b_k t} f(t+a_k)\}_{k=1}^N

is independent is an open, dense subset of

L
2

(

R

)

L^2(\mathbf {R})

. It is conjectured that this set is all of

L
2

(

R

)
∖
{
0
}

L^2(\mathbf {R}) \setminus \{0\}

.
Extinction in nonautonomous competitive Lotka-Volterra systems
Authors: de Oca Francisco , Zeeman Mary
Published: July 2002

It is well known that for the two species autonomous competitive Lotka-Volterra model with no fixed point in the open positive quadrant, one of the species is driven to extinction, whilst the other population stabilises at its own carrying capacity. In this paper we prove a generalisation of this result to nonautonomous systems of arbitrary finite dimension. That is, for thennspecies nonautonomous competitive Lotka-Volterra model, we exhibit simple algebraic criteria on the parameters which guarantee that all but one of the species is driven to extinction. The restriction of the system to the remaining axis is a nonautonomous logistic equation, which has a unique solutionu(t)u(t)that is strictly positive and bounded for all time; see Coleman (Math. Biosci.45(1979), 159–173) and Ahmad (Proc. Amer. Math. Soc.117(1993), 199–205). We prove in addition that all solutions of thenn-dimensional system with strictly positive initial conditions are asymptotic tou(t)u(t).
A counterexample concerning smooth approximation
Authors: Bishop Christopher
Published: July 2002

We answer a question of Smith, Stanoyevitch and Stegenga in the negative by constructing a simply connected planar domain

Ω
\Omega

with no two-sided boundary points and for which every point on

Ω
c

\Omega ^c

is an

m
2

m_2

-limit point of

Ω
c

\Omega ^c

and such that

C
∞

(

Ω
¯

)

C^\infty (\overline {\Omega })

is not dense in the Sobolev space

W

k
,
p

(
Ω
)

W^{k,p}(\Omega )

.
The statistics of continued fractions for polynomials over a finite field
Authors: Friesen Christian , Hensley Doug
Published: July 2002

Given a finite field

F
F

of order

q
q

and polynomials

a
,
b
∈
F
[
X
]

a,b\in F[X]

of degrees

m
>
n

m>n

respectively, there is the continued fraction representation

b

/

a
=

a
1

+
1

/

(

a
2

+
1

/

(

a
3

+
⋯
+
1

/

a
r

)
)

b/a=a_1+1/(a_2+1/(a_3+\dots +1/a_r))

. Let

C
F
(
n
,
k
,
q
)

CF(n,k,q)

denote the number of such pairs for which

deg
⁡
b
=
n
,
deg
⁡
a
>
n
,

\deg b=n, \deg a>n,

and for

1
≤
j
≤
r
,

1\le j\le r,

deg
⁡

a
j

≤
k

\deg a_j \le k

. We give both an exact recurrence relation, and an asymptotic analysis, for

C
F
(
n
,
k
,
q
)

CF(n,k,q)

. The polynomial associated with the recurrence relation turns out to be of P-V type. We also study the distribution of

r
r

. Averaged over all

a
a

and

b
b

as above, this presents no difficulties. The average value of

r
r

is

n
(
1
−
1

/

q
)

n(1-1/q)

, and there is full information about the distribution. When

b
b

is fixed and only

a
a

is allowed to vary, we show that this is still the average. Moreover, few pairs give a value of

r
r

that differs from this average by more than

O
(

n

/

q

)
.

O(\sqrt {n/q}).