bluuebunny/crossref_metadata_2025 huggingface dataset:
Hausdorff dimension, pro-𝑝 groups, and Kac-Moody algebras
Authors: Barnea Yiftach , Shalev Aner
Published: July 2002

Every finitely generated profinite group can be given the structure of a metric space, and as such it has a well defined Hausdorff dimension function. In this paper we study Hausdorff dimension of closed subgroups of finitely generated pro-

p
p

groups

G
G

. We prove that if

G
G

is

p
p

-adic analytic and

H

≤
c

G

H \le _c G

is a closed subgroup, then the Hausdorff dimension of

H
H

is

dim
⁡
H

/

dim
⁡
G

\dim H/\dim G

(where the dimensions are of

H
H

and

G
G

as Lie groups). Letting the spectrum

Spec
⁡
(
G
)

\operatorname {Spec}(G)

of

G
G

denote the set of Hausdorff dimensions of closed subgroups of

G
G

, it follows that the spectrum of

p
p

-adic analytic groups is finite, and consists of rational numbers. We then consider some non-

p
p

-adic analytic groups

G
G

, and study their spectrum. In particular we investigate the maximal Hausdorff dimension of non-open subgroups of

G
G

, and show that it is equal to

1
−

1

d
+
1

1 - {1 \over {d+1}}

in the case of

G
=
S

L
d

(

F
p

[
[
t
]
]
)

G = SL_d(F_p[[t]])

(where

p
>
2

p > 2

), and to

1

/

2

1/2

if

G
G

is the so called Nottingham group (where

p
>
5

p >5

). We also determine the spectrum of

S

L
2

(

F
p

[
[
t
]
]
)

SL_2(F_p[[t]])

(

p
>
2

p>2

) completely, showing that it is equal to

[
0
,
2

/

3
]
∪
{
1
}

[0,2/3] \cup \{ 1 \}

. Some of the proofs rely on the description of maximal graded subalgebras of Kac-Moody algebras, recently obtained by the authors in joint work with E. I. Zelmanov.
Second variation of superminimal surfaces into self-dual Einstein four-manifolds
Authors: Montiel Sebastián , Urbano Francisco
Published: July 2002

The index of a compact orientable superminimal surface of a self-dual Einstein four-manifold

M
M

with positive scalar curvature is computed in terms of its genus and area. Also a lower bound of its nullity is obtained. Applications to the cases

M
=

S

4

M=\mathbb {S}^4

and

M
=

C

P

2

M=\mathbb {C}\mathbb {P}^2

are given, characterizing the standard Veronese immersions and their twistor deformations as those with lowest index.
Time-dependent coating flows in a strip, Part I: The linearized problem
Authors: Friedman Avner , Velázquez Juan
Published: July 2002

This work is concerned with time-dependent coating flow in a strip

0
>
y
>
1

0 > y > 1

. The Navier-Stokes equations are satisfied in the fluid region, the bottom substrate

y
=
0

y = 0

is moving with fixed velocity

(
U
,
0
)

(U,0)

, and fluid is entering the strip through the upper boundary

y
=
1

y = 1

. The free boundary has the form

y
=
f
(
x
,
t
)

y = f(x,t)

for

−
∞
>
x
>
R
(
t
)

-\infty > x > R(t)

, where

R
(
t
)

R(t)

is the moving contact point. Our objective is to prove that if the initial data are close to those of a stationary solution (the existence of such a solution was established by the authors in an earlier paper) then the time-dependent problem has a unique solution with smooth free boundary, at least for a small time interval. In this Part I we study the linearized problem, about the stationary solution, and obtain sharp estimates for the solution and its derivatives. These estimates will be used in Part II to establish existence and uniqueness for the full nonlinear problem.
Verma type modules of level zero for affine Lie algebras
Authors: Futorny Viatcheslav
Published: July 2002

We study the structure of Verma type modules of level zero induced from non-standard Borel subalgebras of an affine Kac-Moody algebra. For such modules in “general position” we describe the unique irreducible quotients, construct a BGG type resolution and prove the BGG duality in certain categories. All results are extended to generalized Verma type modules of zero level.
Generalized Weil’s reciprocity law and multiplicativity theorems
Authors: Némethi András
Published: July 2002

Fix a one-dimensional group variety

G
G

with Euler–characteristic

χ
(
G
)
=
0

\chi (G)=0

, and a quasi–projective variety

Y
Y

, both defined over

C

\mathbf {C}

. For any

f
∈
H
o
m
(
Y
,
G
)

f\in Hom(Y,G)

and constructible sheaf

F

\mathcal {F}

on

Y
Y

, we construct an invariant

c

F

(
f
)
∈
G

c_{\mathcal {F}}(f)\in G

, which provides substantial information about the topology of the fiber–structure of

f
f

and the structure of

F

\mathcal {F}

along the fibers of

f
f

. Moreover,

c

F

:
H
o
m
(
Y
,
G
)
→
G

c_{\mathcal {F}}:Hom(Y,G)\to G

is a group homomorphism.
A theorem of the Dore-Venni type for noncommuting operators
Authors: Monniaux Sylvie , Prüss Jan
Published: July 2002

A theorem of the Dore-Venni type for the sum of two closed linear operators is proved, where the operators are noncommuting but instead satisfy a certain commutator condition. This result is then applied to obtain optimal regularity results for parabolic evolution equations

u
˙

(
t
)
+
L
(
t
)
u
(
t
)
=
f
(
t
)

\dot {u}(t)+L(t)u(t)=f(t)

and evolutionary integral equations
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u left-parenthesis t right-parenthesis plus integral Subscript 0 Superscript t Baseline a left-parenthesis t minus s right-parenthesis upper L left-parenthesis s right-parenthesis u left-parenthesis s right-parenthesis d s equals g left-parenthesis t right-parenthesis">

u
(
t
)
+

∫
0
t

a
(
t
−
s
)
L
(
s
)
u
(
s
)
d
s
=
g
(
t
)

u(t)+\int _0^ta(t-s)L(s)u(s)ds = g(t)

which are nonautonomous. The domains of the involved operators

L
(
t
)

L(t)

may depend on

t
t

, but

L
(
t

)

−
1

L(t)^{-1}

is required to satisfy a certain smoothness property. The results are then applied to parabolic partial differential and integro-differential equations.
Lexicographic TAF Algebras
Authors: Peters Justin , Poon Yiu
Published: July 2002

Lexicographic TAF algebras constitute a class of triangular AF algebras which are determined by a countable ordered set

Ω
\Omega

, a dimension function, and a third parameter. While some of the important examples of TAF algebras belong to the class, most algebras in this class have not been studied. The semigroupoid of the algebra, the lattice of invariant projections, the Jacobson radical, and for some cases the automorphism group are computed. Necessary and sufficient conditions for analyticity are given. The results often involve the order properties of the set

Ω
\Omega

.
Correction and extension of “Measurable quotients of unipotent translations on homogeneous spaces”
Authors: Witte Dave
Published: July 2002

The statements of Main Theorem 1.1 and Theorem 2.1 of the author’s paper [Trans. Amer. Math. Soc. 345 (1994), 577–594] should assume that

Γ
\Gamma

 is discrete and

G
G

 is connected. (Corollaries 1.3, 5.6, and 5.8 are affected similarly.) These restrictions can be removed if the conclusions of the results are weakened to allow for the possible existence of transitive, proper subgroups of 

G
G

. In this form, the results can be extended to the setting where

G
G

is a product of real and

p
p

-adic Lie groups.
The residual spectrum of 𝑈(2,2)
Authors: Kon-No Takyua
Published: July 2002

Let

G
G

be the quasi-split unitary group

U
(
2
,
2

)

k
′

/

k

U(2,2)_{k’/k}

of four variables attached to a quadratic extension

k
′

/

k

k’/k

of number fields. An irreducible decomposition of the non-cuspidal discrete spectrum of

L
2

L^2

-automorphic forms of

G
G

is obtained.
Limit theorems for random transformations and processes in random environments
Authors: Kifer Yuri
Published: July 2002

I derive general relativized central limit theorems and laws of iterated logarithm for random transformations both via certain mixing assumptions and via the martingale differences approach. The results are applied to Markov chains in random environments, random subshifts of finite type, and random expanding in average transformations where I show that the conditions of the general theorems are satisfied and so the corresponding (fiberwise) central limit theorems and laws of iterated logarithm hold true in these cases. I consider also a continuous time version of such limit theorems for random suspensions which are continuous time random dynamical systems.
Recognizing constant curvature discrete groups in dimension 3
Authors: Cannon J. , Swenson E.
Published: July 2002

We characterize those discrete groups

G
G

which can act properly discontinuously, isometrically, and cocompactly on hyperbolic

3
3

-space

H

3

\mathbb {H}^3

in terms of the combinatorics of the action of

G
G

on its space at infinity. The major ingredients in the proof are the properties of groups that are negatively curved (in the large) (that is, Gromov hyperbolic), the combinatorial Riemann mapping theorem, and the Sullivan-Tukia theorem on groups which act uniformly quasiconformally on the

2
2

-sphere.
Necessary conditions for optimal control problems with state constraints
Authors: Vinter R. , Zheng H.
Published: July 2002

Necessary conditions of optimality are derived for optimal control problems with pathwise state constraints, in which the dynamic constraint is modelled as a differential inclusion. The novel feature of the conditions is the unrestrictive nature of the hypotheses under which these conditions are shown to be valid. An Euler Lagrange type condition is obtained for problems where the multifunction associated with the dynamic constraint has values possibly unbounded, nonconvex sets and satisfies a mild ‘one-sided’ Lipschitz continuity hypothesis. We recover as a special case the sharpest available necessary conditions for state constraint free problems proved in a recent paper by Ioffe. For problems where the multifunction is convex valued it is shown that the necessary conditions are still valid when the one-sided Lipschitz hypothesis is replaced by a milder, local hypothesis. A recent ‘dualization’ theorem permits us to infer a strengthened form of the Hamiltonian inclusion from the Euler Lagrange condition. The necessary conditions for state constrained problems with convex valued multifunctions are derived under hypotheses on the dynamics which are significantly weaker than those invoked by Loewen and Rockafellar to achieve related necessary conditions for state constrained problems, and improve on available results in certain respects even when specialized to the state constraint free case. Proofs make use of recent ‘decoupling’ ideas of the authors, which reduce the optimization problem to one to which Pontryagin’s maximum principle is applicable, and a refined penalization technique to deal with the dynamic constraint.
Connected finite loop spaces with maximal tori
Authors: Møller J. , Notbohm D.
Published: July 2002

Finite loop spaces are a generalization of compact Lie groups. However, they do not enjoy all of the nice properties of compact Lie groups. For example, having a maximal torus is a quite distinguished property. Actually, an old conjecture, due to Wilkerson, says that every connected finite loop space with a maximal torus is equivalent to a compact connected Lie group. We give some more evidence for this conjecture by showing that the associated action of the Weyl group on the maximal torus always represents the Weyl group as a crystallographic group. We also develop the notion of normalizers of maximal tori for connected finite loop spaces, and prove for a large class of connected finite loop spaces that a connected finite loop space with maximal torus is equivalent to a compact connected Lie group if it has the right normalizer of the maximal torus. Actually, in the cases under consideration the information about the Weyl group is sufficient to give the answer. All this is done by first studying the analogous local problems.
Newton’s method on the complex exponential function
Authors: Haruta Mako
Published: July 2002

We show that when Newton’s method is applied to the product of a polynomial and the exponential function in the complex plane, the basins of attraction of roots have finite area.
Two special cases of Ganea’s conjecture
Authors: Strom Jeffrey
Published: July 2002

Ganea conjectured that for any finite CW complex

X
X

and any

k
>
0

k>0

,

cat
⁡
(
X
×

S
k

)
=
cat
⁡
(
X
)
+
1

\operatorname {cat}(X\times S^k) =\operatorname {cat}(X) + 1

. In this paper we prove two special cases of this conjecture. The main result is the following. Let

X
X

be a

(
p
−
1
)

(p-1)

-connected

n
n

-dimensional CW complex (not necessarily finite). We show that if

cat
⁡
(
X
)
=

⌊

n
p

⌋

+
1

\operatorname {cat}(X) = \left \lfloor {n \over p} \right \rfloor + 1

and

n
≢
−
1
mod
⁡
p

n\not \equiv -1 \operatorname {mod} p

(which implies

p
>
1

p>1

), then

cat
⁡
(
X
×

S
k

)
=
cat
⁡
(
X
)
+
1

\operatorname {cat}(X\times S^k) =\operatorname {cat}(X) +1

. This is proved by showing that

wcat
⁡
(
X
×

S
k

)
=
wcat
⁡
(
X
)
+
1

\operatorname {wcat}(X\times S^k) =\operatorname {wcat}(X) + 1

in a much larger range, and then showing that under the conditions imposed,

cat
⁡
(
X
)
=
wcat
⁡
(
X
)

\operatorname {cat}(X)=\operatorname {wcat}(X)

. The second special case is an extension of Singhof’s earlier result for manifolds.
Entropy and periodic points for transitive maps
Authors: Alsedà Ll. , Kolyada S. , Llibre J. , Snoha Ľ.
Published: July 2002

The aim of this paper is to investigate the connection between transitivity, density of the set of periodic points and topological entropy for low dimensional continuous maps. The paper deals with this problem in the case of the

n
n

–star and the circle among the one–dimensional spaces and in some higher dimensional spaces. Particular attention is paid to triangular maps and to extensions of transitive maps to higher dimensions without increasing topological entropy.
Supports of derivations, free factorizations, and ranks of fixed subgroups in free groups
Authors: Bergman George
Published: July 2002

For

F
F

a free group of finite rank, it is shown that the fixed subgroup of any set

B
B

of endomorphisms of

F
F

has rank

≤
rank
⁡
(
F
)

\leq \operatorname {rank} (F)

, generalizing a recent result of Dicks and Ventura. The proof involves the combinatorics of derivations of groups. Some related questions are examined.
Deformations of dihedral 2-group extensions of fields
Authors: Black Elena
Published: July 2002

Given a

G
G

-Galois extension of number fields

L

/

K

L/K

we ask whether it is a specialization of a regular

G
G

-Galois cover of

P

K

1

\mathbb {P}^{1}_{K}

. This is the “inverse" of the usual use of the Hilbert Irreducibility Theorem in the Inverse Galois problem. We show that for many groups such arithmetic liftings exist by observing that the existence of generic extensions implies the arithmetic lifting property. We explicitly construct generic extensions for dihedral

2
2

-groups under certain assumptions on the base field

k
k

. We also show that dihedral groups of order

8
8

and

16
16

have generic extensions over any base field

k
k

with characteristic different from

2
2

.
On the number of terms in the middle of almost split sequences over tame algebras
Authors: de la Peña J. , Takane M.
Published: July 2002

Let

A
A

be a finite dimensional tame algebra over an algebraically closed field

k
k

. It has been conjectured that any almost split sequence

0
→
X
→

⊕

i
=
1

n

Y
i

→
Z
→
0

0 \to X \to \oplus _{i=1} ^n Y_i \to Z \to 0

with

Y
i

Y_i

indecomposable modules has

n
≤
5

n \le 5

and in case

n
=
5

n=5

, then exactly one of the

Y
i

Y_i

is a projective-injective module. In this work we show this conjecture in case all the

Y
i

Y_i

are directing modules, that is, there are no cycles of non-zero, non-iso maps

Y
i

=

M
1

→

M
2

→
⋯
→

M
s

=

Y
i

Y_i =M_1 \to M_2 \to \cdots \to M_s=Y_i

between indecomposable

A
A

-modules. In case,

Y
1

Y_1

and

Y
2

Y_2

are isomorphic, we show that

n
≤
3

n \le 3

and give precise information on the structure of

A
A

.
Chaotic solutions in differential inclusions: chaos in dry friction problems
Authors: Fečkan Michal
Published: July 2002

The existence of a continuum of many chaotic solutions is shown for certain differential inclusions which are small periodic multivalued perturbations of ordinary differential equations possessing homoclinic solutions to hyperbolic fixed points. Applications are given to dry friction problems. Singularly perturbed differential inclusions are investigated as well.
Decomposing Euclidean space with a small number of smooth sets
Authors: Steprāns Juris
Published: July 2002

Let the cardinal invariant

s

n

{\mathfrak s}_{n}

denote the least number of continuously smooth

n
n

-dimensional surfaces into which

(
n
+
1
)

(n+1)

-dimensional Euclidean space can be decomposed. It will be shown to be consistent that

s

n

{\mathfrak s}_{n}

is greater than

s

n
+
1

{\mathfrak s}_{n+1}

. These cardinals will be shown to be closely related to the invariants associated with the problem of decomposing continuous functions into differentiable ones.
Partial subdifferentials, derivates and Rademacher’s Theorem
Authors: Bessis D. , Clarke F.
Published: July 2002

In this paper, we present new partial subdifferentiation formulas in nonsmooth analysis, based upon the study of two directional derivatives. Simple applications of these formulas include a new elementary proof of Rademacher’s Theorem in

R

n

{\mathbb R}^n

, as well as some results on Gâteaux and Fréchet differentiability for locally Lipschitz functions in a separable Hilbert space. Résumé. Dans cet article, nous présentons de nouvelles formules de sousdifférentiation partielle en analyse nonlisse, basées sur l’étude de deux dérivées directionnelles. Une simple application de ces formules nous permet d’obtenir une nouvelle preuve élémentaire du théorème de Rademacher dans

R

n

{\mathbb R}^{n}

, ainsi que certains résultats sur la différentiabilité Gâteaux ou Fréchet des fonctions localement Lipschitz sur un espace de Hilbert séparable.
Convexity properties of holomorphic mappings in ℂⁿ
Authors: Roper Kevin , Suffridge Ted
Published: July 2002

Not many convex mappings on the unit ball in

C

n

{\mathbb C}^n

for

n
>
1

n>1

are known. We introduce two families of mappings, which we believe are actually identical, that both contain the convex mappings. These families which we have named the “Quasi-Convex Mappings, Types A and B” seem to be natural generalizations of the convex mappings in the plane. It is much easier to check whether a function is in one of these classes than to check for convexity. We show that the upper and lower bounds on the growth rate of such mappings is the same as for the convex mappings.
An estimate for a first-order Riesz operator on the affine group
Authors: Sjögren Peter
Published: July 2002

On the affine group of the line, which is a solvable Lie group of exponential growth, we consider a right-invariant Laplacian

Δ
\Delta

. For a certain right-invariant vector field

X
X

, we prove that the first-order Riesz operator

X

Δ

−
1

/

2

X\Delta ^{-1/2}

is of weak type (1, 1) with respect to the left Haar measure of the group. This operator is therefore also bounded on

L
p

,

1
>
p
≤
2

L^p, \; 1>p\leq 2

. Locally, the operator is a standard singular integral. The main part of the proof therefore concerns the behaviour of the kernel of the operator at infinity and involves cancellation.
Combinatorial families that are exponentially far from being listable in Gray code sequence
Authors: Chinburg Ted , Savage Carla , Wilf Herbert
Published: July 2002

Let

S
(
n
)

S(n)

be a collection of subsets of

{
1
,
.
.
.
,
n
}

\{1,...,n\}

. In this paper we study numerical obstructions to the existence of orderings of

S
(
n
)

S(n)

for which the cardinalities of successive subsets satisfy congruence conditions. Gray code orders provide an example of such orderings. We say that an ordering of

S
(
n
)

S(n)

is a Gray code order if successive subsets differ by the adjunction or deletion of a single element of

{
1
,
…
,
n
}

\{1,\ldots ,n\}

. The cardinalities of successive subsets in a Gray code order must alternate in parity. It follows that if

d
(
S
(
n
)
)

d(S(n))

is the difference between the number of elements of

S
(
n
)

S(n)

having even (resp. odd) cardinality, then

|

d
(
S
(
n
)
)

|

−
1

|d(S(n))| - 1

is a lower bound for the cardinality of the complement of any subset of

S
(
n
)

S(n)

which can be listed in Gray code order. For

g
≥
2

g \ge 2

, the collection

B
(
n
,
g
)

B(n,g)

of

g
g

-blockfree subsets of

{
1
,
…
,
n
}

\{1,\ldots ,n\}

is defined to be the set of all subsets

S
S

of

{
1
,
…
,
n
}

\{1,\ldots ,n\}

such that

|

a
−
b

|

≥
g

|a-b| \ge g

if

a
,
b
∈
S

a,b \in S

and

a
≠
b

a \ne b

. We will construct a Gray code order for

B
(
n
,
2
)

B(n,2)

. In contrast, for

g
>
2

g > 2

we find the precise (positive) exponential growth rate of

d
(
B
(
n
,
g
)
)

d(B(n,g))

with

n
n

as

n
→
∞

n \to \infty

. This implies

B
(
n
,
g
)

B(n,g)

is far from being listable in Gray code order if

n
n

is large. Analogous results for other kinds of orderings of subsets of

B
(
n
,
g
)

B(n,g)

are proved using generalizations of

d
(
B
(
n
,
g
)
)

d(B(n,g))

. However, we will show that for all

g
g

, one can order

B
(
n
,
g
)

B(n,g)

so that successive elements differ by the adjunction and/or deletion of an integer from

{
1
,
…
,
n
}

\{1,\ldots ,n\}

. We show that, over an

A
A

-letter alphabet, the words of length

n
n

which contain no block of

k
k

consecutive letters cannot, in general, be listed so that successive words differ by a single letter. However, if

k
>
2

k>2

and

A
>
2

A>2

or if

k
=
2

k=2

and

A
>
3

A>3

, such a listing is always possible.
The Calabi invariant and the Euler class
Authors: Tsuboi Takashi
Published: July 2002

We show the following relationship between the Euler class for the group of the orientation preserving diffeomorphisms of the circle and the Calabi invariant for the group of area preserving diffeomorphisms of the disk which are the identity along the boundary. A diffeomorphism of the circle admits an extension which is an area preserving diffeomorphism of the disk. For a homomorphism

ψ
\psi

from the fundamental group
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="mathematical left-angle a 1 comma midline-horizontal-ellipsis comma a Subscript 2 g Baseline semicolon left-bracket a 1 comma a 2 right-bracket midline-horizontal-ellipsis left-bracket a Subscript 2 g minus 1 Baseline comma a Subscript 2 g Baseline right-bracket mathematical right-angle">

⟨

a

1

,
⋯
,

a

2
g

;
[

a

1

,

a

2

]
⋯
[

a

2
g
−
1

,

a

2
g

]
⟩

\langle a_{1}, \cdots , a_{2g} ; [a_{1},a_{2}]\cdots [a_{2g-1},a_{2g}]\rangle

of a closed surface to the group of the diffeomorphisms of the circle, by taking the extensions

ψ
(
a

~

i

)

\widetilde {\psi (a}_{i})

for the generators

a

i

a_{i}

, one obtains the product
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-bracket ModifyingAbove psi left-parenthesis a With tilde Subscript 1 Baseline right-parenthesis comma ModifyingAbove psi left-parenthesis a With tilde Subscript 2 Baseline right-parenthesis right-bracket midline-horizontal-ellipsis left-bracket ModifyingAbove psi left-parenthesis a With tilde Subscript 2 g minus 1 Baseline right-parenthesis comma ModifyingAbove psi left-parenthesis a With tilde Subscript 2 g Baseline right-parenthesis right-bracket">

[

ψ
(
a

~

1

)
,

ψ
(
a

~

2

)
]
⋯
[

ψ
(
a

~

2
g
−
1

)
,

ψ
(
a

~

2
g

)
]

[\widetilde {\psi (a}_{1}),\widetilde {\psi (a}_{2})]\cdots [\widetilde {\psi (a}_{2g-1}),\widetilde {\psi (a}_{2g})]

of their commutators, and this is an area preserving diffeomorphism of the disk which is the identity along the boundary. Then the Calabi invariant of this area preserving diffeomorphism is a non-zero multiple of the Euler class of the associated circle bundle evaluated on the fundamental cycle of the surface.
Rarified sums of the Thue-Morse sequence
Authors: Drmota Michael , Skałba Mariusz
Published: July 2002

Let

q
q

be an odd number and

S

q
,
0

(
n
)

S_{q,0}(n)

the difference between the number of

k
>
n

k>n

,

k
≡
0
mod

q

k\equiv 0\bmod \,q

, with an even binary digit sum and the corresponding number of

k
>
n

k>n

,

k
≡
0
mod

q

k\equiv 0\bmod \,q

, with an odd binary digit sum. A remarkable theorem of Newman says that

S

3
,
0

(
n
)
>
0

S_{3,0}(n)>0

for all

n
n

. In this paper it is proved that the same assertion holds if

q
q

is divisible by 3 or

q
=

4
N

+
1

q=4^N+1

. On the other hand, it is shown that the number of primes

q
≤
x

q\le x

with this property is

o
(
x

/

log
⁡
x
)

o(x/\log x)

. Finally, analoga for “higher parities” are provided.
On modules of bounded multiplicities for the symplectic algebras
Authors: Britten D. , Lemire F.
Published: July 2002

Simple infinite dimensional highest weight modules having bounded weight multipicities are classified as submodules of a tensor product. Also, it is shown that a simple torsion free module of finite degree tensored with a finite dimensional module is completely reducible.
Brownian sheet images and Bessel-Riesz capacity
Authors: Khoshnevisan Davar
Published: July 2002

We show that the image of a 2–dimensional set under

d
d

–dimensional, 2–parameter Brownian sheet can have positive Lebesgue measure if and only if the set in question has positive (

d

/

2

d/2

)–dimensional Bessel–Riesz capacity. Our methods solve a problem of J.-P. Kahane.
Embeddings of open manifolds
Authors: Cardim Nancy
Published: July 2002

Let

T
O
P
(
M
)

TOP(M)

be the simplicial group of homeomorphisms of

M
M

. The following theorems are proved. Theorem A. Let

M
M

be a topological manifold of dim

≥
\geq

5 with a finite number of tame ends

ε

i

\varepsilon _{i}

,

1
≤
i
≤
k

1\leq i\leq k

. Let

T
O

P

e
p

(
M
)

TOP^{ep}(M)

be the simplicial group of end preserving homeomorphisms of

M
M

. Let

W

i

W_{i}

be a periodic neighborhood of each end in

M
M

, and let

p

i

:

W

i

→

R

p_{i}: W_{i} \to \mathbb {R}

be manifold approximate fibrations. Then there exists a map
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f colon upper T upper O upper P Superscript e p Baseline left-parenthesis upper M right-parenthesis right-arrow product Underscript i Endscripts upper T upper O upper P Superscript e p Baseline left-parenthesis upper W Subscript i Baseline right-parenthesis">

f
:
T
O

P

e
p

(
M
)
→

∏

i

T
O

P

e
p

(

W

i

)

f: TOP^{ep}(M) \to \prod _{i} TOP^{ep}(W_{i})

such that the homotopy fiber of

f
f

is equivalent to

T
O

P

c
s

(
M
)

TOP_{cs}(M)

, the simplicial group of homeomorphisms of

M
M

which have compact support. Theorem B. Let

M
M

be a compact topological manifold of dim

≥
\geq

5, with connected boundary

∂
M

\partial M

, and denote the interior of

M
M

by

I
n
t
M

Int M

. Let

f
:
T
O
P
(
M
)
→
T
O
P
(
I
n
t
M
)

f: TOP(M)\to TOP(Int M)

be the restriction map and let

G

\mathcal {G}

be the homotopy fiber of

f
f

over

i

d

I
n
t
M

id_{Int M}

. Then

π

i

G

\pi _{i} \mathcal {G}

is isomorphic to

π

i

C

(
∂
M
)

\pi _{i} \mathcal {C} (\partial M)

for

i
>
0

i > 0

, where

C

(
∂
M
)

\mathcal {C} (\partial M)

is the concordance space of

∂
M

\partial M

. Theorem C. Let

q

0

:
W
→

R

q_{0}: W \to \mathbb {R}

be a manifold approximate fibration with dim

W
≥

W \geq

5. Then there exist maps
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="alpha colon pi Subscript i Baseline upper T upper O upper P Superscript e p Baseline left-parenthesis upper W right-parenthesis right-arrow pi Subscript i Baseline upper T upper O upper P left-parenthesis ModifyingAbove upper W With caret right-parenthesis">

α
:

π

i

T
O

P

e
p

(
W
)
→

π

i

T
O
P
(

W
^

)

\alpha : \pi _{i} TOP^{ep}(W) \to \pi _{i} TOP(\hat W)

and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="beta colon pi Subscript i Baseline upper T upper O upper P left-parenthesis ModifyingAbove upper W With caret right-parenthesis right-arrow pi Subscript i Baseline upper T upper O upper P Superscript e p Baseline left-parenthesis upper W right-parenthesis">

β
:

π

i

T
O
P
(

W
^

)
→

π

i

T
O

P

e
p

(
W
)

\beta : \pi _{i} TOP(\hat W) \to \pi _{i} TOP^{ep}(W)

for

i
>
1

i >1

, such that

β
∘
α
≃
i
d

\beta \circ \alpha \simeq id

, where

W
^

\hat W

is a compact and connected manifold and

W
W

is the infinite cyclic cover of

W
^

\hat W

.
On the 𝐿²→𝐿^{∞} norms of spectral multipliers of “quasi-homogeneous” operators on homogeneous groups
Authors: Sikora Adam
Published: July 2002

We study the

L
2

→

L

∞

L^2 \to L^{\infty }

norms of spectral projectors and spectral multipliers of left-invariant elliptic and subelliptic second-order differential operators on homogeneous Lie groups. We obtain a precise description of the

L
2

→

L

∞

L^2 \to L^{\infty }

norms of spectral multipliers for some class of operators which we call quasi-homogeneous. As an application we prove a stronger version of Alexopoulos’ spectral multiplier theorem for this class of operators.
Gauge Invariant Eigenvalue Problems in ℝⁿ and in ℝⁿ₊
Authors: Lu Kening , Pan Xing-Bin
Published: July 2002

This paper is devoted to the study of the eigenvalue problems for the Ginzburg-Landau operator in the entire plane

R

2

{\mathbb {R}}^{2}

and in the half plane

R

+

2

{\mathbb {R}}^{2}_{+}

. The estimates for the eigenvalues are obtained and the existence of the associate eigenfunctions is proved when

c
u
r
l
A

curl A

is a non-zero constant. These results are very useful for estimating the first eigenvalue of the Ginzburg-Landau operator with a gauge-invariant boundary condition in a bounded domain, which is closely related to estimates of the upper critical field in the theory of superconductivity.
Symmetry of ground states for a semilinear elliptic system
Authors: Zou Henghui
Published: July 2002

Let

n
≥
3

n\ge 3

and consider the following system

Δ

u

+

f

(

u

)
=
0
,

u

>
0
,

x
∈

R

n

.

\begin{equation*} \Delta \mathbf {u}+\mathbf {f}(\mathbf {u})=0,\quad \mathbf {u}>0,\qquad x\in \mathbf {R}^n.\end{equation*}

By using the Alexandrov-Serrin moving plane method, we show that under suitable assumptions every slow decay solution of (I) must be radially symmetric.
Embeddings in generalized manifolds
Authors: Bryant J. , Mio W.
Published: July 2002

We prove that a (

2
m
−
n
+
1

2m-n+1

)-connected map

f
:

M
m

→

X
n

f\colon M^m\to X^n

from a compact PL

m
m

-manifold

M
M

to a generalized

n
n

-manifold

X
X

with the disjoint disks property,

3
m
≤
2
n
−
2

3m\le 2n-2

, is homotopic to a tame embedding. There is also a controlled version of this result, as well as a version for noncompact

M
M

and proper maps

f
f

that are properly (

2
m
−
n
+
1

2m-n+1

)-connected. The techniques developed lead to a general position result for arbitrary maps

f
:
M
→
X

f\colon M\to X

,

3
m
≤
2
n
−
2

3m\le 2n-2

, and a Whitney trick for separating

P
L

PL

submanifolds of

X
X

that have intersection number 0, analogous to the well-known results when

X
X

is a manifold.
Pag1p, a Novel Protein Associated with Protein Kinase Cbk1p, Is Required for Cell Morphogenesis and Proliferation inSaccharomyces cerevisiae
Authors: Du Li-Lin , Novick Peter
Published: July 2002

Protein kinases in the Cot-1/Orb6/Ndr/Warts family are important regulators of cell morphogenesis and proliferation. Cbk1p, a member of this family in Saccharomyces cerevisiae, has previously been shown to be required for normal morphogenesis in vegetatively growing cells and in haploid cells responding to mating pheromone. A mutant of PAG1, a novel gene in S. cerevisiae, displayed defects similar to those ofcbk1 mutants. pag1 andcbk1 mutants share a common set of suppressors, including the disruption of SSD1, a gene encoding an RNA binding protein, and the overexpression of Sim1p, an extracellular protein. These genetic results suggest that PAG1 andCBK1 act in the same pathway. Furthermore, we found that Pag1p and Cbk1p localize to the same polarized peripheral sites and that they coimmunoprecipitate with each other. Pag1p is a conserved protein. The homologs of Pag1p in other organisms are likely to form complexes with the Cbk1p-related kinases and function with those kinases in the same biological processes.
Dynein Supports Motility of Endoplasmic Reticulum in the FungusUstilago maydis
Authors: Wedlich-Söldner Roland , Schulz Irene , Straube Anne , Steinberg Gero
Published: July 2002

The endoplasmic reticulum (ER) of most vertebrate cells is spread out by kinesin-dependent transport along microtubules, whereas studies in Saccharomyces cerevisiae indicated that motility of fungal ER is an actin-based process. However, microtubules are of minor importance for organelle transport in yeast, but they are crucial for intracellular transport within numerous other fungi. Herein, we set out to elucidate the role of the tubulin cytoskeleton in ER organization and dynamics in the fungal pathogen Ustilago maydis. An ER-resident green fluorescent protein (GFP)-fusion protein localized to a peripheral network and the nuclear envelope. Tubules and patches within the network exhibited rapid dynein-driven motion along microtubules, whereas conventional kinesin did not participate in ER motility. Cortical ER organization was independent of microtubules or F-actin, but reformation of the network after experimental disruption was mediated by microtubules and dynein. In addition, a polar gradient of motile ER-GFP stained dots was detected that accumulated around the apical Golgi apparatus. Both the gradient and the Golgi apparatus were sensitive to brefeldin A or benomyl treatment, suggesting that the gradient represents microtubule-dependent vesicle trafficking between ER and Golgi. Our results demonstrate a role of cytoplasmic dynein and microtubules in motility, but not peripheral localization of the ER inU. maydis.
SCPD: a promoter database of the yeast Saccharomyces cerevisiae.
Authors: Zhu J , Zhang M Q
Published: July 2002

MOTIVATION: In order to facilitate a systematic study of the promoters and transcriptionally regulatory cis-elements of the yeast Saccharomyces cerevisiae on a genomic scale, we have developed a comprehensive yeast-specific promoter database, SCPD. RESULTS: Currently SCPD contains 580 experimentally mapped transcription factor (TF) binding sites and 425 transcriptional start sites (TSS) as its primary data entries. It also contains relevant binding affinity and expression data where available. In addition to mechanisms for promoter information (including sequence) retrieval and a data submission form, SCPD also provides some simple but useful tools for promoter sequence analysis. AVAILABILITY: SCPD can be accessed from the URL http://cgsigma.cshl.org/jian. The database is continually updated.
SCHOOL QUALITY AND RETURNS TO EDUCATION OF U.S. IMMIGRANTS
Authors: Bratsberg Bernt , Terrell Dek
Published: July 2002

Using the U.S. labor market as a common point of reference, this article investigates the influence of source country school quality on the returns to education of immigrants. Based on 1980 and 1990 census data, we first estimate country‐of‐origin specific returns to education. Results reveal that immigrants from Japan and northern Europe receive high returns and immigrants from Central America receive low returns. Next we examine the relationship between school quality measures and these returns. Holding per capita GDP and other factors constant, immigrants from countries with lower pupil‐teacher ratios and greater expenditures per pupil earn higher returns to education.)
Inducible chromosomal translocation of AML1 and ETO genes through Cre/loxP‐mediated recombination in the mouse
Authors: Buchholz Frank , Refaeli Yosef , Trumpp Andreas , Bishop J Michael
Published: July 2002

Transgenic mice have been used to explore the role of chromosomal translocations in the genesis of tumors. But none of these efforts has actually involved induction of a translocation in vivo. Here we report the use of Cre recombinase to replicate in vivo the t(8;21) translocation found in human acute myeloid leukemia (AML). As in the human tumors, the murine translocation fuses the genes AML1 and ETO. We used homologous recombination to place loxP sites at loci that were syntenic with the break points for the human translocation. Cre activity was provided in mice by a transgene under the control of the Nestin promoter, or in cultured B cells by infecting with a retroviral vector encoding Cre. In both instances, Cre activity mediated interchromosomal translocations that fused the AML1 and ETO genes. Thus, reciprocal chromosomal translocations that closely resemble rearrangements found in human cancers can be achieved in mice.
Infectious exacerbations of chronic bronchitis: diagnosis and management
Authors: Sethi Sanjay
Published: July 2002

Chronic bronchitis is an increasing cause of significant morbidity and mortality. Despite treatment, respiratory tract infection is the most common identifiable cause of death for patients with chronic obstructive pulmonary disease. Repeated infectious exacerbations may ultimately cause acute and chronic lung injury. The most common bacterial aetiologies of acute exacerbations of chronic bronchitis (AECB) include Haemophilus influenzae, Moraxella catarrhalis and Streptococcus pneumoniae.Pseudomonas aeruginosa is often a nosocomial pathogen and is becoming more prevalent in patients with severe underlying disease. Viruses are responsible for approximately one-third of acute exacerbations overall. Atypical pathogens are causative pathogens in <10% of episodes. The diagnosis of AECB is often based on clinical impression, although suspicion of bacterial infection can be enhanced by quantitative Gram's stains from appropriately obtained sputum specimens. However, a specific microbiological diagnosis is only needed in certain specific situations. Management of AECB involves non-drug interventions (e.g. smoking cessation) and antibiotic treatment. Recommendations for antibiotic use in patients with known or highly suspected AECB are still evolving. The selection of an antibiotic for treatment of an infectious episode must consider underlying patient co-morbidities, likely pathogens, resistance issues and individual antibiotic properties. Cephalosporins, β-lactam/β-lactamase inhibitor combinations and macrolides are all reasonable choices. However, due to the increasing prevalence of resistance to standard antibiotics among common respiratory pathogens, and increased incidence of Pseudomonas spp., fluoroquinolones should be a first-line treatment for AECB in patients who have chronic bronchitis complicated by co-morbid illness, severe obstruction (FEV 1 < 50%), old age (>65 years) or have recurrent exacerbations. In patients who do not have these risk factors (i.e. those with simple chronic bronchitis), agents such as co-trimoxazole remain useful.
Transgenic study of energy homeostasis equation: implications and confounding influences
Authors: INUI AKIO
Published: July 2002

Recently novel molecular mediators and regulatory pathways for feeding and body weight regulation have been identified in the brain and the periphery. Mice lacking or overexpressing these mediators or receptors have been produced by molecular genetic techniques, and observations on mutant mice have shed new light on the role of each element in the homeostatic loop of body weight regulation. However, the interpretation of the phenotype is under the potential influence of developmental compensation and other genetic and environmental confounds. Specific alterations of the mediators and the consequences of the altered expression patterns are reviewed here and discussed in the context of their functions as suggested from conventional pharmacological studies. Advanced gene targeting strategies in which genes can be turned on or off at desired tissues and times would undoubtedly lead to a better understanding of the highly integrated and redundant systems for energy homeostasis equation.— Inui, A. Transgenic study of energy homeostasis equation: implications and confounding influences FASEB J. 14, 2158‐2170 (2000)
Feature binding, attention and object perception
Authors: Treisman Anne
Published: July 2002

The seemingly effortless ability to perceive meaningful objects in an integrated scene actually depends on complex visual processes. The ‘binding problem’ concerns the way in which we select and integrate the separate features of objects in the correct combinations. Experiments suggest that attention plays a central role in solving this problem. Some neurological patients show a dramatic breakdown in the ability to see several objects; their deficits suggest a role for the parietal cortex in the binding process. However, indirect measures of priming and interference suggest that more information may be implicitly available than we can consciously access.
Protein–protein interactions and protein modules in the control of neurotransmitter release
Authors: Benfenati Fabio , Onofri Franco , Giovedí Silvia
Published: July 2002

Information transfer among neurons is operated by neurotransmitters stored in synaptic vesicles and released to the extracellular space by an efficient process of regulated exocytosis. Synaptic vesicles are organized into two distinct functional pools, a large reserve pool in which vesicles are restrained by the actin–based cytoskeleton, and a quantitatively smaller releasable pool in which vesicles approach the presynaptic membrane and eventually fuse with it on stimulation. Both synaptic vesicle trafficking and neurotransmitter release depend on a precise sequence of events that include release from the reserve pool, targeting to the active zone, docking, priming, fusion and endocytotic retrieval of synaptic vesicles. These steps are mediated by a series of specific interactions among cytoskeletal, synaptic vesicle, presynaptic membrane and cytosolic proteins that, by acting in concert, promote the spatial and temporal regulation of the exocytotic machinery. The majority of these interactions are mediated by specific protein modules and domains that are found in many proteins and are involved in numerous intracellular processes. In this paper, the possible physiological role of these multiple protein–protein interactions is analysed, with ensuing updating and clarification of the present molecular model of the process of neurotransmitter release.
Misattribution, false recognition and the sins of memory
Authors: Schacter Daniel L. , Dodson Chad S.
Published: July 2002

Memory is sometimes a troublemaker. Schacter has classified memory's transgressions into seven fundamental ‘sins’: transience, absent–mindedness, blocking, misattribution, suggestibility, bias and persistence. This paper focuses on one memory sin, misattribution, that is implicated in false or illusory recognition of episodes that never occurred. We present data from cognitive, neuropsychological and neuroimaging studies that illuminate aspects of misattribution and false recognition. We first discuss cognitive research examining possible mechanisms of misattribution associated with false recognition. We also consider ways in which false recognition can be reduced or avoided, focusing in particular on the role of distinctive information. We next turn to neuropsychological research concerning patients with amnesia and Alzheimer's disease that reveals conditions under which such patients are less susceptible to false recognition than are healthy controls, thus providing clues about the brain mechanisms that drive false recognition. We then consider neuroimaging studies concerned with the neural correlates of true and false recognition, examining when the two forms of recognition can and cannot be distinguished on the basis of brain activity. Finally, we argue that even though misattribution and other memory sins are annoying and even dangerous, they can also be viewed as by–products of adaptive features of memory.
Episodic memory: insights from semantic dementia
Authors: Hodges John R. , Graham Kim S.
Published: July 2002

Semantic dementia, also known as the temporal lobe variant of fronto– temporal dementia, results in a progressive yet relatively pure loss of semantic knowledge about words, objects and people, and is associated with asymmetric, focal atrophy of the antero–lateral temporal lobes. Semantic dementia provides a unique opportunity to study the organization of long–term memory particularly since initial observations suggested sparing of episodic memory. Recent studies reveal, however, a more complex but theoretically revealing pattern. On tests of autobiographical memory, patients with semantic dementia show a ‘reverse step function’ with sparing of recall of events from the most recent 2 to 5 years but impairment on more distant life periods. Anterograde recognition memory for visual materials is extremely well preserved, except in the most deteriorated cases, although performance is heavily reliant upon perceptual information about the studied stimuli, particularly for items that are no longer known by the subjects. On tests of verbal anterograde memory such as word learning, performance is typically poor even for words which are ‘known’ to the patients. A source discrimination experiment, designed to evaluate familiarity and recollection–based anterograde memory processes, found that patients with semantic dementia showed good item detection, although recollection of source was sometimes impaired. Semantic knowledge about studied items and measures of item detection and source discrimination were largely independent. The implications of these findings for models of long–term memory are discussed. The results support the concept that episodic memory, or at least the recall of temporally specific autobiographical experiences, draws upon a number of separable memory processes, some of which can function independently of semantic knowledge.
Environmental refugees: a growing phenomenon of the 21st century
Authors: Myers Norman
Published: July 2002

There is a new phenomenon in the global arena: environmental refugees. These are people who can no longer gain a secure livelihood in their homelands because of drought, soil erosion, desertification, deforestation and other environmental problems, together with the associated problems of population pressures and profound poverty. In their desperation, these people feel they have no alternative but to seek sanctuary elsewhere, however hazardous the attempt. Not all of them have fled their countries, many being internally displaced. But all have abandoned their homelands on a semi–permanent if not permanent basis, with little hope of a foreseeable return. In 1995, environmental refugees totalled at least 25 million people, compared with 27 million traditional refugees (people fleeing political oppression, religious persecution and ethnic troubles). The total number of environmental refugees could well double by the year 2010, and increase steadily for a good while thereafter as growing numbers of impoverished people press ever harder on overloaded environments. When global warming takes hold, there could be as many as 200 million people overtaken by sea–level rise and coastal flooding, by disruptions of monsoon systems and other rainfall regimes, and by droughts of unprecedented severity and duration.