bluuebunny/crossref_metadata_2025 huggingface dataset:
Approximating topological metrics by Riemannian metrics
Authors: Ferry Steven C. , Okun Boris L.
Published: June 2010

We study the relation between (topological) inner metrics and Riemannian metrics on smoothable manifolds. We show that inner metrics on smoothable manifolds can be approximated by Riemannian metrics. More generally, if

f
:
M
→
X

f:M \to X

is a continuous surjection from a smooth manifold to a compact metric space with

f

−
1

(
x
)

{f^{ - 1}}(x)

connected for every

x
∈
X

x \in X

, then there is a metric d on X and a sequence of Riemannian metrics

{

ψ
i

}

\{ {\psi _i}\}

on M so that

(
M
,

ψ
i

)

(M,{\psi _i})

converges to (X, d) in Gromov-Hausdorff space. This is used to obtain a (fixed) contractibility function

ρ
\rho

and a sequence of Riemannian manifolds with

ρ
\rho

as contractibility function so that

lim
(
M
,

ψ
i

)

\lim (M,{\psi _i})

is infinite dimensional. Using results of Dranishnikov and Ferry, this also gives examples of nonhomeomorphic manifolds M and N and a contractibility function

ρ
\rho

so that for every

ε
>
0

\varepsilon > 0

there are Riemannian metrics

ϕ
ε

{\phi _\varepsilon }

and

ψ
ε

{\psi _\varepsilon }

on M and N so that

(
M
,

ϕ
ε

)

(M,{\phi _\varepsilon })

and

(
N
,

ψ
ε

)

(N,{\psi _\varepsilon })

have contractibility function

ρ
\rho

and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="d Subscript upper G upper H Baseline left-parenthesis left-parenthesis upper M comma phi Subscript epsilon Baseline right-parenthesis comma left-parenthesis upper N comma psi Subscript epsilon Baseline right-parenthesis right-parenthesis greater-than epsilon">

d

G
H

(
(
M
,

ϕ
ε

)
,
(
N
,

ψ
ε

)
)
>
ε

{d_{GH}}((M,{\phi _\varepsilon }),(N,{\psi _\varepsilon })) > \varepsilon

.
Surfaces with orthogonal families of circles
Authors: Ivey Thomas
Published: June 2010

The lines of curvature on a cyclide of Dupin are circular arcs. A surface which carries two orthogonal families of circular arcs must arise as an integral surface of an overdetermined exterior differential system. We show that the only solutions of this system are the cyclides of Dupin.
Menger manifolds homeomorphic to their 𝑛-homotopy kernels
Authors: Iwamoto Yutaka
Published: June 2010

We give a necessary and sufficient condition that an

(
n
+
1
)

(n + 1)

-dimensional Menger manifold (

μ

n
+
1

{\mu ^{n + 1}}

-manifold) is homeomorphic to its n-homotopy kernel. Such a

μ

n
+
1

{\mu ^{n + 1}}

-manifold is called a

μ
∞

n
+
1

\mu _\infty ^{n + 1}

-manifold. We also prove the following results: (1) Each homeomorphism between two Z-sets in a

μ
∞

n
+
1

\mu _\infty ^{n + 1}

-manifold M extends to an ambient homeomorphism of M onto itself if it is n-homotopic to id in M. (2) An n-homotopy equivalence between two

μ
∞

n
+
1

\mu _\infty ^{n + 1}

-manifolds is n-homotopic to a homeomorphism. (3) Each map from a

μ
∞

n
+
1

\mu _\infty ^{n + 1}

-manifold into a

μ

n
+
1

{\mu ^{n + 1}}

-manifold is n-homotopic to an open embedding.
Four-point affine Lie algebras
Authors: Bremner Murray
Published: June 2010

We consider Lie algebras of the form

g

⊗
R

\mathfrak {g} \otimes R

where

g

\mathfrak {g}

is a simple complex Lie algebra and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R equals double-struck upper C left-bracket s comma s Superscript negative 1 Baseline comma left-parenthesis s minus 1 right-parenthesis Superscript negative 1 Baseline comma left-parenthesis s minus a right-parenthesis Superscript negative 1 Baseline right-bracket">

R
=

C

[
s
,

s

−
1

,

(
s
−
1

)

−
1

,

(
s
−
a

)

−
1

]

R = \mathbb {C}[s,{s^{ - 1}},{(s - 1)^{ - 1}},{(s - a)^{ - 1}}]

for

a
∈

C

−
{
0
,
1
}

a \in \mathbb {C} - \{ 0,1\}

. After showing that R is isomorphic to a quadratic extension of the ring

C

[
t
,

t

−
1

]

\mathbb {C}[t,{t^{ - 1}}]

of Laurent polynomials, we prove that

g
⊗
R

g \otimes R

is a quasi-graded Lie algebra with a triangular decomposition. We determine the universal central extension of

g

⊗
R

\mathfrak {g} \otimes R

and show that the cocycles defining it are closely related to ultraspherical (Gegenbauer) polynomials.
The embedding theorem for the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type
Authors: Han Y.-S.
Published: June 2010

In this note the classical embedding theorem for the Besov and Triebel-Lizorkin spaces on

R
n

{R^n}

is generalized to the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type. The proof is new even for

R
n

{R^n}

case.
Projections in some simple 𝐶*-crossed products
Authors: Jeong Ja A , Park Gie-Hyun
Published: June 2010

Let

α
\alpha

be an outer action by a finite group G on a simple

C
∗

{C^ \ast }

-algebra A. If each hereditary

C
∗

{C^ \ast }

-subalgebra of A has an approximate identity consisting of projections, then every hereditary

C
∗

{C^ \ast }

-subalgebra of the crossed product

A

×
α

G

A{ \times _\alpha }G

has a projection.
Isometries of unbounded Fredholm modules over reduced group 𝐶*-algebras
Authors: Park Efton
Published: June 2010

In an earlier paper, the author defined the isometry group of an unbounded Fredholm module over a unital

C
∗

{C^ \ast }

-algebra. In this paper, the author studies a class of unbounded Fredholm modules over a reduced group

C
∗

{C^ \ast }

-algebra, and he shows that the isometry groups of these unbounded Fredholm modules are always compact Lie groups. The author also proves a result about the fixed point algebra of such an isometry.
A new duality theorem for semisimple modules and characterization of Villamayor rings
Authors: Faith Carl , Menal Pere
Published: June 2010

We prove the theorem: If R is a ring whose right ideals satisfy the double annihilator condition with respect to a semisimple right R-module W, then every right ideal is an intersection of maximal right ideals, consequently R is a right V (for Villamayor) ring, and W is then necessarily a cogenerator of

mod
-
R

\bmod \text {-}R

. (The converse is well known.) We use this to give a new proof of a theorem of ours on right Johns rings.
Local minimizers of integral functionals are global minimizers
Authors: Giner E.
Published: June 2010

We show that local minimizers of integral functionals associated with a measurable integrand

f
:
Ω
×
E
→

R

∪
{
±
∞
}

f:\Omega \times E \to \mathbb {R} \cup \{ \pm \infty \}

are actually global minimizers. Here

(
Ω
,

S

,
μ
)

(\Omega , \mathcal {S},\mu )

is a measured space with an atomless

σ
\sigma

-finite positive measure, E is a separable Banach space, and the integral functional
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper I Subscript f Baseline left-parenthesis x right-parenthesis equals integral Subscript normal upper Omega Superscript asterisk Baseline f left-parenthesis omega comma x left-parenthesis omega right-parenthesis right-parenthesis d mu">

I
f

(
x
)
=

∫
Ω
∗

f
(
ω
,
x
(
ω
)
)
d
μ

{I_f}(x) = \smallint _\Omega ^ \ast f(\omega ,x(\omega ))d\mu

is defined on

L
p

(
Ω
,
E
)

{L_p}(\Omega ,E)

or, more generally, on some decomposable set of measurable mappings x from

Ω
\Omega

into E.
Generic embeddings and the failure of box
Authors: Burke Douglas
Published: June 2010

We prove that if {

a
⊆

κ
+

|

a \subseteq {\kappa ^ + }|

order type of a is a cardinal} is stationary, then Jensen’s principle

◻

κ

{\square _\kappa }

fails. We also show that

∀
κ

◻

k

\forall \kappa {\square _k}

is consistent with a superstrong cardinal.
On abstract Fubini theorems for finitely additive integration
Authors: de Amo E. , Díaz Carrillo M.
Published: June 2010

A Fubini theorem for positive linear functionals on the vector lattice of the real-valued functions is given. This result properly contains that of the Riemann-

μ
\mu

-abstract integral.
An elementary proof of the Traczyk-Yokota criteria for periodic knots
Authors: Przytycki Józef H.
Published: June 2010

Traczyk used the first coefficient of the skein (Homfly) polynomial to find powerful criteria for r periodic knots. The criteria were extended by Yokota to

(
r
−
1
)

/

2

(r - 1)/2

first coefficients of the skein polynomial. We give here a short, elementary proof of the Traczyk-Yokota criteria. The main tool is the Jaeger composition product, the same product which is a base for Turaev’s Hopf algebra structure of links in a handlebody.
Relations among homotopy operations for simplicial commutative algebras
Authors: Goerss Paul G. , Lada Thomas J.
Published: June 2010

The homotopy groups of a simplicial commutative algebra over the field with two elements support natural operations. Here we write the relations among these operations in an admissible form.
A note on multiplication of strong operator measurable functions
Authors: Schlüchtermann G.
Published: June 2010

Let

(
Ω
,
Σ
,
μ
)

(\Omega ,\Sigma ,\mu )

be a finite and positive measure space, and let

U
1

,
…
,

U
n

{U_1}, \ldots ,{U_n}

be strongly measurable functions with values in the space of bounded linear operators on a Banach space. Then the product

U
1

⋯

U
n

{U_1} \cdots {U_n}

is again strongly measurable.
On the determinant and the holonomy of equivariant elliptic operators
Authors: Tsuboi Kenji
Published: June 2010

Let M be a closed oriented smooth manifold, G a compact Lie group consisting of diffeomorphisms of

M
,
P
→
Z

M,P \to Z

a principal G-bundle with a connection and D a G-equivariant elliptic operator. Then a locally constant family of elliptic operators and its determinant line bundle over Z are naturally defined by D. Moreover the holonomy of the determinant line bundle is defined by the connection in P. In this note, we give an explicit formula to calculate the holonomy (Theorem 1.4) and give a proof of the Witten holonomy formula (Theorem 1.7) in the special case above.
Buildings as inner ideal geometries
Authors: Dillon Meighan I.
Published: June 2010

We consider a Chevalley-type group

G
(
V
)

G(V)

associated to an integrable representation of a Kac-Moody algebra and show that the associated Kac-Moody group

G
(
A
)

G(A)

is a universal cover for

G
(
V
)

G(V)

. This observation strengthens a result of Kac-Peterson on representations of

G
(
A
)

G(A)

. It also implies that the building associated to an affine Lie algebra can be realized as an inner ideal geometry.
On Fredholm operators in quarter-plane Toeplitz algebras
Authors: Jiang Xinhui
Published: June 2010

In this note we explicitly construct a Fredholm operator of index one in any skew quarter-plane Toeplitz algebra and determine the K-theory of related

C
∗

{C^ \ast }

-algebras.
Extinction in competitive Lotka-Volterra systems
Authors: Zeeman M. L.
Published: June 2010

It is well known that for the two species autonomous competitive Lotka-Volterra model with no fixed point in the open positive quadrant, one of the species is driven to extinction, whilst the other population stabilises at its own carrying capacity. In this paper we prove a generalisation of this result to arbitrary finite dimension. That is, for the n-species autonomous competitive Lotka-Volterra model, we exhibit simple algebraic criteria on the parameters which guarantee that all but one of the species is driven to extinction, whilst the one remaining population stabilises at its own carrying capacity.
A proper 𝐺ₐ action on 𝐶⁵ which is not locally trivial
Authors: Deveney James K. , Finston David R.
Published: June 2010

The quotient of a proper holomorphic

G
a

{G_a}

action on

C

n

{{\mathbf {C}}^n}

is known to carry the structure of a complex analytic manifold, and in the case of a rational algebraic action, the geometric quotient exists as an algebraic space. An example is given of a proper rational algebraic action for which the quotient is not a variety, and therefore the action is not locally trivial in the Zariski topology.
On the 2-class groups of cyclotomic fields whose maximal real subfields have odd class numbers
Authors: Horie Kuniaki , Horie Mitsuko
Published: June 2010

This paper first makes a simple remark about the structure as a group of the ideal class group of any algebraic number field, then studies the 2-rank of the ideal class group of any cyclotomic field whose maximal real subfield has odd class number, and finally determines the structure of the ideal class groups of some cyclotomic fields.
On the finite images of some one-relator groups
Authors: Moldavanski D. , Sibyakova N.
Published: June 2010

It is shown that the group

G
=
⟨
a
,
b
;

a

−
1

b
a
=

b
k

⟩
(
k
≠
0
)

G = \langle a,b;{a^{ - 1}}ba = {b^k}\rangle (k \ne 0)

is determined in the class of all residually finite one-relator groups by the set of its finite images.
View-obstruction problems and Kronecker’s theorem
Authors: Chen Yong Gao
Published: June 2010

In this paper we show how the quantitative forms of Kronecker’s theorem in Diophantine approximations can be applied to investigate view-obstruction problems. In particular we answer a question in [Yong-Gao Chen, On a conjecture in Diophantine approximation, III, J. Number Theory 39 (1991), 91-103].
Isometries of spheres
Authors: Everling Ulrich
Published: June 2010

In a Euclidean space of dimension two or more, any mapping that preserves unit distance is an isometry; this is the theorem of Beckmann and Quarles. We prove a similar theorem for spheres, assuming that a given distance less than a quarter great circle is preserved.
Universal Pettis integrability property
Authors: Stefánsson Gunnar F.
Published: June 2010

Functions into duals and pre-duals of weakly compactly generated spaces (WCG) are studied. We show that a universally weakly measurable function f into a dual of a WCG has the RS property. Also, for such a function, we sharpen the decomposition obtained by E. M. Bator (1988). We show that bounded weakly measurable functions into pre-duals of WCG spaces are always Pettis integrable, universally weakly measurable, or not.
An example of almost flat affine connections on the three-dimensional sphere
Authors: Agaoka Yoshio
Published: June 2010

We show the existence of almost flat affine structures on the three-dimensional sphere, and prove that the Pontryagin numbers serve as the obstruction to the existence of such structures.
Direct computation of the spectral function
Authors: Boumenir Amin
Published: June 2010

We would like to find an explicit formula for the spectral function of the following Sturm-Liouville problem:
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout Enlarged left-brace 1st Row upper L f identical-to minus StartFraction d squared Over d x squared EndFraction f left-parenthesis x right-parenthesis plus q left-parenthesis x right-parenthesis f left-parenthesis x right-parenthesis comma x greater-than-or-equal-to 0 comma 2nd Row f prime left-parenthesis 0 right-parenthesis minus m f left-parenthesis 0 right-parenthesis equals 0 period EndLayout">

{

L
f
≡
−

d
2

d

x
2

f
(
x
)
+
q
(
x
)
f
(
x
)
,

x
≥
0
,

f
′

(
0
)
−
m
f
(
0
)
=
0.

\left \{ {\begin {array}{*{20}{c}} {Lf \equiv - \frac {{{d^2}}}{{d{x^2}}}f(x) + q(x)f(x),\quad x \geq 0,} \hfill \\ {f’(0) - mf(0) = 0.} \hfill \\ \end {array} } \right .

\]
A simple operational calculus argument will help us obtain an explicit formula for the transmutation kernel. The expression of the spectral function is then obtained through the nonlinear integral equation found in the Gelfand-Levitan theory.
Cohomology ring of the orbit space of certain free 𝑍_{𝑝}-actions
Authors: Dotzel Ronald M. , Singh Tej B.
Published: June 2010

In this paper, we consider actions of

G
=

Z
p

G = {Z_p}

(with p an odd prime) on spaces X which are of cohomology type (0, 0) (i.e., have the

mod
-
p

\bmod \text {-}p

cohomology of the one-point union of an n-sphere, a 2n-sphere and a a 3n-sphere, n odd). If X is not totally non-homologous to zero in

X
G

{X_G}

we determine the fixed set, give examples of all possibilities for the fixed set and compute the cohomology ring structure of the orbit space in the case where G acts freely. In [4], we considered fixed sets for related spaces, when X is totally non-homologous to zero in

X
G

{X_G}

.
A new characterization of totally projective groups of cardinality ℵ₁
Authors: Hill Paul
Published: June 2010

A new characterization is given for totally projective groups of cardinality not exceeding

ℵ
1

{\aleph _1}

. The new description is in terms of what we call a v-basis. The question about the structure of larger groups having a v-basis is left open, but we establish some closure properties of such groups.
Markov’s exponent of compact sets in 𝐂ⁿ
Authors: Baran M. , Pleśniak W.
Published: June 2010

We introduce the notion of Markov’s exponent of a compact set in

C

n

{\mathbb {C}^n}

and show that it is invariant under regular analytic maps.
Small representations of finite distributive lattices as congruence lattices
Authors: Grätzer George , Rival Ivan , Zaguia Nejib
Published: June 2010

A recent result of G. Grätzer, H. Lakser, and E. T. Schmidt states that for any distributive lattice D with n join-irreducible elements, there exists a lattice L with

O
(

n
2

)

O({n^2})

elements, whose congruence lattice ConL is isomorphic to D. We show that this result is best possible.
Twisted torus bundles over arithmetic varieties
Authors: Lee Min Ho
Published: June 2010

A twisted torus is a nilmanifold which is the quotient of a real Heisenberg group by a cocompact discrete subgroup. We construct fiber bundles over arithmetic varieties whose fibers are isomorphic to a twisted torus, and express the complex cohomology of such bundles over certain Riemann surfaces in terms of automorphic forms.
Global attractivity for a population model with time delay
Authors: So Joseph W.-H. , Yu J. S.
Published: June 2010

In this paper we give a sufficient condition which guarantees the global attractivity of the zero solution of a population growth equation.
The limiting distribution of the St. Petersburg game
Authors: Vardi Ilan
Published: June 2010

The St. Petersburg game is a well-known example of a random variable which has infinite expectation. Csörgő and Dodunekova have recently shown that the accumulated winnings do not have a limiting distribution, but that if measurements are taken at a subsequence

b
n

{b_n}

, then a limiting distribution exists exactly when the fractional parts of

log
2

b
n

{\log _2}{b_n}

approach a limit. In this paper the characteristic functions of these distributions are computed explicitly and found to be continuous, self-similar, nowhere differentiable functions.
Limit theorems for Markov processes on topological groups
Authors: Foguel S. R.
Published: June 2010

Limit theorems for

P
n

(
x
,
A
)

{P^n}(x,A)

, as

n
→
∞

n \to \infty

, are established, where

P
(
x
,
A
)

P(x,A)

is the transition probability of a Markov process on a topological group. The transition probability is assumed to satisfy certain commutativity relations with translations. Thus special cases of our investigation are spatially homogenous processes and processes induced by automorphisms of the group.
Extremal problems in the class of close-to-convex functions
Authors: Pinchuk Bernard
Published: June 2010

The class K of normalized close-to-convex functions in

D
=
{
z
:

|

z

|

>
1
}

D = \{ z:|z| > 1\}

has a parametric representation involving two Stieltjes integrals. Using a variational method due to G. M. Goluzin [2] for classes of analytic functions defined by a Stieltjes integral, variational formulas are developed for K. With these variational formulas, two general extremal problems within K are solved. The first problem is to maximize the functional

Re
⁡
F
[
log
⁡

f
′

(
z
)
]

\operatorname {Re} F[\log f’(z)]

over K where

F
(
w
)

F(w)

is a given entire function and z a given point in D. A special case of this is the rotation theorem for K. The second problem solved is a general coefficient problem. Both problems are solved by characterizing the measures which appear in the integral representation for the extremal functions. The classes of convex univalent functions in D and functions whose derivative has a positive real part in D are proper subclasses of K. The methods used to solve the extremal problems in K can be used for these subclasses as well. Some of the results for the subclasses are known and are not presented here, even though the methods differ from those used previously. It should be mentioned that Goluzin originally used these methods to solve extremal problems of the first type mentioned above within the classes of starlike and typically real functions.
A topologically strongly mixing symbolic minimal set
Authors: Petersen K. E.
Published: June 2010

Recent papers by the author, Keynes and Robertson, and others have shown that weakly mixing minimal flows are objects of considerable interest, but examples of such flows, other than the horocycle flows, have been scarce. We give here a “machinal” construction of a bilateral sequence with entries from 0, 1 whose orbit closure is topologically strongly mixing and minimal. We prove in addition that the flow we obtain has entropy zero, is uniquely ergodic, and fails to be measure-theoretically strongly mixing.
Two methods of integrating Monge-Ampère’s equations
Authors: Matsuda Michihiko
Published: June 2010

Modifying Monge’s method and Laplace’s one respectively, we shall give two methods of integration of Monge-Ampère’s equations. Although they seem quite different, the equivalence of our two methods will be shown. The first method will be from a point of view different from that of Lewy. The second will present a solution to a problem of Goursat.
Compact riemannian manifolds with essential groups of conformorphisms.
Authors: Ledger A. J. , Obata Morio
Published: June 2010

A solution to the following conjecture: A compact connected riemannian

n
n

-manifold

(
n
>
2
)

(n > 2)

with an essential group of conformorphisms is conformorphic to a euclidean

n
n

-sphere.
Topology and the duals of certain locally compact groups
Authors: Schochetman I.
Published: June 2010

We consider some topological questions concerning the dual space of a (separable) extension

G
G

of a type I, regularly embedded subgroup

N
N

. The dual

G
^

\hat G

is known to have a fibre-like structure. The fibres are in bijective correspondence with certain subsets of dual spaces of associated stability subgroups. These subsets in turn are in bijective correspondence with certain projective dual spaces. Under varying hypotheses, we give sufficient conditions for these bijections to be homeomorphisms, we determine the support of the induced representation

U
L

U^L

(for

L
∈

N
^

L \in \hat N

) and we give necessary and sufficient conditions for a union of fibres in

G
^

\hat G

to be closed. In a much more general context we study the Hausdorff and CCR separation properties of the dual of an extension. We then completely describe the dual space topology of the above extension

G
G

in an interesting case. The preceding results are then applied to the case where

N
N

is abelian and

G

/

N

G/N

is compact.
A collection of sequence spaces
Authors: Calder J. R. , Hill J. B.
Published: June 2010

This paper concerns a collection of sequence spaces we shall refer to as

d
α

{d_\alpha }

spaces. Suppose

α
=
(

α
1

,

α
2

,
…
)

\alpha = ({\alpha _1},{\alpha _2}, \ldots )

is a bounded number sequence and

α
i

≠
0

{\alpha _i} \ne 0

for some

i
i

. Suppose

P

\mathcal {P}

is the collection of permutations on the positive integers. Then

d
α

{d_\alpha }

denotes the set to which the number sequence

x
=
(

x
1

,

x
2

,
…
)

x = ({x_1},{x_2}, \ldots )

belongs if and only if there exists a number

k
>
0

k > 0

such that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="h Subscript alpha Baseline left-parenthesis x right-parenthesis equals l u b Subscript p element-of script upper P Baseline sigma-summation Underscript i equals 1 Overscript normal infinity Endscripts StartAbsoluteValue x Subscript upper F left-parenthesis i right-parenthesis Baseline alpha Subscript i Baseline EndAbsoluteValue greater-than k period">

h
α

(
x
)
=

lub

p
∈

P

⁡

∑

i
=
1

∞

|

x

F
(
i
)

α
i

|

>
k
.

h_\alpha (x) = \operatorname {lub}_{p \in \mathcal {P}} \sum \limits _{i = 1}^\infty |x_{F(i)} \alpha _i| > k.

\]

h
α

h_\alpha

is a norm on

d
α

d_\alpha

and

(

d
α

,

h
α

)

(d_\alpha , h_\alpha )

is complete. We classify the

d
α

{d_\alpha }

spaces and compare them with

l
1

{l_1}

and

m
m

. Some of the

d
α

{d_\alpha }

spaces are shown to have a semishrinking basis that is not shrinking. Further investigation of the bases in these spaces yields theorems concerning the conjugate space properties of

d
α

{d_\alpha }

. We characterize the sequences

β
\beta

such that, given

α
,

d
β

,
=

d
α

\alpha ,{d_\beta }, = {d_\alpha }

. A class of manifolds in the first conjugate space of

d
α

{d_\alpha }

is examined. We establish some properties of the collection of points in the first conjugate space of a normed linear space

S
S

that attain their maximum on the unit ball in

S
S

. The effect of renorming

c
0

{c_0}

and

l
1

{l_1}

with

h
α

{h_\alpha }

and related norms is studied in terms of the change induced on this collection of functionals.
Existence and uniqueness of fixed-points for semigroups of affine maps.
Authors: Huff Robert E.
Published: June 2010

The Day fixed-point theorem is extended to include both existence and uniqueness. For uniqueness of fixed-points, continuity for pointwise limits of a semigroup of continuous affine maps is needed ; necessary and sufficient conditions for this are obtained and compared with the stronger condition of equicontinuity. The comparison is between, on the one hand, the above condition, separate continuity, and weak compactness, and, on the other hand, equicontinuity, joint continuity, and strong compactness. An extension of the Kakutani fixed-point theorem results. Also as a corollary, known necessary and sufficient conditions for continuity of the convolution operation are obtained.
The Hasse invariant of a vector bundle
Authors: Patterson Richard R.
Published: June 2010

The object of this work is to define, by analogy with algebra, the Witt group and the graded Brauer group of a topological space

X
X

. A homomorphism is defined between them analogous to the generalized Hasse invariant. Upon evaluation, the Witt group is seen to be

K
~

O
(
X
)

\tilde KO(X)

, the graded Brauer group

1
+

H
1

(
X
;

Z
2

)
+

H
2

(
X
;

Z
2

)

1 + {H^1}(X;{Z_2}) + {H^2}(X;{Z_2})

with truncated cup product multiplication, while the homomorphism is given by Stiefel-Whitney classes:

1
+

w
1

+

w
2

1 + {w_1} + {w_2}

.
A fundamental solution of the parabolic equation on Hilbert space. II. The semigroup property
Authors: Piech M. Ann
Published: June 2010

The existence of a family of solution operators

{

q
t

:
t
>
0
}

\{ {q_t}:t > 0\}

corresponding to a fundamental solution of a second order infinite-dimensional differential equation of the form

∂
u

/

∂
t
=
L
u

\partial u/\partial t = Lu

was previously established by the author. In the present paper, it is established that these operators are nonnegative, and satisfy the condition

q
s

q
t

=

q

s
+
t

{q_s}{q_t} = {q_{s + t}}

.
Geometry associated with semisimple flat homogeneous spaces
Authors: Ochiai Takushiro
Published: June 2010

Our object is Cartan connections with semisimple flat homogeneous spaces as standard spaces. We study these from the viewpoint of

G
G

-structures of second order. This allows us especially to treat classical projective and conformal connections in the unifying manner. We also consider its application to the problem of certain geometric transformations.
Structure of the semigroup of semigroup extensions
Authors: Fulp R. O. , Stepp J. W.
Published: June 2010

Let

B
B

denote a compact semigroup with identity and

G
G

a compact abelian group. Let

Ext
⁡
(
B
,
G
)

\operatorname {Ext} (B,G)

denote the semigroup of extensions of

G
G

by

B
B

. We show that

Ext
⁡
(
B
,
G
)

\operatorname {Ext} (B,G)

is always a union of groups. We show that it is a semilattice whenever

B
B

is. In case

B
B

is also an abelian inverse semigroup with its subspace of idempotent elements totally disconnected, we obtain a determination of the maximal groups of a commutative version of

Ext
⁡
(
B
,
G
)

\operatorname {Ext} (B,G)

in terms of the extension functor of discrete abelian groups.
Operations in polyadic algebras
Authors: Daigneault Aubert
Published: June 2010

A new treatment of P. R. Halmos’ theory of terms and operations in (locally finite) polyadic algebras (of infinite degree) is given that is considerably simpler than the original one.
Homomorphisms of commutative cancellative semigroups into nonnegative real numbers
Authors: Putcha Mohan S. , Tamura Takayuki
Published: June 2010

Let S be a commutative cancellative semigroup and

T
0

{T_0}

be a cofinal subsemigroup of S. Let

h
0

{h_0}

be a homomorphism of

T
0

{T_0}

into the semigroup of nonnegative real numbers under addition. We prove that Kobayashi’s condition [2] is necessary and sufficient for

h
0

{h_0}

to be extended to S. Further, we find a necessary and sufficient condition in order that the extension be unique. Related to this, the “boundedness condition” is introduced. For further study, several examples are given.
Nonregular ultrafilters and large cardinals
Authors: Ketonen Jussi
Published: June 2010

The relationship between the existence of nonregular ultrafilters and large cardinals in the constructible universe is studied.
Indecomposable homogeneous plane continua are hereditarily indecomposable
Authors: Hagopian Charles L.
Published: June 2010

F. Burton Jones [7] proved that every decomposable homogeneous plane continuum is either a simple closed curve or a circle of homogeneous nonseparating plane continua. Recently the author [5] showed that no subcontinuum of an indecomposable homogeneous plane continuum is hereditarily decomposable. It follows from these results that every homogeneous plane continuum that has a hereditarily decomposable subcontinuum is a simple closed curve. In this paper we prove that no subcontinuum of an indecomposable homogeneous plane continuum is decomposable. Consequently every homogeneous nonseparating plane continuum is hereditarily indecomposable. Parts of our proof follow one of R. H. Bing’s arguments [2]. At the Auburn Topology Conference in 1969, Professor Jones [8] outlined an argument for this theorem and stated that the details would be supplied later. However, those details have not appeared.
The Cartesian product structure and 𝐶^{∞} equivalances of singularities
Authors: Ephraim Robert
Published: June 2010

In this paper the cartesian product structure of complex analytic singularities is studied. A singularity is called indecomposable if it cannot be written as the cartesian product of two singularities of lower dimension. It is shown that there is an essentially unique way to write any reduced irreducible singularity as a cartesian product of indecomposable singularities. This result is applied to give an explicit description of the set of reduced irreducible complex singularities having a given underlying real analytic structure.
The primitive lifting problem in the equivalence problem for transitive pseudogroup structures: a counterexample
Authors: Molino Pierre
Published: June 2010

A transitive Lie pseudogroup

Γ
M

{\Gamma _M}

on M is a primitive extension of

Γ
N

{\Gamma _N}

if

Γ
N

{\Gamma _N}

is the quotient of

Γ
M

{\Gamma _M}

by an invariant fibration

π
:
M
→
N

\pi :M \to N

and if the pseudogroup induced by

Γ
M

{\Gamma _M}

on the fiber of

π
\pi

is primitive. In the present paper an example of this situation is given with the following property (counterexample to the primitive lifting property): the equivalence theorem is true for almost-

Γ
N

{\Gamma _N}

-structures but false for almost-

Γ
M

{\Gamma _M}

-structures.
Generic Fréchet-differentiability and perturbed optimization problems in Banach spaces
Authors: Ekeland Ivar , Lebourg Gérard
Published: June 2010

We define a function F on a Banach space V to be locally

ε
\varepsilon

-supported by

u
∗

∈

V
∗

{u^\ast } \in {V^\ast }

at

u
∈
V

u \in V

if there exists an

η
>
0

\eta > 0

such that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar v minus u double-vertical-bar less-than-or-slanted-equals eta right double arrow upper F left-parenthesis v right-parenthesis greater-than-or-slanted-equals upper F left-parenthesis u right-parenthesis plus mathematical left-angle u Superscript asterisk Baseline comma v minus u mathematical right-angle minus epsilon double-vertical-bar v minus u double-vertical-bar">

‖

v
−
u

‖

⩽
η
⇒
F
(
v
)
⩾
F
(
u
)
+
⟨

u
∗

,
v
−
u
⟩
−
ε

‖

v
−
u

‖

\left \| {v - u} \right \| \leqslant \eta \Rightarrow F(v) \geqslant F(u) + \langle {u^\ast },v - u\rangle - \varepsilon \left \| {v - u} \right \|

. We prove that if the Banach space V admits a nonnegative Fréchet-differentiable function with bounded nonempty support, then, for any

>
0

> 0

and every lower semicontinuous function F, there is a dense set of points

u
∈
V

u \in V

at which F is locally

ε
\varepsilon

-supported. The applications are twofold. First, to the study of functions defined as pointwise infima; we prove for instance that every concave continuous function defined on a Banach space with Fréchet-differentiable norm is Fréchet-differentiable generically (i.e. on a countable intersection of open dense subsets). Then, to the study of optimization problems depending on a parameter

u
∈
V

u \in V

; we give general conditions, mainly in the framework of uniformly convex Banach spaces with uniformly convex dual, under which such problems generically have a single optimal solution, depending continuously on the parameter and satisfying a first-order necessary condition.
Subgroups of finitely presented solvable linear groups
Authors: Thomson Michael W.
Published: June 2010

Let G be a finitely generated solvable linear group. It is shown that there exists a finitely presented solvable linear group H with G embedded in H.
Nonzero-sum stochastic differential games with stopping times and free boundary problems
Authors: Bensoussan Alain , Friedman Avner
Published: June 2010

One is given a diffusion process and two payoffs which depend on the process and on two stopping times

τ
1

,

τ
2

{\tau _1},{\tau _2}

. Two players are to choose their respective stopping times

τ
1

,

τ
2

{\tau _1},{\tau _2}

so as to achieve a Nash equilibrium point. The problem whether such times exist is reduced to finding a “regular” solution

(

u
1

,

u
2

)

({u_1},{u_2})

of a quasi-variational inequality. Existence of a solution is established in the stationary case and, for one space dimension, in the nonstationary case; for the latter situation, the solution is shown to be regular if the game is of zero sum.
The oscillatory behavior of certain derivatives
Authors: O’Malley Richard J. , Weil Clifford E.
Published: June 2010

The derivatives considered are the approximate derivative and the kth Peano derivative. The main results strengthen the Darboux property, which both of these derivatives possess. Theorem. If the approximate derivative

f

ap

′

{f’_{{\text {ap}}}}

of f exists on an interval and if, for

M
⩾
0
,

f

ap

′

M \geqslant 0,{f’_{{\text {ap}}}}

attains both M and — M, then there is an open subinterval where

f

ap

′

=

f
′

{f’_{{\text {ap}}}} = f’

and on which

f
′

f’

attains both M and — M. The other main theorem is obtained from this one by replacing the approximate derivative by the kth Peano derivative.
Kernel functions on domains with hyperelliptic double
Authors: Barker William H.
Published: June 2010

In this paper we show that the structure of the Bergman and Szegö kernel functions is especially simple on domains with hyperelliptic double. Each such domain is conformally equivalent to the exterior of a system of slits taken from the real axis, and on such domains the Bergman kernel function and its adjoint are essentially the same, while the Szegö kernel function and its adjoint are elementary and can be written in a closed form involving nothing worse than fourth roots of polynomials. Additionally, a number of applications of these results are obtained.
Singularities of spaces of flat bundles over complex manifolds
Authors: Wong B.
Published: June 2010

We use Fox differential calculus on free group to study the singularities of complex analytic varieties arising from flat bundles over complex manifolds. Criteria of regularity in terms of cohomology of the fundamental group of the underlying manifold are established.
Boundary behavior of harmonic forms on a rank one symmetric space
Authors: Kaplan Aroldo , Putz Robert
Published: June 2010

We study the boundary behavior of 1-forms on a rank-one symmetric space M satisfying the equations

d
ω
=
0
=
δ
ω

d\omega = 0 = \delta \omega

; the role of boundary is played by a nilpotent (Iwasawa) group

N
¯

\bar N

of isometries of M. For forms satisfying certain

H
p

{H^p}

integrability conditions, we obtain the existence of boundary values in an appropriate sense, characterize these boundary values by means of fractional and singular integral operators on the group

N
¯

\bar N

, and exhibit explicit isomorphisms between

H
p

{H^p}

spaces of forms on M and the ordinary

L
p

{L^p}

spaces of functions on the group

N
¯

\bar N

.
Derivatives of entire functions and a question of Pólya. II
Authors: Hellerstein Simon , Williamson Jack
Published: June 2010

It is shown that if f is an entire function of infinite order, which is real on the real axis and has, along with

f
′

f’

, only real zeros, then

f
f

has nonreal zeros (in fact, infinitely many). The finite order case was treated by the authors in a preceding paper. The combined results show that the only real entire functions f for which

f
,

f
′

f,f’

, and

f
f

have only real zeros are those in the Laguerre-Pólya class, i.e.
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis z right-parenthesis equals z Superscript m Baseline exp left-brace minus a z squared plus b z plus c right-brace product Underscript n Endscripts left-parenthesis 1 minus StartFraction z Over z Subscript n Baseline EndFraction right-parenthesis e Superscript z slash z Super Subscript n Superscript Baseline comma">

f
(
z
)
=

z
m

exp
⁡
{
−
a

z
2

+
b
z
+
c
}

∏
n

(

1
−

z

z
n

)

e

z

/

z
n

,

f(z) = {z^m}\exp \{ - a{z^2} + bz + c\} \prod \limits _n {\left ( {1 - \frac {z}{{{z_n}}}} \right )} {e^{z/{z_n}}},

\]

a
⩾
0
,
b
,
c

a \geqslant 0,b,c

and the

z
n

{z_n}

real, and

Σ

z
n

−
2

>
∞

\Sigma z_n^{ - 2} > \infty

. This gives a strong affirmative version of an old conjecture of Pólya.
Group presentations corresponding to spines of 3-manifolds. III
Authors: Osborne R. P. , Stevens R. S.
Published: June 2010

Continuing after the previous papers of this series, attention is devoted to RR-systems having two towns (i.e., to compact 3-manifolds with spines corresponding to group presentations having two generators). An interesting kind of symmetry is noted and then used to derive some useful results. Specifically, the following theorems are proved: Theorem 1. Let

ϕ
\phi

be a group presentation corresponding to a spine of a compact orientable 3-manifold, and let w be a relator of

ϕ
\phi

involving just two generators a and b. If w is cyclically reduced, then either (a) w can be “written backwards" (i.e., if

w
=

a

m
1

b

m
1

a

m
2

b

n
2

…

a

m
k

b

n
k

w = {a^{{m_1}}}{b^{{m_1}}}{a^{{m_2}}}{b^{{n_2}}} \ldots {a^{{m_k}}}{b^{{n_k}}}

, then w is a cyclic conjugate of

b

n
k

a

m
k

…

b

n
2

a

m
2

b

n
1

a

m
1

{b^{{n_k}}}{a^{{m_k}}} \ldots {b^{{n_2}}}{a^{{m_2}}}{b^{{n_1}}}{a^{{m_1}}}

), or (b) w lies in the commutator subgroup of the free group on a and b. Theorem 2. (Loose translation). If

ϕ
\phi

is a group presentation with two generators and if the corresponding 2-complex

K
ϕ

{K_\phi }

is a spine of a closed orientable 3-manifold then,

K
ϕ

{K_\phi }

is a spine of a closed orientable 3-manifold if and (except for two minor cases) only if

ϕ
\phi

has two relators and among the six allowable types of syllables (3 in each generator), exactly four occur an odd number of times. Further, each of the two relators can be “written backwards."
P.R.-regulated systems of notation and the subrecursive hierarchy equivalence property
Authors: Zemke Fred
Published: June 2010

We can attempt to extend the Grzegorczyk Hierarchy transfinitely by defining a sequence of functions indexed by the elements of a system of notation

S

\mathcal {S}

, using either iteration (majorization) or enumeration techniques to define the functions. (The hierarchy is then the sequence of classes of functions elementary in the functions of the sequence of functions.) In this paper we consider two sequences

{

F
s

}

s
∈

S

{\{ {F_s}\} _{s \in \mathcal {S}}}

and

{

G
s

}

s
∈

S

{\{ {G_s}\} _{s \in \mathcal {S}}}

defined by iteration and a sequence

{

E
s

}

s
∈

S

{\{ {E_s}\} _{s \in \mathcal {S}}}

defined by enumeration; the corresponding hierarchies are

{

F

s

}
,
{

G

s

}
,
{

E

s

}

\{ {\mathcal {F}_s}\} ,\{ {\mathcal {G}_s}\} ,\{ \mathcal {E}{_s}\}

. We say that

S

\mathcal {S}

has the subrecursive hierarchy equivalence property if these two conditions hold: (I)

E

s

=

F

s

=

G

s

{\mathcal {E}_s} = {\mathcal {F}_s} = {\mathcal {G}_s}

for all

s
∈

S

s \in \mathcal {S}

; (II)

E

s

=

E

t

{\mathcal {E}_s} = {\mathcal {E}_t}

for all

s
,
t
∈

S

s,t \in \mathcal {S}

such that

|

s

|

=

|

t

|

(

|

s

|

|s| = |t|(|s|

is the ordinal denoted by s). We show that a certain type of system of notation, called p.r.-regulated, has the subrecursive hierarchy equivalence property. We present a nontrivial example of such a system of notation, based on Schütte’s Klammersymbols. The resulting hierarchy extends those previously in print, which used the so-called standard fundamental sequences for limits

>

ε
0

> {\varepsilon _0}

.
Structure of symmetric tensors of type (0,2) and tensors of type (1,1) on the tangent bundle
Authors: Mok Kam Ping , Patterson E. M. , Wong Yung Chow
Published: June 2010

The concepts of M-tensor and M-connection on the tangent bundle TM of a smooth manifold M are used in a study of symmetric tensors of type (0, 2) and tensors of type (1, 1) on TM. The constructions make use of certain local frames adapted to an M-connection. They involve extending known results on TM using tensors on M to cases in which these tensors are replaced by M-tensors. Particular attention is devoted to (pseudo-) Riemannian metrics on TM, notably those for which the vertical distribution on TM is null or nonnull, and to the construction of almost product and almost complex structures on TM.
Higher order Massey products and links
Authors: O’Neill Edward J.
Published: June 2010

In this paper we generalize Steenrod’s functional cup products, calling the generalizations functional triple products, and relate them with Massey 4-products. We then study certain links using this machinery and a new relation that is satisfied by 4-products under conditions on X which permit applications to links. Finally, many examples illustrating the connection between Massey higher products, both ordinary and matrix, and links are presented. This material constituted a portion of the author’s doctoral dissertation. The author would like to thank his thesis advisor Professor W. S. Massey for his encouragement and guidance.
Automorphisms of the deformation space of a Kleinian group
Authors: Gentilesco James A.
Published: June 2010

In the following paper, we determine the biholomorphic automorphisms of a cross-product of Teichmüller spaces. This in turn helps us to determine the biholomorphic automorphisms of the deformation space of a Kleinian group using the fact that its holomorphic universal covering space is a cross-product of Teichmüller spaces. Among other interesting results, we show that in general the deformation space is not a homogeneous space.
Sheaf constructions and their elementary properties
Authors: Burris Stanley , Werner Heinrich
Published: June 2010

We are interested in sheaf constructions in model-theory, so an attempt is made to unify and generalize the results to date, namely various forms of the Feferman-Vaught Theorem, positive decidability results, and constructions of model companions. The task is considerably simplified by introducing a new definition of sheaf constructions over Boolean spaces.
The equivalence of ×^{𝑡}𝐶≈×^{𝑡}𝐷 and 𝐽×𝐶≈𝐽×𝐷
Authors: Hirshon Ronald
Published: June 2010

Let C satisfy the maximal condition for normal subgroups and let

×

t

C

≈

×

t

D

\times {\,^t}C\, \approx \, \times {\,^t}D

for some positive integer t. Then

C

×

J

≈

D

×

J

C\, \times \,J\, \approx \,D\, \times \,J

where J is the infinite cyclic group. If

×

s

C

≈

×

t

D

\times {\,^s}C\, \approx \, \times {\,^t}D

and

s
⩾

t

s \geqslant \,t

, there exists a finitely generated free abelian group S such that C is a direct factor of

D

×

S

D\, \times \,S

.
Nash rings on planar domains
Authors: Efroymson Gustave A.
Published: June 2010

Let D be a semialgebraic domain in

R
2

{R^2}

. Let

N
D

{N_D}

denote the Nash ring of algebraic analytic functions on D. Let

A
D

{A_D}

denote the ring of analytic functions on D. The main theorem of this paper implies that if

B

\mathcal {B}

is a prime ideal of

N
D

{N_D}

, then

B

A
D

\mathcal {B}{A_D}

is also prime. This result is proved by considering

p

(

x
,

y

)

p\left ( {x,\,y} \right )

in

R

[

x
,

y

]

\textbf {R}[{x,\,y}]

and showing that

p
(

x
,

y

)

p({x,\,y})

can be put into a form so that its factorization in

N
D

{N_D}

is given by looking at its local factorization as a polynomial in y with coefficients which are analytic functions of x. Then for more general domains, a construction using the “complex square root” enables one to reduce to the case already considered.
The commuting block maps problem
Authors: Coven Ethan M. , Hedlund G. A. , Rhodes Frank
Published: June 2010

A block map is a map

f
:

{

0

,

1

}
n

→

{
0
,

1
}

f:\,{\{ {\text {0}},\,{\text {1}}\} ^n}\, \to \,\{ 0,\,1\}

for some

n

⩾

1

n\, \geqslant \,1

. A block map f induces an endomorphism

f
∞

{f_\infty }

of the full 2-shift

(
X
,

σ
)

(X,\,\sigma )

. We define composition of block maps so that

(
f
∘
g

)
∞

=

f
∞

∘

g
∞

{(f \circ g)_\infty }\, = \,{f_\infty } \circ {g_\infty }

. The commuting block maps problem (for f) is to determine

C

(
f
)

=

{
g

|

f
∘
g

=

g
∘
f
}

\mathcal {C}(f)\, = \,\{ g|f \circ g\, = \,g \circ f\}

. We solve the commuting block maps problem for a number of classes of block maps.
Cell-like 0-dimensional decompositions of 𝐸³
Authors: Starbird Michael
Published: June 2010

Let G be a cell-like, 0-dimensional upper semicontinuous decomposition of

E
3

{E^3}

. It is shown that if

Γ
\Gamma

is a tame 1-complex which is a relatively closed subset of a saturated open set U whose boundary misses the nondegenerate elements of G, then there is a homeomorphism

h
:

E
3

→

E
3

h:{E^3} \to {E^3}

so that

h

|

E
3

−
U
=

id

h|{E^3} - U = {\text {id}}

and

h
(
Γ
)

h(\Gamma )

misses the nondegenerate elements of G. This theorem implies a disjoint disk type criterion for shrinkability of G. This criterion in turn provides a direct proof of the recent result of Starbird and Woodruff that if G is an u.s.c. decomposition of

E
3

{E^3}

into points and countably many cellular, tamely embedded polyhedra, then

E
3

/

G

{E^3}/G

is homeomorphic to

E
3

{E^3}

.