bluuebunny/crossref_metadata_2025 huggingface dataset:
On zero-diagonal operators and traces
Authors: Fan Peng , Fong Che Kao , Herrero Domingo A.
Published: June 2010

A Hilbert space operator

A
A

is called zero-diagonal if there exists an orthonormal basis

ϕ
=
{

e
j

}

j
=
1

∞

\phi = \{ {e_j}\} _{j = 1}^\infty

such that

⟨

A

e
j

,

e
j

⟩

=
0

\left \langle {A{e_j},{e_j}} \right \rangle = 0

for all

j
j

. It is known that

T
T

is the norm limit of a sequence

{

A
k

}

\{ {A_k}\}

of zero-diagonal operators iff

0
∈

W
e

(
T
)

0 \in {W_e}(T)

, the essential numerical range of

T
T

. Our first result says that if

0
∈

W
e

(
T
)

0 \in {W_e}(T)

and

J

\mathcal {J}

is an ideal of compact operators strictly larger than the trace class, then the sequence

{

A
k

}

\{ {A_k}\}

can be chosen so that

|

T
−

A
k

|

J

→
0

|T - {A_k}{|_\mathcal {J}} \to 0

(

J

\mathcal {J}

cannot be replaced by the trace class!). If

A
A

is zero-diagonal, then the series

∑

j
=
1

∞

⟨

A

e
j

,

e
j

⟩

\sum _{j = 1}^\infty \left \langle {A{e_j},{e_j}} \right \rangle

converges to a value (zero) that can be called "the trace of

A
A

with respect to the basis

ϕ
\phi

". Our second result provides, for each operator

T
T

, the structure of the set of all possible "traces" of

T
T

(in the above sense). In particular, this set is always either the whole complex plane, a straight line, a singleton, or the empty set.
A note on the convolution of probability measures
Authors: Caby Errol
Published: June 2010

Simple proofs of the continuity of the convolution of measures for certain topologies are presented. In addition, results on the compactness of probability measures and on infinite convolutions of probability measures are obtained.
Random reals and Souslin trees
Authors: Laver Richard
Published: June 2010

It is consistent that there are no Souslin trees in any random extension of

V
V

; thus, the continuum can be singular of cofinality

ω
1

{\omega _1}

with Souslin’s hypothesis holding.
Maximal ideals in subalgebras of 𝐶(𝑋)
Authors: Redlin Lothar , Watson Saleem
Published: June 2010

Let

X
X

be a completely regular space, and let

A
(
X
)

A(X)

be a subalgebra of

C
(
X
)

C(X)

containing

C
∗

(
X
)

{C^ * }(X)

. We study the maximal ideals in

A
(
X
)

A(X)

by associating a filter

Z
(
f
)

Z(f)

to each

f
∈
A
(
X
)

f \in A(X)

. This association extends to a one-to-one correspondence between

M

(
A
)

\mathcal {M}(A)

(the set of maximal ideals of

A
(
X
)

A(X)

) and

β
X

\beta X

. We use the filters

Z
(
f
)

Z(f)

to characterize the maximal ideals and to describe the intersection of the free maximal ideals in

A
(
X
)

A(X)

. Finally, we outline some of the applications of our results to compactifications between

υ
X

\upsilon X

and

β
X

\beta X

.
On the partial sums of convex functions of order 1/2
Authors: Singh Ram
Published: June 2010

Let

f

(
z
)

=
z
+

a
2

z
2

+
…

f\left ( z \right ) = z + {a_2}{z^2} + \ldots

be regular and univalently convex of order

1

/

2

1/2

in the unit disc

U
U

and let

s
n

(

z
,
f

)

{s_n}\left ( {z,f} \right )

denote its

n
n

th partial sum. In the present note we determine the radius of convexity of

s
n

(

z
,
f

)

{s_n}\left ( {z,f} \right )

, depending on

n
n

, and generalize and sharpen a result of Ruscheweyh concerning the partial sums of convex functions. We also prove that for every

n
≥
1
,

Re

(

s
n

(

z
,
f

)

/

z

)

>
1

/

2

n \geq 1,{\text {Re}}\left ( {{s_n}\left ( {z,f} \right )/z} \right ) > 1/2

in

U
U

.
Finding octonion algebras in associative algebras
Authors: Faulkner John R.
Published: June 2010

An embedding of octonion algebras in central simple degree three associative algebras is given.
Noncommutative regular local rings of dimension 3
Authors: Snider Robert L.
Published: June 2010

A left and right Noetherian local ring of global dimension 3 is a domain.
The regularity of Dunford-Pettis operators
Authors: Holub James R.
Published: June 2010

Let

λ
\lambda

denote a symmetric, solid Banach sequence space having

{

e
i

}

i
=
1

∞

\left \{ {{e_i}} \right \}_{i = 1}^\infty

as a symmetric basis and considered as a Banach lattice with order defined coordinatewise. A complete description of the relationship between regular and Dunford-Pettis operators

T
:

L
1

[
0
,
1
]
→
λ

T:{L^1}[0,1] \to \lambda

is given. The results obtained complete earlier work of Gretsky and Ostroy and of the author in this area.
Hilbert’s tenth problem for a class of rings of algebraic integers
Authors: Pheidas Thanases
Published: June 2010

We show that

Z

{\mathbf {Z}}

is diophantine over the ring of algebraic integers in any number field with exactly two nonreal embeddings into

C

{\mathbf {C}}

of degree

≥
3

\geq 3

over

Q

{\mathbf {Q}}

.
Applications of a new 𝐾-theoretic theorem to soluble group rings
Authors: Kropholler P. H. , Linnell P. A. , Moody J. A.
Published: June 2010

Let

R
R

be a ring and let

G
G

be a soluble group. In this situation we shall give necessary and sufficient conditions for

R
G

RG

to have a right Artinian right quotient ring. In the course of this work, we shall also consider the Goldie rank problem for soluble groups and record an affirmative answer to the zero divisor conjecture for soluble groups.
A necessary and sufficient condition for a 3-manifold to have Heegaard genus one
Authors: Hass Joel , Thompson Abigail
Published: June 2010

Let

M
M

be a closed

3
3

-manifold. R. H. Bing showed that

M
M

is homeomorphic to

S
3

{S^3}

if and only if every simple closed curve in

M
M

can be isotoped to lie inside a

3
3

-ball. We generalize this to show that there is a solid torus

T
T

imbedded in

M
M

such that every simple closed curve in

M
M

can be isotoped to lie in

T
T

if and only if

M
M

has a genus one Heegaard splitting.
Weakly almost periodic elements in 𝐿_{∞}(𝐺) of a locally compact group
Authors: Lau Anthony To Ming , Wong James C. S.
Published: June 2010

Let

G
G

be a locally compact abelian group with dual group

G
G

acting on

L
∞

(
G
)

{L_\infty }(G)

by pointwise multiplication. We show that if

L
∞

(
G
)

{L_\infty }(G)

contains a nonzero element

f
f

such that

O
(
f
)
=

{

x
⋅
f
:
χ
∈

G
^

}

O(f) = \left \{ {x \cdot f:\chi \in \hat G} \right \}

is relatively compact in the weak (or norm) topology of

L
∞

(
G
)

{L_\infty }(G)

, then

G
G

is discrete. In this case

O
(
f
)

O(f)

is relatively compact in the weak or norm topology of

L
∞

(
G
)

{L_\infty }(G)

if and only if

f
f

vanishes at infinity. A related result when

G
G

acts on the von Neumann algebra

V
N
(
G
)

VN(G)

is also determined.
Nonexistence of 4-dimensional almost Kaehler manifolds of constant curvature
Authors: Blair David E.
Published: June 2010

It is shown that in dimension 4 there are no almost Kaehler manifolds of constant curvature unless the constant is 0, in which case the manifold is Kaehlerian. This was previously shown in dimensions

≥
8

\geq 8

by Z. Olszak and remains open in dimension 6.
On small Iwasawa invariants and imaginary quadratic fields
Authors: Sands Jonathan W.
Published: June 2010

If

p
p

is an odd prime that does not divide the class number of the imaginary quadratic field

k
k

, and the cyclotomic

Z

p

{\mathbb {Z}_p}

-extension of

k
k

has

λ
\lambda

-invariant less than or equal to two, we prove that every totally ramified

Z

p

{\mathbb {Z}_p}

-extension of

k
k

has

μ
\mu

-invariant equal to zero and

λ
\lambda

-invariant less than or equal to two. Combined with a result of Bloom and Gerth, this has the consequence that

μ
=
0

\mu = 0

for every

Z

p

{\mathbb {Z}_p}

-extension of

k
k

, under the same assumptions. In the principal case under consideration, Iwasawa’s formula for the power of

p
p

in the class number of the

n
n

th layer of a

Z

p

{\mathbb {Z}_p}

-extension becomes valid for all

n
n

, and is completely explicit.
The group determinant determines the group
Authors: Formanek Edward , Sibley David
Published: June 2010

Let

G
=

{

g
1

,
…
,

g
n

}

G = \left \{ {{g_1}, \ldots ,{g_n}} \right \}

be a finite group of order

n
n

, let

K
K

be a field whose characteristic is prime to

n
n

, and let

{

x
g

|

g
∈
G

}

\left \{ {{x_g}\left | {g \in G} \right .} \right \}

be independent commuting variables over

K
K

. The group determinant of

G
G

is the determinant of the

n
×
n

n \times n

matrix

(

x

g
i

g
j

−
1

)

\left ( {{x_{{g_i}g_j^{ - 1}}}} \right )

. We show that two groups with the same group determinant are isomorphic.
Zapping small filters
Authors: Laflamme Claude
Published: June 2010

We show two methods for diagonalizing filters of the form

F
σ

{F_\sigma }

, first without adding an unbounded real, the other while preserving

P
P

-points; the interest lies in an attempt at destroying maximal almost disjoint families with least damage.
Ergodic theorems for semigroups of operators
Authors: Ruess W. M. , Summers W. H.
Published: June 2010

We establish ergodic theorems for Eberlein-weakly almost periodic motions and almost-orbits of semigroups of operators. The results apply to solutions of a class of (generally, nonlinear) evolution equations.
A short proof of a theorem of Adjan
Authors: Zhang Louxin
Published: June 2010

In this note, using the technique of rewriting, we give a short proof of a theorem of Adjan: the word problem is decidable for special one-relator monoids

(
A
;
w
=
e
)

(A;w = e)

.
Periodicity of Somos sequences
Authors: Robinson Raphael M.
Published: June 2010

Various sequences related to one introduced by Michael Somos are shown to be periodic

mod
m

\bmod m

for every

m
m

, although the problem remains open for the original sequence. Some observations are made concerning the prime divisors and the rate of growth of certain sequences.
A short proof of the Frobenius theorem
Authors: Lundell Albert T.
Published: June 2010

By separating the algebraic and analytic aspect of Frobenius’ theorem on involutive distributions, we are able to give a simplified proof.
On absolute summability factors
Authors: Bor Hüseyin
Published: June 2010

In this paper a theorem on

|

N
¯

,

p
n

|

k

|\overline N ,{p_n}{|_k}

summability factors, which generalizes a theorem of Mazhar (Indian J. Math. 14 (1972), 45-48) on

|

C
,
1

|

k

|C,1{|_k}

summability factors, has been proved.
The length of elements in free solvable groups
Authors: Droms Carl , Lewin Jacques , Servatius Herman
Published: June 2010

We examine the relationship between the complexity of the word problem for a presentation and the complexity of the problem of determining the length of a shortest word equivalent to a given word. Our main result is that the length of the element represented by a word in a free solvable group can be determined in polynomial time.
An extension of the Heinz-Kato theorem
Authors: Furuta Takayuki
Published: June 2010

An extension of the Heinz-Kato theorem is given.
The unitability of 1-prime lattice-ordered rings with squares positive
Authors: Ma Jing Jing
Published: June 2010

It is shown that an l-prime lattice-ordered ring with squares positive and an f-superunit can be embedded in a unital l-prime lattice-ordered ring with squares positive.
On extremal extensions of regular contents and measures
Authors: Adamski Wolfgang
Published: June 2010

Within the framework of regular extensions of contents and measures we show that every regular content admits an extremal extension. Under an additional assumption we can also prove the existence of extremal measure extensions.
Best constants for two nonconvolution inequalities
Authors: Christ Michael , Grafakos Loukas
Published: June 2010

The norm of the operator which averages

|

f

|

|f|

in

L
p

(

R

n

)

{L^p}({\mathbb {R}^n})

over balls of radius

δ

|

x

|

\delta |x|

centered at either 0 or x is obtained as a function of n , p and

δ
\delta

. Both inequalities proved are n-dimensional analogues of a classical inequality of Hardy in

R

1

{\mathbb {R}^1}

. Finally, a lower bound for the operator norm of the Hardy-Littlewood maximal function on

L
p

(

R

n

)

{L^p}({\mathbb {R}^n})

is given.
On the shrinkability of decompositions of 3-manifolds
Authors: Voxman William L.
Published: June 2010

An upper semicontinuous decomposition

G
G

of a metric space

M
M

is said to be shrinkable in case for each covering

U

\mathcal {U}

of the union of the nondegenerate elements, for each

ε
>
0

\varepsilon > 0

, and for an arbitrary homeomorphism

h
h

from

M
M

onto

M
M

, there exists a homeomorphism

f
f

from

M
M

onto itself such that (1) if

x
∈
M
−
(
∪
{
U
:
U
∈

U

}
)

x \in M - ( \cup \{ U:U \in \mathcal {U}\} )

, then

f
(
x
)
=
h
(
x
)

f(x) = h(x)

, (2) for each

g
∈
G

g \in G

, (a)

diam
⁡
f
[
g
]
>
ε

\operatorname {diam} f[g] > \varepsilon

and (b) there exists

D
∈

U

D \in \mathcal {U}

such that

h
[
D
]
⊃
h
[
g
]
∪
f
[
g
]

h[D] \supset h[g] \cup f[g]

. Our main result is that if

G
G

is a cellular decomposition of a

3
3

-manifold

M
M

, then

M

/

G
=
M

M/G = M

if and only if

G
G

is shrinkable. We also define concepts of local and weak shrinkability, and we show the equivalence of the various types of shrinkability for certain cellular decompositions. Some applications of these notions are given, and extensions of theorems of Bing and Price are proved.
Infinite products which are Hilbert cubes
Authors: West James E.
Published: June 2010

Let

Q
Q

denote the Hilbert cube. It is shown that if

P
P

and

P
′

P’

are compact polyhedra of the same simple homotopy type then

P
×
Q

P \times Q

and

P
′

×
Q

P’ \times Q

are homeomorphic. A consequence of this result is that the Cartesian product of a countable, locally finite simplicial complex with a separable, infinite-dimensional Fréchet space is a manifold modelled on the Fréchet space. It is also proved that a countably infinite product of nondegenerate spaces is a Hilbert cube provided that the product of each of the spaces with the Hilbert cube is a Hilbert cube. Together with the first result, this establishes that a countably infinite product of nondegenerate, compact, contractible polyhedra is a Hilbert cube. In addition, a proof is given of the (previously unpublished) theorem of R. D. Anderson that a countably infinite product of nondegenerate dendra is a Hilbert cube.
Weak convergence of conditioned sums of independent random vectors.
Authors: Liggett Thomas M.
Published: June 2010

Conditions are given for the weak convergence of processes of the form

(

X

n

(
t
)

|

X

n

(
1
)
∈

E
n

)

({{\mathbf {X}}_n}(t)|{{\mathbf {X}}_n}(1) \in {E^n})

to tied-down stable processes, where

(

X

n

(
t
)

({{\mathbf {X}}_n}(t)

is constructed from normalized partial sums of independent and identically distributed random vectors which are in the domain of attraction of a multidimensional stable law. The conditioning events are defined in terms of subsets

E
n

{E^n}

of

R
d

{R^d}

which converge in an appropriate sense to a set of measure zero. Assumptions which the sets

E
n

{E^n}

must satisfy include that they can be expressed as disjoint unions of “asymptotically convex” sets. The assumptions are seen to hold automatically in the special case in which

E
n

{E^n}

is taken to be a “natural” neighborhood of a smooth compact hypersurface in

R
d

{R^d}

.
Group extensions and cohomology for locally compact groups. III
Authors: Moore Calvin C.
Published: June 2010

We shall define and develop the properties of cohomology groups

H
n

(
G
,
A
)

{H^n}(G,A)

which can be associated to a pair (G, A) where G is a separable locally compact group operating as a topological transformation group of automorphisms on the polonais abelian group A. This work extends the results in [29] and [30], and these groups are to be viewed as analogues of the Eilenberg-Mac Lane groups for discrete G and A. Our cohomology groups in dimension one are classes of continuous crossed homomorphisms, and in dimension two classify topological group extensions of G by A. We characterize our cohomology groups in all dimensions axiomatically, and show that two different cochain complexes can be used to construct them. We define induced modules and prove a version of Shapiro’s lemma which includes as a special case the Mackey imprimitivity theorem. We show that the abelian groups

H
n

(
G
,
A
)

{H^n}(G,A)

are themselves topological groups in a natural way and we investigate this additional structure.
Metacompactness, paracompactness, and interior-preserving open covers
Authors: Junnila Heikki J. K.
Published: June 2010

In this paper metacompactness and paracompactness are characterized in terms of the existence of closure-preserving closed refinements and interior-preserving open star-refinements of interior-preserving directed open covers of a topological space. Several earlier results on metacompact spaces and paracompact spaces are obtained as corollaries to these characterizations. For a Tychonoff-space X, metacompactness of X is characterized in terms of orthocompactness of

X

×

β
X

X\, \times \,\beta X

.
The fixed point property and unbounded sets in Hilbert space
Authors: Ray William O.
Published: June 2010

It is shown that a closed convex subset K of a real Hilbert space H has the fixed point property for nonexpansive mappings if and only if K is bounded.
Réalisation de morphismes donnés en cohomologie et suite spectrale d’Eilenberg-Moore
Authors: Vigué-Poirrier Micheline
Published: June 2010

On construit une suite d’obstructions à la réalisation par une application entre types d’homotopie rationnelle, d’un morphisme donné en cohomologie. On donne, sous des hypothèses de finitude, des conditions simples d’existence de réalisation. On montre aussi que, pour des algèbres différentielles commutatives graduées sur un corps de caractéristique

0
0

, la réalisation d’un morphisme donné en cohomologie dépend, en général, du corps de base. La technique utilisée est la construction du modèle minimal bigradué d’un homomorphisme d’algèbres commutatives graduées, puis du modèle filtré d’une application continue, par déformation des différentielles du modèle bigradué de l’application induite en cohomologie. Cette construction est utilisée pour donner une méthode explicite de calcul de la suite spectrale d’Eilenberg-Moore

(

E
i

,

d
i

)

({E_i},{d_i})

d’un carré fibré. On en déduit des critères pour que

d
i

=
0
,
i
⩾
2

{d_i} = 0,i \geqslant 2

.
A study of the local components of the Hecke algebra mod 𝑙
Authors: Jochnowitz Naomi
Published: June 2010

We use information about modular forms

mod
l

\bmod l

to study the local structure of the Hecke ring. In particular, we find nontrivial lower bounds for the dimensions of the Zariski tangent spaces of the local components of the Hecke ring

mod
l

\bmod l

. These results suggest that the local components of the Hecke ring

mod
l

\bmod l

are more complex than originally expected. We also investigate the inverse limits of the Hecke rings of weight

k
mod
l

k\bmod l

as

k
k

varies within a fixed congruence class

mod
l
−
1

\bmod l - 1

. As an immediate corollary to some of the above results, we show that when

k
k

is sufficiently large, an arbitrary prime

l
l

must divide the index of the classical Hecke ring

T

k

{{\mathbf {T}}_k}

in the ring of integers of

T

k

⊗

Q

{{\mathbf {T}}_k} \otimes {\mathbf {Q}}

.
Relations between 𝐻^{𝑝}ᵤ and 𝐿^{𝑝}ᵤ with polynomial weights
Authors: Strömberg Jan-Olov , Wheeden Richard L.
Published: June 2010

Relations between

L
u
p

L_u^p

and

H
u
p

H_u^p

of the real line are studied in the case when

p
>
1

p > 1

and

u
(
x
)
=

|

q
(
x
)

|

p

w
(
x
)

u(x) = |q(x){|^p}w(x)

, where

q
(
x
)

q(x)

is a polynomial and

w
(
x
)

w(x)

satisfies the

A
p

{A_p}

condition. It turns out that

H
u
p

H_u^p

and

L
u
p

L_u^p

can be identified when all the zeros of

q
q

are real, and that otherwise

H
u
p

H_u^p

can be identified with a certain proper subspace of

L
u
p

L_u^p

. In either case, a complete description of the distributions in

H
u
p

H_u^p

is given. The questions of boundary values and of the existence of dense subsets of smooth functions are also considered.
Counting interval graphs
Authors: Hanlon Phil
Published: June 2010

In this paper we enumerate interval graphs (up to isomorphism) along with labelled interval graphs, identity interval graphs, transitive interval graphs and various sorts of unit interval graphs. The enumeration makes use of a structural decomposition of interval graphs which leads to a characterization of those interval graphs having a unique interval representation. Several tables are included.
Large cardinals and strong model theoretic transfer properties
Authors: Foreman Matthew
Published: June 2010

In this paper we prove the following theorem:

[

C
o
n

(

Z
F
C

+

t
h
e
r
e

i
s

a

2
−

h
u
g
e

c
a
r
d
i
n
a
l
)
⇒
f
o
r

a
l
l

n

[{\rm {Con}}({\rm {ZFC}}\,{\rm { + }}\,there\,is\,a\,{\rm {2 - }}huge\,cardinal) \Rightarrow for\,all\,n

\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper C normal o normal n left-parenthesis normal upper Z normal upper F normal upper C plus left-parenthesis normal alef Subscript n plus 3 Baseline comma normal alef Subscript n plus 2 Baseline comma normal alef Subscript n plus 1 Baseline right-parenthesis two headed right-arrow left-parenthesis normal alef Subscript n plus 2 Baseline comma normal alef Subscript n plus 1 Baseline comma normal alef Subscript n Baseline right-parenthesis right-parenthesis">

C
o
n

(

Z
F
C
+

(

ℵ

n
+
3

,

ℵ

n
+
2

,

ℵ

n
+
1

)
↠
(

ℵ

n
+
2

,

ℵ

n
+
1

,

ℵ
n

)
)

{\rm {Con}}({\rm {ZFC + }}({\aleph _{n + 3}},{\aleph _{n + 2}},{\aleph _{n + 1}}) \twoheadrightarrow ({\aleph _{n + 2}},{\aleph _{n + 1}},{\aleph _n}))

\]
. We do this by using iterated forcing to collapse the

2
2

-huge cardinal to

ℵ

n
+
1

{\aleph _{n + 1}}

and extending the elementary embedding generically.
Spaces of complex null geodesics in complex-Riemannian geometry
Authors: LeBrun Claude
Published: June 2010

The notion of a complex - Riemannian

n
n

-manifold, meaning a complex

n
n

-manifold with a nondegenerate complex quadratic form on each tangent space which varies holomorphically from point to point, is briefly developed. It is shown that, provided

n
⩾
4

n \geqslant 4

, every such manifold locally arises canonically as the moduli space of all quadrics of a fixed normal-bundle type in an associated space of complex null geodesies. This relationship between local geometry and global complex analysis is stable under deformations.
The ill-posed Hele-Shaw model and the Stefan problem for supercooled water
Authors: DiBenedetto Emmanuele , Friedman Avner
Published: June 2010

The Hele-Shaw flow of a slow viscous fluid between slightly separated plates is analyzed in the ill-posed case when the fluid recedes due to absorption through a core

G
G

. Necessary and sufficient conditions are given on the initial domain occupied by the fluid to ensure the existence of a solution. Regularity of the free boundary is established in certain rather general cases. Similar results are obtained for the analogous parabolic version, which models the one-phase Stefan problem for supercooled water.
A partial order on the regions of 𝑅ⁿ dissected by hyperplanes
Authors: Edelman Paul H.
Published: June 2010

We study a partial order on the regions of

R

n

{{\mathbf {R}}^n}

dissected by hyperplanes. This includes a computation of the Möbius function and, in some cases, of the homotopy type. Applications are presented to zonotopes, the weak Bruhat order on Weyl groups and acyclic orientations of graphs.
Minimal cyclic-4-connected graphs
Authors: Robertson Neil
Published: June 2010

A theory of cyclic-connectivity is developed, matroid dual to the standard vertex-connectivity. The cyclic-

4
4

-connected graphs minimal under the elementary operations of single-edge deletion or contraction and removal of a trivalent vertex are classified. These turn out to belong to three simple infinite families of indecomposable graphs, or to be decomposable into constituent subgraphs which themselves belong to three simple infinite families. This is modeled after W. T. Tutte’s theorem classifying the minimal

3
3

-connected graphs under single-edge deletion or contraction as forming the single infinite family of "wheels." Such theorems serve two main purposes: (1) illustrating the structure of graphs in the class by isolating a type of extremal graph, and (2) by providing a set-up so that induction on

|

E
(
G
)

|

|E(G)|

can be carried out effectively within the class.
On contractions of semisimple Lie groups
Authors: Dooley A. H. , Rice J. W.
Published: June 2010

A limiting formula is given for the representation theory of the Cartan motion group associated to a Riemannian symmetric pair

(
G
,
K
)

(G,K)

in terms of the representation theory of

G
G

.
Obstruction theory and multiparameter Hopf bifurcation
Authors: Ize Jorge
Published: June 2010

The Hopf bifurcation problem is treated as an example of an equivariant bifurcation. The existence of a local bifurcating solution is given by the nonvanishing of an obstruction to extending a map defined on a complex projective space and is computed using the complex Bott periodicity theorem. In the case of the classical Hopf bifurcation the results of Chow, Mallet-Paret and Yorke are recovered without using any special index as the Fuller degree: There is bifurcation if the number of exchanges of stability is nonzero. A global theorem asserts that the sum of the local invariants on a bounded component of solutions must be zero.
Singular integrals and approximate identities on spaces of homogeneous type
Authors: Aimar Hugo
Published: June 2010

In this paper we give conditions for the

L
2

{L^2}

-boundedness of singular integrals and the weak type

(
1
,
1
)

(1,1)

of approximate identities on spaces of homogeneous type. Our main tools are Cotlar’s lemma and an extension of a theorem of Zó.
An analytic set-valued selection and its applications to the corona theorem, to polynomial hulls and joint spectra
Authors: Slodkowski Zbigniew
Published: June 2010

It is shown that for every annulus

P
=
{
z
∈

C

n

:
δ
>

|

z

|

>
r
}

P = \{ z \in {{\mathbf {C}}^n}:\delta > |z| > r\}

,

δ
>
0

\delta > 0

, there exists a set-valued correspondence

z
→
K
(
z
)
:
P
→

2

C

n

z \to K(z):P \to {2^{{{\mathbf {C}}^n}}}

, whose graph is a bounded relatively closed subset of the manifold

{
(
z
,
w
)
∈
P
×

C

n

:

z
1

w
1

+
⋯
+

z
n

w
n

=
1
}

\{ (z,w) \in P \times {{\mathbf {C}}^n}:{z_1}{w_1} + \cdots + {z_n}{w_n} = 1\}

which can be covered by

n
n

-dimensional analytic manifolds. The analytic set-valued selection

K
K

obtained thereby is then applied to several problems in complex analysis and spectral theory which involve solving the equation

a
1

x
1

+
⋯
+

a
n

x
n

=
y

{a_1}{x_1} + \cdots + {a_n}{x_n} = y

. For example, an elementary proof is given of the following special case of a theorem due to Oka: every bounded pseudoconvex domain in

C

2

{{\mathbf {C}}^2}

is a domain of holomorphy.
Vector bundles and projective modules
Authors: Vaserstein Leonid N.
Published: June 2010

Serre and Swan showed that the category of vector bundles over a compact space

X
X

is equivalent to the category of finitely generated projective modules over the ring of continuous functions on

X
X

. In this paper, titled after the famous paper by Swan, this result is extended to an arbitrary topological space

X
X

. Also the well-known homotopy classification of the vector bundles over compact

X
X

up to isomorphism is extended to arbitrary

X
X

. It is shown that the

K
0

{K_0}

-functor and the Witt group of the ring of continuous functions on

X
X

coincide, and they are homotopy-type invariants of

X
X

.
Relative pressure, relative equilibrium states, compensation functions and many-to-one codes between subshifts
Authors: Walters Peter
Published: June 2010

Let

S
:
X
→
X
,
T
:
Y
→
Y

S:X \to X,T:Y \to Y

be continuous maps of compact metrizable spaces, and let

π
:
X
→
Y

\pi :X \to Y

be a continuous surjection with

π
∘
S
=
T
∘
π

\pi \circ S = T \circ \pi

. We investigate the notion of relative pressure, which was introduced by Ledrappier and Walters, and study some maximal relative pressure functions that tie in with relative equilibrium states. These ideas are connected with the notion of compensation function, first considered by Boyle and Tuncel, and we show that a compensation function always exists when

S
S

and

T
T

are subshifts. A function

F
∈
C
(
X
)

F \in C(X)

is a compensation function if

P
(
S
,
F
+
ϕ
∘
π
)
=
P
(
T
,
ϕ
)
∀
ϕ
∈
C
(
Y
)

P(S,F + \phi \circ \pi ) = P(T,\phi )\forall \phi \in C(Y)

. When

S
S

and

T
T

are topologically mixing subshifts of finite type, we relate compensation functions to lifting

T
T

-invariant measures to

S
S

-invariant measures, obtaining some results of Boyle and Tuncel. We use compensation functions to describe different types of quotient maps

π
\pi

. An example is given where no compensation function exists.
Weighted nonlinear potential theory
Authors: Adams David R.
Published: June 2010

The potential theoretic idea of the "thinness of a set at a given point" is extended to the weighted nonlinear potential theoretic setting—the weights representing in general singularities/degeneracies—and conditions on these weights are given that guarantee when two such notions are equivalent at the given point. When applied to questions of boundary regularity for solutions to (degenerate) elliptic second-order partial differential equations in bounded domains, this result relates the boundary Wiener criterion for one operator to that of another, and in the linear case gives conditions for boundary regular points to be the same for various operators. The methods also yield two weight norm inequalities for Riesz potentials
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis integral left-parenthesis upper I Subscript alpha Baseline asterisk f right-parenthesis Superscript q Baseline v d x right-parenthesis Superscript 1 slash q Baseline less-than-or-slanted-equals left-parenthesis integral f Superscript p Baseline w d x right-parenthesis Superscript 1 slash p Baseline comma">

(

∫

(

I
α

∗

f
)

q

v

d
x

)

1

/

q

⩽

(

∫

f
p

w

d
x

)

1

/

p

,

{\left ( {\int {{{({I_\alpha }{\ast }f)}^q}v\,dx} } \right )^{1/q}} \leqslant {\left ( {\int {{f^p}w\,dx} } \right )^{1/p}},

\]

1
>
p
⩽
q
>
∞

1 > p \leqslant q > \infty

, which at least in the first-order case

(
α
=
1
)

(\alpha = 1)

have found some use in a number of places in analysis.
The axioms of supermanifolds and a new structure arising from them
Authors: Rothstein Mitchell J.
Published: June 2010

An analysis of supermanifolds over an arbitrary graded-commmutative algebra is given, proceeding from a set of axioms the first of which is that the derivations of the structure sheaf of a supermanifold are locally free. These axioms are satisfied not by the sheaf of

G
∞

{G^\infty }

functions, as has been asserted elsewhere, but by an extension of this sheaf. A given

G
∞

{G^\infty }

manifold may admit many supermanifold extensions, and it is unknown at present whether there are

G
∞

{G^\infty }

manifolds that admit no such extension. When the underlying graded-commutative algebra is commutative, the axioms reduce to the Berezin-Kostant supermanifold theory.
Chaotic functions with zero topological entropy
Authors: Smítal J.
Published: June 2010

Recently Li and Yorke introduced the notion of chaos for mappings from the class

C
0

(
I
,
I
)

{C^0}(I,I)

, where

I
I

is a compact real interval. In the present paper we give a characterization of the class

M
⊂

C
0

(
I
,
I
)

M \subset {C^0}(I,I)

of mappings chaotic in this sense. As is well known,

M
M

contains the mappings of positive topological entropy. We show that

M
M

contains also certain (but not all) mappings that have both zero topological entropy and infinite attractors. Moreover, we show that the complement of

M
M

consists of maps that have only trajectories approximate by cycles. Finally, it turns out that the original Li and Yorke notion of chaos can be replaced by (an equivalent notion of)

δ
\delta

-chaos, distinguishable on a certain level

δ
>
0

\delta > 0

.
Seifert matrices and boundary link cobordisms
Authors: Ko Ki Hyoung
Published: June 2010

To an

m
m

-component boundary link of odd dimension, a matrix is associated by taking the Seifert pairing on a Seifert surface of the link. An algebraic description of the set of boundary link cobordism classes of boundary links is obtained by using this matrix invariant.
Induced group actions, representations and fibered skew product extensions
Authors: Fabec R. C.
Published: June 2010

Let

G
G

be a locally compact group acting ergodically on

Y
Y

. We introduce the notion of an action of this group action and study the notions of induced group actions, ergodicity, and fibered product extensions in this context. We also characterize fibered skew product actions built over a cocycle.
VMO, ESV, and Toeplitz operators on the Bergman space
Authors: Zhu Ke He
Published: June 2010

This paper studies the largest

C
∗

{C^*}

-subalgebra

Q
Q

of

L
∞

(

D

)

{L^\infty }({\mathbf {D}})

such that the Toeplitz operators

T
f

{T_f}

on the Bergman space

L
a
2

(

D

)

L_a^2({\mathbf {D}})

with symbols

f
f

in

Q
Q

have a symbol calculus modulo the compact operators.

Q
Q

is characterized by a condition of vanishing mean oscillation near the boundary. I also give several other necessary and sufficient conditions for a bounded function to be in

Q
Q

. After decomposing

Q
Q

in a "nice" way, I study the Fredholm theory of Toeplitz operators with symbols in

Q
Q

. The essential spectrum of

T
f

(
f
∈
Q
)

{T_f}(f \in Q)

is shown to be connected and computable in terms of the Stone-Cěch compactification of

D

{\mathbf {D}}

. The results in this article partially answer a question posed in [3] and give several new necessary and sufficient conditions for a bounded analytic function on the open unit disc to be in the little Bloch space

B

0

{\mathcal {B}_0}

.
𝐾_{𝑙+1}-free graphs: asymptotic structure and a 0-1 law
Authors: Kolaitis Ph. G. , Prömel H. J. , Rothschild B. L.
Published: June 2010

The structure of labeled

K

l
+
1

{K_{l + 1}}

-free graphs is investigated asymptotically. Through a series of stages of successive refinement the structure of "almost all" such graphs is found sufficiently precisely to prove that they are in fact

l
l

-colorable (

l
l

-partite). With the asymptotic information obtained it is shown also that in the class of

K

l
+
1

{K_{l + 1}}

-free graphs there is a first-order labeled

0
0

-

1
1

law. With this result, and those cases already known, we can say that any infinite class of finite undirected graphs with amalgamations, induced subgraphs and isomorphisms has a

0
0

-

1
1

law.
Branched coverings of 2-complexes and diagrammatic reducibility
Authors: Gersten S. M.
Published: June 2010

The condition that all spherical diagrams in a

2
2

-complex be reducible is shown to be equivalent to the condition that all finite branched covers be aspherical. This result is related to the study of equations over groups. Furthermore large classes of

2
2

-complexes are shown to be diagrammatically reducible in the above sense; in particular, every

2
2

-complex has a subdivision which admits a finite branched cover which is diagrammatically reducible.
Nilpotent spaces of sections
Authors: Møller Jesper Michael
Published: June 2010

The space of sections of a fibration is nilpotent provided the base is finite

C
W

CW

-complex and the fiber is nilpotent. Moreover, localization commutes with the formation of section spaces.
Oscillatory integrals and Fourier transforms of surface carried measures
Authors: Cowling Michael , Mauceri Giancarlo
Published: June 2010

We suppose that

S
S

is a smooth hypersurface in

R

n
+
1

{{\mathbf {R}}^{n + 1}}

with Gaussian curvature

κ
\kappa

and surface measure

d
S

dS

,

w
w

is a compactly supported cut-off function, and we let

μ
α

{\mu _\alpha }

be the surface measure with

d

μ
α

=
w

κ
α

d
S

d{\mu _\alpha } = w{\kappa ^\alpha }\,dS

. In this paper we consider the case where

S
S

is the graph of a suitably convex function, homogeneous of degree

d
d

, and estimate the Fourier transform

μ
^

α

{\hat \mu _\alpha }

. We also show that if

S
S

is convex, with no tangent lines of infinite order, then

μ
^

α

(
ξ
)

{\hat \mu _\alpha }(\xi )

decays as

|

ξ

|

−
n

/

2

|\xi {|^{ - n / 2}}

provided

α
⩾
[
(
n
+
3
)

/

2
]

\alpha \geqslant [(n + 3)/2]

. The techniques involved are the estimation of oscillatory integrals; we give applications involving maximal functions.
Estimates for (\overline∂-𝜇∂)⁻¹ and Calderón’s theorem on the Cauchy integral
Authors: Semmes Stephen W.
Published: June 2010

One can view the Cauchy integral operator as giving the solution to a certain

∂
¯

\overline \partial

problem. If one has a quasiconformal mapping on the plane that takes the real line to the curve, then this

∂
¯

\bar \partial

problem on the curve can be pulled back to a

∂
¯

−
μ
∂

\bar \partial - \mu \partial

problem on the line. In the case of Lipschitz graphs (or chordarc curves) with small constant, we show how a judicial choice of q.c. mapping and suitable estimates for

∂
¯

−
μ
∂

\bar \partial - \mu \partial

gives a new approach to the boundedness of the Cauchy integral. This approach has the advantage that it is better suited to related problems concerning

H
∞

{H^\infty }

than the usual singular integral methods. Also, these estimates for the Beltrami equation have application to quasiconformal and conformal mappings, taken up in a companion paper.
Normal structure in dual Banach spaces associated with a locally compact group
Authors: Lau Anthony To Ming , Mah Peter F.
Published: June 2010

In this paper we investigated when the dual of a certain function space defined on a locally compact group has certain geometric properties. More particularly, we asked when weak

∗

^{*}

compact convex subsets in these spaces have normal structure, and when the norm of these spaces satisfies one of several types of Kadec-Klee property. As samples of the results we have obtained, we have proved, among other things, the following two results: (1) The measure algebra of a locally compact group has weak

∗

^{*}

-normal structure iff it has property SUKK

∗

^{*}

iff it has property SKK

∗

^{*}

iff the group is discrete; (2) Among amenable locally compact groups, the Fourier-Stieltjes algebra has property SUKK

∗

^{*}

iff it has property SKK

∗

^{*}

iff the group is compact. Consequently the Fourier-Stieltjes algebra has weak

∗

^{*}

-normal structure when the group is compact.
Iterating the basic construction
Authors: Pimsner Mihai , Popa Sorin
Published: June 2010

Let

N
⊂
M

N \subset M

be a pair of type II

1

_{1}

factors with finite Jones’ index and

N
⊂
M
⊂

M
1

⊂

M
2

⊂
⋯
⊂

M
n

⊂
⋯
⊂

M

2
n
+
1

N \subset M \subset {M_1} \subset {M_2} \subset \cdots \subset {M_n} \subset \cdots \subset {M_{2n + 1}}

be the associated tower of type II

1

_{1}

factors obtained by iterating Jones’ basic construction. We give an explicit formula of a projection in

M

2
n
+
1

{M_{2n + 1}}

which implements the conditional expectation of

M
n

{M_n}

onto

N
N

, thus showing that

M

2
n
+
1

{M_{2n + 1}}

comes naturally from the basic construction associated to the pair

N
⊂

M
n

N \subset {M_n}

. From this we deduce several properties of the relative commutant

N
′

∩

M
n

N’ \cap {M_n}

.
Finite covers of 3-manifolds containing essential tori
Authors: Luecke John
Published: June 2010

It is shown in this paper that if a Haken

3
3

-manifold contains an incompressible torus that is not boundary-parallel then either it has a finite cover that is a torus-bundle over the circle or it has finite covers with arbitrarily large first Betti number.
Electrophoretic traveling waves
Authors: Fife P. C. , Palusinski O. A. , Su Y.
Published: June 2010

An existence-uniqueness-approximability theory is given for a prototypical mathematical model for the separation of ions in solution by an imposed electric field. The separation is accomplished during the formation of a traveling wave, and the mathematical problem consists in finding a traveling wave solution of a set of diffusion-advection equations coupled to a Poisson equation. A basic small parameter

ε
\varepsilon

appears in an apparently singular manner, in that when

ε
=
0

\varepsilon = 0

(which amounts to assuming the solution is everywhere electrically neutral), the last (Poisson) equation loses its derivative, and becomes an algebraic relation among the concentrations. Since this relation does not involve the function whose derivative is lost, the type of "singular" perturbation represented here is nonstandard. Nevertheless, the traveling wave solution depends in a regular manner on

ε
\varepsilon

, even at

ε
=
0

\varepsilon = 0

; and one of the principal aims of the paper is to show this regular dependence.
Peripherally specified homomorphs of knot groups
Authors: Johnson Dennis , Livingston Charles
Published: June 2010

Let

G
G

be a group and let

μ
\mu

and

λ
\lambda

be elements of

G
G

. Necessary and sufficient conditions are presented for the solution of the following problem: Is there a knot

K
K

in

S
3

{S^3}

and a representation

ρ
:

π
1

(

S
3

−
K
)
→
G

\rho :{\pi _1}({S^3} - K) \to G

such that

ρ
(
m
)
=
μ

\rho (m) = \mu

and

ρ
(
l
)
=
λ

\rho (l) = \lambda

, where

m
m

and

l
l

are the meridian and longitude of

K
K

?
Numerical evaluation of Wiener integrals
Authors: Konheim Alan G. , Miranker Willard L.
Published: June 2010

A systematic study of quadrature formulae for the Wiener integral

∫

F
[
x
]
w
(
d
x
)

\int {F[x]w(dx)}

of the type

∫

F
[
θ
(
u
,
⋅
)
]
ν
(
d
u
)

\int {F[\theta (u, \cdot )]\nu (du)}

is presented. The Cameron and Vladimirov quadrature formulae, which are the function space analogues of Simpson’s Rule, are shown to fit into this framework. Numerical results are included.
Stochastic quadrature formulas
Authors: Haber Seymour
Published: June 2010

A class of formulas for the numerical evaluation of multiple integrals is described, which combines features of the Monte-Carlo and the classical methods. For certain classes of functions—defined by smoothness conditions—these formulas provide the fastest possible rate of convergence to the integral. Asymptotic error estimates are derived, and a method is described for obtaining good a posteriori error bounds when using these formulas. Equal-coefficients formulas of this class, of degrees up to 3, are constructed.
On the computation of Debye functions of integer orders
Authors: Ng E. W. , Devine C. J.
Published: June 2010

An efficient method is presented for the computation of Debye functions of integer orders to twenty significant decimal digits.
Lower bounds for relatively prime amicable numbers of opposite parity.
Authors: Hagis Peter
Published: June 2010

Whether or not a pair of relatively prime amicable numbers exists is an open question. In this paper it is proved that if

m
m

and

n
n

are a pair of relatively prime amicable numbers of opposite parity then

m
n

mn

is greater than

10

121

{10^{121}}

and

m
m

and

n
n

are each greater than

10

60

{10^{60}}

.
Unitary amicable numbers
Authors: Hagis Peter
Published: June 2010

Two positive integers are said to be unitary amicable if the sum of the unitary divisors of each is equal to their sum. In this paper a table of such numbers is given, and some theorems concerning them are proved.
On the effects of scaling of the Peaceman-Rachford method
Authors: Widlund Olof B.
Published: June 2010

The alternating direction method of Peaceman and Rachford is considered for elliptic difference schemes of second order and with two independent variables. An earlier result of the author’s on the rapid convergence of multi-parameter noncommutative problems is described and a connection is established between that result and theorems on optimal scaling of band matrices. Simple algorithms to decrease the condition number and increase the rate of convergence are discussed.
Some transformations of monotone sequences
Authors: Wimp Jet
Published: June 2010

In this paper, we discuss a class of methods for summing sequences which are generalizations of a method due to Salzer. The methods are not regular, and in contrast to the classical regular methods, seem to work best on sequences which are monotone. In our main theorem, we determine a class of convergent sequences for which the methods yield sequences which converge to the same sum.
The asymptotic expansion of a hypergeometric function ₂𝐹₂(1,𝛼;𝜌₁,𝜌₂;𝑧)
Authors: Kim Shoon K.
Published: June 2010

The asymptotic expansion of a hypergeometric function

2

F
2

(
1
,
α
;

ρ
1

,

ρ
2

;
z
)

_2{F_2}(1,\alpha ;{\rho _1},{\rho _2};z)

is given in terms of hypergeometric functions

2

F
0

(

z

−
1

)

_2{F_0}({z^{ - 1}})

and

3

F
1

(

z

−
1

)

_3{F_1}({z^{ - 1}})

.
Numerical construction of Gaussian quadrature formulas for ∫₀¹(-𝐿𝑜𝑔𝑥)⋅𝑥^{𝛼}⋅𝑓(𝑥)⋅𝑑𝑥 and ∫₀^{∞}𝐸_{𝑚}(𝑥)⋅𝑓(𝑥)⋅𝑑𝑥
Authors: Danloy Bernard
Published: June 2010

Most nonclassical Gaussian quadrature rules are difficult to construct because of the loss of significant digits during the generation of the associated orthogonal polynomials. But, in some particular cases, it is possible to develop stable algorithms. This is true for at least two well-known integrals, namely
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Subscript 0 Superscript 1 Baseline minus left-parenthesis upper L o g x right-parenthesis dot x Superscript alpha Baseline dot f left-parenthesis x right-parenthesis dot d x and integral Subscript 0 Superscript normal infinity Baseline upper E Subscript m Baseline left-parenthesis x right-parenthesis dot f left-parenthesis x right-parenthesis dot d x period">

∫
0
1

−
(

Log

x
)
⋅

x
α

⋅
f
(
x
)
⋅
d
x

and

∫
0
∞

E
m

(
x
)
⋅
f
(
x
)
⋅

d
x
.

\int _0^1 { - ({\operatorname {Log}}\;x) \cdot {x^\alpha } \cdot f(x) \cdot dx\quad {\text {and}}\quad \int _0^\infty {{E_m}(x) \cdot f(x) \cdot } dx.}

\]
A new approach is presented, which makes use of known classical Gaussian quadratures and is remarkably well-conditioned since the generation of the orthogonal polynomials requires only the computation of discrete sums of positive quantities. Finally, some numerical results are given.
A stable algorithm for computing the inverse error function in the “tail-end” region
Authors: Fettis Henry E.
Published: June 2010

An iterative algorithm, simple enough to be executed on a desk top automatic computer, is given for computing the inverse of the function

x
=

erfc

(
y
)

x = {\operatorname {erfc}}(y)

for small values of x.
On the eigenvectors of a finite-difference approximation to the Sturm-Liouville eigenvalue problem
Authors: Gekeler Eckart
Published: June 2010

This paper is concerned with a centered finite-difference approximation to to the nonselfadjoint Sturm-Liouville eigenvalue problem
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row upper L left-bracket u right-bracket equals minus left-bracket a left-parenthesis x right-parenthesis u Subscript x Baseline right-bracket Subscript x Baseline minus b left-parenthesis x right-parenthesis u Subscript x Baseline plus c left-parenthesis x right-parenthesis u equals lamda u comma 0 greater-than x greater-than 1 comma 2nd Row u left-parenthesis 0 right-parenthesis equals u left-parenthesis 1 right-parenthesis equals 0 period EndLayout">

L
[
u
]
=
−

[
a
(
x
)

u
x

]

x

−
b
(
x
)

u
x

+
c
(
x
)
u
=
λ
u
,

0
>
x
>
1
,

u
(
0
)
=
u
(
1
)
=
0.

\begin {array}{*{20}{c}} {L[u] = - {{[a(x){u_x}]}_x} - b(x){u_x} + c(x)u = \lambda u,\quad 0 > x > 1,} \hfill \\ {u(0) = u(1) = 0.} \hfill \\ \end {array}

\]
It is shown that the eigenvectors

W
p

{W_p}

of the

M
×
M

M \times M

-matrix (

Δ
x
=
1

/

(
M
+
1
)

\Delta x = 1/(M + 1)

mesh size), which approximates L, are bounded in the maximum norm independent of M if they are normalized so that

|

W
p

|

2

=
1

|{W_p}{|_2} = 1

.