bluuebunny/crossref_metadata_2025 huggingface dataset:
An elementary proof of Titchmarsh’s convolution theorem
Authors: Doss Raouf
Published: June 2010

We give an elementary proof of the following theorem of Titchmarsh. Suppose

f
,
g

f,g

are integrable on the interval

(

0
,
2
T

)

\left ( {0,2T} \right )

and that the convolution

f
∗
g

(
t
)

=

∫
0
t

f

(

t
−
x

)

g

(
x
)

d
x

=
0

f * g\left ( t \right ) = \int _0^t {f\left ( {t - x} \right )g\left ( x \right )dx} = 0

on

(

0
,
2
T

)

\left ( {0,2T} \right )

. Then there are nonnegative numbers

α
,
β

\alpha ,\beta

with

α
+
β
≥
2
T

\alpha + \beta \geq 2T

for which

f

(
x
)

=
0

f\left ( x \right ) = 0

for almost all

x
x

in

(

0
,
α

)

\left ( {0,\alpha } \right )

and

g

(
x
)

=
0

g\left ( x \right ) = 0

for almost all

x
x

in

(

0
,
β

)

\left ( {0,\beta } \right )

.
A characterization of discrete Banach lattices with order continuous norms
Authors: Wnuk Witold
Published: June 2010

We give a characterization of those

σ
\sigma

-Dedekind complete Banach lattices for which every continuous linear operator

T
:
E
→

c
0

T:E \to {c_0}

is a difference of two positive linear operators from

E
E

into

c
0

{c_0}

.
A splitting theorem for 4-dimensional manifolds of nonnegative curvature
Authors: Walschap Gerard
Published: June 2010

A structure theorem for four-dimensional open manifolds of non-negative curvature is stated. More generally, it is shown that any manifold with soul

S
S

of codimension 2 admits a Riemannian submersion onto

S
S

, which splits as a metric product whenever

S
S

has flat normal bundle.
Defining jump classes in the degrees below 0’
Authors: Shore Richard A.
Published: June 2010

We prove that, for each degree

c

{\mathbf {c}}

r.e. in and above

0

(
3
)

{{\mathbf {0}}^{(3)}}

, the class of degrees

x

≤

0

′

{\mathbf {x}} \leq {\mathbf {0}}’

with

x

(
3
)

=

c

{{\mathbf {x}}^{(3)}} = {\mathbf {c}}

is definable without parameters in

D

(
≤

0
′

)

\mathcal {D}( \leq 0’)

, the degrees below

0
′

{\mathbf {0’}}

. Indeed the same definitions work below any r.e. degree

r

{\mathbf {r}}

in place of

0
′

{\mathbf {0’}}

. Thus for each r.e. degree

r

{\mathbf {r}}

,

Th
⁡
(

D

(
≤

r

)
)

\operatorname {Th} (\mathcal {D}( \leq {\mathbf {r}}))

uniquely determines

r

(
3
)

{{\mathbf {r}}^{(3)}}

.
Some fibred cobordism groups are not finitely generated
Authors: Astey L. , Greenberg P. , Micha E. , Pastor G.
Published: June 2010

By showing that certain Pontrjagin classes are fibre cobordism invariants "of connected type" we produce infinitely many examples of fibre cobordism groups which are not finitely generated.
The free genus of doubled knots
Authors: Livingston Charles
Published: June 2010

The free genus of an untwisted doubled knot in

S
3

{S^3}

can be arbitrarily large.
Factorizations of Lebesgue measure via convolutions
Authors: Levenberg Norman , Martin Gaven J. , Shields Allen L. , Zdravkovska Smilka
Published: June 2010

Given a continuous, increasing function

ϕ
:
[
0
,
∞
)
→
[
0
,
∞
)

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

with

ϕ
(
0
)
=
0

\phi (0) = 0

, we define the Hausdorff

ϕ
\phi

-measure of a bounded set

E
E

in the unit interval

I
=
[
0
,
1
]

I = [0,1]

as

H
ϕ

(
E
)
=

lim

δ
→
0

H
ϕ

,
δ

(
E
)

{H_\phi }(E) = {\lim _{\delta \to 0}}{H_\phi }{,_\delta }(E)

where

H
ϕ

,
δ

E
=
inf

∑

i
=
1

∞

ϕ
(

t
i

)

{H_\phi }{,_\delta }E = \inf \sum \nolimits _{i = 1}^\infty {\phi ({t_i})}

and the infimum is taken over all countable covers of

E
E

by intervals

U
i

{U_i}

with

t
i

=

|

U
i

|

=

{t_i} = \left | {{U_i}} \right | =

length of

U
i

>
δ

{U_i} > \delta

. We show that given any such

ϕ
\phi

, there exist closed, nowhere dense sets

E
1

,

E
2

⊂
I

{E_1},{E_2} \subset I

with

H
ϕ

(

E
1

)
=

H
ϕ

(

E
2

)
=
0

{H_\phi }({E_1}) = {H_\phi }({E_2}) = 0

and

E
1

+

E
2

≡

{

a
+
b
:
a
∈

E
1

,
b
∈

E
2

}

=
I

{E_1} + {E_2} \equiv \left \{ {a + b:a \in {E_1},b \in {E_2}} \right \} = I

. The sets

E
i

(
i
=
1
,
2
)

{E_i}(i = 1,2)

are constructed as Cantor-type sets

E
i

=

⋂

n
=
1

∞

E

i
,
n

{E_i} = \bigcap \nolimits _{n = 1}^\infty {{E_{i,n}}}

where

E

i
,
n

{E_{i,n}}

is a finite union of disjoint closed intervals. In addition, we give a simple geometric proof that the natural probability measures

μ
i

{\mu _i}

supported on

E
i

{E_i}

which arise as weak limits of normalized Lebesgue measure on

E

i
,
n

{E_{i,n}}

have the property that the convolution

μ
1

∗

μ
2

{\mu _1}*{\mu _2}

is Lebesgue measure on

I
I

.
Interior and boundary regularity of solutions to a plasma type equation
Authors: Kwong Ying C.
Published: June 2010

In this paper, we will consider a plasma type equation with homogeneous boundary condition and nonnegative initial data such that there is a finite extinction

T
∗

{T^*}

. We will show that the solution is a positive classical solution in the interior of the parabolic cylinder and it decays to zero at the boundary at a certain explicit rate.
Jump distributions on [-1,1] whose orthogonal polynomials have leading coefficients with given asymptotic behavior
Authors: Lubinsky D. S.
Published: June 2010

We construct an explicit even jump distributiondα(x)d\alpha (x)on[−1,1][-1,1]for whichγn(dα){\gamma _n}(d\alpha ), the leading coefficient of thennth orthonormal polynomial fordα(x)d\alpha (x), has any given asymptotic behavior. For example, if{ξn}1∞\{ {\xi _n}\} _1^\inftyis a strictly increasing sequence with limit∞\infty, andξ3n+1/ξ3n→1{\xi _{{3^{n + 1}}}}/{\xi _{{3^n}}} \to 1asn→∞n \to \infty, we can ensure thatlimn→∞γn(dα)2−n/ξn=1{\lim _{n \to \infty }}{\gamma _n}(d\alpha ){2^{ - n}}/{\xi _n} = 1. As a consequence, we havelimn→∞γn−1(dα)/γn(dα)=1/2{\lim _{n \to \infty }}{\gamma _{n - 1}}(d\alpha )/{\gamma _n}(d\alpha ) = 1/2; that is,dαd\alphabelongs to Nevai’s classM\mathcal {M}. This positively and explicitly answers a question of Al. Magnus.
Finite coverings by normal subgroups
Authors: Brodie M. A. , Chamberlain R. F. , Kappe L.-C.
Published: June 2010

B. H. Neumann’s characterization of groups possessing a finite covering by proper subgroups and Baer’s characterization of groups with finite coverings by abelian subgroups are refined to results about finite coverings by normal subgroups. Various corollaries about the structure of groups having such finite coverings are derived. Using the method employed for the main theorem, a simplified proof of an earlier result of the third author concerning finite coverings by word subgroups is given.
Continuity of additive 𝜅-metric functions and metrization of 𝜅-metric spaces
Authors: Isiwata Takesi
Published: June 2010

For an additive

κ
\kappa

-metric space

X
X

with an

s

(
x
)

s\left ( x \right )

-continuous

κ
\kappa

-metric

d

(

x
,
C

)

d\left ( {x,C} \right )

, we prove that

X
X

is metrizable, and that if

d

(

x
,
C

)

d\left ( {x,C} \right )

is locally regular, then

z

(

x
,
y

)

z\left ( {x,y} \right )

is bicontinuous, and

ρ

(

x
,
y

)

=
z

(

x
,
y

)

+
z

(

x
,
y

)

\rho \left ( {x,y} \right ) = z\left ( {x,y} \right ) + z\left ( {x,y} \right )

is a metric on

X
X

which agrees with the topology of

X
X

.
A characterization of maximal connected spaces and maximal arcwise connected spaces
Authors: Clark Bradd , Schneider Victor
Published: June 2010

The concept of a maximal connected space was developed by J. P. Thomas and maximal connected expansions of the reals were discovered by Guthrie, Stone, Wage, and Simon. This paper gives necessary and sufficient conditions for a space to be maximal connected. Also necessary and sufficient conditions for the join of two connected topologies to be connected are given in the special case that one of the topologies is atomic. Finally the concept of a maximal arcwise connected topology is given and used to show that every connected simplicial complex admits both a maximal arcwise connected extension and a maximal connected extension.
Dimension of dense subalgebras of 𝐶(𝑋)
Authors: Sancho de Salas Juan B. , Sancho de Salas Ma. Teresa
Published: June 2010

The real spectrum of any

R

{\mathbf {R}}

-algebra

A
A

is the set of all maximal ideals of

A
A

with residue field

R

{\mathbf {R}}

, endowed with the initial topology for the functions induced by the elements of

A
A

. We prove that a compact metric space

X
X

has dimension

≤
n

\leq n

if and only if

X
X

is the real spectrum of an algebra of Krull dimension

≤
n

\leq n

; so that the dimension of

X
X

is the minimum of the Krull dimensions of all dense subalgebra of

C
(
X
)

C(X)

. Moreover, we prove that a compact Hausdorff space

X
X

has covering dimension

≤
n

\leq n

if and only if every countably generated subalgebra of

C
(
X
)

C(X)

is contained in the closure of a subalgebra of Krull dimension

≤
n

\leq n

.
The Albert quadratic form for an algebra of degree four
Authors: Mammone Pasquale , Shapiro Daniel B.
Published: June 2010

Suppose

K
K

is a field and the

K
K

-algebra

A
A

is expressed as a tensor product of two quaternion algebras

A
≅

H
1

⊗

H
2

A \cong {H_1} \otimes {H_2}

. Let

N
i

{N_i}

be the norm form on

H
i

{H_i}

and define the "Albert form"

α
A

{\alpha _A}

to be the

6
6

-dimensional quadratic form determined by

α

A

⊥

⟨

1
,
−
1

⟩

≅

N
1

⊥
−

N
2

\alpha _{A} \bot \left \langle {1, - 1} \right \rangle \cong {N_1} \bot - {N_2}

. In [Adv. in Math. 48 (1983), 149-165] Jacobson proved: (1) any two Albert forms for

A
A

are similar; (2) if

A
A

and

B
B

are algebras of this type, then

A
≅
B

A \cong B

if and only if

α
A

{\alpha _A}

and

α
B

{\alpha _B}

are similar. The authors prove this result using quadratic forms and Clifford algebras, avoiding the application of Jacobson’s theory of Jordan norms.
Preorders compatible with probability measures defined on a Boolean algebra
Authors: Schwarze M. G.
Published: June 2010

We use nonstandard analysis techniques to find conditions for the existence of a strictly positive measure weakly compatible with a preorder defined in a Boolean algebra generated by denumerably many atoms.
Extremal Minkowski additive selections of compact convex sets
Authors: Živaljević Rade T.
Published: June 2010

A function

f
:

K

n

→

R
n

f:{\mathcal {K}^n} \to {R^n}

, defined on the set of all compact convex sets in

R
n

{R^n}

, is a Minkowski additive selection, provided

f
(
K
+
L
)
=
f
(
K
)
+
f
(
L
)

f(K + L) = f(K) + f(L)

and

f
(
K
)
∈
K

f(K) \in K

for all

K
,
L
∈

K

n

K,L \in {\mathcal {K}^n}

. The paper deals with selections which are extremal in some sense, in particular we characterize the set of all Minkowski additive selections which have the property

f
(
K
)
∈

ext

(
K
)

f(K) \in {\text {ext}}(K)

for all

K
∈

K

n

K \in {\mathcal {K}^n}

, where

ext

(
K
)

{\text {ext}}(K)

is the set of all extreme points of

K
K

.
A pinching theorem for cusps of negatively curved manifolds with finite volume
Authors: Kanai Masahiko
Published: June 2010

We give a new proof of the following theorem of M. Gromov: For a noncompact complete riemannian manifold

M
M

of negative curvature with finite volume, each cusp of

M
M

is diffeomorphic to

N
×
[
0
,
∞
)

N \times [0,\infty )

with

N
N

being a compact flat space form provided that the sectional curvature of

M
M

satisfies the pinching condition

−
4
>
−

Λ
2

≤
K
≤
−
1

- 4 > - {\Lambda ^2} \leq K \leq - 1

.
Well-bounded and scalar-type spectral operators on spaces not containing 𝑐₀
Authors: Doust Ian
Published: June 2010

It is known that a necessary and sufficient condition for a well-bounded operator on a weakly complete complex Banach space to be scalar-type spectral is that its decomposition of the identity be of bounded variation. We show in this paper that this condition is necessary and sufficient exactly when the Banach space does not contain a subspace isomorphic to

c
0

{c_0}

.
An iteration process for nonexpansive mappings with applications to fixed point theory in product spaces
Authors: Kirk W. A.
Published: June 2010

A uniform transfinite iteration procedure for selecting fixed points of nonexpansive mappings is introduced. This procedure, which applies to arbitrary nonexpansive mappings in Banach spaces having Kadec-Klee norm and to strictly contractive mappings in reflexive Banach spaces, is used to generalize a fixed point theorem of Kirk and Sternfeld for nonexpansive mappings in product spaces.
Every semiprimary ring is the endomorphism ring of a projective module over a quasihereditary ring
Authors: Dlab Vlastimil , Ringel Claus Michael
Published: June 2010

The paper provides a proof of the following statement: Given a semiprimary ring

R
R

, there is a quasi-hereditary ring

A
A

and an idempotent

e
∈
A

e \in A

such that

R
≃
e
A
e

R \simeq eAe

.
Regularity of mappings of 𝐺-structures of Frobenius type
Authors: Han Chong-Kyu
Published: June 2010

A notion of Frobenius type for a

G
G

-structure is defined. It is shown that a mapping

f
f

between

C
∞

(

resp

.

C
ω

)

{C^\infty }({\text {resp}}{\text {.}}{C^\omega })

manifolds with a

G
G

-structure of the Frobenius type is

C
∞

(

resp

.

C
ω

)

{C^\infty }({\text {resp}}{\text {.}}{C^\omega })

if

f
∈

C
k

f \in {C^k}

, where the integer

k
k

depends on the order of the Frobenius type. It is also shown that a

G
G

-structure of finite order is of the Frobenius type.
Highest weight modules for Hermitian symmetric pairs of exceptional type
Authors: Enright Thomas J. , Shelton Brad
Published: June 2010

We analyze the categories of highest weight modules with a semiregular generalized infinitesimal character for the two exceptional Hermitian symmetric cases. These categories are completely described, and, as a consequence, we see that the combinatorial description of the general (regular integral) categories of highest weight modules previously given in the classical cases holds also in the exceptional cases.
Compactifications with almost locally compact outgrowth
Authors: Rayburn Marlon C.
Published: June 2010

An extension of a result of Hatzenbuhler and Mattson gives a sufficient condition that the locally compact part of an arbitrary Tichonov space has a compactification with a countably infinite outgrowth. This leads to a characterization for almost locally compact outgrowths, and some sufficient conditions for their existence. Examples are given showing the conditions are not necessary.
Periodic point free homeomorphism of 𝑇²
Authors: Handel Michael
Published: June 2010

Suppose that

f
:

T
2

→

T
2

f:{T^2} \to {T^2}

is an orientation preserving homeomorphism of the torus that is homotopic to the identity and that has no periodic points. We show that there is a direction

θ
\theta

and a number

ρ
\rho

such that every orbit of

f
f

has rotation number

ρ
\rho

in the direction

θ
\theta

.
Classification of finite groups with all elements of prime order
Authors: Deaconescu Marian
Published: June 2010

A finite group having all (nontrivial) elements of prime order must be a

p
p

-group of exponent

p
p

, or a nonnilpotent group of order

p
a

q

{p^a}q

, or it is isomorphic to the simple group

A
5

{A_5}

.
A 𝑝-adic analogue of the Gauss-Bonnet theorem for certain Mumford curves
Authors: Freije Richard M.
Published: June 2010

If

K
K

is a local field,

L
L

a quadratic extension,

Γ
\Gamma

a Schottky group co-compact in

PG

L

2

(
K
)

{\text {PG}}{{\text {L}}_2}(K)

then the quotient

L
−
K

/

Γ

L - K/\Gamma

corresponds to the

L
L

-points of a Mumford curve. In this paper we calculate

∫

L
−
K

/

Γ

d

M

\int _{L - K/\Gamma } {d\mathcal {M}}

where

M

\mathcal {M}

is an

PG

L

2

(
K
)

{\text {PG}}{{\text {L}}_2}(K)

invariant measure on

L
−
K

L - K

, in terms of the genus of the corresponding curve.
Almost commuting unitary matrices
Authors: Exel Ruy , Loring Terry
Published: June 2010

A pair of square matrices is said to be almost commuting if their commutator is small in norm. We give an elementary proof of a theorem of Voiculescu showing that not all almost commuting pairs can be perturbed to a commuting pair.
The Henselian defect for valued function fields
Authors: Ohm Jack
Published: June 2010

The notion of defect for finite algebraic extensions of valued fields is classical and due to Ostrowski. Recently Matignon has generalized Ostrowski’s definition to rk 1 (residually transcendental) valued function fields and used it to prove a very sharp version of the genus reduction inequality for

1
−
dim

1 - \dim

function fields. The further generalization of the notion of defect to valued function fields of arbitrary rk is treated here.
Holomorphic sectional curvature of some pseudoconvex domains
Authors: McNeal Jeffery D.
Published: June 2010

The holomorphic sectional curvatures in the Bergman metric of a smooth bounded pseudoconvex domain in

C

2

{{\mathbf {C}}^2}

are shown to be bounded in absolute value near a poinit of finite type in the boundary
Lens spaces and Dehn surgery
Authors: Bleiler Steven A. , Litherland Richard A.
Published: June 2010

The question of when a lens space arises by Dehn surgery is discussed with a characterization given for satellite knots. The lens space

L

(

2
,
1

)

L\left ( {2,1} \right )

, i.e. real projective

3
3

-space, is shown to be unobtainable by surgery on a symmetric knot.
The Stieltjes moments problem for rapidly decreasing functions
Authors: Duran Antonio J.
Published: June 2010

We prove the following result: If

(

a
n

)

n

{\left ( {{a_n}} \right )_n}

is a sequence of complex numbers, then there exists a

C

∞

{\mathcal {C}^\infty }

-function

f
f

such that

f
f

and all its derivatives are rapidly decreasing functions,

f

(
t
)

=
0

f\left ( t \right ) = 0

for

t
>
0

t > 0

and

∫
0

+
∞

t
n

f

(
t
)

d
t
=

a
n

\int _0^{ + \infty } {{t^n}f\left ( t \right )dt = {a_n}}

. We extend this result for a generalized Stieltjes moments problem. Also, we characterize the

C
∞

{C^\infty }

-functions

f
f

in

(

0
,
+
∞

)

\left ( {0, + \infty } \right )

such that

f
f

and all its derivatives are rapidly decreasing functions in

(

0
,
+
∞

)

\left ( {0, + \infty } \right )

and with null moments.
Comparison between the Kobayashi and Carathéodory distances on strongly pseudoconvex bounded domains in 𝐶ⁿ
Authors: Venturini Sergio
Published: June 2010

In this paper we prove that the ratio between the Carathéodory distance and the Kobayashi distance in a strongly pseudoconvex bounded domain in

C

n

{{\mathbf {C}}^n}

is arbitrarily close to 1 whenever at least one of the points is sufficiently near the boundary.
First eigenvalue of the Laplacean and torsion of parallelizable Riemannian manifolds
Authors: Ghanaat Patrick
Published: June 2010

Lower and upper bounds for the smallest positive eigenvalue of the Laplacean on a parallelizable Riemannian manifold are combined to obtain an explicit lower bound for the torsion of global orthonormal frame fields in terms of the diameter of the metric.
A necessary and sufficient condition for convergence in law of random sums of random variables under nonrandom centering
Authors: Finkelstein Mark , Tucker Howard G.
Published: June 2010

Let

{

X
n

}

\{X_n\}

be a sequence of independent, identically distributed (i.i.d.) random variables with common mean

μ
≠
0

\mu \ne 0

and variance

σ
2

>
0

\sigma ^2 > 0

. Let

{

S
n

}

\{S_n\}

be a sequence of nonnegative integer-valued random variables such that for each

n
n

the random variables

S
n

S_n

,

X
1

X_1

,

X
2

X_2

, … are independent. Then
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper X 1 plus midline-horizontal-ellipsis plus upper X Subscript upper S Sub Subscript n Subscript Baseline minus n mu right-parenthesis slash StartRoot n sigma squared EndRoot right-arrow Overscript script upper L Endscripts">

(

X
1

+
⋯
+

X

S
n

−
n
μ
)

/

n

σ
2

→

L

(X_1 + \dots + X_{S_n} - n \mu ) / \sqrt {n\sigma ^2} \stackrel {\mathcal {L}}{\rightarrow } {}

(some)

Z
Z

if and only if

(

S
n

−
n
)

/

n

→

L

(S_n - n)/\sqrt {n} \stackrel {\mathcal {L}}{\rightarrow } {}

(some)

U
U

, in which case the distribution of

Z
Z

is that of

X
+
Y

X+Y

, where

X
X

and

Y
Y

are independent random variables,

X
X

being

N

(
0
,
1
)

\mathcal {N}(0, 1)

and

Y
Y

having the same distribution as

μ
U

/

σ

\mu U/\sigma

.
Homology of branched cyclic covers of knots
Authors: Ocken Stanley
Published: June 2010

This paper presents a new formula for the first integral homology group of the branched cyclic

p
p

-fold cover

Σ
p

{\Sigma _p}

of a knot

K
K

in the

3
3

-sphere. Given a diagram of

K
K

with

k
k

crossings, let

A
(
t
)

A(t)

be the

(
k
−
1
)
×
(
k
−
1
)

(k - 1) \times (k - 1)

Alexander matrix of the diagram. Let

C
=
A

(
1

)

−
1

A
(
0
)

C = A{(1)^{ - 1}}A(0)

, and let

I
I

be the identity matrix. Then

(
C
−
I

)
p

−

C
p

{(C - I)^p} - {C^p}

is a presentation matrix for

H
1

(

Σ
p

)

{H_1}({\Sigma _p})

.
On nonselfadjoint operator algebras
Authors: Effros Edward G. , Ruan Zhong-Jin
Published: June 2010

The

M
M

-ideals in a (not necessarily self-adjoint) unital operator algebra are the closed two sided ideals containing a contractive relative identity. The spatial tensor product of unital operator algebras need not be a minimal matricial cross-norm tensor product.
A spread relation for entire functions with negative zeros
Authors: Abi-Khuzam Faruk F.
Published: June 2010

Let

g
g

be a canonical product having only real negative zeros and nonintegral order

λ
\lambda

, and let

ϕ
\phi

be the set function defined by

2
π
ϕ
(
E
)
=

∫
E

π
λ
csc
⁡
π
λ
cos
⁡
λ
θ
d
θ

2\pi \phi (E) = {\smallint _E}\pi \lambda \csc \pi \lambda \cos \lambda \theta d\theta

. It is shown that if

E
(
r
)

E(r)

is the set of values of

θ
∈
(
−
π
,
π
]

\theta \in ( - \pi ,\pi ]

where

|

g
(
r

e

i
θ

)

|

≥
1
,

r
n

|g(r{e^{i\theta }})| \geq 1,{r_n}

is a sequence of Polya peaks of

g
g

and

δ
\delta

is the deficiency of the value zero of

g
g

then

ϕ
(
E
(

r
n

)
)
≥
2

(
1
−
δ

)

−
1

\phi (E({r_n})) \geq 2{(1 - \delta )^{ - 1}}

. This inequality leads to a sharp spread relation for

g
g

.
Convergence of the Schur algorithm
Authors: Njåstad Olav
Published: June 2010

Convergence of the Schur algorithm outside the unit circle is discussed with the aid of convergence theory for Schur continued fractions.
On contractions without disjoint invariant subspaces
Authors: Takahashi Katsutoshi
Published: June 2010

Assume

T
T

is a contraction with the following property: there exists an operator

X
X

with dense range such that

X
T
=
W
X

XT = WX

where

W
W

is a bilateral shift. We give a necessary and sufficient condition that

T
T

has no disjoint invariant subspaces.
Pseudoholomorphicity of closed minimal surfaces in constantly curved 4-spaces
Authors: Yau Chi-Ming
Published: June 2010

The twistor lifts of a minimal surface in a constantly curved

4
4

-space are studied. Computing the Laplacian of the length of their differentials provides a topological condition for pseudoholomorphicity. Geometric conditions for holomorphicity of surfaces in flat spaces are found.
Connected plane sets which contain no nondegenerate connected simple graph
Authors: Garrett B. D.
Published: June 2010

Open questions are answered by showing that, if for each vertical line

L
L

in the plane,

1
>

k
L

≤
c

1 > {k_L} \leq c

is a cardinal number, there is a connected subset

H
H

of the plane such that, if

L
L

is a vertical line, then

L
∩
H

L \cap H

has cardinality

k
L

{k_L}

and, if

g
g

is a nondegenerate connected subset of

H
H

, then

g
g

contains two points of some vertical line.
The de Branges-Rovnyak model
Authors: Guyker James
Published: June 2010

A characterization, extending results of A. Beurling, L. de Branges and J. Rovnyak, of those Hilbert spaces of formal power series, which are isometrically equal to a de Branges-Rovnyak (scalar-valued) function space

H

(
b
)

\mathcal {H}(b)

, is obtained.
An inequality with applications to the subellipticity of the \overline∂-Neumann problem
Authors: Ho Lop-Hing
Published: June 2010

We prove an interesting inequality in this note. This inequality will be used to remove an unnecessary assumption in [2]. That paper dealt with the sufficient condition for the subellipticity of the

∂
¯

\bar \partial

-Neumann problem on nonpseudoconvex domains. We will then state the revised theorem and show why the original assumption can be removed.
Boundaries and modular ideals on locally compact groups
Authors: Moran William , Willis George A.
Published: June 2010

The purpose of this paper is to exhibit an example of a modular ideal of the form

L
1

(
G
)
∗
(
δ
(
e
)
−
μ
)

{L^1}(G) * (\delta (e) - \mu )

, where

μ
\mu

is a probability measure on the locally compact group

G
G

which has all of its convolution powers purely singular.
A note on the Jacobian condition and two points at infinity
Authors: McKay James H. , Wang Stuart Sui Sheng
Published: June 2010

If two polynomials

F
F

and

G
G

satisfy the Jacobian condition and the Newton polygon of

F
F

has an edge of negative slope, then the sum of terms of

F
F

along this edge has at most two distinct irreducible factors and their exponents must be different. Moreover, the slope is either a (negative) integer and the edge touches the

y
y

-axis or a (negative) Egyptian fraction and the edge touches the

x
x

-axis. Furthermore, there is an elementary automorphism which reduces the size of the Newton polygon.
Maximal triangular subalgebras need not be closed
Authors: Poon Yiu Tung
Published: June 2010

We give an example to show that a maximal triangular subalgebra need not be closed.
A note on linear automorphisms over 𝑅
Authors: Hajja Mowaffaq
Published: June 2010

Let

K
K

be a rational (= purely transcendental) extension of (the field)

k
k

, and let

s
s

be a

k
k

-automorphism of

K
K

of finite order. Let

s
s

be linear in the sense that

K
K

has a base

B
B

(i.e., a transcendence basis

B
B

with

K
=
k
(
B
)

K = k(B)

) for which the

k
k

-submodule

Σ
(
k
b
:
b
∈
B
)

\Sigma (kb:b \in B)

of

K
K

generated by

B
B

is stabilized by

s
s

. In [1, Question 6], it is asked whether

s
s

is completely determined by its order (and

tr
.

deg
k

(
K
)

\operatorname {tr} .{\deg _k}(K)

) and it is proved that, when

k
k

is the complex number field

C

{\mathbf {C}}

, then the answer to this question is affirmative iff

tr
.

deg

C

(
K
)
>
1

\operatorname {tr} .{\deg _{\mathbf {C}}}(K) > 1

[1, Corollary 9, Question 6 and Lemma 7]. In this paper, we solve the problem for the field

R

{\mathbf {R}}

of real numbers under the condition that

tr
.

deg

R

(
K
)

\operatorname {tr} .{\deg _{\mathbf {R}}}(K)

is

≠
2
,
3

\ne 2,3

. For

tr
.

deg

R

(
K
)
=
2

or

3

\operatorname {tr} .{\deg _{\mathbf {R}}}(K) = 2\;{\text {or}}\;3

, the problem remains open.
Invariant signed measures and the cancellation law
Authors: Laczkovich M.
Published: June 2010

Let

X
X

be a set, and let the group

G
G

act on

X
X

. We show that, for every

A
,
B
⊂
X

A,B \subset X

, the following are equivalent: (i)

A
A

and

B
B

are

G
G

-equidecomposable; and (ii)

ϑ
(
A
)
=
ϑ
(
B
)

\vartheta (A) = \vartheta (B)

for every

G
G

-invariant finitely additive signed measure

ϑ
\vartheta

. If the sets and the pieces of the decompositions are restricted to belong to a given

G
G

-invariant field

A

\mathcal {A}

, then

(

i

)
⇔
(

ii

)

({\text {i}}) \Leftrightarrow ({\text {ii}})

if and only if the cancellation law

(
n
[
A
]
=
n
[
B
]
⇒
[
A
]
=
[
B
]
)

(n[A] = n[B] \Rightarrow [A] = [B])

holds in the space

(
X
,
G
,

A

)

(X,G,\mathcal {A})

. We show that the cancellation law may fail even if the transformation group

G
G

is Abelian.
On the semiring 𝐿⁺(𝐶₀(𝑋))
Authors: Chan Jor-Ting
Published: June 2010

Let

X
X

and

Y
Y

be locally compact Hausdorff spaces. Let

C
0

(
X
)

{C_0}(X)

(resp.

C
0

(
Y
)

{C_0}(Y)

) denote the Banach space of all continuous functions on

X
X

vanishing at infinity on

X
X

(resp.

Y
Y

) and

L
+

(

C
0

(
X
)
)

{L^ + }({C_0}(X))

(resp.

L
+

(

C
0

(
Y
)
)

{L^ + }({C_0}(Y))

) the semiring of positive operators on

C
0

(
X
)

{C_0}(X)

(resp.

C
0

(
Y
)

{C_0}(Y)

). We prove that if there exists a semiring isomorphism

φ
\varphi

from

L
+

(

C
0

(
X
)
)

{L^ + }({C_0}(X))

onto

L
+

(

C
0

(
Y
)
)

{L^ + }({C_0}(Y))

, then

X
X

and

Y
Y

are homeomorphic. If

X
X

and

Y
Y

are assumed to be compact then the same conclusion holds under the milder condition that

φ
\varphi

is an affine isomorphism and

φ
(

I

C
(
X
)

)

\varphi ({I_{C(X)}})

is order bounded.
Asymptotic behavior of stable manifolds
Authors: Fečkan Michal
Published: June 2010

The relation between local stable manifolds of an ordinary differential equation and its discretization is studied. We show that a local stable manifold of a hyperbolic fixed point of an ordinary differential equation is the limit of local stable manifolds of the same fixed point of its discretizations as the discretization parameter

h
>
0

h > 0

approaches 0.
Equivalence of variational inequalities with Wiener-Hopf equations
Authors: Shi Peter
Published: June 2010

We show that a variational inequality is equivalent to a generalized Wiener-Hopf equation in the sense that, if one of them has a solution so does the other one. Moreover, their solutions can be transformed to each other by a simple formula. Applications are considered.
The relationships of spans of convex continua in 𝑅ⁿ
Authors: West Thelma
Published: June 2010

It has been conjectured that

σ
∗

(
X
)
≥

1
2

σ
0
∗

(
X
)

{\sigma ^ * }(X) \geq \tfrac {1}{2}\sigma _0^ * (X)

for each nonempty connected metric space

X
X

. In this paper we show that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma Superscript asterisk Baseline left-parenthesis upper X right-parenthesis greater-than-or-equal-to StartFraction StartRoot 13 EndRoot Over 4 EndFraction sigma 0 Superscript asterisk Baseline left-parenthesis upper X right-parenthesis">

σ
∗

(
X
)
≥

13

4

σ
0
∗

(
X
)

{\sigma ^ * }(X) \geq \tfrac {{\sqrt {13} }}{4}\sigma _0^ * (X)

for each convex continuum

X
X

in

R
n

{R^n}

. We also show that under certain conditions a lower bound for the ratio

σ
∗

(
X
)

/

σ
0
∗

(
X
)

{\sigma ^ * }(X)/\sigma _0^ * (X)

is larger than

13

4

\tfrac {{\sqrt {13} }}{4}

. It has also been conjectured that

σ
∗

(
X
)
≥
σ
(
X
)

/

2

{\sigma ^ * }(X) \geq \sigma (X)/2

and that

σ
0
∗

(
X
)
≥

σ
0

(
X
)

/

2

\sigma _0^ * (X) \geq {\sigma _0}(X)/2

for each nonempty connected metric space

X
X

. We show that these two inequalities hold when

X
X

is a convex continuum in

R
n

{R^n}

.
Simply connected manifolds with no conjugate points which are flat outside a compact set
Authors: Croke Christopher B.
Published: June 2010

In this note we improve a previous result to show that euclidean

n
n

-space

(
n
≥
3
)

(n \geq 3)

is the only simply connected manifold without conjugate points which is flat outside a compact set.
Sierpiński sets and strong first category
Authors: Jasiński Jakub , Weiss Tomasz
Published: June 2010

We prove that if

S
S

is a Sierpinski set and

N
⊆

R

N \subseteq \mathbb {R}

is an

F
σ

{F_\sigma }

set of measure zero, then

(
N
+
t
)
∩
S
=
∅

(N + t) \cap S = \emptyset

for some

t
∈

R

t \in \mathbb {R}

. A similar result holds for generalized Sierpinski sets under Martin’s Axiom.
Carleson measures in Hardy and weighted Bergman spaces of polydiscs
Authors: Jafari F.
Published: June 2010

The importance of theorems on Carleson measures has been well recognized [3]. In [1] Chang has given a characterization of the bounded measures on

L
p

(

T
n

)

{L^p}({T^n})

using what one may characterize as the bounded identity operators from Hardy spaces of polydiscs in

L
p

{L^p}

spaces. In [4] Hastings gives a similar result for (unweighted) Bergman spaces of polydiscs. In this paper we characterize the bounded identity operators from weighted Bergman spaces of polydiscs into

L
p

{L^p}

spaces, and classify those operators which are compact on the Hardy and weighted Bergman spaces in terms of Carleson-type conditions. We give two immediate applications of these results here, and a much broader class of applications elsewhere [5].
Ordered rings over which output sets are recursively enumerable sets
Authors: Michaux Christian
Published: June 2010

In a recent paper [BSS], L. Blum, M. Shub, and S. Smale developed a theory of computation over the reals and over commutative ordered rings; in

§
9

\S 9

of [BSS] they showed that over the reals (and over any real closed field) the class of recursively enumerable sets and the class of output sets are the same; it is a question (Problem 9.1 in [BSS]) to characterize ordered rings with this property (abbreviated by O = R.E. here). In this paper we prove essentially that in the class of (linearly) ordered rings of infinite transcendence degree over

Q

\mathbb {Q}

, that are dense (for the order) in their real closures, only real closed fields have property O = R.E.
Principal distributions for almost unperturbed Schrödinger pairs of operators
Authors: Xia Daoxing
Published: June 2010

The relation between the principal distribution for an almost unperturbed Schrödinger pair operators

{
U
,
V
}

\{ U,V\}

and the unitary operator

W
W

satisfying

V
=

W

−
1

U
W

V = {W^{ - 1}}UW

is found.
Comparison theorems for the 𝜈-zeroes of Legendre functions 𝑃^{𝑚}_{𝜈}(𝑧₀) when -1<𝑧₀<1
Authors: Baginski Frank E.
Published: June 2010

We consider the problem of ordering the elements of

{

ν
j
m

(

z
0

)
}

\{ \nu _j^m({z_0})\}

, the set of

ν
\nu

-zeroes of Legendre functions

P
ν
m

(

z
0

)

P_\nu ^m({z_0})

for

m
=
0
,
1
,
…

m = 0,1, \ldots

and

z
0

∈
(
−
1
,
1
)

{z_0} \in ( - 1,1)

. In general, we seek to determine conditions on

(
m
,
j
)

(m,j)

and

(
n
,
i
)

(n,i)

under which we can assert that

ν
j
m

>

ν
i
n

\nu _j^m > \nu _i^n

. A number of such results were established in [2] for

z
0

∈
[
0
,
1
)

{z_0} \in [0,1)

, and in the work that we present here we extend a number of these to the case

z
0

∈
(
−
1
,
1
)

{z_0} \in ( - 1,1)

. In addition, we prove

ν

j
+
1

m

>

ν
j

m
+
2

\nu _{j + 1}^m > \nu _j^{m + 2}

for

z
0

∈
(
−
1
,
0
)

{z_0} \in ( - 1,0)

and

ν
2
3

>

ν
1
6

\nu _2^3 > \nu _1^6

for

z
0

∈
(
−
1
,
1
)

{z_0} \in ( - 1,1)

. Using the results established here and in [2], we are able to determine the ordering of the first eleven

ν
\nu

-zeroes of

P
ν
m

(

z
0

)

P_\nu ^m({z_0})

for

0
>

z
0

>
1

0 > {z_0} > 1

and show that the twelfth

ν
\nu

-zero is not necessarily distinct.
𝛼-invariant and 𝑆¹ actions
Authors: Ono Kaoru
Published: June 2010

If a closed spin manifold admits an

S
1

{S^1}

action of odd type, then its

α
\alpha

-invariant vanishes.
The second Birkhoff theorem for optical Hamiltonian systems
Authors: Polterovich Leonid
Published: June 2010

Consider a smooth Hamiltonian function on the cotangent bundle of the

n
n

-dimensional torus such that its restriction on every fiber is strictly convex. Let

L
L

be a Lagrange invariant torus of the Hamiltonian flow which is homologous to the zero section. We show that, under some assumptions,

L
L

is a smooth section of the cotangent bundle.
Differentiable functions which do not satisfy a uniform Lipschitz condition of any order
Authors: Hata Masayoshi
Published: June 2010

The aim of this paper is to construct two kinds of absolutely continuous functions. One is differentiable everywhere but does not satisfy a uniform Lipschitz condition of any order on some large class of subintervals, while the other is differentiable almost everywhere but does not satisfy a uniform Lipschitz condition of any order on any subintervals.
On the Diophantine equation ∑ⁿᵢ₌₁𝑥ᵢ/𝑑ᵢ≡0 (mod 1)
Authors: Sun Qi , Wan Da Qing
Published: June 2010

Let

d
1

,
…
,

d
n

{d_1}, \ldots ,{d_n}

be

n
n

positive integers. The purpose of this note is to study the number of solutions and the least solutions of the following diophantine equation:
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis 1 right-parenthesis StartFraction x 1 Over d 1 EndFraction plus midline-horizontal-ellipsis plus StartFraction x Subscript n Baseline Over d Subscript n Baseline EndFraction identical-to 0 left-parenthesis mod 1 right-parenthesis comma 1 less-than-or-equal-to x Subscript i Baseline less-than-or-equal-to d Subscript i Baseline minus 1 comma">

(
1
)

x
1

d
1

+
⋯
+

x
n

d
n

≡
0
(
mod
1
)
,

1
≤

x
i

≤

d
i

−
1
,

(1)\quad \frac {{{x_1}}}{{{d_1}}} + \cdots + \frac {{{x_n}}}{{{d_n}}} \equiv 0(\bmod 1),\quad 1 \leq {x_i} \leq {d_i} - 1,

\]
which arises from diagonal hypersurfaces over a finite field. In particular, we determine all the

d
i

{d_i}

’s for which (1) has a unique solution.
Comaximizable primes
Authors: Heitmann Raymond C. , McAdam Stephen
Published: June 2010

Let

P
1

,
…
,

P
n

(

n
≥
2

)

{P_1}, \ldots ,{P_n}\left ( {n \geq 2} \right )

be not necessarily distinct nonzero prime ideals in the Noetherian, but not Henselian, domain

R
R

. We show that there is a finitely generated integral extension domain

T
T

of

R
R

, containing distinct, pairwise comaximal prime ideals

Q
1

,
…
,

Q
n

{Q_1}, \ldots ,{Q_n}

lying over

P
1

,
…
,

P
n

{P_1}, \ldots ,{P_n}

respectively.
Explicit construction of universal operator algebras and applications to polynomial factorization
Authors: Blecher David P. , Paulsen Vern I.
Published: June 2010

Using the characterization of unital operator algebras developed in [6], we give explicit internal definitions of the free product and the maximal operator-algebra tensor product of operator algebras and of the group operator algebra

OA

(
G
)

{\text {OA}}(G)

of a discrete semigroup

G
G

(if

G
G

is a discrete group, then

OA

(
G
)

{\text {OA}}(G)

coincides with the group

C
∗

{C^ * }

-algebra

C
∗

(
G
)
)

{C^*}(G))

). This approach leads to new factorization theorems for polynomials in one and two variables.
Counterexamples concerning bitriangular operators
Authors: Lambrou M. S. , Longstaff W. E.
Published: June 2010

An operator on a separable Hilbert space is called bitriangular if it and its adjoint have upper triangular representations with respect to two (perhaps different) orthonormal bases. Although bitriangular operators have some tractable properties and seem to be the right context for generalization of matrices to infinite dimensions, we give counterexamples to various open problems regarding this class of operators. The counterexamples make use of a property that an

M
M

-basis may or may not have.
What makes 𝑇𝑜𝑟^{𝑅}₁(𝑅/𝐼,𝐼) free?
Authors: Goto Shiro , Suzuki Naoyoshi
Published: June 2010

Let

I
I

be a nonprincipal ideal in a Noetherian local ring

R
R

and let

H
1

(
I
)

{H_1}(I)

be the first homology module of the Koszul complex

K
.
(
I
)

K.(I)

associated with a minimal basis of

I
I

. Then

T
:=

Tor

1
R

(
R

/

I
,
I
)

T: = {\text {Tor}}_1^R(R/I,I)

is a free

R

/

I

R/I

-module if and only if both the

R

/

I

R/I

-modules

I

/

I
2

I/{I^2}

and

H
1

(
I
)

{H_1}(I)

are free. When this is 2 2 the case, we have a canonical decomposition

T
≅

Λ
2

(
I

/

I
2

)
⊕

H
1

(
I
)

T \cong {\Lambda ^2}(I/{I^2}) \oplus {H_1}(I)

as well as the equality

rank

R

/

I

T
=

β
2

(
R

/

I
)

{\text {rank}_{R/I}}T = {\beta _2}(R/I)

. (Here

β
2

(
R

/

I
)

{\beta _2}(R/I)

denotes the second Betti number of the

R
R

-module

R

/

I

R/I

.) Some consequences are discussed too.
Fonctions qui opérent sur les espaces de Besov
Authors: Bourdaud Gérard , Kateb Dalila
Published: June 2010

On caractérise les fonctions qui opèrent, par composition à gauche, sur l’espace de Besov

B

p
,
q

s

(

R

n

)

B_{p,q}^s({\mathbb {R}^n})

et sur l’espace de Triebel-Lizorkin

F

p
,
q

s

(

R

n

)

F_{p,q}^s({\mathbb {R}^n})

,pour

0
>
s
>
1

et

s
≠
n

/

p

0 > s > 1{\text {et}}s \ne n/p

. Ce sont les fonctions, s’annulant en zéro, lipschitziennes (pour

s
>
n

/

p

s > n/p

) ou localement lipschitziennes (pour

s
>
n

/

p

s > n/p

).
Bielliptic curves and symmetric products
Authors: Harris Joe , Silverman Joe
Published: June 2010

We show that the twofold symmetric product of a nonhyperelliptic, nonbielliptic curve does not contain any elliptic curves. Applying a theorem of Faltings, we conclude that such a curve defined over a number field

K
K

has only finitely many points over all quadratic extensions of

K
K

. We illustrate our theory with the modular curves

X
0

(
N
)
,

X
1

(
N
)
,
X
(
N
)

{X_0}(N),{X_1}(N),X(N)

.
On the class 𝐴_{1,ℵ₀}
Authors: Prunaru Bebe
Published: June 2010

The solvability of certain systems of simultaneous equations in the predual of a dual operator algebra is studied. The main result is a geometric criterion for membership in the class

A

1
,

ℵ
0

{A_{1,{\aleph _0}}}

.
On the existence of weakly 𝑛-dimensional spaces
Authors: van Mill Jan , Pol Roman
Published: June 2010

Using a certain method for constructing peculiar large-dimensional spaces in every compactum with sufficiently large dimension, we present for every

n
n

an easy example of a weakly

n
n

-dimensional space.
On the compositum of two power series rings
Authors: Abhyankar Shreeram S. , Heinzer William , Wiegand Sylvia
Published: June 2010

This paper concerns subrings of the bivariate power series ring over a field.
A fixed point approach to homological perturbation theory
Authors: Barnes Donald W. , Lambe Larry A.
Published: June 2010

We show that the problem addressed by classical homological perturbation theory can be reformulated as a fixed point problem leading to new insights into the nature of its solutions. We show, under mild conditions, that the solution is essentially unique.
Additive properties of multiplicative subgroups of finite index in fields
Authors: Berrizbeitia Pedro
Published: June 2010

Gallai’s theorem, an

n
n

-dimensional generalization of Van der Waerden’s theorem on arithmetic progression, is used to prove the following theorem: Let

F
F

be a field and

G
⊆

F
∗

G \subseteq {F^ * }

a subgroup of finite index

n
n

. There is a positive integer

N
N

, which depends only on

n
n

, so that if

Char

F
=
0

{\text {Char}}F = 0

or

Char

F
≥
N

{\text {Char}}F \geq N

, then

G
−
G
=
F

G - G = F

.
Finitely embedded commutative rings
Authors: Faith Carl
Published: June 2010

A theorem of Ginn and Moss [G-M] states that a right finitely embedded (= with finite essential right socle) two-sided Noetherian ring is Artinian. An example of Schelter and Small [S-S] can be applied to show that the theorem fails for right finitely embedded rings with the ascending chain conditions on right and left annihilators. We show here, however, that finitely embedded commutative rings with the acc on annihilator (= acc

⊥
\bot

) are Artinian. The proof uses the author’s characterization in [Fl] of acc

⊥
\bot

rings, and the Levitzki [L] and Herstein-Small [H-S] theorem on the nilpotency of nil ideals in

2
2

-sided ace

⊥
\bot

rings. A corollary is a result of Shizhong [Sh] that shows commutative subdirectly irreducible acc

⊥
\bot

rings are QF.
Henselian rings and Weierstrass polynomials
Authors: Nashier Budh
Published: June 2010

We give two characterizations of a one-dimensional Henselian domain. If

(

A
,

M

)

\left ( {A,\mathcal {M}} \right )

is a local domain of Krull dimension at least two, or if

(

A
,

M

)

\left ( {A,\mathcal {M}} \right )

is a one-dimensional Henselian local domain, then a polynomial

f
f

in

A

[
T
]

A\left [ T \right ]

is Weierstrass if and only if

(

M

,
T

)

\left ( {\mathcal {M},T} \right )

is the only maximal ideal of

A

[
T
]

A\left [ T \right ]

that contains

f
f

.
Array convergence of functions of the first Baire class
Authors: Knaust Helmut
Published: June 2010

We show that every array

(
x
(
i
,
j
)
:
1
≤
i
>
j
>
∞
)

(x(i,j):1 \leq i > j > \infty )

of elements in a pointwise compact subset of the Baire-

1
1

functions on a Polish space, whose iterated pointwise limit

lim
i

lim
j

x
(
i
,
j
)

{\lim _i}{\lim _j}x(i,j)

exists, is converging Ramsey-uniformly. An array

(
x

(
i
,
j

)

i
>
j

)

(x{(i,j)_{i > j}})

in a Hausdorff space

T
T

is said to converge Ramsey-uniformly to some

x
x

in

T
T

, if every subsequence of the positive integers has a further subsequence

(

m
i

)

({m_i})

such that every open neighborhood

U
U

of

x
x

in

T
T

contains all elements

x
(

m
i

,

m
j

)

x({m_i},{m_j})

with

i
>
j

i > j

except for finitely many

i
i

.
Monotonicity of the forcing term and existence of positive solutions for a class of semilinear elliptic problems
Authors: Sudhasree Gadam
Published: June 2010

We study the existence of positive solutions to the equationΔu+f(u)+λg(‖x‖)=0\Delta u + f(u) + \lambda g(\left \| x \right \|) = 0in the unit ball inRN{\mathbb {R}^N}with Dirichlet boundary conditions, whereffis superlinear withf(0)=0f(0) = 0andλ\lambdais a real parameter. We prove that ifggis monotonically increasing, then there exists anα>0\alpha > 0such that forλ>α\lambda > \alphathe above equation has no positive solution. This is in contrast to the case ofggmonotonically decreasing, where positive solutions exist for all negative values ofλ\lambda.
Conditional analytic Feynman integrals on abstract Wiener spaces
Authors: Chung Dong Myung
Published: June 2010

In this paper we define the concept of a conditional analytic Feynman integral of a function

F
F

on an abstract Wiener space

B
B

given a function

X
X

and then establish the existence of the conditional Feynman integral for all functions in the Fresnel class on

B
B

. We also use the conditional Feynman integral to provide a fundamental solution to the Schrödinger equation.
Determinant expression of Selberg zeta functions. III
Authors: Koyama Shin-ya
Published: June 2010

We will prove that for

P
S
L
(
2

,

R

)

\operatorname {PSL(2},{\mathbf {R}})

and its cofinite subgroup, the Selberg zeta function is expressed by the determinant of the Laplacian. We will also give an explicit calculation in case of congruence subgroups, and deduce that the part of the determinant of the Laplacian composed of the continuous spectrum is expressed by Dirichlet

L
L

-functions.
On purity of inertia
Authors: Harbater David
Published: June 2010

This paper considers the phenomenon of inertia groups jumping at regular points of the branch locus of a cover, especially in mixed characteristic. After giving conditions under which this cannot occur, these ideas are applied to the problem of obtaining groups as Galois groups of unramified covers of the affine line in finite characteristic.
A second category set with only first category functions
Authors: Komjáth P.
Published: June 2010

If the existence of a measurable cardinal is consistent then it is consistent in that there is a second category set

A
⊆
R

A \subseteq R

such that every

A
→
A

A \to A

function, as a subset of

R
2

{R^2}

, is of first category. Some other connected results are also proved.
Proper knots in open 3-manifolds have locally unknotted representatives
Authors: Nanyes Ollie
Published: June 2010

Churchard and Spring [1] conjectured that all proper knots in open

3
3

-manifolds are equivalent to (properly isotopic to) a locally unknotted proper knot. This paper proves the conjecture.
An example of a Hilbert transform
Authors: Samotij Krzysztof
Published: June 2010

We construct a nonnegative integrable function on the real line

R

\mathbf {R}

whose Hilbert transform cannot be almost everywhere dominated by the HardyLittlewood maximal function of any finite measure on

R

\mathbf {R}

.
Common fixed points in hyperbolic Riemann surfaces and convex domains
Authors: Abate Marco , Vigué Jean-Pierre
Published: June 2010

In this paper we prove that a commuting family of continuous self-maps of a bounded convex domain in

C

n

{\mathbb {C}^n}

which are holomorphic in the interior has a common fixed point. The proof makes use of three basic ingredients: iteration theory of holomorphic maps, a precise description of the structure of the boundary of a convex domain, and a similar result for commuting families of self-maps of a hyperbolic domain of a compact Riemann surface.