bluuebunny/crossref_metadata_2025 huggingface dataset:
Kaehler structures on 𝐾_{𝐂}/(𝐏,𝐏)
Authors: Chuah Meng-Kiat
Published: July 2002

Let

K
K

be a compact connected semi-simple Lie group, let

G
=

K

C

G = K_{\mathbf C}

, and let

G
=
K
A
N

G = KAN

be an Iwasawa decomposition. To a given

K
K

-invariant Kaehler structure

ω
\omega

on

G

/

N

G/N

, there corresponds a pre-quantum line bundle

L

{\mathbf L}

on

G

/

N

G/N

. Following a suggestion of A.S. Schwarz, in a joint paper with V. Guillemin, we studied its holomorphic sections

O

(

L

)

{\mathcal O}({\mathbf L})

as a

K
K

-representation space. We defined a

K
K

-invariant

L
2

L^2

-structure on

O

(

L

)

{\mathcal O}({\mathbf L})

, and let

H
ω

⊂

O

(

L

)

H_\omega \subset {\mathcal O}({\mathbf L})

denote the space of square-integrable holomorphic sections. Then

H
ω

H_\omega

is a unitary

K
K

-representation space, but not all unitary irreducible

K
K

-representations occur as subrepresentations of

H
ω

H_\omega

. This paper serves as a continuation of that work, by generalizing the space considered. Let

B
B

be a Borel subgroup containing

N
N

, with commutator subgroup

(
B
,
B
)
=
N

(B,B)=N

. Instead of working with

G

/

N
=
G

/

(
B
,
B
)

G/N = G/(B,B)

, we consider

G

/

(
P
,
P
)

G/(P,P)

, for all parabolic subgroups

P
P

containing

B
B

. We carry out a similar construction, and recover in

H
ω

H_\omega

the unitary irreducible

K
K

-representations previously missing. As a result, we use these holomorphic sections to construct a model for

K
K

: a unitary

K
K

-representation in which every irreducible

K
K

-representation occurs with multiplicity one.
Matrix polynomials and the index problem for elliptic systems
Authors: Rowley B.
Published: July 2002

The main new results of this paper concern the formulation of algebraic conditions for the Fredholm property of elliptic systems of P.D.E.’s with boundary values, which are equivalent to the Lopatinskii condition. The Lopatinskii condition is reformulated in a new algebraic form (based on matrix polynomials) which is then used to study the existence of homotopies of elliptic boundary value problems. The paper also contains an exposition of the relevant parts of the theory of matrix polynomials and the theory of elliptic systems of P.D.E.’s.
Existence and nonexistence of global positive solutions to nonlinear diffusion problems with nonlinear absorption through the boundary
Authors: Wang Mingxin , Wu Yonghui
Published: July 2002

This paper deals with the existence and nonexistence of global positive solutions to

u
t

=
Δ
ln
⁡
(
1
+
u
)

u_t=\Delta \ln (1+u)

in

Ω
×
(
0
,
+
∞
)

\Omega \times (0, +\infty )

,
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartFraction partial-differential ln left-parenthesis 1 plus u right-parenthesis Over partial-differential n EndFraction equals StartRoot 1 plus u EndRoot left-parenthesis ln left-parenthesis 1 plus u right-parenthesis right-parenthesis Superscript alpha Baseline on partial-differential normal upper Omega times left-parenthesis 0 comma plus normal infinity right-parenthesis comma">

∂
ln
⁡
(
1
+
u
)

∂
n

=

1
+
u

(
ln
⁡
(
1
+
u
)

)

α

on
∂
Ω
×
(
0
,
+
∞
)
,

\frac {\partial \ln (1+u)}{\partial n}=\sqrt {1+u}(\ln (1+u))^{\alpha } \quad \text {on} \partial \Omega \times (0, +\infty ),

\]
and

u
(
x
,
0
)
=

u
0

(
x
)

u(x, 0)=u_0(x)

in

Ω
\Omega

. Here

α
≥
0

\alpha \geq 0

is a parameter,

Ω
⊂

R

N

\Omega \subset \mathbb {R}^N

is a bounded smooth domain. After pointing out the mistakes in Global behavior of positive solutions to nonlinear diffusion problems with nonlinear absorption through the boundary, SIAM J. Math. Anal. 24 (1993), 317–326, by N. Wolanski, which claims that, for

Ω
=

B
R

\Omega =B_R

the ball of

R

N

\mathbb {R}^N

, the positive solution exists globally if and only if

α
≤
1

\alpha \leq 1

, we reconsider the same problem in general bounded domain

Ω
\Omega

and obtain that every positive solution exists globally if and only if

α
≤

1

/

2

\alpha \leq {1/2}

.
Classification problems for shifts on modules over a principal ideal domain
Authors: Fagnani Fabio , Zampieri Sandro
Published: July 2002

In this paper we study symbolic dynamics over alphabets which are modules over a principal ideal domain, considering topological shifts which are also submodules. Our main result is the classification, up to algebraic and topological conjugacy, of the torsion-free, transitive, finite memory shifts.
A Characterization of Minimal Locally Finite Varieties
Authors: Kearnes Keith , Szendrei Ágnes
Published: July 2002

In this paper we describe a one–variable Mal′cev–like condition satisfied by any locally finite minimal variety. We prove that a locally finite variety is minimal if and only if it satisfies this Mal′cev–like condition and it is generated by a strictly simple algebra which is nonabelian or has a trivial subalgebra. Our arguments show that the strictly simple generator of a minimal locally finite variety is unique, it is projective and it embeds into every member of the variety. We give a new proof of the structure theorem for strictly simple abelian algebras that generate minimal varieties.
Topological conjugacy of linear endomorphisms of the 2-torus
Authors: Adler Roy , Tresser Charles , Worfolk Patrick
Published: July 2002

We describe two complete sets of numerical invariants of topological conjugacy for linear endomorphisms of the two-dimensional torus, i.e., continuous maps from the torus to itself which are covered by linear maps of the plane. The trace and determinant are part of both complete sets, and two candidates are proposed for a third (and last) invariant which, in both cases, can be understood from the topological point of view. One of our invariants is in fact the ideal class of the Latimer-MacDuffee-Taussky theory, reformulated in more elementary terms and interpreted as describing some topology. Merely, one has to look at how closed curves on the torus intersect their image under the endomorphism. Part of the intersection information (the intersection number counted with multiplicity) can be captured by a binary quadratic form associated to the map, so that we can use the classical theories initiated by Lagrange and Gauss. To go beyond the intersection number, and shortcut the classification theory for quadratic forms, we use the rotation number of Poincaré.
Correlation dimension for iterated function systems
Authors: Chin Wai , Hunt Brian , Yorke James
Published: July 2002

The correlation dimension of an attractor is a fundamental dynamical invariant that can be computed from a time series. We show that the correlation dimension of the attractor of a class of iterated function systems in

R

N

\mathbf {R}^N

is typically uniquely determined by the contraction rates of the maps which make up the system. When the contraction rates are uniform in each direction, our results imply that for a corresponding class of deterministic systems the information dimension of the attractor is typically equal to its Lyapunov dimension, as conjected by Kaplan and Yorke.
The Group of Galois Extensions Over Orders in 𝐾𝐶_{𝑝²}
Authors: Underwood Robert
Published: July 2002

In this paper we characterize all Galois extensions over

H
H

where

H
H

is an arbitrary

R
R

-Hopf order in

K

C

p

2

KC_{p^{2}}

. We conclude that the abelian group of

H
H

-Galois extensions is isomorphic to a certain quotient of units groups in

R
×
R

R\times R

. This result generalizes the classification of

H
H

-Galois extensions, where

H
⊂
K

C

p

H\subset KC_{p}

, due to Roberts, and also to Hurley and Greither.
Unramified cohomology and Witt groups of anisotropic Pfister quadrics
Authors: Sujatha R.
Published: July 2002

The unramified Witt group of an anisotropic conic over a field

k
k

, with

c
h
a
r
 
k
≠
2

char~k \neq 2

, defined by the form

⟨
1
,
−
a
,
−
b
⟩

\langle 1,-a,-b\rangle

is known to be a quotient of the Witt group

W
(
k
)

W(k)

of

k
k

and isomorphic to

W
(

k

)

/

⟨
1
,
−
a
,
−
b
,
a
b
⟩
W
(

k

)

W( {k})/\langle 1,-a,-b,ab \rangle W( {k})

. We compute the unramified cohomology group

H

n
r

3

k
(

C

)

H^{3}_{nr}{k({C})}

, where

C
C

is the three dimensional anisotropic quadric defined by the quadratic form

⟨
1
,
−
a
,
−
b
,
a
b
,
−
c
⟩

\langle 1,-a,-b,ab,-c\rangle

over

k
k

. We use these computations to study the unramified Witt group of

C
C

.
Existence of conservation laws and characterization of recursion operators for completely integrable systems
Authors: Grifone Joseph , Mehdi Mohamad
Published: July 2002

Using the Spencer-Goldschmidt version of the Cartan-Kähler theorem, we give conditions for (local) existence of conservation laws for analytical quasi-linear systems of two independent variables. This result is applied to characterize the recursion operator (in the sense of Magri) of completely integrable systems.
Matrix extensions and eigenvalue completions, the generic case
Authors: Helton William , Rosenthal Joachim , Wang Xiaochang
Published: July 2002

In this paper we provide new necessary and sufficient conditions for the so-called eigenvalue completion problem.
Compact groups and fixed point sets
Authors: Chigogidze Alex , Hofmann Karl , Martin John
Published: July 2002

Some structure theorems for compact abelian groups are derived and used to show that every closed subset of an infinite compact metrizable group is the fixed point set of an autohomeomorphism. It is also shown that any metrizable product containing a positive-dimensional compact group as a factor has the property that every closed subset is the fixed point set of an autohomeomorphism.
On measures ergodic with respect to an analytic equivalence relation
Authors: Louveau Alain , Mokobodzki Gabriel
Published: July 2002

In this paper, we prove that the set of probability measures which are ergodic with respect to an analytic equivalence relation is an analytic set. This is obtained by approximating analytic equivalence relations by measures, and is used to give an elementary proof of an ergodic decomposition theorem of Kechris.
Restriction of stable bundles in characteristic 𝑝
Authors: Nakashima Tohru
Published: July 2002

Let

k
k

be an algebraically closed field of characteristic

p
>
0

p>0

. Let

X
X

be a nonsingular projective variety defined over

k
k

and

H
H

an ample line bundle on

X
X

. We shall prove that there exists an explicit number

m

0

m_{0}

such that if

E
E

is a

μ
\mu

-stable vector bundle of rank at most three, then the restriction

E

|
D

E_{\vert D}

is

μ
\mu

-stable for all

m
≥

m

0

m\geq m_{0}

and all smooth irreducible divisors

D
∈
|
m
H
|

D\in \vert mH\vert

. This result has implications to the geometry of the moduli space of

μ
\mu

-stable bundles on a surface or a projective space.
Minimal sets and varieties
Authors: Kearnes Keith , Kiss Emil , Valeriote Matthew
Published: July 2002

The aim of this paper is twofold. First some machinery is established to reveal the structure of abelian congruences. Then we describe all minimal, locally finite, locally solvable varieties. For locally solvable varieties, this solves problems 9 and 10 of Hobby and McKenzie. We generalize part of this result by proving that all locally finite varieties generated by nilpotent algebras that have a trivial locally strongly solvable subvariety are congruence permutable.
A condition on the value function both necessary and sufficient for full regularity of minimizers of one-dimensional variational problems
Authors: Sychev M. , Mizel V.
Published: July 2002

We study two-point Lagrange problems for integrands

L
=
L
(
t
,
u
,
v
)

L= L(t,u,v)

:
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row 1st Column upper F left-bracket u right-bracket equals integral Subscript a Superscript b Baseline upper L left-parenthesis t comma u left-parenthesis t right-parenthesis comma ModifyingAbove u With dot left-parenthesis t right-parenthesis right-parenthesis 2nd Column a m p semicolon d t right-arrow inf comma 2nd Row 1st Column Blank 2nd Column a m p semicolon u element-of script upper A equals left-brace v element-of upper W Superscript 1 comma 1 Baseline left-parenthesis left-bracket a comma b right-bracket semicolon double-struck upper R Superscript n Baseline right-parenthesis vertical-bar v left-parenthesis a right-parenthesis equals upper A comma v left-parenthesis b right-parenthesis equals upper B right-brace period EndLayout">

F
[
u
]
=

∫
a
b

L
(
t
,
u
(
t
)
,

u
˙

(
t
)
)

a
m
p
;

d
t
→
inf
,

a
m
p
;
u
∈

A

=
{
v
∈

W

1
,
1

(
[
a
,
b
]
;

R

n

)

|

v
(
a
)
=
A
,
v
(
b
)
=
B
}
.

\begin{equation}\tag {P} \begin {split} F[u]=\int _a^b L(t,u(t),\dot u(t))&\,dt \to \inf ,\\ & u\in \mathcal A=\{v\in W^{1,1} ([a,b];\mathbb R^n)|v(a)=A,v(b)=B\}. \end{split} \end{equation}

Under very weak regularity hypotheses [

L
L

is Hölder continuous and locally elliptic on each compact subset of

R

×

R

n

×

R

n

\mathbb R\times \mathbb R^n\times \mathbb R^n

] we obtain, when

L
L

is of superlinear growth in

v
v

, a characterization of problems in which the minimizers of (P) are

C
1

C^1

-regular for all boundary data. This characterization involves the behavior of the value function

S
S

:

R

×

R

n

×

R

×

R

n

→

R

\mathbb R\times \mathbb R^n\times \mathbb R\times \mathbb R^n\to \mathbb R

defined by

S
(
a
,
A
,
b
,
B
)
=

inf

A

F

S(a,A,b,B)=\inf _{\mathcal A} F

. Namely, all minimizers for (P) are

C
1

C^1

-regular in neighborhoods of

a
a

and

b
b

if and only if

S
S

is Lipschitz continuous at

(
a
,
A
,
b
,
B
)

(a,A,b,B)

. Consequently problems (P) possessing no singular minimizers are characterized in cases where not even a weak form of the Euler-Lagrange equations is available for guidance. Full regularity results for problems where

L
L

is nearly autonomous, nearly independent of

u
u

, or jointly convex in

(
u
,
v
)

(u,v)

are presented.
Lévy processes in semisimple Lie groups and stability of stochastic flows
Authors: Liao Ming
Published: July 2002

We study the asymptotic stability of stochastic flows on compact spaces induced by Levy processes in semisimple Lie groups. It is shown that the Lyapunov exponents can be determined naturally in terms of root structure of the Lie group and there is an open subset whose complement has a positive codimension such that, after a random rotation, each of its connected components is shrunk to a single moving point exponentially under the flow.
Comparison theorems and orbit counting in hyperbolic geometry
Authors: Pollicott Mark , Sharp Richard
Published: July 2002

In this article we address an interesting problem in hyperbolic geometry. This is the problem of comparing different quantities associated to the fundamental group of a hyperbolic manifold (e.g. word length, displacement in the universal cover, etc.) asymptotically. Our method involves a mixture of ideas from both “thermodynamic” ergodic theory and the automaton associated to strongly Markov groups.
Local Boundary Regularity of the Szego Projection and Biholomorphic Mappings of Non-Pseudoconvex Domains
Authors: Ma Peiming
Published: July 2002

It is shown that the Szegő projection

S
S

of a smoothly bounded domain

Ω
\Omega

, not necessarily pseudoconvex, satisfies local regularity estimates at certain boundary points, provided that condition

R
R

holds for

Ω
\Omega

. It is also shown that any biholomorphic mapping

f
:
Ω
→
D

f:\Omega \rightarrow D

between smoothly bounded domains extends smoothly near such points, provided that a weak regularity assumption holds for

D
D

.
Comultiplications on free groups and wedges of circles
Authors: Arkowitz Martin , Gutierrez Mauricio
Published: July 2002

By means of the fundamental group functor, a co-H-space structure or a co-H-group structure on a wedge of circles is seen to be equivalent to a comultiplication or a cogroup structure on a free group

F
F

. We consider individual comultiplications on

F
F

and their properties such as associativity, coloop structure, existence of inverses, etc. as well as the set of all comultiplications of

F
F

. For a comultiplication

m
m

of

F
F

we define a subset

Δ

m

⊆
F

\Delta _{m} \subseteq F

of quasi-diagonal elements which is basic to our investigation of associativity. The subset

Δ

m

\Delta _{m}

can be determined algorithmically and contains the set of diagonal elements

D

m

D_{m}

. We show that

D

m

D_{m}

is a basis for the largest subgroup

A

m

A_{m}

of

F
F

on which

m
m

is associative and that

A

m

A_{m}

is a free factor of

F
F

. We also give necessary and sufficient conditions for a comultiplication

m
m

on

F
F

to be a coloop in terms of the Fox derivatives of

m
m

with respect to a basis of

F
F

. In addition, we consider inverses of a comultiplication, the collection of cohomomorphisms between two free groups with comultiplication and the action of the group

Aut
⁡
F

\operatorname {Aut} F

on the set of comultiplications of

F
F

. We give many examples to illustrate these notions. We conclude by translating these results from comultiplications on free groups to co-H-space structures on wedges of circles.
On the classification of irregular surfaces of general type with nonbirational bicanonical map
Authors: Catanese Fabrizio , Ciliberto Ciro , Lopes Margarida
Published: July 2002

The present paper is devoted to the classification of irregular surfaces of general type with

p

g

≥
3

p_{g}\geq 3

and nonbirational bicanonical map. Our main result is that, if

S
S

is such a surface and if

S
S

is minimal with no pencil of curves of genus

2
2

, then

S
S

is the symmetric product of a curve of genus

3
3

, and therefore

p

g

=
q
=
3

p_{g}=q=3

and

K

2

=
6

K^{2}=6

. Furthermore we obtain some results towards the classification of minimal surfaces with

p

g

=
q
=
3

p_{g}=q=3

. Such surfaces have

6
≤

K

2

≤
9

6\leq K^{2}\leq 9

, and we show that

K

2

=
6

K^{2}=6

if and only if

S
S

is the symmetric product of a curve of genus

3
3

. We also classify the minimal surfaces with

p

g

=
q
=
3

p_{g}=q=3

with a pencil of curves of genus

2
2

, proving in particular that for those one has

K

2

=
8

K^{2}=8

.
On zeta functions and Iwasawa modules
Authors: Oh Jangheon
Published: July 2002

We study the relation between zeta-functions and Iwasawa modules. We prove that the Iwasawa modules

X

k
(

ζ

p

)

−

X^{-}_{k({\zeta }_{p})}

for almost all

p
p

determine the zeta function

ζ

k

{\zeta }_{k}

when

k
k

is a totally real field. Conversely, we prove that the

λ
\lambda

-part of the Iwasawa module

X

k

X_{k}

is determined by its zeta-function

ζ

k

{\zeta }_{k}

up to pseudo-isomorphism for any number field

k
.

k.

Moreover, we prove that arithmetically equivalent CM fields have also the same

μ

−

{\mu }^{-}

-invariant.
Towards a Halphen theory of linear series on curves
Authors: Chiantini L. , Ciliberto C.
Published: July 2002

A linear series

g

δ

N

g^{N}_{\delta }

on a curve

C
⊂

P

3

C\subset \mathbf {P}^{3}

is primary when it does not contain the series cut by planes. For such series, we provide a lower bound for the degree

δ
\delta

, in terms of deg(

C
C

), g(

C
C

) and of the number

s
=
min
{
i
:

h

0

I

C

(
i
)
≠
0
}

s=\min \{i:h^{0}\mathcal {I}_{C}(i)\neq 0\}

. Examples show that the bound is sharp. Extensions to the case of general linear series and to the case of curves in higher projective spaces are considered.
A theorem on zeta functions associated with polynomials
Authors: Eie Minking , Chen Kwang-Wu
Published: July 2002

Let

β
=
(

β

1

,
…
,

β

r

)

\beta =(\beta _{1},\ldots ,\beta _{r})

be an

r
r

-tuple of non-negative integers and

P

j

(
X
)

P_{j}(X)

(
j
=
1
,
2
,
…
,
n
)

(j=1,2,\ldots ,n)

be polynomials in

R

[

X

1

,
…
,

X

r

]

{\mathbb {R}}[X_{1},\ldots ,X_{r}]

such that

P

j

(
n
)
>
0

P_{j}(n)>0

for all

n
∈

N

r

n\in {\mathbb {N}}^{r}

and the series

∑

n
∈

N

r

P

j

(
n

)

−
s

\begin{equation*}\sum _{n\in {\mathbb {N}}^{r}} P_{j}(n)^{-s}\end{equation*}

is absolutely convergent for Re

s
>

σ

j

>
0

s>\sigma _{j}>0

. We consider the zeta functions
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Z left-parenthesis upper P Subscript j Baseline comma beta comma s right-parenthesis equals sigma-summation Underscript n element-of double-struck upper N Superscript r Baseline Endscripts n Superscript beta Baseline upper P Subscript j Baseline left-parenthesis n right-parenthesis Superscript negative s Baseline comma Re s greater-than StartAbsoluteValue beta EndAbsoluteValue plus sigma Subscript j Baseline comma 1 less-than-or-equal-to j less-than-or-equal-to n period">

Z
(

P

j

,
β
,
s
)
=

∑

n
∈

N

r

n

β

P

j

(
n

)

−
s

,

Re
s
>

|

β

|

+

σ

j

,

1
≤
j
≤
n
.

\begin{equation*}Z(P_{j},\beta ,s)=\sum _{n\in {\mathbb {N}}^{r}}n^{\beta } P_{j}(n)^{-s},\quad \text {Re} s>|\beta |+\sigma _{j}, \quad 1\leq j\leq n.\end{equation*}

All these zeta functions

Z
(

∏

j
=
1

n

P

j

,
β
,
s
)

Z(\prod ^{n}_{j=1} P_{j},\beta ,s)

and

Z
(

P

j

,
β
,
s
)

(
j
=
1
,
2
,
…
,
n
)

Z(P_{j},\beta ,s)\quad (j=1,2,\ldots ,n)

are analytic functions of

s
s

when Re

s

\, s

is sufficiently large and they have meromorphic analytic continuations in the whole complex plane. In this paper we shall prove that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Z left-parenthesis product Underscript j equals 1 Overscript n Endscripts upper P Subscript j Baseline comma beta comma 0 right-parenthesis equals StartFraction 1 Over n EndFraction sigma-summation Underscript j equals 1 Overscript n Endscripts upper Z left-parenthesis upper P Subscript j Baseline comma beta comma 0 right-parenthesis period">

Z
(

∏

j
=
1

n

P

j

,
β
,
0
)
=

1
n

∑

j
=
1

n

Z
(

P

j

,
β
,
0
)
.

\begin{equation*}Z(\prod _{j=1}^{n} P_{j},\beta ,0)=\frac {1}{n} \sum _{j=1}^{n} Z(P_{j},\beta ,0).\end{equation*}

As an immediate application, we use it to evaluate the special values of zeta functions associated with products of linear forms as considered by Shintani and the first author.
Haar Measure and the Artin Conductor
Authors: Gross Benedict , Gan Wee
Published: July 2002

Let

G
G

be a connected reductive group, defined over a local, non-archimedean field

k
k

. The group

G
(
k
)

G(k)

is locally compact and unimodular. In On the motive of a reductive group, Invent. Math. 130 (1997), by B. H. Gross, a Haar measure

|

ω
G

|

|\omega _G|

was defined on

G
(
k
)

G(k)

, using the theory of Bruhat and Tits. In this note, we give another construction of the measure

|

ω
G

|

|\omega _G|

, using the Artin conductor of the motive

M
M

of

G
G

over

k
k

. The equivalence of the two constructions is deduced from a result of G. Prasad.
Maximal function estimates of solutions to general dispersive partial differential equations
Authors: Heinig Hans , Wang Sichun
Published: July 2002

Let

u
(
x
,
t
)
=
(

S
Ω

f
)
(
x
,
t
)

u(x,t)=(S_\Omega f)(x,t)

be the solution of the general dispersive initial value problem:
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="partial-differential Subscript t Baseline u minus i normal upper Omega left-parenthesis upper D right-parenthesis u equals 0 comma u left-parenthesis x comma 0 right-parenthesis equals f left-parenthesis x right-parenthesis comma left-parenthesis x comma t right-parenthesis element-of double-struck upper R Superscript n Baseline times double-struck upper R">

∂
t

u
−
i
Ω
(
D
)
u
=
0
,

u
(
x
,
0
)
=
f
(
x
)
,

(
x
,
t
)
∈

R

n

×

R

\partial _tu-i\Omega (D)u=0, \quad u(x,0)=f(x), \qquad (x,t)\in \mathbb {R}^n \times \mathbb {R}

\]
and

S
Ω

∗
∗

f

S^{**}_\Omega f

the global maximal operator of

S
Ω

f

S_\Omega f

. Sharp weighted

L
p

L^p

-esimates for

S
Ω

∗
∗

f

S^{**}_\Omega f

with

f
∈

H
s

(

R

n

)

f\in H_s(\mathbb {R}^n)

are given for general phase functions

Ω
\Omega

.
These are the differentials of order 𝑛
Authors: Laksov Dan , Thorup Anders
Published: July 2002

We answer P.-A. Meyer’s question “Qu’est ce qu’une différentielle d’ordre

n
n

?”. In fact, we present a general theory of higher order differentials based upon a construction of universal objects for higher order differentials. Applied to successive tangent spaces on a differentiable manifold, our theory gives the higher order differentials of Meyer as well as several new results on differentials on differentiable manifolds. In addition our approach gives a natural explanation of the quite mysterious multiplicative structure on higher order differentials observed by Meyer. Applied to iterations of the first order Kähler differentials our theory gives an algebra of higher order differentials for any smooth scheme. We also observe that much of the recent work on higher order osculation spaces of varieties fits well into the framework of our theory.
Local tomography with nonsmooth attenuation
Authors: Katsevich A.
Published: July 2002

Local tomography for the Radon transform with nonsmooth attenuation is proposed and justified. The main theoretical tool is analysis of singularities of pseudodifferential operators with nonsmooth symbols. Results of numerical testing of local tomography are presented.
A symplectic jeu de taquin bijection between the tableaux of King and of De Concini
Authors: Sheats Jeffrey
Published: July 2002

The definitions, methods, and results are entirely combinatorial. The symplectic jeu de taquin algorithm developed here is an extension of Schützenberger’s original jeu de taquin and acts on a skew form of De Concini’s symplectic standard tableaux. This algorithm is used to construct a weight preserving bijection between the two most widely known sets of symplectic tableaux. Anticipated applications to Knuth relations and to decomposing symplectic tensor products are indicated.
Positive definite spherical functions on Olshanskii domains
Authors: Hilgert Joachim , Neeb Karl-Hermann
Published: July 2002

Let

G
G

be a simply connected complex Lie group with Lie algebra

g

\mathfrak {g}

,

h

\mathfrak {h}

a real form of

g

\mathfrak {g}

, and

H
H

the analytic subgroup of

G
G

corresponding to

h

\mathfrak {h}

. The symmetric space

M

=
H
∖
G

{\mathcal {M}}=H\backslash G

together with a

G
G

-invariant partial order

≤
\le

is referred to as an Ol

′

’

shanskiĭ space. In a previous paper we constructed a family of integral spherical functions

ϕ

μ

\phi _{\mu }

on the positive domain

M

+

:=
{
H
x
:
H
x
≥
H
}

{\mathcal {M}}^{+} := \{Hx\colon Hx\ge H\}

of

M

{\mathcal {M}}

. In this paper we determine all of those spherical functions on

M

+

{\mathcal {M}}^{+}

which are positive definite in a certain sense.
Ergodic sequences in the Fourier-Stieltjes algebra and measure algebra of a locally compact group
Authors: Lau Anthony , Losert Viktor
Published: July 2002

Let

G
G

be a locally compact group. Blum and Eisenberg proved that if

G
G

is abelian, then a sequence of probability measures on

G
G

is strongly ergodic if and only if the sequence converges weakly to the Haar measure on the Bohr compactification of

G
.

G.

In this paper, we shall prove an extension of Blum and Eisenberg’s Theorem for ergodic sequences in the Fourier-Stieltjes algebra of

G
.

G.

We shall also give an improvement to Milnes and Paterson’s more recent generalization of Blum and Eisenberg’s result to general locally compact groups, and we answer a question of theirs on the existence of strongly (or weakly) ergodic sequences of measures on

G
.

G.
Second-order subgradients of convex integral functionals
Authors: Moussaoui Mohammed , Seeger Alberto
Published: July 2002

The purpose of this work is twofold: on the one hand, we study the second-order behaviour of a nonsmooth convex function

F
F

defined over a reflexive Banach space

X
X

. We establish several equivalent characterizations of the set

∂
2

F
(

x
¯

,

y
¯

)

\partial ^2F(\overline x,\overline y)

, known as the second-order subdifferential of

F
F

at

x
¯

\overline x

relative to

y
¯

∈
∂
F
(

x
¯

)

\overline y\in \partial F(\overline x)

. On the other hand, we examine the case in which

F
=

I
f

F=I_f

is the functional integral associated to a normal convex integrand

f
f

. We extend a result of Chi Ngoc Do from the space

X
=

L

R

d

p

X=L_{\mathbb R^d}^p

(
1
>
p
>
+
∞
)

(1>p>+\infty )

to a possible nonreflexive Banach space

X
=

L
E
p

X=L_E^p

(
1
≤
p
>
+
∞
)

(1\le p>+\infty )

. We also establish a formula for computing the second-order subdifferential

∂
2

I
f

(

x
¯

,

y
¯

)

\partial ^2 I_f(\overline x,\overline y)

.
A global condition for periodic Duffing-like equations
Authors: Montecchiari Piero , Nolasco Margherita , Terracini Susanna
Published: July 2002

We study Duffing-like equations of the type

q
¨

=
q
−
α
(
t
)

W
′

(
q
)

\ddot q= q - \alpha (t)W’(q)

,with

α
∈
C
(

R

,

R

)

\alpha \in C(\mathbb {R} ,\mathbb {R} )

periodic. We prove that if the stable and unstable manifolds to the origin do not coincide, then the system exhibits positive topological entropy.
Reducibility and nonreducibility between ℓ^{𝑝} equivalence relations
Authors: Dougherty Randall , Hjorth Greg
Published: July 2002

We show that, for

1
≤
p
>
q
>
∞

1 \le p > q > \infty

, the relation of

ℓ

p

\ell ^{p}

-equivalence between infinite sequences of real numbers is Borel reducible to the relation of

ℓ

q

\ell ^{q}

-equivalence (i.e., the Borel cardinality of the quotient

R

N

/

ℓ

p

{\mathbb {R}}^{\mathbb {N}}/\ell ^{p}

is no larger than that of

R

N

/

ℓ

q

{\mathbb {R}}^{\mathbb {N}}/\ell ^{q}

), but not vice versa. The Borel reduction is constructed using variants of the triadic Koch snowflake curve; the nonreducibility in the other direction is proved by taking a putative Borel reduction, refining it to a reduction map that is not only continuous but ‘modular,’ and using this nicer map to derive a contradiction.
Low-dimensional linear representations of 𝐴𝑢𝑡𝐹_{𝑛},𝑛≥3
Authors: Potapchik A. , Rapinchuk A.
Published: July 2002

We classify all complex representations of

A
u
t

F
n

,

\mathrm {Aut} \: F_n,

the automorphism group of the free group

F
n

F_n

(
n
≥
3
)
,

(n \geq 3),

of dimension

≤
2
n
−
2.

\leq 2n - 2.

Among those representations is a new representation of dimension

n
+
1

n + 1

which does not vanish on the group of inner automorphisms.
Linking forms, reciprocity for Gauss sums and invariants of 3-manifolds
Authors: Deloup Florian
Published: July 2002

We study invariants of

3
3

-manifolds derived from finite abelian groups equipped with quadratic forms. These invariants arise in Turaev’s theory of modular categories and generalize those of H. Murakami, T. Ohtsuki and M. Okada. The crucial algebraic tool is a new reciprocity formula for Gauss sums, generalizing classical formulas of Cauchy, Kronecker, Krazer and Siegel. We use this reciprocity formula to give an explicit formula for the invariants and to generalize them to higher dimensions.
The 𝐾𝑂-theory of toric manifolds
Authors: Bahri Anthony , Bendersky Martin
Published: July 2002

Toric manifolds, a topological generalization of smooth projective toric varieties, are determined by an

n
n

-dimensional simple convex polytope and a function from the set of codimension-one faces into the primitive vectors of an integer lattice. Their cohomology was determined by Davis and Januszkiewicz in 1991 and corresponds with the theorem of Danilov-Jurkiewicz in the toric variety case. Recently it has been shown by Buchstaber and Ray that they generate the complex cobordism ring. We use the Adams spectral sequence to compute the

K
O

KO

-theory of all toric manifolds and certain singular toric varieties.
𝐿^{𝑝} estimates for nonvariational hypoelliptic operators with 𝑉𝑀𝑂 coefficients
Authors: Bramanti Marco , Brandolini Luca
Published: July 2002

Let

X
1

,

X
2

,
…
,

X
q

X_1,X_2,\ldots ,X_q

be a system of real smooth vector fields, satisfying Hörmander’s condition in some bounded domain

Ω
⊂

R

n

\Omega \subset \mathbb {R}^n

(

n
>
q

n>q

). We consider the differential operator

L

=

∑

i
=
1

q

a

i
j

(
x
)

X
i

X
j

,

\begin{equation*} \mathcal {L}=\sum _{i=1}^qa_{ij}(x)X_iX_j, \end{equation*}

where the coefficients

a

i
j

(
x
)

a_{ij}(x)

are real valued, bounded measurable functions, satisfying the uniform ellipticity condition:
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="mu StartAbsoluteValue xi EndAbsoluteValue squared less-than-or-equal-to sigma-summation Underscript i comma j equals 1 Overscript q Endscripts a Subscript i j Baseline left-parenthesis x right-parenthesis xi Subscript i Baseline xi Subscript j Baseline less-than-or-equal-to mu Superscript negative 1 Baseline StartAbsoluteValue xi EndAbsoluteValue squared">

μ

|

ξ

|

2

≤

∑

i
,
j
=
1

q

a

i
j

(
x
)

ξ
i

ξ
j

≤

μ

−
1

|

ξ

|

2

\begin{equation*} \mu |\xi |^2\leq \sum _{i,j=1}^qa_{ij}(x)\xi _i\xi _j\leq \mu ^{-1}|\xi |^2 \end{equation*}

for a.e.

x
∈
Ω

x\in \Omega

, every

ξ
∈

R

q

\xi \in \mathbb {R}^q

, some constant

μ
\mu

. Moreover, we assume that the coefficients

a

i
j

a_{ij}

belong to the space VMO (“Vanishing Mean Oscillation”), defined with respect to the subelliptic metric induced by the vector fields

X
1

,

X
2

,
…
,

X
q

X_1,X_2,\ldots ,X_q

. We prove the following local

L

p

\mathcal {L}^p

-estimate:
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar upper X Subscript i Baseline upper X Subscript j Baseline f double-vertical-bar Subscript script upper L Sub Superscript p Subscript left-parenthesis normal upper Omega prime right-parenthesis Baseline less-than-or-equal-to c left-brace double-vertical-bar script upper L f double-vertical-bar Subscript script upper L Sub Superscript p Subscript left-parenthesis normal upper Omega right-parenthesis Baseline plus double-vertical-bar f double-vertical-bar Subscript script upper L Sub Superscript p Subscript left-parenthesis normal upper Omega right-parenthesis Baseline right-brace">

‖

X
i

X
j

f
‖

L

p

(

Ω
′

)

≤
c

{

‖

L

f
‖

L

p

(
Ω
)

+

‖
f
‖

L

p

(
Ω
)

}

\begin{equation*} \left \|X_iX_jf\right \|_{\mathcal {L}^p(\Omega ’)}\leq c\left \{\left \|\mathcal {L}f\right \|_{\mathcal {L}^p(\Omega )}+\left \|f\right \|_{\mathcal {L}^p(\Omega )}\right \} \end{equation*}

for every

Ω
′

⊂⊂
Ω

\Omega ’\subset \subset \Omega

,

1
>
p
>
∞

1>p>\infty

. We also prove the local Hölder continuity for solutions to

L

f
=
g

\mathcal {L}f=g

for any

g
∈

L

p

g\in \mathcal {L}^p

with

p
p

large enough. Finally, we prove

L

p

\mathcal {L}^p

-estimates for higher order derivatives of

f
f

, whenever

g
g

and the coefficients

a

i
j

a_{ij}

are more regular.
Decomposition theorems for groups of diffeomorphisms in the sphere
Authors: de la Llave R. , Obaya R.
Published: July 2002

We study the algebraic structure of several groups of differentiable diffeomorphisms in

S

n

\mathbf {S}^n

. We show that any given sufficiently smooth diffeomorphism can be written as the composition of a finite number of diffeomorphisms which are symmetric under reflection, essentially one-dimensional and about as differentiable as the given one.
Numeration systems and Markov partitions from self similar tilings
Authors: Praggastis Brenda
Published: July 2002

Using self similar tilings we represent the elements of

R

n

\mathbb {R}^n

as digit expansions with digits in

R

n

\mathbb {R}^n

being operated on by powers of an expansive linear map. We construct Markov partitions for hyperbolic toral automorphisms by considering a special class of self similar tilings modulo the integer lattice. We use the digit expansions inherited from these tilings to give a symbolic representation for the toral automorphisms.
Automorphism scheme of a finite field extension
Authors: de Salas Pedro
Published: July 2002

Let

k
→
K

k\to K

be a finite field extension and let us consider the automorphism scheme

A
u

t
k

K

Aut_kK

. We prove that

A
u

t
k

K

Aut_kK

is a complete

k
k

-group, i.e., it has trivial centre and any automorphism is inner, except for separable extensions of degree 2 or 6. As a consequence, we obtain for finite field extensions

K
1

,

K
2

K_1, K_2

of

k
k

, not being separable of degree 2 or 6, the following equivalence:

K
1

≃

K
2

⇔
A
u

t
k

K
1

≃
A
u

t
k

K
2

.

\begin{equation*} K_1\simeq K_2 \Leftrightarrow Aut_kK_1\simeq Aut_kK_2.\end{equation*}
𝑝-central groups and Poincaré duality
Authors: Weigel Thomas
Published: July 2002

In this note we investigate the mod

p
p

cohomology ring of finite

p
p

-central groups with a certain extension property. For

p
p

odd it turns out that the structure of the cohomology ring characterizes this class of groups up to extensions by

p
′

p’

-groups. For certain examples the cohomology ring can be calculated explicitly. As a by-product one gets an alternative proof of a theorem of M.Lazard which states that the Galois cohomology of a uniformly powerful pro-

p
p

-group of rank

n
n

is isomorphic to

Λ
[

x

1

,
.
.
,

x

n

]

\Lambda [x_{1},..,x_{n}]

.
Connectedness properties of limit sets
Authors: Bowditch B.
Published: July 2002

We study convergence group actions on continua, and give a criterion which ensures that every global cut point is a parabolic fixed point. We apply this result to the case of boundaries of relatively hyperbolic groups, and consider implications for connectedness properties of such spaces.
Invariance principles and Gaussian approximation for strictly stationary processes
Authors: Volný Dalibor
Published: July 2002

We show that in any aperiodic and ergodic dynamical system there exists a square integrable process

(
f
∘

T

i

)

(f\circ T^{i})

the partial sums of which can be closely approximated by the partial sums of Gaussian i.i.d. random variables. For

(
f
∘

T

i

)

(f\circ T^{i})

both weak and strong invariance principles hold.
The maximality of the core model
Authors: Schimmerling E. , Steel J.
Published: July 2002

Our main results are: 1) every countably certified extender that coheres with the core model

K
K

is on the extender sequence of

K
K

, 2)

K
K

computes successors of weakly compact cardinals correctly, 3) every model on the maximal 1-small construction is an iterate of

K
K

, 4) (joint with W. J. Mitchell)

K
‖
κ

K\|\kappa

is universal for mice of height

≤
κ

\le \kappa

whenever

κ
≥

ℵ
2

\kappa \geq \aleph _2

, 5) if there is a

κ
\kappa

such that

κ
\kappa

is either a singular countably closed cardinal or a weakly compact cardinal, and

◻

κ

>
ω

\square _\kappa ^{>\omega }

fails, then there are inner models with Woodin cardinals, and 6) an

ω
\omega

-Erdös cardinal suffices to develop the basic theory of

K
K

.
Livsic theorems for hyperbolic flows
Authors: Walkden C.
Published: July 2002

We consider Hölder cocycle equations with values in certain Lie groups over a hyperbolic flow. We extend Livšic’s results that measurable solutions to such equations must, in fact, be Hölder continuous.
Error estimates for 3-d narrow finite elements
Authors: Durán Ricardo
Published: July 2002

We obtain error estimates for finite element approximations of the lowest degree valid uniformly for a class of three-dimensional narrow elements. First, for the Lagrange interpolation we prove optimal error estimates, both in order and regularity, in

L

p

L^{p}

for

p
>
2

p>2

. For

p
=
2

p=2

it is known that this result is not true. Applying extrapolation results we obtain an optimal order error estimate for functions sligthly more regular than

H

2

H^{2}

. These results are valid both for tetrahedral and rectangular elements. Second, for the case of rectangular elements, we obtain optimal, in order and regularity, error estimates for an average interpolation valid for functions in

W

1
+
s
,
p

W^{1+s,p}

with

1
≤
p
≤
∞

1\le p\le \infty

and

0
≤
s
≤
1

0\le s\le 1

.
Hecke-Clifford superalgebras, crystals of type 𝐴_{2ℓ}⁽²⁾ and modular branching rules for ̂𝑆_{𝑛}
Authors: Brundan Jonathan , Kleshchev Alexander
Published: July 2002

This paper is concerned with the modular representation theory of the affine Hecke-Clifford superalgebra, the cyclotomic Hecke-Clifford superalgebras, and projective representations of the symmetric group. Our approach exploits crystal graphs of affine Kac-Moody algebras.
Rogawski’s conjecture on the Jantzen filtration for the degenerate affine Hecke algebra of type A
Authors: Suzuki Takeshi
Published: July 2002

The functors constructed by Arakawa and the author relate the representation theory of

g
l

n

\mathfrak {gl}_n

and that of the degenerate affine Hecke algebra

H
ℓ

H_\ell

of

G
L

ℓ

\mathrm {GL}_\ell

. They transform the Verma modules over

g
l

n

\mathfrak {gl}_n

to the standard modules over

H
ℓ

H_\ell

. In this paper we prove that they transform the simple modules to the simple modules (in more general situations than in the previous paper). We also prove that they transform the Jantzen filtration on the Verma modules to that on the standard modules. We obtain the following results for the representations of

H
ℓ

H_\ell

by translating the corresponding results for

g
l

n

\mathfrak {gl}_n

through the functors: (i) the (generalized) Bernstein-Gelfand-Gelfand resolution for a certain class of simple modules, (ii) the multiplicity formula for the composition series of the standard modules, and (iii) its refinement concerning the Jantzen filtration on the standard modules, which was conjectured by Rogawski.
The invariant polynomials on simple Lie superalgebras
Authors: Sergeev Alexander
Published: July 2002

Chevalley’s theorem states that for any simple finite dimensional Lie algebra

g

\mathfrak {g}

: (1) the restriction homomorphism of the algebra of polynomials

S
(

g

∗

)
⟶
S
(

h

∗

)

S(\mathfrak {g}^*)\longrightarrow S(\mathfrak {h}^*)

onto the Cartan subalgebra

h

\mathfrak {h}

induces an isomorphism

S
(

g

∗

)

g

≅
S
(

h

∗

)

W

S(\mathfrak {g}^*)^{\mathfrak {g}}\cong S(\mathfrak {h}^*)^{W}

, where

W
W

is the Weyl group of

g

\mathfrak {g}

; (2) each

g

\mathfrak {g}

-invariant polynomial is a linear combination of the polynomials

tr
⁡
ρ
(
x

)
k

\operatorname {tr} \rho (x)^k

, where

ρ
\rho

is a finite dimensional representation of

g

\mathfrak {g}

. None of these facts is necessarily true for simple Lie superalgebras. We reformulate Chevalley’s theorem as formula

(
∗
)

(*)

below to include Lie superalgebras. Let

h

\mathfrak {h}

be the split Cartan subalgebra of

g

\mathfrak {g}

; let

R
=

R
+

∪

R
−

R=R_+\cup R_-

be the set of nonzero roots of

g

\mathfrak {g}

, the union of positive and negative ones. Set

R
~

+

=
{
α
∈

R
+

∣
−
α
∈

R
−

}

\tilde R_+=\{\alpha \in R_+\mid -\alpha \in R_-\}

. For each root

α
∈

R
~

+

\alpha \in \tilde R_+

denote by

g

(
α
)

\mathfrak {g}(\alpha )

the Lie superalgebra generated by

h

\mathfrak {h}

and the root superspaces

g

α

\mathfrak {g}_\alpha

and

g

−
α

\mathfrak {g}_{-\alpha }

. Let the image of

S
(

g

(
α

)
∗

)

g

(
α
)

S(\mathfrak {g}(\alpha )^*)^{\mathfrak {g}(\alpha )}

under the restriction homomorphism

S
(

g

(
α

)
∗

)
⟶
S
(

h

∗

)

S(\mathfrak {g}(\alpha )^*)\longrightarrow S(\mathfrak {h}^*)

be denoted by

I

α

(

h

∗

)

I^{\alpha }(\mathfrak {h}^*)

and the image of

S
(

g

∗

)

g

S(\mathfrak {g}^*)^{\mathfrak {g}}

by

I
(

h

∗

)

I(\mathfrak {h}^*)

. Then
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row with Label left-parenthesis asterisk right-parenthesis EndLabel upper I left-parenthesis German h Superscript asterisk Baseline right-parenthesis equals intersection Underscript alpha element-of upper R overTilde Subscript plus Baseline Endscripts upper I Superscript alpha Baseline left-parenthesis German h Superscript asterisk Baseline right-parenthesis period EndLayout">

(*)

I
(

h

∗

)
=

⋂

α
∈

R
~

+

I

α

(

h

∗

)
.

\begin{equation*} I(\mathfrak {h}^*)=\bigcap \limits _{\alpha \in \tilde R_+}I^{\alpha }(\mathfrak {h}^*).\tag *{(*)} \end{equation*}

Chevalley’s theorem for anti-invariant polynomials is also presented.
The Howe duality and the projective representations of symmetric groups
Authors: Sergeev Alexander
Published: July 2002

The symmetric groupSk\mathfrak {S}_{k}possesses a nontrivial central extension, whose irreducible representations, different from the irreducible representations ofSk\mathfrak {S}_{k}itself, coincide with the irreducible representations of the algebraAk\mathfrak {A}_{k}generated by indeterminatesτi,j\tau _{i, j}fori≠ji\neq j,1≤i,j≤n1\leq i, j\leq nsubject to the relations<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row tau Subscript i comma j Baseline equals minus tau Subscript j comma i Baseline comma tau Subscript i comma j Superscript 2 Baseline equals 1 comma tau Subscript i comma j Baseline tau Subscript m comma l Baseline equals minus tau Subscript m comma l Baseline tau Subscript i comma j Baseline if StartSet i comma j EndSet intersection StartSet m comma l EndSet equals normal empty-set semicolon tau Subscript i comma j Baseline tau Subscript j comma m Baseline tau Subscript i comma j Baseline equals tau Subscript j comma m Baseline tau Subscript i comma j Baseline tau Subscript j comma m Baseline equals minus tau Subscript i comma m Baseline for any i comma j comma l comma m period EndLayout">τi,j=−τj,i,τi,j2=1,τi,jτm,l=−τm,lτi,j if {i,j}∩{m,l}=∅; τi,jτj,mτi,j=τj,mτi,jτj,m=−τi,m for any i,j,l,m.\begin{gather*} \tau _{i, j}=-\tau _{j, i}, \quad \tau _{i, j}^{2}=1, \quad \tau _{i, j}\tau _{m, l}=-\tau _{m, l}\tau _{i, j}\text { if }\{i, j\}\cap \{m, l\}=\emptyset ;\ \tau _{i, j}\tau _{j, m}\tau _{i, j}=\tau _{j, m}\tau _{i, j}\tau _{j, m}=-\tau _{i, m}\; \; \text { for any } i, j, l, m. \end{gather*}Recently M. Nazarov realized irreducible representations ofAk\mathfrak {A}_{k}and Young symmetrizers by means of the Howe duality between the Lie superalgebraq(n)\mathfrak {q}(n)and the Hecke algebraHk=Sk∘ClkH_{k}=\mathfrak {S}_{k}\circ Cl_{k}, the semidirect product ofSk\mathfrak {S}_{k}with the Clifford algebraClkCl_{k}onkkindeterminates. Here I construct one more analog of Young symmetrizers inHkH_{k}as well as the analogs of Specht modules forAk\mathfrak {A}_{k}andHkH_{k}.
Testing a Mathematical Model of the Yeast Cell Cycle
Authors: Cross Frederick R. , Archambault Vincent , Miller Mary , Klovstad Martha
Published: July 2002

We derived novel, testable predictions from a mathematical model of the budding yeast cell cycle. A key qualitative prediction of bistability was confirmed in a strain simultaneously lacking cdc14 and G1 cyclins. The model correctly predicted quantitative dependence of cell size on gene dosage of the G1 cyclinCLN3, but it incorrectly predicted strong genetic interactions between G1 cyclins and the anaphase- promoting complex specificity factor Cdh1. To provide constraints on model generation, we determined accurate concentrations for the abundance of all nine cyclins as well as the inhibitor Sic1 and the catalytic subunit Cdc28. For many of these we determined abundance throughout the cell cycle by centrifugal elutriation, in the presence or absence of Cdh1. In addition, perturbations to the Clb-kinase oscillator were introduced, and the effects on cyclin and Sic1 levels were compared between model and experiment. Reasonable agreement was obtained in many of these experiments, but significant experimental discrepancies from the model predictions were also observed. Thus, the model is a strong but incomplete attempt at a realistic representation of cell cycle control. Constraints of the sort developed here will be important in development of a truly predictive model.