bluuebunny/crossref_metadata_2025 huggingface dataset:
Response and sensitivity of the nocturnal boundary layer over land to added longwave radiative forcing
Authors: McNider R. T. , Steeneveld G. J. , Holtslag A. A. M. , Pielke R. A. , Mackaro S. , Pour‐Biazar A. , Walters J. , Nair U. , Christy J.
Published: June 2012

One of the most significant signals in the thermometer‐observed temperature record since 1900 is the decrease in the diurnal temperature range over land, largely due to rising of the minimum temperatures. Generally, climate models have not well replicated this change in diurnal temperature range. Thus, the cause for night‐time warming in the observed temperatures has been attributed to a variety of external causes. We take an alternative approach to examine the role that the internal dynamics of the stable nocturnal boundary layer (SNBL) may play in affecting the response and sensitivity of minimum temperatures to added downward longwave forcing. As indicated by previous nonlinear analyses of a truncated two‐layer equation system, the SNBL can be very sensitive to changes in greenhouse gas forcing, surface roughness, heat capacity, and wind speed. A new single‐column model growing out of these nonlinear studies is used to examine the SNBL. Specifically, budget analyses of the model are provided that evaluate the response of the boundary layer to forcing and sensitivity to mixing formulations. Based on these model analyses, it is likely that part of the observed long‐term increase in minimum temperature is reflecting a redistribution of heat by changes in turbulence and not by an accumulation of heat in the boundary layer. Because of the sensitivity of the shelter level temperature to parameters and forcing, especially to uncertain turbulence parameterization in the SNBL, there should be caution about the use of minimum temperatures as a diagnostic global warming metric in either observations or models.
Thermochromic effect at room temperature of Sm0.5Ca0.5MnO3 thin films
Authors: Boileau A. , Capon F. , Barrat S. , Laffez P. , Pierson J. F.
Published: June 2012

Sm0.5Ca0.5MnO3 thermochromic thin films were synthesized using dc reactive magnetron co-sputtering and subsequent annealing in air. The film structure was studied by x-ray diffraction analysis. To validate the thermochromic potentiality of Sm0.5Ca0.5MnO3, electrical resistivity and infrared transmittance spectra were recorded for temperatures ranging from 77 K to 420 K. The temperature dependence of the optical band gap was estimated in the near infrared range. Upon heating, the optical transmission decreases in the infrared domain showing a thermochromic effect over a wide wavelength range at room temperature.
A polymer-based surface grating coupler with an embedded Si3N4 layer
Authors: Wang Linghua , Li Yanlu , Garcia Porcel Marco , Vermeulen Diedrik , Han Xiuyou , Wang Jinyan , Jian Xigao , Baets Roel , Zhao Mingshan , Morthier Geert
Published: June 2012

Polymer has been considered to be an ideal material option for integrated photonics devices. To measure these devices, normally the route of edge coupling is chosen to couple the light into or out of the polymer waveguide, which, however, demands a more difficult alignment procedure compared to the surface coupling. Due to the relatively low refractive indices of polymers, implementing the surface grating coupler for surface coupling in this material system remains a challenge. In this paper, we present a polymer-based surface grating coupler. Rather than through expensive complementary metal–oxide–semiconductor (CMOS) fabrication, the device is fabricated through a simple and fast UV-based soft imprint technique utilizing self-developed low-loss polymer material. The coupling efficiency is enhanced by embedding a thin Si3N4 layer between the waveguide core and under cladding layer. Around −19.8 dB insertion loss from single-mode fiber (SMF) to single-mode fiber is obtained for a straight waveguide with a grating coupler at each end. If the output light is collected with a multimode fiber, the insertion loss can be reduced to around −17.3 dB. Near 12% of the coupling efficiency is achieved between the polymer waveguide and SMF. The 3 dB bandwidth of the transmission is 32 nm and is centered at 1550 nm. The proposed surface grating coupler and its easy fabrication method would be very attractive for practical applications.
Charge transfer equilibria in ambient-exposed epitaxial graphene on (0001¯) 6 H-SiC
Authors: Sidorov Anton N. , Gaskill Kurt , Buongiorno Nardelli Marco , Tedesco Joseph L. , Myers-Ward Rachel L. , Eddy Charles R. , Jayasekera Thushari , Kim Ki Wook , Jayasingha Ruwantha , Sherehiy Andriy , Stallard Robert , Sumanasekera Gamini U.
Published: June 2012

The transport properties of electronic materials have been long interpreted independently from both the underlying bulk-like behavior of the substrate or the influence of ambient gases. This is no longer the case for ultra-thin graphene whose properties are dominated by the interfaces between the active material and its surroundings. Here, we show that the graphene interactions with its environments are critical for the electrostatic and electrochemical equilibrium of the active device layers and their transport properties. Based on the prototypical case of epitaxial graphene on (0001¯) 6 H-SiC and using a combination of in-situ thermoelectric power and resistance measurements and simulations from first principles, we demonstrate that the cooperative occurrence of an electrochemically mediated charge transfer from the graphene to air, combined with the peculiar electronic structure of the graphene/SiC interface, explains the wide variation of measured conductivity and charge carrier type found in prior reports.
Extraction of dielectric and magnetic properties of carbonyl iron powder composites at high frequencies
Authors: Zivkovic I. , Murk A.
Published: June 2012

In this paper, we examine carbonyl iron composites in silicone rubber and epoxy matrices. Transmission measurements were performed at W (70 to 110 GHz) and Ka (26 to 40 GHz) bands and effective permittivity and permeability of composites with 10% volume fraction of carbonyl iron powder (CIP) were extracted at these frequencies. To extract permittivity and permeability of carbonyl iron powder in W and Ka bands, we use Looyenga formula. We extract permittivity and permeability of CIP from both silicone rubber and epoxy based composites and good agreement is achieved.
Influence of pressure on exciton states and interband optical transitions in wurtzite InGaN/GaN coupled quantum dot nanowire heterostructures with polarization and dielectric mismatch
Authors: Zhang Min , Shi Jun-Jie
Published: June 2012

Considering the hydrostatic pressure, the spontaneous and piezoelectric polarization, the dielectric mismatch, and 3D confinement of the electron and hole, the exciton states and interband optical transitions in [0001]-oriented wurtzite InxGa1−xN/GaN strained coupled quantum dot (QD) nanowire heterostructures (NWHETs) have been investigated by using the effective mass approximation, the simplified coherent potential approximation, and a variational approach. Our results show that the hydrostatic pressure, the strong built-in electric field (BEF), and the dielectric mismatch have a significant influence on the exciton states and interband optical transitions. The exciton binding energy increases almost linearly with the hydrostatic pressure for a given QD NWHET. The emission wavelength has a blue-shift (red-shift) if the hydrostatic pressure (QD height or the potential barrier thickness) increases. Our calculations also indicate that the radiative decay time has a quick increase with increasing of the QD height and the barrier thickness. The radiative decay time decreases if the hydrostatic pressure increases. The BEF (dielectric mismatch) dramatically decreases (increases) the exciton binding energy. The physical reason has been analyzed in depth.
Not in our name: collective identity of the Serbian Women in Black
Authors: Bilić Bojan
Published: June 2012

The Belgrade-based activist groupWomen in Blackhas been for twenty years now articulating a feminist anti-war stance in an inimical socio-political climate. The operation of this anti-patriarchal and anti-militarist organization, which has resisted numerous instances of repression, has not been until now systematically approached from a social movement perspective. This paper draws upon a range of empirical methods, comprising life-story interviews, documentary analysis and participant observation, to address the question as to how it was possible for this small circle of activists to remain on the Serbian/post-Yugoslav civic scene for the last two decades. My central argument is that a consistent collective identity, which informs the group's resource mobilization and strategic options, holds the key to the surprising survival of this activist organization. I apply recent theoretical advances on collective identity to the case of the BelgradeWomen in Blackwith the view of promoting a potentially fruitful cross-fertilization between non-Western activism and the Western conceptual apparatus for studying civic engagement.
Nonstandard construction of the stochastic integral and applications to stochastic differential equations. I
Authors: Hoover Douglas N. , Perkins Edwin
Published: June 2012

R. M. Anderson has developed a nonstandard approach to Itô integration in which the Itô integral is interpreted as an internal Riemann-Stieltjes sum. In this paper we extend this approach to integration with respect to semimartingales. Lifting and pushing down theorems are proved for local martingales, semimartingales and other right-continuous processes on a Loeb space.
Homogeneous continua in Euclidean (𝑛+1)-space which contain an 𝑛-cube are 𝑛-manifolds
Authors: Prajs Janusz R.
Published: June 2012

Let

X
X

be a homogeneous continuum and let

E
n

{E^n}

be Euclidean

n
n

-space. We prove that if

X
X

is properly contained in a connected

(
n
+
1
)

(n + 1)

-manifold, then

X
X

contains no

n
n

-dimensional umbrella (i.e. a set homeomorphic to the set
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace left-parenthesis x 1 comma ellipsis comma x Subscript n plus 1 Baseline right-parenthesis element-of upper E Superscript n plus 1 Baseline colon x 1 squared plus midline-horizontal-ellipsis plus x Subscript n plus 1 Superscript 2 Baseline less-than-or-equal-to 1">

{
(

x
1

,
…
,

x

n
+
1

)
∈

E

n
+
1

:

x
1
2

+
⋯
+

x

n
+
1

2

≤
1

\{ ({x_1}, \ldots ,{x_{n + 1}}) \in {E^{n + 1}}:x_1^2 + \cdots + x_{n + 1}^2 \leq 1

and

x

n
+
1

≤
0

{x_{n + 1}} \leq 0

and either

x
1

=
⋯
=

x
n

=
0

{x_1} = \cdots = {x_n} = 0

or

x

n
+
1

=
0
}

{x_{n + 1}} = 0\}

). Combining this fact with an earlier result of the author we conclude that if

X
X

lies in

E

n
+
1

{E^{n + 1}}

and topologically contains

E
n

{E^n}

, then

X
X

is an

n
n

-manifold.
Extending 𝐻^{𝑝} functions from subvarieties to real ellipsoids
Authors: Adachi Kenzō
Published: June 2012

Let

Ω
\Omega

be a domain in

C
n

{C^n}

which is a somewhat generalized type of the real ellipsoid. Let

V
V

be a subvariety in

Ω
\Omega

which intersects

∂
Ω

\partial \Omega

transversally. Then there exists an operator

E
:

H
p

(
V
)
→

H
p

(
Ω
)

E:{H^p}(V) \to {H^p}(\Omega )

satisfying

E
f

|

ν

=
f

Ef{|_\nu } = f

.
Weak stability in the global 𝐿¹-norm for systems of hyperbolic conservation laws
Authors: Temple Blake
Published: June 2012

We prove that solutions for systems of two conservation laws which are generated by Glimm’s method are weakly stable in the global

L
1

{L^1}

-norm. The method relies on a previous decay result of the author, together with a new estimate for the

L
1

{L^1}

Lipschitz constant that relates solutions at different times. The estimate shows that this constant can be bounded by the supnorm of the solution, and is proved for any number of equations. The techniques do not rely on the existence of a family of entropies, and moreover the results would generalize immediately to more than two equations if one were to establish the stability of solutions in the supnorm for more than two equations.
Ergodic and mixing properties of equilibrium measures for Markov processes
Authors: Andjel Enrique D.
Published: June 2012

Let

S
(
t
)

S(t)

be the semigroup corresponding to a Markov process on a metric space

X
X

. Suppose

S
(
t
)

S(t)

commutes with a homeomorphism

T
T

of

X
X

. We prove that under certain conditions, an equilibrium measure for the process is ergodic under

T
T

. We also show that, under stronger conditions this measure must be mixing under

T
T

. Several applications of these results are given.
Metrizable spaces where the inductive dimensions disagree
Authors: Kulesza John
Published: June 2012

A method for constructing zero-dimensional metrizable spaces is given. Using generalizations of Roy’s technique, these spaces can often be shown to have positive large inductive dimension. Examples of

N

{\mathbf {N}}

-compact, complete metrizable spaces with

ind
=
0

\operatorname {ind} = 0

and

Ind
=
1

\operatorname {Ind} = 1

are provided, answering questions of Mrowka and Roy. An example with weight

c

\mathfrak {c}

and positive Ind such that subspaces with smaller weight have

Ind
=
0

\operatorname {Ind} = 0

is produced in ZFC. Assuming an additional axiom, for each cardinal

λ
\lambda

a space of positive Ind with all subspaces with weight less than

λ
\lambda

strongly zero-dimensional is constructed.
Zero integrals on circles and characterizations of harmonic and analytic functions
Authors: Globevnik Josip
Published: June 2012

We determine the kernels of two circular Radon transforms of continuous functions on an annulus and use this to obtain a characterization of harmonic functions in the open unit disc which involves Poisson averages over circles computed at only one point of the disc and to obtain a version of Morera’s theorem which involves only the circles which surround the origin.
Semisimple representations of quivers
Authors: Le Bruyn Lieven , Procesi Claudio
Published: June 2012

We discuss the invariant theory of the variety of representations of a quiver and present generators and relations. We connect this theory of algebras with a trace satisfying a formal Cayley-Hamilton identity
Laws of trigonometry on 𝑆𝑈(3)
Authors: Aslaksen Helmer
Published: June 2012

The orbit space of congruence classes of triangles in

S
U
(
3
)

SU(3)

has dimension

8
8

. Each corner is given by a pair of tangent vectors

(
X
,
Y
)

(X,Y)

, and we consider the

8
8

functions

tr

X
2

,
i

tr

X
3

,

tr

Y
2

,
i

tr

Y
3

,

tr

X
Y
,
i

tr

X
2

Y
,
i

tr

X

Y
2

{\text {tr}}{X^2},i{\text {tr}}{X^3},{\text {tr}}{Y^2},i{\text {tr}}{Y^3},{\text {tr}}XY,i{\text {tr}}{X^2}Y,i{\text {tr}}X{Y^2}

and

tr

X
2

Y
2

{\text {tr}}{X^2}{Y^2}

which are invariant under the full isometry group of

S
U
(
3
)

SU(3)

. We show that these

8
8

corner invariants determine the isometry class of the triangle. We give relations (laws of trigonometry) between the invariants at the different corners, enabling us to determine the invariants at the remaining corners, including the values of the remaining side and angles, if we know one set of corner invariants. The invariants that only depend on one tangent vector we will call side invariants, while those that depend on two tangent vectors will be called angular invariants. For each triangle we then have

6
6

side invariants and

12
12

angular invariants. Hence we need

18
−
8
=
10

18 - 8 = 10

laws of trigonometry. If we restrict to

S
U
(
2
)

SU(2)

, we get the cosine laws of spherical trigonometry. The basic tool for deriving these laws is a formula expressing

tr

(

exp

X

exp

Y
)

{\text {tr}}({\operatorname {exp}}X{\operatorname {exp}}Y)

in terms of the corner invariants.
Elliptic problems involving an indefinite weight
Authors: Faierman M.
Published: June 2012

We consider a selfadjoint elliptic eigenvalue problem, which is derived formally from a variational problem, of the form

L
u
=
λ
ω
(
x
)
u

Lu = \lambda \omega (x)u

in

Ω
\Omega

,

B
j

u
=
0

{B_j}u = 0

on

Γ
\Gamma

,

j
=
1
,
…
,
m

j = 1, \ldots ,m

, where

L
L

is a linear elliptic operator of order

2
m

2m

defined in a bounded open set

Ω
⊂

R

n

(
n
≥
2
)

\Omega \subset {{\mathbf {R}}^n}\quad (n \geq 2)

with boundary

Γ
\Gamma

, the

B
j

{B_j}

are linear differential operators defined on

Γ
\Gamma

, and

ω
\omega

is a real-valued function assuming both positive and negative values. For our problem we prove the completeness of the eigenvectors and associated vectors in two function spaces which arise naturally in such an indefinite problem. We also establish some results concerning the eigenvalues of the problem which complement the known results and investigate the structure of the principal subspaces.
Semialgebraic expansions of 𝐶
Authors: Marker David
Published: June 2012

We prove no nontrivial expansion of the field of complex numbers can be obtained from a reduct of the field of real numbers.
Sums of linked ideals
Authors: Ulrich Bernd
Published: June 2012

It is shown that the sum of two geometrically linked ideals in the linkage class of a complete intersection is again an ideal in the linkage class of a complete intersection. Conversely, every Gorenstein ideal (of height at least two) in the linkage class of a complete intersection can be obtained as a "generalized localization" of a sum of two geometrically linked ideals in the linkage class of a complete intersection. We also investigate sums of doubly linked Gorenstein ideals. As an application, we construct a perfect prime ideal which is strongly nonobstructed, but not strongly Cohen-Macaulay, and a perfect prime ideal which is not strongly nonobstructed, but whose entire linkage class is strongly Cohen-Macaulay.
Unknotted homology classes on unknotted surfaces in 𝑆³
Authors: Trace Bruce
Published: June 2012

Suppose

F
F

is a closed, genus

g
g

surface which is standardly embedded in

S
3

{S^3}

. Let

γ
\gamma

denote a primitive element in

H
1

(
F
)

{H_1}(F)

which satisfies

θ
F

(
γ
,
γ
)
=
0

{\theta _F}(\gamma ,\gamma ) = 0

where

θ
F

{\theta _F}

is the Seifert pairing on

F
F

. We obtain a number theoretic condition which is equivalent to

γ
\gamma

being realizable by a curve (in

F
F

) which is unknotted in

S
3

{S^3}

. Various related observations are included.
Boundedness versus periodicity over commutative local rings
Authors: Gasharov Vesselin N. , Peeva Irena V.
Published: June 2012

Over commutative graded local artinian rings, examples are constructed of periodic modules of arbitrary minimal period and modules with bounded Betti numbers, which are not eventually periodic. They provide counterexamples to a conjecture of D. Eisenbud, that every module with bounded Betti numbers over a commutative local ring is eventually periodic of period

2
2

. It is proved however, that the conjecture holds over rings of small length.
Holomorphic maps which preserve intrinsic metrics or measures
Authors: Graham Ian
Published: June 2012

Suppose that

M
M

is a domain in a taut complex manifold

M
′

M’

, and that

Ω
\Omega

is a strictly convex bounded domain in

C

n

{{\mathbf {C}}^n}

. We consider the following question: given a holomorphic map

F
:
M
→
Ω

F:M \to \Omega

which is an isometry for the infinitesimal Kobayashi metric at one point, must

F
F

be biholomorphic? With an additional technical assumption on the behavior of the Kobayashi distance near points of

∂
M

\partial M

, we show that

F
F

gives a biholomorphism of

M
M

with an open dense subset of

Ω
\Omega

. Moreover,

F
F

extends as a homeomorphism from a larger domain

M
~

\tilde M

to

Ω
\Omega

. We also give some related results—refinements of theorems of Bland and Graham and Fornaess and Sibony, and the answer to a question of Graham and Wu.
Classifying sets of measure zero with respect to their open covers
Authors: Just Winfried , Laflamme Claude
Published: June 2012

Developing ideas of Borel and Fréchet, we define a partial preorder which classifies measure zero sets of reals according to their open covers and study the induced partial order on the equivalence classes. The more "rarefied" a set of measure zero, the higher it will range in our partial order. Main results: The sets of strong measure zero form one equivalence class that is the maximum element of our order. There is a second highest class that contains all uncountable closed sets of measure zero. There is a minimum class that contains all dense

G
δ

{G_\delta }

-subsets of the real line of measure zero. There exist at least four classes, and if Martin’s axiom holds, then there are as many classes as subsets of the real line. It is also consistent with ZFC that there is a second lowest class.
Abstract functional-differential equations and reaction-diffusion systems
Authors: Martin R. H. , Smith H. L.
Published: June 2012

Several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a Banach space setting. The ideas are applied to reaction-diffusion systems that have time delays in the nonlinear reaction terms. The techniques presented here include differential inequalities, invariant sets, and Lyapunov functions, and therefore they provide for a wide range of applicability. The results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays.
Families of rational surfaces preserving a cusp singularity
Authors: McEwan Lee J.
Published: June 2012

Families of rational surfaces containing resolutions of cusp singularities are explicitly constructed. It is proved that the families constructed are universal deformations at each point. Two different monodromy formulas are established; one of these is shown to be connected to automorphisms of Inoue-Hirzebruch surfaces. Some evidence (but no proof) is offered for the conjecture that finite base changes of the families we construct are the versal-deformation spaces for singular Inoue-Hirzebruch surfaces.
Λ(𝑞) processes
Authors: Blei Ron C.
Published: June 2012

Motivated by some classical notions in harmonic analysis,

Λ
(
q
)

\Lambda (q)

processes are introduced in the context of a study of stochastic interdependencies. An extension of a classical theorem of Salem and Zygmund regarding random Fourier series is obtained. The Littlewood exponent of

Λ
(
q
)

\Lambda (q)

processes is estimated and, in some archetypical cases, computed.
Multipliers, linear functionals and the Fréchet envelope of the Smirnov class 𝑁_{*}(𝑈ⁿ)
Authors: Nawrocki Marek
Published: June 2012

Linear topological properties of the Smirnov class

N

∗

(

U

n

)

{N_{\ast }}({\mathbb {U}^n})

of the unit polydisk

U

n

{\mathbb {U}^n}

in

C

n

{\mathbb {C}^n}

are studied. All multipliers of

N

∗

(

U

n

)

{N_{\ast }}({\mathbb {U}^n})

into the Hardy spaces

H
p

(

U

n

)
,

0
>
p
⩽
∞

{H_p}({\mathbb {U}^n}),\;0 > p \leqslant \infty

, are described. A representation of the continuous linear functionals on

N

∗

(

U

n

)

{N_{\ast }}({\mathbb {U}^n})

is obtained. The Fréchet envelope of

N

∗

(

U

n

)

{N_{\ast }}({\mathbb {U}^n})

is constructed. It is proved that if

n
>
1

n > 1

, then

N

∗

(

U

n

)

{N_{\ast }}({\mathbb {U}^n})

is not isomorphic to

N

∗

(

U

1

)

{N_{\ast }}(\mathbb {U}{^1})

.
𝐿^{𝑝} inequalities for entire functions of exponential type
Authors: Rahman Qazi I. , Schmeisser G.
Published: June 2012

Let

f
f

be an entire function of exponential type

τ
\tau

belonging to

L
p

{L^p}

on the real line. It has been known since a long time that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Subscript negative normal infinity Superscript normal infinity Baseline StartAbsoluteValue f prime left-parenthesis x right-parenthesis EndAbsoluteValue Superscript p Baseline d x less-than-or-equal-to tau Superscript p Baseline integral Subscript negative normal infinity Superscript normal infinity Baseline StartAbsoluteValue f left-parenthesis x right-parenthesis EndAbsoluteValue Superscript p Baseline d x if p greater-than-or-equal-to 1 period">

∫

−
∞

∞

|

f
′

(
x
)

|

p

d
x
≤

τ
p

∫

−
∞

∞

|

f
(
x
)

|

p

d
x

if

p
≥
1.

\int _{ - \infty }^\infty {{{\left | {f’(x)} \right |}^p}dx \leq {\tau ^p}\int _{ - \infty }^\infty {{{\left | {f(x)} \right |}^p}dx\quad {\text {if}}\;p \geq 1.} }

\]
We prove that the same inequality holds also for

0
>
p
>
1

0 > p > 1

. Various other estimates of the same kind have been obtained.
Large deviations in dynamical systems
Authors: Young Lai-Sang
Published: June 2012

We prove some large deviation estimates for continuous maps of compact metric spaces and apply them to attractors in differentiable dynamics, rate of escape problems, and to shift spaces.
Curves on 𝐾-theory and the de Rham homology of associative algebras
Authors: Ryan John G.
Published: June 2012

This paper describes the generalization to arbitrary associative algebras of the complex of "typical curves on algebraic

K
K

-theory" and shows, in particular, that for certain

Q

{\mathbf {Q}}

-algebras,

A
A

, the complex is isomorphic to the "generalized de Rham complex,"

(
H

H
∗

(
A
)
,
B
)

(H{H_*}(A),B)

, in which

B
B

is Connes’ operator acting on the Hochschild homology groups of

A
A

.
On the nonimmersion of products of real projective spaces
Authors: Song Hyun-Jong , Wilson W. Stephen
Published: June 2012

In this paper we utilize

B

P
∗

(

)

B{P^*}(\;)

, a generalized cohomology theory associated with the Brown-Peterson spectrum to prove a nonimmersion theorem for products of real projective spaces.
Interpretations of Euclidean geometry
Authors: Świerczkowski S.
Published: June 2012

Following Tarski, we view

n
n

-dimensional Euclidean geometry as a first-order theory

E
n

{E_n}

with an infinite set of axioms about the relations of betweenness (among points on a line) and equidistance (among pairs of points). We show that for

k
>
n

k > n

,

E
n

{E_n}

does not admit a

k
k

-dimensional interpretation in the theory RCF of real closed fields, and we deduce that

E
n

{E_n}

cannot be interpreted

r
r

-dimensionally in

E
s

{E_s}

, when

r
⋅
s
>
n

r \cdot s > n

.
On the bihomogeneity problem of Knaster
Authors: Kuperberg Krystyna
Published: June 2012

The author constructs a locally connected, homogeneous, finitedimensional, compact, metric space which is not bihomogeneous, thus providing a compact counterexample to a problem posed by B. Knaster around 1921.
On a multiplier conjecture for univalent functions
Authors: Gruenberg V. , Rønning F. , Ruscheweyh St.
Published: June 2012

Let

S

\mathcal {S}

be the set of normalized univalent functions, and let

D

\mathcal {D}

be the subset of

S

\mathcal {S}

containing functions with the property:
\[

|

f
"
(
z
)

|

≤

Re

f
′

(
z
)
,

|
z
|

>
1

\left | {f"(z)} \right | \leq {\text {Re}}f’(z),\quad \left | z \right | > 1

\]
. We present and discuss the following conjecture: For

f
∈

D

,

g,

h
∈

co

¯

(

S

)

f \in \mathcal {D},{\text {g,}}h \in \overline {{\text {co}}} (\mathcal {S})

,
\[

Re

1
z

(
f
∗

g

∗
h
)
(
z
)
>
0
,

|
z
|

>
1

{\text {Re}}\frac {1}{z}(f * {\text {g}} * h)(z) > 0,\quad \left | z \right | > 1

\]
. In particular, we prove that the conjecture holds with

S

\mathcal {S}

replaced by

C

\mathcal {C}

, the class of close-to-convex functions, and show its truth for a number of special members of

D

\mathcal {D}

. These latter results are extensions of old ones of Szegà and Kobori about sections of univalent functions.
On the integrals of a singular real analytic differential form in 𝑅ⁿ
Authors: Meziani A.
Published: June 2012

In this paper, we study the constancy on the fibers for the continuous integrals of a complex-valued real analytic differential form in

R
n

{R^n}

. Then we prove an isomorphism result between the space of smooth integrals and a space built from spaces of Whitney functions.
Global families of limit cycles of planar analytic systems
Authors: Perko L. M.
Published: June 2012

The global behavior of any one-parameter family of limit cycles of a planar analytic system

x
˙

=
f
(
x
,
λ
)

\dot x = f(x,\lambda )

depending on a parameter

λ
∈
R

\lambda \in R

is determined. It is shown that any one-parameter family of limit cycles belongs to a maximal one-parameter family which is either open or cyclic. If the family is open, then it terminates as the parameter or the orbits become unbounded, or it terminates at a critical point or on a (compound) separatrix cycle of the system. This implies that the periods in a one-parameter family of limit cycles can become unbounded only if the orbits become unbounded or if they approach a degenerate critical point or (compound) separatrix cycle of the system. This is a more specific result for planar analytic systems than Wintner’s principle of natural termination for

n
n

-dimensional systems where the periods can become unbounded in strange ways. This work generalizes Duffs results for one-parameter families of limit cycles generated by a one-parameter family of rotated vector fields. In particular, it is shown that the behavior at a nonsingular, multiple limit cycle of any one-parameter family of limit cycles is exactly the same as the behavior at a multiple limit cycle of a one-parameter family of limit cycles generated by a one-parameter family of rotated vector fields.
The Schrödinger equation with a quasi-periodic potential
Authors: Surace Steve
Published: June 2012

We consider the Schràdinger equation
\[

−

d
2

d

x
2

ψ
+
ε
(
cos
⁡
x
+
cos
⁡
(
α
x
+
ϑ
)
)
ψ
=
E
ψ

- \frac {{{d^2}}} {{d{x^2}}}\psi + \varepsilon (\cos x + \cos (\alpha x + \vartheta ))\psi = E\psi

\]
where

ε
\varepsilon

is small and

σ
\sigma

satisfies the Diophantine inequality
\[

|

p
+
q
α

|

≥
C

/

q
2

for

p

,

q
∈

Z

,
q
≠
0.

|p + q\alpha | \geq C/{q^2}{\text {for}}p{\text {,}}q \in {\mathbf {Z}},q \ne 0.

\]
. We look for solutions of the form
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="psi left-parenthesis x right-parenthesis equals e Superscript i upper K x Baseline q left-parenthesis x right-parenthesis equals e Superscript i upper K x Baseline sigma-summation psi Subscript m n Baseline e Superscript i n x Baseline e Superscript i m left-parenthesis alpha x plus theta right-parenthesis">

ψ
(
x
)
=

e

i
K
x

q
(
x
)
=

e

i
K
x

∑

ψ

m
n

e

i
n
x

e

i
m
(
α
x
+
ϑ
)

\psi (x) = {e^{iKx}}q(x) = {e^{iKx}}\sum {{\psi _{mn}}{e^{inx}}} {e^{im(\alpha x + \vartheta )}}

\]
. If we try to solve for

ψ
=

ψ

m
n

\psi = {\psi _{mn}}

we are led to the Schràdinger equation on the lattice

Z

2

{{\mathbf {Z}}^2}

\[

H
(
K
)
ψ
=
(
ε
Δ
+
V
(
K
)
)
ψ
=
E
ψ

H(K)\psi = (\varepsilon \Delta + V(K))\psi = E\psi

\]
where

Δ
\Delta

is the discrete Laplacian (without diagonal terms) and

V
(
K
)

V(K)

is some potential on

Z

2

{{\mathbf {Z}}^2}

. We have two main results: (1) For

ε
\varepsilon

sufficiently small,

H
(
K
)

H(K)

has pure point spectrum for almost every

K
K

. (2) For

ε
\varepsilon

sufficiently small, the operator
\[

−

d
2

/

d

x
2

+
ε
(
cos
⁡
x
+
cos
⁡
(
α
x
+
ϑ
)
)

- {d^2}/d{x^2} + \varepsilon (\cos x + \cos (\alpha x + \vartheta ))

\]
has no point spectrum. To prove our results, we must get decay estimates on the Green’s function

(
E
−
H

)

−
1

{(E - H)^{ - 1}}

. The decay of the eigenfunction follows from this. In general, we must keep track of small divisors which can make the Green’s function large. This is accomplished by a KAM (Kolmogorov, Arnold, Moser) type of multiscale perturbation analysis.
The initial-Neumann problem for the heat equation in Lipschitz cylinders
Authors: Brown Russell M.
Published: June 2012

We prove existence and uniqueness for solutions of the initial-Neumann problem for the heat equation in Lipschitz cylinders when the lateral data is in

L
p

{L^p}

,

1
>
p
>
2
+
ε

1 > p > 2+\varepsilon

, with respect to surface measure. For convenience, we assume that the initial data is zero. Estimates are given for the parabolic maximal function of the spatial gradient. An endpoint result is established when the data lies in the atomic Hardy space

H
1

{H^1}

. Similar results are obtained for the initial-Dirichlet problem when the data lies in a space of potentials having one spatial derivative and half of a time derivative in

L
p

{L^p}

,

1
>
p
>
2
+
ε

1 > p > 2+\varepsilon

, with a corresponding Hardy space result when

p
=
1

p = 1

. Using these results, we show that our solutions may be represented as single-layer heat potentials. By duality, it follows that solutions of the initial-Dirichlet problem with data in

L
q

{L^q}

,

2
−

ε
′

>
q
>
∞

2 - \varepsilon ’ > q > \infty

and BMO may be represented as double-layer heat potentials.
A canonical extension for analytic functions on Banach spaces
Authors: Zalduendo Ignacio
Published: June 2012

Given Banach spaces

E
E

and

F
F

, a Banach space

G

E
F

{G_{EF}}

is presented in which

E
E

is embedded and which seems a natural space to which extend

F
F

-valued analytic functions. Any

F
F

-valued analytic function defined on a subset

U
U

of

E
E

may be extended to an open neighborhood of

U
U

in

G

E
F

{G_{EF}}

. This extension generalizes that of Aron and Berner. It is also related to the Arens product in Banach algebras, to the functional calculus for bounded linear operators, and to an old problem of duality in spaces of analytic functions. A characterization of the Aron-Berner extension is given in terms of continuity properties of first-order differentials.
Equivariant BP-cohomology for finite groups
Authors: Yagita N.
Published: June 2012

The Brown-Peterson cohomology rings of classifying spaces of finite groups are studied, considering relations to the other generalized cohomology theories. In particular,

BP

∗

(
M
)

{\operatorname {BP} ^{\ast }}(M)

are computed for minimal nonabelian

p
p

-groups

M
M

. As an application, we give a necessary condition for the existence of nonabelian

p
p

-subgroups of compact Lie groups.
Uniqueness of the critical point of the solutions to some semilinear elliptic boundary value problems in 𝑅²
Authors: Sakaguchi Shigeru
Published: June 2012

We consider some two-dimensional semilinear elliptic boundary value problems over a bounded convex domain in

R

2

{{\mathbf {R}}^2}

and show the uniqueness of the critical point of the solutions.
The minimal normal extension for 𝑀_{𝑧} on the Hardy space of a planar region
Authors: Spraker John
Published: June 2012

Multiplication by the independent variable on

H
2

(
R
)

{H^2}(R)

for

R
R

a bounded open region in the complex plane

C

\mathbb {C}

is a subnormal operator. This paper characterizes its minimal normal extension

N
N

. Any normal operator is determined by a scalar-valued spectral measure and a multiplicity function. It is a consequence of some standard operator theory that a scalar-valued spectral measure for

N
N

is harmonic measure for

R
R

,

ω
\omega

. This paper investigates the multiplicity function

m
m

for

N
N

. It is shown that

m
m

is bounded above by two

ω
\omega

-a.e., and necessary and sufficient conditions are given for

m
m

to attain this upper bound on a set of positive harmonic measure. Examples are given which indicate the relationship between

N
N

and the boundary of

R
R

.
Bundle theories for topological manifolds
Authors: Hughes C. B. , Taylor L. R. , Williams E. B.
Published: June 2012

Manifold approximate fibrations arise in the geometric topology of manifolds and group actions on topological manifolds. The primary purpose of this paper is to classify manifold approximate fibrations in terms of the lifting problem for a certain bundle. Our classification meshes well with the classical classifications of fibrations and bundles and, hence, we are able to attack questions such as the following. When is a fibration controlled homotopy equivalent to a manifold approximate fibration? When is a manifold approximate fibration controlled homeomorphic to a bundle?
The crank of partitions mod 8,9 and 10
Authors: Garvan Frank G.
Published: June 2012

Recently new combinatorial interpretations of Ramanujan’s partition congruences modulo

5
5

,

7
7

and

11
11

were found. These were in terms of the crank. A refinement of the congruence modulo

5
5

is proved. The number of partitions of

5
n
+
4

5n + 4

with even crank is congruent to

0
0

modulo

5
5

. The residue of the even crank modulo

10
10

divides these partitions into five equal classes. Other relations for the crank modulo

8
8

,

9
9

and

10
10

are also proved. The dissections of certain generating functions associated with these results are calculated. All of the results are proved by elementary methods.
Tauberian theorems for the Laplace-Stieltjes transform
Authors: Batty C. J. K.
Published: June 2012

Let

α
:
[
0
,
∞
)
→

C

\alpha :[0,\infty ) \to {\mathbf {C}}

be a function of locally bounded variation, with

α
(
0
)
=
0

\alpha (0) = 0

, whose Laplace-Stieltjes transform

g
(
z
)
=

∫
0
∞

e

−
z
t

d
α
(
t
)

g(z) = \int _0^\infty {{e^{ - zt}}d\alpha (t)}

is absolutely convergent for

Re
⁡
z
>
0

\operatorname {Re} z > 0

. Let

E
E

be the singular set of

g
g

in

i

R

i{\mathbf {R}}

, and suppose that

0
∉
E

0 \notin E

. Various estimates for

lim

sup

t
→
∞

|

α
(
t
)
−
g
(
0
)

|

\lim {\sup _{t \to \infty }}|\alpha (t) - g(0)|

are obtained. In particular,

α
(
t
)
→
g
(
0
)

\alpha (t) \to g(0)

as

t
→
∞

t \to \infty

if
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row left-parenthesis i right-parenthesis upper E is null comma 2nd Row left-parenthesis ii right-parenthesis sup Underscript y element-of upper E Endscripts sup Underscript t greater-than 0 Endscripts StartAbsoluteValue integral Subscript 0 Superscript t Baseline e Superscript minus i y s Baseline d alpha left-parenthesis s right-parenthesis EndAbsoluteValue greater-than normal infinity comma 3rd Row left-parenthesis iii right-parenthesis limit Underscript delta down-arrow 0 Endscripts limit sup Underscript t right-arrow normal infinity Endscripts sup Underscript t minus delta less-than-or-slanted-equals s less-than-or-slanted-equals t Endscripts StartAbsoluteValue alpha left-parenthesis s right-parenthesis minus alpha left-parenthesis t right-parenthesis EndAbsoluteValue equals 0 period EndLayout">

(

i)

E

is null,

(ii)

sup

y
∈
E

sup

t
>
0

|

∫
0
t

e

−
i
y
s

d
α
(
s
)

|

>
∞
,

(

iii)

lim

δ
↓
0

lim

sup

t
→
∞

sup

t
−
δ
⩽
s
⩽
t

|

α
(
s
)
−
α
(
t
)

|

=
0.

\begin {gathered} ({\text {i)}}\quad E\,{\text {is null,}} \hfill \\ {\text {(ii)}}\quad \sup \limits _{y \in E} \sup \limits _{t > 0} \left | {\int _0^t {{e^{ - iys}}\,d\alpha (s)} } \right | > \infty , \hfill \\ ({\text {iii)}}\quad \lim \limits _{\delta \downarrow 0} \lim \sup \limits _{t \to \infty } \sup \limits _{t - \delta \leqslant s \leqslant t} |\alpha (s) - \alpha (t)| = 0. \hfill \\ \end {gathered}

\]
This result contains Tauberian theorems for Laplace transforms, power series, and Dirichlet series.
Lie algebra modules with finite-dimensional weight spaces. I
Authors: Fernando S. L.
Published: June 2012

Let

g

\mathfrak {g}

denote a reductive Lie algebra over an algebraically closed field of characteristic zero, and let

h

\mathfrak {h}

denote a Cartan subalgebra of

g

\mathfrak {g}

. In this paper we study finitely generated

g

\mathfrak {g}

-modules that decompose into direct sums of finite dimensional

h

\mathfrak {h}

-weight spaces. We show that the classification of irreducible modules in this category can be reduced to the classification of a certain class of irreducible modules, those we call torsion free modules. We also show that if

g

\mathfrak {g}

is a simple Lie algebra that admits a torsion free module, then

g

\mathfrak {g}

is of type

A
A

or

C
C

.
A Plancherel formula for parabolic subgroups
Authors: Nakata Mie
Published: June 2012

We obtain explicit Plancherel formulas for the parabolic subgroups

P
P

of

p
p

-adic unitary groups which fix one dimensional isotropic subspaces. By means of certain limits of difference operators (called strong derivatives), we construct a Dixmier-Pukanszky operator which compensates for the nonunimodularity of the group

P
P

. Then, we compute the Plancherel formula of

N
⋅
A

N \cdot A

, where

N
N

is the nilradical of

P
P

and

A
=

Q
p
′

A = {Q’_p}

, the multiplicative group of nonzero

p
p

-adic numbers, by formulating a

p
p

-adic change of variable formula and using the strong derivative.
Rotation and winding numbers for planar polygons and curves
Authors: Grünbaum Branko , Shephard G. C.
Published: June 2012

The winding and rotation numbers for closed plane polygons and curves appear in various contexts. Here alternative definitions are presented, and relations between these characteristics and several other integer-valued functions are investigated. In particular, a point-dependent "tangent number" is defined, and it is shown that the sum of the winding and tangent numbers is independent of the point with respect to which they are taken, and equals the rotation number.
A continuous localization and completion
Authors: Iwase Norio
Published: June 2012

The main goal of this paper is to construct a localization and completion of Bousfield-Kan type as a continuous functor for a virtually nilpotent CW-complex. Then the localization and completion of an

A
n

{A_n}

-space is given to be an

A
n

{A_n}

-homomorphism between

A
n

{A_n}

-spaces. For any general compact Lie group, this gives a continuous equivariant localization and completion for a virtually nilpotent

G
G

-CW-complex. More generally, we have a continuous localization with respect to a system of core rings for a virtually nilpotent

D

\mathbf {D}

-CW-complex for a polyhedral category

D

\mathbf {D}

.
Hypersurface variations are maximal. II
Authors: Carlson James A.
Published: June 2012

We show that certain variations of Hodge structure defined by sufficiently ample hypersurfaces are maximal integral manifolds of Griffiths’ horizontal distribution.
Lie supergroup actions on supermanifolds
Authors: Boyer Charles P. , Sánchez-Valenzuela O. A.
Published: June 2012

Lie supergroups are here understood as group objects in the category of supermanifolds (as in [

2
2

,

5
5

, and

15
15

]). Actions of Lie supergroups in supermanifolds are defined by means of diagrams of supermanifold morphisms. Examples of such actions are given. Among them emerge the linear actions discussed in [

2
2

,

5
5

, and

12
12

] and the natural actions on the Grassmannian supermanifolds studied in [

6
6

-

9
9

and

13
13

]. The nature of the isotropy subsupergroup associated to an action is fully elucidated; it is exhibited as an embedded subsupergroup in the spirit of the theory of smooth manifolds and Lie groups and with no need for the Lie-Hopf algebraic approach of Kostant in [

3
3

]. The notion of orbit is also discussed. Explicit calculations of isotropy subsupergroups are included. Also, an alternative proof of the fact that the structural sheaf of a Lie supergroup is isomorphic to the sheaf of sections of a trivial exterior algebra bundle is given, based on the triviality of its supertangent bundle.
Algebraic hulls and smooth orbit equivalence
Authors: Iozzi Alessandra
Published: June 2012

For

i
=
1
,
2
,

i = 1,2,

let

F

i

{\mathcal {F}_i}

be foliations on smooth manifolds

M
i

{M_i}

determined by the actions of connected Lie groups

H
i

{H_i}

; we describe here some results which provide an obstruction, in terms of a geometric invariant of the actions, to the existence of a diffeomorphism between the

F

i
′

s

\mathcal {F}_i’{\text {s}}

.
Characteristic numbers for unoriented 𝑍-homology manifolds
Authors: Buoncristiano Sandro , Hacon Derek
Published: June 2012

It is shown that the analogue of Thom’s theorem on Stiefel-Whitney numbers holds for

Z

{\mathbf {Z}}

-homology manifolds
Classification of balanced sets and critical points of even functions on spheres
Authors: Coffman Charles V.
Published: June 2012

The Lyusternik-Schnirelman approach to the study of critical points of even functionals on the sphere

S
N

{S^N}

employs min-max or max-min principles whose formulation uses a numerical invariant that is defined for compact balanced subsets of

S
N

{S^N}

. The Krasnosel’skii genus is an example. Here we study a general class of such invariants (which is quite large) with particular attention to the following questions: formulation of dual variational principles, multiplicity results for critical points, and determination of the Morse index of nondegenerate critical points.
Brownian motion in a wedge with variable skew reflection
Authors: Rogers L. C. G.
Published: June 2012

Does planar Brownian motion confined to a wedge by skew reflection on the sides approach the vertex of the wedge? This question has been answered by Varadhan and Williams in the case where the direction of reflection is constant on each of the sides, but here we address the question when the direction reflected is allowed to vary. A necessary condition, and a sufficient condition, are obtained for the vertex to be reached. The conditions are of a geometric nature, and the gap between them is quite small.
Characterizations of turbulent one-dimensional mappings via 𝜔-limit sets
Authors: Evans Michael J. , Humke Paul D. , Lee Cheng Ming , O’Malley Richard J.
Published: June 2012

The structure of

ω
\omega

-limit sets for nonturbulent functions is studied, and various characterizations for turbulent and chaotic functions are obtained. In particular, it is proved that a continuous function mapping a compact interval into itself is turbulent if and only if there exists an

ω
\omega

-limit set which is a unilaterally convergent sequence
The construction of analytic diffeomorphisms for exact robot navigation on star worlds
Authors: Rimon Elon , Koditschek Daniel E.
Published: June 2012

A Euclidean Sphere World is a compact connected submanifold of Euclidean

n
n

-space whose boundary is the disjoint union of a finite number of

(
n
−
1
)

(n - 1)

dimensional Euclidean spheres. A Star World is a homeomorph of a Euclidean Sphere World, each of whose boundary components forms the boundary of a star shaped set. We construct a family of analytic diffeomorphisms from any analytic Star World to an appropriate Euclidean Sphere World "model." Since our construction is expressed in closed form using elementary algebraic operations, the family is effectively computable. The need for such a family of diffeomorphisms arises in the setting of robot navigation and control. We conclude by mentioning a topological classification problem whose resolution is critical to the eventual practicability of these results.
Stability of travelling wave solutions of diffusive predator-prey systems
Authors: Gardner R. , Jones C. K. R. T.
Published: June 2012

The stability of travelling wave solutions of singularly perturbed, diffusive predator-prey systems is proved by showing that the linearized operator about such a solution has no unstable spectrum and that the translation eigenvalue atλ=0\lambda = 0is simple. The proof illustrates the application of some recently developed geometric and topological methods for counting eigenvalues.
On the existence of conformal measures
Authors: Denker Manfred , Urbański Mariusz
Published: June 2012

A general notion of conformal measure is introduced and some basic properties are studied. Sufficient conditions for the existence of these measures are obtained, using a general construction principle. The geometric properties of conformal measures relate equilibrium states and Hausdorff measures. This is shown for invariant subsets of

S
1

{S^1}

under expanding maps.
A discrete approach to monotonicity of zeros of orthogonal polynomials
Authors: Ismail Mourad E. H. , Muldoon Martin E.
Published: June 2012

We study the monotonicity with respect to a parameter of zeros of orthogonal polynomials. Our method uses the tridiagonal (Jacobi) matrices arising from the three-term recurrence relation for the polynomials. We obtain new results on monotonicity of zeros of associated Laguerre, Al-Salam-Carlitz, Meixner and Pollaczek polynomials. We also derive inequalities for the zeros of the Al-Salam-Carlitz and Meixner polynomials.