bluuebunny/crossref_metadata_2025 huggingface dataset:
Eigenvalue estimate on complete noncompact Riemannian manifolds and applications
Authors: do Carmo Manfredo , Zhou Detang
Published: July 2002

We obtain some sharp estimates on the first eigenvalues of complete noncompact Riemannian manifolds under assumptions of volume growth. Using these estimates we study hypersurfaces with constant mean curvature and give some estimates on the mean curvatures.
Causal compactification and Hardy spaces
Authors: Ólafsson G. , Ørsted B.
Published: July 2002

Let

M

=
G

/

H

\mathcal {M}=G/H

be a irreducible symmetric space of Cayley type. Then

M

\mathcal {M}

is diffeomorphic to an open and dense

G
G

-orbit in the Shilov boundary of

G

/

K
×
G

/

K

G/K\times G/K

. This compactification of

M

\mathcal {M}

is causal and can be used to give answers to questions in harmonic analysis on

M

\mathcal {M}

. In particular we relate the Hardy space of

M

\mathcal {M}

to the classical Hardy space on the bounded symmetric domain

G

/

K
×
G

/

K

G/K\times G/K

. This gives a new formula for the Cauchy-Szegö kernel for

M

\mathcal {M}

.
Limit sets of discrete groups of isometries of exotic hyperbolic spaces
Authors: Corlette Kevin , Iozzi Alessandra
Published: July 2002

Let

Γ
\Gamma

be a geometrically finite discrete group of isometries of hyperbolic space

H

F

n

\mathcal {H}_{\mathbb {F}}^n

, where

F

=

R

,

C

,

H

\mathbb {F}= \mathbb {R}, \mathbb {C}, \mathbb {H}

or

O

\mathbb {O}

(in which case

n
=
2

n=2

). We prove that the critical exponent of

Γ
\Gamma

equals the Hausdorff dimension of the limit sets

Λ
(
Γ
)

\Lambda (\Gamma )

and that the smallest eigenvalue of the Laplacian acting on square integrable functions is a quadratic function of either of them (when they are sufficiently large). A generalization of Hopf ergodicity theorem for the geodesic flow with respect to the Bowen-Margulis measure is also proven.
Dehn surgery on arborescent links
Authors: Wu Ying-Qing
Published: July 2002

This paper studies Dehn surgery on a large class of links, called arborescent links. It will be shown that if an arborescent link

L
L

is sufficiently complicated, in the sense that it is composed of at least

4
4

rational tangles

T
(

p

i

/

q

i

)

T(p_{i}/q_{i})

with all

q

i

>
2

q_{i} > 2

, and none of its length 2 tangles are of the form

T
(
1

/

2

q

1

,
1

/

2

q

2

)

T(1/2q_{1}, 1/2q_{2})

, then all complete surgeries on

L
L

produce Haken manifolds. The proof needs some result on surgery on knots in tangle spaces. Let

T
(
r

/

2
s
,
p

/

2
q
)
=
(
B
,

t

1

∪

t

2

∪
K
)

T(r/2s, p/2q) = (B, t_{1}\cup t_{2}\cup K)

be a tangle with

K
K

a closed circle, and let

M
=
B
−
Int
⁡
N
(

t

1

∪

t

2

)

M = B - \operatorname {Int} N(t_{1}\cup t_{2})

. We will show that if

s
>
1

s>1

and

p
≢
±
1

p \not \equiv \pm 1

mod

2
q

2q

, then

∂
M

\partial M

remains incompressible after all nontrivial surgeries on

K
K

. Two bridge links are a subclass of arborescent links. For such a link

L
(
p

/

q
)

L(p/q)

, most Dehn surgeries on it are non-Haken. However, it will be shown that all complete surgeries yield manifolds containing essential laminations, unless

p

/

q

p/q

has a partial fraction decomposition of the form

1

/

(
r
−
1

/

s
)

1/(r-1/s)

, in which case it does admit non-laminar surgeries.
Bourgin-Yang type theorem and its application to 𝑍₂-equivariant Hamiltonian systems
Authors: Izydorek Marek
Published: July 2002

We will be concerned with the existence of multiple periodic solutions of asymptotically linear Hamiltonian systems with the presence of

Z
2

Z_2

–action. To that purpose we prove a new version of the Bourgin–Yang theorem. Using the notion of the crossing number we also introduce a new definition of the Morse index for indefinite functionals.
Knot invariants from symbolic dynamical systems
Authors: Silver Daniel , Williams Susan
Published: July 2002

If

G
G

is the group of an oriented knot

k
k

, then the set

Hom
⁡
(
K
,
Σ
)

\operatorname {Hom} (K, \Sigma )

of representations of the commutator subgroup

K
=
[
G
,
G
]

K = [G,G]

into any finite group

Σ
\Sigma

has the structure of a shift of finite type

Φ

Σ

\Phi _{\Sigma }

, a special type of dynamical system completely described by a finite directed graph. Invariants of

Φ

Σ

\Phi _{\Sigma }

, such as its topological entropy or the number of its periodic points of a given period, determine invariants of the knot. When

Σ
\Sigma

is abelian,

Φ

Σ

\Phi _{\Sigma }

gives information about the infinite cyclic cover and the various branched cyclic covers of

k
k

. Similar techniques are applied to oriented links.
Multi-separation, centrifugality and centripetality imply chaos
Authors: Mai Jiehua
Published: July 2002

Let

I
I

be an interval.

I
I

need not be compact or bounded. Let

f
:
I
→
I

f:I\rightarrow I

be a continuous map, and

(

x
0

,

x
1

,
⋯
,

x
n

)

(x_0, x_1, \cdots , x_n)

be a trajectory of

f
f

with

x
n

≤

x
0

>

x
1

x_n\leq x_0>x_1

or

x
1

>

x
0

≤

x
n

x_1>x_0\leq x_n

. Then there is a point

v
∈
I

v\in I

such that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="min left-brace right-brace comma comma x 0 comma midline-horizontal-ellipsis comma xn greater-than v equals f left-parenthesis v right-parenthesis greater-than max left-brace right-brace comma comma x 0 comma midline-horizontal-ellipsis comma xn">

min
{

x
0

,
⋯
,

x
n

}
>
v
=
f
(
v
)
>
max
{

x
0

,
⋯
,

x
n

}

\min \{x_0, \cdots , x_n\}>v=f(v)>\max \{x_0, \cdots , x_n\}

. A point

y
∈
I

y\in I

is called a centripetal point of

f
f

relative to

v
v

if

y
>
f
(
y
)
>
v

y>f(y)>v

or

v
>
f
(
y
)
>
y

v>f(y)>y

, and

y
y

is centrifugal if

f
(
y
)
>
y
>
v

f(y)>y>v

or

v
>
y
>
f
(
y
)

v>y>f(y)

. In this paper we prove that if there exist

k
k

centripetal points of

f
f

in

{

x
0

,
⋯
,

x

n
−
1

}
,
k
≥
1

\{x_0, \cdots , x_{n-1}\}, k\geq 1

, then

f
f

has periodic points of some odd (

≠
1

\not = 1

) period

p
≤
(
n
−
2
)

/

k
+
2

p\leq (n-2)/k+2

. In addition, we also prove that if

(

x
0

,

x
1

,
⋯
,

x

n
−
1

(x_0, x_1, \cdots , x_{n-1}

) is multi-separated by Fix(

f
f

), or there exists a centrifugal point of

f
f

in

{

x
0

,
⋯
,

x

n
−
1

}

\{x_0, \cdots , x_{n-1}\}

, then

f
f

is turbulent and hence has periodic points of all periods.
Operating points in infinite nonlinear networks approximated by finite networks
Authors: Calvert Bruce , Zemanian Armen
Published: July 2002

Given a nonlinear infinite resistive network, an operating point can be determined by approximating the network by finite networks obtained by shorting together various infinite sets of nodes, and then taking a limit of the nodal potential functions of the finite networks. Initially, by taking a completion of the node set of the infinite network under a metric given by the resistances, limit points are obtained that represent generalized ends, which we call “terminals,” of the infinite network. These terminals can be shorted together to obtain a generalized kind of node, a special case of a 1-node. An operating point will involve Kirchhoff’s current law holding at 1-nodes, and so the flow of current into these terminals is studied. We give existence and bounds for an operating point that also has a nodal potential function, which is continuous at the 1-nodes. The existence is derived from the said approximations.
The Quantum Cohomology Ring of Flag Varieties
Authors: Ciocan-Fontanine Ionuţ
Published: July 2002

We describe the small quantum cohomology ring of complete flag varieties by algebro-geometric methods, as presented in our previous work Quantum cohomology of flag varieties (Internat. Math. Res. Notices, no. 6 (1995), 263–277). We also give a geometric proof of the quantum Monk formula.
On sectional genus of quasi-polarized 3-folds
Authors: Fukuma Yoshiaki
Published: July 2002

Let

X
X

be a smooth projective variety over

C

\mathbb {C}

and

L
L

a nef-big (resp. ample) divisor on

X
X

. Then

(
X
,
L
)

(X,L)

is called a quasi-polarized (resp. polarized) manifold. Then we conjecture that

g
(
L
)
≥
q
(
X
)

g(L)\geq q(X)

, where

g
(
L
)

g(L)

is the sectional genus of

L
L

and

q
(
X
)
=
dim
⁡

H

1

(

O

X

)

q(X)=\operatorname {dim}H^{1}(\mathcal {O}_{X})

is the irregularity of

X
X

. In general it is unknown whether this conjecture is true or not, even in the case of

dim
⁡
X
=
2

\operatorname {dim}X=2

. For example, this conjecture is true if

dim
⁡
X
=
2

\operatorname {dim}X=2

and

dim
⁡

H

0

(
L
)
>
0

\operatorname {dim}H^{0}(L)>0

. But it is unknown if

dim
⁡
X
≥
3

\operatorname {dim}X\geq 3

and

dim
⁡

H

0

(
L
)
>
0

\operatorname {dim}H^{0}(L)>0

. In this paper, we prove

g
(
L
)
≥
q
(
X
)

g(L)\geq q(X)

if

dim
⁡
X
=
3

\operatorname {dim}X=3

and

dim
⁡

H

0

(
L
)
≥
2

\operatorname {dim}H^{0}(L)\geq 2

. Furthermore we classify polarized manifolds

(
X
,
L
)

(X,L)

with

dim
⁡
X
=
3

\operatorname {dim}X=3

,

dim
⁡

H

0

(
L
)
≥
3

\operatorname {dim}H^{0}(L)\geq 3

, and

g
(
L
)
=
q
(
X
)

g(L)=q(X)

.
The 𝒰-Lagrangian of a convex function
Authors: Lemaréchal Claude , Oustry François , Sagastizábal Claudia
Published: July 2002

At a given point

p
¯

\bar {p}

, a convex function

f
f

is differentiable in a certain subspace

U

\mathcal {U}

(the subspace along which

∂
f
(

p
¯

)

\partial f(\bar {p})

has 0-breadth). This property opens the way to defining a suitably restricted second derivative of

f
f

at

p
¯

\bar {p}

. We do this via an intermediate function, convex on

U

\mathcal {U}

. We call this function the

U

\mathcal {U}

-Lagrangian; it coincides with the ordinary Lagrangian in composite cases: exact penalty, semidefinite programming. Also, we use this new theory to design a conceptual pattern for superlinearly convergent minimization algorithms. Finally, we establish a connection with the Moreau-Yosida regularization.
Ultrafilters on 𝜔-their ideals and their cardinal characteristics
Authors: Shelah Saharon , Brendle Jörg , Shelah Saharon
Published: July 2002

For a free ultrafilter

U

\mathcal {U}

on

ω
\omega

we study several cardinal characteristics which describe part of the combinatorial structure of

U

\,\mathcal {U}

. We provide various consistency results; e.g. we show how to force simultaneously many characters and many

π
\pi

–characters. We also investigate two ideals on the Baire space

ω

ω

\omega ^{\omega }

naturally related to

U

\mathcal {U}

and calculate cardinal coefficients of these ideals in terms of cardinal characteristics of the underlying ultrafilter.
On the distribution of points in projective space of bounded height
Authors: Choi Kwok-Kwong
Published: July 2002

In this paper we consider the uniform distribution of points in compact metric spaces. We assume that there exists a probability measure on the Borel subsets of the space which is invariant under a suitable group of isometries. In this setting we prove the analogue of Weyl’s criterion and the Erdös-Turán inequality by using orthogonal polynomials associated with the space and the measure. In particular, we discuss the special case of projective space over completions of number fields in some detail. An invariant measure in these projective spaces is introduced, and the explicit formulas for the orthogonal polynomials in this case are given. Finally, using the analogous Erdös-Turán inequality, we prove that the set of all projective points over the number field with bounded Arakelov height is uniformly distributed with respect to the invariant measure as the bound increases.
The second bounded cohomology of an amalgamated free product of groups
Authors: Fujiwara Koji
Published: July 2002

We study the second bounded cohomology of an amalgamated free product of groups, and an HNN extension of a group. As an application, we show that a group with infinitely many ends has infinite dimensional second bounded cohomology.
Odd primary 𝑏𝑜 resolutions and classification of the stable summands of stunted lens spaces
Authors: González Jesús
Published: July 2002

The classification of the stable homotopy types of stunted lens spaces and their stable summands can be obtained by proving the triviality of certain stable classes in the homotopy groups of these spaces. This is achieved in the 2-primary case by Davis and Mahowald using classical Adams spectral sequence techniques. We obtain the odd primary analogue using the corresponding Adams spectral sequence based at the spectrum representing odd primary connective

K
K

-theory. The methods allow us to answer a stronger problem: the determination of the smallest stunted space where such stable classes remain null homotopic. A technical problem prevents us from giving an answer in all situations; however, in a quantitative way, the number of cases missed is very small.
Reducibility of some induced representations of 𝑝-adic unitary groups
Authors: Murnaghan Fiona , Repka Joe
Published: July 2002

In this paper we study reducibility of those representations of quasi-split unitary

p
p

-adic groups which are parabolically induced from supercuspidal representations of general linear groups. For a supercuspidal representation associated via Howe’s construction to an admissible character, we show that in many cases a criterion of Goldberg for reducibility of the induced representation reduces to a simple condition on the admissible character.
Dense Egyptian fractions
Authors: Martin Greg
Published: July 2002

Every positive rational number has representations as Egyptian fractions (sums of reciprocals of distinct positive integers) with arbitrarily many terms and with arbitrarily large denominators. However, such representations normally use a very sparse subset of the positive integers up to the largest denominator. We show that for every positive rational there exist representations as Egyptian fractions whose largest denominator is at most

N
N

and whose denominators form a positive proportion of the integers up to

N
N

, for sufficiently large

N
N

; furthermore, the proportion is within a small factor of best possible.
Derivatives of Wronskians with applications to families of special Weierstrass points
Authors: Gatto Letterio , Ponza Fabrizio
Published: July 2002

Let

π
:

X

⟶
S

\pi : \mathcal {X} \longrightarrow S

be a flat proper family of smooth connected projective curves parametrized by some smooth scheme of finite type over

C

\mathbb {C}

. On every such a family, suitable derivatives “along the fibers” (in the sense of Lax) of the relative wronskian, as defined by Laksov and Thorup, are constructed. They are sections of suitable jets extensions of the

g
(
g
+
1
)

/

2

g(g+1)/2

-th tensor power of the relative canonical bundle of the family itself. The geometrical meaning of such sections is discussed: the zero schemes of the

(
k
−
1
)

(k-1)

-th derivative (

k
≥
1

k\geq 1

) of a relative wronskian correspond to families of Weierstrass Points (WP’s) having weight at least

k
k

. The locus in

M

g

M_{g}

, the coarse moduli space of smooth projective curves of genus

g
g

, of curves possessing a WP of weight at least

k
k

, is denoted by

w
t
(
k
)

wt(k)

. The fact that

w
t
(
2
)

wt(2)

has the expected dimension for all

g
≥
2

g\geq 2

was implicitly known in the literature. The main result of this paper hence consists in showing that

w
t
(
3
)

wt(3)

has the expected dimension for all

g
≥
4

g\geq 4

. As an application we compute the codimension

2
2

Chow (

Q
Q

-)class of

w
t
(
3
)

wt(3)

for all

g
≥
4

g\geq 4

, the main ingredient being the definition of the

k
k

-th derivative of a relative wronskian, which is the crucial tool which the paper is built on. In the concluding remarks we show how this result may be used to get relations among some codimension

2
2

Chow (

Q
Q

-)classes in

M

4

M_{4}

(

g
≥
4

g\geq 4

), corresponding to varieties of curves having a point

P
P

with a suitable prescribed Weierstrass Gap Sequence, relating to previous work of Lax.
Rotating an interval and a circle
Authors: Blokh Alexander , Misiurewicz Michał
Published: July 2002

We compare periodic orbits of circle rotations with their counterparts for interval maps. We prove that they are conjugate via a map of modality larger by at most 2 than the modality of the interval map. The proof is based on observation of trips of inhabitants of the Green Islands in the Black Sea.
An equivariant smash spectral sequence and an unstable box product
Authors: Intermont Michele
Published: July 2002

Let

G
G

be a finite group. We construct a first quadrant spectral sequence which converges to the equivariant homotopy groups of the smash product

X
∧
Y

X \wedge Y

for suitably connected, based

G
G

-CW complexes

X
X

and

Y
Y

. The

E
2

E^2

term is described in terms of a tensor product functor of equivariant

Π
\Pi

-algebras. A homotopy version of the non-equivariant Künneth theorem and the equivariant suspension theorem of Lewis are both shown to be special cases of the corner of the spectral sequence. We also give a categorical description of this tensor product functor which is analogous to the description in equivariant stable homotopy theory of the box product of Mackey functors. For this reason, the tensor product functor deserves to be called an “unstable box product”.
𝐶*-algebras generated by a subnormal operator
Authors: Chan Kit , C̆uc̆ković Z̆eljko
Published: July 2002

Using the functional calculus for a normal operator, we provide a result for generalized Toeplitz operators, analogous to the theorem of Axler and Shields on harmonic extensions of the disc algebra. Besides that result, we prove that if

T
T

is an injective subnormal weighted shift, then any two nontrivial subspaces invariant under

T
T

cannot be orthogonal to each other. Then we show that the

C
∗

C^*

-algebra generated by

T
T

and the identity operator contains all the compact operators as its commutator ideal, and we give a characterization of that

C
∗

C^*

-algebra in terms of generalized Toeplitz operators. Motivated by these results, we further obtain their several-variable analogues, which generalize and unify Coburn’s theorems for the Hardy space and the Bergman space of the unit ball.
Deforming a map into a harmonic map
Authors: Yang Deane
Published: July 2002

This paper presents some existence and uniqueness theorems for harmonic maps between complete noncompact Riemannian manifolds. In particular, we obtain as a corollary a recent result of Hardt–Wolf on the existence of harmonic quasi-isometries of the hyperbolic plane.
CH with no Ostaszewski spaces
Authors: Eisworth Todd , Roitman Judith
Published: July 2002

There are models of CH without Ostaszeswki spaces. If

X
X

is locally compact and sub-Ostaszewski, there is a forcing

P
X

P_X

which does not add reals and which forces “

X
X

is not sub-Ostaszewski”.
A speciality theorem for Cohen-Macaulay space curves
Authors: Schlesinger Enrico
Published: July 2002

We prove a version of the Halphen Speciality Theorem for locally Cohen-Macaulay curves in

P

3

\mathbb {P}^3

. To prove the theorem, we strengthen some results of Okonek and Spindler on the spectrum of the ideal sheaf of a curve. As an application, we classify curves

C
C

having index of speciality as large as possible once we fix the degree of

C
C

and the minimum degree of a surface containing

C
C

.
The viscous Cahn-Hilliard equation: Morse decomposition and structure of the global attractor
Authors: Grinfeld M. , Novick-Cohen A.
Published: July 2002

In this paper we establish a Morse decomposition of the stationary solutions of the one-dimensional viscous Cahn-Hilliard equation by explicit energy calculations. Strong non-degeneracy of the stationary solutions is proven away from turning points and points of bifurcation from the homogeneous state and the dimension of the unstable manifold is calculated for all stationary states. In the unstable case, the flow on the global attractor is shown to be semi-conjugate to the flow on the global attractor of the Chaffee-Infante equation, and in the metastable case close to the nonlocal reaction–diffusion limit, a partial description of the structure of the global attractor is obtained by connection matrix arguments, employing a partial energy ordering and the existence of a weak lap number principle.
Hardy spaces and a Walsh model for bilinear cone operators
Authors: Gilbert John , Nahmod Andrea
Published: July 2002

The study of bilinear operators associated to a class of non-smooth symbols can be reduced to ther study of certain special bilinear cone operators to which a time frequency analysis using smooth wave-packets is performed. In this paper we prove that when smooth wave-packets are replaced by Walsh wave-packets the corresponding discrete Walsh model for the cone operators is not only

L

p

L^{p}

-bounded, as Thiele has shown in his thesis for the Walsh model corresponding to the bilinear Hilbert transform, but actually improves regularity as it maps into a Hardy space. The same result is expected to hold for the special bilinear cone operators.
Théorie d’Iwasawa des représentations 𝑝-adiques d’un corps local
Authors: Cherbonnier Frédéric , Colmez Pierre
Published: July 2002

This paper takes up the study of Iwasawa theory of

p
p

-adic representations of a local field via the theory of

(
φ
,
Γ
)

(\varphi ,\Gamma )

-modules. In particular, a vast generalisation of Coleman’s isomorphism is given as well as an explicit reciprocity law relating this isomorphism to Bloch-Kato’s exponential maps in the case of a de Rham representation.
BEAUTY-X: enhanced BLAST searches for DNA queries.
Authors: Worley K C , Culpepper P , Wiese B A , Smith R F
Published: July 2002

SUMMARY: BEAUTY (BLAST Enhanced Alignment Utility) is an enhanced version of the BLAST database search tool that facilitates identification of the functions of matched sequences. Three recent improvements to the BEAUTY program described here make the enhanced output (1) available for DNA queries, (2) available for searches of any protein database, and (3) more up-to-date, with periodic updates of the domain information. AVAILABILITY: BEAUTY searches of the NCBI and EMBL non-redundant protein sequence databases are available from the BCM Search Launcher Web pages (http://gc.bcm.tmc. edu:8088/search-launcher/launcher.html). BEAUTY Post-Processing of submitted search results is available using the BCM Search Launcher Batch Client (version 2.6) (ftp://gc.bcm.tmc. edu/pub/software/search-launcher/). SUPPLEMENTARY INFORMATION: Example figures are available at http://dot.bcm.tmc. edu:9331/papers/beautypp.html CONTACT: (kworley,culpep)@bcm.tmc.edu
Single-dose oral ciprofloxacin compared with cefotaxime and placebo for prophylaxis during transurethral surgery
Authors: Klimberg Ira W. , Malek G. H. , Cox Clair E. , Patterson A. Lynn , Whalen Edward , Kowalsky Steven F. , Echols Roger M.
Published: July 2002

To determine the efficacy and safety of single-dose oral ciprofloxacin prophylaxis for the prevention of post-operative bacteriuria following transurethral resection of the prostate or bladder tumour, a prospective, randomized, double-blind, placebo-controlled trial was conducted. Five hundred and eighteen patients were randomized in a 2:2:1 ratio to receive ciprofloxacin 500 mg, cefotaxime 1 g or placebo 30- 90 min before surgery. Of the 368 efficacy-evaluable patients, five (3.3%) ciprofloxacin, seven (4.8%) cefotaxime and five (7.0%) placebo recipients had post- operative bacteriuria (≥10 4 cfu/mL) during post-operative days 2- 15. Five (3.4%) ciprofloxacin, five (3.4%) cefotaxime and one (2.4%) placebo recipients were considered clinical failures, of whom one, two and one patients, respectively, had concomitant bacteriuria. Drug-related adverse events were reported in six of 204 (3%) ciprofloxacin, 12 of 197 (6%) cefotaxime and one of 101 (1%) placebo patients. The observed rates of post-operative bacteriuria suggest that a single 500 mg dose of ciprofloxacin is suitable prophylaxis for transurethral surgery.
Antiviral CD4 and CD8 T–cell memory: differences in the size of the response and activation requirements
Authors: Whitmire Jason K. , Murali-Krishna Kaja , Altman John , Ahmed Rafi
Published: July 2002

Following acute lymphocytic choriomeningitis virus (LCMV) infection, there is a potent antiviral CD8 T–cell response that eliminates the infection. This initial CD8 T–cell response is followed by a period of memory during which elevated numbers of virus–specific CD8 T cells remain in the mouse. CD4 T cells are also activated after LCMV infection, but relatively less is known about the magnitude and duration of the CD4 response. In this study, we used intracellular staining for interferon–γ to measure both CD4 and CD8 responses in the same mice at the single cell level. After LCMV infection, there was an increase in the number of activated CD4 T cells and an associated increase in the number of virus–specific CD4 T cells. At the peak of this expansion phase, the frequency of virus–specific CD4 T cells was 1 in 20 (0.5–1.0 × 106 per spleen). Like the CD8 response, long–term CD4 memory could be found up to a year after the infection with frequencies of approximately 1 in 260 (0.5–1.5 × 105 per spleen). However, the magnitude of virus–specific CD8 T cells was greater than virus–specific CD4 T cells during all phases of the immune response (expansion, death, and memory). At day 8, there were 20– to 35–fold more virusspecific CD8 Tcells than CD4 Tcells. This initial difference in cell number lasted into the memory phase as there remained a ten– to 20–fold difference in the CD8 and CD4 responses. These results highlight the importance of the expansion phase in determining the size of the memory T–cell pool. In addition to the difference in the magnitude, the activation requirements of CD8 and CD4 T–cell responses were different: CD8 T responses were not affected by blockade of CD40– CD40 ligand interaction whereas CD4 responses were reduced 90%. So while there is long–term memory in both the CD8 and CD4 compartments, the rules regulating the activation of CD8 and CD4 T cells and the overall magnitude of the responses are different.
Hippocampal Activations during Repetitive Learning and Recall of Geometric Patterns
Authors: Grön Georg , Bittner Daniel , Schmitz Bernd , Wunderlich Arthur P. , Tomczak Reinhard , Riepe Matthias W.
Published: July 2002

Hippocampal activation is required for episodic memory. Encoding and retrieval of novel and memorable items have been related to different locations in the hippocampus; however, the data remain ambiguous. The application of a newly designed keyboard allowed investigation of brain activation during encoding and free immediate and delayed recall with functional magnetic resonance imaging (fMRI) in young healthy controls (n = 12). Because of the repetitive learning and recall conditions, an individual learning gradient was used to contrast neural activity at different individual levels of novelty. During learning, subjects were asked to memorize 10 geometric patterns requiring the establishment of intra-item associations for memorization. After learning, subjects were asked to recall the items actively via the keyboard. Learning and recall were alternated five times. Delayed recall was scanned about 15 min after the fifth immediate recall condition without subjects having seen the items again. Left-sided anterior hippocampal activity was observed during conditions of initial learning as well as maximum recall. Neural activity during delayed recall did not reveal hippocampal responses and was characterized by a transition of neural activity from occipitoparietal regions to bilateral temporal cortices. We conclude that both lateralization and segregation depend on the specific relational characteristics of the stimuli requiring establishment of intra-item associations for encoding as well as retrieval. The absence of hippocampal activation during delayed recall together with the increase of lateral temporal involvement possibly corresponds with an emerging transition from episodic to long-term memory.
Relative speeds of Kodak computed radiography phosphors and screen‐film systems
Authors: Huda Walter , Rill Lynn N. , Bruner Angela P.
Published: July 2002

Relative mAs values required to generate a constant plate readout signal for the Kodak Ektascan general purpose (GP‐25) and high resolution (HR) photostimulable phosphors were measured as a function of x‐ray beam quality and for a range of representative x‐ray examinations. The signal intensity was determined from the exposure index (EI) generated during the read out of uniformly exposed phosphor imaging plates. These data were compared to the corresponding relative mAs values required to produce a constant film density of Lanex screen‐film combinations with nominal speeds of 40, 400, and 600. The relative detection performance of the photostimulable phosphors generally decreased with increasing kVp and beam filtration. The relative response of GP‐25 phosphors was independent of examination type, and modified by ∼10% when scattered radiation was present. The HR phosphor was more efficient than a Lanex Single Fine extremity screen used with an EM‐1 film. These relative response data will be useful for selecting the x‐ray technique factors which minimize patient dose in x‐ray examinations performed with photostimulable phosphors.
Radon decay in bone marrow fat cells and the possible induction of leukaemia
Authors: Utteridge Tammy D.
Published: July 2002

The alpha particle radiation dose to haemopoietic stem cells and marrow was determined with Monte Carlo modeling using input data generated from autopsy specimens of normal marrow and compared with the dose estimates obtained using the Bristol image analysis and dose calculation system on those same marrow specimens. There was very good agreement between the two dose calculation methods. The project confirmed that the spatial distribution of haemopoietic stem cells in normal human marrow was random, and a trimodal distribution of haemopoietic stem cell diameters was described (possibly due to different stages of the cell cycle, as previously described in the mouse). Modeling of the dose to marrow with different fat fractions showed a positive linear relationship between the fat fraction and both the proportion of haemopoietic stem cells “hit” and the proportion of “hit” survivors. Modeling of the dose to haemopoietic stem cells in the marrow of the underground miners showed a positive linear relationship between the radon concentration in external air and both the proportion of haemopoietic stem cells “hit” and the proportion of “hit” survivors. In all the modeling the mean number of alpha particle passages per haemopoietic stem cell was approximately 1.02, with doses of 0.86, 0.20, and 0.12 Gy for haemopoietic stem cells of diameter 5.71, 11.63, and 14.79 μm, respectively.
Pulsed brachytherapy: A formalism to account for the variation in dose rate of the stepping source
Authors: Narayana Vrinda , Orton Colin G.
Published: July 2002

Pulsed brachytherapy is an endeavor to mimic low dose rate (LDR) treatments using a single higher activity source (a medium dose rate) that is periodically introduced into the patient (i.e., pulsed) using a remote afterloader. It has been reported that by a careful choice of pulse length and frequency and using the ERD bioeffect dose model, therapeutic advantage (TA) values slightly less than unity can be achieved where TA has been defined as the ratio of tumor ERD for PB to tumor ERD for LDR treatments for constant late‐reacting normal tissue ERD. These calculations are based upon a uniform average dose rate in each pulse and equal repair rate constants for both tumor and normal tissue. In this paper, it is demonstrated that TAs of greater than 1 might be possible, depending upon the repair rate constants assumed for the tissues involved. Furthermore, for PB treatments the dose rate at a point of interest during each pulse is not uniform, since the treatment involves a single stepping source. A generalized ERD equation based on the linear quadratic model has been developed to account for the variation in the dose rate and, subsequently, to maximize the TA. Our calculations indicate that PB performed with 40 pulses in 120 hours with an irradiation time of 30 minutes per pulse with a delay time of two and a half hours is the best replacement for a LDR treatment that delivers 60 Gy in 120 hours.
Local x‐ray tomography for in vivo bone structure examinations
Authors: Laib Andres , Rüegsegger Peter
Published: July 2002

Precise information about the microarchitecture of cancellous bone would be helpful to further fracture risk prediction in individual patients. Recently 3D‐QCT of the distal radius has been introduced to this end. The validity of this new procedure is limited by the spatial resolution of the CT images, which in turn is limited by the x‐ray dose. Local tomography, where only the region of interest has to be scanned with x rays, might provide a way out of this dilemma. In this work the feasibility of local tomography for in vivo trabecular bone structure assessment is studied. In a first part the accuracy of structural indices obtainable with local tomography is compared with the accuracy of results from global (traditional) tomographic measurements. The results show that local tomography generates no substantial degradation in the structural indices. In a second part, the reduction in the radiation dose of local tomography is quantified with Monte Carlo simulations of the x‐ray scanning procedure. The results show that skin dose at the lower forearm can be reduced by a factor of 4–6, if the CT measurements are restricted to the distal radius. We conclude that with the help of local tomography in vivo 3D‐QCT examinations of the trabecular bone microarchitecture are feasible with a skin dose of 0.1 mGy at resolution, or with a skin dose of 1 mGy at a resolution of The increased resolution is expected to further improve the accuracy and precision of current in vivo bone structure examinations, allowing a detailed analysis of the processes of bone changes due to aging, disease, and treatment.
A comparison of Monte Carlo and analytic first scatter dose spread arrays
Authors: McGary J. E. , Boyer A. L. , Mackie T. R.
Published: July 2002

We compare first scattered point dose spread arrays generated by Monte Carlo and an analytic method. The analytic method models energy deposition using Klein‐Nishina cross sections for Compton scatter and approximations for electron transport. Assumptions in the analytic method are shown to be valid within a region of the point dose spread kernel in which meaningful comparisons can be made. Differences between the models are less than 10% for the forward scatter directions for radii greater than the electron range associated with the first scattered Compton photon. Differences in the backscatter region are discussed and indicate that the analytic model is useful for identifying large errors that might be present in numerically generated first scatter point dose spread arrays. The analytic method is simple and useful for validating first scatter kernels.
The effect of contrast medium and balloon shape on dosimetry for arterial irradiation with
Authors: Fox R. A. , Henson P. W.
Published: July 2002

The radiation dosimetry associated with the use of the beta particle emitter in an angioplasty balloon is investigated for the case when the balloon has an elliptical rather than circular cross section and when iodinated x‐ray contrast medium is included inside the balloon. It is found that the elliptical cross section introduces significant dose corrections when the eccentricity of the ellipse is equal to or greater than 0.7. However, for cases where the artery is nearly circular in cross section, the corrections are likely to be small. As expected, the dose is reduced along the major axis of the ellipse and increased along the minor axis. The corrections are greatest at larger distances from the surface of the balloon. The effect on dose of contrast in the balloon is significant for 33% Omnipaque in saline. Since this is a typical concentration of contrast that is used for imaging the radiation‐filled balloon, correction for the effects of contrast medium in the balloon should in general be applied. To enable corrections to be readily applied for other types and concentrations of contrast media, formulas have been derived that allow the dose correction to be calculated for a range of balloon diameters and at various distances from the surface of the balloon. To undertake this calculation, the elemental composition and density of the material in the balloon needs to be known.
Treatment planning considerations and quality assurance for CT‐guided transischiorectal implantation of the prostate
Authors: Molloy Janelle A. , Williams Mark B.
Published: July 2002

A CT‐guided technique for prostate brachytherapy has been developed which can be performed on patients with large prostates and which allows real time evaluation and modification of implant geometry. The patient is positioned prone and radioactive Pd 103 or I 125 seeds are implanted through the transischiorectal space. Needles are inserted through a template whose plane is oriented at a nominal angle of 26° away from the horizontal to facilitate needle penetration through the ischiorectal space. The CT gantry is tilted 26°, so that its plane is orthogonal to that of the template. The oblique geometry between the CT gantry and direction of couch translation must be considered during source position planning, implantation, and post‐treatment evaluation. This consideration is presented along with discussion of relevant quality assurance procedures and recommended tolerances. The mechanical and radiological tolerances of the CT scanner must be consistent with the high level of precision required in radiation therapy. Special emphasis was placed on gantry laser and image plane alignment, sensitivity and radiation profiles, and spatial accuracy of image reconstruction, table translation, and gantry tilt.
Algorithms and functionality of an intensity modulated radiotherapy optimization system
Authors: Wu Qiuwen , Mohan Radhe
Published: July 2002

The main purpose of this paper is to describe formalisms, algorithms, and certain unique features of a system for optimization of intensity modulated radiotherapy (IMRT). The system is coupled to a commercial treatment planning system with an accurate dose calculation engine based on the kernel superposition algorithm. The system was designed for use for research as well as for routine clinical practice. It employs dose– and dose–volume‐based objective functions. The system can optimize IMRT plans with multiple target volumes simultaneously. Each target volume may be assigned a different prescription dose with constraints on either underdosing, or overdosing, or both. For organs at risk more than one constraint may be applied. This feature allows simultaneous treatment of primary, regional disease and electively treated nodes. The system allows specification of constraints on logical combinations of anatomic structures, such as a region of overlap between the prostate planning target volume and rectum or the volume of lung excluding the tumor. The optimization may also be performed on plans which, in addition to intensity‐modulated beams, include other modalities such as non‐IMRT photon and electron beams and brachytherapy sources. The various features of the system are illustrated with one phantom example and two clinical examples: a brain stereotactic radiosurgery case and a nasopharynx case. In the cylindrical phantom example, the use of the system for overlap regions is demonstrated. The brain stereotactic radiosurgery example shows the improvement of IMRT plans over the conventional arcs based plan and the three‐dimensional conformal plan with multiple fixed gantry angles and demonstrates the application of our system to cases where small grid sizes are important. The nasopharynx example shows the potential of IMRT to simultaneously treat large and boost fields. It also illustrates the power of IMRT to protect normal anatomic structures for highly complex situations and the efficiency in planning and delivery achievable with IMRT. The overall IMRT planning time is typically less than 2 h on a Sun Ultrasparc workstation, most of which is spent in repeated computation of dose distributions.
Charge density on a thin straight wire: The first visit
Authors: Jackson J. D.
Published: July 2002

The problem of the linear charge density on a long straight conducting wire was considered and solved using a variational technique over 123 years ago. We describe the who and where and summarize his results. We also eat humble pie.
A large-aperture array of nonlinked receivers for acoustic positioning of biological sound sources
Authors: Møhl B. , Wahlberg M. , Heerfordt A.
Published: July 2002

A system of independent recording units that can be used to form an arbitrarily large acoustic array is described. Position of units and timing of signals are obtained from Global Positioning System (GPS) with precisions within 2.5 m and 50 microseconds, respectively. An integrated hardware and software solution is presented and results reported from a four-unit feasibility test in shallow water. Sound sources at a distance of 2 km were located within 2 to 138 m of GPS-derived positions.
Atmospheric turbulence conditions leading to focused and folded sonic boom wave fronts
Authors: Piacsek Andrew A.
Published: July 2002

The propagation and subsequent distortion of sonic booms with rippled wave fronts are investigated theoretically using a nonlinear time-domain finite-difference scheme. This work seeks to validate the rippled wave front approach as a method for explaining the significant effects of turbulence on sonic booms [A. S. Pierce and D. J. Maglieri, J. Acoust. Soc. Am. 51, 702–721 (1971)]. A very simple description of turbulence is employed in which velocity perturbations within a shallow layer of the atmosphere form strings of vortices characterized by their size and speed. Passage of a steady-state plane shock front through such a vortex layer produces a periodically rippled wave front which, for the purposes of the present investigation, serves as the initial condition for a finite-difference propagation scheme. Results show that shock strength and ripple curvature determine whether ensuing propagation leads to wave front folding. High resolution images of the computed full wave field provide insights into the spiked and rounded features seen in sonic booms that have propagated through turbulence.
Temporal integration of loudness in listeners with hearing losses of primarily cochlear origin
Authors: Buus So/ren , Florentine Mary , Poulsen Torben
Published: July 2002

To investigate how hearing loss of primarily cochlear origin affects the loudness of brief tones, loudness matches between 5- and 200-ms tones were obtained as a function of level for 15 listeners with cochlear impairments and for seven age-matched controls. Three frequencies, usually 0.5, 1, and 4 kHz, were tested in each listener using a two-interval, two-alternative forced-choice (2I, 2AFC) paradigm with a roving-level, up–down adaptive procedure. Results for the normal listeners generally were consistent with published data [e.g., , J. Acoust Soc. Am. 99, 1633–1644 (1996)]. The amount of temporal integration—defined as the level difference between equally loud short and long tones—varied nonmonotonically with level and was largest at moderate levels. No consistent effect of frequency was apparent. The impaired listeners varied widely, but most showed a clear effect of level on the amount of temporal integration. Overall, their results appear consistent with expectations based on knowledge of the general properties of their loudness-growth functions and the equal-loudness-ratio hypothesis, which states that the loudness ratio between equal-SPL long and brief tones is the same at all SPLs. The impaired listeners’ amounts of temporal integration at high SPLs often were larger than normal, although it was reduced near threshold. When evaluated at equal SLs, the amount of temporal integration well above threshold usually was in the low end of the normal range. Two listeners with abrupt high-frequency hearing losses (slopes >50 dB/octave) showed larger-than-normal maximal amounts of temporal integration (40 to 50 dB). This finding is consistent with the shallow loudness functions predicted by our excitation-pattern model for impaired listeners [, in Modeling Sensorineural Hearing Loss, edited by W. Jesteadt (Erlbaum, Mahwah, NJ, 1997), pp. 187–198]. Loudness functions derived from impaired listeners’ temporal-integration functions indicate that restoration of loudness in listeners with cochlear hearing loss usually will require the same gain whether the sound is short or long.
Free vibration of a fluid-filled hollow sphere of a functionally graded material with spherical isotropy
Authors: Chen W. Q. , Wang X. , Ding H. J.
Published: July 2002

An exact, three-dimensional method is developed in the paper to analyze the free vibration of a spherically isotropic hollow sphere made of a functionally graded material and filled with a compressible fluid medium. The material is assumed to be inhomogeneous along the radial direction. By introducing three displacement functions and employing the function expansion method, the governing equations are simplified to an uncoupled second-order ordinary differential equation, and a coupled system of two such equations. Solutions to these equations are given when the elastic constants and the mass density are power functions of the radial direction. To investigate the effect of material gradient on the natural frequencies, numerical calculations are finally performed.
The Transient Response of a Viscoelastic Torsional Pendulum
Authors: Elder Alexander S.
Published: July 2002

The pendulum consists of a circular viscoelastic rod fixed at one end and attached to a disk at the other end. The disk, initially at rest, is subjected to a step function of torque. The subsequent motion is analyzed in terms of normal modes and normal coordinates. The normal modes are found by separation of variables. The characteristic numbers associated with these modes depend only on the moments of inertia of the disk and rod. The normal coordinates satisfy integro-differential equations of the Volterra type. The mechanical properties of polyisobutylene at 25°C were represented in differential operator form. The Volterra integral equations were then solved by means of the Laplace transforms. An analysis of the numerical results shows that only the oscillatory part of the fundamental mode should persist after a short time. This result is in qualitative agreement with observations. This method of analysis may be applied to other dynamic problems in linear viscoelasticity provided the characteristic equation can be reduced to a form that does not involve the mechanical properties of the material.