bluuebunny/crossref_metadata_2025 huggingface dataset:
Pseudocharacters on free semigroups invariant with respect to their automorphism groups
Authors: Faĭziev V.
Published: July 2002

Let

F

\mathcal {F}

be a free semigroup and let

A
A

be an automorphism group of

F

\mathcal {F}

. A description is given of the space of real functions

φ
\varphi

on semigroup

F

\mathcal {F}

satisfying the following conditions: 1) the set

{
φ
(
x
y
)
−
φ
(
x
)
−
φ
(
y
)
;

x
,
y
∈

F

}

\{\varphi (xy)-\varphi (x)-\varphi (y);\,\, x,y\in \mathcal {F} \}

is bounded; 2)

φ
(

x

n

)
=
n
φ
(
x
)

\varphi (x^{n}) = n\varphi (x)

for any

x
∈

F

x\in \mathcal {F}

and

n
∈
N

n\in N

; 3)

φ
(

x

τ

)
=
φ
(
x
)

∀
x
∈

F

\varphi (x^{\tau }) = \varphi (x) \quad \forall x\in \mathcal {F}

, and

∀
τ
∈
A

\forall \tau \in A

.
Minkowski’s inequality for two variable difference means
Authors: Losonczi László , Páles Zsolt
Published: July 2002

We study Minkowski’s inequality
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper D Subscript a b Baseline left-parenthesis x 1 plus x 2 comma y 1 plus y 2 right-parenthesis less-than-or-equal-to upper D Subscript a b Baseline left-parenthesis x 1 comma y 1 right-parenthesis plus upper D Subscript a b Baseline left-parenthesis x 2 comma y 2 right-parenthesis left-parenthesis x 1 comma x 2 comma y 1 comma y 2 element-of double-struck upper R Subscript plus Baseline right-parenthesis">

D

a

b

(

x
1

+

x
2

,

y
1

+

y
2

)
≤

D

a

b

(

x
1

,

y
1

)
+

D

a

b

(

x
2

,

y
2

)

(

x
1

,

x
2

,

y
1

,

y
2

∈

R

+

)

D_{a\,b}(x_1+x_2, y_1+y_2)\le D_{a\,b}(x_1, y_1)+D_{a\,b}(x_2,y_2) \quad (x_1,x_2, y_1,y_2\in \mathbb R_+)

\]
and its reverse where

D

a

b

D_{a\,b}

is the difference mean introduced by Stolarsky. We give necessary and sufficient conditions (concerning the parameters

a
,
b

a,b

) for the inequality above (and for its reverse) to hold.
A note on the cohomology of finitary modules
Authors: Meierfrankenfeld U.
Published: July 2002

Let

G
G

be a group,

D
D

a division ring and

V
V

a

D
G

DG

-module.

V
V

is called finitary provided that

V

/

C
V

(
g
)

V/C_V(g)

is finite dimensional for all

g
∈
G

g\in G

. We investigate the first and second degree cohomology of finitary modules in terms of a local system for

G
G

.
Stability of the surjectivity of endomorphisms and isometries of ℬ(ℋ)
Authors: Molnár Lajos
Published: July 2002

We determine the largest positive number

c
c

with the property that whenever

Φ
,
Ψ

\Phi ,\Psi

are endomorphisms, respectively unital isometries of the algebra of all bounded linear operators acting on a separable Hilbert space,

‖
Φ
(
A
)
−
Ψ
(
A
)
‖
>
c
‖
A
‖

\| \Phi (A)-\Psi (A)\|>c\| A\|

holds for every nonzero

A
A

and

Φ
\Phi

is surjective, then so is

Ψ
\Psi

. It turns out that in the first case we have

c
=
1

c=1

, while in the second one

c
=
2

c=2

.
Metrizability of sequential topological groups with point-countable 𝑘-networks
Authors: Shibakov Alexander
Published: July 2002

We prove that a Hausdorff sequential topological group with a point-countable

k
k

-network is metrizable iff its sequential order is less than

ω

1

\omega _{1}

. In the non Hausdorff case metrizability may be replaced by

σ
\sigma

-locally finite base.
Hardy’s theorem for the 𝑛-dimensional Euclidean motion group
Authors: Sundari M.
Published: July 2002

An uncertainty principle, due to Hardy, for Fourier transform pairs on

R

\Bbb R

says that if the function

f
f

is “very rapidly decreasing”, then the Fourier transform cannot also be “very rapidly decreasing” unless

f
f

is identically zero. In this paper we state and prove an analogue of Hardy’s theorem for the

n
n

-dimensional Euclidean motion group.
A representation theorem for Schauder bases in Hilbert space
Authors: Jaffard Stephane , Young Robert
Published: July 2002

A sequence of vectors

{

f
1

,

f
2

,

f
3

,
…
}

\{f_1,f_2,f_3,\dotsc \}

in a separable Hilbert space

H
H

is said to be a Schauder basis for

H
H

if every element

f
∈
H

f\in H

has a unique norm-convergent expansion
\[

f
=
∑

c
n

f
n

.

f=\sum c_nf_n.

\]
If, in addition, there exist positive constants

A
A

and

B
B

such that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A sigma-summation StartAbsoluteValue c Subscript n Baseline EndAbsoluteValue squared less-than-or-equal-to double-vertical-bar sigma-summation c Subscript n Baseline f Subscript n Baseline double-vertical-bar squared less-than-or-equal-to upper B sigma-summation StartAbsoluteValue c Subscript n Baseline EndAbsoluteValue squared comma">

A
∑

|

c
n

|

2

≤

‖
∑

c
n

f
n

‖

2

≤
B
∑

|

c
n

|

2

,

A\sum |c_n|^2\le \left \|\sum c_nf_n\right \|^2\le B\sum |c_n|^2,

\]
then we call

{

f
1

,

f
2

,

f
3

,
…
}

\{f_1,f_2,f_3,\dotsc \}

a Riesz basis. In the first half of this paper, we show that every Schauder basis for

H
H

can be obtained from an orthonormal basis by means of a (possibly unbounded) one-to-one positive self adjoint operator. In the second half, we use this result to extend and clarify a remarkable theorem due to Duffin and Eachus characterizing the class of Riesz bases in Hilbert space.
Tight compactly supported wavelet frames of arbitrarily high smoothness
Authors: Gröchenig Karlheinz , Ron Amos
Published: July 2002

Based on Ron and Shen’s new method for constructing tight wave- let frames, we show that one can construct, for any dilation matrix, and in any spatial dimension, tight wavelet frames generated by compactly supported functions with arbitrarily high smoothness.
Remarks on the results by Koskela concerning the radial uniqueness for Sobolev functions
Authors: Mizuta Yoshihiro
Published: July 2002

In this note we aim to complete the results by Koskela concerning the radial uniqueness for Sobolev functions. Let

φ
\varphi

be a positive nonincreasing function on the interval

(
0
,
∞
)

(0,\infty )

, and let

B

\mathbf {B}

denote the unit ball of

R
n

R^n

. Consider a

p
p

-precise function

u
u

on

B

\mathbf {B}

such that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Underscript upper U left-parenthesis epsilon right-parenthesis Endscripts StartAbsoluteValue nabla u left-parenthesis x right-parenthesis EndAbsoluteValue Superscript p Baseline d x less-than-over-equals epsilon Superscript p Baseline phi left-parenthesis epsilon right-parenthesis for any epsilon greater-than 0 comma">

∫

U
(
ε
)

|

∇
u
(
x
)

|

p

d
x
≦

ε
p

φ
(
ε
)

for any 

ε
>
0

,

\int _{U(\varepsilon )} |\nabla u(x)|^p dx \leqq \varepsilon ^p \varphi (\varepsilon ) \hspace {2em} \text {for any $\varepsilon > 0$,}

\]
where

U
(
ε
)
=
{
x
∈

B

:

|

u
(
x
)

|

>
ε
}

U(\varepsilon ) = \{x \in \mathbf {B} : |u(x)|> \varepsilon \}

. We give conditions on

φ
\varphi

which assure that

u
=
0

u = 0

whenever

u
u

has vanishing fine boundary limits on a set of positive

p
p

-capacity. We are also concerned with the sharpness.
Pseudo-uniform convergence, a nonstandard treatment
Authors: Vakil Nader
Published: July 2002

We introduce and study the notion of pseudo-uniform convergence which is a weaker variant of quasi-uniform convergence. Applications include the following nonstandard characterization of weak convergence. Let

X
X

be an infinite set,

B
(
X
)

B(X)

the Banach space of all bounded real-valued functions on

X
,

X,

{

f

n

:
n
∈
N
}

\{f_{n}: n\in N\}

a bounded sequence in

B
(
X
)
,

B(X),

and

f
∈
B
(
X
)
.

f\in B(X).

Then the sequence converges weakly to

f
f

if and only if the convergence is pointwise on

X
X

and, for each strictly increasing function

σ
:
N
→
N

\sigma :N\to N

, each

x

∈

∗

X

x\in ^{*}X

, and each

n

∈

∗

N

∞

n\in ^{*}N_{\infty }

, there is an unlimited

m
≤
n

m\leq n

such that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="Superscript asterisk Baseline f Sub Superscript asterisk Subscript sigma left-parenthesis m right-parenthesis left-parenthesis x right-parenthesis asymptotically-equals Superscript asterisk Baseline f left-parenthesis x right-parenthesis">

∗

f

∗

σ
(
m
)

(
x
)

≃

∗

f
(
x
)

^{*}f_{ ^{*}\sigma (m)}(x) \simeq ^{*}f(x)

.
A theorem of the alternative in Banach lattices
Authors: Lasserre Jean
Published: July 2002

We consider a linear sytem in a Banach lattice and provide a simple theorem of the alternative (or Farkas lemma) without the usual closure condition.
Applications of pseudo-monotone operators with some kind of upper semicontinuity in generalized quasi-variational inequalities on non-compact sets
Authors: Chowdhury Mohammad , Tan Kok-Keong
Published: July 2002

Let

E
E

be a topological vector space and

X
X

be a non-empty subset of

E
E

. Let

S
:
X
→

2

X

S:X\rightarrow 2^{X}

and

T
:
X
→

2

E

∗

T:X\rightarrow 2^{E^{*}}

be two maps. Then the generalized quasi-variational inequality (GQVI) problem is to find a point

y
^

∈
S
(

y
^

)

\hat y\in S(\hat y)

and a point

w
^

∈
T
(

y
^

)

\hat w\in T(\hat y)

such that

R
e
⟨

w
^

,

y
^

−
x
⟩
≤
0

Re\langle \hat w,\hat y-x\rangle \leq 0

for all

x
∈
S
(

y
^

)

x\in S(\hat y)

. We shall use Chowdhury and Tan’s 1996 generalized version of Ky Fan’s minimax inequality as a tool to obtain some general theorems on solutions of the GQVI on a paracompact set

X
X

in a Hausdorff locally convex space where the set-valued operator

T
T

is either strongly pseudo-monotone or pseudo-monotone and is upper semicontinuous from

c
o
(
A
)

co(A)

to the weak

∗

^{*}

-topology on

E

∗

E^{*}

for each non-empty finite subset

A
A

of

X
X

.
On the extended Hilbert’s inequality
Authors: Mingzhe Gao , Bichen Yang
Published: July 2002

In this paper, it is shown that the extended Hilbert’s inequality for double series can be refined by the aid of the Euler-Maclaurin summation formula. The extreme cases

p
→

1
+

p\rightarrow 1^+

and

q
→
+
∞

q\rightarrow +\infty

are discussed.
A remark about Λ(𝑝)-sets and Rosenthal sets
Authors: Li Daniel
Published: July 2002

There exist

Λ
(
p
)

\Lambda (p)

-sets which are not Rosenthal sets.

Résumé. Il existe des ensembles

Λ
(
p
)

\Lambda (p)

qui ne sont pas des ensembles de Rosenthal.
Simple quotients of hyperbolic 3-manifold groups
Authors: Long D. , Reid A.
Published: July 2002

We show that hyperbolic

3
3

-manifolds have residually simple fundamental group.
A note on harmonic forms on complete manifolds
Authors: Tam Luen-fai
Published: July 2002

In this note, we will prove that under certain conditions, the space of polynomial growth harmonic functions and harmonic forms with a fixed growth rate on manifolds which are asymptotically nonnegatively curved is finite dimensional. This is a partial generalization of the works of Li and Colding-Minicozzi. We will also give an explicit estimate for the dimension in case the manifold is a complete surface of finite total curvature. This is a generalization to harmonic forms of the work of Li and the author.
A note on complete intersections of height three
Authors: Watanabe Junzo
Published: July 2002

Let

k
k

be a field of characteristic 0. If

I
⊂
k
[
x
,
y
,
z
]

I \subset k[x,y,z]

is a complete intersection generated by three homogeneous elements of degrees

d
1

,

d
2

,

d
3

d_1,d_2,d_3

with

2
≤

d
1

≤

d
2

≤

d
3

2 \le d_1 \le d_2 \le d_3

, then the reduction of

I
I

by a general linear form is minimally generated by three elements if and only if

d
3

≤

d
1

+

d
2

−
2

d_3 \le d_1+d_2-2

.
Eigenvalues of some distal functions
Authors: Egawa Jirō
Published: July 2002

In this paper we construct distal functions of another type discussed by Salehi (1991). Let

a
(
t
)

a(t)

be an almost periodic function with the mean value 0, which has unbounded integral, and

Φ
\Phi

a continuous periodic function with the prime period 1. If

Φ
\Phi

satisfies some additional condition, then

f
(
t
)
=
Φ
(

∫
0
t

a
(
s
)

d
s
)

f(t)=\Phi (\int ^t_0a(s)\,ds)

is a distal function, which is not almost periodic, and the set of eigenvalues of

f
f

is the module of

a
a

.
On complete metric spaces containing the Sierpinski curve
Authors: Prajs Janusz
Published: July 2002

It is proved that a complete metric space topologically contains the Sierpiński universal plane curve if and only if it has a subset with so-called bypass property, i.e. it has a subset

K
K

containing an arc such that for each

a
∈
K

a\in K

and for each open arc

A
⊂
K

A\subset K

with

a
∈
A

a\in A

, there exists an arbitrary small arc in

K
∖
{
a
}

K\setminus \{a\}

joining the two components of

A
∖
{
a
}

A\setminus \{a\}

.
Duality and local group cohomology
Authors: Hewitt P.
Published: July 2002

Let

G
G

be a group, let

k
k

be a field, and let

L

{\mathcal {L}}

be a local system — an upwardly directed collection of subgroups whose union is

G
G

. In this paper we give a short, elementary proof of the following result: If either

A
A

is a

k
k

-

k
G

kG

-bimodule, or else

k
k

is finite dimensional over its center, then
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E x t Subscript upper G Superscript asterisk Baseline left-parenthesis upper A comma upper B Superscript logical-or Baseline right-parenthesis equals limit Underscript left-arrow Endscripts Underscript upper L element-of script upper L Endscripts upper E x t Subscript upper L Superscript asterisk Baseline left-parenthesis upper A comma upper B Superscript logical-or Baseline right-parenthesis">

Ext

G

∗

⁡
(
A
,

B

∨

)
=

lim
←

L
∈

L

⁡

Ext

L

∗

⁡
(
A
,

B

∨

)

\operatorname {Ext}^{*}_{G}(A,B^{\vee }) =\varprojlim _{L\in \mathcal {L}} \operatorname {Ext}^{*}_{L}(A,B^{\vee })

. From this we deduce as easy corollaries some recent results of Meierfrankenfeld and Wehrfritz on the cohomology of a finitary module.
The Schatten space 𝑆₄ is a 𝑄-algebra
Authors: Le Merdy Christian
Published: July 2002

For any

1
≤
p
≤
∞

1 \leq p \leq \infty

, let

S

p

S_{p}

denote the classical

p
p

-Schatten space of operators on the Hilbert space

ℓ

2

\ell _{2}

. It was shown by Varopoulos (for

p
≥
2

p \geq 2

) and by Blecher and the author (full result) that for any

1
≤
p
≤
∞
,

S

p

1 \leq p \leq \infty , S_{p}

equipped with the Schur product is an operator algebra. Here we prove that

S

4

S_{4}

(and thus

S

p

S_{p}

for any

2
≤
p
≤
4

2 \leq p \leq 4

) is actually a

Q
Q

-algebra, which means that it is isomorphic to some quotient of a uniform algebra in the Banach algebra sense.
On component groups of 𝐽₀(𝑁) and degeneracy maps
Authors: Ling San
Published: July 2002

For an integer

M
>
1

M>1

and a prime

p
≥
5

p \geq 5

not dividing

M
M

, we study the kernel of the degeneracy map

Φ

M
p
,
p

r

→

Φ

M

p
r

,
p

\Phi _{Mp,p}^r \rightarrow \Phi _{Mp^r, p}

, where

Φ

M
p
,
p

\Phi _{Mp,p}

and

Φ

M

p
r

,
p

\Phi _{Mp^r, p}

are the component groups of

J
0

(
M
p
)

J_0(Mp)

and

J
0

(
M

p
r

)

J_0(Mp^r)

, respectively. This is then used to determine the kernel of the degeneracy map

J
0

(
M
p

)
2

→

J
0

(
M

p
2

)

J_0(Mp)^2 \rightarrow J_0(Mp^2)

when

J
0

(
M
)
=
0

J_0(M) =0

. We also compute the group structure of

Φ

M

p
2

,
p

\Phi _{Mp^2, p}

in some cases.
On a classical theorem in the theory of Fourier integrals
Authors: Sasvári Zoltán
Published: July 2002

In this note we give a short proof of a classical theorem in the theory of Fourier integrals.
Periodic solutions for nonautonomous second order systems with sublinear nonlinearity
Authors: Tang Chun-Lei
Published: July 2002

The existence and multiplicity of periodic solutions are obtained for nonautonomous second order systems with sublinear nonlinearity by using the least action principle and the minimax methods.
Discriminants of convex curves are homeomorphic
Authors: Shapiro B.
Published: July 2002

For a given real generic curve

γ
:

S

1

→

P

n

\gamma : S^{1}\to \mathbb {P}^{n}

let

D

γ

D_{\gamma }

denote the ruled hypersurface in

P

n

\mathbb {P}^{n}

consisting of all osculating subspaces to

γ
\gamma

of codimension 2. In this note we show that for any two convex real projective curves

γ

1

:

S

1

→

P

n

\gamma _{1}:S^{1}\to \mathbb {P}^{n}

and

γ

2

:

S

1

→

P

n

\gamma _{2}:S^{1}\to \mathbb {P}^{n}

the pairs

(

P

n

,

D

γ

1

)

(\mathbb {P}^{n},D_{\gamma _{1}})

and

(

P

n

,

D

γ

2

)

(\mathbb {P}^{n},D_{\gamma _{2}})

are homeomorphic.
A necessary and sufficient condition for upper hemicontinuous set-valued mappings without compact-values being upper demicontinuous
Authors: Yang Gan-Shang , Yuan George
Published: July 2002

The purpose of this article is to give a characterization of an upper hemicontinuous mapping with non-empty convex values being upper demicontinuous, i.e., we show that an upper hemicontinuous set-valued mapping with non-empty convex values (not necessarily compact-valued) is upper demicontinuous if and only if the set-valued mapping has no interior asymptotic plane.
Derived tubular strongly simply connected algebras
Authors: Barot M. , de la Peña J.
Published: July 2002

Let

A
A

be a finite dimensional algebra over an algebraically closed field

k
k

. Assume

A
=
k
Q

/

I

A=kQ/I

for a connected quiver

Q
Q

and an admissible ideal

I
I

of

k
Q

kQ

. We study algebras

A
A

which are derived equivalent to tubular algebras. If

A
A

is strongly simply connected and

Q
Q

has more than six vertices, then

A
A

is derived tubular if and only if (i) the homological quadratic form

χ
A

\chi _A

is a non-negative of corank two and (ii) no vector of

χ
A

−
1

(
1
)

\chi _A ^{-1}(1)

is orthogonal (with respect tho the homological bilinear form) to the radical of

χ
A

\chi _A

.
A 𝜅-normal, not densely normal Tychonoff space
Authors: Just Winfried , Tartir Jamal
Published: July 2002

We give an example of a

κ
\kappa

-normal space which is not densely normal.
The ideal of polynomials vanishing on a commutative ring
Authors: Gilmer Robert
Published: July 2002

We determine equivalent conditions on a commutative Artinian ring

S
S

in order that the ideal of

S
[
t
]

S[t]

consisting of polynomials that vanish on

S
S

should be principal. Our results correct an error in a paper of Niven and Warren.
Automata and transcendence of the Tate period in finite characteristic
Authors: Allouche Jean-Paul , Thakur Dinesh
Published: July 2002

Using the techniques of automata theory, we give another proof of the function field analogue of the Mahler-Manin conjecture and prove transcendence results for the power series associated to higher divisor functions

σ
k

(
n
)
=

∑

d

|

n

d
k

\sigma _k(n)=\sum _{d|n}d^k

.
The Chevalley-Warning theorem and a combinatorial question on finite groups
Authors: Sury B.
Published: July 2002

Recently, W. D. Gao (1996) proved the following theorem: For a cyclic group

G
G

of prime order, and any element

a
a

in it, and an arbitrary sequence

g
1

,
…
,

g

2
p
−
1

g_1, \ldots , g_{2p-1}

of

2
p
−
1

2p-1

elements from

G
G

, the number of ways of writing

a
a

as a sum of exactly

p
p

of the

g
i

g_i

’s is

1
1

or

0
0

modulo

p
p

according as

a
a

is zero or not. The dual purpose of this note is (i) to give an entirely different type of proof of this theorem; and (ii) to solve a conjecture of J. E. Olson (1976) by answering an analogous question affirmatively for solvable groups.
Volume growth and holonomy in nonnegative curvature
Authors: Tapp Kristopher
Published: July 2002

The volume growth of an open manifold of nonnegative sectional curvature is proven to be bounded above by the difference between the codimension of the soul and the maximal dimension of an orbit of the action of the normal holonomy group of the soul. Additionally, an example of a simply-connected soul with a non-compact normal holonomy group is constructed.
Examples of vector bundles admitting unique ASD connections on quaternion-Kähler manifolds
Authors: Nagatomo Yasuyuki
Published: July 2002

We prove a series of rigidity theorems. Examples of higher rank ASD vector bundles are given on quaternion-Kähler manifolds, which admit the one and only ASD connections modulo the gauge equivalence.
The necessary and sufficient conditions for the global stability of type-𝐾 Lotka-Volterra system
Authors: Caifeng Tu , Jifa Jiang
Published: July 2002

This paper provides necessary and sufficient conditions for the type-

K
K

Lotka-Volterra system to have a globally asymptotically stable positive steady state. The generalization of such a result is given.
Geometrical significance of the Löwner-Heinz inequality
Authors: Andruchow E. , Corach G. , Stojanoff D.
Published: July 2002

It is proven that the Löwner-Heinz inequality

‖

A

t

B

t

‖
≤
‖
A
B

‖

t

{\|A^{t}B^{t}\|\le \|AB\|^{t}}

, valid for all positive invertible operators

A
,
B

{A, B}

on the Hilbert space

H

{\mathcal H }

and

t
∈
[
0
,
1
]

{t\in [0,1]}

, has equivalent forms related to the Finsler structure of the space of positive invertible elements of

L

(

H

)

{\mathcal L (\mathcal H )}

or, more generally, of a unital

C

∗

{C^{*}}

-algebra. In particular, the Löwner-Heinz inequality is equivalent to some type of “nonpositive curvature" property of that space.
Von Neumann algebras and linear independence of translates
Authors: Linnell Peter
Published: July 2002

For

x
,
y
∈

R

x,y \in \mathbb {R}

and

f
∈

L
2

(

R

)

f \in L^2(\mathbb {R})

, define

(
x
,
y
)
f
(
t
)
=

e

2
π
i
y
t

f
(
t
+
x
)

(x,y) f(t) = e^{2\pi iyt} f(t+x)

and if

Λ
⊆

R

2

\Lambda \subseteq \mathbb {R}^2

, define

S
(
f
,
Λ
)
=
{
(
x
,
y
)
f
∣
(
x
,
y
)
∈
Λ
}

S(f, \Lambda ) = \{(x,y)f \mid (x,y) \in \Lambda \}

. It has been conjectured that if

f
≠
0

f\ne 0

, then

S
(
f
,
Λ
)

S(f,\Lambda )

is linearly independent over

C

\mathbb {C}

; one motivation for this problem comes from Gabor analysis. We shall prove that

S
(
f
,
Λ
)

S(f, \Lambda )

is linearly independent if

f
≠
0

f \ne 0

and

Λ
\Lambda

is contained in a discrete subgroup of

R

2

\mathbb {R}^2

, and as a byproduct we shall obtain some results on the group von Neumann algebra generated by the operators

{
(
x
,
y
)
∣
(
x
,
y
)
∈
Λ
}

\{(x,y) \mid (x,y) \in \Lambda \}

. Also, we shall prove these results for the obvious generalization to

R

n

\mathbb {R}^n

.
Stability of additive mappings on large subsets
Authors: Sánchez Félix
Published: July 2002

We study mappings from a group into a Banach space which are “nearly additive” on large subsets.
Periodic hyperfunctions and Fourier series
Authors: Chung Soon-Yeong , Kim Dohan , Lee Eun Gu
Published: July 2002

Every periodic hyperfunction is a bounded hyperfunction and can be represented as an infinite sum of derivatives of bounded continuous periodic functions. Also, Fourier coefficients

c

α

c_{\alpha }

of periodic hyperfunctions are of infra-exponential growth in

R

n

\mathbb {R}^{n}

, i.e.,

c

α

>

C

ϵ

e

ϵ

|

α

|

c_{\alpha }> C_{\epsilon }e^{\epsilon |\alpha |}

for every

ϵ
>
0

\epsilon >0

and every

α
∈

Z

n

\alpha \in \mathbb {Z}^{n}

. This is a natural generalization of the polynomial growth of the Fourier coefficients of distributions. To show these we introduce the space

B

L

p

\mathcal {B}_{L^{p}}

of hyperfunctions of

L

p

L^{p}

growth which generalizes the space

D

L

p

′

\mathcal {D}’_{L^{p}}

of distributions of

L

p

L^{p}

growth and represent generalized functions as the initial values of smooth solutions of the heat equation.
Local automorphisms
Authors: Crist Randall
Published: July 2002

We show that any linear map on a finite dimensional CSL algebra

A

\mathcal {A}

which at each point is equal to the value of some automorphism of

A

\mathcal {A}

is either an automorphism or can be factored as an automorphism and the transpose of a self-adjoint summand of

A

\mathcal {A}

. New examples of local mappings are constructed.
Maximal estimates for the (𝐶,𝛼) means of 𝑑-dimensional Walsh-Fourier series
Authors: Weisz Ferenc
Published: July 2002

The

d
d

-dimensional dyadic martingale Hardy spaces

H

p

H_{p}

are introduced and it is proved that the maximal operator of the

(
C
,
α
)

(C,\alpha )

(
α
=
(

α

1

,
…
,

α

d

)
)

(\alpha =(\alpha _{1},\ldots ,\alpha _{d}))

means of a Walsh-Fourier series is bounded from

H

p

H_{p}

to

L

p

L_{p}

(
1

/

(

α

k

+
1
)
>
p
>
∞
)

(1/(\alpha _{k}+1)>p>\infty )

and is of weak type

(

L

1

,

L

1

)

(L_{1},L_{1})

, provided that the supremum in the maximal operator is taken over a positive cone. As a consequence we obtain that the

(
C
,
α
)

(C,\alpha )

means of a function

f
∈

L

1

f \in L_{1}

converge a.e. to the function in question. Moreover, we prove that the

(
C
,
α
)

(C,\alpha )

means are uniformly bounded on

H

p

H_{p}

whenever

1

/

(

α

k

+
1
)
>
p
>
∞

1/(\alpha _{k}+ 1)>p > \infty

. Thus, in case

f
∈

H

p

f \in H_{p}

, the

(
C
,
α
)

(C,\alpha )

means converge to

f
f

in

H

p

H_{p}

norm. The same results are proved for the conjugate

(
C
,
α
)

(C,\alpha )

means, too.
On the Ornstein-Uhlenbeck operator in 𝐿² spaces with respect to invariant measures
Authors: Lunardi Alessandra
Published: July 2002

We consider a class of elliptic and parabolic differential operators with unbounded coefficients in

R

n

\mathbb R^n

, and we study the properties of the realization of such operators in suitable weighted

L
2

L^2

spaces.
Extreme points in triangular UHF algebras
Authors: Hudson Timothy , Katsoulis Elias , Larson David
Published: July 2002

We examine the strongly extreme point structure of the unit balls of triangular UHF algebras. The semisimple triangular UHF algebras are characterized as those for which this structure is minimal in the sense that every strongly extreme point belongs to the diagonal. In contrast to this, for the class of full nest algebras we prove a Krein-Milman type theorem which asserts that every operator in the open unit ball of the algebra is a convex combination of strongly extreme points.
Local multiple sequence alignment using dead-end elimination
Authors: V.Lukashin Alexander , J.Rosa Joseph
Published: July 2002

Motivation: Local multiple sequence alignment is a basic tool for extracting functionally important regions shared by a family of protein sequences. We present an effectively polynomial-time algorithm for rigorously solving the local multiple alignment problem.

Results: The algorithm is based on the dead-end elimination procedure that makes it possible to avoid an exhaustive search. In the framework of the sum-of-pairs scoring system, certain rejection criteria are derived in order to eliminate those sequence segments and segment pairs that can be mathematically shown to be inconsistent (dead-ending) with the globally optimal alignment. Iterative application of the elimination criteria results in a rapid reduction of combinatorial possibilities without considering them explicitly. In the vast majority of cases, the procedure converges to a unique globally optimal solution. In contrast to the exhaustive search, whose computational complexity is combinatorial, the algorithm is computationally feasible because the number of operations required to eliminate the dead-ending segments and segment pairs grows quadratically and cubically, respectively, with the total number of sequence elements. The method is illustrated on a set of protein families for which the globally optimal alignments are well recognized.

Availability: The source code of the program implementing the algorithm is available upon request from the authors.

Contact: alex˙lukashin@biogen.com
MPSA: integrated system for multiple protein sequence analysis
with client/server capabilities
Authors: Blanchet Christophe , Combet Christophe , Geourjon Christophe , Deléage Gilbert
Published: July 2002

Summary: MPSA is a stand-alone software intended to protein sequence analysis with a high integration level and Web clients/server capabilities. It provides many methods and tools, which are integrated into an interactive graphical user interface. It is available for most Unix/Linux and non-Unix systems. MPSA is able to connect to a Web server (e.g. http://pbil.ibcp.fr/NPSA) in order to perform large-scale sequence comparison on up-to-date databanks.

Availability: Free to academic http://www.ibcp.fr/mpsa/

Contact: c.blanchet@ibcp.fr
Turning Silk Purses into Sows' Ears: Environmental History and the Chemical Industry
Authors: Smith John K.
Published: July 2002

Recently, environmental historians have called for histories of the environmental damage caused by chemical companies in the era before strict federal regulation, which began in the late 1960s. This article examines how chemical companies, pollution experts, and government agencies defined the problems of pollution and sought remedies for it. With a few exceptions, until the mid-1930s chemical companies dealt with pollution problems in an ad hoc fashion, acting in response to complaints. National attention to water pollution began during the New Deal, when Roosevelt appointed a National Resources Committee and legislation was introduced that would have established federal control of water pollution. These events galvanized the industry to begin to pay systematic attention to water pollution by establishing pollution engineering positions, forming trade association committees, and organizing symposia at professional meetings.
Cigarette Smoking and Adolescents: Messages They See and Hear
Authors: Crawford Myra A. ,   The Tobacco Control Network Writing Group
Published: July 2002

Cigarette smoking is the primary preventable cause of mortality and morbidity in the US. But in the mid-1990s, more than one-third of US teenagers were smokers, despite their awareness of the health risks and negative consequences of tobacco use.

In 1996, as part of a three-year qualitative study to explore differences in adolescent smoking by gender and ethnicity, members of the Tobacco Control Network examined messages that teens receive about cigarette smoking. Consisting of 178 focus groups with 1175 teenagers covering all levels of smoking experience, the study included teens from five ethnic groups, stratified by gender and ethnicity, from urban and rural areas across the US. The authors reviewed the sources and content of messages that teens reported were most influential in their decisions to smoke or not smoke cigarettes.

Family and peers, school, television, and movies were the primary sources for both pro- and antismoking messages.

The authors conclude that a lack of clear, consistent antismoking messages leaves teens vulnerable to the influences of pro-smoking messages from a variety of sources. Interventions need to be culture- and gender-specific. Family-based interventions appear to be needed and efficacious, but resource intensive. Building self-esteem may prove to be a promising intervention.
The National Birth Defects Prevention Study
Authors: Yoon PW , Rasmussen SA , Lynberg MC , Moore CA , Anderka M , Carmichael SL , Costa P , Druschel C , Hobbs CA , Romitti PA , Langlois PH , Edmonds LD
Published: July 2002

The National Birth Defects Prevention Study was designed to identify infants with major birth defects and evaluate genetic and environmental factors associated with the occurrence of birth defects. The ongoing case-control study covers an annual birth population of 482,000 and includes cases identified from birth defect surveillance registries in eight states. Infants used as controls are randomly selected from birth certificates or birth hospital records. Mothers of case and control infants are interviewed and parents are asked to collect buccal cells from themselves and their infants for DNA testing. Information gathered from the interviews and the DNA specimens will be used to study independent genetic and environmental factors and gene-environment interactions for a broad range of birth defects.

As of December 2000, 7470 cases and 3821 controls had been ascertained in the eight states. Interviews had been completed with 70% of the eligible case and control mothers, buccal cell collection had begun in all of the study sites, and researchers were developing analysis plans for the compiled data.

This study is the largest and broadest collaborative effort ever conducted among the nation's leading birth defect researchers.

The unprecedented statistical power that will result from this study will enable scientists to study the epidemiology of some rare birth defects for the first time. The compiled interview data and banked DNA of approximately 35 categories of birth defects will facilitate future research as new hypotheses and improved technologies emerge.
Project Joy: Faith Based Cardiovascular Health Promotion for African American Women
Authors: Yanek Lisa R. , Becker Diane M. , Moy Taryn F. , Gittelsohn Joel , Koffman Dyann Matson
Published: July 2002

Objective.

The authors tested the impact on cardiovascular risk profiles of African American women ages 40 years and older after one year of participation in one of three church-based nutrition and physical activity strategies: a standard behavioral group intervention, the standard intervention supplemented with spiritual strategies, or self-help strategies.

Methods.

Women were screened at baseline and after one year of participation. The authors analyzed intention-to-treat within group and between groups using a generalized estimating equations adjustment for intra-church clustering. Because spiritual strategies were added to the standard intervention by participants themselves, the results from both active groups were similar and, thus, combined for comparisons with the self-help group.

Results.

A total of 529 women from 16 churches enrolled. Intervention participants exhibited significant improvements in body weight (−1.1 lbs), waist circumference (−0.66 inches), systolic blood pressure (−1.6 mmHg), dietary energy (−117 kcal), dietary total fat (−8 g), and sodium intake (−145 mg). The self-help group did not. In the active intervention group, women in the top decile for weight loss at one year had even larger, clinically meaningful changes in risk outcomes (−19.8 lbs).

Conclusions.

Intervention participants achieved clinically important improvements in cardiovascular disease risk profiles one year after program initiation, which did not occur in the self-help group. Church-based interventions can significantly benefit the cardiovascular health of African American women.
Mitochondrial DNA deletion mutations colocalize with segmental electron transport system abnormalities, muscle fiber atrophy, fiber splitting, and oxidative damage in sarcopenia
Authors: WANAGAT JONATHAN , CAO ZHENGJIN , PATHARE PRANALI , AIKEN JUDD M.
Published: July 2002

The in vivo cellular impact of age‐associated mitochondrial DNA mutations is unknown. We hypothesized that mitochondrial DNA deletion mutations contribute to the fiber atrophy and loss that cause sarcopenia, the age‐related decline of muscle mass and function. We examined 82,713 rectus femoris muscle fibers from Fischer 344 ×Brown Norway F1 hybrid rats of ages 5, 18, and 38 months through 1000 microns by serial cryosectioning and histochemical staining for cytochrome c oxidase and succinate dehydrogenase. Between 5 and 38 months of age, the rectus femoris muscle in the hybrid rat demonstrated a 33% decrease in mass concomitant with a 30% decrease in total fibers at the muscle mid‐belly. We observed significant increases in the number of mitochondrial abnormalities with age from 289 ± 8 ETS abnormal fibers in the entire 5‐month‐old rectus femoris to 1094 ± 126 in the 38‐month‐old as calculated from the volume density of these abnormalities. Segmental mitochondrial abnormalities contained mitochondrial DNA deletion mutations as revealed by laser capture microdissection and whole mitochondrial genome amplification. Muscle fibers harboring mitochondrial deletions often displayed atrophy, splitting and increased steady‐state levels of oxidative nucleic damage. These data suggest a causal role for age‐associated mitochondrial DNA deletion mutations in sarcopenia.—Wanagat, J., Cao, Z., Pathare, P., Aiken, J. M. Mitochondrial DNA deletion mutations colocalize with segmental electron transport system abnormalities, muscle fiber atrophy, fiber splitting, and oxidative damage in sarcopenia. FASEB J. 15, 322‐332 (2001)
Microsatellite and trinucleotide-repeat evolution: evidence for mutational bias and different rates of evolution in different lineages
Authors: Rubinsztein David C. , Amos Bill , Cooper Gillian
Published: July 2002

Microsatellites are stretches of repetitive DNA, where individual repeat units comprise one to six bases. These sequences are often highly polymorphic with respect to repeat number and include trinucleotide repeats, which are abnormally expanded in a number of diseases. It has been widely assumed that microsatellite loci are as likely to gain and lose repeats when they mutate. In this review, we present population genetic and empirical data arguing that microsatellites, including normal alleles at trinucleotide repeat disease loci, are more likely to expand in length when they mutate. In addition, our experiments suggest that the rates of expansion of such sequences differ in related species.
DIAN: A Novel Algorithm for Genome Ontological Classification
Authors: Pouliot Yannick , Gao Jing , Su Qiaojuan Jane , Liu Guozhen Gordon , Ling Xuefeng Bruce
Published: July 2002

Faced with the determination of many completely sequenced genomes, computational biology is now faced with the challenge of interpreting the significance of these data sets. A multiplicity of data-related problems impedes this goal: Biological annotations associated with raw data are often not normalized, and the data themselves are often poorly interrelated and their interpretation unclear. All of these problems make interpretation of genomic databases increasingly difficult. With the current explosion of sequences now available from the human genome as well as from model organisms, the importance of sorting this vast amount of conceptually unstructured source data into a limited universe of genes, proteins, functions, structures, and pathways has become a bottleneck for the field. To address this problem, we have developed a method of interrelating data sources by applying a novel method of associating biological objects to ontologies. We have developed an intelligent knowledge-based algorithm, DIAN, to support biological knowledge mapping, and, in particular, to facilitate the interpretation of genomic data. In this respect, the method makes it possible to inventory genomes by collapsing multiple types of annotations and normalizing them to various ontologies. By relying on a conceptual view of the genome, researchers can now easily navigate the human genome in a biologically intuitive, scientifically accurate manner.
A performance comparison of flat‐panel imager‐based MV and kV cone‐beam CT
Authors: Groh B. A. , Siewerdsen J. H. , Drake D. G. , Wong J. W. , Jaffray D. A.
Published: July 2002

The use of cone‐beam computed tomography (CBCT) has been proposed for guiding the delivery of radiation therapy, and investigators have examined the use of both kilovoltage (kV) and megavoltage (MV) x‐ray beams in the development of such CBCT systems. In this paper, the inherent contrast and signal‐to‐noise ratio (SNR) performance for a variety of existing and hypothetical detectors for CBCT are investigated analytically as a function of imaging dose and object size. Theoretical predictions are compared to the results of experimental investigations employing large‐area flat‐panel imagers (FPIs) at kV and MV energies. Measurements were performed on two different FPI‐based CBCT systems: a bench‐top prototype incorporating an FPI and kV x‐ray source (100 kVp x rays), and a system incorporating an FPI mounted on the gantry of a medical linear accelerator (6 MV x rays). The SNR in volume reconstructions was measured as a function of dose and found to agree reasonably with theoretical predictions. These results confirm the theoretically predicted advantages of employing kV energy x rays in imaging soft‐tissue structures found in the human body. While MV CBCT may provide a valuable means of correcting 3D setup errors and may offer an advantage in terms of simplicity of mechanical integration with a linear accelerator (e.g., implementation in place of a portal imager), kV CBCT offers significant performance advantages in terms of image contrast and SNR per unit dose for visualization of soft‐tissue structures. The relatively poor SNR performance at MV energies is primarily a result of the low x‐ray quantum efficiencies (∼a few percent or less) that are currently achieved with FPIs at high energies. Furthermore, kV CBCT with an FPI offers the potential of combined volumetric and radiographic/fluoroscopic imaging using the same device.
An approximation of central‐axis absorbed dose in narrow photon beams
Authors: Nizin P. S. , Mooij R. B.
Published: July 2002

In narrow photon beams of therapeutic energy range, the absorbed dose derived from experimental measurements is subject to a significant error. The error stems from high dose gradients characteristic to small radiation fields and from finite probe dimensions. In this study, a simple model for the narrow‐beam absorbed dose is described. It is shown that broad‐beam dose data are sufficient to predict a narrow‐beam dose. The dose is calculated as a sum of primary and scatter components given in the form of respective analytical functions. For both functions, numerical coefficients are determined in broad‐beam geometry. The model is evaluated by comparing calculated dose values with the Monte Carlo simulated narrow‐beam dose data for 6 and 15 MV x rays.
Continuous mixture modeling via goodness‐of‐fit cores
Authors: Aylward Stephen R.
Published: July 2002

This dissertation introduces a novel technique for consistently and accurately modeling the distributions of data. The technique is ideal for representing distributions that arise in a variety of problems including the driving problem of this dissertation, representing the distributions of intensities associated with tissues in medical images containing intensity inhomogeneities. Intensity inhomogeneities arise in MR images due to inhomogeneous fields, in x‐ray CT images due to beam hardening, and in SPECT images due to deficiencies in attenuation compensation. Within regions of such images, a tissue's intensity distribution is Gaussian. Between regions, however, the mean and variance of a tissue's Gaussian may vary as a result of inhomogeneities. That is, a tissue's intensities throughout an inhomogeneous image have a generalized projective Gaussian distribution (GPGD). Traditionally, GPGDs have been modeled using finite Gaussian mixture models (FGMMs). The dissertation demonstrates that GPGDs are better represented by continuous Gaussian mixture models (CGMMs). Gaussian goodness‐of‐fit cores define CGMMs. For GPGDs, Monte Carlo and ROC analysis demonstrate that classifiers utilizing CGMMs provide as consistent labelings as and better true‐positive rates than FGMMs. The CGMM‐based classification of gray and white matter in an inhomogeneous magnetic resonance image is demonstrated.
Bent Laue crystal monochromator for producing areal x‐ray beams
Authors: Zhong Zhong
Published: July 2002

A bent Laue crystal monochromator for diffraction of areal monochromatic x‐ray beams from a polyenergetic x‐ray rotating anode source has been developed at the National Synchrotron Light Source (NSLS). The monochromatic beam, with a solid angle of more than 5 degrees×5 degrees and energy range tunable from 15 keV to 100 keV, is completely separated from the white beam at a distance of less than 1 m from the source. The absolute reflectivity of the monochromator ranges from 10% to 40%, depending on the energy of the x rays being diffracted and on the source size. The energy bandwidth, around 2%, is controllable by varying the diffraction planes used, the crystal thickness, the asymmetry angle and the bending radius. A single emission line from an x‐ray tube source can be selectively diffracted into the entire exit‐beam solid angle. The monochromator was tested using a compact rotating anode x‐ray source at Science Research Laboratory (SRL). The ‐alpha characteristic lines (both ‐alpha1 and ‐alpha2) of cerium and barium targets were diffracted by the monochromator and used for the above and below iodine ‐edge imaging of phantoms with several concentrations of iodine contrast agent. Digital subtraction of the images produced an iodine image. The potential applications of the device in clinical radiography are discussed.
Maximum likelihood estimation in calibrating a stereo camera setup
Authors: Muijtjens Arno M. M. , Roos Jef M. A. , Arts Theo , Hasman Arie
Published: July 2002

Motion and deformation of the cardiac wall may be measured by following the positions of implanted radiopaque markers in three dimensions, using two x‐ray cameras simultaneously. Regularly, calibration of the position measurement system is obtained by registration of the images of a calibration object, containing 10–20 radiopaque markers at known positions. Unfortunately, an accidental change of the position of a camera after calibration requires complete recalibration. Alternatively, redundant information in the measured image positions of stereo pairs can be used for calibration. Thus, a separate calibration procedure can be avoided. In the current study a model is developed that describes the geometry of the camera setup by five dimensionless parameters. Maximum Likelihood (ML) estimates of these parameters were obtained in an error analysis. It is shown that the ML estimates can be found by application of a nonlinear least squares procedure. Compared to the standard unweighted least squares procedure, the ML method resulted in more accurate estimates without noticeable bias. The accuracy of the ML method was investigated in relation to the object aperture. The reconstruction problem appeared well conditioned as long as the object aperture is larger than 0.1 rad. The angle between the two viewing directions appeared to be the parameter that was most likely to cause major inaccuracies in the reconstruction of the 3‐D positions of the markers. Hence, attempts to improve the robustness of the method should primarily focus on reduction of the error in this parameter.
Measurement of x‐ray attenuation coefficients of aqueous solutions of indocyanine green and glycated chitosan
Authors: Xu Fang , Liu Hong , Wu Xizeng , Jiang Hangyi , Nordquist Robert E. , Chen Wei R.
Published: July 2002

We report our experimental results of measurements of x‐ray attenuation coefficients of aqueous solutions of a light absorbing dye, indocyanine green, and an immunoadjuvant, glycated chitosan. In the treatment of metastatic tumors in rats using a novel laser immunotherapy these solutions were administered in situ. The x‐ray attenuation data of the solutions are essential to development of an x‐ray digital imaging system for monitoring the administration of the solution, as well as for the distribution and the diffusion of the solution in tumors and in surrounding tissue. The composition of the solutions, the measurement system configuration, and the technique used to determine the attenuation coefficients are described. The experimental results show that glycated chitosan has a higher attenuation coefficient compared to indocyanine green and water. Our experimental data proved that, even at low concentrations, the x‐ray attenuation through these aqueous solutions could be differentiated. Therefore, a digital x‐ray imaging technique can be used effectively in monitoring and controlling the intratumor diffusion and distributions of these solutions.