bluuebunny/crossref_metadata_2025 huggingface dataset:
Phase-unifying mirrors for high-power XeF excimer lasers
Authors: De Tomasi F. , Aghamkar P. , Perrone M. R. , Protopapa M. L. , Piegari A. , Andre’ B. , Ravel G.
Published: March 2003

A phase-unifying unstable cavity of magnification factor M=5.8 has been applied to a high-power, commercial XeF laser, and the measurements for characterizing near- and far-field beam properties are reported. A laser beam of 280 mJ, 30 ns duration, a cross section of 2.4×1.3 cm2, and a beam quality factor of 4.3 along the discharge direction (x axis) and of 2.1 along the y direction has been obtained. The beam exhibits a smooth far-field profile with more than 90% of the total near-field energy within a far-field full angle θ⩽0.04 mrad. The beam angular stability is of 0.009 and of 0.004 mrad along x and y, respectively.
Tomographic imaging with a terahertz binary lens
Authors: Wang S. , Zhang X.-C.
Published: March 2003

The focal length of a binary lens is linearly proportional to the frequency of the imaging beam; this property allows objects at various positions along the beam propagation path to be uniquely imaged on the same imaging plane with different corresponding frequencies. We reconstructed tomographic images of objects by assembling the frequency-dependent images, and demonstrated three-dimensional tomographic imaging using a binary lens with broadband terahertz pulses.
Self-assembled gradient nanoparticle-polymer multilayers investigated by an advanced characterization method: microbeam grazing incidence x-ray scattering
Authors: Roth S. V. , Burghammer M. , Riekel C. , Müller-Buschbaum P. , Diethert A. , Panagiotou P. , Walter H.
Published: March 2003

We investigated a gradient of nanometer-sized, self-assembled gold clusters on top of a thin polymer film. Using an advanced characterization method for gradient surfaces and thin films, the characteristic change in cluster height is detected. Our unprecedented approach combining a powerful thin-film characterization method with a micrometer-sized x-ray beam enhances the spatial resolution used thus far by two orders of magnitude. We show that this advanced concept allows for a nondestructive and contact-free reconstruction of the three-dimensional structure and morphology of the nanocluster gradient layer. Despite its change in thickness, the individual clusters’ in-plane shape and distance remains constant.
Excitonic luminescence from nonsymmetric heterovalent AlAs/GaAs/ZnSe quantum wells
Authors: Kudelski A. , Bindley U. , Furdyna J. K. , Dobrowolska M. , Wojtowicz T.
Published: March 2003

We report the observation of excitons localized in an asymmetric GaAs quantum well (QW) embedded between AlAs and ZnSe barriers. Samples with different QW thicknesses (10, 15, and 18 monolayers) have been studied, showing clear confining effects in the photoluminescence emission. To achieve confinement in the GaAs QWs, it was necessary to design the band alignment across the AlAs/GaAs/ZnSe layer sequence, and to carefully tailor the growth conditions in order to achieve the required band alignment profile.
Optimizing the giant magnetoresistance of NiFe/Cu/Co pseudo spin-valves prepared by magnetron sputtering
Authors: Paul Amitesh , Damm Thorsten , Bürgler Daniel E. , Stein Simon , Kohlstedt Hermann , Grünberg Peter
Published: March 2003

We study the dependence of magnetic and magnetotransport properties of NiFe/Cu/Co pseudo spin-valves on the pressure of the Ar sputtering gas during magnetron deposition. The giant magnetoresistance (GMR) ratio as a function of the sputtering pressure behaves nonmonotonically with a maximum of about 4% at an intermediate pressure of 0.87×10−2 mbar. Magneto-optic Kerr-effect measurements reveal different coercive fields and independent switching of the Co and NiFe layers. The structural characterization by x-ray scattering shows no significant pressure dependence. However, we observe by atomic force microscopy a variation of the grain structure with increasing sputtering pressure; the grain size first decreases and then the grains start clustering for highest pressures. The reduced coercive field and the lower GMR ratio indicate that the clustered grains have weaker magnetic pinning and increased spin-independent scattering.
The importance of bias pulse rise time for determining shallow implanted dose in plasma immersion ion implantation
Authors: Kwok D. T. K. , Bilek M. M. M. , McKenzie D. R. , Chu P. K.
Published: March 2003

The composition of the low-energy ions arising from the rise and fall time periods of the voltage pulse in plasma immersion ion implantation (PIII) are simulated by particle-in-cell (PIC) modeling. It is shown that more than 70% of the low-energy ions with an energy corresponding to less than half of the applied voltage come from the short rise time period. Although the fall time period is typically 30 times longer than the rise time, less than 25% of the low-energy ions originate from it. Based on the PIC results, the depth profile of the implanted ions is derived using the Monte-Carlo code SRIM2000 [J. F. Ziegler, The Stopping and Range of Ions in Solids (Pergamon, New York, 1985)]. The low-energy ions are found to be implanted to a much shallower depth than ions introduced during the fall time period the concentration profile which decays more sharply into the bulk. These results indicate that the most effective way to reduce or increase the surface concentration is by adjusting the rise time of the PIII voltage pulse. This will require a power supply capable of fast rise times and good matching between power supply and load.
Rescaled electrical properties of ZnO/low density polyethylene nanocomposites
Authors: Hong J. I. , Schadler L. S. , Siegel R. W. , Mårtensson E.
Published: March 2003

ZnO/low density polyethylene (LDPE) nanocomposites were prepared using melt mixing with good dispersion of the ZnO nanoparticles. The electrical properties (dc resistivity and breakdown strength) of the composite with various concentrations of ZnO up to the percolation limit were measured and compared to the corresponding electrical properties of submicron ZnO filled LDPE. It was observed that the nanocomposites exhibited a lower percolation limit and a slower decrease in resistivity with filler concentration compared to the conventional composite. The dielectric breakdown strength was also found to be higher for the nanocomposite at high filler concentration.
Point-contact current-imaging atomic force microscopy: Measurement of contact resistance between single-walled carbon nanotubes in a bundle
Authors: Otsuka Yoichi , Naitoh Yasuhisa , Matsumoto Takuya , Kawai Tomoji
Published: March 2003

Conductance of bundled single-walled carbon nanotubes (b-SWCNTs) are measured by point-contact current-imaging atomic force microscopy (PCI–AFM). Simultaneous mapping of the topographic information and current through SWCNTs enable us to investigate the relationship between structure and conductance. Variation in resistance of a b-SWCNT indicates that the resistance between SWCNTs was higher than 107 Ω with strong voltage dependence. Because PCI–AFM measurement can obtain vertical conductance information, this approach appears to be a powerful technique for characterization of nanoscale electronic devices.
Level degeneracy and temperature-dependent carrier distributions in self-organized quantum dots
Authors: Kim K. , Norris T. B. , Ghosh S. , Singh J. , Bhattacharya P.
Published: March 2003

Using femtosecond three-pulse pump–probe spectroscopy, we investigated the transparency condition for the ground and first excited states in self-organized In0.4Ga0.6As quantum dots at different temperatures and wavelengths. The temperature-dependent behavior of the transparency condition is consistent with calculations using a multilevel model with a large density of states in the quantum-well reservoir. The twofold spatial degeneracy of the first excited state and the temperature dependence of the thermal equilibrium processes were experimentally observed.
A predictive tool in micro- and nanoengineering: Straightforward estimation of conformal film growth efficiency
Authors: De Virgiliis A. , Azzaroni O. , Salvarezza R. C. , Albano E. V.
Published: March 2003

It is shown that the conformal film growth (CFG) efficiency (εCFG) of micro- and nanoscale cavities can be rationalized in terms of relevant physical and geometric parameters. Based on extensive numerical simulations and using the dynamic scaling theory of interface growth, it is concluded that the relevant quantity for the evaluation of εCFG is the so-called physical aspect ratio SP=L/Mβ/α, where α (β) is the roughness (growth) exponent that governs the dynamic evolution of the system, and L (M) is the typical depth (width) of the cavity. The theoretical predictions are in excellent agreement with recently reported experimental data for the super conformal filling of electrodeposited copper and chemically deposited silver in confined geometries [J. Electrochem. Soc. 147, 4524 (2000)], thus providing the basis of a tool to manage micro- and nano-engineering-related problems not completely resolved so far.
Effects of geometry and doping on the operation of molecular transistors
Authors: Yang Zhongqin , Lang Norton D. , Di Ventra Massimiliano
Published: March 2003

We report first-principles calculations of current versus gate voltage characteristics of a molecular transistor with a phenyldithiolate molecule as active element. We show that (i) when the molecule is placed in proximity to the gate electrode, current modulation and resonant tunneling can occur at very small gate voltages. This is due to the first-order perturbation of the electronic states induced by the electrostatic potential of the gate in the molecular region. Such perturbation is present even if the molecule does not have an intrinsic dipole moment. (ii) The molecular transistor can be converted from n-type to p-type by the simple co-adsorption of a single oxygen atom placed near the molecule. While the latter finding suggests that the character of molecular transistors can be easily changed by doping the electrode surfaces, it also puts severe constraints on the experimental control of such structures for molecular electronics applications.
Dynamic crossover in supercooled liquids induced by high pressure
Authors: Casalini Riccardo , Paluch Marian , Roland C. Michael
Published: March 2003

The physics underlying the dynamics of molecules near their glass temperature, Tg, comprises one of the major unsolved problems in condensed matter. Of particular interest are the striking changes in relaxation properties observed at temperatures ∼1.2 times higher than Tg. Herein, we describe experiments in which these changes in dynamics are induced by pressure variations. For several supercooled liquids, the relaxation time associated with the change in dynamics is found to be invariant to both temperature and pressure. That is, the time scale of the molecular motions determines the onset of strong intermolecular cooperativity and the accompanying dynamical changes. While thermodynamic variables such as temperature and pressure influence the crossover in dynamics, the governing variable is the time scale.
Fuzzy Urban Sets: Theory and Application to Desakota Regions in China
Authors: Heikkila Eric J , Shen Ti-Yan , Yang Kai-Zhong
Published: March 2003

This paper outlines a method for using the mathematics of fuzzy sets that is well suited to measure and characterize periurbanizing ( desakota) systems typical of China, Southeast Asia, and other areas experiencing rapid urbanization. Drawing on Kosko's ‘fuzzy hypercube’, we derive three distinct but interdependent measures: (1) extent of urbanization, (2) level of fuzziness, and (3) degree of entropy. The feasibility of the proposed method is demonstrated by using remote sensing data for Ningbo, China.
Neighbourhood Land Use and Performance: The Evolution of Neighbourhood Morphology over the 20th Century
Authors: Filion Pierre , Hammond Karen
Published: March 2003

To what extent does the evolution of 20th-century residential area planning and development reflect the profound changes that have affected society over this period? How much was this evolution shaped by successive planning models formulated over the last century? The paper reports on an analysis of the land-use patterns of four neighbourhoods developed at different times over the 20th century. Data originate from field surveys and a systematic measurement of the land uses of the study areas. Findings paint a mixed picture. They show that some societal changes (rising affluence for example) have affected neighbourhood morphology, whereas others (such as cultural diversification) have left few traces. A comparison of different land-use features identifies both the advantages and downsides of each neighbourhood's morphology. It becomes difficult in this light to perceive the evolution of neighbourhood planning as a linear progression towards improved land-use efficiency and quality of life.
Accessibility and Mode-Destination Choice Decisions: Exploring Travel in Three Neighborhoods in Puget Sound, WA
Authors: Limanond Thirayoot , Niemeier Debbie A
Published: March 2003

Despite the popularity of the neotraditional development concept, attempts to investigate the effectiveness of various mixed-use core (MUC) designs in terms of induced localized walking trips are rare. In this study, we use the logsum measure of accessibility derived from a random utility model to investigate how neighborhood design and regional setting affect mode and destination choices for shopping and how these effects vary by income and day of week. We then use the random utility model to simulate changes in the design configuration of the neighborhood MUC and evaluate the effects of the changes on within-neighborhood-accessibility and travel-decision parameters. Our results provide insight on how traditional neighborhood residents choose destinations and modes for their shopping travel and how the geometric design of the MUC can affect travel decisions. We found that local and regional accessibility have interrelated effects on the choice decisions of traditional residents, which results in variations in travel decisions over neighborhood space. In addition, these variations appear even after controlling for income groups and day of week. In simulations evaluating the effectiveness of alternative MUC designs, we find that the optimal MUC design is the one that maximizes proximity to all residential locations in the neighborhood. That is, MUC designs that are confined to the center of the neighborhood are less effective in inducing within-neighborhood shopping.
Computing with Ambiguity
Authors: Knight Terry
Published: March 2003

In a previous paper, emergence and ways of computing with emergence were discussed. Emergence goes hand in hand with ambiguity. Ambiguity, of a particular kind, is foundational in shape grammars. Shape grammars compute with shapes that have ambiguous or indefinite parts. This part ambiguity is exploited easily and well in shape grammar computations. Another kind of ambiguity is considered here. This is representational ambiguity—an ambiguity of the nature of the elements that make up shapes. Shapes are represented with elements—points, lines, planes, and solids—that can have ambiguous and fluid interpretations as material, conceptual, symbolic, or other entities. Like part ambiguity, representational ambiguity is integral to the beginning, exploratory stages of a design process. Among the best and most explicit treatments of representational ambiguity were those given by two prominent design theorists of the 20th century, Wassily Kandinsky and Paul Klee. Informal examples of representational ambiguity from the writings of Kandinsky and Klee are reviewed here. These are used to motivate ways of handling representational ambiguity computationally. New kinds of algebras for shape grammar computations that support some of the ambiguities suggested by Kandinsky and Klee, as well as other kinds, are proposed.
Texture Preference and Global Frequency Magnitudes
Authors: Schira Gretchen
Published: March 2003

A relationship between human preferences for physical properties of visual texture is established in this paper. The author asks whether there is a measurable correlation between aesthetic ratings for textural images and their physical properties. A bank of Gabor filters covering a range of frequencies and orientations are used to extract properties. Three studies are conducted and the correlations between aesthetic ratings and the properties were significant and large. The correlations proved robust when image identifiability was incorporated in the first and third studies and removed from the second study. In this, it is suggested that memory and association are not exclusively driving (aesthetic) preference; that it is also tuned to properties of spatial frequency and orientation of certain visual stimuli.
Convex Land Acquisition with Zero-One Programming
Authors: Williams Justin C
Published: March 2003

The land-acquisition problem involves selecting multiple discrete parcels to be acquired for a particular land use. In previous models, typical selection criteria have been land cost, land area, and spatial attributes such as contiguity and compactness. Here I introduce a new spatial attribute, convexity. I develop a way to approximate convex shapes in continuous space with ‘cellularly convex’ shapes composed of grid cells. A zero-one programming model is formulated for finding minimum-cost cellularly convex regions of specified area. Computational experience with 144-cell and 1024-cell demonstration problems is reported, and results and extensions are discussed.
Ecospatial Outcomes of Neoliberal Planning: Habitat Management in Auckland Region, New Zealand
Authors: Coombes Brad L
Published: March 2003

In line with the paradigmatic shift towards spatial ecology, it is generally accepted that the conservation value of a habitat remnant cannot be determined in isolation from its wider landscape. Sensitivity to the spatial context of forest patches should, therefore, characterise habitat management. Conversely, neoliberal planning disregards ecospatial configuration because it abandons resource decisionmaking to the spatially ad hoc outcomes of market processes. Analysis of bush-lot subdivision—the foremost protection mechanism for indigenous habitat on private land in the Auckland Region—demonstrates that the neoliberal agenda for planning contradicts fundamental tenets of conservation ecology. With its foundations in voluntarism and market mechanisms, bush-lot subdivision induces selection bias in the location of protected remnants. Strategic and interventionist approaches will be required to moderate the impact of habitat loss, fragmentation, and perforation.
Neighborhoods as Service Providers: A Methodology for Evaluating Pedestrian Access
Authors: Talen Emily
Published: March 2003

Research on neighborhoods is dominated by a focus on the social aspects of neighborhood life. The ability of neighborhoods to function as service providers is a critical and understudied aspect of neighborhood research. This paper offers a methodological contribution of the analysis of neighborhoods as service providers. Provision of services is defined in terms of accessibility, or the spatial proximities between residents and the facilities. Because the focus is on neighborhoods, access is defined on the basis of the pedestrian rather than the automobile. In addition, the needs of the neighborhood population are considered. A case study of Portland, Oregon, is used to demonstrate how an evaluation of pedestrian access could be conducted at the neighborhood scale.
The Aperture Problems in the Pulfrich Effect
Authors: Ito Hiroyuki
Published: March 2003

The Pulfrich effect yields a perceived depth for horizontally moving objects but not for vertically moving ones. In this study the Pulfrich effect was measured by translating oblique lines seen through a circular window, which made motion direction ambiguous. Overlaying random dots that moved horizontally, vertically, or diagonally controlled the perceptual motion direction of the lines. In experiment 1, when the lines were seen to move horizontally, the effect was strongest in spite of the same physical motion of the lines. Experiment 2 was performed to test the above conditions again, excluding the Pulfrich effect of the dots on the depth of the lines. The overlaid dots were presented to one eye only. The result showed that the Pulfrich effect of the lines was persistently strong in spite of the perceptual changes in motion direction. Experiment 3 also showed that the Pulfrich depth was independent of the perceived horizontal speed in a plaid display. The Pulfrich effect was determined by measuring the horizontal disparity component, independently of the perceived motion direction. These results demonstrate that the aperture problems in motion and stereopsis in the Pulfrich effect are solved independently.
Projective boundedness and convolution of Fréchet measures
Authors: Blei R. , Caggiano J.
Published: March 2003

Fréchet measures of order

n
n

(

F

n

\mathcal {F}_n

-measures) are the measure- theoretic analogues of bounded

n
n

-linear forms on products of

C
0

(
K
)

C_0(K)

spaces. In an LCA setting, convolution of

F

2

\mathcal {F}_2

-measures is always defined, while there exist

F

3

\mathcal {F}_3

-measures whose convolution cannot be defined. In a three-dimensional setting, we demonstrate the existence of an

F

2

\mathcal {F}_2

-measure which cannot be convolved with arbitrary

F

3

\mathcal {F}_3

-measures.
Some new embeddings and nonimmersions of real projective spaces
Authors: Davis Donald , Zelov Vitaly
Published: March 2003

We obtain new families of embeddings and nonimmersions of real projective spaces in Euclidean space. The method involves obstruction theory, and includes several new insights.
On the density of the set of generators of a polynomial algebra
Authors: Drensky Vesselin , Shpilrain Vladimir , Yu Jie-Tai
Published: March 2003

Let

K
[
X
]
=
K
[

x
1

,
.
.
.
,

x
n

]
,
 
n
≥
2
,

K[X] = K[x_1,...,x_n], ~n \ge 2,

be the polynomial algebra over a field

K
K

of characteristic

0
0

. We call a polynomial

 
p
∈
K
[
X
]

~p \in K[X]

coordinate (or a generator) if

K
[
X
]
=
K
[
p
,

p
2

,
.
.
.
,

p
n

]

K[X] = K[p, p_2, ..., p_n]

for some polynomials

 

p
2

,
.
.
.
,

p
n

~p_2, ..., p_n

. In this note, we give a simple proof of the following interesting fact: for any polynomial

 
h
 

~h~

of the form

 
(

x
i

+
q
)
,

~(x_i + q),

where

q
q

is a polynomial without constant and linear terms, and for any integer

 
m
≥
2

~m \ge 2

, there is a coordinate polynomial

 
p
 

~p~

such that the polynomial

(
p
−
h
)

(p-h)

has no monomials of degree

≤
m

\leq m

. A similar result is valid for coordinate

k
k

-tuples of polynomials, for any

k
>
n

k > n

. This contrasts sharply with the situation in other algebraic systems. On the other hand, we establish (in the two-variable case) a result related to a different kind of density. Namely, we show that given a non-coordinate two-variable polynomial, any sufficiently small perturbation of its non-zero coefficients gives another non-coordinate polynomial.
On the pointwise maximum of convex functions
Authors: Fitzpatrick S. , Simons S.
Published: March 2003

We study the conjugate of the maximum,

f
∨
g

f \vee g

, of

f
f

and

g
g

when

f
f

and

g
g

are proper convex lower semicontinuous functions on a Banach space

E
E

. We show that

(
f
∨
g

)

∗
∗

=

f

∗
∗

∨

g

∗
∗

(f \vee g)^{**} = f^{**} \vee g^{**}

on the bidual,

E

∗
∗

E^{**}

, of

E
E

provided that

f
f

and

g
g

satisfy the Attouch-Brézis constraint qualification, and we also derive formulae for

(
f
∨
g

)

∗

(f \vee g)^{*}

and for the “preconjugate” of

f

∗

∨

g

∗

f^{*}\vee g^{*}

.
On a theorem by Farb and Masur
Authors: Fujiwara Koji
Published: March 2003

Farb and Masur showed that an irreducible lattice in a semisimple Lie group of rank at least two always has finite image by a homomorphism into the outer automorphism group of a closed, orientable surface group. We point out that their theorem extends to the outer automorphism groups of a certain class of torsion-free, freely indecomposable word-hyperbolic groups.
Weak type estimates for cone multipliers on 𝐻^{𝑝} spaces, 𝑝<1
Authors: Hong Sunggeum
Published: March 2003

We consider operators

T

δ

T^{\delta }

associated with the Fourier multipliers
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis 1 minus StartFraction StartAbsoluteValue xi Superscript prime Baseline EndAbsoluteValue squared Over xi Subscript n plus 1 Superscript 2 Baseline EndFraction right-parenthesis Subscript plus Superscript delta Baseline comma left-parenthesis xi prime comma xi Subscript n plus 1 Baseline right-parenthesis element-of double-struck upper R Superscript n Baseline times double-struck upper R comma">

(

1
−

|

ξ

′

|

2

ξ

n
+
1

2

)

+

δ

,

(

ξ

′

,

ξ

n
+
1

)
∈

R

n

×

R

,

\begin{equation*}{\bigg (}1- \frac {|{\xi }’|^{2}}{{\xi }_{n+1}^{2}} {\bigg )}_{+}^{\delta },\quad \quad ({\xi }’,\xi _{n+1}) \in {\mathbb R}^{n} \times {\mathbb R},\end{equation*}

and show that

T

δ

T^{\delta }

is of weak type

(
p
,
p
)

(p,p)

on

H

p

(

R

n
+
1

)

H^{p}({\mathbb R}^{n+1})

,

0
>
p
>
1

0 > p > 1

, for the critical value

δ
=
n
(

1
p

−

1
2

)
−

1
2

\delta = n(\frac {1}{p}-\frac {1}{2}) - \frac {1}{2}

.
Embedding obstructions and 4-dimensional thickenings of 2-complexes
Authors: Krushkal Vyacheslav
Published: March 2003

The vanishing of Van Kampen’s obstruction is known to be necessary and sufficient for embeddability of a simplicial

n
n

-complex into

R

2
n

{\mathbb {R}}^{2n}

for

n
≠
2

n\neq 2

, and it was recently shown to be incomplete for

n
=
2

n=2

. We use algebraic-topological invariants of four-manifolds with boundary to introduce a sequence of higher embedding obstructions for a class of

2
2

-complexes in

R

4

{\mathbb {R}}^4

.
ℛ-compact spaces with 𝒳<ℰ𝓍𝓅_{ℛ}𝒳
Authors: Mrowka S.
Published: March 2003

Answering a question of Arhangel’skii, we show—under GCH—that for most cardinals

m

\mathfrak {m}

there exists an

R

\mathscr {R}

-compact space

X
X

such that

weight
⁡
X
=

m

\operatorname {weight} X = \mathfrak {m}

but

X
X

does not embed in a closed fashion into the product of

m

\mathfrak {m}

copies of

R

\mathscr {R}

.
Four-genus and four-dimensional clasp number of a knot
Authors: Murakami Hitoshi , Yasuhara Akira
Published: March 2003

For a knot

K
K

in the

3
3

-sphere, by using the linking form on the first homology group of the double branched cover of the

3
3

-sphere, we investigate some numerical invariants,

4
4

-genus

g
∗

(
K
)

g^*(K)

, nonorientable

4
4

-genus

γ
∗

(
K
)

\gamma ^*(K)

and

4
4

-dimensional clasp number

c
∗

(
K
)

c^*(K)

, defined from the four-dimensional viewpoint. T. Shibuya gave an inequality

g
∗

(
K
)
≤

c
∗

(
K
)

g^*(K)\leq c^*(K)

, and asked whether the equality holds or not. From our result in this paper, we find that the equality does not hold in general.
A sharp Schwarz inequality on the boundary
Authors: Osserman Robert
Published: March 2003

A number of classical results reflect the fact that if a holomorphic function maps the unit disk into itself, taking the origin into the origin, and if some boundary point

b
b

maps to the boundary, then the map is a magnification at

b
b

. We prove a sharp quantitative version of this result which also sharpens a classical result of Loewner.
Sobolev type inequalities for general symmetric forms
Authors: Wang Feng-Yu
Published: March 2003

A general version of the Sobolev type inequality, including both the classical Sobolev inequality and the logarithmic Sobolev one, is studied for general symmetric forms by using isoperimetric constants. Some necessary and sufficient conditions are presented as results. The main results are illustrated by two examples of birth-death processes.
Loop spaces and the compression theorem
Authors: Wiest Bert
Published: March 2003

For a smooth, finite-dimensional manifold

M
M

with a submanifold

S
S

we study the topology of the straight loop space

Ω
S

s
t

M

\Omega ^{st}_SM

, the space of loops whose intersections with

S
S

are subject to a certain transversality condition. Our main tool is Rourke and Sanderson’s compression theorem. We prove that the homotopy type of the straight loop space of a link in

S
3

S^3

depends only on the number of link components.
Strongly asymptotically stable Frobenius-Perron operators
Authors: Zaharopol Radu
Published: March 2003

Let

(
X
,
Σ
,
μ
)

(X,\Sigma ,\mu )

be a

σ
\sigma

-finite measure space and let
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T colon upper L Superscript 1 Baseline left-parenthesis upper X comma normal upper Sigma comma mu right-parenthesis right-arrow upper L Superscript 1 Baseline left-parenthesis upper X comma normal upper Sigma comma mu right-parenthesis">

T
:

L
1

(
X
,
Σ
,
μ
)
→

L
1

(
X
,
Σ
,
μ
)

T : L^1(X,\Sigma ,\mu ) \to L^1(X,\Sigma ,\mu )

be a Frobenius-Perron operator. In 1997 Bartoszek and Brown proved that if

T
T

overlaps supports and if there exists

h
∈

L
1

(
X
,
Σ
,
μ
)

h \in L^1(X,\Sigma ,\mu )

,

h
>
0

h > 0

on

X
X

, such that

T
h
=
h

Th = h

, then

T
T

is (strongly) asymptotically stable. In the note we prove that instead of assuming that

h
>
0

h > 0

on

X
X

, it is enough to assume that

h
≥
0

h\geq 0

and

h
≠
0

h\neq 0

. More precisely, we prove that

T
T

is asymptotically stable if and only if

T
T

overlaps supports and there exists

h
∈

L
1

(
X
,
Σ
,
μ
)

h\in L^1(X,\Sigma ,\mu )

,

h
≥
0

h\geq 0

,

h
≠
0

h\neq 0

, such that

T
h
=
h

Th=h

.
On a characterization of finite vector bundles as vector bundles admitting a flat connection with finite monodromy group
Authors: Biswas Indranil , Holla Yogish , Schumacher Georg
Published: March 2003

We prove that a holomorphic vector bundle

E
E

over a compact connected Kähler manifold admits a flat connection, with a finite group as its monodromy, if and only if there are two distinct polynomials

f
f

and

g
g

, with nonnegative integral coefficients, such that the vector bundle

f
(
E
)

f(E)

is isomorphic to

g
(
E
)

g(E)

. An analogous result is proved for vector bundles over connected smooth quasi-projective varieties, of arbitrary dimension, admitting a flat connection with finite monodromy group. When the base space is a connected projective variety, or a connected smooth quasi-projective curve, the above characterization of vector bundles admitting a flat connection with finite monodromy group was established by M. V. Nori.
Alexander numbering of knotted surface diagrams
Authors: Carter J. , Kamada Seiichi , Saito Masahico
Published: March 2003

A generic projection of a knotted oriented surface in 4-space divides

3
3

-space into regions. The number of times (counted with sign) that a path from infinity to a given region intersects the projected surface is called the Alexander numbering of the region. The Alexander numbering is extended to branch and triple points of the projections. A formula that relates these indices is presented.
Entire regularizations of strongly continuous groups and products of analytic generators
Authors: Cioranescu Ioana , Keyantuo Valentin
Published: March 2003

Using entire regularizations of

C
0

−

C_0-

groups, we give a characterization of their analytic generators which we apply to the study of products of such generators.
Totally nonnegative and oscillatory elements in semisimple groups
Authors: Fomin Sergey , Zelevinsky Andrei
Published: March 2003

We generalize the well known characterizations of totally nonnegative and oscillatory matrices, due to F. R. Gantmacher, M. G. Krein, A. Whitney, C. Loewner, M. Gasca, and J. M. Peña to the case of an arbitrary complex semisimple Lie group.
Perturbed Dolbeault operators and the homology Todd class
Authors: Fox Jeffrey , Haskell Peter
Published: March 2003

This paper discusses the role played by perturbed Dolbeault operators in relating the coherent sheaf and elliptic operator perspectives on the

K
K

homology of projective varieties. Among the consequences are index formulas for perturbed Dolbeault operators.
Note on a Littlewood-Paley inequality
Authors: Wilson J.
Published: March 2003

We show that a recent result of Littlewood-Paley type, due to the author, is essentially best-possible.
Pointwise convergence of a class of non-orthogonal wavelet expansions
Authors: Zayed Ahmed
Published: March 2003

Non-orthogonal wavelet expansions associated with a class of mother wavelets is considered. This class of wavelets comprises mother wavelets that are not necessarily integrable over the whole real line, such as Shannon’s wavelet. The pointwise convergence of these wavelet expansions is investigated. It is shown that, unlike other wavelet expansions, the ones under consideration do not necessarily converge pointwise to the functions at points of continuity, unless a more stringent condition, such as bounded variation, is imposed.
On weighted polynomial approximation with monotone weights
Authors: Borichev Alexander
Published: March 2003

We construct an even weight

W
W

monotone on the right half line such that the logarithmic integral of the largest

log
\log

-convex minorant of

W
W

converges and the polynomials are dense in

C
(
W
)

C(W)

.
One-step extension of the Bergman shift
Authors: Choi Yong , Han Jin Kyu , Lee Woo
Published: March 2003

In this paper we answer a question of Curto and Fialkow: there exists a quadratically hyponormal weighted shift which is not positively quadratically hyponormal.
Pyramidal vectors and smooth functions on Banach spaces
Authors: Deville R. , Matheron E.
Published: March 2003

We prove that if

X
X

,

Y
Y

are Banach spaces such that

Y
Y

has nontrivial cotype and

X
X

has trivial cotype, then smooth functions from

X
X

into

Y
Y

have a kind of “harmonic" behaviour. More precisely, we show that if

Ω

\,\Omega

is a bounded open subset of

X
X

and

f
:

Ω
¯

→
Y

f:{\overline {\Omega }}\to Y

is

C

1

C^{1}

-

\,

smooth with uniformly continuous Fréchet derivative, then

f
(
∂
Ω
)

f(\partial \Omega )

is dense in

f
(

Ω
¯

)

f({\overline {\Omega }})

. We also give a short proof of a recent result of P. Hájek.
Duals and topological center of a class of matrix algebras with applications
Authors: Esslamzadeh G.
Published: March 2003

We characterize the topological center of a class of matrix algebras, which are called

ℓ

1

\ell ^{1}

-Munn algebras. This involves a characterization of Arens regular semigroup algebras for a large class of semigroups, which is an extension of Young’s Theorem for semigroups. We show by some counter examples that only up to a certain extent Young’s Theorem can be generalized.
Irreducible constituents of faithful induced characters
Authors: Isaacs I.
Published: March 2003

Let

G
G

be a finite group, and suppose

χ
\chi

is a character of

G
G

obtained by inducing an irreducible character of some subgroup of

G
G

. If

χ
\chi

is faithful, we show that some irreducible constituent of

χ
\chi

has a solvable kernel. This yields an improved version of a theorem of Evdokimov and Ponomarenko.
The undecidability of cyclotomic towers
Authors: Videla Carlos
Published: March 2003

Let

Q

(

p
∞

)

\mathbb {Q}(p^\infty )

be the field obtained by adjoining to

Q

\mathbb {Q}

all

p
p

–power roots of unity where

p
p

is a prime number. We prove that the theory of

Q

(

p
∞

)

\mathbb {Q}(p^\infty )

is undecidable.
Equlibrium measure of a product subset of ℂⁿ
Authors: Błocki Zbigniew
Published: March 2003

In this note we show that an equilibrium measure of a product of two subsets ofCn{\mathbb {C}}^{n}andCm{\mathbb {C}}^{m}, respectively, is a product of their equilibrium measures. We also obtain a formula for(ddcmax{u,v})p(dd^{c}\max \{u,v\})^{p}, whereu,vu,vare locally bounded plurisubharmonic functions and2≤p≤n2\leq p\leq n.
Openness of induced projections
Authors: Charatonik Janusz , Charatonik Włodzimierz , Illanes Alejandro
Published: March 2003

For continua

X
X

and

Y
Y

it is shown that if the projection

f
:
X
×
Y
→
X

f:X\times Y\to X

has its induced mapping

C
(
f
)

C(f)

open, then

X
X

is

C

∗

C^{*}

-smooth. As a corollary, a characterization of dendrites in these terms is obtained.
Isometrical embeddings of separable Banach spaces into the set of nowhere approximatively differentiable and nowhere Hölder functions
Authors: Hencl Stanislav
Published: March 2003

The well-known Banach-Mazur theorem says that every separable Banach space can be isometrically embedded into

C
(
[
0
,
1
]
)

C([ 0,1])

. We prove that this embedding can have the property that the image of each nonzero element is a nowhere approximatively differentiable and nowhere Hölder function. It improves a recent result of L. Rodriguez-Piazza where the images are nowhere differentiable functions.
Uniqueness of the trace and simplicity
Authors: Murphy Gerard
Published: March 2003

It is proved that for certain large classes of unital C*-algebras, the existence of a unique, faithful tracial state implies simplicity. An example is given to show that this implication does not hold for all unital C*-algebras.
Lamé differential equations and electrostatics
Authors: Dimitrov Dimitar , Van Assche Walter
Published: March 2003

The problem of existence and uniqueness of polynomial solutions of the Lamé differential equation

A
(
x
)

y

′
′

+
2
B
(
x
)

y
′

+
C
(
x
)
y
=
0
,

\begin{equation*} A(x) y^{\prime \prime } + 2 B(x) y’ + C(x) y = 0, \end{equation*}

where

A
(
x
)
,
B
(
x
)

A(x), B(x)

and

C
(
x
)

C(x)

are polynomials of degree

p
+
1
,
p

p+1, p

and

p
−
1

p-1

, is under discussion. We concentrate on the case when

A
(
x
)

A(x)

has only real zeros

a

j

a_{j}

and, in contrast to a classical result of Heine and Stieltjes which concerns the case of positive coefficients

r

j

r_{j}

in the partial fraction decomposition
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper B left-parenthesis x right-parenthesis slash upper A left-parenthesis x right-parenthesis equals sigma-summation Underscript j equals 0 Overscript p Endscripts r Subscript j Baseline slash left-parenthesis x minus a Subscript j Baseline right-parenthesis">

B
(
x
)

/

A
(
x
)
=

∑

j
=
0

p

r

j

/

(
x
−

a

j

)

B(x)/A(x) = \sum _{j=0}^{p} r_{j}/(x-a_{j})

, we allow the presence of both positive and negative coefficients

r

j

r_{j}

. The corresponding electrostatic interpretation of the zeros of the solution

y
(
x
)

y(x)

as points of equilibrium in an electrostatic field generated by charges

r

j

r_{j}

at

a

j

a_{j}

is given. As an application we prove that the zeros of the Gegenbauer-Laurent polynomials are the points of unique equilibrium in a field generated by two positive and two negative charges.
Non-closed sums of closed ideals in Banach algebras
Authors: Dixon P.
Published: March 2003

A major difficulty in Banach algebra theory is that sums of closed ideals need not be closed. We survey the known results and present examples showing that they are in most directions the best possible. We also give a new sufficient condition for closure in the uniform algebra setting.
A note on summability of multiple Laguerre expansions
Authors: Xu Yuan
Published: March 2003

A simple structure of the multiple Laguerre polynomial expansions is used to study the Cesàro summability above the critical index for the convolution type Laguerre expansions. The multiple Laguerre polynomial expansion of an

ℓ

1

\ell ^{1}

-radial function

f

0

(

|

x

|

)

f_{0}(|\mathbf x|)

is shown to be an

ℓ

1

\ell ^{1}

-radial function that coincides with the Laguerre polynomial expansion of

f

0

f_{0}

, which allows us to settle the problem of summability below the critical index for the

ℓ

1

\ell ^{1}

-radial functions.
A note on Pontrjagin forms
Authors: Datta Mahuya
Published: March 2003

Let

P
P

be a principal

O
(
2
m
)

O(2m)

bundle over a manifold

M
M

of dimension

4
m

4m

, and let

p
p

be its

m
m

-dimensional Pontrjagin class. In this paper, we aim at answering the following question: Which representatives of the class

p
p

can be realised as the Pontrjagin form of some connection on

P
P

?
Stochastic stability of generalized SRB measures of Axiom A basic sets
Authors: Pei-Dong Liu , Hong-Wen Zheng
Published: March 2003

In this note we prove that the generalized SRB measure of an Axiom A basic set is stable under random diffeomorphisms type perturbations.
Estimates in surfaces with positive constant Gauss curvature
Authors: Gálvez José , Martínez Antonio
Published: March 2003

We give optimal bounds of the height, curvature, area and volume of

K
K

-surfaces in

R

3

\mathbb {R}^3

bounding a planar curve. The spherical caps are characterized as the unique

K
K

-surfaces achieving these bounds.
Composition operators on Dirichlet-type spaces
Authors: Hibschweiler R.
Published: March 2003

The Dirichlet-type space

D

p

 
(
1
≤
p
≤
2

D^{p}\ (1 \leq p \leq 2

) is the Banach space of functions analytic in the unit disc with derivatives belonging to the Bergman space

A

p

A^{p}

. Let

Φ
\Phi

be an analytic self-map of the disc and define

C

Φ

(
f
)
=
f
∘
Φ

C_{\Phi }(f) = f \circ \Phi

for

f
∈

D

p

f \in D^{p}

. The operator

C

Φ

:

D

p

→

D

p

C_{\Phi }: D^{p} \rightarrow D^{p}

is bounded (respectively, compact) if and only if a related measure

μ

p

\mu _{p}

is Carleson (respectively, compact Carleson). If

C

Φ

C_{\Phi }

is bounded (or compact) on

D

p

D^{p}

, then the same behavior holds on

D

q

 
(
1
≤
q
>
p

D^{q}\ (1 \leq q > p

) and on the weighted Dirichlet space

D

2
−
p

D_{2-p}

. Compactness on

D

p

D^{p}

implies that

C

Φ

C_{\Phi }

is compact on the Hardy spaces and the angular derivative exists nowhere on the unit circle. Conditions are given which, together with the angular derivative condition, imply compactness on the space

D

p

D^{p}

. Inner functions which induce bounded composition operators on

D

p

D^{p}

are discussed briefly.
Random iterations of holomorphic maps in complex Banach spaces
Authors: Włodarczyk K. , Klim D. , Gontarek E.
Published: March 2003

Conditions guaranteeing the uniform convergence to constant maps of random iterations of holomorphic contractions on unbounded domains in complex Banach spaces are established.
Trace-class perturbation and strong convergence: Wave operators revisited
Authors: Xia Jingbo
Published: March 2003

We give a new construction of wave operators for a self-adjoint operator under trace-class perturbation. This construction requires no quantitative estimates.
Existence-uniqueness and long time behavior for a class of nonlocal nonlinear parabolic evolution equations
Authors: Ackleh Azmy , Ke Lan
Published: March 2003

We establish existence and uniqueness of solutions for a general class of nonlocal nonlinear evolution equations. An application of this theory to a class of nonlinear reaction-diffusion problems that arise in population dynamics is presented. Furthermore, conditions on the initial population density for this class of problems that result in finite time extinction or persistence of the population is discussed. Numerical evidence corroborating our theoretical results is given.
Directed inverse limits of spatial locales
Authors: He Wei , Plewe Till
Published: March 2003

In this note we consider spatiality of directed inverse limits of spatial locales. We give an example which shows that directed inverse limits of compact spatial locales are not necessarily spatial. This answers a question posed by John Isbell. We also give a condition which, if satisfied by the maps of a directed inverse system, implies that taking limits preserves local compactness and hence produces spatial locales.
A counterexample concerning Whitney reversible properties
Authors: Charatonik Janusz , Charatonik Włodzimierz
Published: March 2003

Two properties of continua are shown which are strong Whitney reversible while not sequential strong Whitney reversible. This answers an old question of S. B. Nadler, Jr.
Positive eigenvalues of second order boundary value problems and a theorem of M. G. Krein
Authors: Clark Steve , Hinton Don
Published: March 2003

Conditions are given which guarantee that the least real eigenvalue is positive for certain boundary value problems for the vector-matrix equation−y′′+p(x)y=γw(x)y-y^{\prime \prime }+p(x)y=\gamma w(x)y. This leads to conditions which guarantee the stable boundedness, according to Krein, for solutions ofy′′+λp(x)y=0y^{\prime \prime }+\lambda p(x)y=0with certain real values ofλ\lambda. As a consequence, a result first stated by Krein is proven.
Forcing a Boolean algebra with predesigned automorphism group
Authors: Hyttinen Tapani , Shelah Saharon
Published: March 2003

For suitable groups

G
G

we will show that one can add a Boolean algebra

B
B

by forcing in such a way that

A
u
t
(
B
)

Aut(B)

is almost isomorphic to

G
G

. In particular, we will give a positive answer to the following question due to J. Roitman: Is

ℵ

ω

\aleph _{\omega }

a possible number of automorphisms of a rich Boolean algebra?
On classes of maps which preserve finitisticness
Authors: Koyama Akira , Moron Manuel
Published: March 2003

We shall prove the following:(1)(1)Letr:X→Yr:X \to Ybe a refinable map between paracompact spaces. ThenXXis finitistic if and only ifYYis finitistic.(2)(2)Letf:X→Yf:X \to Ybe a hereditary shape equivalence between metric spaces. Then ifXXis finitistic,YYis finitistic.
A Ramsey theorem for measurable sets
Authors: Laczkovich M.
Published: March 2003

We prove that if

X
X

is a perfect Polish space and

[
X

]
2

=

P
0

∪
…
∪

P

k
−
1

[X]^2 =P_0 \cup \ldots \cup P_{k-1}

is a partition with universally measurable pieces, then there is Cantor set

C
⊂
X

C\subset X

with

[
C

]
2

⊂

P
i

[C]^2 \subset P_i

for some

i
.

i.
Approximation of convex bodies by axially symmetric bodies
Authors: Lassak Marek
Published: March 2003

Let

C
C

be an arbitrary planar convex body. We prove that

C
C

contains an axially symmetric convex body of area at least

2
3

|

C

|

\frac {2}{3}|C|

. Also approximation by some specific axially symmetric bodies is considered. In particular, we can inscribe a rhombus of area at least

1
2

|

C

|

\frac {1}{2}|C|

in

C
C

, and we can circumscribe a homothetic rhombus of area at most

2

|

C

|

2|C|

about

C
C

. The homothety ratio is at most

2
2

. Those factors

1
2

\frac {1}{2}

and

2
2

, as well as the ratio

2
2

, cannot be improved.
Positive solutions of a logistic equation on unbounded intervals
Authors: Ma Li , Xu Xingwang
Published: March 2003

In this paper, we study the existence of positive solutions of a one-parameter family of logistic equations on

R
+

R_+

or on

R
R

. These equations are stationary versions of the Fisher equations and the KPP equations. We also study the blow-up region of a sequence of the solutions when the parameter approaches a critical value and the non-existence of positive solutions beyond the critical value. We use the direct method and the sub and super solution method.
A proof of Weinberg’s conjecture on lattice-ordered matrix algebras
Authors: Ma Jingjing , Wojciechowski Piotr
Published: March 2003

Let

F

\mathbf {F}

be a subfield of the field of real numbers and let

F

n

\mathbf {F}_{n}

(

n
≥
2

n \geq 2

) be the

n
×
n

n \times n

matrix algebra over

F

\mathbf {F}

. It is shown that if

F

n

\mathbf {F}_{n}

is a lattice-ordered algebra over

F

\mathbf {F}

in which the identity matrix 1 is positive, then

F

n

\mathbf {F}_{n}

is isomorphic to the lattice-ordered algebra

F

n

\mathbf {F}_{n}

with the usual lattice order. In particular, Weinberg’s conjecture is true.
Continuity and differentiability for weighted Sobolev spaces
Authors: Mizuta Yoshihiro , Shimomura Tetsu
Published: March 2003

Our aim in this paper is to discuss continuity and differentiability of functions in weighted Sobolev spaces in the limiting case of Sobolev’s imbedding theorem.