bluuebunny/crossref_metadata_2025 huggingface dataset:
Threshold voltage control in organic thin film transistors with dielectric layer modified by a genetically engineered polypeptide
Authors: Dezieck Alex , Acton Orb , Leong Kirsty , Oren Ersin Emre , Ma Hong , Tamerler Candan , Sarikaya Mehmet , Jen Alex K.-Y.
Published: July 2010

Precise control over the threshold voltage of pentacene-based organic thin film transistors was achieved by inserting a genetically engineered quartz-binding polypeptide at the semiconductor-dielectric interface. A 30 V range was accessed with the same peptide by adjusting the pH of the solution for peptide assembly while leaving other device properties unaffected. Mobility of 0.1–0.2 cm2 V−1 s−1 and on/off current ratio of >106 could be achieved for all devices regardless of the presence of the neutral peptide or the peptide assembled in acidic or basic conditions. This shift in threshold voltages is explained by the generation of charged species and dipoles due to variation in assembling conditions. Controlling device characteristics such as threshold voltage is essential for integration of transistors into electronic circuits.
Correlation between charge transfer exciton recombination and photocurrent in polymer/fullerene solar cells
Authors: Hallermann Markus , Da Como Enrico , Feldmann Jochen , Izquierdo Marta , Filippone Salvatore , Martín Nazario , Jüchter Sabrina , von Hauff Elizabeth
Published: July 2010

We correlate carrier recombination via charge transfer excitons (CTEs) with the short circuit current, Jsc, in polymer/fullerene solar cells. Near infrared photoluminescence spectroscopy of CTE in three blends differing for the fullerene acceptor, gives unique insights into solar cell characteristics. The energetic position of the CTE is directly correlated with the open-circuit voltage, Voc, and more important Jsc decreases with increasing CTE emission intensity. CTE emission intensity is discussed from the perspective of blend morphology. The work points out the fundamental role of CTE recombination and how optical spectroscopy can be used to derive information on solar cell performances.
Thermomorphological study of the terahertz lattice modes in polyvinylidene fluoride and high-density polyethylene
Authors: Wietzke Steffen , Jansen Christian , Reuter Marco , Jung Tilmann , Hehl Judith , Kraft Dietmar , Chatterjee Sangam , Greiner Andreas , Koch Martin
Published: July 2010

Semicrystalline polymers possess a complex morphology comprising both crystalline and amorphous domains. We investigate two representatives from this group, polyvinylidene fluoride and high-density polyethylene, with terahertz time-domain spectroscopy. Intriguingly, the thermal gradient of lattice modes arising from the crystalline phase changes at the glass transition. Thus, terahertz spectroscopy can identify the glass transition temperature Tg even in highly crystalline polymers, where conventional methods such as differential scanning calorimetry fail. Furthermore, these findings provide experimental evidence of the strong interactions between the amorphous and the crystalline domains, as the glass transition is an exclusive feature of the mobile amorphous fraction.
Integration of HfO2 on Si/SiC heterojunctions for the gate architecture of SiC power devices
Authors: Gammon P. M. , Pérez-Tomás A. , Jennings M. R. , Guy O. J. , Rimmer N. , Llobet J. , Mestres N. , Godignon P. , Placidi M. , Zabala M. , Covington J. A. , Mawby P. A.
Published: July 2010

In this paper we present a method for integrating HfO2 into the SiC gate architecture, through the use of a thin wafer bonded Si heterojunction layer. Capacitors consisting of HfO2 on Si, SiC, Si/SiC, and SiO2/SiC have been fabricated and electrically tested. The HfO2/Si/SiC capacitors minimize leakage, with a breakdown electric field of 3.5 MV/cm through the introduction of a narrow band gap semiconductor between the two wide band gap materials. The Si/SiC heterojunction was analyzed using transmission electron microscopy, energy dispersive x-ray, and Raman analysis, proving that the interface is free of contaminants and that the Si layer remains unstressed.
Energetics of local clusters in Cu64.5Zr35.5 metallic liquid and glass
Authors: Wu S. Q. , Wang C. Z. , Hao S. G. , Zhu Z. Z. , Ho K. M.
Published: July 2010

Correlation between the cluster energy and its population and dynamics can provide a better understanding of the complicated energy landscape of disordered metallic systems. We propose a method to analyze the cluster energy distribution for different kinds of short-range order (local clusters) in liquid and glass systems. By applying this analysis to an interesting and important glass forming system—Cu64.5Zr35.5 we observe a direct correlation between the energy and dynamics of the cluster in this realistic glass-forming system. This study suggests that dynamic arrest originates from the environment-dependent energetics of local clusters.
Yarbus, Eye Movements, and Vision
Authors: Tatler Benjamin W , Wade Nicholas J , Kwan Hoi , Findlay John M , Velichkovsky Boris M
Published: July 2010

The impact of Yarbus's research on eye movements was enormous following the translation of his book Eye Movements and Vision into English in 1967. In stark contrast, the published material in English concerning his life is scant. We provide a brief biography of Yarbus and assess his impact on contemporary approaches to research on eye movements. While early interest in his work focused on his study of stabilised retinal images, more recently this has been replaced with interest in his work on the cognitive influences on scanning patterns. We extended his experiment on the effect of instructions on viewing a picture using a portrait of Yarbus rather than a painting. The results obtained broadly supported those found by Yarbus.
Monkeying around with the Gorillas in Our Midst: Familiarity with an Inattentional-Blindness Task Does Not Improve the Detection of Unexpected Events
Authors: Simons Daniel J
Published: July 2010

When people know to look for an unexpected event (eg, a gorilla in a basketball game), they tend to notice that event. But does knowledge that an unexpected event might occur improve the detection of other unexpected events in a similar scene? Subjects watched a new video in which, in addition to the gorilla, two other unexpected events occurred: a curtain changed color, and one player left the scene. Subjects who knew about videos like this one consistently spotted the gorilla in the new video, but they were slightly less likely to notice the other events. Foreknowledge that unexpected events might occur does not enhance the ability to detect other such events.
Alcoholism: Development of the Diagnostic Concept
Authors: Sellman Doug
Published: July 2010

This paper traces the diagnostic concepts of alcoholism featured in the major classification systems over the past 40 years. The description of alcoholism as a diagnostic concept has undergone considerable transformation over this time, but an international consensus now exists in the DSM-IIIR [2] criteria and ICD-10 [3]. Alcoholism is equated with alcohol dependence, and both definitions draw largely on the description of the alcohol dependence syndrome by Edwards and Gross [4]. Although the presence of withdrawal symptoms and relief use (key aspects of so-called physical addiction) is part of both systems, they are not necessary to make the diagnosis in either. Future directions and clinical implications of these developments are discussed.
The Clinical Features of Tourette's Disorder: An Australian Study Using a Structured Interview Schedule
Authors: Chee Kit-Yun , Sachdev Perminder
Published: July 2010

The clinical features of an Australian series of patients fulfilling DSM-III-R criteria for Tourette's Syndrome (TS) were examined. Fifty patients, recruited from a hospital-based outpatient clinic and a self-help group, were interviewed using a structured schedule.

TS is a complex disorder with wide ranging manifestations. Forty male and ten female TS patients with a mean age of 20.8 years (SD11.2) were assessed. The mean age of onset of tics was 8.3 years (SD 3.3). Simple motor tics occurring in the rostral body regions were more common (eye 86%, face and head 80%) when compared both to simple tics occurring caudally (leg 52%) and complex motor tics (58%). Simple vocal tics were more common (94%) than complex ones (44%). There was a rostrocaudal pattern in the age of onset and severity of simple motor tics. Rates of comorbidity were 32%, 18% and 30% for Attention-Deficit Hyperactivity Disorder, Major Depression and Generalised Anxiety Disorder respectively and this was reflected in the considerable proportion (32%) of the sample who first presented for reasons other than their tics. There were substantial delays between the age of first presentation and diagnosis of TS owing to the insidious onset of the disorder, misdiagnosis and delays in presentation for help.

A comparison of the features of the present patients with those of other published studies revealed similarities with some differences. Better clinical recognition of the symptoms and modes of presentation of TS may improve existing delays in diagnosis and treatment.
Fluoxetine Induced Dyskinesia
Authors: Mander Alastair , McCausland Michael , Workman B. , Flamer H. , Christophidis Nicholas
Published: July 2010

A case of fluoxetine induced dyskinesia in an elderly woman with previous use of low dose haloperidol is described. In contrast to neuroleptic induced tardive dyskinesia it was characterised by a rapid onset after commencing fluoxetine and rapid resolution on cessation. In the case discussion we describe other cases of fluoxetine induced extrapyramidal syndromes and possible mechanisms.
The Reactivation of Post-Traumatic Stress Disorder in Later Life
Authors: Macleod A. D.
Published: July 2010

The natural history of chronic PTSD was observed by reviewing the veteran's medical records, which had been commenced at enlistment, prior to active service. The masking of intrusive symptoms in mid-life was usual. A terminal phase of symptomatic reactivation in older age may occur. The indelibility of the memory of fear is demonstrated by these veterans.

The reticence to retell the trauma story remains a major obstacle in the study of the mental health sequelae of warfare. War-related psychiatric disorder in the elderly male is easily missed. Direct questioning regarding military service is advisable. The ineffectiveness of the management strategies offered to World War II PTSD sufferers is clearly apparent.

Forty-five World War II veterans reporting recent reactivation of chronic posttraumatic stress disorder (PTSD) symptoms were clinically assessed in order to determine war pension disability. In the course of these examinations, factors implicated in the exacerbation of their re-experiencing and arousal symptoms were recorded. The most prominent of these factors was that of physical ill health. Retirement, loneliness, comorbid psychiatric illness, anniversaries, service reunions, and alcohol and psychotropic medication usage were other factors.
Depression in Patients with HIV and AIDS
Authors: Judd Fiona K. , Mijch Anne M.
Published: July 2010

In this paper we review studies of depression in patients with HIV/AIDS. Methodological issues of importance in understanding and evaluating depression in this patient population are described, and methodological variations between studies, particularly in reference to methods of case detection, diagnostic criteria used and characteristics of the populations studied, are identified. The findings reported in the current literature in general are contrary to what would be expected from an examination of the significant biological and psychosocial stresses of individuals with HIV, and are inconsistent with those of other life-threatening illnesses and CNS diseases. Clear conclusions regarding the prevalence of depression and its effect in patients with HIV/AIDS cannot yet be made.
Intensive Cognitive-Behaviour Group Therapy for Diagnostically Heterogeneous Groups of Patients with Psychiatric Disorder
Authors: Manning J. J. , Hooke G. R. , Tannenbaum D. A. , Blythe T. H. , Clarke T. M.
Published: July 2010

This uncontrolled study evaluates the efficacy of a combined treatment of medications (for the majority of patients) and a closed group, intensive (two-week) cognitive-behaviour therapy programme for heterogeneous groups of psychiatric patients. Five hundred and thirty-one patients at a private psychiatric clinic were included in the study. Self-report measures of depression, anxiety, self-esteem and “locus of control’ were administered before and after treatment and at intervals up to one year later. Statistically and clinically significant improvements were found in all measures and these improvements were maintained up to one year. The results provide support for the efficacy of the treatment.
Electrode Placement, Stimulus Dosing and Seizure Monitoring during ECT
Authors: Murugesan G.
Published: July 2010

Electroconvulsive therapy is one of the most useful, safe and predictable treatment modalities in psychiatry. For optimal results proper application of the procedure is essential. Over the years the procedure has undergone considerable refinement, yet not all those who administer the treatment are fully conversant with this. This paper addresses issues relating to electrode placement, stimulus dosing and seizure monitoring from practical and clinical points of view. Right unilateral ECT, if administered with high electrical stimulus, produces results close to bilateral treatment with substantially less cognitive impairment. However, certain patients may only respond to bilateral ECT. Adequate training for clinicians administering ECT is recommended.
Sar1 bends membranes into shape
Authors: Short Ben
Published: July 2010

The small GTPase forms an organized scaffold that can regulate the pinching of vesicles from the ER.
Elasticity of SrTiO3 perovskite under high pressure in cubic, tetragonal and orthorhombic phases
Authors: Hachemi A , Hachemi H , Ferhat-Hamida A , Louail L
Published: July 2010

We investigated the athermal high-pressure behavior of the elastic properties of SrTiO3 (STO) up to 26 GPa in cubic, tetragonal and orthorhombic phases using the ab initio pseudo-potential method. Our results for the cubic phase are in good agreement with experiment and previous pseudo-potential calculations. There are no studies for the tetragonal and orthorhombic phases under high pressure available for comparison. To date, there are no global data on elastic parameters under high pressure for STO. We establish data when we report the results of our structural and elastic study under high pressure in the three phases. Our calculations show that the cubic–tetragonal phase transition occurs at 6 GPa and the tetragonal–orthorhombic phase transition at 14 GPa. A third and unknown phase transition from orthorhombic Cmcm to monoclinic P21 /m was observed at 24 GPa, but no study has explored it. The orthorhombic phase is unstable and this instability may be due to ferroelectricity at high pressure. The elastic properties of STO are also strongly pressure dependent with instabilities near the phase transition pressure. STO is more resistant to plastic deformation and to fracture in the cubic phase than in the tetragonal and orthorhombic phases.
Quadratic Jordan algebras and cubing operations
Authors: McCrimmon Kevin
Published: July 2010

In this paper we show how the Jordan structure can be derived from the squaring and cubing operations in a quadratic Jordan algebra, and give an alternate axiomatization of unital quadratic Jordan algebras in terms of operator identities involving only a single variable. Using this we define nonunital quadratic Jordan algebras and show they can be imbedded in unital algebras. We show that a noncommutative Jordan algebra

A

\mathfrak {A}

(over an arbitrary ring of scalars) determines a quadratic Jordan algebra

A

+

{\mathfrak {A}^ + }

.
Existence and uniqueness of solutions of boundary value problems for two dimensional systems of nonlinear differential equations
Authors: Waltman Paul
Published: July 2010

The paper considers the nonlinear system

x
′

=
f
(
t
,
x
,
y
)
,

y
′

=
g
(
t
,
x
,
y
)

x’ = f(t,x,y),y’ = g(t,x,y)

with linear and nonlinear two point boundary conditions. With a Lipschitz condition, an interval of uniqueness for linear boundary conditions is determined using a comparison theorem. A corresponding existence theorem is established. Under the assumption of uniqueness, a general existence theorem is established for quite general nonlinearities in the functions and in the boundary conditions. Examples are provided. The results extend previous work on second order scalar differential equations.
Linear ordinary differential equations with boundary conditions on arbitrary point sets
Authors: Golomb Michael , Jerome Joseph
Published: July 2010

Boundary-value problems for differential operators

Λ
\Lambda

of order

2
m

2m

which are the Euler derivatives of quadratic functionals are considered. The boundary conditions require the solution

F
F

to coincide with a given function

f
∈

H

L

(
R
)

f \in {\mathcal {H}_L}(R)

at the points of an arbitrary closed set

B
B

, to satisfy at the isolated points of

B
B

the knot conditions of

2
m

2m

-spline interpolations, and to lie in

H

L

(
R
)

{\mathcal {H}_L}(R)

. Existence of solutions (called “

Λ
\Lambda

-splines knotted on

B
B

") is proved by consideration of the associated variational problem. The question of uniqueness is treated by decomposing the problem into an equivalent set of problems on the disjoint intervals of the complement of

B
′

B’

, where

B
′

B’

denotes the set of limit points of

B
B

. It is also shown that

Λ
\Lambda

, considered as an operator from

L

2

(
R
)

{\mathcal {L}_2}(R)

to

L

2

(
R
)

{\mathcal {L}_2}(R)

), with appropriately restricted domain, has a unique selfadjoint extention

Λ
B

{\Lambda _B}

if one postulates that the domain of

Λ
B

{\Lambda _B}

contains only functions of

H

L

(
R
)

{\mathcal {H}_L}(R)

which vanish on

B
.
I
+

Λ
B

B.I + {\Lambda _B}

has a bounded inverse which serves to solve the inhomogeneous equation

Λ
F
=
G

\Lambda F = G

with homogeneous boundary conditions. Approximations to the

Λ
\Lambda

-splines knotted on

B
B

are constructed, consisting of

Λ
\Lambda

-splines knotted on finite subsets

B
n

{B_n}

of

B
B

, with

∪

B
n

\cup {B_n}

dense in

B
B

. These approximations

F
n

{F_n}

converge to

F
F

in the sense of

H

L

(
R
)

{\mathcal {H}_L}(R)

.
Embedding of abelian subgroups in 𝑝-groups
Authors: Konvisser Marc W.
Published: July 2010

Research concerning the embedding of abelian subgroups in

p
p

-groups generally has proceeded in two directions; either considering abelian subgroups of small index (cf. J. L. Alperin, Large abelian subrgoups of

p
p

-groups, Trans. Amer. Math. Soc. 117 (1965), 10-20) or considering elementary abelian subgroups of small order (cf. B. Huppert, Endliche Gruppen. I, Springer-Verlag, Berlin, 1967, p. 303). The following new theorems extend these results: Theorem A. Let

G
G

be a

p
p

-group and

M
M

a normal subgroup of

G
G

. (a) If

M
M

contains an abelian subgroup of index

p
p

, then

M
M

contains an abelian subgroup of index

p
p

which is normal in

G
G

. (b) If

p
≠
2

p \ne 2

and

M
M

contains an abelian subgroup of index

p
2

{p^2}

, then

M
M

contains an abelian subgroup of index

p
2

{p^2}

which is normal in

G
G

. Theorem B. Let

G
G

be a

p
p

-group,

p
≠
2
,
M

p \ne 2, M

a normal subgroup of

G
G

, and let

k
k

be 2, 3, 4, or 5. If

M
M

contains an elementary abelian subgroup of order

p
k

{p^k}

, then

M
M

contains an elementary abelian subgroup of order

p
k

{p^k}

which is normal in

G
G

.
Irreducible congruences of prime power degree
Authors: Hanneken C. B.
Published: July 2010

The number of conjugate sets of irreducible congruences of degree

m
m

belonging to

G
F
(
p
)
,
p
>
2

GF(p),p > 2

, relative to the group

G
G

of linear fractional transformations with coefficients belonging to the same field has been determined for

m
≦
8

m \leqq 8

. In this paper the irreducible congruences of prime power degree

q
α

,
q
>
2

{q^\alpha },q > 2

, are considered and the number of conjugate sets relative to

G
G

is determined.
The prime radical in special Jordan rings
Authors: Erickson T. S. , Montgomery S.
Published: July 2010

If R is an associative ring, we consider the special Jordan ring

R
+

{R^ + }

, and when R has an involution, the special Jordan ring S of symmetric elements. We first show that the prime radical of R equals the prime radical of

R
+

{R^ + }

, and that the prime radical of R intersected with S is the prime radical of S. Next we give an elementary characterization, in terms of the associative structure of R, of primeness of S. Finally, we show that a prime ideal of R intersected with S is a prime Jordan ideal of S.
Positive one-relator groups
Authors: Baumslag Gilbert
Published: July 2010

A group G which can be defined by a single relation in which there are no negative exponents is residually solvable. If G is also torsion-free then it is locally indicable and hence its integral group ring has no zero divisors.
Semigroups on finitely floored spaces
Authors: McCharen John D.
Published: July 2010

This paper is concerned with certain aspects of acyclicity in a compact connected topological semigroup, and applications to the admissibility of certain multiplications on continua. The principal result asserts that if S is a semigroup on a continuum, finitely floored in dimension 2, then

S
=
E
S
E

S = ESE

implies

S
=
K

S = K

.
Summability in amenable semigroups
Authors: Mah Peter F.
Published: July 2010

A theory of summability is developed in amenable semigroups. We give necessary and (or) sufficient conditions for matrices to be almost regular, almost Schur, strongly regular, and almost strongly regular. In particular, when the amenable semigroup is the additive positive integers, our theorems yield those results of J. P. King, P. Schaefer and G. G. Lorentz for some of the matrices mentioned above.
Some iterated logarithm results related to the central limit theorem.
Authors: Tomkins R. J.
Published: July 2010

An iterated logarithm theorem is presented for sequences of independent, not necessarily bounded, random variables, the distribution of whose partial sums is related to the standard normal distribution in a particular manner. It is shown that if a sequence of independent random variables satisfies the Central Limit Theorem with a sufficiently rapid rate of convergence, then the law of the iterated logarithm holds. In particular, it is demonstrated that these results imply several known iterated logarithm results, including Kolmogorov’s celebrated theorem.
Representations of metabelian groups realizable in the real field
Authors: Basmaji B. G.
Published: July 2010

A necessary and sufficient condition is found such that all the nonlinear irreducible representations of a metabelian group are realizable in the real field, and all such groups with cyclic commutator subgroups are determined.
Value distribution of harmonic polynomials in several real variables.
Authors: Marden Morris
Published: July 2010

Using Bergman’s integral operator method, the author studies an arbitrary axisymmetric harmonic polynomial

H
(
x
,
ρ
)

H(x,\rho )

in

R
3

{R^3}

and

R
N

{R^N}

in relation to its associate polynomial

h
(
ζ
)

h(\zeta )

in

C
C

. His results pertain to the value distributions and critical circles of

H
(
x
,
ρ
)

H(x,\rho )

in certain cones; bounds on the gradient of an

H
(
x
,
ρ
)

H(x,\rho )

assumed bounded in sphere

x
2

+

ρ
2

≦
1

{x^2} + {\rho ^2} \leqq 1

; axisymmetric harmonic vectors. Corresponding results are also obtained for axisymmetric harmonic functions

F
(
x
,
ρ
)

F(x,\rho )

with rational associate

f
(
ζ
)

f(\zeta )

.
Limit theorems for measures on nonmetrizable locally compact abelian groups
Authors: Bossard David C.
Published: July 2010

In a recent book, Parthasarathy provides limit theorems for sums of independent random variables defined on a metrizable locally compact abelian group. These results make heavy use of the metric assumption. This paper consists of a reworking of certain results contained in Parthasarathy to see what can be done without the metric restriction. Among the topics considered are: necessary and sufficient conditions for a limit law to have an idempotent factor; the relationship between limits of compound Poisson laws and limits of sums of independent random variables; and a representation theorem for certain limit laws.
Automorphisms of a free associative algebra of rank 2. I
Authors: Czerniakiewicz Anastasia J.
Published: July 2010

Let

R

⟨
2
⟩

=
R

⟨

x
,
y

⟩

{R_{\left \langle 2 \right \rangle }} = R\left \langle {x,y} \right \rangle

be the free associative algebra of rank 2, on the free generators

x
x

and

y
y

, over

R
R

(

R
R

a field, a Euclidean domain, etc.). We prove that if

φ
\varphi

is an automorphism of

R

⟨
2
⟩

{R_{\left \langle 2 \right \rangle }}

that keeps

(
x
y
−
y
x
)

(xy - yx)

fixed (up to multiplication by an element of

R
R

), then

φ
\varphi

is tame, i.e. it is a product of elementary automorphisms of

R

⟨
2
⟩

{R_{\left \langle 2 \right \rangle }}

. This follows from a more general result about endomorphisms of

R

⟨
2
⟩

{R_{\left \langle 2 \right \rangle }}

via a theorem due to H. Jung [6] concerning automorphisms of a commutative and associative algebra of rank 2.
Maximal and minimal topologies
Authors: Cameron Douglas E.
Published: July 2010

A topological space

(
X
,
T
)

(X,T)

with property

R

{\text {R}}

is maximal

R

{\text {R}}

(minimal

R

{\text {R}}

) if

T
T

is a maximal (minimal) element in the set

R

(
X
)

{\text {R}}(X)

of all topologies on the set

X
X

having property

R

{\text {R}}

with the partial ordering of set inclusions. The properties of maximal topologies for compactness, countable compactness, sequential compactness, Bolzano-Weierstrass compactness, and Lindelöf are investigated and the relations between these spaces are investigated. The question of whether any space having one of these properties has a strictly stronger maximal topology is investigated. Some interesting product theorems are discussed. The properties of minimal topologies and their relationships are discussed for the quasi-

P
P

, Hausdorff quasi-

P
P

, and

P
P

topologies.
Semigroups that are the union of a group on 𝐸³ and a plane
Authors: Knowles Frank
Published: July 2010

In Semigroups on a half-space, Trans. Amer. Math. Soc. 147 (1970), 1-53, Horne considers semigroups that are the union of a group

G
G

and a plane

L
L

such that

G
∪
L

G \cup L

is a three-dimensional half-space and

G
G

is the interior. After proving a great many things about half-space semigroups, Horne introduces the notion of a radical and determines all possible multiplications in

L
L

for a half-space semigroup with empty radical. (It turns out that

S
S

has empty radical if and only if each

G
G

-orbit in

L
L

contains an idempotent.) An example is provided for each configuration in

L
L

. However, no attempt was made to show that the list of examples actually exhausted the possibilities for a half-space semigroup without radical. Another way of putting this problem is to determine when two different semigroups can have the same maximal group. In this paper we generalize Horne’s results, for a semigroup without zero, by showing that if

S
S

is any locally compact semigroup in which

L
L

is the boundary of

G
G

, then

S
S

is a half-space. Moreover, we are able to answer completely, for semigroups without radical and without a zero, the question posed above. It turns out that, with one addition (which we provide), Horne’s list of half-space semigroups without radical and without zero is complete.
A strong duality theorem for separable locally compact groups
Authors: Ernest John
Published: July 2010

We obtain a duality theorem for separable locally compact groups, where the group is regained from the set of factor unitary representations. Loosely stated, the group is isomorphic to the group of nonzero bounded, operator valued maps on the set of factor representations, which preserve unitary equivalence, direct sums, and tensor products. The axiom involving tensor products is formulated in terms of direct integral theory. The topology of G may be regained from the irreducible representations alone. Indeed a sequence

{

x
i

}

\{ {x_i}\}

in G, converges to x in G if and and only if

π
(

x
i

)

\pi ({x_i})

converges strongly to

π
(
x
)

\pi (x)

for each irreducible representation

π
\pi

of G. This result supplies the missing topological part of the strong duality theorem of N. Tatsuuma for type I separable locally compact groups (based on irreducible representations). Our result also generalizes this Tatsuuma strong duality theorem to the nontype I case.
The bifurcation of solutions in Banach spaces
Authors: Hall William S.
Published: July 2010

Let

L
:
D
⊂
X
→
D
⊂

X
∗

L:D \subset X \to D \subset {X^ \ast }

be a densely defined linear map of a reflexive Banach space X to its conjugate

X
∗

{X^\ast }

. Define M and

M
∗

{M^\ast }

to be the respective null spaces of L and its formal adjoint

L
∗

{L^\ast }

. Let

f
:
X
→

X
∗

f:X \to {X^\ast }

be continuous. Under certain conditions on

L
∗

{L^\ast }

and f there exist weak solutions to

L
u
=
f
(
u
)

Lu = f(u)

provided for each

w
∈
X
,
v
(
w
)
∈
M

w \in X,v(w) \in M

can be found such that

f
(
v
(
w
)
+
w
)

f(v(w) + w)

annihilates

M
∗

{M^ \ast }

. Neither M and

M
∗

{M^\ast }

nor their annihilators need be the ranges of continuous linear projections. The results have applications to periodic solutions of partial differential equations.
Rearrangements
Authors: Minc Henryk
Published: July 2010

It is shown that if
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a Superscript left-parenthesis t right-parenthesis Baseline equals left-parenthesis a 1 Superscript left-parenthesis t right-parenthesis Baseline comma a 2 Superscript left-parenthesis t right-parenthesis Baseline comma ellipsis comma a Subscript n Superscript left-parenthesis t right-parenthesis Baseline right-parenthesis comma t equals 1 comma ellipsis comma m">

a

(
t
)

=
(

a
1

(
t
)

,

a
2

(
t
)

,
…
,

a
n

(
t
)

)
,
t
=
1
,
…
,
m

{a^{(t)}} = (a_1^{(t)},a_2^{(t)}, \ldots ,a_n^{(t)}),t = 1, \ldots ,m

, are nonnegative

n
n

-tuples, then the maxima of
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript i equals 1 Overscript n Endscripts a Subscript i Superscript left-parenthesis 1 right-parenthesis Baseline a Subscript i Superscript left-parenthesis 2 right-parenthesis Baseline midline-horizontal-ellipsis a Subscript i Superscript left-parenthesis m right-parenthesis">

∑

i
=
1

n

a
i

(
1
)

a
i

(
2
)

⋯

a
i

(
m
)

\sum \nolimits _{i = 1}^n {a_i^{(1)}a_i^{(2)} \cdots a_i^{(m)}}

of

∏

i
=
1

n

min

t

(

a
i

(
t
)

)

\prod \nolimits _{i = 1}^n {{{\min }_t}(a_i^{(t)})}

and of

Σ

i
=
1

n

\Sigma _{i = 1}^n

min

(

a
i

(
t
)

)

(a_i^{(t)})

, and the minima of
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="product Underscript i equals 1 Overscript n Endscripts left-parenthesis a Subscript i Superscript left-parenthesis 1 right-parenthesis Baseline plus a Subscript i Superscript left-parenthesis 2 right-parenthesis Baseline plus midline-horizontal-ellipsis plus a Subscript i Superscript left-parenthesis m right-parenthesis Baseline right-parenthesis">

∏

i
=
1

n

(

a
i

(
1
)

+

a
i

(
2
)

+

⋯
+

a
i

(
m
)

)

\prod \nolimits _{i = 1}^n {(a_i^{(1)} + a_i^{(2)} + } \cdots + a_i^{(m)})

, of

∏

i
=
1

n

max

t

(

a
i

(
t
)

)

\prod \nolimits _{i = 1}^n {{{\max }_t}(a_i^{(t)})}

and of

∑

i
=
1

n

max

t

(

a
i

(
t
)

)

\sum \nolimits _{i = 1}^n {{{\max }_t}(a_i^{(t)})}

are attained when the

n
n

-tuples

a

(
1
)

,

a

(
2
)

,
…
,

a

(
m
)

{a^{(1)}},{a^{(2)}}, \ldots ,{a^{(m)}}

are similarly ordered. Necessary and sufficient conditions for equality are obtained in each case. An application to bounds for permanents of

(
0
,
1
)

(0,1)

-matrices is given.
Studies in the representation theory of finite semigroups
Authors: Zalcstein Yechezkel
Published: July 2010

This paper is a continuation of [14], developing the representation theory of finite semigroups further. The main result, Theorem 1.24, states that if the group of units U of a mapping semigroup (X, S) is multiply transitive with a sufficiently high degree of transitivity, then for certain irreducible characters

χ
\chi

of U,

χ
\chi

can be “extended” formally to an irreducible character of S. This yields a partial generalization of a well-known theorem of Frobenius on the characters of multiply-transitive groups and provides the first nontrivial explicit formula for an irreducible character of a finite semigroup. The paper also contains preliminary results on the “spectrum” (i.e., the set of ranks of the various elements) of a mapping semigroup.
Implicitly defined mappings in locally convex spaces
Authors: McDermott Terrence S.
Published: July 2010

Results on existence, uniqueness, continuity and differentiability of implicit functions in locally convex, linear topological spaces are obtained, and certain of these results are applied to obtain results on the existence and continuous dependence on parameters of global solutions for a nonlinear Volterra integral equation.
On isomorphisms between ideals in rings of continuous functions
Authors: Rudd David
Published: July 2010

A ring of continuous functions is a ring of the form

C
(
X
)

C(X)

, the ring of all continuous real-valued functions on a completely regular Hausdorff space

X
X

. For an arbitrary ideal

I
I

in

C
(
X
)

C(X)

, the author shows that the maximal ideals of

I
I

are precisely the ideals of the form

I
∩
M

I \cap M

, for some maximal ideal

M
M

in

C
(
X
)

C(X)

not containing

I
I

. The author shows that any ring isomorphism between ideals in any two rings of continuous functions preserves order, boundedness, and lattice structure; and he uses these results to obtain one of the main theorems: An isomorphism of a maximal ideal in

C
(
X
)

C(X)

onto a maximal idea in

C
(
Y
)

C(Y)

can be extended to an isomorphism of

C
(
X
)

C(X)

onto

C
(
Y
)

C(Y)

. Another of the main theorems characterizes those isomorphisms between

C
∗

(
X
)

{C^ \ast }(X)

and

C
∗

(
Y
)

{C^ \ast }(Y)

(the subrings of bounded functions in

C
(
X
)

C(X)

and

C
(
Y
)

C(Y)

respectively) which can be extended to isomorphisms between

C
(
X
)

C(X)

and

C
(
Y
)

C(Y)

. The author proves that, given any ideal

I
I

in

C
(
X
)

C(X)

, there exists a space

X
(
I
)

X(I)

so that the uniform closure of

I
I

is isomorphic to a maximal ideal in

C
(
X
(
I
)
)

C(X(I))

.
Degenerate evolution equations in Hilbert space
Authors: Friedman Avner , Schuss Zeev
Published: July 2010

We consider the degenerate evolution equation

c
1

(
t
)
d
u

/

d
t
+

c
2

(
t
)
A
(
t
)
u
=
f
(
t
)

{c_1}(t)du/dt + {c_2}(t)A(t)u = f(t)

in Hilbert space, where

c
1

≧
0
,

c
2

≧
0
,

c
1

+

c
2

>
0
;
A
(
t
)

{c_1} \geqq 0,{c_2} \geqq 0,{c_1} + {c_2} > 0;A(t)

is an unbounded linear operator satisfying the usual conditions which ensure that there is a unique solution for the Cauchy problem

d
u

/

d
t
+
A
(
t
)
u
=
f
(
t
)

i
n

(
0
,
T
]
,
u
(
0
)
=

u
0

du/dt + A(t)u = f(t){\rm {in}}(0,T],u(0) = {u_0}

. We prove the existence and uniqueness of a weak solution, and differentiability theorems. Applications to degenerate parabolic equations are given.
Bounds for solutions to a class of nonlinear integral equations
Authors: Martin Robert H.
Published: July 2010

In this paper a bound is obtained for solutions to a class of nonlinear Stieltjes integral equations. The class of equations under consideration have been previously studied by J. S. Mac Nerney. It is shown that the bound obtained here is in some sense a best bound, and in the linear case, reduces to a previous result of the author.
Minimal convergence spaces
Authors: Kent D. C. , Richardson G. D.
Published: July 2010

We are primarily concerned with minimal

P

{\text {P}}

convergence spaces, where

P

{\text {P}}

is one of the following convergence space properties: Hausdorff,

T

2

,
λ

{{\text {T}}_2}, \lambda

-regular,

λ
\lambda

-Urysohn, and first countable,

λ
\lambda

an infinite cardinal number. Our conclusions usually resemble the corresponding topological results, but with some deviations ; for instance, a minimal Hausdorff convergence space is always compact, whereas a countable minimal regular convergence space need not be compact.
Some examples in degree of approximation by rational functions
Authors: Aharonov D. , Walsh J. L.
Published: July 2010

We exhibit examples of (1) series that converge more rapidly than any geometric series where the function represented has a natural boundary, (2) the convergence of a series with maximum geometric degree of convergence yet having limit points of poles of the series everywhere dense on a circumference in the complement of

E
E

, (3) a Padé table for an entire function whose diagonal has poles every-where dense in the plane and (4) a corresponding example for the table of rational functions of best approximation of prescribed type.
A theorem and a counterexample in the theory of semigroups of nonlinear transformations
Authors: Crandall Michael G. , Liggett Thomas M.
Published: July 2010

This paper studies the basic method in current use for constructively obtaining a generator from a given semigroup of nonlinear transformations on a Banach space. The method is shown to succeed in real two-dimensional Banach spaces and to fail in a particular three-dimensional example. Other results of independent interest are obtained. For example, it is shown that the concepts of “maximal accretive” and “hyperaccretive” (equivalently,

m
m

-accretive or hypermaximal accretive) coincide in

R
n

{R^n}

with the maximum norm.
Relative types of points in 𝛽𝑁-𝑁
Authors: Steiner A. K. , Steiner E. F.
Published: July 2010

Using the concepts of type and relative type for points in

β
N
−
N

\beta N - N

, as introduced by W. Rudin, M. E. Rudin, and Z. Frolik, an inductive method is presented for constructing types. The relative types are described for points having these constructed types and a point in

β
N
−
N

\beta N - N

is found which has exactly

c
c

relative types.
Quotient sheaves and valuation rings
Authors: Cunningham Joel
Published: July 2010

In this paper a construction of a quotient sheaf of a sheaf of rings is given. This construction is analogous to the Utumi ring of quotients of a ring. For a valuation ring V, a sheaf of rings corresponding to V is introduced and its quotient sheaf is computed. It is shown that this quotient sheaf corresponds to the completion of V in case V is discrete rank one and that V is maximal if and only if its associated sheaf of rings is its own quotient sheaf.
A characterization of the group 𝑈₃(4)
Authors: Lyons Richard
Published: July 2010

Let T be a Sylow 2-subgroup of the projective special unitary group

U
3

(
4
)

{U_3}(4)

, and let G be a finite group with Sylow 2-subgroups isomorphic to T. It is shown that if G is simple, then

G
≅

U
3

(
4
)

G \cong {U_3}(4)

; if G has no proper normal subgroup of odd order or index, then

G
≅

U
3

(
4
)

G \cong {U_3}(4)

or T.
The structure of certain unitary representations of infinite symmetric groups
Authors: Lieberman Arthur
Published: July 2010

Let S be an infinite set,

β
\beta

an infinite cardinal number, and

G
β

(
S
)

{G_\beta }(S)

the group of those permutations of S whose support has cardinal number less than

β
\beta

. If T is any nonempty set,

S
T

{S^T}

is the set of functions from T to S. The canonical representation

Λ
β
T

\Lambda _\beta ^T

of

G
β

(
S
)

{G_\beta }(S)

on

L
2

(

S
T

)

{L^2}({S^T})

is the direct sum of factor representations. Factor representations of types

I

∞

,

II
1

{{\text {I}}_\infty },{\text {II}_1}

, and

II
∞

{\text {II}_\infty }

occur in this decomposition, depending upon S,

β
\beta

, and T; the type

II
1

{\text {II}_1}

factor representations are quasi-equivalent to the left regular representation. Let

G
β

(
S
)

{G_\beta }(S)

have the topology of pointwise convergence on S.

G
β

(
S
)

{G_\beta }(S)

is a topological group but is not locally compact. Every continuous representation of

G
β

(
S
)

{G_\beta }(S)

is the direct sum of irreducible representations. Let

Γ
\Gamma

be a nontrivial continuous irreducible representation of

G
β

(
S
)

{G_\beta }(S)

. Then

Γ
\Gamma

is continuous iff

Γ
\Gamma

is equivalent to a subrepresentation of

Λ
β
T

\Lambda _\beta ^T

for some nonempty finite set T iff there is a nonempty finite subset Z of S such that the restriction of

Γ
\Gamma

to the subgroup of those permutations which leave Z pointwise fixed contains the trivial representation of this subgroup.
Two point boundary value problems for nonlinear functional differential equations
Authors: Waltman Paul , Wong James S. W.
Published: July 2010

This paper is concerned with the existence of solutions of two point boundary value problems for functional differential equations. Specifically, we consider
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="y prime left-parenthesis t right-parenthesis equals upper L left-parenthesis t comma y Subscript t Baseline right-parenthesis plus f left-parenthesis t comma y Subscript t Baseline right-parenthesis comma upper M y Subscript a Baseline plus upper N y Subscript b Baseline equals psi comma">

y
′

(
t
)
=
L
(
t
,

y
t

)
+
f
(
t
,

y
t

)
,

M

y
a

+
N

y
b

=
ψ
,

y’(t) = L(t,{y_t}) + f(t,{y_t}),\quad M{y_a} + N{y_b} = \psi ,

\]
where M and N are linear operators on

C
[
0
,
h
]

C[0,h]

. Growth conditions are imposed on f to obtain the existence of solutions. This result is then specialized to the case where

L
(
t
,

y
t

)
=
A
(
t
)
y
(
t
)

L(t,{y_t}) = A(t)y(t)

, that is, when the reduced linear equation is an ordinary rather than a functional differential equation. Several examples are discussed to illustrate the results.
Weakly almost periodic functionals carried by hypercosets
Authors: Dunkl Charles F. , Ramirez Donald E.
Published: July 2010

For G a compact group and H a closed normal subgroup, we show that a weakly almost periodic (w.a.p.) linear functional on the Fourier algebra of G/H lifts to a w.a.p. linear functional on the Fourier algebra of G.
Slices of maps and Lebesgue area
Authors: Ziemer William P.
Published: July 2010

For a large class of k dimensional surfaces, S, it is shown that the Lebesgue area of S can be essentially expressed in terms of an integral of the

k
−
1

k - 1

area of a family, F, of

k
−
1

k - 1

dimensional surfaces that cover S. The family F is regarded as being composed of the slices of F. The definition of the

k
−
1

k - 1

area of a surface restricted to one of its slices is formulated in terms of the theory developed by H. Federer, [F3].
A class of complete orthogonal sequences of broken line functions
Authors: Sox J. L.
Published: July 2010

A class of orthonormal sets of continuous broken line functions is defined. Each member is shown to be complete in

L
2

(
0
,
1
)

{L_2}(0,1)

and pointwise convergence theorems are obtained for the Fourier expansions relative to these sets.
Convolution operators on Lebesgue spaces of the half-line
Authors: Daniel Victor W.
Published: July 2010

In this paper we determine the lattice of closed invariant subspaces for certain convolution operators on Lebesgue spaces

L
p

(
d
σ
)

{L^p}(d\sigma )

where

σ
\sigma

is a suitable weighted measure on the half-line. We exploit the rather close relationship between convolution operators and the collection of right translation operators

{

T
λ

}

λ
≧
0

{\{ {T_\lambda }\} _{\lambda \geqq 0}}

on

L
p

(
d
σ
)

{L^p}(d\sigma )

. We show that a convolution operator K and the collection

{

T
λ

}

λ
≧
0

{\{ {T_\lambda }\} _{\lambda \geqq 0}}

have the same lattice of closed invariant subspaces provided the kernel k of K is a cyclic vector. The converse also holds if we assume in addition that the closed span of

{

T
λ

k

}

λ
≧
0

{\{ {T_\lambda }k\} _{\lambda \geqq 0}}

is all of

L
p

(
d
σ
)

{L^p}(d\sigma )

. We show that the lattice of closed right translation invariant subspaces of

L
p

(
d
σ
)

{L^p}(d\sigma )

is totally ordered by set inclusion whenever

σ
\sigma

has compact support. Thus in this case a convolution operator K is unicellular if and only if its kernel is a cyclic vector. Finally, we show for suitable weighted measures

σ
\sigma

on the half-line that the convolution operators on

L
p

(
d
σ
)

{L^p}(d\sigma )

are Volterra.
On the rank of a space
Authors: Allday Christopher
Published: July 2010

The rank of a space is defined as the dimension of the highest dimensional torus which can act almost-freely on the space. (By an almost-free action is meant one for which all the isotropy subgroups are finite.) This definition is shown to extend the classical definition of the rank of a Lie group. A conjecture giving an upper bound for the rank of a space in terms of its rational homotopy is investigated.
One-dimensional basic sets in the three-sphere
Authors: Gibbons Joel C.
Published: July 2010

This paper is a continuation of Williams’ classification of one-dimensional attracting sets of a diffeomorphism on a compact manifold [Topology 6 (1967)]. After defining the knot presentation of a solenoid in

S
3

{S^3}

and some knottheoretic preliminaries, we prove Theorem: If

∑
1

,

h
1

{\sum _1},{h_1}

and

∑
2

,

h
2

{\sum _2},{h_2}

are shift classes of oriented solenoids admitting elementary presentations K,

K
,

g
1

K,{g_1}

and K,

K
,

g
2

K,{g_2}

, resp., where
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="g 1 Superscript asterisk Baseline equals left-parenthesis g 2 Superscript asterisk Baseline right-parenthesis Superscript t Baseline colon upper H 1 left-parenthesis upper K right-parenthesis right-arrow upper H 1 left-parenthesis upper K right-parenthesis">

g
1

∗

=

(

g
2

∗

)
t

:

H
1

(
K
)
→

H
1

(
K
)

{g_1}^ \ast = {({g_2}^ \ast )^t}:{H_1}(K) \to {H_1}(K)

, there is an Anosov-Smale diffeomorphism f of

S
3

{S^3}

such that

Ω
(
f
)

\Omega (f)

consists of a source

Λ
−

{\Lambda ^ - }

and a sink

Λ
+

{\Lambda ^ + }

for which

Λ
+

,
f

/

Λ
+

{\Lambda ^ + },f/{\Lambda ^ + }

and

Λ
−

,

f

−
1

/

Λ
−

{\Lambda ^ - },{f^{ - 1}}/{\Lambda ^ - }

are conjugate, resp., to

∑
1

,

h
1

{\sum _1},{h_1}

and

∑
2

,

h
2

{\sum _2},{h_2}

. (The author has proved [Proc. Amer. Math. Soc., to appear] that if f is an Anosov-Smale map of

S
3

,
Ω
(
f
)

{S^3},\Omega (f)

has dimension one, and contains no hyperbolic sets, then f has the above structure.) We also prove Theorem: there is a nonempty

C
1

{C^1}

-open set

F
2

{F_2}

in the class of such diffeomorphisms for which

K
=

S
1

K = {S^1}

and

g
1

=

g
2

{g_1} = {g_2}

is the double covering such that each f in

F
2

{F_2}

defines a loop t in

S
3

{S^3}

, stable up to

C
1

{C^1}

perturbations, for which at every x in t the generalized stable and unstable manifolds through x are tangent at x.
Tangential limits of functions orthogonal to invariant subspaces
Authors: Protas David
Published: July 2010

For any inner function

φ
\varphi

, let

M
⊥

{M^ \bot }

be the orthogonal complement of

φ

H
2

\varphi {H^2}

, in

H
2

{H^2}

, where

H
2

{H^2}

is the usual Hardy space. The relationship between the tangential convergence of all functions in

M
⊥

{M^ \bot }

and the finiteness of certain sums and integrals involving

φ
\varphi

is studied. In particular, it is shown that the tangential convergence of all functions in

M
⊥

{M^ \bot }

is a stronger condition than the tangential convergence of

φ
\varphi

, itself.