bluuebunny/crossref_metadata_2025 huggingface dataset:
Publisher’s Note: “Review Article—Dielectrophoresis: Status of the theory, technology, and applications” [Biomicrofluidics 4, 022811 (2010)]
Authors: Pethig Ronald
Published: July 2010

A review is presented of the present status of the theory, the developed technology and the current applications of dielectrophoresis (DEP). Over the past 10 years around 2000 publications have addressed these three aspects, and current trends suggest that the theory and technology have matured sufficiently for most effort to now be directed towards applying DEP to unmet needs in such areas as biosensors, cell therapeutics, drug discovery, medical diagnostics, microfluidics, nanoassembly, and particle filtration. The dipole approximation to describe the DEP force acting on a particle subjected to a nonuniform electric field has evolved to include multipole contributions, the perturbing effects arising from interactions with other cells and boundary surfaces, and the influence of electrical double-layer polarizations that must be considered for nanoparticles. Theoretical modelling of the electric field gradients generated by different electrode designs has also reached an advanced state. Advances in the technology include the development of sophisticated electrode designs, along with the introduction of new materials (e.g., silicone polymers, dry film resist) and methods for fabricating the electrodes and microfluidics of DEP devices (photo and electron beam lithography, laser ablation, thin film techniques, CMOS technology). Around three-quarters of the 300 or so scientific publications now being published each year on DEP are directed towards practical applications, and this is matched with an increasing number of patent applications. A summary of the US patents granted since January 2005 is given, along with an outline of the small number of perceived industrial applications (e.g., mineral separation, micropolishing, manipulation and dispensing of fluid droplets, manipulation and assembly of micro components). The technology has also advanced sufficiently for DEP to be used as a tool to manipulate nanoparticles (e.g., carbon nanotubes, nano wires, gold and metal oxide nanoparticles) for the fabrication of devices and sensors. Most efforts are now being directed towards biomedical applications, such as the spatial manipulation and selective separation/enrichment of target cells or bacteria, high-throughput molecular screening, biosensors, immunoassays, and the artificial engineering of three-dimensional cell constructs. DEP is able to manipulate and sort cells without the need for biochemical labels or other bioengineered tags, and without contact to any surfaces. This opens up potentially important applications of DEP as a tool to address an unmet need in stem cell research and therapy.
Mass Spectrometry of Benzyne and Cyclopentadienylideneketene
Authors: Monsandl Thomas , Macfarlane Graham , Flammang Robert , Wentrup Curt
Published: July 2010

The formation of cyclopentadienylideneketene 2 and benzyne 1 in flash vacuum thermolysis reactions is investigated by on-line mass spectrometry. Compounds 13, 14, and 15 all afford ketene 2, which decomposes to benzyne and CO in the high-temperature regime. Cyclopentadienylideneketene 2 is stable on the microsecond time-scale of neutralization-reionization experiments. Collisional activation mass spectrometry of m/z 76 from 14, 15, and 5 indicates that the C6H4•+ ions most likely undergo ring opening in the mass spectrometer.
New Thermal Routes to ortho-Benzyne
Authors: Cahill Katharine J. , Ajaz Aida , Johnson Richard P.
Published: July 2010

There is experimental evidence that intermediate ortho-benzynes can be made by intramolecular [2 + 4] cycloaddition of a 1,3-diyne with an alkyne. Computations by several groups support a concerted mechanism for the cycloaddition of butadiyne with acetylene. High temperature benzyne cycloreversion has also been demonstrated experimentally; this may in fact be a common reaction in hydrocarbon fuel combustion. Following leads from earlier pyrolysis experiments, herein we predict that cycloaddition of benzyne with butadiyne can proceed by a stepwise mechanism to 2,3-naphthyne. However, a slightly lower energy path leads to a benzocyclobutadiene. ortho-Benzyne can be generated by solution-phase and solid-phase reaction in a microwave reactor. We have developed the method of microwave flash pyrolysis (MFP) for high temperature solid-phase microwave reactions. MFP reaction of phthalic anhydride, a classic benzyne precursor, results in a typical suite of products expected from a relatively high concentration of benzyne.
Flash Vacuum Pyrolytic Generation of Arynes - in Retrospect
Authors: Brown Roger F. C.
Published: July 2010

The development of the chemistry of benzyne and of arynes under flash vacuum pyrolytic conditions was strongly influenced by a parallel study of the chemistry of propadienones, and by the discovery of the acetylene/methylenecarbene rearrangement. A limited range of typical aryne reactions studied at The Australian National University and at Monash University from 1965 to 1996 is described, and pathways of aryne formation are considered.
Theta burst stimulation dissociates attention and action updating in human inferior frontal cortex
Authors: Verbruggen Frederick , Aron Adam R. , Stevens Michaël A. , Chambers Christopher D.
Published: July 2010

Everyday circumstances require efficient updating of behavior. Brain systems in the right inferior frontal cortex have been identified as critical for some aspects of behavioral updating, such as stopping actions. However, the precise role of these neural systems is controversial. Here we examined how the inferior frontal cortex updates behavior by combining reversible cortical interference (transcranial magnetic stimulation) with an experimental task that measures different types of updating. We found that the right inferior frontal cortex can be functionally segregated into two subregions: a dorsal region, which is critical for visual detection of changes in the environment, and a ventral region, which updates the corresponding action plan. This dissociation reconciles competing accounts of prefrontal organization and casts light on the neural architecture of human cognitive control.
Phosphorylation stabilizes Nanog by promoting its interaction with Pin1
Authors: Moretto-Zita Matteo , Jin Hua , Shen Zhouxin , Zhao Tongbiao , Briggs Steven P. , Xu Yang
Published: July 2010

Embryonic stem cells (ESCs) can undergo unlimited self-renewal and retain the pluripotency to differentiate into all cell types in the body, thus holding great promise as a renewable source of cells for human therapy. The mechanisms that maintain self-renewal of ESCs remain unclear. Here we show that Nanog, a transcription factor crucial for the self-renewal of ESCs, is phosphorylated at multiple Ser/Thr-Pro motifs. This phosphorylation promotes the interaction between Nanog and the prolyl isomerase Pin1, leading to Nanog stabilization by suppressing its ubiquitination. Inhibition of Pin1 activity or disruption of Pin1–Nanog interaction in ESCs suppresses their capability to self-renew and to form teratomas in immunodeficient mice. Therefore, in addition to the stringent transcriptional regulation of Nanog, the expression level of Nanog is also modulated by posttranslational mechanisms.
Remuneration disparities in Oceania: Papua New Guinea and Solomon Islands
Authors: Marai Leo , Kewibu Vincent , Kinkin Elly , Peniop John Peter , Salini Christian , Kofana Genesis
Published: July 2010

This paper explores the impact of remuneration differences on workers in the Solomon Islands and Papua New Guinea. In these countries remunerative differences are linked to government policy (in Papua New Guinea) and job contracts (in the Solomon Islands), and have impacted on industrial relations in both settings (strike action). A total of N = 350 professionals (n = 60 expatriates) from 54 organizations in aid, government, higher education and industry (mean response rate = 36%) responded to an organizational survey form. Remuneration ratios between international and local respondents based on the World Bank's index of purchasing power parity approached 9:1. In both sites staff compared pay and benefits (remuneration) packages: Internationally remunerated staff rated their ability higher than their local counterparts did; locally remunerated groups reported more injustice in remuneration, were more demotivated by the gaps, and were more likely to be thinking about leaving the organization. In‐country workshops of N = 40 largely local stakeholders from aid and community organizations plus government ministries considered the survey's findings and recommended: in Solomon Islands, (a) introducing a policy of localization, (b) establishing a remuneration commission (already existent in Papua New Guinea), and (c) reducing the remunerative gap; in Papua New Guinea, (d) reversing the post‐Independence “dual pay system” (currently official policy), (e) instituting pay‐for‐performance, and (f) ensuring the existent localization policy is applied to recruitment, selection, and staff career planning and management.
Abnormalities in Noetherian rings
Authors: Arnold J. T. , Boisen M. B.
Published: July 2010

If

P
⊆
Q

P \subseteq Q

are prime ideals in some ring R and if rank

Q
=

rank

(
Q

/

P
)
+

rank

P
+
k

Q = {\text {rank}}(Q/P) + {\text {rank}}\;P + k

, then

P
⊂
Q

P \subset Q

is said to be k-abnormal and k is called the degree of abnormality. The paper consists of two examples. The first example is a Noetherian integral domain in which the set of degrees of abnormality is unbounded. Let P be a prime ideal of R and set

W
=
{
Q

/

Q

W = \{ Q/Q

is a prime ideal and

P
⊂
Q

P \subset Q

is abnormal}. The second example is a local domain such that

{
k

|

P
⊂
Q

\{ k|P \subset Q

is k-abnormal for some

Q
∈
W
}
≠
{
k

|

P
⊂
Q

Q \in W\} \ne \{ k|P \subset Q

is k-abnormal for some Q minimal in W}.
On a conjecture of Hunt and Murray concerning 𝑞-plurisubharmonic functions
Authors: Kalka Morris
Published: July 2010

We discuss the conjecture of Hunt and Murray on uniqueness of the Dirichlet problem for the generalized complex Monge-Ampère equation. We define a class of q-plurisubharmonic functions, prove uniqueness in this class, and show that in some cases the solution found by Hunt and Murray is in our class.
A nonlinear theroem of ergodic type. II
Authors: Feathers G. , Dotson W. G.
Published: July 2010

A theorem is proved concerning the relationship between a certain collection of mappings and a fixed point for that collection of mappings. The conditions on the mappings are very similar to ones in a paper by W. F. Eberlein.
That quasinilpotent operators are norm-limits of nilpotent operators revisited
Authors: Apostol C. , Foiaş C. , Pearcy C.
Published: July 2010

A new short proof is given that every quasinilpotent operator on a separable, infinite dimensional, complex Hilbert space is a norm-limit of nilpotent operators.
Slicing the cube in 𝑅ⁿ and probability (bounds for the measure of a central cube slice in 𝑅ⁿ by probability methods)
Authors: Hensley Douglas
Published: July 2010

A cube of dimension n and side 1 is cut by a hyperplane of dimension

n
−
1

n - 1

through its center. The usual

n
−
1

n - 1

measure of the intersection is bounded between 1 and M, independent of n. The proof uses an inequality for sums of independent random variables.
Diophantine correct models of arithmetic
Authors: Lipshitz L.
Published: July 2010

A countable nonstandard model of arithmetic is diophantine correct if and only if it can be embedded in arbitrarily short nonstandard initial segments of itself.
A simple proof of a covering property of locally compact groups
Authors: Milnes P. , Bondar J. V.
Published: July 2010

We give a simple proof of the following result of Emerson and Greenleaf. Theorem. Let V be a relatively compact subset with nonvoid interior of a locally compact group G. Then there exist a subset

T
⊂
G

T \subset G

and a natural number M such that

G
=

∪

t
∈
T

t
V

G = { \cup _{t \in T}}tV

and at most M of the tV’s,

t
∈
T

t \in T

, intersect.
A new and constructive proof of the Borsuk-Ulam theorem
Authors: Meyerson Mark D. , Wright Alden H.
Published: July 2010

The Borsuk-Ulam Theorem [1] states that if f is a continuous function from the n-sphere to n-space

(
f
:

S
n

→

R

n

)

(f:{S^n} \to {{\mathbf {R}}^n})

then the equation

f
(
x
)
=
f
(
−
x
)

f(x) = f( - x)

has a solution. It is usually proved by contradiction using rather advanced techniques. We give a new proof which uses only elementary techniques and which finds a solution to the equation. If f is piecewise linear our proof is constructive in every sense; it is even easily implemented on a computer.
A comparison of Chehata’s and Clifford’s ordinally simple ordered groups
Authors: Feil Todd
Published: July 2010

Chehata and Clifford gave the two most well-known examples of ordinally simple ordered groups. Chehata’s example is also algebraically simple. These two examples are shown to be similar. Clifford’s ordered group is shown to have a nonabelian algebraically simple subgroup.
Goldie conditions in finite normalizing extensions
Authors: Lanski Charles
Published: July 2010

Let S be a finite normalizing extension of a ring R. If M is an S module, then M has finite uniform dimension if and only if it has finite uniform dimension when considered as an R module. Consequently, when S is a right Goldie ring, R is also a right Goldie ring. Conversely, if R is a semiprime right Goldie ring and S is a prime ring, then S is a Goldie ring. Finally, when both S and R are semiprime right Goldie rings, the quotient ring of R embeds in the quotient ring of S.
Subgroups of 𝑎𝑥+𝑏 and the splitting of triangular group schemes
Authors: Waterhouse William C.
Published: July 2010

The subgroup schemes of the

a
x
+
b

ax + b

group are computed. This leads to a quick proof that a triangular group scheme over an algebraically closed field is a semidirect product of unipotent and diagonalizable subgroups.
Normality can be relaxed in the asymptotic Fuglede-Putnam theorem
Authors: Furuta Takayuki
Published: July 2010

The original form of the Fuglede-Putnam theorem states that the operator equation

A
X
=
X
B

AX = XB

implies

A
∗

X
=
X

B
∗

{A^ \ast }X = X{B^ \ast }

when A and B are normal. In our previous paper we have relaxed the normality in the hypotheses on A and B as follows: if A and

B
∗

{B^ \ast }

are subnormal and if X is an operator such that

A
X
=
X
B

AX = XB

, then

A
∗

X
=
X

B
∗

{A^ \ast }X = X{B^ \ast }

. We shall show asymptotic versions of this generalized Fuglede-Putnam theorem; these results are also extensions of results of Moore and Rogers.
The equality of unilateral derivates
Authors: Evans M. J. , Humke P. D.
Published: July 2010

C. J. Neugebauer has shown that if f is a continuous function of bounded variation defined on the real line, then the set E where the upper right derivate differs from the upper left derivate is of measure zero and first category. Here it is shown that this result is best possible; that is, given any measure zero first category set K, there is a continuous function of bounded variation for which

K
⊆
E

K \subseteq E

. It is also shown that if f is monotone, then E is

σ
\sigma

-porous. This result can be used to provide an elementary proof of the fact that for an arbitrary function f the left and right essential cluster sets are identical except at a

σ
\sigma

-porous set of points, a result first proved by L. Zajíček.
A normal form for a special class of curvature operators
Authors: Zoltek Stanley M.
Published: July 2010

In the case of a 4-dimensional oriented inner product space Singer and Thorpe found a canonical form for a curvature operator which commutes with a generator of

Λ
4

{\Lambda ^4}

, and used it to prove that the curvature function is completely determined by its critical point behavior. In dimension 5 we extend these results to curvature operators which commute with an element of

Λ
4

{\Lambda ^4}

.
The existence of 𝑄-sets is equivalent to the existence of strong 𝑄-sets
Authors: Przymusiński Teodor C.
Published: July 2010

In this note we prove that the existence of an uncountable Q-set is equivalent to the existence of an uncountable strong Q-set, i.e. a Q-set all finite powers of which are Q-sets.
Ultraproduct invariant logics
Authors: Sgro J.
Published: July 2010

In this paper we give a construction of logics via the property of being preserved from the models to their ultraproduct. Specific examples are given which include some cardinality quantifiers.
Relations among characteristic classes of 𝑛-manifolds imbedded in 𝑅^{𝑛+𝑘}
Authors: Papastavridis Stavros
Published: July 2010

Let

I
n

⊆

H
∗

(
B
O
;

Z
2

)

{I_n} \subseteq {H^ \ast }(BO;{Z_2})

be the (graded) set of those normal characteristic classes which are zero on all compact, closed

C
∞

{C^\infty }

manifolds. Let

I

n
,
k

⊆

H
∗

(
B
O
;

Z
2

)

{I_{n,k}} \subseteq {H^ \ast }(BO;{Z_2})

be the set of those characteristic classes which are zero on all n-manifolds which imbed in

R

n
+
k

{R^{n + k}}

. Let K be the (graded) ideal in

H
∗

(
B
O
;

Z
2

)

{H^ \ast }(BO;{Z_2})

generated by the Stiefel-Whitney classes

w
k

,

w

k
+
1

,

w

k
+
2

,

w

k
+
3

,
…

{w_k},{w_{k + 1}},{w_{k + 2}},{w_{k + 3}}, \ldots

. We will prove the following result: If
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="1 less-than-or-slanted-equals i less-than-or-slanted-equals min left-brace right-brace comma left-parenthesis right-parenthesis minus minus times times 2 k 2 comma slash slash left-parenthesis right-parenthesis minus minus plus plus nk 12">

1
⩽
i
⩽
min
{
(
2
k
−
2
)
,
(
n
+
k
−
1
)

/

2
}

1 \leqslant i \leqslant \min \{ (2k - 2),(n + k - 1)/2\}

, then

I

n
,
k

i

=

I
n
i

+

K
i

I_{n,k}^i = I_n^i + {K^i}

. Also, we will prove an analogous result for manifolds with an extra structure.
Note on asymptotic prime divisors, analytic spreads and the altitude formula
Authors: Ratliff L. J.
Published: July 2010

The main result gives several characterizations of Noetherian domains that satisfy the altitude formula in terms of analytic spreads and asymptotic prime divisors.
Local solvability of constant coefficient partial differential equations as a small divisor problem
Authors: Dadok Jiri , Taylor Michael
Published: July 2010

Local solvability of

P
(
D
)
u
=
f

P(D)u = f

is reduced to a small divisor problem in Fourier series.
Orientability of fixed point sets
Authors: Edmonds Allan L.
Published: July 2010

It is proved that the fixed point set of a smooth involution which preserves orientation and a spin structure on a smooth manifold is necessarily orientable. As an application it is proved that a simply connected spin

4
4

-manifold with nonzero signature admits no involution which acts by multiplication by

−
1

- 1

on its second rational homology group.
An unknotting theorem in 𝑄^{∞}-manifolds
Authors: Liem Vo Thanh
Published: July 2010

In this note, we prove the following unknotting theorem. Theorem. Let

M
M

be a

Q
∞

{Q^\infty }

-manifold and let

F
:
X
×
I
→
M

F:X \times I \to M

be a homotopy such that

F
0

{F_0}

and

F
1

{F_1}

are

Q
∞

{Q^\infty }

-deficient embeddings. Then, there is an isotopy

H
:
M
×
I
→
M

H:M \times I \to M

such that

H
0

=

id

{H_0} = {\text {id}}

and

H
1

∘

F
0

=

F
1

{H_1} \circ {F_0} = {F_1}

. Moreover, if

F
F

is limited by an open cover

α
\alpha

of

M
M

and is stationary on a closed subset

X
0

{X_0}

of

X
X

, then we may choose

H
H

to also be limited by

S

t

4

(
α
)

{\text {S}}{{\text {t}}^4}(\alpha )

and to be the identity on

F
(

X
0

×
I
)

F({X_0} \times I)

. However, a similar unknotting theorem for

Z
Z

-embeddings does not hold true in

Q
∞

{Q^\infty }

and

R
∞

{R^\infty }

.
(CA) closures of analytic groups
Authors: Zerling David
Published: July 2010

An analytic group

G
G

is called

(
C
A
)

(CA)

if the group of inner automorphisms of

G
G

is closed in the Lie group of all bicontinuous automorphisms of

G
G

. We introduce the notion of a

(
C
A
)

(CA)

closure for an analytic group and show that every analytic group possesses a

(
C
A
)

(CA)

closure. The definition of uniqueness for such a

(
C
A
)

(CA)

closure is developed and a sufficient condition for uniqueness is given. We also develop new sufficient conditions for a closed normal analytic subgroup of a

(
C
A
)

(CA)

analytic group to be

(
C
A
)

(CA)

.
Semirings satisfying properties of distributive type
Authors: Kaya Arif , Satyanarayana M.
Published: July 2010

Any distributive lattice admits a semiring structure in a natural way and this particular semiring satisfies some new distributive properties. The purpose of this note is to study whether a semiring with some or all of these new distributive properties admits the natural distributive lattice structure, and thus obtain Birkhoff’s theorem as a corollary. Furthermore, characterizations of semirings satisfying some or all of these new distributive properties are obtained.
A remark on the spaces 𝑉^{𝑝}_{Λ,𝛼}
Authors: Goffman Casper , Liu Fon Che , Waterman Daniel
Published: July 2010

A function

f
∈

L
p

f \in {L^p}

,

p
⩾
1

p \geqslant 1

, over an interval in

R
n

{R^n}

, is in

V

Λ
,
α

p

V_{\Lambda ,\alpha }^p

if, corresponding to the

i
i

th coordinate direction,

i
=
1
,
…
,
n

i = 1, \ldots ,n

, there is an equivalent function which is of

Λ
\Lambda

-bounded variation on a.e. line

l
i

{l_i}

in that direction and whose

Λ
\Lambda

-variation on those lines is in

L
α

{L^\alpha }

,

α
⩾
1

\alpha \geqslant 1

, as a function of the other

(
n
−
1
)

(n - 1)

variables. For each

i
i

, another equivalent function may be chosen so that on a.e.

l
i

{l_i}

it has an internal saltus at each point. It is shown that for this function, the

Λ
\Lambda

-variation on the lines

l
i

{l_i}

is a measurable function of the other variables. This was known for

n
=
2

n = 2

; for

n
>
2

n > 2

, the measurability was previously assumed as an additional hypothesis. The classes

V

Λ
,
α

p

V_{\Lambda ,\alpha }^p

are Banach spaces and have been shown to be of interest in the study of localization of multiple Fourier series.
On the existence of global solutions of the nonlinear parabolic equation of Eells-Sampson over product manifolds
Authors: Nishikawa Seiki
Published: July 2010

We extend results of Lemaire and Hamilton on the existence of global solutions of the equation in the title to warped product manifolds with boundaries.
A new proof of the equivalence of the Hahn-Banach extension and the least upper bound properties
Authors: Ioffe A. D.
Published: July 2010

The paper contains a new proof of the fact that the Hahn-Banach majorized extension theorem for linear operators is valid iff the range ordered space is conditionally complete. The proof is based on quite different principles than the original proof of Bonnice, Silverman and To. The key element is a reformulation of the extension problem in terms of linear selections of special convex-valued mappings called fans.
Entire functions that share real zeros and real ones
Authors: Czubiak Thomas P. , Gundersen Gary G.
Published: July 2010

We find all pairs of nonconstant entire functions that have the same zeros and ones (ignoring multiplicities), when the zeros and ones are all real.
Equivalent conditions for decomposable operators
Authors: Lange Ridgley
Published: July 2010

Several new characterizations of an arbitrary decomposable operator on Banach space are given; for example, one of these is in terms of spectral conditions on an arbitrary invariant subspace, while another uses the spectral manifold

X
T

(

G
−

)

{X_T}({G^ - })

(rather than

X
T

(
F
)

{X_T}(F)

). From these results a short proof of Frunzǎ’s duality theorem is derived. Finally we give sufficient conditions that the predual of a decomposable operator is of the same class.
Convergence of a class of cubic interpolatory splines
Authors: Chatterjee A. , Dikshit H. P.
Published: July 2010

The interpolation problem of matching a cubic spline at one intermediate point and cubic spline with multiple knots at two intermediate points between the successive knots are studied when the interpolatory points are not necessarily equispaced.
Two-dimensional, almost periodic linear systems with proximal and recurrent behavior
Authors: Johnson Russell A.
Published: July 2010

We prove that there exist two-dimensional, almost periodic linear systems, with arbitrary basis of frequencies, the angular coordinates of whose solutions have both proximal and recurrent behavior. Such behavior is completely unlike that of any periodic system.
Explicit formulas for the coefficients of Faber polynomials with respect to univalent functions of the class Σ
Authors: Todorov Pavel G.
Published: July 2010

In this note, we obtain three natural explicit formulas for the coefficients of the Faber polynomials with respect to the univalent functions of the class

∑
\sum

. As an application, we obtain two new explicit formulas for the Grunsky coefficients of functions in

∑
\sum

; these formulas are simpler than those due to Schur [2] and Hummel [4]. The method used in this paper is different from the one that we used to obtain explicit expressions for the Grunsky coefficients for functions of the class

S
S

[6].
Joint continuity of separately continuous functions
Authors: Christensen Jens Peter Reus
Published: July 2010

It is shown that a separately continuous function

f
:
X
×
Y
→
Z

f:X \times Y \to Z

from the product of a certain type of Hausdorff space

X
X

and a compact Hausdorff space

Y
Y

into a metrizable space

Z
Z

is jointly continuous on a set of the type

A
×
Y

A \times Y

, where

A
A

is a dense

G
δ

{G_\delta }

set in

X
X

. The class of Hausdorff spaces

X
X

in question is defined by a gametheoretic condition. The result improves (and simplifies the proof of) a recent result of Namioka. Many "deep" theorems in functional analysis and automatic continuity theory are easy corollaries.
Spaces for which all compact metric spaces are remainders
Authors: Hatzenbuhler James , Mattson Don A.
Published: July 2010

Let

X
X

be a locally compact, completely regular, Hausdorff space, and let

K
(
X
)

K(X)

be the lattice of compactifications of

X
X

. Conditions on

K
(
X
)

K(X)

and an internal condition are obtained which characterize when

X
X

has all compact metric spaces as remainders.
Periods of periodic points of maps of the circle which have a fixed point
Authors: Block Louis
Published: July 2010

For a continuous map

f
f

of the circle to itself, let

P
(
f
)

P(f)

denote the set of positive integers

n
n

such that

f
f

has a periodic point of (least) period

n
n

. Results are obtained which specify those sets, which occur as

P
(
f
)

P(f)

, for some continuous map

f
f

of the circle to itself having a fixed point. These results extend a theorem of Šarkovskii on maps of the interval to maps of the circle which have a fixed point.
Differentiability via one-sided directional derivatives
Authors: Fabián Marián
Published: July 2010

Let

F
F

be a continuous mapping from an open subset

D
D

of a separable Banach space

X
X

into a Banach space

Y
Y

. We show that if the one sided directional derivative

D
x
+

F
(
a
)

D_x^ + F(a)

of

F
F

at

a
a

in the direction

x
x

exists for each

(
a
,
x
)

(a,x)

from a dense

G
δ

{G_\delta }

subset

S
S

of an open set

D
×
U
⊂
X
×
X

D \times U \subset X \times X

, then

F
F

is Gâteaux differentiable on a dense

G
δ

{G_\delta }

subset of

D
D

. Similar results are obtained for Fréchet differentiability when

X
X

is finite-dimensional and for

w
∗

{w^ * }

-Gâteaux differentiability.
On the weight and pseudoweight of linearly ordered topological spaces
Authors: Hart Klaas Pieter
Published: July 2010

We derive a simple formula for the weight of a LOTS using the pseudoweight. As an application we give a very short proof of the nonorderability of the Sorgenfrey-line.
Concavity of powers of a convolution
Authors: Hensley Douglas
Published: July 2010

A short geometric proof of a result of Brascamp and Lieb on concavity of powers of a convolution is given.
On a certain transitivity of the graded ring associated with an ideal
Authors: Trung Ngô Viêt
Published: July 2010

A simple but useful result will be given concerning a certain transitivity of the property that the graded ring associated with an ideal is a domain. As a consequence, we compute the graded rings associated with the defining prime ideals of certain determinantal varieties or of their projections from infinity to a hyperplane and get two new classes of primes having the equality of ordinary and symbolic powers in polynomial rings over a field.
An anisotropic locally hyperbolic quadratic space
Authors: Bertuccioni Inta
Published: July 2010

We construct a semilocal normal domain

A
A

and a quadratic space over

A
A

, which is locally hyperbolic but anisotropic. This answers a question of H. Bass.
Analytic functions into Banach spaces and a new characterization for isomorphic embeddings
Authors: Wrobel V.
Published: July 2010

Let

T
:
E
→
F

T:E \to F

be a continuous linear injection between complex Banach spaces. It is shown that

T
T

is a topological monomorphism if and only if every function

f
:
D
→
E

f:D \to E

on the open unit disc of the complex plane, for which

T
∘
f

T \circ f

is analytic, is itself analytic.
Isometries of 𝐴_{𝐶}(𝐾)
Authors: Rao T. S. S. R. K.
Published: July 2010

We completely describe isometries of

A

C

(
K
)

{A_{\mathbf {C}}}(K)

, when

K
K

is a compact Choquet simplex, using facially continuous functions on the extreme boundary.
A bounded analytic function in the unit disk with a level set component of infinite length
Authors: Barth K. F. , Clunie J. G.
Published: July 2010

The authors construct a bounded analytic function in the unit disk with a level set component of infinite length. The example is of the form

exp
⁡
i
B
(
z
)

\exp iB(z)

where

B
(
z
)

B(z)

is a Blaschke Product.
On Fourier integral operators
Authors: El Kohen A.
Published: July 2010

We consider operators of the form:

∫

−
∞

∞

F
t

φ
(
t
)

d
t

\int _{ - \infty }^\infty {{F_t}\varphi (t)\;dt}

, where

F
t

{F_t}

is a

1
1

-parameter family of Fourier integral operators and

φ
(
t
)

d
t

\varphi (t)\;dt

a tempered distribution on the real line and show that these operators are sums of pseudo-differential and Fourier integral operators. Here, we give the typical case where

φ
(
t
)

d
t
=

p

.

v

.

{

1

/

t

}

\varphi (t)\;dt = {\text {p}}.{\text {v}}.\left \{ {1/t} \right \}

. An application to singular integrals on variable curves is given.
On holomorphic graded manifolds
Authors: Green Paul
Published: July 2010

Kostant’s definition of a

C
∞

{C^\infty }

-graded manifold is adapted to the holomorphic category. It is shown that, in contrast to the

C
∞

{C^\infty }

case, there exist holomorphic graded manifolds with structure sheaf not isomorphic to the sheaf of sections of a bundle of exterior algebras.
A note on degree theory for gradient mappings
Authors: Amann Herbert
Published: July 2010

In this note we give a simple proof for the essentially known fact, that the Leray-Schauder degree of the gradient of a coercive functional on a large ball of a Hilbert space is one. As a simple application we show that the local index of an isolated local minimum of a

C
1

{C^1}

-functional on a Hilbert space equals one.
On the monodromy of higher logarithms
Authors: Ramakrishnan Dinakar
Published: July 2010

The (multivalued) higher logarithms are interpreted, by studying their monodromy, as giving well-defined maps from

P

C

1

−

{

3

points

}

{\mathbf {P}}_{\mathbf {C}}^1 - \left \{ {3\;{\text {points}}} \right \}

into certain complex nilmanifolds with

C

∗

{{\mathbf {C}}^ * }

-actions.
Jumping to a uniform upper bound
Authors: Hodes Harold
Published: July 2010

A uniform upper bound on a class of Turing degrees is the Turing degree of a function which parametrizes the collection of all functions whose degree is in the given class. I prove that if

a
_

\underline a

is a uniform upper bound on an ideal of degrees then

a
_

\underline a

is the jump of a degree

c
_

\underline c

with this additional property: there is a uniform bound

b
_

>

a
_

\underline b > \underline a

so that

b
_

∨

c
_

>

a
_

\underline b \vee \underline c > \underline a

.
Baire sections for group homomorphisms
Authors: Graf S. , Mägerl G.
Published: July 2010

The following result is proved: Let

X
X

and

Y
Y

be compact topological groups and

p
p

be a continuous group homomorphism from

Y
Y

onto

X
X

. Then there exists a map

q
q

from

X
X

to

Y
Y

such that

p
∘
q
=

i

d

X

p \circ q = {\text {i}}{{\text {d}}_X}

and

q

−
1

(
B
)

{q^{ - 1}}(B)

is a Baire set in

Y
Y

for every Baire subset

B
B

of

X
X

.
Foliation preserving Lie group actions and characteristic classes
Authors: Suzuki Haruo
Published: July 2010

Let

F

~

\tilde {\mathcal {F}}

be a codimension

k
k

foliation of a manifold

M
M

and

F

\mathcal {F}

a subfoliation of

F

~

\tilde {\mathcal {F}}

with codimension

q
q

. Let a Lie group

G
G

of dimension

k
k

act on

M
M

transversally locally freely to

F

~

\tilde {\mathcal {F}}

and preserving

F

\mathcal {F}

. Let

F

′

\mathcal {F}’

be the foliation determined by

F

\mathcal {F}

and the

G
G

-action. Then we have the following relations between exotic classes of

F

\mathcal {F}

and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper F prime colon alpha Subscript script upper F Baseline left-parenthesis left-bracket ModifyingAbove c With caret Subscript upper I Baseline c Subscript upper J Baseline right-bracket right-parenthesis equals alpha Subscript script upper F Sub Superscript prime Subscript Baseline left-parenthesis left-bracket ModifyingAbove c With caret Subscript upper I Baseline c Subscript upper J Baseline right-bracket right-parenthesis">

F

′

:

α

F

(
[

c
^

I

c
J

]
)
=

α

F

′

(
[

c
^

I

c
J

]
)

\mathcal {F}’:{\alpha _\mathcal {F}}([{\hat c_I}{c_J}]) = {\alpha _{\mathcal {F}’}}([{\hat c_I}{c_J}])

for

I
=
(

i
1

,
…
,

i
λ

)

I = ({i_1}, \ldots ,{i_\lambda })

,

J
=
(

j
1

,
…
,

j
μ

)

J = ({j_1}, \ldots ,{j_\mu })

,

1
⩽

j
γ

,

j
l

⩽
q
−
k

1 \leqslant {j_\gamma },{j_l} \leqslant q - k

, and

α

F

(
[

c
^

I

c
J

]
)
=
0

{\alpha _\mathcal {F}}([{\hat c_I}{c_J}]) = 0

otherwise.
Local isometries of compact metric spaces
Authors: Całka Aleksander
Published: July 2010

By local isometries we mean mappings which locally preserve distances. A few of the main results are: 1. For each local isometry

f
f

of a compact metric space

(
M
,
ρ
)

(M,\rho )

into itself there exists a unique decomposition of

M
M

into disjoint open sets,

M
=

M
0
f

∪
⋯
∪

M
n
f

M = M_0^f \cup \cdots \cup M_n^f

,

(
0
⩽
n
>
∞
)

(0 \leqslant n > \infty )

such that (i)

f
(

M
0
f

)
=

M
0
f

f(M_0^f) = M_0^f

, and (ii)

f
(

M
i
f

)
=

M

i
−
1

f

f(M_i^f) = M_{i - 1}^f

and

M
i
f

≠
∅

M_i^f \ne \emptyset

for each

i
,
1
⩽
i
⩽
n

i, 1 \leqslant i \leqslant n

. 2. Each local isometry of a metric continuum into itself is a homeomorphism onto itself. 3. Each nonexpansive local isometry of a metric continuum into itself is an isometry onto itself. 4. Each local isometry of a convex metric continuum into itself is an isometry onto itself.
The dimension of inverse limit and 𝑁-compact spaces
Authors: Charalambous M. G.
Published: July 2010

For each

k
=
1
,
2
,
…
,
∞

k = 1,2, \ldots ,\infty

,

N
N

, we construct a normal

N
N

-compact space

X
X

with

dim
⁡
X
=
k

\dim X = k

, where dim denotes covering dimension, which is the limit space of a sequence of zero-dimensional Lindelöf spaces.
Graphs with subconstituents containing 𝐿₃(𝑝)
Authors: Weiss Richard
Published: July 2010

Let

Γ
\Gamma

be a finite connected undirected graph,

G
G

a vertex-transitive subgroup of

aut
⁡
(
Γ
)

\operatorname {aut} (\Gamma )

,

{
x
,
y
}

\{ x,y\}

an edge of

Γ
\Gamma

and

G
i

(
x
,
y
)

{G_i}(x,y)

the subgroup of

G
G

fixing every vertex at a distance of at most

i
i

from

x
x

or

y
y

. We show that if the stabilizer

G
x

{G_x}

contains a normal subgroup inducing

L
3

(
p
)

{L_3}(p)

,

p
p

a prime, on the set of vertices adjacent to

x
x

, then

G
5

(
x
,
y
)
=
1

{G_5}(x,y) = 1

.
𝐿₀-valued vector measures are bounded
Authors: Kalton N. J. , Peck N. T. , Roberts James W.
Published: July 2010

Every vector measure taking values in

L
0

(
0
,
1
)

{L_0}(0,1)

has bounded range.
Jordan triple forms of Jordan algebras
Authors: Neher Erhard
Published: July 2010

We show that a central nondegenerate Jordan triple system over a field of characteristic

≠
2

\ne 2

has a nonzero center iff it is scalar isomorphic to a Jordan algebra. As an application we classify Jordan triple forms of Jordan algebras.
The octic periodic polynomial
Authors: Evans Ronald J.
Published: July 2010

The coefficients and the discriminant of the octic period polynomial

ψ
8

(
z
)

{\psi _8}(z)

are computed, where, for a prime

p
=
8
f
+
1

p = 8f + 1

,

ψ
8

(
z
)

{\psi _8}(z)

denotes the minimal polynomial over

Q

{\mathbf {Q}}

of the period

(
1

/

8
)

∑

n
=
1

p
−
1

exp
⁡
(
2
π
i

n
8

/

p
)

(1/8)\sum \nolimits _{n = 1}^{p - 1} {\exp (2\pi i{n^8}/p)}

. Also, the finite set of prime octic nonresidues

(

mod

p
)

(\mod p)

which divide integers represented by

ψ
8

(
z
)

{\psi _8}(z)

is characterized.
Lebesgue constants for Jacobi expansions
Authors: Cartwright Donald I.
Published: July 2010

Sharp estimates are given for the Lebesgue constants
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue EndAbsoluteValue StartAbsoluteValue s Subscript n Baseline EndAbsoluteValue StartAbsoluteValue EndAbsoluteValue Subscript p Baseline equals sup left-brace double-vertical-bar s Subscript n Baseline f double-vertical-bar Subscript p Baseline colon f element-of upper L Subscript w Superscript p Baseline comma double-vertical-bar f double-vertical-bar Subscript p Baseline less-than-or-slanted-equals 1 right-brace">

|

|

|

s
n

|

|

|

p

=
sup

{

‖

s
n

f

‖

p

:
f
∈

L
w
p

,

‖
f
‖

p

⩽
1

}

|||{s_n}||{|_p} = \sup \left \{ {{{\left \| {{s_n}f} \right \|}_p}:f \in L_w^p,{{\left \| f \right \|}_p} \leqslant 1} \right \}

for

p
p

outside the Pollard interval

(

p
0
′

,

p
0

)

({p’_0},{p_0})

, where

s
n

f

{s_n}f

is the

n
n

th partial sum of the Jacobi expansion of a function

f
f

which is in the

L
p

{L^p}

space with respect to the weight

w
(
x
)
=

(
1
−
x

)
α

(
1
+
x

)
β

w(x) = {(1 - x)^\alpha }{(1 + x)^\beta }

on

[
−
1
,
1
]

[ - 1,1]

.
The extension of measurable functions
Authors: Shortt R. M.
Published: July 2010

Say a measurable space

(
Y
,

B

)

(Y,\mathcal {B})

has the extension property (resp. the extension property in the restricted sense) if for every measurable space

(
X
,

S

)

(X,\mathcal {S})

and every subset

A
A

of

X
X

(resp. subset

A
A

of

X
X

with

X
∖
A

X\backslash A

singleton), each function

f
:
A
→
Y

f:A \to Y

measurable for

S

(
A
)
=
{
B
∩
A
:
B
∈

S

}

\mathcal {S}(A) = \{ B \cap A:B \in \mathcal {S}\}

may be extended to a measurable function

g
:
X
→
Y

g:X \to Y

. A countably generated and separated

(
Y
,

B

)

(Y,\mathcal {B})

has the extension property if and only if it is a standard space, i.e. it is isomorphic to a Borel subset of the real line. The discrete space

(
Y
,

2
Y

)

(Y,{2^Y})

has the extension property in the restricted sense if and only if the cardinality of

Y
Y

is not two-valued measurable.
On inequalities of periodic functions and their derivatives
Authors: Ditzian Z.
Published: July 2010

The inequality
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar f double-vertical-bar Subscript upper B Baseline less-than-or-slanted-equals a Subscript k Baseline double-vertical-bar f Superscript left-parenthesis k right-parenthesis Baseline double-vertical-bar Subscript upper B">

‖
f
‖

B

⩽

a
k

‖

f

(
k
)

‖

B

{\left \| f \right \|_B} \leqslant {a_k}{\left \| {{f^{(k)}}} \right \|_B}

is proved for many spaces of periodic functions. An analogue for sequences is also given.
Nonoscillation theorems for a second order sublinear ordinary differential equation
Authors: Kwong Man Kam , Wong J. S. W.
Published: July 2010

A number of known and a conjectured nonoscillation criteria for sublinear Emden-Fowler equations are shown to be equivalent. One of these criteria is then extended to cover cases in which a growth condition on the coefficient of the equation is not satisfied.
Approximating the absolutely continuous measures invariant under general maps of the interval
Authors: Boyarsky Abraham
Published: July 2010

Let

τ
:
I
→
I

\tau :I \to I

be a nonsingular, piecewise continuous transformation which admits a unique absolutely continuous invariant measure

μ
\mu

with density function

f
∗

{f^ * }

. The main result establishes the fact that

f
∗

{f^ * }

can be approximated weakly by the density functions of a sequence of measures invariant under piecewise linear Markov maps

{

τ
n

}

\left \{ {{\tau _n}} \right \}

which approach

τ
\tau

uniformly.
Distortion and coefficient estimation of schlicht functions
Authors: Hu Ke
Published: July 2010

Let
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S left-parenthesis k right-parenthesis equals left-brace f left-parenthesis z right-parenthesis equals z plus sigma-summation Underscript n equals 2 Overscript normal infinity Endscripts a Subscript n Baseline z Superscript n Baseline element-of upper S comma limit Overscript bar Endscripts Underscript rho right-arrow 1 Superscript minus Baseline Endscripts StartFraction left-parenthesis 1 minus rho right-parenthesis squared Over rho EndFraction max Underscript StartAbsoluteValue z EndAbsoluteValue equals rho Endscripts StartAbsoluteValue f left-parenthesis z right-parenthesis EndAbsoluteValue equals alpha Subscript f Baseline greater-than-or-slanted-equals k greater-than 0 right-brace period">

S
(
k
)
=

{

f
(
z
)
=
z
+

∑

n
=
2

∞

a
n

z
n

∈
S
,

lim
¯

ρ
→

1
−

(
1
−
ρ
)

2

ρ

max

|
z
|

=
ρ

|

f
(
z
)

|

=

α
f

⩾
k
>
0

}

.

S(k) = \left \{ {f(z) = z + \sum \limits _{n = 2}^\infty {{a_n}{z^n} \in S,} \;{{\overline {\lim } }_{\rho \to {1^ - }}}\frac {{{{(1 - \rho )}^2}}}{\rho }\max \limits _{\left | z \right | = \rho } \left | {f(z)} \right | = {\alpha _f} \geqslant k > 0} \right \}.

\]
In this paper, we prove that for

f
(
z
)
∈
S
(
k
)

f(z) \in S(k)

the inequality
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue a Subscript n Baseline EndAbsoluteValue greater-than n NestedStartRoot StartFraction upper P plus StartRoot left-parenthesis 1 plus p right-parenthesis upper A Superscript 1 slash 2 Baseline minus p EndRoot Over 1 plus upper P EndFraction NestedEndRoot">

|

a
n

|

>
n

P
+

(
1
+
p
)

A

1

/

2

−
p

1
+
P

\left | {{a_n}} \right | > n\sqrt {\frac {{P + \sqrt {(1 + p){A^{1/2}} - p} }}{{1 + P}}}

\]
holds where

p
=

k
2

/

(
1
−

k
2

)

p = {k^2}/(1 - {k^2})

and

1
⩽
A
>

(
1.0657

)
8

1 \leqslant A > {(1.0657)^8}

. This strengthens a recent result of Horowitz.
On the first order theory of the arithmetical degrees
Authors: Odifreddi Piergiorgio
Published: July 2010

The first order theory of the arithmetical degrees with arithmetical jump is not elementarily equivalent to the first order theory of the Turing degrees with jump.
Embeddings in minimal Hausdorff spaces
Authors: Vermeer J.
Published: July 2010

We show that not every semiregular space is embeddable as an open and dense set of some minimal Hausdorff space. Also a space is constructed for which it is not decidable in Z.F.C whether such an embedding exists.
On Newman’s theorem for finite-to-one open mappings on manifolds
Authors: McAuley L. F. , Robinson Eric E.
Published: July 2010

We prove the following important generalization of a famous theorem by Newman: If

(
M
,
d
)

(M,d)

is a closed manifold, there is an

ε
>
0

\varepsilon > 0

such that if

Y
Y

is a closed manifold and

f
:
M
↠
Y

f:M \twoheadrightarrow Y

is a finite-to-one open surjective mapping which is not a homeomorphism, then there is at least one

y
∈
Y

y \in Y

such that diam

f

−
1

(
y
)
⩾
ε

{f^{ - 1}}(y) \geqslant \varepsilon

. A version of the above theorem was first proved by Černavskii using rather complicated covering arguments. Our proof by comparison is much simpler and uses modern homology theory.
The group of automorphisms of a distributively generated near ring
Authors: Malone J. J.
Published: July 2010

S. D. Scott has shown that the group of automorphisms of the near ring generated by the automorphisms of a given group is isomorphic to the automorphism group of the given group if that group’s automorphism is complete. Here that theorem is generalized by showing that the group of automorphisms of a near ring distributively generated by its units is a subgroup of the group of automorphisms of the group of units. The results obtained are used to find the automorphism groups of certain near rings.
An analogue of Hilbert’s Theorem 90
Authors: Adolphson Alan
Published: July 2010

We prove a theorem on

p
p

-adic analytic functions that formally resembles Hilbert’s Theorem 90 and state a general open problem of which it is a special case.
On a Tauberian theorem for the 𝐿¹-convergence of Fourier sine series
Authors: Bray William O.
Published: July 2010

In a recent Tauberian theorem of Stanojević [3] for the

L
1

{L^1}

-convergence of Fourier series, the notion of asymptotically even sequences is introduced. These conditions are satisfied if the Fourier coefficients

{

f
^

(
n
)
}

\{ \hat f(n)\}

are even

(

f
^

(
−
n
)
=

f
^

(
n
)
)

(\hat f( - n) = \hat f(n))

, a case formally equivalent to cosine Fourier series. This paper applies the Tauberian method of Stanojević [3] separately to cosine and sine Fourier series and shows that the notion of asymptotic evenness can be circumvented in each case.
Nonexistence of invariant measures
Authors: Promislow David
Published: July 2010

Let

G
G

be a group acting on a set

X
X

. Suppose that for some positive integer

r
r

,

G
G

contains a free group

F
F

of rank

>
r

> r

and the intersection of any stabilizer with

F
F

has rank

⩽
r

\leqslant r

. A graph theoretic approach is used to show that there is no invariant measure on

X
X

.
A correction note on: “Generalized Hewitt-Savage theorems for strictly stationary processes” [Proc. Amer. Math. Soc. 63 (1977), no. 2, 313–316; MR0501304 (58 #18695)] by R. Isaac
Authors: Palacios José Luis
Published: July 2010

Conditions on the distribution of a process

{

X
n

,
n
∈
I
}

\{ {X_n},n \in I\}

are given under which the invariant, tail and exchangeable

σ
\sigma

-fields coincide; the index set

I
I

is either the positive integers or all the integers. The results proven here correct similar statements given in [3].
The Lévy-Lindeberg central limit theorem in 𝐿_{𝑝}, 0<𝑝<1
Authors: Giné Evarist
Published: July 2010

A

L
p

(
T
,
Σ
,
μ
)

{L_p}(T,\Sigma ,\mu )

-valued r.v.

X
X

,

0
>
p
>
1

0 > p > 1

, satisfies the Lévy-Lindeberg central limit theorem if and only if it is centered and pregaussian, that is, if and only if
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Underscript upper T Endscripts left-parenthesis upper E upper X squared left-parenthesis t right-parenthesis right-parenthesis Superscript p slash 2 Baseline d mu left-parenthesis t right-parenthesis greater-than normal infinity">

∫
T

(
E

X
2

(
t
)
)

p

/

2

d
μ
(
t
)
>
∞

\int \limits _T {{{(E{X^2}(t))}^{p/2}}d\mu (t) > \infty }

E
X
(
t
)
=
0

EX(t) = 0

-a.e. and

μ
\mu

.
Characterizations of ℱ-fibrations
Authors: Morgan C.
Published: July 2010

We obtain a reformulation of May’s notion of an "

F

\mathcal {F}

-fibration" and use it to sharpen results of Booth, Heath and Piccinini on the characterization of universal

F

\mathcal {F}

-fibrations.