bluuebunny/crossref_metadata_2025 huggingface dataset:
The automorphism group of a compact group action
Authors: Curtis W. D.
Published: July 2010

This paper contains results on the structure of the group,

Diff
G
r

⁡
(
M
)

\operatorname {Diff} _G^r(M)

, of equivariant

C
r

{C^r}

-diffeomorphisms of a free action of the compact Lie group

G
G

on

M
M

.

Diff
G
r

⁡
(
M
)

\operatorname {Diff} _G^r(M)

is shown to be a locally trivial principal bundle over a submanifold of

Diff
r

(
X
)
,
X

{\operatorname {Diff} ^r}(X),X

the orbit manifold. The structural group of this bundle is

E
r

(
G
,
M
)

{E^r}(G,M)

, the set of equivariant

C
r

{C^r}

-diffeomorphisms which induce the identity on

X
X

.

E
r

(
G
,
M
)

{E^r}(G,M)

is shown to be a submanifold of

Diff
r

(
M
)

{\operatorname {Diff} ^r}(M)

and in fact a Banach Lie group

(
r
>
∞
)

(r > \infty )

.
Isolated invariant sets for flows on vector bundles
Authors: Selgrade James F.
Published: July 2010

This paper studies isolated invariant sets for linear flows on the projective bundle associated to a vector bundle, e.g., the projective tangent flow to a smooth flow on a manifold. It is shown that such invariant sets meet each fiber, roughly in a disjoint union of linear subspaces. Isolated invariant sets which are intersections of attractors and repellers (Morse sets) are discussed. We show that, over a connected chain recurrent set in the base space, a Morse filtration gives a splitting of the projective bundle into a direct sum of invariant subbundles. To each factor in this splitting there corresponds an interval of real numbers (disjoint from those for other factors) which measures the exponential rate of growth of the orbits in that factor. We use these results to see that, over a connected chain recurrent set, the zero section of the vector bundle is isolated if and only if the flow is hyperbolic. From this, it follows that if no equation in the hull of a linear, almost periodic differential equation has a nontrivial bounded solution then the solution space of each equation has a hyperbolic splitting.
Induced automorphisms on Fricke characters of free groups
Authors: Horowitz Robert D.
Published: July 2010

The term character in this paper will denote the character of a group element under a general or indeterminate representation of the group in the special linear group of

2
×
2

2 \times 2

matrices with determinant 1; the properties of characters of this type were first studied by R. Fricke in the late nineteenth century. Theorem 1 determines the automorphisms of a free group which leave the characters invariant. In a previous paper it was shown that the character of each element in the free group

F
n

{F_n}

of finite rank

n
n

can be identified with an element of a certain quotient ring of the commutative ring of polynomials with integer coefficients in

2
n

−
1

{2^n} - 1

indeterminates. It follows that any automorphism of

F
n

{F_n}

induces in a natural way an automorphism on this quotient ring. Corollary 1 shows that for

n
⩾
3

n \geqslant 3

the group of induced automorphisms of

F
n

{F_n}

is isomorphic to the group of outer automorphism classes of

F
n

{F_n}

. The possibility is thus raised that the induced automorphisms may be useful in studying the structure of this group. Theorem 2 gives a characterization for the group of induced automorphisms of

F
2

{F_2}

in terms of an invariant polynomial.
Rings with idempotents in their nuclei
Authors: Rich Michael
Published: July 2010

Let

R
R

be a prime nonassociative ring. If the set of idempotents of

R
R

is a subset of the nucleus of

R
R

or of the alternative nucleus of

R
R

then it is shown that

R
R

is respectively an associative or an alternative ring. Also if

R
R

has one idempotent

≠
0
,
1

\ne 0,1

which is in the Jordan nucleus or in the noncommutative Jordan nucleus then it is shown that

R
R

is respectively a Jordan or a noncommutative Jordan ring.
A generalisation of supersoluble groups
Authors: Haggarty R. J.
Published: July 2010

A

p
p

-soluble group

G
G

belongs to the class

F
(
n
,
p
)

F(n,p)

whenever the ranks of the

p
p

-chief factors of

G
G

divide

n
n

and

G
G

has order coprime to

n
n

. A group in

F
(
n
,
p
)

F(n,p)

is characterised by the embedding of its maximal subgroups. Whenever

N
1

{N_1}

and

N
2

{N_2}

are normal subgroups of

G
G

, of coprime indices in

G
G

, which lie in

F
(
n
,
p
)

F(n,p)

, then

G
G

lies in

F
(
n
,
p
)

F(n,p)

also.

F
(
n
)

F(n)

denotes the intersection, taken over all primes

p
p

, of the classes

F
(
n
,
p
)

F(n,p)

. Simple groups all of whose proper subgroups lie in

F
(
n
)

F(n)

are determined. Given an integer

n
>
2

n > 2

, there exist an integer

m
m

with the same prime divisors as

n
n

and a soluble group

G
G

such that

G
G

lies in

F
(
m
)

F(m)

but

G
G

does not possess a Sylow tower. (We may take

m
=
n

m = n

provided that

n
n

is not a multiple of 1806.) Furthermore, when

n
n

is odd, an example of a soluble group

G
G

, all of whose proper subgroups lie in

F
(
n
)

F(n)

but

G
G

has no Sylow tower, is given.
On constructing least squares solutions to two-point boundary value problems
Authors: Locker John
Published: July 2010

For an

n
n

th order linear boundary value problem

L
f
=

g
0

Lf = {g_0}

in the Hilbert space

L
2

[
a
,
b
]

{L^2}[a,b]

, a sequence of approximate solutions is constructed which converges to the unique least squares solution of minimal norm. The method is practical from a computational viewpoint, and it does not require knowing the null spaces of the differential operator

L
L

or its adjoint

L
∗

{L^ \ast }

.
Theta constants and cusp forms
Authors: Crisalli A. J.
Published: July 2010

For principal congruence subgroups of levels 2 and 4 a basis for their cusp forms consisting of monomials of theta constants is displayed. Some conditions for the vanishing of Poincaré series of these groups are found.
An embedding theorem for matrices of commutative cancellative semigroups
Authors: Streilein James
Published: July 2010

In this paper it is shown that each semigroup which is a matrix of commutative cancellative semigroups has a “quotient semigroup” which is a completely simple semigroup with abelian maximal subgroups. This result is proved by explicitly constructing the quotient semigroup. The paper also gives necessary and sufficient conditions for a semigroup of the type being considered in the paper to be isomorphic to a Rees matrix semigroup over a commutative cancellative semigroup. Several special cases and examples are also briefly discussed.
Two weight function norm inequalities for the Poisson integral
Authors: Muckenhoupt Benjamin
Published: July 2010

Let

f
(
x
)

f(x)

denote a complex valued function with period

2
π

2\pi

, let
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P Subscript r Baseline left-parenthesis f comma x right-parenthesis equals StartFraction 1 Over 2 pi EndFraction integral Subscript negative pi Superscript pi Baseline StartFraction left-parenthesis 1 minus r squared right-parenthesis f left-parenthesis y right-parenthesis d y Over 1 minus 2 r cosine left-parenthesis x minus y right-parenthesis plus r squared EndFraction">

P
r

(
f
,
x
)
=

1

2
π

∫

−
π

π

(
1
−

r
2

)
f
(
y
)
d
y

1
−
2
r
cos
⁡
(
x
−
y
)
+

r
2

{P_r}(f,x) = \frac {1}{{2\pi }}\int _{ - \pi }^\pi {\frac {{(1 - {r^2})f(y)dy}}{{1 - 2r\cos (x - y) + {r^2}}}}

\]
be the Poisson integral of

f
(
x
)

f(x)

and let

|

I

|

|I|

denote the length of an interval

I
I

. For

1
⩽
p
>
∞

1 \leqslant p > \infty

and nonnegative

U
(
x
)

U(x)

and

V
(
x
)

V(x)

with period

2
π

2\pi

it is shown that there is a

C
C

, independent of

f
f

, such that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sup Underscript 0 less-than-or-slanted-equals r greater-than 1 Endscripts integral Subscript negative pi Superscript pi Baseline StartAbsoluteValue upper P Subscript r Baseline left-parenthesis f comma x right-parenthesis EndAbsoluteValue Superscript p Baseline upper U left-parenthesis x right-parenthesis d x less-than-or-slanted-equals upper C integral Subscript negative pi Superscript pi Baseline StartAbsoluteValue f left-parenthesis x right-parenthesis EndAbsoluteValue Superscript p Baseline upper V left-parenthesis x right-parenthesis d x">

sup

0
⩽
r
>
1

∫

−
π

π

|

P
r

(
f
,
x
)

|

p

U
(
x
)
d
x
⩽
C

∫

−
π

π

|

f
(
x
)

|

p

V
(
x
)
d
x

\sup \limits _{0 \leqslant r > 1} \int _{ - \pi }^\pi {|{P_r}(f,x){|^p}U(x)dx \leqslant C\int _{ - \pi }^\pi {|f(x){|^p}V(x)dx} }

\]
if and only if there is a

B
B

such that for all intervals

I
I

\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-bracket StartFraction 1 Over StartAbsoluteValue upper I EndAbsoluteValue EndFraction integral Underscript upper I Endscripts upper U left-parenthesis x right-parenthesis d x right-bracket left-bracket StartFraction 1 Over StartAbsoluteValue upper I EndAbsoluteValue EndFraction integral Underscript upper I Endscripts left-bracket upper V left-parenthesis x right-parenthesis right-bracket Superscript negative 1 slash left-parenthesis p minus 1 right-parenthesis Baseline d x right-bracket Superscript p minus 1 period Baseline less-than-or-slanted-equals upper B period">

[

1

|

I

|

∫
I

U
(
x
)
d
x

]

[

1

|

I

|

∫
I

[
V
(
x
)
]

−
1

/

(
p
−
1
)

d
x

]

p
−
1.

⩽
B
.

\left [ {\frac {1}{{|I|}}\int _I {U(x)dx} } \right ]{\left [ {\frac {1}{{|I|}}\int _I {{{[V(x)]}^{ - 1/(p - 1)}}dx} } \right ]^{p - 1.}} \leqslant B.

\]
Similar results are obtained for the nonperiodic case and in the case where

U
(
x
)
d
x

U(x)dx

and

V
(
x
)
d
x

V(x)dx

are replaced by measures.
Generalized quantifiers and compact logic
Authors: Shelah Saharon
Published: July 2010

We solve a problem of Friedman by showing the existence of a logic stronger than first-order logic even for countable models, but still satisfying the general compactness theorem, assuming e.g. the existence of a weakly compact cardinal. We also discuss several kinds of generalized quantifiers.
Conical vectors in induced modules
Authors: Lepowsky J.
Published: July 2010

Let

g

\mathfrak {g}

be a real semisimple Lie algebra with Iwasawa decomposition

g

=

k

⊕

a

⊕

n

\mathfrak {g} = \mathfrak {k} \oplus \mathfrak {a} \oplus \mathfrak {n}

, and let

m

\mathfrak {m}

be the centralizer of

a

\mathfrak {a}

in

k

\mathfrak {k}

. A conical vector in a

g

\mathfrak {g}

-module is defined to be a nonzero

m

⊕

n

\mathfrak {m} \oplus \mathfrak {n}

-invariant vector. The

g

\mathfrak {g}

-modules which are algebraically induced from one-dimensional

(

m

⊕

a

⊕

n

)

(\mathfrak {m} \oplus \mathfrak {a} \oplus \mathfrak {n})

-modules on which the action of

m

\mathfrak {m}

is trivial have “canonical generators” which are conical vectors. In this paper, all the conical vectors in these

g

\mathfrak {g}

-modules are found, in the special case

dim
⁡

a

=
1

\dim \mathfrak {a} = 1

. The conical vectors have interesting expressions as polynomials in two variables which factor into linear or quadratic factors. Because it is too difficult to determine the conical vectors by direct computation, metamathematical “transfer principles” are proved, to transfer theorems about conical vectors from one Lie algebra to another; this reduces the problem to a special case which can be solved. The whole study is carried out for semisimple symmetric Lie algebras with splitting Cartan subspaces, over arbitrary fields of characteristic zero. An exposition of the Kostant-Mostow double transitivity theorem is included.
Monads defined by involution-preserving adjunctions
Authors: Palmquist Paul H.
Published: July 2010

Consider categories with involutions which fix objects, functors which preserve involution, and natural transformations. In this setting certain natural adjunctions become universal and, thereby, become constructible from abstract data. Although the formal theory of monads fails to apply and the Eilenberg-Moore category fails to fit, both are successfully adapted to this setting, which is a 2-category. In this 2-category, each monad (= triple = standard construction) defined by an adjunction is characterized by a pair of special equations. Special monads have universal adjunctions which realize them and have both underlying Frobenius monads and adjoint monads. Examples of monads which do (respectively, do not) satisfy the special equations arise from finite monoids (= semigroups with unit) which are (respectively, are not) groups acting on the category of linear transformations between finite dimensional Euclidean (= positive definite inner product) spaces over the real numbers. More general situations are exposed.
On automorphism groups and endomorphism rings of abelian 𝑝-groups
Authors: Hausen Jutta
Published: July 2010

Let

A
A

be a noncyclic abelian

p
p

-group where

p
⩾
5

p \geqslant 5

, and let

p
∞

A

{p^\infty }A

be the maximal divisible subgroup of

A
A

. It is shown that

A

/

p
∞

A

A/{p^\infty }A

is bounded and nonzero if and only if the automorphism group of

A
A

contains a minimal noncentral normal subgroup. This leads to the following connection between the ideal structure of certain rings and the normal structure of their groups of units: if the noncommutative ring

R
R

is isomorphic to the full ring of endomorphisms of an abelian

p
p

-group,

p
⩾
5

p \geqslant 5

, then

R
R

contains minimal twosided ideals if and only if the group of units of

R
R

contains minimal noncentral normal subgroups.
Characteristic principal bundles
Authors: Smith Harvey A.
Published: July 2010

Characteristic principal bundles are the duals of commutative twisted group algebras. A principal bundle with locally compact second countable (Abelian) group and base space is characteristic iff it supports a continuous eigenfunction for almost every character measurably in the characters, also iff it is the quotient by Z of a principal E-bundle for every E in

Ext

(
G
,
Z
)

{\operatorname {Ext}}(G,Z)

and a measurability condition holds. If a bundle is locally trivial, n.a.s.c. for it to be such a quotient are given in terms of the local transformations and Čech cohomology of the base space. Although characteristic G-bundles need not be locally trivial, the class of characteristic G-bundles is a homotopy invariant of the base space. The isomorphism classes of commutative twisted group algebras over G with values in a given commutative

C
∗

{C^\ast }

-algebra A are classified by the extensions of G by the integer first Čech cohomology group of the maximal ideal space of A.
The absolute continuity of phase operators
Authors: Dombrowski J. , Fricke G. H.
Published: July 2010

This paper studies the spectral properties of a class of operators known as phase operators which originated in the study of harmonic oscillator phase. Ifantis conjectured that such operators had no point spectrum. It was later shown that certain phase operators were, in fact, absolutely continuous and that all phase operators at least had an absolutely continuous part. The present work completes the discussion by showing that all phase operators are absolutely continuous.
Semifree actions on homotopy spheres
Authors: Wang Kai
Published: July 2010

In this paper, we study the semifree

Z
m

{Z_m}

actions on homotopy sphere pairs. We show that in some cases the equivariant normal bundle to the fixed point set is equivariantly stably trivial. We compute the rank of the torsion free part of the group of semifree actions on homotopy sphere pairs in some cases. We also show that there exist infinitely many semifree

Z

4
s

{Z_{4s}}

actions on even dimensional homotopy sphere pairs.
Torus actions on a cohomology product of three odd spheres
Authors: Allday Christopher
Published: July 2010

The main purpose of this paper is to describe how a torus group may act on a space,

X
X

, whose rational cohomology ring is isomorphic to that of a product of three odd-dimensional spheres, in such a way that the fixed point set is nonempty, and

X
X

is not totally nonhomologous to zero in the associated

X
X

-bundle,

X
T

→

B
T

{X_T} \to {B_T}

. In the first section of the paper some general results on the cohomology theory of torus actions are established. In the second section the cohomology theory of the above type of action is described; and in the third section the results of the first two sections are used to prove a Golber formula for such actions, which, under certain conditions, bears an interesting interpretation in terms of rational homotopy.
Conservative dynamical systems involving strong forces
Authors: Gordon William B.
Published: July 2010

We consider conservative dynamical systems associated with potentials

V
V

which have singularities at a set

S
:
V
(
x
)
→
−
∞

S:V(x) \to - \infty

as

x
→
S

x \to S

. It is shown that various “action” integrals satisfy Condition

C
C

of Palais and Smale provided that the potential satisfy a certain strong force (SF) condition. Hence, e.g., we establish the existence in SF systems of periodic trajectories which wind around

S
S

and have arbitrary given topological (homotopy) type and which have arbitrary given period, and also periodic trajectories which make arbitrarily tight loops around

S
S

. Similar results are also obtained concerning the existence of trajectories which wind around

S
S

and join two given points. The SF condition is shown to be closely related to the completeness (in the riemannian sense) of certain Jacobi metrics associated with the potential

V
V

, and this fact permits the use of the standard results of riemannian geometry in the analysis of SF systems. The SF condition excludes the gravitational case, and the action integrals do not satisfy the Palais-Smale condition in the gravitational case. The Jacobi metrics associated with gravitational potentials are not complete. For SF systems there exist trajectories which join two given points and make arbitrarily tight loops around

S
S

, and this is not the case in the gravitational two body problem. On the other hand, for SF systems any smooth family of

λ
\lambda

-periodic trajectories (

λ
\lambda

fixed) is bounded away from

S
S

, and this also is not the case for gravitational systems. Thus the definition of the SF condition is “well motivated", and leads to the disclosure of certain differences between the behavior of SF systems and gravitational (and other weak force) systems.
𝐼-rings
Authors: Nicholson W. K.
Published: July 2010

A ring

R
R

, possibly with no identity, is called an

I
0

{I_0}

-ring if each one-sided ideal not contained in the Jacobson radical

J
(
R
)

J(R)

contains a nonzero idempotent. If, in addition, idempotents can be lifted modulo

J
(
R
)
,
R

J(R),R

is called an

I
I

-ring. A survey of when these properties are inherited by related rings is given. Maximal idempotents are examined and conditions when

I
0

{I_0}

-rings have an identity are given. It is shown that, in an

I
0

{I_0}

-ring

R
R

, primitive idempotents are local and primitive idempotents in

R

/

J
(
R
)

R/J(R)

can always be lifted. This yields some characterizations of

I
0

{I_0}

-rings

R
R

such that

R

/

J
(
R
)

R/J(R)

is primitive with nonzero socle. A ring

R
R

(possibly with no identity) is called semiperfect if

R

/

J
(
R
)

R/J(R)

is semisimple artinian and idempotents can be lifted modulo

J
(
R
)

J(R)

. These rings are characterized in several new ways: among them as

I
0

{I_0}

-rings with no infinite orthogonal family of idempotents, and as

I
0

{I_0}

-rings

R
R

with

R

/

J
(
R
)

R/J(R)

semisimple artinian. Several other properties are derived. The connection between

I
0

{I_0}

-rings and the notion of a regular module is explored. The rings

R
R

which have a regular module

M
M

such that

J
(
R
)
=
ann
⁡
(
M
)

J(R) = \operatorname {ann} (M)

are studied. In particular they are

I
0

{I_0}

-rings. In addition, it is shown that, over an

I
0

{I_0}

-ring, the endomorphism ring of a regular module is an

I
0

{I_0}

-ring with zero radical.
Under the degree of some finite linear groups. II
Authors: Blau Harvey I.
Published: July 2010

Let

G
G

be a finite group with a cyclic Sylow

p
p

-subgroup for some prime

p
≥
13

p \geq 13

. Assume that

G
G

is not of type

L
2

(
p
)

{L_2}(p)

, and that

G
G

has a faithful indecomposable modular representation of degree

d
≤
p

d \leq p

. Some known lower bounds for

d
d

are improved, in case the center of the group is trivial, as a consequence of results on the degrees

(
mod

p
)

\pmod p

of irreducible Brauer characters in the principal

p
p

-block.
Topological properties of subanalytic sets
Authors: Hardt Robert M.
Published: July 2010

The stratification of a semianalytic or subanalytic set (that is, a set which locally is the proper analytic image of some semianalytic set) leads easily, by consecutive projections in Euclidean space, to a CW decomposition. In the category of subanalytic sets and continuous maps with subanalytic graphs, theories of slicing, intersection, and homology result through use of the topological chains defined by subanalytic sets.
Duality for Hadamard products with applications to extremal problems for functions regular in the unit disc
Authors: Ruscheweyh Stephan
Published: July 2010

Let

A
A

be the set of functions regular in the unit disc

U

\mathcal {U}

and

A
0

{A_0}

the set of all functions

f
∈
A

f \in A

which satisfy

f
(
0
)
=
1

f(0) = 1

. For

V
⊂

A
0

V \subset {A_0}

define the dual set
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper V Superscript asterisk Baseline equals left-brace f element-of upper A 0 vertical-bar f asterisk g not-equals 0 for all g element-of upper V comma z element-of script upper U right-brace comma upper V Superscript asterisk asterisk Baseline equals left-parenthesis upper V Superscript asterisk Baseline right-parenthesis Superscript asterisk">

V
∗

=
{
f
∈

A
0

|

f
∗
g
≠
0

 for all 

g
∈
V
,
z
∈

U

}
,

V

∗
∗

=

(

V
∗

)
∗

{V^ \ast } = \{ f \in {A_0}|f \ast g \ne 0{\text { for all }}g \in V,z \in \mathcal {U}\} ,{V^{ \ast \ast }} = {({V^ \ast })^ \ast }

. Here

f
∗
g

f \ast g

denotes the Hadamard product. THEOREM. Let

V
⊂

A
0

V \subset {A_0}

have the following properties: (i)

V
V

is compact, (ii)

f
∈
V

f \in V

implies

f
(
x
z
)
∈
V

f(xz) \in V

for all

|

x

|

⩽
1

|x| \leqslant 1

. Then

λ
(
V
)
=
λ
(

V

∗
∗

)

\lambda (V) = \lambda ({V^{ \ast \ast }})

for all continuous linear functionals

λ
\lambda

on

A
A

. This theorem has many applications to functions in

A
A

which are defined by properties like bounded real part, close-to-convexity, univalence etc.
Extensions and liftings of positive linear mappings on Banach lattices
Authors: Lotz Heinrich P.
Published: July 2010

Let F be a closed sublattice of a Banach lattice G. We show that any positive linear mapping from F into

L
1

(
μ
)

{L^1}(\mu )

or

C
(
X
)

C(X)

for a Stonian space X has a positive norm preserving extension to G. A dual result for positive norm preserving liftings is also established. These results are applied to obtain extension and lifting theorems for order summable and majorizing linear mappings. We also obtain some partial results concerning positive extensions and liftings of compact linear mappings.
Binary digit distribution over naturally defined sequences
Authors: Newman D. J. , Slater Morton
Published: July 2010

In a previous paper the first author showed that multiples of 3 prefer to have an even number of ones in their binary digit expansion. In this paper it is shown that in some general classes of naturally defined sequences, the probability that a member of a particular sequence has an even number of ones in its binary expansion is

1

/

2

1/2

.
On the extension of mappings in Stone-Weierstrass spaces
Authors: D’Aristotle Anthony J.
Published: July 2010

N. Veličko generalized the well-known result of A. D. Taĭmanov on the extension of continuous functions by showing that Taĭmanov’s theorem holds when

Y
Y

(the image space) is

H
H

-closed and Urysohn and the mapping

f
f

is weakly

θ
\theta

-continuous. We obtain, in a more direct fashion, an even stronger generalization of this theorem. We proceed to show that the class of all SW spaces is not reflective in the category of all completely Hausdorff spaces and continuous mappings. However, an epi-reflective situation is achieved by suitably enlarging the class of admissible morphisms. We conclude by establishing a number of results about SW extension spaces.
Strongly prime rings
Authors: Handelman David , Lawrence John
Published: July 2010

A ring R is (right) strongly prime (SP) if every nonzero twosided ideal contains a finite set whose right annihilator is zero. Examples are domains, prime Goldie rings and simple rings; however, this notion is asymmetric and a right but not left SP ring is exhibited. All SP rings are prime, and every prime ring may be embedded in an SP ring. SP rings are nonsingular, and a regular SP ring is simple; since faithful rings of quotients of SP rings are SP, the complete ring of quotients of an SP ring is simple. All SP rings are coefficient rings for some primitive group ring (a generalization of a result proved for domains by Formanek), and this was the initial motivation for their study. If the group ring RG is SP, then R is SP and G contains no nontrivial locally finite normal subgroups. Coincidentally, SP rings coincide with the ATF rings of Rubin, and so every SP ring has a unique maximal proper torsion theory, and (0) and R are the only torsion ideals.(

1

^{1}

) A list of questions is appended.
Flat analytic extensions
Authors: Viola-Prioli Ana M. D.
Published: July 2010

This paper is concerned, in the first place, with the conditions to be imposed on an ideal

I
I

of the power series ring in one indeterminate

A
[
[
x
]
]

A[[x]]

(

A
A

noetherian) in order that the analytic extension

B
=
A
[
[
x
]
]

/

I

B = A[[x]]/I

be a flat

A
A

-module. Also the relationship between the projectivity and finiteness of

B
B

is found when the content of

I
I

(the ideal of

A
A

generated by the coefficients of all power series in

I
I

) equals

A
A

. A generalization of this result to the power series ring in any finite number of indeterminates is obtained when

A
A

is local, noetherian of Krull

dim
≥
1

\dim \geq 1

, and under certain restrictions on

I
I

, for the global case but only for domains. Finally, a contribution to the problem of the finiteness of

I
I

when

A
[
[
x
]
]

/

I

A[[x]]/I

is a flat analytic extension is given for

A
A

a local ring, not necessarily noetherian.
Conversion from nonstandard to standard measure spaces and applications in probability theory
Authors: Loeb Peter A.
Published: July 2010

Let

(
X
,

A

,
ν
)

(X,\mathcal {A},\nu )

be an internal measure space in a denumerably comprehensive enlargement. The set X is a standard measure space when equipped with the smallest standard

σ
\sigma

-algebra

M

\mathfrak {M}

containing the algebra

A

\mathcal {A}

, where the extended real-valued measure

μ
\mu

on

M

\mathfrak {M}

is generated by the standard part of

ν
\nu

. If f is

A

\mathcal {A}

-measurable, then its standard part

0

f

^0f

is

M

\mathfrak {M}

-measurable on X. If f and

μ
\mu

are finite, then the

ν
\nu

-integral of f is infinitely close to the

μ
\mu

-integral of

0

f

^0f

. Applications include coin tossing and Poisson processes. In particular, there is an elementary proof of the strong Markov property for the stopping time of the jth event and a construction of standard sample functions for Poisson processes.
The hyperspace of the closed unit interval is a Hilbert cube
Authors: Schori R. M. , West J. E.
Published: July 2010

Let X be a compact metric space and let

2
X

{2^X}

be the space of all nonvoid closed subsets of X topologized with the Hausdorff metric. For the closed unit interval I the authors prove that

2
I

{2^I}

is homeomorphic to the Hilbert cube

I
∞

{I^\infty }

, settling a conjecture of Wojdyslawski that was posed in 1938. The proof utilizes inverse limits and near-homeomorphisms, and uses (and developes) several techniques and theorems in infinite-dimensional topology.
𝑍-sets in ANR’s
Authors: Henderson David W.
Published: July 2010

(1) Let A be a closed Z-set in an ANR X. Let

F

\mathcal {F}

be an open cover of X. Then there is a homotopy inverse

f
:
X
→
X
−
A

f:X \to X - A

to the inclusion

X
−
A
→
X

X - A \to X

such that f and both homotopies are limited by

F

\mathcal {F}

. (2) If, in addition, X is a manifold modeled on a metrizable locally convex TVS, F, such that F is homeomorphic to

F
ω

{F^\omega }

, then there is a homotopy

j
:
X
×
I
→
X

j:X \times I \to X

limited by

F

\mathcal {F}

such that the closure (in X) of

j
(
X
×
{
1
}
)

j(X \times \{ 1\} )

is contained in

X
−
A

X - A

.
Ramsey graphs and block designs. I
Authors: Parsons T. D.
Published: July 2010

This paper establishes a connection between a certain class of Ramsey numbers for graphs and the class of symmetric block designs admitting a polarity. The main case considered here relates the projective planes over Galois fields to the Ramsey numbers

R
(

C
4

,

K

1
,
n

)
=
f
(
n
)

R({C_4},{K_{1,n}}) = f(n)

. It is shown that, for every prime power

q
,
f
(

q
2

+
1
)
=

q
2

+
q
+
2

q,f({q^2} + 1) = {q^2} + q + 2

, and

f
(

q
2

)
=

q
2

+
q
+
1

f({q^2}) = {q^2} + q + 1

.
Spectral analysis of finite convolution operators
Authors: Frankfurt Richard
Published: July 2010

In this paper the similarity problem for operators of the form
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis asterisk right-parenthesis upper T colon f left-parenthesis x right-parenthesis right-arrow integral Subscript 0 Superscript x Baseline k left-parenthesis x minus t right-parenthesis f left-parenthesis t right-parenthesis d t">

(
∗
)

T
:
f
(
x
)
→

∫
0
x

k
(
x
−
t
)
f
(
t
)
d
t

( \ast )\;T:f(x) \to \smallint _0^xk(x - t)f(t)dt

on

L
2

(
0
,
1
)

{L^2}(0,1)

is studied. Let

K
(
z
)
=

∫
0
1

k
(
t
)

e

i
t
z

d
t

K(z) = \smallint _0^1\;k(t){e^{itz}}dt

. A function

C
(
z
)

C(z)

is called a symbol for T if

C
(
z
)

C(z)

can be written in the form

C
(
z
)
=
K
(
z
)
+

e

i
z

G
(
z
)

C(z) = K(z) + {e^{iz}}G(z)

, where

G
(
z
)

G(z)

is a function bounded and analytic in a half plane

y
>
δ

y > \delta

, for some real number

δ
\delta

. Under suitable restrictions, it is shown that two operators of the form

(
∗
)

( \ast )

will be similar if they possess symbols which are asymptotically close together as

z
→
∞

z \to \infty

in some half plane

y
>
δ

y > \delta

.
The zeroes of nonnegative holomorphic curvature operators
Authors: Naveira A. M. , Fuertes C.
Published: July 2010

Here, we study the structure of points in a holomorphic Grassmann’s submanifold where the holomorphic sectional curvature assumes its minimum and maximum. For spaces of nonnegative holomorphic sectional curvature we study the set of points on which it assumes the value zero. We show that the minimum and maximum sets of holomorphic sectional curvature are the intersections of a holomorphic Grassmann’s submanifold with linear complex holomorphic subspaces of type (1, 1).
Pointwise bounds on eigenfunctions and wave packets in 𝑁-body quantum systems. III
Authors: Simon Barry
Published: July 2010

We provide a number of bounds of the form
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue psi EndAbsoluteValue less-than-or-slanted-equals upper O left-parenthesis exp left-parenthesis minus alpha StartAbsoluteValue x EndAbsoluteValue Superscript alpha Baseline right-parenthesis right-parenthesis comma alpha greater-than 1">

|

ψ

|

⩽
O
(
exp
⁡
(
−
α

|

x

|

α

)
)
,
α
>
1

|\psi | \leqslant O(\exp ( - \alpha |x{|^\alpha })),\alpha > 1

, for

L
2

{L^2}

-eigenfunctions

ψ
\psi

of

−
Δ
+
V

- \Delta + V

with

V
→
∞

V \to \infty

rapidly as

|

x

|

→
∞

|x| \to \infty

. Our strongest results assert that if

|

V
(
x
)

|

⩾
c

x

2
m

|V(x)| \geqslant c{x^{2m}}

near infinity, then
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue psi left-parenthesis x right-parenthesis EndAbsoluteValue less-than-or-slanted-equals upper D Subscript epsilon Baseline exp left-parenthesis minus left-parenthesis c minus epsilon right-parenthesis Superscript 1 slash 2 Baseline left-parenthesis m plus 1 right-parenthesis Superscript negative 1 Baseline x Superscript m plus 1 Baseline right-parenthesis">

|

ψ
(
x
)

|

⩽

D
ε

exp
⁡
(
−

(
c
−
ε

)

1

/

2

(
m
+
1

)

−
1

x

m
+
1

)

|\psi (x)| \leqslant {D _\varepsilon }\exp ( - {(c - \varepsilon )^{1/2}}{(m + 1)^{ - 1}}{x^{m + 1}})

, and if

|

V
(
x
)

|

⩽
c

x

2
m

|V(x)| \leqslant c{x^{2m}}

neat infinity, then for the ground state eigenfunction,
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Omega comma normal upper Omega left-parenthesis x right-parenthesis greater-than-or-slanted-equals upper E Subscript epsilon Baseline exp left-parenthesis minus left-parenthesis c plus epsilon right-parenthesis Superscript 1 slash 2 Baseline left-parenthesis m plus 1 right-parenthesis Superscript negative 1 Baseline x Superscript m plus 1 Baseline right-parenthesis">

Ω
,
Ω
(
x
)
⩾

E
ε

exp
⁡
(
−

(
c
+
ε

)

1

/

2

(
m
+
1

)

−
1

x

m
+
1

)

\Omega ,\Omega (x) \geqslant {E _\varepsilon }\exp ( - {(c + \varepsilon )^{1/2}}{(m + 1)^{ - 1}}{x^{m + 1}})

.
On coverings and hyperalgebras of affine algebraic groups
Authors: Takeuchi Mitsuhiro
Published: July 2010

Over an algebraically closed field of characteristic zero, the universal group covering of a connected affine algebraic group, if such exists, can be constructed canonically from its Lie algebra only. In particular the isomorphism classes of simply connected affine algebraic groups are in 1-1 correspondence with the isomorphism classes of finite dimensional Lie algebras of some sort. We shall consider the counterpart of these results (due to Hochschild) in case of a positive characteristic, replacing the Lie algebra by the “hyperalgebra". We show that the universal group covering of a connected affine algebraic group scheme can be constructed canonically from its hyperalgebra only and hence, in particular, that the category of simply connected affine algebraic group schemes is equivalent to a subcategory of the category of hyperalgebras of finite type which contains all the semisimple hyperalgebras.
Commuting and topological densities and liftings
Authors: McMinn Trevor J.
Published: July 2010

For fairly general conditions on a measure space, a group of bijections on the space and a topology on the space, densities and lifttings commuting with members of the group and with topologies finer than the given topology are obtained.
A property of finite 𝑝-groups with trivial multiplicator
Authors: Jones Michael R.
Published: July 2010

A sufficient condition for a finite

2
2

-generator

p
p

-group to have nontrivial multiplicator is given. To show that this result is best possible, a finite

2
2

-group with trivial multiplicator is constructed.
Embeddings and immersions of manifolds in Euclidean space
Authors: Bausum David R.
Published: July 2010

The problem of computing the number of embeddings or immersions of a manifold in Euclidean space is treated from a different point of view than is usually taken. Also, a theorem dealing with the existence of an embedding of

M
m

{M^m}

in

R

2
m
−
2

{R^{2m - 2}}

is given.
Obstruction theory with coefficients in a spectrum
Authors: Mahowald Mark , Rigdon Robert
Published: July 2010

In this paper an obstruction theory with coefficients in a spectrum is developed. An idea of orientability of a fiber bundle with respect to a spectrum is introduced and for bundles orientable with respect to the spectrum a resolution is produced which corresponds to a modified Postnikov tower in the classical case.
Generalized inverses and spectral theory
Authors: Apostol Constantin , Clancey Kevin
Published: July 2010

The concept of a generalized spectral projection associated with a subset in the semi-Fredholm domain of a bounded operator on a Hilbert space is introduced. These generalized spectral projections possess many of the desirable properties of spectral projections associated with spectral sets. In particular, generalized spectral projections are used to separate finite sets of singular points from the semi-Fredholm domain.
Composition series and intertwining operators for the spherical principal series. II
Authors: Johnson Kenneth D.
Published: July 2010

In this paper, we consider the connected split rank one Lie group of real type

F
4

{F_4}

which we denote by

F
4
1

F_4^1

. We first exhibit

F
4
1

F_4^1

as a group of operators on the complexification of A. A. Albert’s exceptional simple Jordan algebra. This enables us to explicitly realize the symmetric space

F
4
1

/

Spin

(
9
)

F_4^1/{\text {Spin}}(9)

as the unit ball in

R

16

{{\mathbf {R}}^{16}}

with boundary

S

15

{S^{15}}

. After decomposing the space of spherical harmonics under the action of

Spin

(
9
)

{\text {Spin}}(9)

, we obtain the matrix of a transvection operator of

F
4
1

/Spin

(
9
)

F_4^1{\text {/Spin}}(9)

acting on a spherical principal series representation. We are then able to completely determine the Jordan Holder series of any spherical principal series representation of

F
4
1

F_4^1

.
An index theorem for 𝑝-adic differential operators
Authors: Adolphson A.
Published: July 2010

A system of first order linear differential operators satisfying conditions arising naturally in geometry (rational function coefficients, regular singularities, non-Liouville exponents) is considered. It is shown that the index of the system on certain spaces of holomorphic functions can be calculated by restricting to a subspace of rational functions. This is applied to obtain an explicit formula for the index of a single kth order linear differential operator.
Units and one-sided units in regular rings
Authors: Ehrlich Gertrude
Published: July 2010

A ring R is unit regular if for every

a
∈
R

a \in R

, there is a unit

x
∈
R

x \in R

such that

a
x
a
=
a

axa = a

, and one-sided unit regular if for every

a
∈
R

a \in R

, there is a right or left invertible element

x
∈
R

x \in R

such that

a
x
a
=
a

axa = a

. In this paper, unit regularity and one-sided unit regularity are characterized within the lattice of principal right ideals of a regular ring R (Theorem 3). If M is an A-module and

R
=

End
A

R = {\text {End}_A}

M is a regular ring, then R is unit regular if and only if complements of isomorphic summands of M are isomorphic, and R is one-sided unit regular if and only if complements of isomorphic summands of M are comparable with respect to the relation “is isomorphic to a submodule of” (Theorem 2). A class of modules is given for whose endomorphism rings it is the case that regularity in conjunction with von Neumann finiteness is equivalent to unit regularity. This class includes all abelian torsion groups and all nonreduced abelian groups with regular endomorphism rings.
An asymptotic formula for an integral in starlike function theory
Authors: London R. R. , Thomas D. K.
Published: July 2010

The paper is concerned with the integral
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H equals integral Subscript 0 Superscript 2 pi Baseline StartAbsoluteValue f EndAbsoluteValue Superscript sigma Baseline StartAbsoluteValue upper F EndAbsoluteValue Superscript tau Baseline left-parenthesis upper R e upper F right-parenthesis Superscript kappa Baseline d theta">

H
=

∫
0

2
π

|

f

|

σ

|

F

|

τ

(
Re
⁡
F

)
κ

d
θ

H = \int _0^{2\pi }|f{|^\sigma }|F{|^\tau }{(\operatorname {Re} F)^\kappa }\;d\theta

\]
in which f is a function regular and starlike in the unit disc,

F
=
z

f
′

/

f

F = zf’/f

, and the parameters

σ
,
τ
,
κ

\sigma ,\tau ,\kappa

are real. A study of H is of interest since various well-known integrals in the theory, such as the length of

f
(

|

z

|

=
r
)

f(|z| = r)

, the area of

f
(

|

z

|

⩽
r
)

f(|z| \leqslant r)

, and the integral means of f, are essentially obtained from it by suitably choosing the parameters. An asymptotic formula, valid as

r
→
1

r \to 1

, is obtained for H when f is a starlike function of positive order

α
\alpha

, and the parameters satisfy

α
σ
+
τ
+
κ
>
1
,
τ
+
κ
⩾
0
,
κ
⩾
0
,
σ
>
0

\alpha \sigma + \tau + \kappa > 1,\tau + \kappa \geqslant 0,\kappa \geqslant 0,\sigma > 0

. Several easy applications of this result are made; some to obtaining old results, two others in proving conjectures of Holland and Thomas.
Signature of links
Authors: Kauffman Louis H. , Taylor Laurence R.
Published: July 2010

Let L be an oriented tame link in the three sphere

S
3

{S^3}

. We study the Murasugi signature,

σ
(
L
)

\sigma (L)

, and the nullity,

η
(
L
)

\eta (L)

. It is shown that

σ
(
L
)

\sigma (L)

is a locally flat topological concordance invariant and that

η
(
L
)

\eta (L)

is a topological concordance invariant (no local flatness assumption here). Known results about the signature are re-proved (in some cases generalized) using branched coverings.
Generalized and classical solutions of the nonlinear stationary Navier-Stokes equations
Authors: Shapiro Victor L.
Published: July 2010

New regularity results in domains of Euclidean 3-space are established for the generalized solutions of the nonlinear stationary Navier-Stokes equations in terms of Dini criteria on the external force.
Some locally convex spaces of continuous vector-valued functions over a completely regular space and their duals
Authors: Katsaras A.
Published: July 2010

The strict, superstrict and the

β
F

{\beta _F}

topologies are defined on a space A of continuous functions from a completely regular space into a Banach space E. Properties of these topologies are discussed and the corresponding dual spaces are identified with certain spaces of operator-valued measures. In case E is a Banach lattice, A becomes a lattice under the pointwise ordering and the strict and superstrict duals of A coincide with the spaces of all

τ
\tau

-additive and all

σ
\sigma

-additive functionals on A respectively.
On the torus theorem and its applications
Authors: Feustel C. D.
Published: July 2010

In this paper, we prove the torus theorem and that manifolds in a certain class of 3-manifolds with toral boundary are determined by their fundamental groups alone. Both of these results were reported by F. Waldhausen. We also give an extension of Waldhausen’s generalization of the loop theorem.
Bernoulli convolutions and differentiable functions
Authors: Kaufman R.
Published: July 2010

Bernoulli convolutions, similar in structure to convolutions with a constant ratio, are considered in relation to differentiable transformations. A space of functions on the Cantor set leads to highly singular measures that nevertheless resemble absolutely continuous measures sufficiently to control their Fourier-Stieltjes transforms.
Total mean curvature of immersed surfaces in 𝐸^{𝑚}
Authors: Chen Bang-yen
Published: July 2010

Total mean curvature and value-distribution of mean curvature for certain pseudo-umbilical surfaces are studied.
Real prime flows
Authors: Keynes H. B. , Newton D.
Published: July 2010

In this paper, we construct examples of real-type prime flows and study these examples in detail. General properties of prime flows are studied, with emphasis on proximality conditions and properties of automorphisms. Examples of prime flows which are not POD are shown to exist, and results analogous to number-theoretic properties, such as a “unique factorisation” theorem, are shown to hold for prime flows.
Partitions of large multipartites with congruence conditions. I
Authors: Robertson M. M. , Spencer D.
Published: July 2010

Let

p
(

n
1

,
…
,

n
j

:

A
1

,
…
,

A
j

)

p({n_1}, \ldots ,{n_j}:{A_1}, \ldots ,{A_j})

be the number of partitions of

(

n
1

,
…
,

n
j

)

({n_1}, \ldots ,{n_j})

where, for

1
⩽
l
⩽
j

1 \leqslant l \leqslant j

, the lth component of each part belongs to the set
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A Subscript l Baseline equals union Underscript h left-parenthesis l right-parenthesis equals 1 Overscript q left-parenthesis l right-parenthesis Endscripts left-brace a Subscript l h left-parenthesis l right-parenthesis Baseline plus upper M v colon v equals 0 comma 1 comma 2 comma ellipsis right-brace">

A
l

=

⋃

h
(
l
)
=
1

q
(
l
)

{

a

l
h
(
l
)

+
M
v
:
v
=
0
,
1
,
2
,
…
}

{A_l} = \bigcup \nolimits _{h(l) = 1}^{q(l)} {\{ {a_{lh(l)}} + Mv :v = 0,1,2, \ldots \} }

and

M
,
q
(
l
)

M,q(l)

and the

a

l
h
(
l
)

{a_{lh(l)}}

are positive integers such that

0
>

a

l
1

>
⋯
>

a

l
q
(
l
)

⩽
M

0 > {a_{l1}} > \cdots > {a_{lq(l)}} \leqslant M

. Asymptotic expansions for

p
(

n
1

,
…
,

n
j

:

A
1

,
…
,

A
j

)

p({n_1}, \ldots ,{n_j}:{A_1}, \ldots ,{A_j})

are derived, when the

n
l

→
∞

{n_l} \to \infty

subject to the restriction that

n
1

⋯

n
j

⩽

n
l

j
+
1
−
∈

{n_1} \cdots {n_j} \leqslant n_l^{j + 1 - \in }

for all l, where

∈
\in

is any fixed positive number. The case

M
=
1

M = 1

and arbitrary j was investigated by Robertson [10] while several authors between 1940 and 1960 investigated the case

j
=
1

j = 1

for different values of M.
On polar relations of abstract homogeneous polynomials
Authors: Zaheer Neyamat
Published: July 2010

In this paper we generalize, to vector spaces over algebraically closed fields of characteristic zero, two well-known classical results due to Laguerre and Grace, concerning, respectively, the relative location of the zeros of a complex-valued polynomial and its polar-derivative and the relative location of the zeros of two apolar polynomials. Vector space analogues of their results were generalized, to a certain degree, by Hörmander, Marden, and Zervos. Our results in this paper further generalize their results and, in the complex plane, improve upon those of Laguerre and Grace. Besides, the present treatment unifies their completely independent approaches into an improved and more systematic and abstract theory. We have also shown that our results are best possible in the sense that they cannot be further generalized in certain directions.
Infinite-dimensional Whitehead and Vietoris theorems in shape and pro-homotopy
Authors: Edwards David A. , Geoghegan Ross
Published: July 2010

In Theorem 3.3 and Remark 3.4 conditions are given under which an infinite-dimensional Whitehead theorem holds in pro-homotopy. Applications to shape theory are given in Theorems 1.1, 1.2, 4.1 and 4.2.
Equivariant stable homotopy and framed bordism
Authors: Kosniowski Czes
Published: July 2010

This paper gives an elementary proof of the result that equivariant stable homotopy is the same as equivariant framed bordism.
Isotropic transport process on a Riemannian manifold
Authors: Pinsky Mark A.
Published: July 2010

We construct a canonical Markov process on the tangent bundle of a complete Riemannian manifold, which generalizes the isotropic scattering transport process on Euclidean space. By inserting a small parameter it is proved that the transition semigroup converges to the Brownian motion semigroup provided that the latter preserves the class

C
0

{C_0}

. The special case of a manifold of negative curvature is considered as an illustration.