bluuebunny/crossref_metadata_2025 huggingface dataset:
Restrictions on arrangements of ovals of projective algebraic curves of odd degree
Authors: Korchagin Anatoly
Published: July 2005

This paper investigates the first part of Hilbert’s 16th problem which asks about topology of the real projective algebraic curves. Using the Rokhlin-Viro-Fiedler method of complex orientation, we obtain new restrictions on the arrangements of ovals of projective algebraic curves of odd degree

d
=
4
k
+
1

d = 4k + 1

,

k
≥
2

k \geq 2

, with nests of depth

k
k

.
Twist decompositions of gluing homeomorphisms of planar Heegaard diagrams of genus two
Authors: Sakata Yoshiko , Ochiai Mitsuyuki , Satoh Kayo
Published: July 2005

We will give a very simple algorithm to decompose a gluing homeomorphism of a planar Heegaard diagram of genus two into Dehn twists associated with the canonical base.
The Riesz decomposition property for the space of regular operators
Authors: Dăneţ Nicolae
Published: July 2005

If

E
E

and

F
F

are Banach lattices such that

E
E

is separable and

F
F

has the countable interpolation property, then the space of all continuous regular operators

L

\mathcal {L}

r

(
E
,
F
)

^r(E,F)

has the Riesz decomposition property. This result is a positive answer to a conjecture posed by A. W. Wickstead.
Invariant linear manifolds for CSL-algebras and nest algebras
Authors: Hopenwasser Alan
Published: July 2005

Every invariant linear manifold for a CSL-algebra,

Alg
⁡

L

\operatorname {Alg} \mathcal {L}

, is a closed subspace if, and only if, each non-zero projection in

L

\mathcal {L}

is generated by finitely many atoms associated with the projection lattice. When

L

\mathcal {L}

is a nest, this condition is equivalent to the condition that every non-zero projection in

L

\mathcal {L}

has an immediate predecessor (

L

⊥

\mathcal {L}^{\perp }

is well ordered). The invariant linear manifolds of a nest algebra are totally ordered by inclusion if, and only if, every non-zero projection in the nest has an immediate predecessor.
A model form for exact 𝑏-metrics
Authors: Joshi M.
Published: July 2005

Any manifold with boundary can be equipped with a

b
b

-metric which takes the form

d

x
2

x
2

+
h
(
x
,
y
,
d
x
,
d
y
)

\frac {dx^2}{x^2} + h(x,y,dx,dy)

with respect to some product decomposition near the boundary, and

h
h

positive definite on restriction to the tangent space of the boundary. Here we show the existence of a product decomposition such that

h
h

is independent of

d
x

dx

modulo terms vanishing to infinite order at the boundary. The uniqueness of this decomposition is also examined.
The Bernstein problem for complete Lagrangian stationary surfaces
Authors: Mese Chikako
Published: July 2005

In this paper, we investigate the global geometric behavior of lagrangian stationary surfaces which are lagrangian surfaces whose area is critical with respect to lagrangian variations. We find that if a complete oriented immersed lagrangian surface has quadratic area growth, one end and finite topological type, then it is minimal and hence holomorphic. The key to the proof is the mean curvature estimate of Schoen and Wolfson combined with the observation that a complete immersed surface of quadratic area growth, finite topology and

L
2

L^2

mean curvature has finite total absolute curvature.
A reflexivity problem concerning the 𝐶*-algebra 𝐶(𝑋)⊗ℬ(ℋ)
Authors: Molnár Lajos
Published: July 2005

Let

X
X

be a compact Hausdorff space and let

H

\mathscr {H}

be a separable Hilbert space. We prove that the group of all order automorphisms of the

C
∗

C^*

-algebra

C
(
X
)
⊗

B

(

H

)

C(X)\otimes \mathscr {B}(\mathscr {H})

is algebraically reflexive.
The Brauer group of Sweedler’s Hopf algebra 𝐻₄
Authors: Van Oystaeyen Fred , Zhang Yinhuo
Published: July 2005

We calculate the Brauer group of the four dimensional Hopf algebra

H
4

H_4

introduced by M. E. Sweedler. This Brauer group

B
M

(
k
,

H
4

,

R
0

)

{\mathrm {BM}}(k,H_4,R_0)

is defined with respect to a (quasi-) triangular structure on

H
4

H_4

, given by an element

R
0

∈

H
4

⊗

H
4

R_0\in H_4\otimes H_4

. In this paper

k
k

is a field . The additive group

(
k
,
+
)

(k,+)

of

k
k

is embedded in the Brauer group and it fits in the exact and split sequence of groups:
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="1 long right-arrow left-parenthesis k comma plus right-parenthesis long right-arrow normal upper B normal upper M left-parenthesis k comma upper H 4 comma upper R 0 right-parenthesis long right-arrow normal upper B normal upper W left-parenthesis k right-parenthesis long right-arrow 1">

1
⟶
(
k
,
+
)
⟶

B
M

(
k
,

H
4

,

R
0

)
⟶

B
W

(
k
)
⟶
1

\begin{equation*} 1\longrightarrow (k,+)\longrightarrow {\mathrm {BM}}(k,H_4,R_0)\longrightarrow {\mathrm {BW}}(k)\longrightarrow 1 \end{equation*}

where

B
W

(
k
)

{\mathrm {BW}(k)}

is the well-known Brauer-Wall group of

k
k

. The techniques involved are close to the Clifford algebra theory for quaternion or generalized quaternion algebras.
Splitting for subalgebras of tensor products
Authors: Zacharias Joachim
Published: July 2005

We prove splitting results for subalgebras of tensor products of operator algebras. In particular, any

C
∗

C^*

-algebra

C
C

s.t.

A
⊗
1
⊆
C
⊆
A
⊗
B

A\otimes 1 \subseteq C \subseteq A \otimes B

is a tensor product

A
⊗

B
0

A\otimes B_0

provided

A
A

is simple and nuclear.
A note on branching theorems
Authors: Johnson Kenneth
Published: July 2005

Let

G
G

be a complex, simply connected semisimple analytic group with

K
K

a closed connected reductive subgroup. Suppose

V
V

is an irreducible holomorphic

G
G

-module and

W
W

an irreducible holomorphic

K
K

-module. We prove that Hom

K

(
W
,
V
)

_{K}(W,V)

possesses the structure of an irreducible

U
(

g

)

K

U(\mathfrak {g})^{K}

-module whenever

Hom

K

(
W
,
V
)

\text {Hom}_{K}(W,V)

is

≠
(
0
)

\neq (0)

. Moreover,

dim
⁡

Hom

K

(
W
,
V
)
≤
1

\dim \text {Hom}_{K} (W,V)\le 1

for all

W
W

and

V
V

if and only if

U

(

g

)

K

U{(\mathfrak {g})}^{K}

is commutative.
Types in reductive 𝑝-adic groups: The Hecke algebra of a cover
Authors: Bushnell Colin , Kutzko Philip
Published: July 2005

In this paper,

F
F

is a non-Archimedean local field and

G
G

is the group of

F
F

-points of a connected reductive algebraic group defined over

F
F

. Also,

τ
\tau

is an irreducible representation of a compact open subgroup

J
J

of

G
G

, the pair

(
J
,
τ
)

(J,\tau )

being a type in

G
G

. The pair

(
J
,
τ
)

(J,\tau )

is assumed to be a cover of a type

(

J

L

,

τ

L

)

(J_{L},\tau _{L})

in a Levi subgroup

L
L

of

G
G

. We give conditions, generalizing those of earlier work, under which the Hecke algebra

H
(
G
,
τ
)

\scr H(G,\tau )

is the tensor product of a canonical image of

H
(
L
,

τ

L

)

\scr H(L,\tau _{L})

and a sub-algebra

H
(
K
,
τ
)

\scr H(K,\tau )

, for a compact open subgroup

K
K

of

G
G

containing

J
J

.
Positive solutions of a degenerate elliptic equation with logistic reaction
Authors: Takeuchi Shingo
Published: July 2005

The degenerate elliptic equation

λ

Δ
p

u
+

u

q
−
1

(
1
−

u
r

)
=
0

\lambda \Delta _p u +u^{q-1}(1-u^r)=0

with zero Dirichlet boundary condition, where

λ
\lambda

is a positive parameter,

2
>
p
>
q

2>p>q

and

r
>
0

r>0

, is studied in three aspects: existence of maximal solution,

λ
\lambda

-dependence of maximal solution and multiplicity of solutions.
Bounding the number of cycles of O.D.E.s in 𝐑ⁿ
Authors: Farkas M. , van den Driessche P. , Zeeman M.
Published: July 2005

Criteria are given under which the boundary of an oriented surface does not consist entirely of trajectories of the

C
1

C^1

differential equation

x
˙

=
f
(
x
)

\dot {x} = f(x)

in

R

n

{\mathbf R}^n

. The special case of an annulus is further considered, and the criteria are used to deduce sufficient conditions for the differential equation to have at most one cycle. A bound on the number of cycles on surfaces of higher connectivity is given by similar conditions.
Pseudo-advection method for the two-dimensional stationary Euler equations
Authors: Nishiyama Takahiro
Published: July 2005

The existence of generalized solutions to the two-dimensional stationary Euler equations with nonvanishing vorticity is proved by a new method completely different from the usual variational approaches.
On the length of the spectral sequence of a Lie algebra extension
Authors: Barnes Donald
Published: July 2005

The length of the spectral sequence of a Lie algebra extension is at most

1
+

1+

the dimension of the quotient algebra. We show that this bound can be attained for arbitrarily large quotient algebras even when the algebra is nilpotent and the extension splits.
Uniform anti-maximum principle for polyharmonic boundary value problems
Authors: Clément Philippe , Sweers Guido
Published: July 2005

A uniform anti-maximum principle is obtained for iterated polyharmonic Dirichlet problems. The main tool, combined with regularity results for weak solutions, is an estimate for positive functions in negative Sobolev norms.
Diagonal type conditions on group C*-algebras
Authors: Spronk Nico , Wood Peter
Published: July 2005

Let

G
G

be a locally compact group with

C

∗

(
G
)

\mathbf {C}^* (G)

and

C

r
∗

(
G
)

\mathbf {C}^*_r (G)

its enveloping and reduced C

∗

^*

-algebras respectively. We show that if

C

∗

(
G
)

\mathbf {C}^*(G)

is residually finite dimensional, then

G
G

is maximally almost periodic, and

C

r
∗

(
G
)

\mathbf {C}^*_r (G)

is residually finite dimensional if and only if

G
G

is both amenable and maximally almost periodic. Letting

λ
G

\lambda _G

be the left regular representation of

G
G

, we show that a certain quasidiagonality condition on

{

λ
G

(
s
)
:
s
∈
G
}

\{\lambda _G(s):s\in G\}

implies that

G
G

is amenable.
Unique ergodicity on compact homogeneous spaces
Authors: Weiss Barak
Published: July 2005

Extending results of a number of authors, we prove that if

U
U

is the unipotent radical of an

R

\mathbb {R}

-split solvable epimorphic subgroup of a real algebraic group

G
G

which is generated by unipotents, then the action of

U
U

on

G

/

Γ

G/\Gamma

is uniquely ergodic for every cocompact lattice

Γ
\Gamma

in

G
G

. This gives examples of uniquely ergodic and minimal two-dimensional flows on homogeneous spaces of arbitrarily high dimension. Our main tools are the Ratner classification of ergodic invariant measures for the action of a unipotent subgroup on a homogeneous space, and a simple lemma (the ‘Cone Lemma’) about representations of epimorphic subgroups.
Note on a Diophantine inequality in several variables
Authors: Barton Jeffrey , Montgomery Hugh , Vaaler Jeffrey
Published: July 2005

We establish estimates for the number of points that belong to an aligned box in

(

R

/

Z

)
N

(\mathbb {R}/\mathbb {Z})^N

in terms of certain exponential sums. These generalize previous results that were known only in case

N
=
1

N=1

.
Parameter dependence of solutions of partial differential equations in spaces of real analytic functions
Authors: Bonet José , Domański Paweł
Published: July 2005

LetΩ⊆Rn\Omega \subseteq \mathbb {R}^nbe an open set and letA(Ω)\mathrm {A}(\Omega )denote the class of real analytic functions onΩ\Omega. It is proved that for every surjective linear partial differential operatorP(D,x):A(Ω)→A(Ω)P(D,x):\mathrm {A}(\Omega )\to \mathrm {A}(\Omega )and every family(fλ)⊆A(Ω)(f_ \lambda )\subseteq \mathrm {A}(\Omega )depending holomorphically onλ∈Cm\lambda \in \mathbb {C}^mthere is a solution family(uλ)⊆A(Ω)(u_ \lambda )\subseteq \mathrm {A}(\Omega )depending onλ\lambdain the same way such thatP(D,x)uλ=fλ,forλ∈Cm.\begin{equation*} P(D,x)u_ \lambda =f_\lambda , \qquad \mathrm {for } \lambda \in \mathbb {C}^m. \end{equation*}The result is a consequence of a characterization of Fréchet spacesEEsuch that the class of “weakly” real analyticEE-valued functions coincides with the analogous class defined via Taylor series. An example shows that the analogous assertions need not be valid ifCm\mathbb {C}^mis replaced by another set.
A note on the existence of a largest topological factor with zero entropy
Authors: Lemańczyk M. , Siemaszko A.
Published: July 2005

Given a topological system

T
T

on a

σ
\sigma

-compact Hausdorff space and its factor

S
S

we show the existence of a largest topological factor

S
^

\hat {S}

containing

S
S

such that for each

S
^

\hat {S}

-invariant measure

μ
\mu

,

h
μ

(

S
^

|

S
)
=
0

h_\mu (\hat {S}|S)=0

. When a relative variational principle holds,

h
(

S
^

)
=
h
(
S
)

h(\hat {S})=h(S)

.
On integers of the form 𝑘2ⁿ+1
Authors: Chen Yong-Gao
Published: July 2005

In this paper we show that the set of positive odd integers

k
k

such that

k

2

n

+
1

k2^{n} +1

has at least three distinct prime factors for all positive integers

n
n

has positive lower asymptotic density.
Normal essential eigenvalues in the boundary of the numerical range
Authors: Salinas Norberto , Velasco Maria
Published: July 2005

A purely geometric property of a point in the boundary of the numerical range of an operator

T
T

on Hilbert space is examined which implies that such a point is the value at

T
T

of a multiplicative linear functional of the

C
∗

C^*

-algebra,

C
∗

(
T
)

C^*(T)

, generated by

T
T

and the identity operator. Roughly speaking, such a property means that the boundary of the numerical range (of

T
T

) has infinite curvature at that point. Furthermore, it is shown that if such a point is not a sharp linear corner of the numerical range of

T
T

, then the multiplicative linear functional vanishes on the compact operators in

C
∗

(
T
)

C^*(T)

.
Behavior of positive radial solutions for quasilinear elliptic equations
Authors: García-Huidobro Marta , Manásevich Raúl , Yarur Cecilia
Published: July 2005

We establish a necessary and sufficient condition so that positive radial solutions to
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="minus div left-parenthesis upper A left-parenthesis StartAbsoluteValue nabla u EndAbsoluteValue right-parenthesis nabla u right-parenthesis equals f left-parenthesis u right-parenthesis comma in upper B Subscript upper R Baseline left-parenthesis 0 right-parenthesis minus StartSet 0 EndSet comma upper R greater-than 0 comma">

−

div

(
A
(

|

∇
u

|

)
∇
u
)
=
f
(
u
)
,

in

 
 

B

R

(
0
)
∖
{
0
}
,
 
R
>
0
,

\begin{equation*} -\textrm {div} (A(|\nabla u|)\nabla u) = f(u),\quad \mbox {in}~~ B_{R}(0)\setminus \{0\},\ R>0, \end{equation*}

having an isolated singularity at

x
=
0

x=0

, behave like a corresponding fundamental solution. Here,

A
:

R

∖
{
0
}
→

R

A:\mathbb R\setminus \{0\}\to \mathbb R

and

f
:
[
0
,
∞
)
→
[
0
,
∞
)

f:[0,\infty )\to [0,\infty )

are continuous functions satisfying some mild growth restrictions.
On contractible 𝑛-dimensional compacta, non-embeddable into ℝ²ⁿ
Authors: Repovš Dušan , Skopenkov Arkady
Published: July 2005

We present a very short proof of a well-known result, that for each

n
n

there exists a contractible

n
n

-dimensional compactum, non-embeddable into

R

2
n

\mathbb {R}^{2n}

.
Some Diophantine equations of the form 𝑥²-𝑝𝑦²=𝑧
Authors: Feit Walter
Published: July 2005

Let

p
=

a

2

+
(
2
b

)

2

p = a^{2} + (2b)^{2}

be a prime. It is shown that each of the two Diophantine equations

x

2

−
p

y

2

=
a

x^{2}-py^{2} =a

or

4
b

4b

has integral solutions.
A note on non-univalent harmonic maps between surfaces
Authors: Wan Tom
Published: July 2005

We show that a decomposition theorem of Duren-Hengartner about planar harmonic maps can be generalized to give a necessary and sufficient condition for a harmonic map between smooth surfaces to be decomposable as a holomorphic map followed by a univalent harmonic embedding.
An arithmetic property of Fourier coefficients of singular modular forms on the exceptional domain
Authors: Chang Shou-Te , Eie Minking
Published: July 2005

We shall develop the theory of Jacobi forms of degree two over Cayley numbers and use it to construct a singular modular form of weight 4 on the 27-dimensional exceptional domain. Such a singular modular form was obtained by Kim through the analytic continuation of a nonholomorphic Eisenstein series. By applying the results in a joint work with Eie, A. Krieg provided an alternative proof that a function with a Fourier expansion obtained by Kim is indeed a modular form of weight 4. This work provides a systematic and general approach to deal with the whole issue.
Hermitian-Einstein metrics for vector bundles on complete Kähler manifolds
Authors: Ni Lei , Ren Huaiyu
Published: July 2005

In this paper, we prove the existence of Hermitian-Einstein metrics for holomorphic vector bundles on a class of complete Kähler manifolds which include Hermitian symmetric spaces of noncompact type without Euclidean factor, strictly pseudoconvex domains with Bergman metrics and the universal cover of Gromov hyperbolic manifolds etc. We also solve the Dirichlet problem at infinity for the Hermitian-Einstein equations on holomorphic vector bundles over strictly pseudoconvex domains.
Tame and Wild Coordinates of 𝐾[𝑧][𝑥,𝑦]
Authors: Drensky Vesselin , Yu Jie-Tai
Published: July 2005

Let

K
K

be a field of characteristic zero. We characterize coordinates and tame coordinates in

K
[
z
]
[
x
,
y
]

K[z][x,y]

, i.e. the images of

x
x

respectively under all automorphisms and under the tame automorphisms of

K
[
z
]
[
x
,
y
]

K[z][x,y]

. We also construct a new large class of wild automorphisms of

K
[
z
]
[
x
,
y
]

K[z][x,y]

which maps

x
x

to a concrete family of nice looking polynomials. We show that a subclass of this class is stably tame, i.e. becomes tame when we extend its automorphisms to automorphisms of

K
[
z
]
[
x
,
y
,
t
]

K[z][x,y,t]

.
Analysis and geometry on manifolds with integral Ricci curvature bounds. II
Authors: Petersen Peter , Wei Guofang
Published: July 2005

We extend several geometrical results for manifolds with lower Ricci curvature bounds to situations where one has integral lower bounds. In particular we generalize Colding’s volume convergence results and extend the Cheeger-Colding splitting theorem.
Coding into 𝐾 by reasonable forcing
Authors: Schindler Ralf-Dieter
Published: July 2005

We present a technique for coding sets “into

K
K

,” where

K
K

is the core model below a strong cardinal. Specifically, we show that if there is no inner model with a strong cardinal then any

X
⊂

ω
1

X\subset \omega _1

can be made

Δ
3
1

\boldsymbol {\Delta }^1_3

(in the codes) in a reasonable and stationary preserving set generic extension.
Comparing Heegaard and JSJ structures of orientable 3-manifolds
Authors: Scharlemann Martin , Schultens Jennifer
Published: July 2005

The Heegaard genus

g
g

of an irreducible closed orientable

3
3

-manifold puts a limit on the number and complexity of the pieces that arise in the Jaco-Shalen-Johannson decomposition of the manifold by its canonical tori. For example, if

p
p

of the complementary components are not Seifert fibered, then

p
≤
g
−
1

p \leq g-1

. This generalizes work of Kobayashi. The Heegaard genus

g
g

also puts explicit bounds on the complexity of the Seifert pieces. For example, if the union of the Seifert pieces has base space

P
P

and

f
f

exceptional fibers, then

f
−
χ
(
P
)
≤
3
g
−
3
−
p

f - \chi (P) \leq 3g - 3 - p

.
The completeness of the isomorphism relation for countable Boolean algebras
Authors: Camerlo Riccardo , Gao Su
Published: July 2005

We show that the isomorphism relation for countable Boolean algebras is Borel complete, i.e., the isomorphism relation for arbitrary countable structures is Borel reducible to that for countable Boolean algebras. This implies that Ketonen’s classification of countable Boolean algebras is optimal in the sense that the kind of objects used for the complete invariants cannot be improved in an essential way. We also give a stronger form of the Vaught conjecture for Boolean algebras which states that, for any complete first-order theory of Boolean algebras that has more than one countable model up to isomorphism, the class of countable models for the theory is Borel complete. The results are applied to settle many other classification problems related to countable Boolean algebras and separable Boolean spaces. In particular, we will show that the following equivalence relations are Borel complete: the translation equivalence between closed subsets of the Cantor space, the isomorphism relation between ideals of the countable atomless Boolean algebra, the conjugacy equivalence of the autohomeomorphisms of the Cantor space, etc. Another corollary of our results is the Borel completeness of the commutative AF

C
∗

C^*

-algebras, which in turn gives rise to similar results for Bratteli diagrams and dimension groups.
Uniqueness of solution to a free boundary problem from combustion
Authors: Lederman C. , Vázquez J. , Wolanski N.
Published: July 2005

We investigate the uniqueness and agreement between different kinds of solutions for a free boundary problem in heat propagation that in classical terms is formulated as follows: to find a continuous function

u
(
x
,
t
)
≥
0
,

u(x,t)\geq 0,

defined in a domain

D

⊂

R

N

×
(
0
,
T
)

\mathcal {D} \subset {\mathbb {R}}^{N}\times (0,T)

and such that
\[

Δ
u
+
∑

a

i

u

x

i

−

u

t

=
0

in

D

∩
{
u
>
0
}
.

\Delta u+\sum a_{i}\,u_{x_{i}}-u_{t}=0\quad \text {in}\quad \mathcal {D}\cap \{u>0\}.

\]
We also assume that the interior boundary of the positivity set,

D

∩
∂
{
u
>
0
}

\mathcal {D} \cap \partial \{u> 0\}

, so-called free boundary, is a regular hypersurface on which the following conditions are satisfied:
\[

u
=
0
,

−
∂
u

/

∂
ν
=
C
.

u=0 ,\quad -\partial u/\partial \nu = C.

\]
Here

ν
\nu

denotes outward unit spatial normal to the free boundary. In addition, initial data are specified, as well as either Dirichlet or Neumann data on the parabolic boundary of

D

\mathcal {D}

. This problem arises in combustion theory as a limit situation in the propagation of premixed flames (high activation energy limit). The problem admits classical solutions only for good data and for small times. Several generalized concepts of solution have been proposed, among them the concepts of limit solution and viscosity solution. We investigate conditions under which the three concepts agree and produce a unique solution.
Isomorphism problems and groups of automorphisms for generalized Weyl algebras
Authors: Bavula V. , Jordan D.
Published: July 2005

We present solutions to isomorphism problems for various generalized Weyl algebras, including deformations of type-A Kleinian singularities and the algebras similar to

U
(

s
l

2

)

U(\mathfrak {sl}_2)

introduced by S. P. Smith. For the former, we generalize results of Dixmier on the first Weyl algebra and the minimal primitive factors of

U
(

s
l

2

)

U(\mathfrak {sl}_2)

by finding sets of generators for the group of automorphisms.
Tracially AF 𝐶*-algebras
Authors: Lin Huaxin
Published: July 2005

Inspired by a paper of S. Popa and the classification theory of nuclearC∗C^*-algebras, we introduce a class ofC∗C^*-algebras which we call tracially approximately finite dimensional (TAF). A TAFC∗C^*-algebra is not an AF-algebra in general, but a “large” part of it can be approximated by finite dimensional subalgebras. We show that if a unital simpleC∗C^*-algebra is TAF then it is quasidiagonal, and has real rank zero, stable rank one and weakly unperforatedK0K_0-group. All nuclear simpleC∗C^*-algebras of real rank zero, stable rank one, with weakly unperforatedK0K_0-group classified so far by theirKK-theoretical data are TAF. We provide examples of nonnuclear simple TAFC∗C^*-algebras. A sufficient condition for unital nuclear separable quasidiagonalC∗C^*-algebras to be TAF is also given. The main results include a characterization of simple rational AF-algebras. We show that a separable nuclear simple TAFC∗C^*-algebraAAsatisfying the Universal Coefficient Theorem and havingK1(A)=0K_1(A)=0andK0(A)=QK_0(A)=\mathbf {Q}is isomorphic to a simple AF-algebra with the sameKK-theory.
Linear maps determining the norm topology
Authors: Jarosz Krzysztof
Published: July 2005

Let

A
A

be a Banach function algebra on a compact space

X
X

, and let

a
∈
A

a\in A

be such that for any scalar

λ
\lambda

the element

a
+
λ
e

a+\lambda e

is not a divisor of zero. We show that any complete norm topology on

A
A

that makes the multiplication by

a
a

continuous is automatically equivalent to the original norm topology of

A
A

. Related results for general Banach spaces are also discussed.
Boundary value problems for higher order parabolic equations
Authors: Brown Russell , Hu Wei
Published: July 2005

We consider a constant coefficient parabolic equation of order

2
m

2m

and establish the existence of solutions to the initial-Dirichlet problem in cylindrical domains. The lateral data is taken from spaces of Whitney arrays which essentially require that the normal derivatives up to order

m
−
1

m-1

lie in

L
2

L^2

with respect to surface measure. In addition, a regularity result for the solution is obtained if the data has one more derivative. The boundary of the space domain is given by the graph of a Lipschitz function. This provides an extension of the methods of Pipher and Verchota on elliptic equations to parabolic equations.
Serre’s generalization of Nagao’s theorem: An elementary approach
Authors: Mason A.
Published: July 2005

Let

C
C

be a smooth projective curve over a field

k
k

. For each closed point

Q
Q

of

C
C

let

C

=

C

(
C
,
Q
,
k
)

\mathcal {C} = \mathcal {C}(C, Q, k)

be the coordinate ring of the affine curve obtained by removing

Q
Q

from

C
C

. Serre has proved that

G

L
2

(

C

)

GL_2(\mathcal {C})

is isomorphic to the fundamental group,

π
1

(
G
,
T
)

\pi _1(G, T)

, of a graph of groups

(
G
,
T
)

(G, T)

, where

T
T

is a tree with at most one non-terminal vertex. Moreover the subgroups of

G

L
2

(

C

)

GL_2(\mathcal {C})

attached to the terminal vertices of

T
T

are in one-one correspondence with the elements of

Cl
⁡
(

C

)

\operatorname {Cl}(\mathcal {C})

, the ideal class group of

C

\mathcal {C}

. This extends an earlier result of Nagao for the simplest case

C

=
k
[
t
]

\mathcal {C} = k[t]

. Serre’s proof is based on applying the theory of groups acting on trees to the quotient graph

X
¯

=
G

L
2

(

C

)
∖
X

\overline {X} = GL_2(\mathcal {C}) \backslash X

, where

X
X

is the associated Bruhat-Tits building. To determine

X
¯

\overline {X}

he makes extensive use of the theory of vector bundles (of rank 2) over

C
C

. In this paper we determine

X
¯

\overline {X}

using a more elementary approach which involves substantially less algebraic geometry. The subgroups attached to the edges of

T
T

are determined (in part) by a set of positive integers

S

\mathcal {S}

, say. In this paper we prove that

S

\mathcal {S}

is bounded, even when Cl

(

C

)

(\mathcal {C})

is infinite. This leads, for example, to new free product decomposition results for certain principal congruence subgroups of

G

L
2

(

C

)

GL_2(\mathcal {C})

, involving unipotent and elementary matrices.
Central extensions and generalized plus-constructions
Authors: Mislin G. , Peschke G.
Published: July 2005

We describe the effect of homological plus-constructions on the homotopy groups of Eilenberg-MacLane spaces in terms of universal central extensions.
Block diagonal polynomials
Authors: Dimant Verónica , Gonzalo Raquel
Published: July 2005

In this paper we introduce and study a certain class of polynomials in spaces with unconditional finite dimensional decomposition. Some applications to the existence of copies of

ℓ
∞

\ell _\infty

in spaces of polynomials and to the stabilization of polynomial algebras are given.
Some results on increments of the partially observed empirical process
Authors: Dindar Zacharie
Published: July 2005

The author investigates the almost sure behaviour of the increments of the partially observed, uniform empirical process. Some functional laws of the iterated logarithm are obtained for this process. As an application, new laws of the iterated logarithm are established for kernel density estimators.
Asymptotic convergence of the Stefan problem to Hele-Shaw
Authors: Quirós Fernando , Vázquez Juan
Published: July 2005

We discuss the asymptotic behaviour of weak solutions to the Hele-Shaw and one-phase Stefan problems in exterior domains. We prove that, if the space dimension is greater than one, the asymptotic behaviour is given in both cases by the solution of the Dirichlet exterior problem for the Laplacian in the interior of the positivity set and by a singular, radial and self-similar solution of the Hele-Shaw flow near the free boundary. We also show that the free boundary approaches a sphere as

t
→
∞

t\to \infty

, and give the precise asymptotic growth rate for the radius.
Group actions on graphs related to Krishnan-Sunder subfactors
Authors: Bhattacharyya Bina
Published: July 2005

We describe the principal graphs of the subfactors studied by Krishnan and Sunder in terms of group actions on Cayley-type graphs. This leads to the construction of a tower of tree algebras, for every positive integer

k
k

, which are symmetries of the Krishnan-Sunder subfactors of index

k
2

k^2

. Using our theory, we prove that the principal graph of the irreducible infinite depth subfactor of index 9 constructed by Krishnan and Sunder is not a tree, contrary to their expectations. We also show that the principal graphs of the Krishnan-Sunder subfactors of index 4 are the affine A and D Coxeter graphs.
The radius of metric regularity
Authors: Dontchev A. , Lewis A. , Rockafellar R.
Published: July 2005

Metric regularity is a central concept in variational analysis for the study of solution mappings associated with “generalized equations”, including variational inequalities and parameterized constraint systems. Here it is employed to characterize the distance to irregularity or infeasibility with respect to perturbations of the system structure. Generalizations of the Eckart-Young theorem in numerical analysis are obtained in particular.
The co-area formula for Sobolev mappings
Authors: Malý Jan , Swanson David , Ziemer William
Published: July 2005

We extend Federer’s co-area formula to mappings

f
f

belonging to the Sobolev class

W

1
,
p

(

R

n

;

R

m

)

W^{1,p}(\mathbb {R}^n;\mathbb {R}^m)

,

1
≤
m
>
n

1 \le m > n

,

p
>
m

p>m

, and more generally, to mappings with gradient in the Lorentz space

L

m
,
1

(

R

n

)

L^{m,1}(\mathbb {R}^n)

. This is accomplished by showing that the graph of

f
f

in

R

n
+
m

\mathbb {R}^{n+m}

is a Hausdorff

n
n

-rectifiable set.
The Orevkov invariant of an affine plane curve
Authors: Neumann Walter , Norbury Paul
Published: July 2005

We show that although the fundamental group of the complement of an algebraic affine plane curve is not easy to compute, it possesses a more accessible quotient, which we call the Orevkov invariant.
Formulas for tamely ramified supercuspidal characters of 𝐺𝐿₃
Authors: Takahashi Tetsuya
Published: July 2005

Let

F
F

denote a

p
p

-adic local field of residual characteristic

p
≠
3

p\ne 3

. This article gives formulas, valid on the regular elliptic set, for the irreducible supercuspidal characters of

GL
3

⁡
(
F
)

\operatorname {GL}_3(F)

which correspond to characters of a ramified Cartan subgroup. In the case in which

F
F

does not contain cube roots of unity, i.e., the case in which ramified cubic extensions of degree

3
3

over

F
F

cannot be Galois, base change results concerning “simple types" due to Bushnell and Henniart (1996) are used in the proofs.
From local to global behavior in competitive Lotka-Volterra systems
Authors: Zeeman E. , Zeeman M.
Published: July 2005

In this paper we exploit the linear, quadratic, monotone and geometric structures of competitive Lotka-Volterra systems of arbitrary dimension to give geometric, algebraic and computational hypotheses for ruling out non-trivial recurrence. We thus deduce the global dynamics of a system from its local dynamics. The geometric hypotheses rely on the introduction of a split Liapunov function. We show that if a system has a fixed point

p
∈
int
⁡

R

+
n

p\in \operatorname {int}{{\mathbf R}^n_+}

and the carrying simplex of the system lies to one side of its tangent hyperplane at

p
p

, then there is no nontrivial recurrence, and the global dynamics are known. We translate the geometric hypotheses into algebraic hypotheses in terms of the definiteness of a certain quadratic function on the tangent hyperplane. Finally, we derive a computational algorithm for checking the algebraic hypotheses, and we compare this algorithm with the classical Volterra-Liapunov stability theorem for Lotka-Volterra systems.
On partitioning the orbitals of a transitive permutation group
Authors: Li Cai , Praeger Cheryl
Published: July 2005

LetGGbe a permutation group on a setΩ\Omegawith a transitive normal subgroupMM. ThenGGacts on the setOrbl(M,Ω)\mathrm {Orbl}(M,\Omega )of nontrivialMM-orbitals in the natural way, and here we are interested in the case whereOrbl(M,Ω)\mathrm {Orbl}(M,\Omega )has a partitionP\mathcal Psuch thatGGacts transitively onP\mathcal P. The problem of characterising such tuples(M,G,Ω,P)(M,G,\Omega ,\mathcal P), called TODs, arises naturally in permutation group theory, and also occurs in number theory and combinatorics. The case where|P||\mathcal P|is a prime-power is important in algebraic number theory in the study of arithmetically exceptional rational polynomials. The case where|P|=2|\mathcal P|=2exactly corresponds to self-complementary vertex-transitive graphs, while the general case corresponds to a type of isomorphic factorisation of complete graphs, called a homogeneous factorisation. Characterising homogeneous factorisations is an important problem in graph theory with applications to Ramsey theory. This paper develops a framework for the study of TODs, establishes some numerical relations between the parameters involved in TODs, gives some reduction results with respect to theGG-actions onΩ\Omegaand onP\mathcal P, and gives some construction methods for TODs.
On the nonexistence of closed timelike geodesics in flat Lorentz 2-step nilmanifolds
Authors: Guediri Mohammed
Published: July 2005

The main purpose of this paper is to prove that there are no closed timelike geodesics in a (compact or noncompact) flat Lorentz 2-step nilmanifold

N

/

Γ
,

N/\Gamma ,

where

N
N

is a simply connected 2-step nilpotent Lie group with a flat left-invariant Lorentz metric, and

Γ
\Gamma

a discrete subgroup of

N
N

acting on

N
N

by left translations. For this purpose, we shall first show that if

N
N

is a 2-step nilpotent Lie group endowed with a flat left-invariant Lorentz metric

g
,

g,

then the restriction of

g
g

to the center

Z
Z

of

N
N

is degenerate. We shall then determine all 2-step nilpotent Lie groups that can admit a flat left-invariant Lorentz metric. We show that they are trivial central extensions of the three-dimensional Heisenberg Lie group

H

3

H_{3}

. If

(
N
,
g
)

\left ( N,g\right )

is one such group, we prove that no timelike geodesic in

(
N
,
g
)

\left ( N,g\right )

can be translated by an element of

N
.

N.

By the way, we rediscover that the Heisenberg Lie group

H

2
k
+
1

H_{2k+1}

admits a flat left-invariant Lorentz metric if and only if

k
=
1.

k=1.
Resolutions of ideals of quasiuniform fat point subschemes of 𝐏²
Authors: Harbourne Brian , Holay Sandeep , Fitchett Stephanie
Published: July 2005

The notion of a quasiuniform fat point subscheme

Z
⊂

P

2

Z\subset \mathbf P^2

is introduced and conjectures for the Hilbert function and minimal free resolution of the ideal

I
I

defining

Z
Z

are put forward. In a large range of cases, it is shown that the Hilbert function conjecture implies the resolution conjecture. In addition, the main result gives the first determination of the resolution of the

m
m

th symbolic power

I
(
m
;
n
)

I(m;n)

of an ideal defining

n
n

general points of

P

2

\mathbf P^2

when both

m
m

and

n
n

are large (in particular, for infinitely many

m
m

for each of infinitely many

n
n

, and for infinitely many

n
n

for every

m
>
2

m>2

). Resolutions in other cases, such as “fat points with tails”, are also given. Except where an explicit exception is made, all results hold for an arbitrary algebraically closed field

k
k

. As an incidental result, a bound for the regularity of

I
(
m
;
n
)

I(m;n)

is given which is often a significant improvement on previously known bounds.
Estimations 𝐿^{𝑝} des solutions de l’équation des ondes sur certaines variétés coniques
Authors: Li Hong-Quan , Lohoue Noël
Published: July 2005

We prove R. Strichartz’s

L
p

L^p

estimates for solutions of the wave equation on some conical manifolds.

Résumé. On prouve des estimations

L
p

L^p

pour les solutions de l’équation des ondes, analogues aux estimations de R. Strichartz, sur certaines variétés coniques.
Quasiconformal groups, Patterson-Sullivan theory, and local analysis of limit sets
Authors: Bonfert-Taylor Petra , Taylor Edward
Published: July 2005

We extend the part of Patterson-Sullivan theory to discrete quasiconformal groups that relates the exponent of convergence of the Poincaré series to the Hausdorff dimension of the limit set. In doing so we define new bi-Lipschitz invariants that localize both the exponent of convergence and the Hausdorff dimension. We find these invariants help to expose and explain the discrepancy between the conformal and quasiconformal setting of Patterson-Sullivan theory.
A generalized Minkowski problem with Dirichlet boundary condition
Authors: Schnurer Oliver
Published: July 2005

We prove the existence of hypersurfaces with prescribed boundary whose Weingarten curvature equals a given function that depends on the normal of the hypersurface.
Exponential averaging for Hamiltonian evolution equations
Authors: Matthies Karsten , Scheel Arnd
Published: July 2005

We derive estimates on the magnitude of non-adiabatic interaction between a Hamiltonian partial differential equation and a high-frequency nonlinear oscillator. Assuming spatial analyticity of the initial conditions, we show that the dynamics can be transformed to the uncoupled dynamics of an infinite-dimensional Hamiltonian system and an anharmonic oscillator, up to coupling terms which are exponentially small in a certain power of the frequency of the oscillator. The result is derived from an abstract averaging theorem for infinite-dimensional analytic evolution equations in Gevrey spaces. Refining upon a similar result by Neishtadt for analytic ordinary differential equations, the temporal estimate crucially depends on the spatial regularity of the initial condition. The result shows to what extent the strong resonances between rapid forcing and highly oscillatory spatial modes can be suppressed by the choice of sufficiently smooth initial data. An application is provided by a system of nonlinear Schrödinger equations, coupled to a rapidly forcing single mode, representing small-scale oscillations. We provide an example showing that the estimates for partial differential equations we derive here are necessarily different from those in the context of ordinary differential equations.
The 𝐿^{𝑝} Dirichlet problem and nondivergence harmonic measure
Authors: Rios Cristian
Published: July 2005

We consider the Dirichlet problem
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout Enlarged left-brace 1st Row 1st Column script upper L u 2nd Column a m p semicolon equals 0 3rd Column a m p semicolon 4th Column a m p semicolon in upper D comma 2nd Row 1st Column u 2nd Column a m p semicolon equals g 3rd Column a m p semicolon 4th Column a m p semicolon on partial-differential upper D EndLayout">

{

L

u

a
m
p
;
=
0

a
m
p
;

a
m
p
;

in 

D

,

u

a
m
p
;
=
g

a
m
p
;

a
m
p
;

on 

∂
D

\left \{ \begin {aligned} \mathcal {L} u & = 0 &&\text {in $D$},\\ u &= g &&\text {on $\partial D$} \end {aligned} \right .

\]
for two second-order elliptic operators
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper L Subscript k Baseline u equals sigma-summation Underscript i comma j equals 1 Overscript n Endscripts a Subscript k Superscript i comma j Baseline left-parenthesis x right-parenthesis partial-differential Subscript i j Baseline u left-parenthesis x right-parenthesis">

L

k

u
=

∑

i
,
j
=
1

n

a
k

i
,
j

(
x
)

∂

i
j

u
(
x
)

\mathcal {L}_k u=\sum _{i,j=1}^na_k^{i,j}(x)\,\partial _{ij} u(x)

,

k
=
0
,
1

k=0,1

, in a bounded Lipschitz domain

D
⊂

R

n

D\subset \mathbb {R}^n

. The coefficients

a
k

i
,
j

a_k^{i,j}

belong to the space of bounded mean oscillation BMO with a suitable small BMO modulus. We assume that

L

0

{\mathcal {L}}_0

is regular in

L
p

(
∂
D
,
d
σ
)

L^p(\partial D, d\sigma )

for some

p
p

,

1
>
p
>
∞

1>p>\infty

, that is,

‖
N
u

‖

L
p

≤
C

‖
g

‖

L
p

\|Nu\|_{L^p}\le C\,\|g\|_{L^p}

for all continuous boundary data

g
g

. Here

σ
\sigma

is the surface measure on

∂
D

\partial D

and

N
u

Nu

is the nontangential maximal operator. The aim of this paper is to establish sufficient conditions on the difference of the coefficients

ε

i
,
j

(
x
)
=

a
1

i
,
j

(
x
)
−

a
0

i
,
j

(
x
)

\varepsilon ^{i,j}(x)=a^{i,j}_1(x)-a^{i,j}_0(x)

that will assure the perturbed operator

L

1

\mathcal {L}_1

to be regular in

L
q

(
∂
D
,
d
σ
)

L^q(\partial D,d\sigma )

for some

q
q

,

1
>
q
>
∞

1>q>\infty

.
Notes on interpolation in the generalized Schur class. II. Nudel’man’s problem
Authors: Alpay D. , Constantinescu T. , Dijksma A. , Rovnyak J.
Published: July 2005

An indefinite generalization of Nudel

′

’

man’s problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides known results on existence criteria for Pick-Nevanlinna and Carathéodory-Fejér interpolation, the method yields new results on generalized interpolation in the sense of Sarason and boundary interpolation, including properties of the finite Hilbert transform relative to weights. The main theorem appeals to the Ball and Helton almost-commutant lifting theorem to provide criteria for the existence of a solution to Nudel

′

’

man’s problem.
Analytic models for commuting operator tuples on bounded symmetric domains
Authors: Arazy Jonathan , Engliš Miroslav
Published: July 2005

For a domainΩ\OmegainCd\mathbb {C}^{d}and a Hilbert spaceH\mathcal {H}of analytic functions onΩ\Omegawhich satisfies certain conditions, we characterize the commutingdd-tuplesT=(T1,…,Td)T=(T_{1},\dots ,T_{d})of operators on a separable Hilbert space HHsuch thatT∗T^{*}is unitarily equivalent to the restriction ofM∗M^{*}to an invariant subspace, whereMMis the operatordd-tupleZ⊗IZ\otimes Ion the Hilbert space tensor product H⊗H\mathcal {H} \otimes H. ForΩ\Omegathe unit disc andH\mathcal {H}the Hardy space H2H^{2}, this reduces to a well-known theorem of Sz.-Nagy and Foias; forH\mathcal {H}a reproducing kernel Hilbert space onΩ⊂Cd\Omega \subset \mathbb {C} ^{d}such that the reciprocal1/K(x,y¯)1/K(x,\overline {y})of its reproducing kernel is a polynomial inxxand y¯\overline y, this is a recent result of Ambrozie, Müller and the second author. In this paper, we extend the latter result by treating spacesH\mathcal {H}for which1/K1/Kceases to be a polynomial, or even has a pole: namely, the standard weighted Bergman spaces (or, rather, their analytic continuation)H=Hν\mathcal {H} =\mathcal {H} _{\nu }on a Cartan domain corresponding to the parameterν\nuin the continuous Wallach set, and reproducing kernel Hilbert spacesH\mathcal {H}for which1/K1/Kis a rational function. Further, we treat also the more general problem when the operatorMMis replaced by M⊕WM\oplus W,WW being a certain generalization of a unitary operator tuple. For the case of the spacesHν\mathcal {H} _{\nu }on Cartan domains, our results are based on an analysis of the homogeneous multiplication operators onΩ\Omega, which seems to be of an independent interest.
Test ideals and base change problems in tight closure theory
Authors: Aberbach Ian , Enescu Florian
Published: July 2005

Test ideals are an important concept in tight closure theory and their behavior via flat base change can be very difficult to understand. Our paper presents results regarding this behavior under flat maps with reasonably nice (but far from smooth) fibers. This involves analyzing, in depth, a special type of ideal of test elements, called the CS test ideal. Besides providing new results, the paper also contains extensions of a theorem by G. Lyubeznik and K. E. Smith on the completely stable test ideal and of theorems by F. Enescu and, independently, M. Hashimoto on the behavior of

F
F

-rationality under flat base change.
The Laplacian MASA in a free group factor
Authors: Sinclair Allan , Smith Roger
Published: July 2005

The Laplacian (or radial) masa in a free group factor is generated by the sum of the generators and their inverses. We show that such a masa

B

\mathcal {B}

is strongly singular and has Popa invariant

δ
(

B

)
=
1

\delta (\mathcal {B}) = 1

. This is achieved by proving that the conditional expectation

E

B

\mathbb {E}_{\mathcal {B}}

onto

B

\mathcal {B}

is an asymptotic homomorphism. We also obtain similar results for the free product of discrete groups, each of which contains an element of infinite order.
Base loci of linear series are numerically determined
Authors: Nakamaye Michael
Published: July 2005

We introduce a numerical invariant, called a moving Seshadri constant, which measures the local positivity of a big line bundle at a point. We then show how moving Seshadri constants determine the stable base locus of a big line bundle.
A condition number theorem for underdetermined polynomial systems
Authors: Dégot Jérôme
Published: July 2005

The condition number of a numerical problem measures the sensitivity of the answer to small changes in the input. In their study of the complexity of Bézout’s theorem, M. Shub and S. Smale prove that the condition number of a polynomial system is equal to the inverse of the distance from this polynomial system to the nearest ill-conditioned one. Here we explain how this result can be extended to underdetermined systems of polynomials (that is with less equations than unknowns).
On the spectrum of the Zhang-Zagier height
Authors: Doche Christophe
Published: July 2005

From recent work of Zhang and of Zagier, we know that their height

H

(
α
)

\mathfrak {H}(\alpha )

is bounded away from 1 for every algebraic number

α
\alpha

different from

0
,
1
,
1

/

2
±

−
3

/

2

0,1,1/2\pm \sqrt {-3}/2

. The study of the related spectrum is especially interesting, for it is linked to Lehmer’s problem and to a conjecture of Bogomolov. After recalling some definitions, we show an improvement of the so-called Zhang-Zagier inequality. To achieve this, we need some algebraic numbers of small height. So, in the third section, we describe an algorithm able to find them, and we give an algebraic number with height

1.2875274
…

1.2875274\ldots

discovered in this way. This search up to degree 64 suggests that the spectrum of

H

(
α
)

\mathfrak {H}(\alpha )

may have a limit point less than 1.292. We prove this fact in the fourth part.
The Euler approximation in state constrained optimal control
Authors: Dontchev A. , Hager William
Published: July 2005

We analyze the Euler approximation to a state constrained control problem. We show that if the active constraints satisfy an independence condition and the Lagrangian satisfies a coercivity condition, then locally there exists a solution to the Euler discretization, and the error is bounded by a constant times the mesh size. The proof couples recent stability results for state constrained control problems with results established here on discrete-time regularity. The analysis utilizes mappings of the discrete variables into continuous spaces where classical finite element estimates can be invoked.