bluuebunny/crossref_metadata_2025 huggingface dataset:
4-manifolds, 3-fold covering spaces and ribbons
Authors: Montesinos José María
Published: July 2010

It is proved that a PL, orientable 4-manifold with a handle presentation composed by 0-, 1-, and 2-handles is an irregular 3-fold covering space of the 4-ball, branched over a 2-manifold of ribbon type. A representation of closed, orientable 4-manifolds, in terms of these 2-manifolds, is given. The structure of 2-fold cyclic, and 3-fold irregular covering spaces branched over ribbon discs is studied and new exotic involutions on

S
4

{S^4}

are obtained. Closed, orientable 4-manifolds with the 2-handles attached along a strongly invertible link are shown to be 2-fold cyclic branched covering spaces of

S
4

{S^4}

. The conjecture that each closed, orientable 4-manifold is a 4-fold irregular covering space of

S
4

{S^4}

branched over a 2-manifold is reduced to studying

γ
#

S
1

×

S
2

\gamma \# {S^1} \times {S^2}

as a nonstandard 4-fold irregular branched covering of

S
3

{S^3}

.
Galerkin methods in the constructive solvability of nonlinear Hammerstein equations with applications to differential equations
Authors: Fitzpatrick P. M. , Petryshyn W. V.
Published: July 2010

We consider the solution of abstract Hammerstein equations by means of a Galerkin approximating scheme. The convergence of the scheme is proven by first establishing an equivalent scheme in a Hilbert space and then proving a convergence result for firmly monotone operators in a Hilbert space. The general results are applied to the case when the involved linear mapping is angle-bounded, and also to the treatment of certain differential equations.
Compactifications of 𝐶ⁿ
Authors: Brenton L. , Morrow J.
Published: July 2010

Let X be a compactification of

C

n

{{\text {C}}^n}

. We assume that X is a compact complex manifold and that

A

=

X

−

C

n

A\, = \,X\, - \,{{\text {C}}^n}

is a proper subvariety of X. If we suppose that A is a Kähler manifold, then we prove that X is projective algebraic,
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H Superscript asterisk Baseline left-parenthesis upper A comma bold upper Z right-parenthesis approximately-equals upper H Superscript asterisk Baseline left-parenthesis bold upper P Superscript n minus 1 Baseline comma bold upper Z right-parenthesis">

H

∗

(

A
,

Z

)

≅

H

∗

(

P

n

−

1

,

Z

)

{H^{\ast }}\left ( {A,\,{\textbf {Z}}} \right )\, \cong \,{H^{\ast }}\left ( {{{\textbf {P}}^{n\, - \,1}},\,{\textbf {Z}}} \right )

, and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H Superscript asterisk Baseline left-parenthesis upper X comma bold upper Z right-parenthesis approximately-equals upper H Superscript asterisk Baseline left-parenthesis bold upper P Superscript n Baseline comma bold upper Z right-parenthesis">

H

∗

(

X
,

Z

)

≅

H

∗

(

P

n

,

Z

)

{H^{\ast }}\left ( {X,\,{\textbf {Z}}} \right )\, \cong \,{H^{\ast }}\left ( {{{\textbf {P}}^n},\,{\textbf {Z}}} \right )

. Various additional conditions are shown to imply that

X

=

P

n

X\, = \,{{\textbf {P}}^n}

. It is known that no additional conditions are needed to imply

X

=

P

n

X\, = \,{{\textbf {P}}^n}

in the cases

n

=

1
,

2

n\, = \,1,\,2

. In this paper we prove that if

n

=

3

n\, = \,3

,

X

=

P

3

X\, = \,{{\textbf {P}}^3}

.
Automorphisms of 𝐺𝐿_{𝑛}(𝑅)
Authors: McDonald B. R.
Published: July 2010

Let R denote a commutative ring having 2 a unit. Let

G

L

n

(
R
)

{\text {G}}{{\text {L}}_n}\left ( R \right )

denote the general linear group of all

n

×

n

n\, \times \,n

invertible matrices over R. Let

∧
\wedge

be an automorphism of

G

L

n

(
R
)

{\text {G}}{{\text {L}}_n}\left ( R \right )

. An automorphism

∧
\wedge

is “stable” if it behaves properly relative to families of commuting involutions (see §IV). We show that if R is connected, i.e., 0 and 1 are only idempotents, then all automorphisms

∧
\wedge

are stable. Further, if

n

⩾

3

n\, \geqslant \,3

, R is an arbitrary commutative ring with 2 a unit, and

∧
\wedge

is a stable automorphism, then we obtain a description of

∧
\wedge

as a composition of standard automorphisms.
On the first occurrence of values of a character
Authors: Kolesnik G. , Straus E. G.
Published: July 2010

Let

χ
\chi

be a character of order

k

(
mod

n
)

k\,(\bmod \, n)

, and let

g
m

(
χ
)

{g_m}(\chi )

be the smallest positive integer at which

χ
\chi

attains its

(
m
+
1
)

(m + 1)

st nonzero value. We consider fixed k and large n and combine elementary group-theoretic considerations with the known results on character sums and sets of integers without large prime factors to obtain estimates for

g
m

(
χ
)

{g_m}(\chi )

.
On the existence of uniformly distributed sequences in compact topological spaces. I
Authors: Losert V.
Published: July 2010

We prove the existence of uniformly distributed sequences for an arbitrary probability measure on a separable dyadic space, e.g. on a separable compact topological group. Some counterexamples for the nonexistence of u.d. sequences in certain dense subsets are given.
On a theorem of Steinitz and Levy
Authors: Moran Gadi
Published: July 2010

Let

∑

n

∈

ω

h
(
n
)

\sum \nolimits _{n\,\, \in \,\omega } {h(n)}

be a conditionally convergent series in a real Banach space B. Let

S
(
h
)

S(h)

denote the set of sums of the convergent rearrangements of this series. A well-known theorem of Riemann states that

S
(
h
)

=

B

S(h)\, = \,B

if

B

=

R

B\, = \,R

, the reals. A generalization of Riemann’s Theorem, due independently to Levy [L] and Steinitz [S], states that if B is finite dimensional, then

S
(
h
)

S(h)

is a linear manifold in B of dimension

>

0

> \,0

. Another generalization of Riemann’s Theorem [M] can be stated as an instance of the Levy-Steinitz Theorem in the Banach space of regulated real functions on the unit interval I. This instance generalizes to the Banach space of regulated B-valued functions on I, where B is finite dimensional, implying a generalization of the Levy-Steinitz Theorem.
Nullity and generalized characteristic classes of differential manifolds
Authors: Tan Sin Leng
Published: July 2010

Using the Kamber-Tondeur construction of characteristic classes for foliated bundes, the author has given a method for constructing generalized characteristic classes for a differentiable manifold M without imposing conditions on M. In particular a vanishing theorem on the manifold M is obtained. The construction is particularly useful if the ordinary characteristic ring Pont*(M) of the manifold M vanishes much below the dimension of M.
Isomorphic factorisations. I. Complete graphs
Authors: Harary Frank , Robinson Robert W. , Wormald Nicholas C.
Published: July 2010

An isomorphic factorisation of the complete graphKp{K_p}is a partition of the lines ofKp{K_p}intotisomorphic spanning subgraphsG; we then writeG|KpG|{K_p}, andG∈Kp/tG \in {K_p}/t. If the set of graphsKp/t{K_p}/tis not empty, then of courset|p(p−1)/2t|p(p - 1)/2. Our principal purpose is to prove the converse. It was found by Laura Guidotti that the converse does hold whenever(t,p)=1(t,p) = 1or(t,p−1)=1(t,p - 1) = 1. We give a new and shorter proof of her result which involves permuting the points and lines ofKp{K_p}. The construction developed in our proof happens to give all the graphs inK6/3{K_6}/3andK7/3{K_7}/3. The Divisibility Theorem asserts that there is a factorisation ofKp{K_p}intotisomorphic parts whenevertdividesp(p−1)/2p(p - 1)/2. The proof to be given is based on our proof of Guidotti’s Theorem, with embellishments to handle the additional difficulties presented by the cases whentis not relatively prime toporp−1p - 1.
On the existence of good Markov strategies
Authors: Hill Theodore Preston
Published: July 2010

In contrast to the known fact that there are gambling problems based on a finite state space for which no stationary family of strategies is at all good, in every such problem there always exist

ε
\varepsilon

-optimal Markov families (in which the strategy depends only on the current state and time) and also

ε
\varepsilon

-optimal tracking families (in which the strategy depends only on the current state and the number of times that state has been previously visited). More generally, this result holds for all finite state gambling problems with a payoff which is shift and permutation invariant.
Frattini subgroups of 3-manifold groups
Authors: Allenby R. B. J. T. , Boler J. , Evans B. , Moser L. E. , Tang C. Y.
Published: July 2010

In this paper it is shown that if the Frattini subgroup of the fundamental group of a compact, orientable, irreducible, sufficiently large 3-manifold is nontrivial then the 3-manifold is a Seifert fibered space. We show further that the Frattini subgroup of the group of a Seifert fibered space is trivial or cyclic. As a corollary to our work we prove that every knot group has trivial Frattini subgroup.
Semi-algebraic groups and the local closure of an orbit in a homogeneous space
Authors: Goto Morikuni
Published: July 2010

Let L be a topological group acting on a locally compact Hausdorff space M as a transformation group. Let m be in M. A subset Q of M is called the local closure of the orbit Lm if Q is the smallest locally compact invariant subset of M with

m

∈

Q

m\, \in \,Q

. A partition
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M equals union Underscript lamda element-of logical-and Endscripts upper Q Subscript lamda Baseline comma upper Q Subscript lamda Baseline intersection upper Q Subscript mu Baseline equals normal empty-set left-parenthesis lamda not-equals mu right-parenthesis">

M
=

⋃

λ
∈
∧

Q
λ

,

Q

λ

∩

Q
μ

=

∅

(

λ
≠
μ

)

M = \,\bigcup \limits _{\lambda \in \wedge } \,{Q_\lambda },\,\,\,\,{Q_{\lambda \,}}\, \cap \,\,{Q_\mu } = \,\emptyset \,\,\,\,\left ( {\lambda \ne \mu } \right )

\]
is called an LC-partition of M with respect to the L action if each

Q
λ

{Q_\lambda }

is the local closure of Lm for any m in

Q
λ

{Q_\lambda }

. Theorem. Let G be a connected Lie group, and let A and B be subgroups of G with only finitely many connected components. Suppose that B is closed. Then the factor space

G

/

B

G/B

has an LC-partition with respect to the A action.
Zeeman’s filtration of homology
Authors: McCrory Clint
Published: July 2010

Geometric interpretations of Zeeman’s filtrations of the homology and cohomology of a triangulable space are given, using an analysis of his spectral sequence for Poincaré duality.
A 3-local characterization of 𝐿₇(2)
Authors: Finkelstein Larry , Frohardt Daniel
Published: July 2010

Recent work of Gorenstein and Lyons on finite simple groups has led to standard form problems for odd primes. The present paper classifies certain simple groups which have a standard 3-component of type

L
5

(
2
)

{L_5}\left ( 2 \right )

.
Borel parametrizations
Authors: Mauldin R. Daniel
Published: July 2010

Let X and Y be uncountable Polish spaces and B a Borel subset oi

X

×

Y

X\, \times \,Y

such that for each x,

B
x

{B_x}

is uncountable. A Borel parametrization of B is a Borel isomorphism, g, of

X

×

E

X\, \times \,E

onto B where E is a Borel subset of Y such that for each x,

g

(

x
,

⋅

)

g\left ( {x,\, \cdot } \right )

maps E onto

B
x

=

{

y
:

(

x
,

y

)

∈

B

}

{B_x}\, = \,\left \{ {y:\,\left ( {x,\,y} \right )\, \in \,B} \right \}

. It is shown that B has a Borel parametrization if and only if B contains a Borel set M such that for each x,

M
x

{M_x}

is a nonempty compact perfect set, or, equivalently, there is an atomless conditional probability distribution,

μ
\mu

, so that for each x,

μ

(

x
,

B
x

)

>

0

\mu \left ( {x,\,{B_x}} \right )\, > \, 0

. It is also shown that if Y is dense-in-itself and

B
x

{B_x}

is not meager, for each x, then B has a Borel parametrization.
A converse of the Borel formula
Authors: Dotzel Ronald M.
Published: July 2010

When an elementary Abelian p-group acts on a

Z
p

{Z_p}

-homology sphere (p a prime), it is known that the Borel formula must hold. Here we ask that the Borel formula hold and determine how this restricts, homologically, the type of space which can occur, assuming spherical fixed sets and connectedness. This is done by constructing a linear model of the action and an equivariant map to the model, the mapping cone of which yields certain homological information.
CR submanifolds of a Kaehler manifold. II
Authors: Bejancu Aurel
Published: July 2010

The differential geometry of CR submanifolds of a Kaehler manifold is studied. Theorems on parallel normal sections and on a special type of flatness of the normal connection on a CR submanifold are obtained. Also, the nonexistence of totally umbilical proper CR submanifolds in an elliptic or hyperbolic complex space is proven.
An algebraic characterization of connected sum factors of closed 3-manifolds
Authors: Row W. H.
Published: July 2010

Let M and N be closed connected 3-manifolds. A knot group of M is the fundamental group of the complement of a tame simple closed curve in M. Denote the set of knot groups of M by K(M). A knot group G of M is realized in N if G is the fundamental group of a compact submanifold of N with connected boundary. Theorem. Every knot group of N is realized in M iff N is a connected sum factor of M. Corollary 1.

K

(
M
)

=

K

(
N
)

K\,(M)\, = \,K\,(N)

iff M is homeomorphic to N. Given M, there exists a knot group

G
M

{G_M}

of M that serves to characterize M in the following sense. Corollary 2.

G
M

{G_M}

is realized in N and

G
N

{G_N}

, is realized in M iff M is homeomorphic to N. Our proof depends heavily on the work of Bing, Feustal, Haken, and Waldhausen in the 1960s and early 1970s. A. C. Conner announced Corollary 1 for orientable 3-manifolds in 1969 which Jaco and Myers have recently obtained using different techniques.
The analytic continuation of the discrete series. I
Authors: Wallach Nolan R.
Published: July 2010

In this paper the analytic continuation of the holomorphic discrete series is defined. The most elementary properties of these representations are developed. The study of when these representations are unitary is begun.
Canonical subgroups of formal groups
Authors: Lubin Jonathan
Published: July 2010

Let R be a complete local domain of mixed characteristic. This paper gives a complete answer to the question: “If F is a one-dimensional formal group over R of finite height, when is there a canonical morphism

F
→

F
′

F \to {F’}

that lifts Frobenius?” For given height h, a universal family of formal groups F with such a morphism is constructed, and the shape of

F
′

{F’}

is described for small values of h.
The transfer and compact Lie groups
Authors: Feshbach Mark
Published: July 2010

Let G be a compact Lie group with H and K arbitrary closed subgroups. Let BG, BH, BK be l-universal classifying spaces, with

ρ
(
H
,
G
)
:
B
H
→
B
G

\rho (H,G):BH \to BG

the natural projection. Then transfer homomorphisms

T
(
H
,
G
)
:
h
(
B
H
)
→
h
(
B
G
)

T(H,G):h(BH) \to h(BG)

are defined for h an arbitrary cohomology theory. One of the basic properties of the transfer for finite coverings is a double coset formula. This paper proves a double coset theorem in the above more general context, expressing

ρ

∗

(
K
,
G
)
∘
T
(
H
,
G
)

{\rho ^{\ast }}(K,G) \circ T(H,G)

as a sum of other compositions. The main theorems were announced in the Bulletin of the American Mathematical Society in May 1977.
A pointwise ergodic theorem for the group of rational rotations
Authors: Dubins Lester E. , Pitman Jim
Published: July 2010

Let f be a bounded, measurable function defined on the multiplicative group

Ω
\Omega

of complex numbers of absolute value 1, and define
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row with Label left-parenthesis left-parenthesis 1 right-parenthesis right-parenthesis EndLabel f Subscript n Baseline left-parenthesis omega right-parenthesis equals StartFraction 1 Over n EndFraction sigma-summation Underscript i equals 1 Overscript n Endscripts f left-parenthesis z Subscript n Superscript i Baseline omega right-parenthesis comma omega element-of normal upper Omega comma EndLayout">

(

(
1
)

)

f
n

(
ω
)
=

1
n

∑

i
=
1

n

f
(

z
n
i

ω
)

,

ω
∈
Ω
,

\begin{equation}\tag {$(1)$}{{f_n}(\omega ) = \frac {1} {n}\sum \limits _{i = 1}^n {f(z_n^i\omega )} ,} \qquad \omega \in \Omega ,\end{equation}

where

z
n

{z_n}

is a primitive nth root of unity. The present paper generalizes this result of Jessen [1934]: if

n
(
k
)

n(k)

is an increasing sequence of positive integers with

n
(
k
)

n(k)

dividing

n
(

k
′

)

n(k’)

whenever

k
>

k
′

k > k’

, then

f

n
(
k
)

{f_{n(k)}}

converges almost surely as

k
→
∞

k \to \infty

.
An axiom for nonseparable Borel theory
Authors: Fleissner William G.
Published: July 2010

Kuratowski asked whether the Lebesgue-Hausdorff theorem held for metrizable spaces. A. Stone asked whether a Borel isomorphism between metrizable spaces must be a generalized homeomorphism. The existence of a Q set refutes the generalized Lebesgue-Hausdorff theorem. In this paper we discuss the consequences of the axiom of the title, among which are “yes” answers to both Kuratowski’s and Stone’s questions. The axiom states that a point finite analytic additive family is

σ
\sigma

discretely decomposable. We show that this axiom is valid in the model constructed by collapsing a supercompact cardinal to

ω
2

{\omega _2}

using Lévy forcing. Our proof displays relationships between

σ
\sigma

discretely decomposable families, analytic additive families and d families.
Complex-foliated structures. I. Cohomology of the Dolbeault-Kostant complexes
Authors: Fischer Hans R. , Williams Floyd L.
Published: July 2010

We study the cohomology of differential complexes, which we shall call Dolbeault-Kostant complexes, defined by certain integrable sub-bundles F of the complex tangent bundle of a manifold M. When M has a complex or symplectic structure and F is chosen to be the bundle of anti-holomorphic tangent vectors or, respectively, a “polarization” then the corresponding complexes are, respectively, the Dolbeault complex and (under further conditions) a complex introduced by Kostant in the context of geometric quantization. A simple condition on F insures that our complexes are elliptic. Assuming ellipticity and compactness of M, for example, one of our key results is a Hirzebruch-Riemann-Roch Theorem.
Structural stability and hyperbolic attractors
Authors: Lopes Artur Oscar
Published: July 2010

A necessary condition for structural stability is presented that in the two dimensional case means that the system has a finite number of topological attractors.
Wiman-Valiron theory for entire functions of finite lower growth
Authors: Fenton P. C.
Published: July 2010

A general method of Wiman-Valiron type for dealing with entire functions of finite lower growth is presented and used to obtain the lower-order version of a result of W. K. Hayman on the real part of entire functions of small lower growth.
The spaces of functions of finite upper 𝑝-variation
Authors: Nelson Robert R.
Published: July 2010

Let y be a Banach space,

1

⩽

p

>

∞

1\, \leqslant \,p\, > \,\infty

, and

U
p

{U_p}

be the semi-normed space of Y-valued Bochner measurable functions of a real variable which have finite upper p-variation. Let

U
~

p

{\tilde U_p}

be the space of

U
p

{U_p}

-equivalence classes. An averaging operator is defined with the aid of the theory of helixes in Banach spaces, which enables us to show that the spaces

U
~

p

{\tilde U_p}

are Banach spaces, to characterize their members, and to show that they are isometrically isomorphic to Banach spaces of Y-valued measures with bounded p-variation.
On the positive spectrum of Schrödinger operators with long range potentials
Authors: Khosrovshahi G. B. , Levine H. A. , Payne L. E.
Published: July 2010

In this paper we are concerned with solutions of the equation

Δ
u

+

p
(
x
)
u

=

0

\Delta u\, + \,p(x)u\, = \,0

in an unbounded domain

Ω
\Omega

in

R
n

{R^n}

,

Ω

⊃

{
x

|

‖
x
‖

⩾

R
0

}

\Omega \, \supset \,\{ x|\,\,\left \| x \right \|\, \geqslant \,{R_0}\}

. The main result is a determination of conditions on the asymptotic behavior of

p
(
x
)

p(x)

sufficient to guarantee that no nontrivial

L
2

{L_2}

solution exists. Our results contain those of previous authors as special cases. The principal application is to the determination of upper bounds for positive eigenvalues of Schrödinger operators.
Smooth orbit equivalence of ergodic 𝑅^{𝑑} actions, 𝑑≥2
Authors: Rudolph Daniel
Published: July 2010

We show here that any two free ergodic finite measure preserving actions of

R

d

{\textbf {R}^d}

,

d

⩾

2

d\, \geqslant \,2

, are orbit equivalent by a measure preserving map which on orbits is

C
∞

{C^\infty }

.
𝜎-connectedness in hereditarily locally connected spaces
Authors: Grispolakis J. , Tymchatyn E. D.
Published: July 2010

B. Knaster, A. Lelek and J. Mycielski [Colloq. Math. 6 (1958), 227-246] had asked whether there exists a hereditarily locally connected planar set, which is the union of countably many disjoint arcs. They gave an example of a locally connected, connected planar set, which is the union of a countable sequence of disjoint arcs. Lelek proved in a paper in Fund. Math. in 1959, that connected subsets of planar hereditarily locally connected continua are weakly

σ
\sigma

-connected (i.e., they cannot be written as unions of countably many disjoint, closed connected subsets). In this paper we generalize the notion of finitely Suslinian to noncompact spaces. We prove that there is a class of spaces, which includes the class of planar hereditarily locally connected spaces and the finitely Suslinian spaces, and which are weakly

σ
\sigma

-connected, thus, answering the above question in the negative. We also prove that arcwise connected, hereditarily locally connected, planar spaces are locally arcwise connected. This answers in the affirmative a question of Lelek [Colloq. Math. 36 (1976), 87-96].
Pseudo-integral operators
Authors: Sourour A. R.
Published: July 2010

Let

(
X
,

a

,

m
)

(X,\,\mathcal {a},\,m)

be a standard finite measure space. A bounded operator T on

L
2

(
X
)

{L^2}(X)

is called a pseudo-integral operator if

(
T
f
)
(
x
)

=

∫

f
(
y
)

μ
(
x
,

d
y
)

(Tf)(x)\, = \,\int {f(y)\,\mu (x,\,dy)}

, where, for every x,

μ
(
x
,

⋅

)

\mu (x,\, \cdot \,)

is a bounded Borel measure on X. Main results: 1. A bounded operator T on

L
2

{L^2}

is a pseudo-integral operator with a positive kernel if and only if T maps positive functions to positive functions. 2. On nonatomic measure spaces every operator unitarily equivalent to T is a pseudo-integral operator if and only if T is the sum of a scalar and a Hilbert-Schmidt operator. 3. The class of pseudo-integral operators with absolutely bounded kernels form a selfadjoint (nonclosed) algebra, and the class of integral operators with absolutely bounded kernels is a two-sided ideal. 4. An operator T satisfies

(
T
f
)
(
x
)

=

∫

f
(
y
)

μ
(
x
,

d
y
)

(Tf)(x)\, = \,\int {f(y)\,\mu (x,\,dy)}

for

f

∈

L
∞

f\, \in \,{L^\infty }

if and only if there exists a positive measurable (almost-everywhere finite) function

Ω
\Omega

such that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue left-parenthesis upper T f right-parenthesis left-parenthesis x right-parenthesis EndAbsoluteValue less-than-or-slanted-equals double-vertical-bar f double-vertical-bar Subscript normal infinity Baseline normal upper Omega left-parenthesis x right-parenthesis">

|

(
T
f
)
(
x
)

|

⩽

‖
f
‖

∞

Ω
(
x
)

\left | {(Tf)(x)} \right |\, \leqslant \,{\left \| f \right \|_\infty }\Omega (x)

.
Some constructions of infinite Möbius planes
Authors: Krier Nicholas
Published: July 2010

New infinite Möbius planes are constructed using transfinite induction. Any infinite affine plane A can be embedded in a Möbius plane M and the construction allows some groups of perspectivities of A to be extended to automorphism groups of M. Given

{

A
α

,

α

∈

J

}

\left \{ {{A_\alpha },\,\alpha \, \in \,J} \right \}

, an infinite collection of s affine planes each of order s, there exist a Möbius plane M and a bijection b from J to the point set of M so that for each

α

∈

J
,

M

b

(
α
)

\alpha \, \in \,J,\,{M_{b\left ( \alpha \right )}}

is isomorphic to

A
α

{A_\alpha }

.
Free states of the gauge invariant canonical anticommutation relations. II
Authors: Baker B. M.
Published: July 2010

A class of representations of the gauge invariant subalgebra of the canonical anticommutation relations (henceforth GICAR) is studied. These representations are induced by restricting the well-known pure, nongauge invariant generalized free states of the canonical anticommutation relations (henceforth CAR). Denoting a state of the CAR by

ω
\omega

, and the unique generalized free state of the CAR such that

ω

(

a

(
f
)

∗

a

(
g
)

)

=

(

f
,
T
g

)

\omega \left ( {a{{\left ( f \right )}^{\ast }}a\left ( g \right )} \right )\, = \,\left ( {f,Tg} \right )

and

ω

(

a

(
f
)

a

(
g
)

)

=

(

S
f
,
g

)

\omega \left ( {a\left ( f \right )a\left ( g \right )} \right )\, = \,\left ( {Sf,g} \right )

by

ω

S
,
T

{\omega _{S,T}}

, it is shown that a pure, nongauge invariant state

ω

S
,
T

{\omega _{S,T}}

induces a factor representation of the GICAR if and only if

T
r

T

(

I
−
T

)

=

∞

Tr\,T\left ( {I - T} \right )\, = \,\infty

.
Simple periodic orbits of mappings of the initial
Authors: Block Louis
Published: July 2010

Let f be a continuous map of a closed, bounded interval into itself. A criterion is given to determine whether or not f has a periodic point whose period is not a power of 2, which just depends on the periodic orbits of f whose period is a power of 2. Also, a lower bound for the topological entropy of f is obtained.
On the asymptotic behavior of a fundamental set of solutions
Authors: Powder Charles
Published: July 2010

We consider nth order homogeneous linear ordinary differential equations whose coefficients have an asymptotic expansion as

x
→
∞

x \to \infty

in terms of real powers of x and are analytic in sectors of the complex plane. In earlier work Bank (Funkcial. Ekvac. 11 (1968), 87-100) developed a method for reading off the asymptotic behavior of solutions directly from the equation, except in certain cases where roots asymptotically coalesce. For our results, we consider coefficients in a field of the type developed by Strodt (Trans. Amer. Math. Soc. 105 (1962), 229-250). By successive algebraic transforms, we show that an equation in the exceptional case can be reduced to the nonexceptional case and so the asymptotic behavior of the solutions can be read from the equation. This generalizes the classical results when

∞
\infty

is a singular point and the coefficients are analytic in neighborhoods of

∞
\infty

. The strength of our results is that the coefficients need not be defined in a full neighborhood of

∞
\infty

, and that the asymptotic behavior can be read directly from the equation.
𝛽-recursion theory
Authors: Friedman Sy D.
Published: July 2010

We define recursion theory on arbitrary limit ordinals using the J-hierarchy for L. This generalizes

α
\alpha

-recursion theory, where the ordinal is assumed to be

Σ
1

{\Sigma _1}

-admissible. The notion of tameness for a recursively enumerable set is defined and the degrees of tame r.e. sets are studied. Post’s Problem is solved when

Σ
1

cf
⁡
β

β

∗

{\Sigma _1}\operatorname {cf} \beta \,\beta {\ast }

. Lastly, simple sets are constructed for all

β
\beta

with the aid of a

β
\beta

-recursive version of Fodor’s Theorem.
Spectral theory for subnormal operators
Authors: Lautzenheiser R. G.
Published: July 2010

We give an example of a subnormal operator T such that

C

∖

σ
(
T
)

{\text {C}}\,\backslash \,\sigma (T)

has an infinite number of components,

int
⁡
(
σ
(
T
)
)

\operatorname {int} (\sigma (T))

has two components U and V, and T cannot be decomposed with respect to U and V. That is, it is impossible to write

T

=

T
1

⊕

T
2

T\, = \,{T_1}\, \oplus \,{T_2}

with

σ
(

T
1

)

=

U
¯

\sigma ({T_1})\, = \,\overline U

and

σ
(

T
2

)

=

V
¯

\sigma ({T_2})\, = \,\overline V

. This example shows that Sarason’s decomposition theorem cannot be extended to the infinitely-connected case. We also use Mlak’s generalization of Sarason’s theorem to prove theorems on the existence of reducing subspaces. For example, if X is a spectral set for T and

K

⊂

X

K\, \subset \,X

, conditions are given which imply that T has a nontrivial reducing subspace

M

\mathcal {M}

such that

σ
(
T

|

M

)

⊂

K

\sigma (T|\mathcal {M})\, \subset \,K

. In particular, we show that if T is a subnormal operator and if

Γ
\Gamma

is a piecewise

C
2

{C^2}

Jordan closed curve which intersects

σ
(
T
)

\sigma (T)

in a set of measure zero on

Γ
\Gamma

, then

T

=

T
1

⊕

T
2

T\, = \,{T_1}\, \oplus \,{T_2}

with

σ
(

T
1

)

⊂

σ
(
T
)

∩

ext
⁡
(
Γ
)

¯

\sigma ({T_1})\, \subset \,\sigma (T)\, \cap \,\overline {\operatorname {ext} (\Gamma )}

and

σ
(

T
2

)

⊂

σ
(
T
)

∩

int
⁡
(
Γ
)

¯

\sigma ({T_2})\, \subset \,\sigma (T)\, \cap \,\overline {\operatorname {int} (\Gamma )}

.
𝑍₍₂₎-knot cobordism in codimension two, and involutions on homotopy spheres
Authors: Liang Chao Chu
Published: July 2010

Let

Z

(
2
)

{Z_{(2)}}

denote the ring of rational 2-adic integers. In this paper, we consider the group

Ψ
k

{\Psi _k}

of

Z

(
2
)

{Z_{(2)}}

-cobordism classes of

Z

(
2
)

−
knot
⁡
(

Σ

k
+
2

,

K
k

)

{Z_{(2)}} - \operatorname {knot} (\Sigma ^{k + 2}, \,{K^k})

, where

Σ
\Sigma

is a 1-connected

Z

(
2
)

{Z_{(2)}}

-sphere

Z

(
2
)

{Z_{(2)}}

-cobordant to

S

k
+
2

{S^{k + 2}}

, and K is a 1-connected

Z

(
2
)

{Z_{(2)}}

-sphere embedded in

Σ
\Sigma

with trivial normal bundle. For

n
⩾
3

n \geqslant 3

, we will prove that

Ψ

2
n

=
0

{\Psi _{2n}} = 0

and

Ψ

2
n
−
1

=

C
ε

(

Z

(
2
)

)

{\Psi _{2n - 1}} = {C_\varepsilon }({Z_{(2)}})

,

ε
=

(
−
1

)
n

\varepsilon = {( - 1)^n}

. Also, we will show that the group

Θ

4
m
−
1

4
m
+
1

\Theta _{4m - 1}^{4m + 1}

of L-equivalence classes of differentiable involutions on

(
4
m
+
1
)

(4m + 1)

-homotopy spheres with codimension two fixed point sets defined by Bredon contains infinitely many copies of Z.
The theorems of Beth and Craig in abstract model theory. I. The abstract setting
Authors: Makowsky J. A. , Shelah S.
Published: July 2010

In the context of abstract model theory various definability properties, their interrelations and their relation to compactness are investigated.
Lattice points and Lie groups. II
Authors: Cahn Robert S.
Published: July 2010

Let

C
C

be the Casimir operator on a compact, simple, simply connected Lie group

G
G

of dimension

n
n

. The number of eigenvalues of

C
C

, counted with their multiplicities, of absolute value less than or equal to

t
t

is asymptotic to

k

t

n

/

2

k t^{n/2}

,

k
k

a constant. This paper shows the error of this estimate to be

O
(

t

2
b
+
a
(
a
−
1
)

/

(
a
+
1
)

)

O({t^{2b + a(a - 1)/(a + 1)}})

; where

a
a

= rank of

G
G

and

b
=
1

/

2
(
n
−
a
)

b = 1/2 (n - a)

.
Uniformly distributed sequences in locally compact groups. II
Authors: Benzinger Leonora
Published: July 2010

We consider the following question. When is there a compactification

G
0

{G_0}

of a locally compact group G (recall that a compact group

G
0

{G_0}

is a compactification of G if there is a continuous homomorphism

ϕ
:
G
→

G
0

\phi :G \to {G_0}

so that

ϕ
(
G
)

\phi (G)

is dense in G) with continuous homomorphism

ϕ
:
G
→

G
0

\phi :G \to {G_0}

with the property that

{

g
ν

}

\{ {g_\nu }\}

is uniformly distributed in G if and only if

{
ϕ
(

g
ν

)
}

\{ \phi ({g_\nu })\}

is uniformly distributed in

G
0

{G_0}

? Such a compactification

G
0

{G_0}

is called a D-compactification of G. We obtain a solution to this problem and thereby generalize to locally compact groups some results of Berg, Rajagopalan, and Rubel concerning D-compactifications of locally compact abelian groups.
Normal structure of the one-point stabilizer of a doubly-transitive permutation group. II
Authors: O’Nan Michael E.
Published: July 2010

The main result is that the socle of the point stabilizer of a doubly-transitive permutation group is abelian or the direct product of an abelian group and a simple group. Under certain circumstances, it is proved that the lengths of the orbits of a normal subgroup of the one point stabilizer bound the degree of the group. As a corollary, a fixed nonabelian simple group occurs as a factor of the socle of the one point stabilizer of at most finitely many doubly-transitive groups.
Choline and Osmotic-Stress Tolerance Induced in Arabidopsis by the Soil Microbe Bacillus subtilis (GB03)
Authors: Zhang Huiming , Murzello Cheryl , Sun Yan , Kim Mi-Seong , Xie Xitao , Jeter Randall M. , Zak John C. , Dowd Scot E. , Paré Paul W.
Published: July 2010

Choline (Cho) is an essential nutrient for humans as well as the precursor of glycine betaine (GlyBet), an important compatible solute in eukaryotes that protects cells from osmotic stress caused by dehydrating conditions. The key enzyme for plant Cho synthesis is phosphoethanolamine N-methyltransferase (PEAMT), which catalyzes all three methylation steps, including the rate-limiting N-methylation of phosphoethanolamine. Herein, we report that the beneficial soil bacterium Bacillus subtilis (strain GB03) enhances Arabidopsis Cho and GlyBet synthesis associated with enhanced plant tolerance to osmotic stress. When stressed with 100 mM exogenous mannitol, GB03-exposed plants exhibit increased transcript level of PEAMT compared with stressed plants without bacterial exposure. Endogenous Cho and GlyBet metabolite pools were elevated by more than two- and fivefold, respectively, by GB03 treatment, consistent with increased stress tolerance. Moreover, in the xipotl mutant line with reduced Cho production, a loss of GB03-induced drought tolerance is observed. Osmotic-stressed plants with or without GB03 exposure show similar levels of abscsisic acid (ABA) accumulation in both shoots and roots, suggesting that GB03-induced osmoprotection is ABA independent. GB03 treatment also improves drought tolerance in soil-grown plants as characterized by phenotypic comparisons, supported by an elevated accumulation of osmoprotectants. These results provide a biological strategy to enhance Cho biosynthesis in plants and, in turn, increase plant tolerance to osmotic stress by elevating osmoprotectant accumulation.
Preparing for battle? Potential intergroup conflict promotes current intragroup affiliation
Authors: Radford Andrew N.
Published: July 2010

Groups of human soldiers increase their affiliative behaviour when moving into combat zones. Despite numerous other species also competing as groups, little is known about how potential intergroup conflict might influence current intragroup affiliative behaviour in non-human animals. Here, I show that allopreening (when one individual preens another) increases in groups of cooperatively breeding green woodhoopoes (
Phoeniculus purpureus
) when they enter areas where conflicts with neighbours are more likely. Self-preening, which is an indicator of stress in other species, did not increase in conflict areas, suggesting that the change in affiliative behaviour is not the simple consequence of greater stress. Instead, because it is the dominant breeding pair that increase their preening of subordinate helpers, it is possible that current affiliative behaviour is being exchanged for agonistic support in any intergroup conflicts that might ensue. These results are important for our understanding of group dynamics, cooperation and the evolution of sociality, but also bring to mind the intriguing possibilities of social contracts and future planning in birds.
An investigation of the magnetosphere–ionosphere response to real and idealized co-rotating interaction region events through global magnetohydrodynamic simulations
Authors: Ilie R. , Liemohn M. W. , Kozyra J. , Borovsky J.
Published: July 2010

This study investigates the role of interplanetary magnetic field (IMF)Bzfluctuations periodicity in the transfer of solar wind mass and energy to the magnetosphere during the co-rotating interaction region/high-speed stream event of 10 November 2003 through global modelling simulations using the space weather modelling framework. To do so, we used both solar wind observations and a variety of idealized inputs as upstream boundary conditions, describing different solar wind configurations for which relative contribution of the peak-to-noise ratio in the inputBzpower spectrum to the periodicity transfer is examined. Fast Fourier transforms of both input to and the response of the magnetosphere reveal that the transfer of IMFBzperiodicity to the magnetosphere is unaltered by other solar wind parameters, although the size of the peak-to-noise ratio of the input signal is the controlling factor that determines this transfer. The global magnetosphere simulation suggests that a threshold amount of power (peak-to-noise ratio) of approximately 10 in the input signal is needed for the magnetosphere to react to the periodicity in the inputBz, while for the cross-polar cap potential, the threshold amount is significantly smaller.
Emotions as infectious diseases in a large social network: the SISa model
Authors: Hill Alison L. , Rand David G. , Nowak Martin A. , Christakis Nicholas A.
Published: July 2010

Human populations are arranged in social networks that determine interactions and influence the spread of diseases, behaviours and ideas. We evaluate the spread of long-term emotional states across a social network. We introduce a novel form of the classical susceptible–infected–susceptible disease model which includes the possibility for ‘spontaneous’ (or ‘automatic’) infection, in addition to disease transmission (the SISa model). Using this framework and data from the Framingham Heart Study, we provide formal evidence that positive and negative emotional states behave like infectious diseases spreading across social networks over long periods of time. The probability of becoming content is increased by 0.02 per year for each content contact, and the probability of becoming discontent is increased by 0.04 per year per discontent contact. Our mathematical formalism allows us to derive various quantities from the data, such as the average lifetime of a contentment ‘infection’ (10 years) or discontentment ‘infection’ (5 years). Our results give insight into the transmissive nature of positive and negative emotional states. Determining to what extent particular emotions or behaviours are infectious is a promising direction for further research with important implications for social science, epidemiology and health policy. Our model provides a theoretical framework for studying the interpersonal spread of any state that may also arise spontaneously, such as emotions, behaviours, health states, ideas or diseases with reservoirs.
OsC6, Encoding a Lipid Transfer Protein, Is Required for Postmeiotic Anther Development In Rice
Authors: Zhang Dasheng , Liang Wanqi , Yin Changsong , Zong Jie , Gu Fangwei , Zhang Dabing
Published: July 2010

Synthesis of lipidic components in anthers, including of the pollen exine, is essential for plant male reproductive development. Plant lipid transfer proteins (LTPs) are small, abundant lipid-binding proteins that have the ability to exchange lipids between membranes in vitro. However, their biological role in male reproductive development remains less understood. Here, we report the crucial role of OsC6 in regulating postmeiotic anther development in rice (Oryza sativa). Found in monocots, OsC6 belongs to a distinct clade from previously identified LTP1 and LTP2 family members found in both dicots and monocots. OsC6 expression is mainly detectable in tapetal cells and weakly in microspores from stage 9 to stage 11 of anther development. Immunological assays indicated that OsC6 is widely distributed in anther tissues such as the tapetal cytoplasm, the extracellular space between the tapetum and middle layer, and the anther locule and anther cuticle. Biochemical assays indicated that recombinant OsC6 has lipid binding activity. Moreover, plants in which OsC6 was silenced had defective development of orbicules (i.e. Ubisch bodies) and pollen exine and had reduced pollen fertility. Furthermore, additional evidence is provided that the expression of OsC6 is positively regulated by a basic helix-loop-helix transcription factor, Tapetum Degeneration Retardation (TDR). Extra granule-like structures were observed on the inner surface of the tdr tapetal layer when the expression of OsC6 was driven by the TDR promoter compared with the tdr mutant. These data suggest that OsC6 plays a crucial role in the development of lipidic orbicules and pollen exine during anther development in rice.
Structural polymorphism of pyrazinium hydrogen sulfate: extending chemistry of the pyrazinium salts with small anions
Authors: Budzianowski Armand , Derzsi Mariana , Leszczyński Piotr J. , Cyrański Michał K. , Grochala Wojciech
Published: July 2010

Two polymorphs (α, β) of pyrazinium hydrogen sulfate (pyzH+HSO_4^-, abbreviated as PHS) with distinctly different hydrogen-bond types and topologies but close electronic energies have been synthesized and characterized for the first time. The α-polymorph (P212121) forms distinct blocks in which the pyzH+and HSO_4^- ions are interconnected through a network of NH...O and OH...O hydrogen bonds. The β-form (P\bar 1) consists of infinite chains of alternating pyzH+and HSO_4^- ions connected by NH...O and OH...N hydrogen bonds. Density functional theory (DFT) calculations indicate the possible existence of a hypothetical polarP1 form of the β-polymorph with an unusually high dipole moment.
Polymorphism and piezochromicity in the three-dimensional network-based phosphate RbCuPO4
Authors: Henry Paul F. , Kimber Simon A. J. , Argyriou Dimitri N.
Published: July 2010

Rubidium copper phosphate, RbCuPO4, forms two room-temperature polymorphs that have been investigated with neutron powder diffraction. Polymorph (II) can be converted quantitatively into (I) by grinding the material or by pelletization, and the phase transition is accompanied by a significant colour change from very pale green to sky blue. Polymorph (II) can be obtained essentially free of (I) by quenching from 723 K. Each polymorph shows two unique Cu atoms: in (I) both sites are four-coordinate in a 2:1 ratio, whereas in (II) the atoms are four- and five-coordinate in a 1:1 ratio. In each case these sites are linked by phosphate tetrahedra to form three-dimensional frameworks based on the 42638-afour-connected net. The Rb atoms are hosted in the six- and eight-ring channels that are similar to those observed in zeolite ABW. The (II) → (I) phase transition is also accompanied by a volume reduction of 2.1% even though the average coordination of the Cu atoms also falls. The structures of the polymorphs are critically examined and compared with those of KNiPO4and KCuPO4in terms of hexagonal close packing containing ordered phosphate arrays. As a result of buckling of the six-ring layers, one-dimensional chains of dimerized copper polyhedra are identified in (II), chains that become trimers with mirror symmetry in (I).
Brilliance, innovation and growth – a big talent story
Authors: Timms Perry
Published: July 2010

Purpose

This paper aims to describe how the Big Lottery Fund is developing its leaders of the future through a talent program which may interest other organizations about to – or already engaged in – doing the same.

Design/methodology/approach

A case study approach is taken by this paper in the form of a chronological story describing the journey undertaken, the challenges faced, solutions deployed and ultimately, lessons learned.

Findings

There are several themes which – if starting the process again – would provide a clearer and more rapid path to successes and deliver an even more enriching program experience for those involved/engaged in it.

Research limitations/implications

There is no specific research in this paper, merely the view of the author who has been involved in delivering the program since conceptual thinking.

Practical implications

There are lessons learned, key outcomes identified and potential good practice processes highlighted through this paper.

Originality/value

There is nothing specifically new in this paper other than very recent experience in managing talent in a challenging environment and where no previous programs existed.
Young people's experiences of vocational education and training (VET)
Authors: Lawy Robert
Published: July 2010

Purpose

The aim of the paper is to locate and understand VET provision for young people in England and Scotland as a set of policies and practices that can also be located within a broader Europe‐wide discourse.

Design/methodology/approach

The research drew upon findings from a longitudinal study that comprised interviews with young people who were in JWT at the outset of the research. The work was conducted in the South West of England in 2007 and 2008 and comprised in‐depth interviews with 13 young people, supported with 155 telephone interviews, a focus group session with three young people, and a participative research seminar with 25 key stakeholders.

Findings

The research showed that although there are nuanced differences in approach, the fundamental basis of the policy rhetorics is the same. Whilst the issues and questions in this paper have been informed by the position in the UK and in particular England, it would seem that the same or similar issues and concerns have become part of the mainstream discourse, certainly within the OECD countries and beyond.

Research limitations/implications

The methodology brings a narrative approach (focused upon individual young people), to bear upon a set of policy discourses within the education and skills agenda. Whilst the approach of the paper does not allow for generalisation, it does highlight the problem with a policy focus that fails to take account of what those most affected by the policies actually value and believe.

Originality/value

This paper draws together policy narratives and the experiences of young people.
Integrated distributed bond graph modeling and neural network for fault diagnosis system of hydro turbine governors
Authors: Guo Jiang , Liu Yajin , Xu Xianglian , Chen Qijuan
Published: July 2010

Purpose

The purpose of this paper is to obtain the characteristic parameters of dynamic trend for hydro turbine governors, and take these as the inputs of the neural network to realize the diagnosis of the system.

Design/methodology/approach

Computer simulation technique has become an important tool in the science research and development. Because of the different degree defaults of the traditional modeling method, a distributed bond graph modeling (BGD) method is presented in this paper. Fault diagnosis and identification have been widely developed in recent years, while many kinds of diagnosis methods have been used in this area. Since it is difficult to get the characteristic parameters of dynamic trend, a new methodology is proposed which integrates BGD and neural network. It gets the characteristic parameters by simulation to the system, and takes these as the inputs of the neural network to realize the diagnosis of the system.

Findings

The paper presents the need for application of two models – conventional procedure and bond graph model approaches.

Practical implications

The paper is a very useful diagnosis tool for operators.

Originality/value

A new methodology is proposed which integrates BGD and neural network. The paper is aimed at operational researches and engineers, the results from simulations are reported and commented in the paper.