bluuebunny/crossref_metadata_2025 huggingface dataset:
Contactless electroreflectance study of band bending in Be-doped GaInNAs/GaAs quantum wells: The origin of photoluminescence enhancement
Authors: Kudrawiec R. , Gladysiewicz M. , Misiewicz J. , Korpijärvi V.-M. , Pakarinen J. , Puustinen J. , Laukkanen P. , Laakso A. , Guina M. , Dumitrescu M. , Pessa M.
Published: July 2010

Contactless electroreflectance (CER) has been applied to study band bending in Be-doped GaInNAs/GaAs quantum wells (QWs). It has been shown that (i) the sign of GaAs-related CER signal changes from positive to negative due to Be-doping and (ii) QW-related CER resonances disappear for Be-doped QWs whereas they are clearly observed for un-doped QWs. The two observations indicate a Be-related shift in the Fermi level above the hole levels in the QW region, i.e., the change in band bending in this system. The results point out that the experimentally-observed enhancement in QW photoluminescence upon Be-doping is associated with a better collection/confinement of photogenerated carriers by the Be-doped GaInNAs QW.
p-Si nanowires/SiO2/n-ZnO heterojunction photodiodes
Authors: Huang Chun-Ying , Yang Ying-Jay , Chen Ju-Ying , Wang Chun-Hsiung , Chen Yang-Fang , Hong Lu-Sheng , Liu Chie-Sheng , Wu Chia-Yin
Published: July 2010

Influence of a SiO2 ultrathin film on n-ZnO/p-silicon nanowires photodiodes has been investigated. With a SiO2 thin layer, the diode characteristics can be significantly improved, which exhibits high responsivity under a reverse bias. Based on the electron conversion efficiency measurement, we show that the ultrathin SiO2 layer with positive fixed charges not only acts as a hole blocking layer but also helps the photogenerated electrons to tunnel through the barrier. In addition, the SiO2 layer can effectively passivate the defects generated by wet etching process. It is expected that our approach can be extended to many other nanoscale heterojunction devices.
Effect of temperature on the La1-xCaxMnO3/SrTiO3:Nb (x=–0.75) heterojunctions
Authors: Lu X. Y. , Sun J. R. , Wei A. D. , Gao W. W. , Shang D. S. , Wang J. , Wang Z. H. , Shen B. G.
Published: July 2010

Influence of temperature on the La1-xCaxMnO3/SrTiO3:Nb heterojunctions with the Ca content ranging from 0 to 0.75 has been experimentally studied. Obvious temperature effect occurs in the junction with a Ca content of 0.1. As experimentally shown, the interfacial barrier is insensitive to temperature below 340 K, and experiences a decrease from ∼1.24 to 0.85 eV as temperature grows from 340 to 375 K. However, the temperature effect in other junctions is weak, and the energy barrier change is typically ∼0.03–0.08 eV. In the scenario of temperature-driven orbital order-disorder transition in the La0.9Ca0.1MnO3 film, the temperature effect can be qualitatively understood.
Single-molecule denaturation mapping of DNA in nanofluidic channels
Authors: Reisner Walter , Larsen Niels B. , Silahtaroglu Asli , Kristensen Anders , Tommerup Niels , Tegenfeldt Jonas O. , Flyvbjerg Henrik
Published: July 2010

Here we explore the potential power of denaturation mapping as a single-molecule technique. By partially denaturing YOYO®-1-labeled DNA in nanofluidic channels with a combination of formamide and local heating, we obtain a sequence-dependent “barcode” corresponding to a series of local dips and peaks in the intensity trace along the extended molecule. We demonstrate that this structure arises from the physics of local denaturation: statistical mechanical calculations of sequence-dependent melting probability can predict the barcode to be observed experimentally for a given sequence. Consequently, the technique is sensitive to sequence variation without requiring enzymatic labeling or a restriction step. This technique may serve as the basis for a new mapping technology ideally suited for investigating the long-range structure of entire genomes extracted from single cells.
Tunnel transport through CoFe2O4 barriers investigated by conducting atomic force microscopy
Authors: Foerster M , Rigato F , Bouzehouane K , Fontcuberta J
Published: July 2010

Conducting atomic force microscopy has been used to monitor the quality of spin-filtering CoFe2O4 tunnel barriers by mapping current as a function of their thickness. We show that appropriate film annealing leads to a substantial improvement of their tunnelling properties. The contact force between tip and sample was identified to have a determining influence on the width of the distribution P(I) in current maps, thus precluding its reliable use to infer barrier characteristics. Therefore, assessment of tunnel transport should be done by means of the typical current which is a well-defined parameter at a given contact force, rather than by the current distribution width.
Temperature dependent photoluminescence of an In(Ga)As/GaAs quantum dot system with different areal density
Authors: Zhou X L , Chen Y H , Liu J Q , Jia C H , Zhou G Y , Ye X L , Xu Bo , Wang Z G
Published: July 2010

We have systematically studied the temperature dependent photoluminescence of a self-assembled In(Ga)As/GaAs quantum dot (QD) system with different areal densities from ∼109 to ∼1011 cm−2. Different carrier channels are revealed experimentally and confirmed theoretically via a modified carrier equation model considering a new carrier transfer channel, i.e. continuum states (CS). The wetting layer is demonstrated to be the carrier quenching channel for the low-density QDs but the carrier transfer channel for the high-density QDs. In particular, for the InGaAs/GaAs QDs with a medium density of ∼1010 cm−2, the CS is verified to be an additional carrier transfer channel in the low temperature regime of 10–60 K, which is studied in detail via our models. The possible carrier channels that act on different temperature regimes are further discussed, and it is demonstrated that density is not a crucial factor in determining the carrier lateral coupling strength.
Comment on ‘What is the mathematical meaning of Steenbeck's principle of minimum power in gas discharge physics?’
Authors: Christen Thomas
Published: July 2010

We comment on a recent paper by Benilov and Naidis (2010 J. Phys. D: Appl. Phys.
43 175204) who claim to have a disproof for the commonly accepted statement, that the Steenbeck principle follows from entropy production (rate) principles. We show that their arguments are erroneous and misleading.
Central separable algebras with purely inseparable splitting rings of exponent one
Authors: Yuan Shuen
Published: July 2010

Classical Galois cohomological results for purely inseparable field extensions of exponent one are generalized here to commutative rings of prime characteristic.
Approximations and representations for Fourier transforms
Authors: Doss Raouf
Published: July 2010

G
G

is a locally compact abelian group with dual

Γ
\Gamma

. If

p
(
γ
)
=

∑
1
N

a
n

(

x
n

,
γ
)

p(\gamma ) = \sum \nolimits _1^N {{a_n}({x_n},\gamma )}

is a trigonometric polynomial, its capacity, by definition is

Σ

|

a
n

|

\Sigma |{a_n}|

. The main theorem is: Let

φ
\varphi

be a measurable function defined on the measurable subset

Λ
\Lambda

of

Γ
\Gamma

. If

φ
\varphi

can be approximated on finite sets in

Λ
\Lambda

by trigonometric polynomials of capacity at most

C
C

(constant), then

φ
=

μ
^

\varphi = \hat \mu

, locally almost everywhere on

Λ
\Lambda

, where

μ
\mu

is a regular bounded measure on

G
G

and

|

|

μ

|

|

≦
C

||\mu || \leqq C

.
Generalizations of 𝑄𝐹-3 algebras
Authors: Colby R. R. , Rutter E. A.
Published: July 2010

This paper consists of three parts. The first is devoted to investigating the equivalence and left-right symmetry of several conditions known to characterize finite dimensional algebras which have a unique minimal faithful representation— QF-

3
3

algebras—in the class of left perfect rings. It is shown that the following conditions are equivalent and imply their right-hand analog:

R
R

contains a faithful

Σ
\Sigma

-injective left ideal,

R
R

contains a faithful

I
I

II

-projective injective left ideal; the injective hulls of projective left

R
R

-modules are projective, and the projective covers of injective left

R
R

-modules are injective. Moreover, these rings are shown to be semi-primary and to include all left perfect rings with faithful injective left and right ideals. The second section is concerned with the endomorphism ring of a projective module over a hereditary or semihereditary ring. More specifically we consider the question of when such an endomorphism ring is hereditary or semihereditary. In the third section we establish the equivalence of a number of conditions similar to those considered in the first section for the class of hereditary rings and obtain a structure theorem for this class of hereditary rings. The rings considered are shown to be isomorphic to finite direct sums of complete blocked triangular matrix rings each over a division ring.
Nonlinear mappings in locally convex spaces
Authors: McDermott Terrence S.
Published: July 2010

A notion of local linear approximation is defined for a nonlinear mapping,

f
f

, defined on one locally convex linear topological space with values in another. By use of this notion, theorems on the local solvability of the equation

y
=
f
(
x
)

y = f(x)

and on the existence of a local inverse for

f
f

are obtained. The continuity and linear approximability of the inverse are discussed. In addition, a relationship between the notion of linear approximation used in the paper and the notion of Fréchet differentiability is shown in the case the intervening spaces are Banach spaces.
Infinite nodal noncommutative Jordan algebras; differentiably simple algebras
Authors: Scribner D. R.
Published: July 2010

The first result is that any differentiably simple algebra of the form

A
=
F
1
+
R

A = F1 + R

, for R a proper ideal, 1 the identity element, and F the base field, must be a subalgebra of a (commutative associative) power series algebra over F, and is truncated if the characteristic is not zero. Moreover the algebra A contains the polynomial subalgebra generated by the indeterminates and identity of the power series algebra. This is used to prove that if A is any simple flexible algebra of the form

A
=
F
1
+
R

A = F1 + R

, R an ideal of

A
+

{A^ + }

, then

A
+

{A^ + }

is a subalgebra of a power series algebra and multiplication in A is determined by certain elements

c

i
j

{c_{ij}}

in A as in
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f g equals f dot g plus one half sigma-summation StartFraction partial-differential f Over partial-differential x Subscript i Baseline EndFraction dot StartFraction partial-differential g Over partial-differential x Subscript j Baseline EndFraction dot c Subscript i j Baseline comma">

f
g
=
f
⋅
g
+

1
2

∑

∂
f

∂

x
i

⋅

∂
g

∂

x
j

⋅

c

i
j

,

fg = f \cdot g + \frac {1}{2}\sum {\frac {{\partial f}}{{\partial {x_i}}} \cdot \frac {{\partial g}}{{\partial {x_j}}} \cdot {c_{ij}},}

\]
where

c

i
j

=
−

c

j
i

{c_{ij}} = - {c_{ji}}

and “

⋅
\cdot

” is the multiplication in

A
+

{A^ + }

. This applies in particular to simple nodal noncommutative Jordan algebras (of characteristic not 2). These results suggest a method of constructing noncommutative Jordan algebras of the given form. We have done this with the restriction that the

c

i
j

{c_{ij}}

lie in F1. The last result is that if A is a finitely generated simple noncommutative algebra of characteristic 0 of this form, then Der (A) is an infinite simple Lie algebra of a known type.
𝜎-finite invariant measures on infinite product spaces
Authors: Hill David G. B.
Published: July 2010

A necessary and sufficient condition in terms of Hellinger integrals is established for the existence of a

σ
\sigma

-finite invariant measure on an infinite product space. Using this it is possible to construct a wide class of transformations on the unit interval which have no

σ
\sigma

-finite invariant measure equivalent to Lebesgue measure. This class includes most of the previously known examples of such transformations.
Integer-valued entire functions
Authors: Robinson Raphael M.
Published: July 2010

The theory of integer-valued entire functions is organized in an improved fashion. Detailed results are proved when the indicator diagram is a line segment. For the first time, a method is developed for treating completely integer-valued functions with an unsymmetrical growth pattern.
The convergence of rational functions of best approximation to the exponential function
Authors: Saff E. B.
Published: July 2010

The object of the paper is to establish convergence throughout the entire complex plane of sequences of rational functions of prescribed types which satisfy a certain degree of approximation to the function

a

e

y
z

a{e^{yz}}

on the disk

|

z

|

≦
ρ

|z| \leqq \rho

. It is assumed that the approximating rational functions have a bounded number of free poles. Estimates are given for the degree of best approximation to the exponential function by rational functions of prescribed types. The results obtained in the paper imply that the successive rows of the Walsh array for

a

e

y
z

a{e^{yz}}

on

|

z

|

≦
ρ

|z| \leqq \rho

converge uniformly to

a

e

y
z

a{e^{yz}}

on each bounded subset of the plane.
Modules over Prüfer domains
Authors: Fakhruddin Syed M.
Published: July 2010

We prove that the category of torsion-free modules over a Prüfer domain is equivalent to a certain category of diagrams. As applications we derive (i) a strong version of Baer-Kulikov-Kaplansky theorem for modules over a valuation ring, (ii) the determination of a complete set of invariants for modules of almost countable rank over an almost-maximal valuation ring, (iii) a new nonhomological proof of the characterization of a maximal valuation ring due to Matlis.
Some characterizations of 𝑛-dimensional 𝐹-spaces
Authors: Canfell M. J.
Published: July 2010

In this paper we obtain characterizations of an

n
n

-dimensional

F
F

-space in terms of the rings of continuous real-valued and complex-valued functions defined on the space. Motivation for these results is the work of Gillman and Henriksen on

U
U

-spaces (

F
F

-spaces of dimension 0) and

T
T

-spaces (

F
F

-spaces of dimension 0 or 1).
Theorems on Cartan subalgebras like some on Carter subgroups
Authors: Stitzinger Ernest L.
Published: July 2010

We consider some results on the Cartan subalgebras of a solvable Lie algebra which are analogues to some results on Carter subgroups of a finite solvable group. Only solvable Lie algebras are considered here.
Generally 𝑝^{𝛼}-torsion complete abelian groups
Authors: Dubois Paul F.
Published: July 2010

A generalized

p
p

-primary cotorsion abelian group

G
G

is a

p
α

{p^\alpha }

-injective, that is satisfies

p
α

Ext
⁡
(
−
,
G
)
=
0

{p^\alpha }\operatorname {Ext} ( - ,G) = 0

, iff

G
t

{G_t}

is

p
α

{p^\alpha }

-injective in the category of torsion abelian groups. Such a torsion group is generally

p
α

{p^\alpha }

-torsion complete, but an example shows that all its Ulm factors need not be complete. The injective properties of generally

p
α

{p^\alpha }

-torsion complete groups are investigated. They are an injectively closed class, and the corresponding class of sequences is the class of

p
α

{p^\alpha }

-pure sequences with split com-c pletion when

α
\alpha

is “accessible". Also, these groups are the

p
α

{p^\alpha }

-high injectives.
Construction of measures and integrals
Authors: Thomson B. S.
Published: July 2010

The systems introduced by R. Henstock and later by E. J. McShane to provide powerful generalizations of the Riemann integral are used to construct outer measures and upper integrals and to develop a Lebesgue type theory in quite general settings.
Nonstandard analysis of dynamical systems. I. Limit motions, stability.
Authors: Hurd A. E.
Published: July 2010

The methods of nonstandard analysis are applied to the study of the qualitative theory of dynamical systems. The nonstandard notions connected with limiting behavior of motions (limit sets, etc.) are developed, and then applied to the study of stability theory, including stability of sets, attracting properties, first prolongations and stability of motions.
A separable postliminal 𝐶*-algebra without maximal closed ideals
Authors: Leptin H.
Published: July 2010

Let

G
G

be the free abelian group with a countable number of generators. We construct a separable locally compact

G
G

-transformation space

X
X

without closed minimal invariant subsets, such that the corresponding

C
∗

{C^ \ast }

-algebra

C
∗

(
G
,
X
)

{C^ \ast }(G,X)

has the properties mentioned in the title. Using

X
X

we also give an example of a transformation space

(
G
,
Z
)

(G,Z)

without closed minimal invariant subset, on which

G
G

acts freely.
New existence theorems for nonlinear equations of Hammerstein type.
Authors: Petryshyn W. V. , Fitzpatrick P. M.
Published: July 2010

Let

X
X

be a real Banach space,

X
∗

{X^ \ast }

its dual,

A
A

a linear map of

X
X

into

X
∗

{X^ \ast }

and

N
N

a nonlinear map of

X
∗

{X^ \ast }

into

X
X

. Using the recent results of Browder and Gupta, Brezis, and Petryshyn, in this paper we study the abstract Hammerstein equation,

w
+
A
N
w
=
0

w + ANw = 0

. Assuming suitable growth conditions on

N
N

, new existence results are obtained under the following conditions on

X
,
A

X,A

and

N
N

. In §1:

X
X

is reflexive,

A
A

bounded with

f
(
x
)
=
(
A
x
,
x
)

f(x) = (Ax,x)

weakly lower semicontinuous,

N
N

bounded and of type

(
M
)

(\text {M} )

. In §2:

X
X

is a general space,

A
A

angle-bounded,

N
N

pseudo-monotone. In §3:

X
X

is weakly complete,

A
A

strictly (strongly) monotone,

N
N

bounded (unbounded) and of type

(
M
)

(\text {M} )

. In §4:

X
X

is a general space,

A
A

is monotone and symmetric,

N
N

is potential. In §5:

X
X

is reflexive and with Schauder basis,

X
∗

{X^ \ast }

strictly convex,

N
N

quasibounded and either monotone, or bounded and pseudo-monotone, or bounded and of type

(
M
)

(\text {M} )

.
On the differentiability of arbitrary real-valued set functions. II.
Authors: Wright Harvel , Snyder W. S.
Published: July 2010

Let f be a real-valued function defined and finite on sets from a family

F

\mathcal {F}

of bounded measurable subsets of Euclidean n-space such that if

T
∈

F

T \in \mathcal {F}

, the measure of T is equal to the measure of the closure of T. An earlier paper [Trans. Amer. Math. Soc. 145 (1969), 439-454] considered the questions of finiteness and boundedness of the upper and lower regular derivates of f and of the existence of a unique finite derivative. The present paper is an extension of the earlier paper and considers the summability of the derivates. Necessary and sufficient conditions are given for each of the upper and lower derivates to be summable on a measurable set of finite measure. A characterization of the integral of the upper derivate is given in terms of the sums of the values of the function over finite collections of mutually disjoint sets from the family.
Structure of the solution set of some first order differential equations of comparison type
Authors: Hallam T. G. , Heidel J. W.
Published: July 2010

The comparison principle is a powerful tool that has a wide variety of applications in ordinary differential equations. The results of this article describe the geometric structure of the solution space of some first order scalar differential equations that may arise in the comparison method. A quite general class of differential equations is found to have a similar solution set configuration as the differential equation of separable variable type. One of the main results establishes, under certain conditions, that there is a unique unbounded solution of the first order differential equation which exists on an interval of the form [

t
0

,
∞

{t_0},\infty

). Furthermore, this unbounded solution separates the solutions that are bounded on [

t
0

,
∞

{t_0},\infty

) from those that are not continuable to all

t
>

t
0

t > {t_0}

.
Local theory of complex functional differential equations
Authors: Oberg Robert J.
Published: July 2010

We consider the equation
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis Superscript asterisk Baseline right-parenthesis f prime left-parenthesis z right-parenthesis equals upper F left-parenthesis z comma f left-parenthesis z right-parenthesis comma f left-parenthesis g left-parenthesis z right-parenthesis right-parenthesis right-parenthesis">

(
∗

)

f
′

(
z
)
=
F
(
z
,
f
(
z
)
,
f
(
g
(
z
)
)
)

( ^\ast )f’(z) = F(z,f(z),f(g(z)))

where

F
(
z
,
u
,
w
)

F(z,u,w)

and

g
(
z
)

g(z)

are given analytic functions and

f
(
z
)

f(z)

is an unknown function. The question of local existence of a solution of

(
∗

)

( ^\ast )

about a point

z
0

{z_0}

is natural only if

g
(

z
0

)
=

z
0

g({z_0}) = {z_0}

. We classify fixed points

z
0

{z_0}

of g as attractive if

|

g
′

(

z
0

)

|

>
1

| {g’({z_0})} | > 1

, indifferent if

|

g
′

(

z
0

)

|

=
1

| {g’({z_0})} | = 1

, and repulsive if

|

g
′

(

z
0

)

|

>
1

| {g’({z_0})} | > 1

. In the attractive case

(
∗

)

( ^\ast )

has a unique analytic solution satisfying an initial condition

f
(

z
0

)
=

w
0

f({z_0}) = {w_0}

. This solution depends continuously on

w
0

{w_0}

and on the functions F and g. For “most” indifferent fixed points the initial-value problem has a unique solution. Around a repulsive fixed point a solution in general does not exist, though in exceptional cases there may exist a singular solution which disappears if the equation is subjected to a suitable small perturbation.
Extensions in certain topological algebraic categories
Authors: Busby Robert C.
Published: July 2010

Categories which we call “sufficiently algebraic” are defined, and for certain objects

A
A

(called faithful) in such categories, and arbitrary objects

C
C

, we partially order the sets

Ext
⁡
(
C
,
A
)

\operatorname {Ext} (C,A)

of extensions of

A
A

by

C
C

. We prove that the maximal elements in

Ext
⁡
(
C
,
A
)

\operatorname {Ext} (C,A)

(with respect to this ordering) are in bijective correspondence with the morphisms from

C
C

to a canonical object

O
(
A
)

O(A)

. If the short five lemma holds in the category, all extensions are maximal and therefore obtained in this way. As an application we compute extensions in certain categories of topological rings. In particular we investigate the possible extensions of one group algebra (of a locally compact group) by another in the category of Banach algebras with norm decreasing homomorphisms, and using some analytic tools we give conditions for the splitting of such extensions. Previous results of the author on extensions of

C
∗

{C^ \ast }

-algebras are also included in this theory as a special case.
Repairing embeddings of 3-cells with monotone maps of 𝐸³
Authors: Boyd William S.
Published: July 2010

If

S
1

{S_1}

is a 2-sphere topologically embedded in Euclidean 3-space

E
3

{E^3}

and

S
2

{S_2}

is the unit sphere about the origin, then there may not be a homeomorphism of

E
3

{E^3}

onto itself carrying

S
1

{S_1}

onto

S
2

{S_2}

. We show here how to construct a map f of

E
3

{E^3}

onto itself such that

f

|

S
1

f|{S_1}

is a homeomorphism of

S
1

{S_1}

onto

S
2

{S_2}

,

f
(

E
3

−

S
1

)
=

E
3

−

S
2

f({E^3} - {S_1}) = {E^3} - {S_2}

and

f

−
1

(
x
)

{f^{ - 1}}(x)

is a compact continuum for each point x in

E
3

{E^3}

. Similar theorems are obtained for 3-cells and disks topologically embedded in

E
3

{E^3}

.
*-taming sets for crumpled cubes. I. Basic properties
Authors: Cannon James W.
Published: July 2010

Is a surface in a 3-manifold tame if it is tame modulo a tame set? This question was answered by the author through the introduction and characterization of taming sets. The purpose of this paper is to introduce and establish the basic properties of the more general and more flexible, but closely related,

∗

^ \ast

-taming set.
*-taming sets for crumpled cubes. II. Horizontal sections in closed sets
Authors: Cannon James W.
Published: July 2010

We prove that a closed subset X of

E
3

{E^3}

is a

∗

^ \ast

-taming set if no horizontal section of X has a degenerate component. This implies, for example, that a 2-sphere S in

E
3

{E^3}

is tame if no horizontal section of S has a degenerate component. It also implies (less obviously) that a 2-sphere S in

E
3

{E^3}

is tame if it can be touched at each point from each side of S by a pencil.
A characterization of the equicontinuous structure relation
Authors: Ellis Robert , Keynes Harvey
Published: July 2010

The main result in the paper is to show that in a large class of minimal transformation groups (including those with abelian phase groups, and point-distal transformation groups), the equicontinuous structure relation is precisely the regionally proximal relation. The techniques involved enable one to recover and extend the previously known characterizations. Several corollaries are indicated, among which the most important is a new criterion (which is easily applicable) for the existence of a nontrivial equicontinuous image of a given transformation group.
A representation theorem for large and small analytic solutions of algebraic differential equations in sectors
Authors: Bank Steven
Published: July 2010

In this paper, we treat first-order algebraic differential equations whose coefficients belong to a certain type of function field. In the particular case where the coefficients are rational functions, our main result states that for any given sector

S
S

in the plane, there exists a positive real number

N
N

, depending only on the equation and the angle opening of

S
S

, such that any solution

y
(
z
)

y(z)

, which is meromorphic in

S
S

and satisfies the condition

z

−
N

y
→
∞

{z^{ - N}}y \to \infty

as

z
→
∞

z \to \infty

in

S
S

, must be of the form

exp
⁡
∫

c

z
m

(
1
+
o
(
1
)
)

\exp \int {c{z^m}(1 + o(1))}

in subsectors, where

c
c

and

m
m

are constants. (From this, we easily obtain a similar representation for analytic solutions in

S
S

, which are not identically zero, and for which

z
K

y
→
0

{z^K}y \to 0

as

z
→
∞

z \to \infty

in

S
S

, where the positive real number

K
K

again depends only on the equation and the angle opening of

S
S

fs
Some new classes of kernels whose Fredholm determinants have order less than one
Authors: Swann Dale W.
Published: July 2010

Let

K
(
s
,
t
)

K(s,t)

be a complex-valued

L
2

{L_2}

kernel on the square

a
≦
s
,
t
≦
b

a \leqq s,t \leqq b

and

{

λ
v

}

\{ {\lambda _v}\}

, perhaps empty, denote the set of finite characteristic values (f.c.v.) of

K
K

, arranged according to increasing modulus. Such f.c.v. are complex numbers appearing in the integral equation
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi Subscript v Baseline left-parenthesis s right-parenthesis equals lamda Subscript v Baseline integral Subscript a Superscript b Baseline upper K left-parenthesis s comma t right-parenthesis phi Subscript v Baseline left-parenthesis t right-parenthesis d t">

ϕ
v

(
s
)
=

λ
v

∫
a
b

K
(
s
,
t
)

ϕ
v

(
t
)
d
t

{\phi _v}(s) = {\lambda _v}\int _a^b {K(s,t){\phi _v}(t)dt}

, where the

ϕ
v

(
s
)

{\phi _v}(s)

are nontrivial

L
2

{L_2}

functions on

[
a
,
b
]

[a,b]

. Further let

k
1

=

∫
a
b

K
(
s
,
s
)

{k_1} = \int _a^b {K(s,s)}

be well defined so that the Fredholm determinant of

K
,
D
(
λ
)

K,D(\lambda )

, exists, and let

μ
\mu

be the order of this entire function. It is shown that (1) if

K
(
s
,
t
)

K(s,t)

is a function of bounded variation in the sense of Hardy-Krause, then

μ
≦
1

\mu \leqq 1

; (2) if in addition to the assumption (1),

K
(
s
,
t
)

K(s,t)

satisfies a uniform Lipschitz condition of order

α
>
0

\alpha > 0

with respect to either variable, then

μ
>
1

\mu > 1

and

k
1

=

Σ
v

1

/

λ
v

{k_1} = {\Sigma _v}1/{\lambda _v}

; (3) if

K
(
s
,
t
)

K(s,t)

is absolutely continuous as a function of two variables and

∂
2

K

/

∂
s
∂
t

{\partial ^2}K/\partial s\partial t

(which exists almost everywhere) belongs to class

L
p

{L_p}

for some

p
>
1

p > 1

, then

μ
>
1

\mu > 1

and

k
1

=

Σ
v

1

/

λ
v

{k_1} = {\Sigma _v}1/{\lambda _v}

. In (2) and (3), the condition

k
1

≠
0

{k_1} \ne 0

implies

K
(
s
,
t
)

K(s,t)

possesses at least one f.c.v.
Using flows to construct Hilbert space factors of function spaces
Authors: Keesling James
Published: July 2010

Let X and Y be metric spaces. Let

G
(
X
)

G(X)

be the group of homeomorphisms of X with the compact open topology. The main result of this paper is that if X admits a nontrivial flow, then

G
(
X
)

G(X)

is homeomorphic to

G
(
X
)
×

l
2

G(X) \times {l_2}

where

l
2

{l_2}

is separable infinite-dimensional Hilbert space. The techniques are applied to other function spaces with the same result. Two such spaces for which our techniques apply are the space of imbeddings of X into Y,

E
(
X
,
Y
)

E(X,Y)

, and the space of light open mappings of X into (or onto) Y, LO (X, Y). Some applications of these results are given. The paper also uses flows to show that if X is the

sin
⁡
(
1

/

x
)

\sin (1/x)

-curve, then

G
(
X
)

G(X)

is homeomorphic to

l
2

×
N

{l_2} \times N

, where N is the integers.
Endomorphism rings of torsionless modules
Authors: Jategaonkar Arun Vinayak
Published: July 2010

Let A be a right order in a semisimple ring

Σ
,

M
A

\Sigma ,{M_A}

be a finite-dimensional torsionless right A-module and

M
^

A

{\hat M_A}

be the injective hull of M. J. M. Zelmanowitz has shown that

Q
=

E
n
d

M
^

A

Q = {\rm {End}}\;{\hat M_A}

is a semisimple ring and

S
=

E
n
d

M
A

S = {\rm {End}}\;{M_A}

is a right order in Q. Further, if A is a two-sided order in

Σ
\Sigma

then S is a two-sided order in Q. We give a conceptual proof of this result. Moreover, we show that if A is a bounded order then so is S. The underlying idea of our proofs is very simple. Rather than attacking

S
=

E
n
d

M
A

S = {\rm {End}}\;{M_A}

directly, we prove the results for

B
=

E
n
d

(

M
A

⊕

A
A

)

B = {\rm {End}}\;({M_A} \oplus {A_A})

. If

e
:

M
A

⊕

A
A

→

M
A

⊕

A
A

e:{M_A} \oplus {A_A} \to {M_A} \oplus {A_A}

is the projection on M along

A
A

{A_A}

then, of course,

S
≅
e
B
e

S \cong eBe

and it is easy to transfer the required information from B to S. The reason why it is any easier to look at B rather than S is that

M
A

⊕

A
A

{M_A} \oplus {A_A}

is a generator in

mod
-
A

\bmod \text {-}A

and a Morita type transfer of properties from A to B is available. We construct an Artinian ring resp. Noetherian prime ring containing a right ideal whose endomorphism ring fails to be Artinian resp. Noetherian from either side.
On the remainders of certain metric spaces
Authors: Magill Kenneth D.
Published: July 2010

Let

X
X

be completely regular and Hausdorff. The family

R

(
X
)

\mathcal {R}(X)

of all those spaces which are remainders of

X
X

in compactifications has attracted a considerable amount of interest. In this paper we determine, in a certain sense, the family

R

(
X
)

\mathcal {R}(X)

for a fairly large number of spaces

X
X

.
Some immersion theorems for manifolds
Authors: Randall A. Duane
Published: July 2010

In this paper we obtain several results on immersing manifolds into Euclidean spaces. For example, a spin manifold

M
n

{M^n}

immerses in

R

2
n
−
3

{R^{2n - 3}}

for dimension

n
≡
0
mod
4

n \equiv 0\bmod 4

and n not a power of 2. A spin manifold

M
n

{M^n}

immerses in

R

2
n
−
4

{R^{2n - 4}}

for

n
≡
7
mod
8

n \equiv 7\bmod 8

and

n
>
7

n > 7

. Let

M
n

{M^n}

be a 2-connected manifold for

n
≡
6
mod
8

n \equiv 6\bmod 8

and

n
>
6

n > 6

such that

H
3

(
M
;
Z
)

{H_3}(M;Z)

has no 2-torsion. Then M immerses in

R

2
n
−
5

{R^{2n - 5}}

and embeds in

R

2
n
−
4

{R^{2n - 4}}

. The method of proof consists of expressing k-invariants in Postnikov resolutions for the stable normal bundle of a manifold by means of higher order cohomology operations. Properties of the normal bundle are used to evaluate the operations.
The components of the automorphism group of a Jordan algebra
Authors: Gordon S. Robert
Published: July 2010

Let

F

\mathfrak {F}

be a semisimple Jordan algebra over an algebraically closed field

Φ
\Phi

of characteristic zero. Let

G
G

be the automorphism group of

F

\mathfrak {F}

and

Γ
\Gamma

the structure groups of

F

\mathfrak {F}

. General results on

G
G

and

Γ
\Gamma

are given, the proofs of which do not involve the use of the classification theory of simple Jordan algebras over

Φ
\Phi

. Specifically, the algebraic components of the linear algebraic groups

G
G

and

Γ
\Gamma

are determined, and a formula for the number of components in each case is given. In the course of this investigation, certain Lie algebras and root spaces associated with

F

\mathfrak {F}

are studied. For each component

G
i

{G_i}

of

G
G

, the index of

G
G

is defined to be the minimum dimension of the

1
1

-eigenspace of the automorphisms belonging to

G
i

{G_i}

. It is shown that the index of

G
i

{G_i}

is also the minimum dimension of the fixed-point spaces of automorphisms in

G
i

{G_i}

. An element of

G
G

is called regular if the dimension of its

1
1

-eigenspace is equal to the index of the component to which it belongs. It is proven that an automorphism is regular if and only if its

1
1

-eigenspace is an associative subalgebra of

F

\mathfrak {F}

. A formula for the index of each component

G
i

{G_i}

is given. In the Appendix, a new proof is given of the fact that the set of primitive idempotents of a simple Jordan algebra over

Φ
\Phi

is an irreducible algebraic set.
Equivariant bordism and Smith theory
Authors: Stong R. E.
Published: July 2010

The relationship between equivariant bordism and Smith homology theory on the category of pairs with involution is studied.
When is 𝜇∗𝐿₁ closed?
Authors: Glicksberg I.
Published: July 2010

For a finite measure

μ
\mu

on a locally compact abelian group, we partially answer the question of when

μ
∗

L
1

\mu \ast {L_1}

is closed in

L
1

{L_1}

.
On knots with nontrivial interpolating manifolds
Authors: Simon Jonathan
Published: July 2010

If a polygonal knot

K
K

in the

3
3

-sphere

S
3

{S^3}

does not separate an interpolating manifold

S
S

for

K
K

, then

S
−
K

S - K

does not carry the first homology of either closed component of

S
3

−
S

{S^3} - S

. It follows that most knots

K
K

with nontrivial interpolating manifolds have the property that a simply connected manifold cannot be obtained by removing a regular neighborhood of

K
K

from

S
3

{S^3}

and sewing it back differently.
Prime entire functions
Authors: Gross Fred
Published: July 2010

Factorizations of various functions are discussed. Complete factorizations of certain classes of functions are given. In particular it is shown that there exist primes of arbitrary growth.
Integration theory on infinite-dimensional manifolds
Authors: Kuo Hui Hsiung
Published: July 2010

The purpose of this paper is to develop a natural integration theory over a suitable kind of infinite-dimensional manifold. The type of manifold we study is a curved analogue of an abstract Wiener space. Let

H
H

be a real separable Hilbert space,

B
B

the completion of

H
H

with respect to a measurable norm and

i
i

the inclusion map from

H
H

into

B
B

. The triple

(
i
,
H
,
B
)

(i,H,B)

is an abstract Wiener space.

B
B

carries a family of Wiener measures. We will define a Riemann-Wiener manifold to be a triple

(

W

,
τ
,
g
)

(\mathcal {W},\tau ,g)

satisfying specific conditions,

W

\mathcal {W}

is a

C
j

{C^j}

-differentiable manifold

(
j
≧
3
)

(j \geqq 3)

modelled on

B
B

and, for each

x
x

in

W

,
τ
(
x
)

\mathcal {W},\tau (x)

is a norm on the tangent space

T
x

(

W

)

{T_x}(\mathcal {W})

of

W

\mathcal {W}

at

x
x

while

g
(
x
)

g(x)

is a densely defined inner product on

T
x

(

W

)

{T_x}(\mathcal {W})

. We show that each tangent space is an abstract Wiener space and there exists a spray on

W

\mathcal {W}

associated with

g
g

. For each point

x
x

in

W

\mathcal {W}

the exponential map, defined by this spray, is a

C

j
−
2

{C^{j - 2}}

-homeomorphism from a

τ
(
x
)

\tau (x)

-neighborhood of the origin in

T
x

(

W

)

{T_x}(\mathcal {W})

onto a neighborhood of

x
x

in

W

\mathcal {W}

. We thereby induce from Wiener measures of

T
x

(

W

)

{T_x}(\mathcal {W})

a family of Borel measures

q
t

(
x
,
⋅
)
,
t
>
0

{q_t}(x, \cdot ),t > 0

, in a neighborhood of

x
x

. We prove that

q
t

(
x
,
⋅
)

{q_t}(x, \cdot )

and

q
s

(
y
,
⋅
)

{q_s}(y, \cdot )

, as measures in their common domain, are equivalent if and only if

t
=
s

t = s

and

d
g

(
x
,
y
)

{d_g}(x,y)

is finite. Otherwise they are mutually singular. Here

d
g

{d_g}

is the almost-metric (in the sense that two points may have infinite distance) on

W

\mathcal {W}

determined by

g
g

. In order to do this we first prove an infinite-dimensional analogue of the Jacobi theorem on transformation of Wiener integrals.
Interpolation theorems for the pairs of spaces (𝐿^{𝑝},𝐿^{∞}) and (𝐿¹,𝐿^{𝑞})
Authors: Lorentz George G. , Shimogaki Tetsuya
Published: July 2010

A Banach space

Z
Z

has the interpolation property with respect to the pair

(
X
,
Y
)

(X,Y)

if each

T
T

, which is a bounded linear operator from

X
X

to

X
X

and from

Y
Y

to

Y
Y

, can be extended to a bounded linear operator from

Z
Z

to

Z
Z

. If

X
=

L
p

,
Y
=

L
∞

X = {L^p},Y = {L^\infty }

we give a necessary and sufficient condition for a Banach function space

Z
Z

on

(
0
,
l
)
,
0
>
l
≦
+
∞

(0,l),0 > l \leqq + \infty

, to have this property. The condition is that

g
≺

p

f

g \prec {}^pf

and

f
∈
Z

f \in Z

should imply

g
∈
Z

g \in Z

; here

g
≺

p

f

g \prec {}^pf

means that

g

∗
p

≺

f

∗
p

{g^{ \ast p}} \prec {f^{ \ast p}}

in the Hardy-Littlewood-Pólya sense, while

h
∗

{h^ \ast }

denotes the decreasing rearrangement of the function

|

h

|

|h|

. If the norms

|

|

T

|

|

X

,

|

|

T

|

|

Y

||T|{|_X},||T|{|_Y}

are given, we can estimate

|

|

T

|

|

Z

||T|{|_Z}

. However, there is a gap between the necessary and the sufficient conditions, consisting of an unknown factor not exceeding

λ
p

,

λ
p

≦

2

1

/

q

,
1

/

p
+
1

/

q
=
1

{\lambda _p},{\lambda _p} \leqq {2^{1/q}},1/p + 1/q = 1

. Similar results hold if

X
=

L
1

,
Y
=

L
q

X = {L^1},Y = {L^q}

. For all these theorems, the complete continuity of

T
T

on

Z
Z

is assured if

T
T

has this property on

X
X

or on

Y
Y

, and if

Z
Z

satisfies a certain additional necessary and sufficient condition, expressed in terms of

|

|

σ
a

|

|

Z

,
a
>
0

||{\sigma _a}|{|_Z},a > 0

, where

σ
a

{\sigma _a}

is the compression operator

σ
a

f
(
t
)
=
f
(
a
t
)
,
0
≦
t
>
l

{\sigma _a}f(t) = f(at),0 \leqq t > l

.
Connections on semisimple Lie groups
Authors: Beck Robert E.
Published: July 2010

The plus and minus connections of Cartan and Schouten, which exist on any Lie group, have the following three properties: (1) the connection is left invariant, (2) the curvature of the connection is zero, (3) the set of maximal geodesics through the identity of the Lie group is equal to the set of one-parameter subgroups of the Lie group. It is shown that the plus and minus connections are the only ones with these properties on a real simple Lie group. On a real semisimple Lie group the connections with these properties are in one-to-one correspondence with the ways of choosing an ideal of the Lie algebra and then choosing a complementary subspace to it.
A constructive ergodic theorem
Authors: Nuber J. A.
Published: July 2010

As discussed by Bishop, Birkhoff’s Ergodic Theorem is not constructively valid. In this paper we present an hypothesis which is necessary and sufficient for the constructive almost everywhere convergence of the Césaro averages of the translates of an integrable function by a measure preserving transformation. In addition necessary and sufficient conditions are given for the limit function to be constructively integrable. Also we present a necessary and sufficient condition that the averages converge to a constant function and give an equivalent formulation of this condition for finite measure spaces. Several interesting examples are given which satisfy these conditions.
A class of regular functions containing spirallike and close-to-convex functions
Authors: Ziegler M. R.
Published: July 2010

A class of functions

A

\mathcal {A}

is defined which contains the spirallike and close-to-convex functions. By decomposing

A

\mathcal {A}

into subclasses in a natural way, some basic properties of

A

\mathcal {A}

and these subclasses are determined, including solutions to extremal problems; distortion theorems; coefficient inequalities; and the radii of convexity and close-to-convexity.
The size function of abelian varieties
Authors: Altman Allen
Published: July 2010

The size function is defined for points in projective space over any field K, finitely generated field over Q, generalizing the height function for number fields. We prove that the size function on the K-rational points of an abelian variety is bounded by a quadratic function.
Uniformly bounded representations for the Lorentz groups
Authors: Wilson Edward N.
Published: July 2010

A family of uniformly bounded class 1 representations of the Lorentz groups is constructed. This family of representations includes, but is larger than, a similar family of representations constructed by Lipsman. The construction technique relies on a multiplicative analysis of various operators under a Mellin transform.
Reflection principle for systems of first order elliptic equations with analytic coefficients
Authors: Yu Chung Ling
Published: July 2010

Let T be a simply connected domain of the

z
=
x
+
i
y

z = x + iy

plane, whose boundary contains a portion

σ
\sigma

of the x-axis. Also let
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A left-parenthesis z comma zeta right-parenthesis comma upper B left-parenthesis z comma zeta right-parenthesis comma upper F left-parenthesis z comma zeta right-parenthesis comma alpha left-parenthesis z right-parenthesis comma beta left-parenthesis z right-parenthesis">

A
(
z
,
ζ
)
,
B
(
z
,
ζ
)
,
F
(
z
,
ζ
)
,
α
(
z
)
,
β
(
z
)

A(z,\zeta ),B(z,\zeta ),F(z,\zeta ),\alpha (z),\beta (z)

and

ρ
(
z
)

\rho (z)

be holomorphic functions for

z
,
ζ
∈
T
∪
σ
∪

T
¯

z,\zeta \in T \cup \sigma \cup \bar T

, with

α
(
z
)
−
i
β
(
z
)
≠
0

\alpha (z) - i\beta (z) \ne 0

for

z
∈

T
¯

∪
σ
,
α
(
z
)
+
i
β
(
z
)
≠
0

z \in \bar T \cup \sigma ,\alpha (z) + i\beta (z) \ne 0

for

z
∈
T
∪
σ

z \in T \cup \sigma

. Furthermore, we assume that

α
(
x
)

\alpha (x)

and

β
(
x
)

\beta (x)

are real valued functions for

x
∈
σ

x \in \sigma

. Our reflection principle states that for any solution

w
=
u
+
i
v

w = u + iv

of an equation of the type
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="partial-differential w slash partial-differential z overbar equals upper A left-parenthesis z comma z overbar right-parenthesis w plus upper B left-parenthesis z comma z overbar right-parenthesis w overbar plus upper F left-parenthesis z comma z overbar right-parenthesis">

∂
w

/

∂

z
¯

=
A
(
z
,

z
¯

)
w
+
B
(
z
,

z
¯

)

w
¯

+
F
(
z
,

z
¯

)

\partial w/\partial \bar z = A(z,\bar z)w + B(z,\bar z)\bar w + F(z,\bar z)

in T under the boundary condition

α
(
x
)
u
+
β
(
x
)
v
=
ρ
(
x
)

\alpha (x)u + \beta (x)v = \rho (x)

on

σ
,
w

\sigma ,w

can be continued analytically across the x-axis, onto the entire mirror image

T
¯

\bar T

.
Restricted mean values and harmonic functions
Authors: Baxter John R.
Published: July 2010

A function h defined on a region R in

R

n

{{\mathbf {R}}^n}

will be said to possess a restricted mean value property if the value of the function at each point is equal to the mean value of the function over one open ball in R, with centre at that point. It is proved here that this restricted mean value property implies h is harmonic under certain conditions.
Tensor products of locally convex modules and applications to the multiplier problem
Authors: Rigelhof Roger
Published: July 2010

In this paper we present a representation theorem for the tensor product of locally convex modules. This theorem has a number of consequences in the study of the multiplier problem in harmonic analysis, and the remainder of the paper is devoted to these applications.
Mapping cylinder neighborhoods of one-complexes in four-space
Authors: Bryant J. L. , Lacher R. C.
Published: July 2010

We prove the following theorem: If K is a 1-complex topologically embedded in

S
4

{S^4}

, and if K has mapping cylinder neighborhoods in

S
4

{S^4}

at almost all of its points, then K is tame. The proof uses engulfing and the theory of proper, one-acyclic mappings of 3-manifolds onto the real line.
Products of complexes and Fréchet spaces which are manifolds
Authors: West James E.
Published: July 2010

It is shown that if a locally finite-dimensional simplicial complex is given the “barycentric” metric, then its product with any Fréchet space X of suitably high weight is a manifold modelled on X, provided that X is homeomorphic to its countably infinite Cartesian power. It is then shown that if X is Banach, all paracompact X-manifolds may be represented (topologically) by such products.
The dominion of Isbell
Authors: Mitchell Barry
Published: July 2010

A well-known characterization of epimorphisms in the category of rings with identity is imitated to give a similar characterization of epimorphisms in the category of small pre-additive categories. From this one deduces Isbell’s “Zigzag Theorem” concerning epimorphisms in Cat.
On subgroups of 𝑀₂₄. I. Stabilizers of subsets
Authors: Choi Chang
Published: July 2010

In this paper we study the orbits of the Mathieu group

M

24

{M_{24}}

on sets of n points,

1
≦
n
≦
12

1 \leqq n \leqq 12

. For

n
≧
6
,

M

24

n \geqq 6,{M_{24}}

is not transitive on these sets, so we may classify the sets into types corresponding to the orbits of

M

24

{M_{24}}

and then show how to construct a set of each type from smaller sets. We determine the stabilizer of a set of each type and describe its representation on the 24 points. From the conclusions, the class of subgroups which are maximal among the intransitives of

M

24

{M_{24}}

can be read off. This work forms the first part of a study which yields, in particular, a complete list of the primitive representations of

M

24

{M_{24}}

.
Extending congruences on semigroups
Authors: Stralka A. R.
Published: July 2010

The two main results are: (1) Let S be a semigroup which satisfies the relation

a
b
c
d
=
a
c
b
d

abcd = acbd

, let A be a subsemigroup of Reg S which is a band of groups and let

[
φ
]

[\varphi ]

be a congruence on A. Then

[
φ
]

[\varphi ]

can be extended to a congruence on S. (2) Let S be a compact topological semigroup which satisfies the relation

a
b
c
d
=
a
c
b
d

abcd = acbd

, let A be a closed subsemigroup of Reg S and let

[
φ
]

[\varphi ]

be a closed congruence on A such that

dim

φ
(
A
)

|

H

=
0

\dim \,\varphi (A)|\mathcal {H} = 0

. Then

[
φ
]

[\varphi ]

can be extended to a closed congruence on S.
Some theorems on the cos 𝜋𝜆 inequality
Authors: Lewis John L.
Published: July 2010

In this paper we consider subharmonic functions

u
≦
1

u \leqq 1

in the unit disk whose minimum modulus and maximum modulus satisfy a certain inequality. We show the existence of an extremal member of this class with largest maximum modulus. We then obtain an upper bound for the maximum modulus of this function in terms of the logarithmic measure of a certain set. We use this upper bound to prove theorems about subharmonic functions in the plane.
Categorical 𝑊*-tensor product
Authors: Dauns John
Published: July 2010

If A and B are von Neumann algebras and

A

⊗
¯

B

A\bar \otimes B

denotes their categorical

C
∗

{C^ \ast }

-tensor product with the universal property, then the von Neumann tensor product

A
∇
B

A\nabla B

of A and B is defined as
\[

A
∇
B
=

(
A

⊗
¯

B

)

∗
∗

/

J
,

A\nabla B = {(A\bar \otimes B)^{ \ast \ast }}/J,

\]
where

J
⊂

(
A

⊗
¯

B

)

∗
∗

J \subset {(A\bar \otimes B)^{\ast \ast }}

is an appropriate ideal. It has the universal property.