bluuebunny/crossref_metadata_2025 huggingface dataset:
Sur les 𝑝-corps
Authors: N’Kanza M.
Published: July 2002

Here we give new examples of fields in characteristic

2
2

whose

u
u

-invariant and

u
^

\hat {u}

-invariant are different:

u
(
K
)
=
2
,

u
^

(
K
)
=

2
m

u(K) = 2, \hat {u}(K) = 2^m

or

∞
(
m
∈

N

,
m
≥
1
)

\infty (m \in \mathbb {N}, m \geq 1)

. These fields are also

p
p

-fields. Résumé. Nous donnons ici de nouveaux exemples de corps

K
K

en caractéristique

2
2

dont le

u
u

-invariant et le

u
^

\hat u

-invariant diffèrent. Plus précisément:

u
(
K
)
=
2

u(K) = 2

et

u
^

(
K
)
=

2
m

\hat {u}(K) = 2^m

ou

∞
(
m
∈

N

,
m
≥
1
)

\infty (m \in \mathbb {N}, m \geq 1)

. Ces corps sont aussi des

p
p

-corps.
On the tangential interpolation problem for matrix-valued 𝐇₂-functions of two variables
Authors: Alpay D. , Bolotnikov V.
Published: July 2002

All solutions of a general tangential interpolation problem for matrix–valued Hardy functions of two variables are described. The minimal norm solution is explicitly expressed in terms of the interpolation data.
Lipschitz precompactness for closed negatively curved manifolds
Authors: Belegradek Igor
Published: July 2002

We prove that, given a integer

n
≥
3

n\ge 3

and a group

π
\pi

, the class of closed Riemannian

n
n

-manifolds of uniformly bounded negative sectional curvatures and with fundamental groups isomorphic to

π
\pi

is precompact in the Lipschitz topology. In particular, the class breaks into finitely many diffeomorphism types.
Weighted integrability of double trigonometric series
Authors: Chen Chang-Pao , Huang Xin-Rong
Published: July 2002

We study the double trigonometric series whose coefficients

c

j
k

c_{jk}

are such that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript j equals negative normal infinity Overscript normal infinity Endscripts sigma-summation Underscript k equals negative normal infinity Overscript normal infinity Endscripts StartAbsoluteValue c Subscript j k Baseline EndAbsoluteValue greater-than normal infinity period">

∑

j
=
−
∞

∞

∑

k
=
−
∞

∞

|

c

j
k

|

>
∞
.

\sum _{j=-\infty }^\infty \sum _{k=-\infty }^\infty |c_{jk}|>\infty .

Then its rectangular partial sums converge uniformly to some

f
∈
C
(

T
2

)

f\in C(T^2)

. We give sufficient conditions for the Lebesgue integrability of
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace f left-parenthesis x comma y right-parenthesis minus f left-parenthesis x comma 0 right-parenthesis minus f left-parenthesis 0 comma y right-parenthesis plus f left-parenthesis 0 comma 0 right-parenthesis right-brace phi left-parenthesis x comma y right-parenthesis">

{
f
(
x
,
y
)
−
f
(
x
,
0
)
−
f
(
0
,
y
)
+
f
(
0
,
0
)
}
ϕ
(
x
,
y
)

\{f(x,y)-f(x,0)-f(0,y)+f(0,0)\}\phi (x,y)

, where

ϕ
(
x
,
y
)
=
1

/

x
y
,
1

/

x

\phi (x,y)=1/xy, 1/x

, or

1

/

y

1/y

. For certain cases, they are also necessary conditions. Our results extend those of Boas and Móricz from the one-dimensional to the two-dimensional series.
Nonuniqueness of phase transitions near the Maxwell line
Authors: Benzoni-Gavage S.
Published: July 2002

We consider the description of propagating phase boundaries in a van der Waals fluid by means of viscocapillary profiles, which are viewed as heteroclinic orbits connecting nonhyperbolic fixed points of a five dimensional dynamical system. A bifurcation analysis enables us to show that, for small viscosities, some distinct propagating phase boundaries share the same metastable state on one side of the front.
Finite families with few symmetric differences
Authors: Marcone Alberto , Parlamento Franco , Policriti Alberto
Published: July 2002

We show that

2

⌈

log
2

⁡
(
m
)
⌉

2^{\lceil \log _2 (m) \rceil }

is the least number of symmetric differences that a family of

m
m

sets can produce. Furthermore we give two characterizations of the set-theoretic structure of the families for which that lower bound is actually attained.
On covering multiplicity
Authors: Sun Zhi-Wei
Published: July 2002

Let

A
=
{

a

s

+

n

s

Z

}

s
=
1

k

A=\{a_{s}+n_{s}\mathbb {Z}\}^{k}_{s=1}

be a system of arithmetic sequences which forms an

m
m

-cover of

Z

\mathbb {Z}

(i.e. every integer belongs at least to

m
m

members of

A
A

). In this paper we show the following surprising properties of

A
A

: (a) For each

J
⊆
{
1
,
⋯
,
k
}

J\subseteq \{1,\cdots ,k\}

there exist at least

m
m

subsets

I
I

of

{
1
,
⋯
,
k
}

\{1,\cdots ,k\}

with

I
≠
J

I\ne J

such that

∑

s
∈
I

1

/

n

s

−

∑

s
∈
J

1

/

n

s

∈

Z

\sum _{s\in I}1/n_{s}-\sum _{s\in J}1/n_{s}\in \mathbb {Z}

. (b) If

A
A

forms a minimal

m
m

-cover of

Z

\mathbb {Z}

, then for any

t
=
1
,
⋯
,
k

t=1,\cdots ,k

there is an

α

t

∈
[
0
,
1
)

\alpha _{t}\in [0,1)

such that for every

r
=
0
,
1
,
⋯
,

n

t

−
1

r=0,1,\cdots ,n_{t}-1

there exists an

I
⊆
{
1
,
⋯
,
k
}
∖
{
t
}

I\subseteq \{1,\cdots ,k\} \setminus \{t\}

for which

[

∑

s
∈
I

1

/

n

s

]
⩾
m
−
1

[\sum _{s\in I}1/n_{s}]\geqslant m-1

and

{

∑

s
∈
I

1

/

n

s

}
=
(

α

t

+
r
)

/

n

t

.

\{\sum _{s\in I}1/n_{s}\} =(\alpha _{t}+r)/n_{t}.
On the minimality of powers of minimal 𝜔-bounded abelian groups
Authors: Dikranjan Dikran , Tonolo Alberto
Published: July 2002

We describe the structure of totally disconnected minimal

ω
\omega

- bounded abelian groups by reducing the description to the case of those of them which are subgroups of powers of the

p
p

-adic integers

Z

p

\mathbb {Z}_{p}

. In this case the description is obtained by means of a functorial correspondence, based on Pontryagin duality, between topological and linearly topologized groups introduced by Tonolo. As an application we answer the question (posed in Pseudocompact and countably compact abelian groups: Cartesian products and minimality, Trans. Amer. Math. Soc. 335 (1993), 775–790) when arbitrary powers of minimal

ω
\omega

-bounded abelian groups are minimal. We prove that the positive answer to this question is equivalent to non-existence of measurable cardinals.
Selective ultrafilters and 𝜔→(𝜔)^{𝜔}
Authors: Eisworth Todd
Published: July 2002

Mathias (Happy families, Ann. Math. Logic. 12 (1977), 59–111) proved that, assuming the existence of a Mahlo cardinal, it is consistent that CH holds and every set of reals in

L
(

R

)

L(\mathbb {R})

is

U

\mathcal {U}

-Ramsey with respect to every selective ultrafilter

U

\mathcal {U}

. In this paper, we show that the large cardinal assumption cannot be weakened.
The groups of quasiconformal homeomorphisms on Riemann surfaces
Authors: Yagasaki Tatsuhiko
Published: July 2002

Suppose

M
M

is a connected Riemann surface. Let

H

(
M
)

{\mathcal H}(M)

denote the homeomorphism group of

M
M

with the compact-open topology, and

H

Q
C

(
M
)

{\mathcal H}^{\mathrm {QC}}(M)

denote the subgroup of quasiconformal mappings of

M
M

onto itself, and let

H

(
M

)
0

{\mathcal H}(M)_0

and

H

Q
C

(
M

)
0

{\mathcal H}^{\mathrm {QC}}(M)_0

denote the identity components of

H

(
M
)

{\mathcal H}(M)

and

H

Q
C

(
M
)

{\mathcal H}^{\mathrm {QC}}(M)

respectively. In this paper we show that the pair
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis script upper H left-parenthesis upper M right-parenthesis Subscript 0 Baseline comma script upper H Superscript normal upper Q normal upper C Baseline left-parenthesis upper M right-parenthesis Subscript 0 Baseline right-parenthesis">

(

H

(
M

)
0

,

H

Q
C

(
M

)
0

)

({\mathcal H}(M)_0, {\mathcal H}^{\mathrm {QC}}(M)_0)

is an

(
s
,
Σ
)

(s, \Sigma )

-manifold, and determine their topological types.
On the existence of maximal Cohen-Macaulay modules over 𝑝th root extensions
Authors: Katz Daniel
Published: July 2002

Let

S
S

be an unramified regular local ring having mixed characteristic

p
>
0

p > 0

and

R
R

the integral closure of

S
S

in a

p
p

th root extension of its quotient field. We show that

R
R

admits a finite, birational module

M
M

such that

d
e
p
t
h
(
M
)
=
d
i
m
(
R
)

depth(M) = dim(R)

. In other words,

R
R

admits a maximal Cohen-Macaulay module.
Infinite homogeneous algebras are anticommutative
Authors: Đoković Dragomir , Sweet Lowell
Published: July 2002

A (non-associative) algebra

A
A

, over a field

k
k

, is called homogeneous if its automorphism group permutes transitively the one dimensional subspaces of

A
A

. Suppose

A
A

is a nontrivial finite dimensional homogeneous algebra over an infinite field. Then we prove that

x

2

=
0

x^{2}=0

for all

x
x

in

A
A

, and so

x
y
=
−
y
x

xy=-yx

for all

x
,
y
∈
A

x,y\in A

.
Identities of incomplete Kloosterman sums
Authors: Yangbo Ye
Published: July 2002

Identities between incomplete Kloosterman sums and incomplete hyper-Kloosterman sums are established.
A mean value theorem on bounded symmetric domains
Authors: Engliš Miroslav
Published: July 2002

LetΩ\Omegabe a Cartan domain of rankrrand genusppandBνB_\nu,ν>p−1\nu >p-1, the Berezin transform onΩ\Omega; the numberBνf(z)B_{\nu }f(z)can be interpreted as a certain invariant-mean-value of a functionffaround zz. We show that a Lebesgue integrable function satisfyingf=Bνf=Bν+1f=⋯=Bν+rff=B_\nu f=B_{\nu +1}f=\dots =B_{\nu +r}f,ν≥p\nu \ge p, must beM\mathcal {M}-harmonic. In a sense, this result is reminiscent of Delsarte’s two-radius mean-value theorem for ordinary harmonic functions on the complexnn-spaceCn\mathbf {C}^{n}, but with the role of radiusrrplayed by the quantity 1/ν1/\nu.
Continuum many Fréchet types of hereditarily strongly infinite-dimensional Cantor manifolds
Authors: Chatyrko Vitalij , Pol Elżbieta
Published: July 2002

In this note we construct a family of continuum many hereditarily strongly infinite-dimensional Cantor manifolds such that for every two spaces from this family, no open subset of one is embeddable into the other.
Extreme points of the unit ball of the Fourier-Stieltjes algebra
Authors: Mah Peter , Miao Tianxuan
Published: July 2002

Let

G
G

be a locally compact group. Among other things, we proved in this paper that for an IN-group

G
G

, the extreme points of the unit ball of the Fourier-Stieltjes algebra

B
(
G
)

B(G)

are not in the Fourier algebra

A
(
G
)

A(G)

if and only if

G
G

is non-compact, or equivalently, there is no irreducible representation of

G
G

which is quasi-equivalent to a subrepresentation of the left regular representation of

G
G

if and only if

G
G

is non-compact. This result is a non-commutative version of the following well known result: For any locally compact group

G
^

\widehat G

, the extreme points of the unit ball of the measure algebra

M
(

G
^

)

M(\widehat G)

are not in the group algebra

L

1

(

G
^

)

L^{1}(\widehat G)

if and only if

G
^

\widehat G

is non-discrete. On the other hand, we also showed that if

B
(
G
)

B(G)

has the RNP, then there are extreme points of the unit ball of

B
(
G
)

B(G)

that are in

A
(
G
)

A(G)

. Since it is well known there are non-compact locally compact group

G
G

for which

B
(
G
)

B(G)

has the RNP, there exist non-compact locally compact groups

G
G

where extreme points of the unit ball of

B
(
G
)

B(G)

can be in

A
(
G
)

A(G)

. This shows that the condition

G
G

be an IN-group cannot be entirely removed.
All non-𝑃-points are the limits of nontrivial sequences in supercompact spaces
Authors: Yang Zhongqiang , Sun Wei
Published: July 2002

A Hausdorff topological space is called supercompact if there exists a subbase such that every cover consisting of this subbase has a subcover consisting of two elements. In this paper, we prove that every non-P-point in any continuous image of a supercompact space is the limit of a nontrivial sequence. We also prove that every non-P-point in a closed

G

δ

G_{\delta }

-subspace of a supercompact space is a cluster point of a subset with cardinal number

≤
c
.

\leq c.

But we do not know whether this statement holds when replacing

c
c

by the countable cardinal number. As an application, we prove in ZFC that there exists a countable stratifiable space which has no supercompact compactification.
A remark on analytic continuation
Authors: Beardon A.
Published: July 2002

A simple example is given to show that the space of germs obtained by analytic continuation of a given germ need not be a covering space in the topological sense.
The length and thickness of words in a free group
Authors: Goldstein R.
Published: July 2002

In this paper we generalize the notion of a cut point of a graph. We assign to each graph a non-negative integer, called its thickness, so that a graph has thickness 0 if and only if it has a cut point. We then apply a method of J. H. C. Whitehead to show that if the coinitial graph of a given word has thickness

t
t

, then any word equivalent to it in a free group of rank

n
n

has length at least

2
n
t

2nt

. We also define what it means for a word in a free group to be separable and we show that there is an algorithm to decide whether or not a given word is separable.
Representations of skew polynomial algebras
Authors: Jøndrup Søren
Published: July 2002

C. De Concini and C. Procesi have proved that in many cases the degree of a skew polynomial algebra is the same as the degree of the corresponding quasi polynomial algebra. We prove a slightly more general result. In fact we show that in case the skew polynomial algebra is a P.I. algebra, then its degree is the degree of the quasi polynomial algebra. Our argument is then applied to determine the degree of some algebras given by generators and relations.
A space on which diameter-type packing measure is not Borel regular
Authors: Joyce H.
Published: July 2002

We construct a separable metric space on which 1-dimensional diameter-type packing measure is not Borel regular.
On compact manifolds with positive isotropic curvature
Authors: Labbi M.-L.
Published: July 2002

In this paper we construct new Riemannian metrics with positive isotropic curvature on compact manifolds which fiber over the circle. We also study the relationship between the positivity of the isotropic curvature and the positivity of the

p
p

-curvature.
Small inductive dimension of completions of metric spaces. II
Authors: Mrówka S.
Published: July 2002

Extending the results of a previous paper under the same title we show that, under

S

(

ℵ

0

)

\mathbf {S}({\aleph _{0}})

,

ind
⁡

c

ν

μ

0

2

=
2

\operatorname {ind}{}_{c}\, \nu \mu _{0}^{2} = 2

.
A perturbed ergodic theorem
Authors: Gologan Radu-Nicolae
Published: July 2002

Using a version of an ergodic lemma due to Cuculescu and Foiaş, we prove a pointwise ergodic theorem for

L
1

L^1

-contractions which can be viewed as a perturbed version of the celebrated ergodic theorem of Chacon and Ornstein. Surprisingly, to some extent, the complex part of the iterates involved have no effect on the ergodic convergence.
Weighted inequalities for iterated convolutions
Authors: Andersen Kenneth
Published: July 2002

Given a fixed exponentpp,1≤p>∞1\le p>\infty, and suitable nonnegative weight functionsvjv_j,j=1,…,mj=1,\dots ,m, an optimal associated weight functionωm\omega _mis constructed for which the iterated convolution product satisfies\[<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Subscript 0 Superscript normal infinity Baseline StartAbsoluteValue left-bracket product Underscript j equals 1 Overscript m Endscripts asterisk upper F Subscript j Baseline right-bracket left-parenthesis x right-parenthesis EndAbsoluteValue Superscript p Baseline StartFraction d x Over omega Subscript m Baseline left-parenthesis x right-parenthesis EndFraction less-than-or-equal-to product Underscript j equals 1 Overscript m Endscripts integral Subscript 0 Superscript normal infinity Baseline StartAbsoluteValue upper F Subscript j Baseline left-parenthesis t right-parenthesis EndAbsoluteValue Superscript p Baseline StartFraction d t Over v Subscript j Baseline left-parenthesis t right-parenthesis EndFraction">∫0∞|[∏j=1m∗Fj](x)|pdxωm(x)≤∏j=1m∫0∞|Fj(t)|pdtvj(t)\int _0^{\infty }\bigg |\bigg [\prod _{j=1}^m*F_j\bigg ](x)\bigg |^p\, \dfrac {dx}{\omega _m(x)}\le \prod _{j=1}^m\int _0^{\infty }|F_j(t)|^p\, \dfrac {dt}{v_j(t)}\]for all complex valued measurable functionsFjF_jwith<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Subscript 0 Superscript normal infinity Baseline StartAbsoluteValue upper F Subscript j Baseline left-parenthesis t right-parenthesis EndAbsoluteValue Superscript p Baseline d t slash v Subscript j Baseline left-parenthesis t right-parenthesis greater-than normal infinity">∫0∞|Fj(t)|pdt/vj(t)>∞\int _0^{\infty }|F_j(t)|^p\,dt/v_j(t)>\infty. Here<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-bracket product Underscript j equals 1 Overscript 2 Endscripts asterisk upper F Subscript j Baseline right-bracket left-parenthesis x right-parenthesis equals left-bracket upper F 1 asterisk upper F 2 right-bracket left-parenthesis x right-parenthesis equals integral Subscript 0 Superscript x Baseline upper F 1 left-parenthesis t right-parenthesis upper F 2 left-parenthesis x minus t right-parenthesis d t">[∏j=12∗Fj](x)=[F1∗F2](x)=∫0xF1(t)F2(x−t)dt[\prod _{j=1}^2*F_j](x)=[F_1*F_2](x)= \int _0^xF_1(t)F_2(x-t)\,dtand for eachm>2m>2,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="product Underscript j equals 1 Overscript m Endscripts asterisk upper F Subscript j Baseline equals left-bracket product Underscript j equals 1 Overscript m minus 1 Endscripts asterisk upper F Subscript j Baseline right-bracket asterisk upper F Subscript m">∏j=1m∗Fj=[∏j=1m−1∗Fj]∗Fm\prod _{j=1}^m*F_j=\bigg [\prod _{j=1}^{m-1}*F_j \bigg ]*F_m. Analogous results are given whenR+=(0,∞)R^+=(0,\infty )is replaced byRnR^nand also when the convolutionF1∗F2F_1*F_2onR+R^+is taken instead to be∫0∞F(t)G(x/t)dt/t\int _0^{\infty }F(t)G(x/t)\,dt/t. The extremal functions are also discussed.
Some corollaries of Frobenius’ normal 𝑝-complement theorem
Authors: Berkovich Yakov
Published: July 2002

For a prime divisorqqof the order of a finite groupGG, we present the set ofqq-subgroups generatingOq,q′(G)\text {O}^{q,q’}(G). In particular, we present the set of primary subgroups ofGGgenerating the last member of the lower central series ofGG. The proof is based on the Frobenius Normalpp-Complement Theorem and basic properties of minimal nonnilpotent groups. LetGGbe a group andΘ\Thetaa group-theoretic property inherited by subgroups and epimorphic images such that all minimal non-Θ\Theta-subgroups (=Θ1=\Theta _{1}-subgroups) ofGGare not nilpotent. Then (see the lemma), ifKKis generated by allΘ1\Theta _{1}-subgroups ofGGit follows thatG/KG/Kis aΘ\Theta-group.
Basic forms for transversely integrable singular Riemannian foliations
Authors: Wolak Robert
Published: July 2002

Basic forms for a transversely integrable singular Riemannian foliation with compact leaves are in one-to-one correspondence with “Weyl"–invariant differential forms on a generalized section of the foliation.
Parallelizability of complex projective Stiefel manifolds
Authors: Astey L. , Gitler S. , Micha E. , Pastor G.
Published: July 2002

The question of parallelizability of the complex projective Stiefel manifolds is settled.
A geometric proof of a theorem about non-dual renormings
Authors: Veselý Libor
Published: July 2002

We give a simple geometric proof of a result by Davis and Johnson that every nonreflexive Banach space

X
X

admits an equivalent norm in which

X
X

is not isometric to a dual space. Moreover, our renorming keeps unchanged the original norm on a given finite-codimensional subspace and makes this subspace norm-one complemented.
Ample divisors on the blow up of 𝐏ⁿ at points
Authors: Ballico E.
Published: July 2002

Fix integers

n
,
k
,
d

n,k,d

with

n
≥
2
,
d
≥
2

n\ge 2,d\ge 2

and

k
>
0

k>0

; if

n
=
2

n=2

assume

d
≥
3

d\ge 3

. Let

P
1

,
…
,

P
k

P_1,\dotsc ,P_k

be general points of the complex projective space

P

n

\mathbf {P}^n

and let

π
:
X
→

P

n

\pi :X\to \mathbf {P}^n

be the blow up of

P

n

\mathbf {P}^n

at

P
1

,
…
,

P
k

P_1,\dotsc ,P_k

with exceptional divisors

E
i

:=

π

−
1

(

P
i

)

E_i:=\pi ^{-1}(P_i)

,

1
≤
i
≤
k

1\le i\le k

. Set

H
:=

π
∗

(

O

P

n

(
1
)
)

H:=\pi ^*(\mathbf {O}_{\mathbf {P}^n}(1))

. Here we prove that the divisor

L
:=
d
H
−

∑

1
≤
i
≤
k

E
i

L:=dH-\sum _{1\le i\le k}E_i

is ample if and only if

L
n

>
0

L^n>0

, i.e. if and only if

d
n

>
k

d^n>k

.
Existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes
Authors: Campana F. , Kreußler B.
Published: July 2002

We prove the existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes

4

C

P

2

4 \mathbb {C}\mathbb {P}^2

. These are the first examples of twistor spaces of algebraic dimension two over a simply connected Riemannian four–manifold with positive scalar curvature. For this purpose we develop a method to distinguish between twistor spaces of algebraic dimension one and two by looking at the order of a certain point in the Picard group of an elliptic curve.
The Pontryagin 4-form
Authors: Dadok Jiri , Harvey Reese
Published: July 2002

The unit

4
4

-planes on which the first Pontryagin form of the Grassmann manifolds achieves its maximum are determined. This is a shorter and unified proof of results first obtained in 1995 by H. Gluck et al. and in 1998 by W. Gu.
Curvature restrictions on convex, timelike surfaces in Minkowski 3-space
Authors: Lin Senchun
Published: July 2002

Suppose that

K
K

and

H
H

are Minkowski Gauss curvature and Minkowski mean curvature respectively on a timelike surface

S
S

that is

C

2

C^{2}

immersed in Minkowski 3-space

E

1

3

E^{3}_{1}

. Suppose also that

0
≢
K
>
0

0\not \equiv K > 0

and that

S
S

is complete as a surface in the underlying Euclidean 3-space

E

3

E^{3}

. It is shown that neither

K
K

nor

H
H

can be bounded away from zero on such a surface

S
S

.
A condition for the stability of ℝ-covered on foliations of 3-manifolds
Authors: Goodman Sue , Shields Sandi
Published: July 2002

We give a sufficient condition for a codimension one, transversely orientable foliation of a closed 3-manifold to have the property that any foliation sufficiently close to it be

R

\mathbb {R}

-covered. This condition can be readily verified for many examples. Further, if an

R

\mathbb {R}

-covered foliation has a compact leaf

L
L

, then any transverse loop meeting

L
L

lifts to a copy of the leaf space, and the ambient manifold fibers over

S
1

S^1

with

L
L

as fiber.
Conformal actions of 𝔰𝔩_{𝔫}(ℝ) and 𝕊𝕃_{𝕟}(ℝ)⋉ℝⁿ on Lorentz manifolds
Authors: Adams Scot , Stuck Garrett
Published: July 2002

We prove that, for

n
≥
3

n\ge 3

, a locally faithful action of

SL
n

⁡
(

R

)
⋉

R

n

\operatorname {SL}_n(\mathbb {R})\ltimes \mathbb {R}^n

or of

SL
n

⁡
(

R

)

\operatorname {SL}_n({\mathbb R})

by conformal transformations of a connected Lorentz manifold must be a proper action.
Traces on algebras of parameter dependent pseudodifferential operators and the eta–invariant
Authors: Lesch Matthias , Pflaum Markus
Published: July 2002

We identify Melrose’s suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space

R

\mathbb {R}

. For a general algebra of parametric pseudodifferential operators, where the parameter space may now be a cone

Γ
⊂

R

p

\Gamma \subset \mathbb {R}^p

, we construct a unique “symbol valued trace”, which extends the

L
2

L^2

–trace on operators of small order. This construction is in the spirit of a trace due to Kontsevich and Vishik in the nonparametric case. Our trace allows us to construct various trace functionals in a systematic way. Furthermore, we study the higher–dimensional eta–invariants on algebras with parameter space

R

2
k
−
1

\mathbb {R}^{2k-1}

. Using Clifford representations we construct for each first order elliptic differential operator a natural family of parametric pseudodifferential operators over

R

2
k
−
1

\mathbb {R}^{2k-1}

. The eta–invariant of this family coincides with the spectral eta–invariant of the operator.
Skein modules and the noncommutative torus
Authors: Frohman Charles , Gelca Răzvan
Published: July 2002

We prove that the Kauffman bracket skein algebra of the cylinder over a torus is a canonical subalgebra of the noncommutative torus. The proof is based on Chebyshev polynomials. As an application, we describe the structure of the Kauffman bracket skein module of a solid torus as a module over the algebra of the cylinder over a torus, and recover a result of Hoste and Przytycki about the skein module of a lens space. We establish simple formulas for Jones-Wenzl idempotents in the skein algebra of a cylinder over a torus, and give a straightforward computation of the

n
n

-th colored Kauffman bracket of a torus knot, evaluated in the plane or in an annulus.
The problem of lacunas and analysis on root systems
Authors: Berest Yuri
Published: July 2002

A lacuna of a linear hyperbolic differential operator is a domain inside its propagation cone where a proper fundamental solution vanishes identically. Huygens’ principle for the classical wave equation is the simplest important example of such a phenomenon. The study of lacunas for hyperbolic equations of arbitrary order was initiated by I. G. Petrovsky (1945). Extending and clarifying his results, Atiyah, Bott and Gårding (1970–73) developed a profound and complete theory for hyperbolic operators with constant coefficients. In contrast, much less is known about lacunas for operators with variable coefficients. In the present paper we study this problem for one remarkable class of partial differential operators with singular coefficients. These operators stem from the theory of special functions in several variables related to finite root systems (Coxeter groups). The underlying algebraic structure makes it possible to extend many results of the Atiyah-Bott-Gårding theory. We give a generalization of the classical Herglotz-Petrovsky-Leray formulas expressing the fundamental solution in terms of Abelian integrals over properly constructed cycles in complex projective space. Such a representation allows us to employ the Petrovsky topological condition for testing regular (strong) lacunas for the operators under consideration. Some illustrative examples are constructed. A relation between the theory of lacunas and the problem of classification of commutative rings of partial differential operators is discussed.
Optimal factorization of Muckenhoupt weights
Authors: Korey Michael
Published: July 2002

Peter Jones’ theorem on the factorization of

A
p

A_p

 weights is sharpened for weights with bounds near 

1
1

, allowing the factorization to be performed continuously near the limiting, unweighted case. When

1
>
p
>
∞

1>p>\infty

and

w
w

is an

A
p

A_p

 weight with bound

A
p

(
w
)
=
1
+
ε

A_p(w)=1+\varepsilon

, it is shown that there exist

A
1

A_1

 weights 

u
,
v

u,v

such that both the formula

w
=
u

v

1
−
p

w=uv^{1-p}

and the estimates

A
1

(
u
)
,

A
1

(
v
)
=
1
+

O

(

ε

)

A_1(u), A_1(v)=1+\mathcal O(\sqrt \varepsilon )

hold. The square root in these estimates is also proven to be the correct asymptotic power as

ε
→
0

\varepsilon \to 0

.
Geometric flow and rigidity on symmetric spaces of noncompact type
Authors: Kim Inkang
Published: July 2002

In this paper we show that, under a suitable condition, every nonsingular geometric flow on a manifold which is modeled on the Furstenberg boundary of

X
X

, where

X
X

is a symmetric space of non-compact type, induces a torus action, and, in particular, if the manifold is a rational homology sphere, then the flow has a closed orbit.
A reduced Tits quadratic form and tameness of three-partite subamalgams of tiled orders
Authors: Simson Daniel
Published: July 2002

Let

D
D

be a complete discrete valuation domain with the unique maximal ideal

p

{\mathfrak {p}}

. We suppose that

D
D

is an algebra over an algebraically closed field

K
K

and

D

/

p

≅
K

D/{\mathfrak {p}} \cong K

. Subamalgam

D
D

-suborders

Λ

∙

\Lambda ^{\bullet }

of a tiled

D
D

-order

Λ
\Lambda

are studied in the paper by means of the integral Tits quadratic form

q

Λ

∙

:

Z

n

1

+
2

n

3

+
2

⟶

Z

q_{\Lambda ^{\bullet }}: {\mathbb {Z}}^{n_{1}+2n_{3}+2 } \,\,\longrightarrow {\mathbb {Z}}

. A criterion for a subamalgam

D
D

-order

Λ

∙

\Lambda ^{\bullet }

to be of tame lattice type is given in terms of the Tits quadratic form

q

Λ

∙

q_{{\Lambda ^{\bullet }}}

and a forbidden list

Ω

1

,
…
,

Ω

17

\Omega _{1},\ldots ,\Omega _{17}

of minor

D
D

-suborders of

Λ

∙

\Lambda ^{\bullet }

presented in the tables.
Bicanonical pencil of a determinantal Barlow surface
Authors: Lee Yongnam
Published: July 2002

In this paper, we study the bicanonical pencil of a Godeaux surface and of a determinantal Barlow surface. This study gives a simple proof for the unobstructedness of deformations of a determinantal Barlow surface. Then we compute the number of hyperelliptic curves in the bicanonical pencil of a determinantal Barlow surface via classical Prym theory.
Representations as elements in affine composition algebras
Authors: Zhang Pu
Published: July 2002

LetAAbe the path algebra of a Euclidean quiver over a finite fieldkk. The aim of this paper is to classify the modulesMMwith the property[M]∈C(A)[M]\in \mathcal {C}(A), whereC(A)\mathcal {C}(A)is Ringel’s composition algebra. Namely, the main result says that if|k|≠2,3|k| \ne 2, 3, then[M]∈C(A)[M]\in \mathcal {C}(A)if and only if the regular direct summand ofMMis a direct sum of modules from non-homogeneous tubes with quasi-dimension vectors non-sincere. The main methods are representation theory of affine quivers, the structure of triangular decompositions of tame composition algebras, and the invariant subspaces of skew derivations. As an application, we see thatC(A)=H(A)\mathcal {C}(A) = \mathcal {H}(A)if and only if the quiver ofAAis of Dynkin type.
The optimal differentiation basis and liftings of 𝐿^{∞}
Authors: Bliedtner Jürgen , Loeb Peter
Published: July 2002

There is an optimal way to differentiate measures when given a consistent choice of where zero limits must occur. The appropriate differentiation basis is formed following the pattern of an earlier construction by the authors of an optimal approach system for producing boundary limits in potential theory. Applications include the existence of Lebesgue points, approximate continuity, and liftings for the space of bounded measurable functions – all aspects of the fact that for every point outside a set of measure

0
0

, a given integrable function has small variation on a set that is “big” near the point. This fact is illuminated here by the replacement of each measurable set with the collection of points where the set is “big”, using a classical base operator. Properties of such operators and of the topologies they generate, e.g., the density and fine topologies, are recalled and extended along the way. Topological considerations are simplified using an extension of base operators from algebras of sets on which they are initially defined to the full power set of the underlying space.
Euclidean weights of codes from elliptic curves over rings
Authors: Voloch José , Walker Judy
Published: July 2002

We construct certain error-correcting codes over finite rings and estimate their parameters. For this purpose, we need to develop some tools, notably an estimate for certain exponential sums and some results on canonical lifts of elliptic curves. These results may be of independent interest.
A bounding question for almost flat manifolds
Authors: Upadhyay Shashidhar
Published: July 2002

We study bounding question for almost flat manifolds by looking at the equivalent description of them as infranilmanifolds

Γ
∖
L
⋊
G

/

G

\Gamma \backslash L\rtimes G/G

. We show that infranilmanifolds

Γ
∖
L
⋊
G

/

G

\Gamma \backslash L \rtimes G/G

bound if

L
L

is a 2-step nilpotent group and

G
G

is finite cyclic and acts trivially on the center of the nilpotent Lie group

L
L

.
The FBI transform on compact 𝒞^{∞} manifolds
Authors: Wunsch Jared , Zworski Maciej
Published: July 2002

We present a geometric theory of the Fourier-Bros-Iagolnitzer transform on a compact

C

∞

{\mathcal {C}^\infty }

manifold

M
M

. The FBI transform is a generalization of the classical notion of the wave-packet transform. We discuss the mapping properties of the FBI transform and its relationship to the calculus of pseudodifferential operators on

M
M

. We also describe the microlocal properties of its range in terms of the “scattering calculus” of pseudodifferential operators on the noncompact manifold

T
∗

M

T^* M

.
Derived equivalence in 𝑆𝐿₂(𝑝²)
Authors: Chuang Joseph
Published: July 2002

We present a proof that Broué’s Abelian Defect Group Conjecture is true for the principal

p
p

-block of the group

S

L
2

(

p
2

)

SL_2(p^2)

. Okuyama has independently obtained the same result using a different approach.
Stratified solutions for systems of conservation laws
Authors: Corli Andrea , Gues Olivier
Published: July 2002

We study a class of weak solutions to hyperbolic systems of conservation (balance) laws in one space dimension, called stratified solutions. These solutions are bounded and “regular” in the direction of a linearly degenerate characteristic field of the system, but not in other directions. In particular, they are not required to have finite total variation. We prove some results of local existence and uniqueness.
Livsic theorems for connected Lie groups
Authors: Pollicott M. , Walkden C.
Published: July 2002

Let

ϕ
\phi

be a hyperbolic diffeomorphism on a basic set

Λ
\Lambda

and let

G
G

be a connected Lie group. Let

f
:
Λ
→
G

f : \Lambda \rightarrow G

be Hölder. Assuming that

f
f

satisfies a natural partial hyperbolicity assumption, we show that if

u
:
Λ
→
G

u : \Lambda \rightarrow G

is a measurable solution to

f
=
u
ϕ
⋅

u

−
1

f=u\phi \cdot u^{-1}

a.e., then

u
u

must in fact be Hölder. Under an additional centre bunching condition on

f
f

, we show that if

f
f

assigns ‘weight’ equal to the identity to each periodic orbit of

ϕ
\phi

, then

f
=
u
ϕ
⋅

u

−
1

f = u\phi \cdot u^{-1}

for some Hölder

u
u

. These results extend well-known theorems due to Livšic when

G
G

is compact or abelian.
Equivariant surgery with middle dimensional singular sets. II: Equivariant framed cobordism invariance
Authors: Morimoto Masaharu
Published: July 2002

Let

G
G

be a finite group and let

f
:
X
→
Y

f : X \to Y

be a degree 1,

G
G

-framed map such that

X
X

and

Y
Y

are simply connected, closed, oriented, smooth manifolds of dimension

n
=
2
k
≧
6

n = 2k \geqq 6

and such that the dimension of the singular set of the

G
G

-space

X
X

is at most

k
k

. In the previous article, assuming

f
f

is

k
k

-connected, we defined the

G
G

-equivariant surgery obstruction

σ
(
f
)

\sigma (f)

in a certain abelian group. There it was shown that if

σ
(
f
)
=
0

\sigma (f) = 0

then

f
f

is

G
G

-framed cobordant to a homotopy equivalence

f
′

:

X
′

→
Y

f’ : X’ \to Y

. In the present article, we prove that the obstruction

σ
(
f
)

\sigma (f)

is a

G
G

-framed cobordism invariant. Consequently, the

G
G

-surgery obstruction

σ
(
f
)

\sigma (f)

is uniquely associated to

f
:
X
→
Y

f : X \to Y

above even if it is not

k
k

-connected.
SRB measures and Pesin’s entropy formula for endomorphisms
Authors: Qian Min , Zhu Shu
Published: July 2002

We present a formulation of the SRB (Sinai-Ruelle-Bowen) property for invariant measures of

C
2

C^2

endomorphisms (maybe non-invertible and with singularities) of a compact manifold via their inverse limit spaces, and prove that this property is necessary and sufficient for Pesin’s entropy formula. This result is a non-invertible endomorphisms version of a result of Ledrappier, Strelcyn and Young.
Shellability in reductive monoids
Authors: Putcha Mohan
Published: July 2002

The purpose of this paper is to extend to monoids the work of Björner, Wachs and Proctor on the shellability of the Bruhat-Chevalley order on Weyl groups. Let

M
M

be a reductive monoid with unit group

G
G

, Borel subgroup

B
B

and Weyl group

W
W

. We study the partially ordered set of

B
×
B

B\times B

-orbits (with respect to Zariski closure inclusion) within a

G
×
G

G\times G

-orbit of

M
M

. This is the same as studying a

W
×
W

W\times W

-orbit in the Renner monoid

R
R

. Such an orbit is the retract of a ‘universal orbit’, which is shown to be lexicograhically shellable in the sense of Björner and Wachs.
Sums of squares in real analytic rings
Authors: Fernando José
Published: July 2002

Let

A
A

be an analytic ring. We show: (1)

A
A

has finite Pythagoras number if and only if its real dimension is

≤
2

\leq 2

, and (2) if every positive semidefinite element of

A
A

is a sum of squares, then

A
A

is real and has real dimension

2
2

.
An existence result for linear partial differential equations with 𝐶^{∞} coefficients in an algebra of generalized functions
Authors: Todorov Todor
Published: July 2002

We prove the existence of solutions for essentially all linear partial differential equations with

C
∞

C^\infty

-coefficients in an algebra of generalized functions, defined in the paper. In particular, we show that H. Lewy’s equation has solutions whenever its right-hand side is a classical

C
∞

C^\infty

-function.
Global smooth solutions for a class of parabolic integrodifferential equations
Authors: Engler Hans
Published: July 2002

The existence and uniqueness of smooth global large data solutions of a class of quasilinear partial integrodifferential equations in one space and one time dimension are proved, if the integral kernel behaves like

t

−
α

t^{-\alpha }

near

t
=
0

t=0

with

α
>
2

/

3

\alpha > 2/3

. An existence and regularity theorem for linear equations with variable coefficients that are related to this type is also proved in arbitrary space dimensions and with no restrictions for

α
\alpha

.
A Tranversality Theorem for Holomorphic Mappings and Stability of Eisenman-Kobayashi Measures
Authors: Kaliman Sh. , Zaidenberg M.
Published: July 2002

We show that Thom’s Transversality Theorem is valid for holomorphic mappings from Stein manifolds. More precisely, given such a mapping

f
:
S
→
M

f:S\rightarrow M

from a Stein manifold

S
S

to a complex manifold

M
M

and given an analytic subset

A
A

of the jet space

J

k

(
S
,
M
)
,

f

J^{k} (S, M), \; f

can be approximated in neighborhoods of compacts by holomorphic mappings whose

k
k

-jet extensions are transversal to

A
A

. As an application the stability of Eisenman-Kobayshi intrinsic

k
k

-measures with respect to deleting analytic subsets of codimension

>
k

>k

is proven. This is a generalization of the Campbell-Howard-Ochiai-Ogawa theorem on stability of Kobayashi pseudodistances.
The Structure and Enumeration of Link Projections
Authors: Bridgeman Martin
Published: July 2002

We define a decomposition of link projections whose pieces we call atoroidal graphs. We describe a surgery operation on these graphs and show that all atoroidal graphs can be generated by performing surgery repeatedly on a family of well-known link projections. This gives a method of enumerating atoroidal graphs and hence link projections by recomposing the pieces of the decomposition.
Measure-Valued Solutions to Initial-Boundary Value Problems for Certain Systems of Conservation Laws: Existence and Dynamics
Authors: Frid Hermano
Published: July 2002

A framework for studying initial-boundary value problems for systems of conservation laws, in what concerns to the existence of measure-valued solutions and their asymptotic behavior, is developed here with the helpful introduction of a class of flux maps which allow a rather complete treatment of these questions including systems of practical importance as those arising in multiphase flow in porous media. The systems of this class may, in general, admit umbilic points, submanifolds where genuine nonlinearity fails, as well as elliptic regions. We prove the existence of measure-valued solutions by using the vanishing viscosity method and, also, finite difference schemes. The main result about the dynamics of the measure@-valued solutions is that for certain special boundary values, given by constant states, the time-averages of these m@-v solutions converge weakly to the Dirac measure concentrated at those states, for a.e. space variable. The rate of convergence of the time-averages of the expected values can be estimated by properties of the flux maps only.
Drinfel´d algebra deformations, homotopy comodules and the associahedra
Authors: Markl Martin , Shnider Steve
Published: July 2002

The aim of this work is to construct a cohomology theory controlling the deformations of a general Drinfel′d algebra

A
A

and thus finish the program which began in [M. Markl and J.D. Stasheff, Deformation theory via deviations, Journal of Algebra, 70 (1994), 122–155], [S. Shnider and S. Sternberg, The cobar construction and a restricted deformation theory for Drinfeld algebras, Journal of Algebra, 169 (1994), 343–366]. The task is accomplished in three steps. The first step, which was taken in the aforementioned articles, is the construction of a modified cobar complex adapted to a non-coassociative comultiplication. The following two steps each involves a new, highly non-trivial, construction. The first construction, essentially combinatorial, defines a differential graded Lie algebra structure on the simplicial chain complex of the associahedra. The second construction, of a more algebraic nature, is the definition of a map of differential graded Lie algebras from the complex defined above to the algebra of derivations on the bar resolution. Using the existence of this map and the acyclicity of the associahedra we can define a so-called homotopy comodule structure (Definition 3.3 below) on the bar resolution of a general Drinfel′d algebra. This in turn allows us to define the desired cohomology theory in terms of a complex which consists, roughly speaking, of the bimodule and bicomodule maps from the bar resolution to the modified cobar resolution. The complex is bigraded but not a bicomplex as in the Gerstenhaber-Schack theory for bialgebra deformations. The new components of the coboundary operator are defined via the constructions mentioned above. The results of the paper were announced in [12].
Murnaghan-Nakayama rules for characters of Iwahori-Hecke algebras of classical type
Authors: Halverson Tom , Ram Arun
Published: July 2002

In this paper we give Murnaghan-Nakayama type formulas for computing the irreducible characters of the Iwahori-Hecke algebras of types

A

n
−
1

,

B
n

A_{n-1}, B_n

, and

D
n

D_n

. Our method is a generalization of a derivation of the Murnaghan-Nakayama formula for the irreducible characters of the symmetric group given by Curtis Greene. Greene’s approach is to sum up the diagonal entries of the matrices of certain cycle permutations in Young’s seminormal representations. The analogues of the Young seminormal representations for the Iwahori-Hecke algebras of types

A

n
−
1

,

B
n

A_{n-1},B_n

, and

D
n

D_n

were given by Hoefsmit.
Presentation and central extensions of mapping class groups
Authors: Gervais Sylvain
Published: July 2002

We give a presentation of the mapping class group

M

\mathcal {M}

of a (possibly bounded) surface, considering either all twists or just non-separating twists as generators. We also study certain central extensions of

M

\mathcal {M}

. One of them plays a key role in studying TQFT functors, namely the mapping class group of a

p
1

p_1

-structure surface. We give a presentation of this extension.
An Index Theory For Quantum Dynamical Semigroups
Authors: Bhat B.
Published: July 2002

W. Arveson showed a way of associating continuous tensor product systems of Hilbert spaces with endomorphism semigroups of type I factors. We do the same for general quantum dynamical semigroups through a dilation procedure. The product system so obtained is the index and its dimension is a numerical invariant for the original semigroup.
Isomorphisms of adjoint Chevalley groups over integral domains
Authors: Chen Yu
Published: July 2002

It is shown that every automorphism of an adjoint Chevalley group over an integral domain containing the rational number field is uniquely expressible as the product of a ring automorphism, a graph automorphism and an inner automorphism while every isomorphism between simple adjoint Chevalley groups can be expressed uniquely as the product of a ring isomorphism, a graph isomorphism and an inner automorphism. The isomorphisms between the elementary subgroups are also found having analogous expressions.
Negative Flows of the potential KP-hierarchy
Authors: Haak Guido
Published: July 2002

We construct a Grassmannian-like formulation for the potential KP-hierarchy including additional “negative” flows. Our approach will generalize the notion of a

τ
\tau

-function to include negative flows. We compare the resulting hierarchy with results by Hirota, Satsuma and Bogoyavlenskii.
A group of paths in ℝ²
Authors: Kenyon Richard
Published: July 2002

We define a group structure on the set of compact “minimal” paths in

R

2

\mathbb {R}^2

. We classify all finitely generated subgroups of this group

G
G

: they are free products of free abelian groups and surface groups. Moreover, each such group occurs in

G
G

. The subgroups of

G
G

isomorphic to surface groups arise from certain topological

1
1

-forms on the corresponding surfaces. We construct examples of such

1
1

-forms for cohomology classes corresponding to certain eigenvectors for the action on cohomology of a pseudo-Anosov diffeomorphism. Using

G
G

we construct a non-polygonal tiling problem in

R

2

\mathbb {R}^2

, that is, a finite set of tiles whose corresponding tilings are not equivalent to those of any set of polygonal tiles. The group

G
G

has applications to combinatorial tiling problems of the type: given a set of tiles

P
P

and a region

R
R

, can

R
R

be tiled by translated copies of tiles in

P
P

?
Cesàro Summability of Two-dimensional Walsh-Fourier Series
Authors: Weisz Ferenc
Published: July 2002

We introduce p-quasi-local operators and the two-dimensional dyadic Hardy spaces

H

p

H_{p}

defined by the dyadic squares. It is proved that, if a sublinear operator

T
T

is p-quasi-local and bounded from

L

∞

L_{\infty }

to

L

∞

L_{\infty }

, then it is also bounded from

H

p

H_{p}

to

L

p

L_{p}

(
0
>
p
≤
1
)

(0>p \leq 1)

. As an application it is shown that the maximal operator of the Cesàro means of a martingale is bounded from

H

p

H_{p}

to

L

p

L_{p}

(
1

/

2
>
p
≤
∞
)

(1/2>p \leq \infty )

and is of weak type (1,1) provided that the supremum in the maximal operator is taken over a positive cone. So we obtain the dyadic analogue of a summability result with respect to two-dimensional trigonometric Fourier series due to Marcinkievicz and Zygmund; more exactly, the Cesàro means of a function

f
∈

L

1

f \in L_{1}

converge a.e. to the function in question, provided again that the limit is taken over a positive cone. Finally, it is verified that if we take the supremum in a cone, but for two-powers, only, then the maximal operator of the Cesàro means is bounded from

H

p

H_{p}

to

L

p

L_{p}

for every

0
>
p
≤
∞

0>p \leq \infty

.
The geometry of uniserial representations of finite dimensional algebras. III: Finite uniserial type
Authors: Huisgen-Zimmermann Birge
Published: July 2002

A description is given of those sequences

S

=
(
S
(
0
)
,
S
(
1
)
,
…
,
S
(
l
)
)

\mathbf {S}= (S(0),S(1),\dots ,S(l))

of simple modules over a finite dimensional algebra for which there are only finitely many uniserial modules with consecutive composition factors

S
(
0
)
,
…
,
S
(
l
)

S(0),\dots , S(l)

. Necessary and sufficient conditions for an algebra to permit only a finite number of isomorphism types of uniserial modules are derived. The main tools in this investigation are the affine algebraic varieties parametrizing the uniserial modules with composition series

S

\mathbf {S}

.