bluuebunny/crossref_metadata_2025 huggingface dataset:
Semigroup compactifications of semidirect products
Authors: Junghenn H. D. , Lerner B. T.
Published: June 2010

Let

S
S

and

T
T

be semigroups,

S\text {\textcircled {𝜏

}} T a semidirect product, and

F
F

a

C
∗

{C^ \ast }

-algebra of bounded, complex-valued functions on

S\text {\textcircled {𝜏

}} T. Necessary and sufficient conditions are given for the

F
F

-compactification of

S\text {\textcircled {𝜏

}} T to be expressible as a semidirect product of compactifications of

S
S

and

T
T

. This result is used to show that the strongly almost periodic compactification of

S\text {\textcircled {𝜏

}} T is a semidirect product and that, in certain general cases, the analogous statement holds for the almost periodic compactification and the left uniformly continuous compactification of

S\text {\textcircled {𝜏

}} T. Applications are made to wreath products.
Weighted estimates for fractional powers of partial differential operators
Authors: Johnson Raymond
Published: June 2010

It is shown that fractional powers defined by the wave polynomial
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P left-parenthesis xi right-parenthesis equals xi Sub Superscript 1 Superscript 2 Baseline plus midline-horizontal-ellipsis plus xi Subscript p Superscript 2 Baseline minus xi Subscript p plus 1 Superscript 2 Baseline minus midline-horizontal-ellipsis minus xi Subscript n Superscript 2">

P
(
ξ
)
=

ξ

1

2

+
⋯
+

ξ
p
2

−

ξ

p
+
1

2

−
⋯
−

ξ
n
2

P(\xi ) = \xi _{^1}^2 + \cdots + \xi _p^2 - \xi _{p + 1}^2 - \cdots - \xi _n^2

, defined in terms of Fourier transforms by

T
λ

f

^

=

|

P
(
ξ
)

|

λ

f
^

\widehat {{T^\lambda }f} = {\left | {P(\xi )} \right |^\lambda }\hat f

, are in the Bernstein subalgebra of functions with integrable Fourier transforms for

λ
>
(
n
−
1
)

/

2

\lambda > (n - 1)/2

, provided

f
∈

C
c
m

f \in C_c^m

with

m
m

large enough. The proof uses embedding theorems for Besov spaces and Stein’s theorem on interpolation of analytic families of operators.
On supercuspidal representations of the metaplectic group
Authors: Meister James
Published: June 2010

The Weil representations associated to anisotropic quadratic forms in one and three variables are used to study supercuspidal representations of the two-fold metaplectic covering group

GL

¯

2

(
k
)

{\overline {{\text {GL}}} _2}(k)

, where

k
k

is a local nonarchimedean field of odd residual characteristic. The principal result is the explicit calculation of certain Whittaker functionals for any square-integrable irreducible admissible genuine representation of

GL

¯

2

(
k
)

{\overline {{\text {GL}}} _2}(k)

. In particular, a recent conjecture of Gelbart and Piatetski-Shapiro is answered by obtaining a bijection between the set of quasicharacters of

k
∗

{k^ \ast }

and the set of irreducible admissible genuine distinguished representations of

GL

¯

2

(
k
)

{\overline {{\text {GL}}} _2}(k)

, i.e. those representations possessing only one Whittaker functional, or, equivalently, those having a unique Whittaker model. The distinguished representations are precisely the representations attached to the Weil representation associated to a one dimensional form. The local piece of the generalized Shimura correspondence between automorphic forms of

GL

¯

2

(

A

)

{\overline {{\text {GL}}} _2}({\mathbf {A}})

and

G

L

2

(

A

)

{\text {G}}{{\text {L}}_2}({\mathbf {A}})

is also treated. Based upon a conjecture of the equivalences among the constituents of the Weil representations associated to two nonequivalent ternary forms, evidence for the explicit form of the local piece of this global correspondence, restricted to supercuspidal representations of

GL

¯

2

(
k
)

{\overline {{\text {GL}}} _2}(k)

, is presented. In this form, the map is shown to be injective and its image is described.
Boolean powers: direct decomposition and isomorphism types
Authors: Hickin Kenneth , Plotkin J. M.
Published: June 2010

We determine properties of Boolean powers of groups and other algebraic structures, and we generalize Jónsson’s theorem on Boolean powers of centerless, directly indecomposable groups. We show that every nonabelian, finitely generated group has

2

ℵ
0

{2^{{\aleph _0}}}

nonisomorphic countable Boolean, and hence subcartesian, powers. We show that nonabelian groups

G
G

such that either (i)

G
G

is not the central product of two nonabelian groups or (ii) every pair of nontrivial normal subgroups of

G
G

intersect nontrivially yield nonisomorphic Boolean powers with respect to nonisomorphic Boolean algebras.
Nonsmooth analysis: differential calculus of nondifferentiable mappings
Authors: Ioffe A. D.
Published: June 2010

A new approach to local analysis of nonsmooth mappings from one Banach space into another is suggested. The approach is essentially based on the use of set-valued mappings of a special kind, called fans, for local approximation. Convex sets of linear operators provide an example of fans. Generally, fans can be considered a natural set-valued extension of linear operators. The first part of the paper presents a study of fans; the second is devoted to calculus and includes extensions of the main theorems of classical calculus.
On two-dimensional normal singularities of type _{∗}𝐴_{𝑛}, _{∗}𝐷_{𝑛} and _{∗}𝐸_{𝑛}
Authors: Ohyanagi Shigeki
Published: June 2010

Let

G
G

be the weighted dual graph associated with a contractible curve

A
=
∪

A
i

A = \cup {A_i}

. There are many combinations of the weights

A
i

⋅

A
i

{A_i} \cdot {A_i}

which make the graph contractible. If

G
G

is a graph which is the weighted dual graph for a rational singularity with any combination of the weights, then

G
G

is either

∗

A
n

{}_ \ast {A_n}

,

∗

D
n

{}_ \ast {D_n}

or

∗

E
n

_\ast {E_n}

.
Fredholm and invertible 𝑛-tuples of operators. The deformation problem
Authors: Curto Raul E.
Published: June 2010

Using J. L. Taylor’s definition of joint spectrum, we study Fredholm and invertible

n
n

-tuples of operators on a Hilbert space. We give the foundations for a "several variables" theory, including a natural generalization of Atkinson’s theorem and an index which well behaves. We obtain a characterization of joint invertibility in terms of a single operator and study the main examples at length. We then consider the deformation problem and solve it for the class of almost doubly commuting Fredholm pairs with a semi-Fredholm coordinate.
Power series methods of summability: positivity and gap perfectness
Authors: Jakimovski A. , Meyer-König W. , Zeller K.
Published: June 2010

A class of power series methods of summability is defined. By means of a positivity argument (Bohman-Korovkin) it is shown that each method of the class is gap perfect. This fact facilitates the proof of Tauberian gap theorems. Several examples are given.
Projective geometry on partially ordered sets
Authors: Faigle Ulrich , Herrmann Christian
Published: June 2010

A set of axioms is presented for a projective geometry as an incidence structure on partially ordered sets of "points" and "lines". The axioms reduce to the axioms of classical projective geometry in the case where the points and lines are unordered. It is shown that the lattice of linear subsets of a projective geometry is modular and that every modular lattice of finite length is isomorphic to the lattice of linear subsets of some finite-dimensional projective geometry. Primary geometries are introduced as the incidence-geometric counterpart of primary lattices. Thus the theory of finite-dimensional projective geometries includes the theory of finite-dimensional projective Hjelmslev-spaces of level

n
n

as a special case. Finally, projective geometries are characterized by incidence properties of points and hyperplanes.
Generalizations of Cesàro continuous functions and integrals of Perron type
Authors: Lee Cheng Ming
Published: June 2010

The linear space of all the Cesàro continuous functions of any order is extended by introducing pointwisely Cesàro continuous functions and exact generalized Peano derivatives. Then six generalized integrals of Perron type are defined and studied. They are based on three recent monotonicity theorems and each depends on an abstract upper semilinear space of certain functions. Some of the integrals are more general than all the integrals in the Cesàro-Perron scale provided that the abstract semilinear space is taken to be the linear space of all the pointwisely Cesàro continuous functions or all the exact generalized Peano derivatives. That such a concrete general integral is possible follows from the fact proved here that each exact generalized Peano derivative is in Baire class one and has the Darboux property. Relations between the pointwisely Cesàro continuous functions or the exact generalized Peano derivatives and functions defined by means of the values of certain Schwartz’s distributions at "points" are also established.
Cartan structures on contact manifolds
Authors: Burdet G. , Perrin M.
Published: June 2010

Owing to the existence of a dilatation generator of eigenvalues

±
2
,
±
1
,
0

\pm 2, \pm 1,0

the symplectic Lie algebra is considered as a

|

2

|

|2|

-graded Lie algebra. The corresponding decomposition of the symplectic group

Sp(2(

n
+
1

),

R

)

{\text {Sp(2(}}n + 1{\text {),}}{\mathbf {R}}{\text {)}}

makes the semidirect product (denoted

L
0

{L^0}

) of the

(
2
n
+
1
)

(2n + 1)

-dimensional Weyl group by the conformal symplectic group

CSp(

2
n
,

R

)

{\text {CSp(}}2n,{\mathbf {R}}{\text {)}}

appear as a privileged subgroup and permits one to construct a

2
n
+
1

2n + 1

-dimensional homogeneous space possessing a natural contact form. Then

Sp

(
2
(
n
+
1
)
,

R

)

{\text {Sp}}(2(n + 1),{\mathbf {R}})

-valued Cartan connections on a

L
0

{L^0}

principal fibre bundle over a

2
n
+
1

2n + 1

-dimensional manifold

B

2
n
+
1

{B_{2n + 1}}

are constructed and called symplectic Cartan connections. The conditions for obtaining a unique symplectic Cartan connection are given. The existence of this unique Cartan connection is used to define the notion of contact structure over

B

2
n
+
1

{B_{2n + 1}}

and it is shown that any

L
0

{L^0}

-structure of degree

2
2

over

B

2
n
+
1

{B_{2n + 1}}

can be considered as a contact structure on it. Moreover it is shown that a contact structure can be associated in a canonical way to any contact manifold.
A perturbation method in critical point theory and applications
Authors: Bahri Abbas , Berestycki Henri
Published: June 2010

This paper is concerned with existence and multiplicity results for nonlinear elliptic equations of the type

−
Δ
u
=

|
u
|

p
−
1

u
+
h
(
x
)

- \Delta u = {\left | u \right |^{p - 1}}u + h(x)

in

Ω
,

u
=
0

\Omega ,\,u = 0

on

∂
Ω

\partial \Omega

. Here,

Ω
⊂

R

N

\Omega \subset {{\mathbf {R}}^N}

is smooth and bounded, and

h
∈

L
2

(
Ω
)

h \in {L^2}(\Omega )

is given. We show that there exists

p
N

>
1

{p_N} > 1

such that for any

p
∈
(
1
,

p
N

)

p \in (1,\,{p_N})

and any

h
∈

L
2

(
Ω
)

h \in {L^2}(\Omega )

, the preceding equation possesses infinitely many distinct solutions. The method rests on a characterization of the existence of critical values by means of noncontractibility properties of certain level sets. A perturbation argument enables one to use the properties of some associated even functional. Several other applications of this method are also presented.
Obstructions to deforming a space curve
Authors: Curtin Daniel J.
Published: June 2010

Mumford described a curve,

γ
\gamma

, in

P

3

{{\mathbf {P}}^3}

that has obstructed infinitesimal deformations (in fact the Hilbert scheme of the curve is generically nonreduced). This paper studies

γ
′

s

\gamma ’{\text {s}}

Hilbert scheme by studying deformations of

γ
\gamma

in

P

3

{{\mathbf {P}}^3}

over parameter spaces of the form

Spec
⁡
(
k
[
t
]

/

(

t
n

)
)
,

n
=
2
,

3
,

…

\operatorname {Spec} (k[t]/({t^n})),\,n = 2,\,3,\, \ldots

. Given a deformation of

γ
\gamma

over

Spec
⁡
(
k
[
t
]

/

(

t
n

)
)

\operatorname {Spec} (k[t]/({t^n}))

one attempts to extend it to a deformation of

γ
\gamma

over

Spec
⁡
(
k
[
t
]

/

(

t

n
+
1

)
)

\operatorname {Spec} (k[t]/({t^{n + 1}}))

. If it will not extend, this deformation is said to be obstructed at the nth order. I show that on a generic version of Mumford’s curve, an infinitesimal deformation (i.e., a deformation over

Spec
⁡
(
k
[
t
]

/

(

t
2

)
)

\operatorname {Spec} (k[t]/({t^2}))

) is either obstructed at the second order, or at no order, in which case we say it is unobstructed.
Algebraic determination of fiberwise PL involutions
Authors: Kim Hayon , Kim Jehpill , Kwun Kyung Whan
Published: June 2010

Some fiberwise PL involutions on fibered

3
3

-manifolds induce the obvious automorphism of the fundamental group. It is shown that this expected behavior of the fundamental group in turn characterizes such fiberwise involutions.
The complexification and differential structure of a locally compact group
Authors: McKennon Kelly
Published: June 2010

The concept of a complexification of a locally compact group is defined and its connections with the differential structure developed. To provide an interpretation in terms of irreducible representations of separable, Type I groups, a duality theorem and Bochner theorem are presented.
Spherical means and geodesic chains on a Riemannian manifold
Authors: Sunada Toshikazu
Published: June 2010

Some spectral properties of spherical mean operators defined on a Riemannian manifold are given. As an application we deduce a statistic property of geodesic chains which is interesting from the view point of geometric probability.
Partitions of products
Authors: Pincus David , Halpern J. D.
Published: June 2010

This paper extends some applications of a theorem of Halpern and Lauchli on partitions of products of finitary trees. The extensions are to weak infinite products of dense linear orderings, and ultrafilter preservation for finite product Sacks forcing.
A network of congruences on an inverse semigroup
Authors: Petrich Mario , Reilly Norman R.
Published: June 2010

A congruence

ρ
\rho

on an inverse semigroup

S
S

is determined uniquely by its kernel and its trace. Denoting by

ρ

min

{\rho ^{\min }}

and

ρ

min

{\rho _{\min }}

the least congruence on

S
S

having the same kernel and the same trace as

ρ
\rho

, respectively, and denoting by

ω
\omega

the universal congruence on

S
S

, we consider the sequence

ω
\omega

,

ω

min

{\omega ^{\min }}

,

ω

min

{\omega _{\min }}

,

(

ω

min

)

min

{({\omega ^{\min }})_{\min }}

,

(

ω

min

)

min

…

{({\omega _{\min }})^{\min }} \ldots

. These congruences, together with the intersections of corresponding pairs, form a sublattice of the lattice of all congruences on

S
S

. We study the properties of these congruences and establish several properties of the quasivarieties of inverse semigroups induced by them.
On the radial limits of analytic and meromorphic functions
Authors: Hwang J. S.
Published: June 2010

Early in the fifties, A. J. Lohwater proved that if

f
(
z
)

f(z)

is analytic in

|

z

|

>
1

|z| > 1

and has the radial limit

0
0

almost everywhere on

|

z

|

=
1

|z| = 1

, then every complex number

ζ
\zeta

is an asymptotic value of

f
(
z
)

f(z)

provided the

ζ
\zeta

-points satisfy the following Blaschke condition:

∑

k
=
1

∞

(
1
−

|

z
k

|

)
>
∞

\sum _{k = 1}^\infty (1 - |{z_k}|) > \infty

, where

f
(

z
k

)
=
ζ

f({z_k}) = \zeta

,

k
=
1

,
2
,
…

k = 1\,,2, \ldots

. We may, therefore, ask under the hypothesis on

f
(
z
)

f(z)

how many complex numbers

ζ
\zeta

are there whose

ζ
\zeta

-points can satisfy the Blaschke condition. We show that there is at most one such number and this one number phenomenon can actually occur if the number is zero.
Type structure complexity and decidability
Authors: Millar T. S.
Published: June 2010

We prove that for every countable homogeneous model

A

\mathcal {A}

such that the set of recursive types of

Th
⁡
(

A

)

\operatorname {Th} (\mathcal {A})

is

∑
2
0

\sum _2^0

,

A

\mathcal {A}

is decidable iff the set of types realized in

A

\mathcal {A}

is a

∑
2
0

\sum _2^0

set of recursive types. As a corollary to a lemma, we show that if a complete theory

T
T

has a recursively saturated model that is decidable in the degree of

T
T

, then

T
T

has a prime model.
Transfer and the spectral sequence of a fibration
Authors: Prieto Carlos
Published: June 2010

The purpose of this paper is to show that transfers for fibrations behave well with respect to spectral sequences which are induced by filtrations of the base space. In particular, for the spectral sequence of a fibration (induced by the skeletal filtration of the base space), one obtains the expected effect on the

E
2

{E_2}

-terms: We prove that the transfer in the

E
2

{E_2}

-terms is determined by the transfer of the fiber (considered trivially as a fibration over a point). As an application, results of Atiyah on the

K
K

-theory of classifying spaces are transcribed to generalized cohomology theories.
A remainder formula and limits of cardinal spline interpolants
Authors: Goodman T. N. T. , Lee S. L.
Published: June 2010

A Peano-type remainder formula
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis x right-parenthesis minus upper S Subscript n Baseline left-parenthesis f semicolon x right-parenthesis equals integral Subscript negative normal infinity Superscript normal infinity Baseline upper K Subscript n Baseline left-parenthesis x comma t right-parenthesis f Superscript left-parenthesis n plus 1 right-parenthesis Baseline left-parenthesis t right-parenthesis d t">

f
(
x
)
−

S
n

(
f
;

x
)
=

∫

−
∞

∞

K
n

(
x
,

t
)

f

(
n
+
1
)

(
t
)

d
t

f(x) - {S_n}(f;\,x) = \int _{ - \infty }^\infty {{K_n}(x,\,t){f^{(n + 1)}}(t)\,dt}

\]
for a class of symmetric cardinal interpolation problems C.I.P.

(
E
,

F
,

x

)

(E,\,F,\,{\mathbf {x}})

is obtained, from which we deduce the estimate
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue EndAbsoluteValue f minus upper S Subscript n comma r Baseline left-parenthesis f semicolon right-parenthesis StartAbsoluteValue EndAbsoluteValue Subscript normal infinity Baseline less-than-or-slanted-equals upper K StartAbsoluteValue EndAbsoluteValue f Superscript left-parenthesis n plus 1 right-parenthesis Baseline StartAbsoluteValue EndAbsoluteValue Subscript normal infinity">

|

|

f
−

S

n
,
r

(
f
;

)

|

|

∞

⩽
K

|

|

f

(
n
+
1
)

|

|

∞

||f - {S_{n,r}}(f;\,)|{|_\infty } \leqslant K||{f^{(n + 1)}}|{|_\infty }

. It is found that the best constant

K
K

is obtained when

x

{\mathbf {x}}

comprises the zeros of the Euler-Chebyshev spline function. The remainder formula is also used to study the convergence of spline interpolants for a class of entire functions of exponential type and a class of almost periodic functions.
Varieties of combinatorial geometries
Authors: Kahn J. , Kung J. P. S.
Published: June 2010

A hereditary class of (finite combinatorial) geometries is a collection of geometries which is closed under taking minors and direct sums. A sequence of universal models for a hereditary class

J

\mathcal {J}

of geometries is a sequence

(

T
n

)

({T_n})

of geometries in

J

\mathcal {J}

with rank

T
n

=
n

{T_n} = n

, and satisfying the universal property: if

G
G

is a geometry in

J

\mathcal {J}

of rank

n
n

, then

G
G

is a subgeometry of

T
n

{T_n}

. A variety of geometries is a hereditary class with a sequence of universal models. We prove that, apart from two degenerate cases, the only varieties of combinatorial geometries are (1) the variety of free geometries, (2) the variety of geometries coordinatizable over a fixed finite field, and (3) the variety of voltage-graphic geometries with voltages in a fixed finite group.
Generalized skew polynomial rings
Authors: Dauns John
Published: June 2010

For a totally ordered cancellative semigroup

Γ
\Gamma

, a skew field

K
K

, let

K
[
Γ
;
ϕ
]

K[\Gamma ;\phi ]

be a skew semigroup ring. If

x
∈
Γ
,

k
∈
K

x \in \Gamma ,\,k \in K

, then

k
x
=
x

k
x

kx = x{k^x}

, where

k
→

k
x

k \to {k^x}

is an endomorphism of

K
K

depending on

x
x

. Ideals of

K
[
Γ
;
ϕ
]

K[\Gamma ;\phi ]

are investigated for various semigroups or groups

Γ
\Gamma

.
The metabelian 𝑝-groups of maximal class. II
Authors: Miech R. J.
Published: June 2010

This paper gives a classification, up to isomorphism, of the metabelian

p
p

-groups of maximal class. A recent idea is used to produce a considerable simplification of an earlier classification scheme for these groups.
Determining Thurston classes using Nielsen types
Authors: Gilman Jane
Published: June 2010

In previous work [3] we showed how the Thurston or Bers classifications of diffeomorphisms of surfaces could be obtained using the Nielsen types of the lifts of the diffeomorphism to the unit disc. In this paper we find improved conditions on the Nielsen types for the Thurston and Bers classes. We use them to verify that an example studied by Nielsen is a pseudo-Anosov diffeomorphism with stretching factor of degree 4. This example is of interest in its own right, but it also serves to illustrate exactly how the Nielsen types are used for verifying examples. We discuss the general usefulness of this method.
An almost sure invariance principle for Hilbert space valued martingales
Authors: Morrow Gregory , Philipp Walter
Published: June 2010

We obtain an almost sure approximation of a martingale with values in a real separable Hilbert space

H
H

by a suitable

H
H

-valued Brownian motion.
Products of 𝑘-spaces and spaces of countable tightness
Authors: Gruenhage G. , Tanaka Y.
Published: June 2010

In this paper, we obtain results of the following type: if

f
:
X
→
Y

f:X \to Y

is a closed map and

X
X

is some "nice" space, and

Y
2

{Y^2}

is a

k
k

-space or has countable tightness, then the boundary of the inverse image of each point of

Y
Y

is "small" in some sense, e.g., Lindelöf or

ω
1

{\omega _1}

-compact. We then apply these results to more special cases. Most of these applications combine the "smallness" of the boundaries of the point-inverses obtained from the earlier results with "nice" properties of the domain to yield "nice" properties on the range.
On the double suspension homomorphism at odd primes
Authors: Harper J. R. , Miller H. R.
Published: June 2010

We work with the

E
1

{E_1}

-term for spheres and the stable Moore space, given by the

Λ
\Lambda

-algebra at odd primes. Writing

W
(
n
)
=
Λ
(
2
n
+
1
)

/

Λ
(
2
n
−
1
)

W(n) = \Lambda (2n + 1)/\Lambda (2n - 1)

and

M
(
0
)
=

H
∗

(

S
0

∪
p

e
1

)

M(0) = {H_ \ast }({S^0}{ \cup _p}{e^1})

, we construct compatible maps

f
n

⋅
W
(
n
)
→
M
(
0
)

⊗
~

Λ

{f_n} \cdot W(n) \to M(0)\tilde \otimes \Lambda

and prove the Metastability Theorem: in homology

f
n

{f_n}

induces an isomorphism for

σ
>
2
(

p
2

−
1
)
(
s
−
2
)
+
p
q
n
−
2
p
−
2

\sigma > 2({p^2} - 1)(s - 2) + pqn - 2p - 2

where

σ
=
stem degree

\sigma = \text {stem degree}

,

s
=
homological degree 

s = \text {homological degree }

resulting from the bigrading of

Λ
\Lambda

and

q
=
2
p
−
2

q = 2p - 2

. There is an operator

υ
1

{\upsilon _1}

corresponding to the Adams stable self-map of the Moore space and

υ
1

{\upsilon _1}

extends to

W
(
n
)

W(n)

. A corollary of the Metastability Theorem and the Localization Theorem of the second author is that the map

f
n

{f_n}

induces an isomorphism on homology after inverting

υ
1

{\upsilon _1}

.
On the oscillation theory of 𝑓′′+𝐴𝑓=0 where 𝐴 is entire
Authors: Bank Steven B. , Laine Ilpo
Published: June 2010

In this paper, we investigate the distribution of zeros of solutions of

f
+
A
(
z
)
f
=
0

f + A(z)f = 0

. More specifically, results are obtained concerning the exponent of convergence of the zero-sequence of a solution in both the case where

A
(
z
)

A(z)

is a polynomial, and the case where

A
(
z
)

A(z)

is transcendental.
Whitney levels in hyperspaces of certain Peano continua
Authors: Goodykoontz Jack T. , Nadler Sam B.
Published: June 2010

Let

X
X

be a Peano continuum. Let

2
x

{2^x}

(resp.,

C
(
X
)

C(X)

) be the space of all nonempty compacta (resp., subcontinua) of

X
X

with the Hausdorff matric. Let

ω
\omega

be a Whitney map defined on

H

=

2

X

\mathcal {H}={2^{X}}

or

C
(
X
)

C(X)

such that

ω
\omega

is admissible (this requires the existence of a certain type of deformation of

H

\mathcal {H}

). If

H

=
C
(
X
)

\mathcal {H}=C(X)

, assume

X
X

contains no free arc. Then, for any

t
0

∈
(
0
,
ω
(
X
)
)

{t_0} \in (0,\omega (X))

, it is proved that

ω

−
1

(

t
0

)
,

ω

−
1

(
[
0
,

t
0

]
)

{\omega ^{ - 1}}({t_0}),\,{\omega ^{ - 1}}([0,\,{t_0}])

, and

ω

−
1

(
[

t
0

,

ω
(
X
)
]
)

{\omega ^{ - 1}}([{t_0},\,\omega (X)])

are Hilbert cubes. This is an analogue of the Curtis-Schori theorem for

H

\mathcal {H}

. A general result for the existance of admissible Whitney maps is proved which implies that these maps exist when

X
X

is starshaped in a Banach space or when

X
X

is a dendrite. Using these results it is shown, for example that being an AR, an ANR, an LC space, or an

L

C

n

{\text {L}}{{\text {C}}^n}

space is not strongly Whitney-reversible.
On the variety of invariant subspaces of a finite-dimensional linear operator
Authors: Shayman Mark A.
Published: June 2010

If

V
V

is a finite-dimensional vector space over

R

\mathbf {R}

or

C

\mathbf {C}

and

A
∈

Hom

(
V
)

A \in {\operatorname {Hom}}(V)

, the set

S
A

(
k
)

{S_A}(k)

of

k
k

-dimensional

A
A

-invariant subspaces is a compact subvariety of the Grassmann manifold

G
k

(
V
)

{G^k}(V)

, but it need not be a Schubert variety. We study the topology of

S
A

(
k
)

{S_A}(k)

. We reduce to the case where

A
A

is nilpotent. In this case we prove that

S
A

(
k
)

{S_A}(k)

is connected but need not be a manifold. However, the subset of

S
A

(
k
)

{S_A}(k)

consisting of those subspaces with a fixed cyclic structure is a regular submanifold of

G
k

(
V
)

{G^k}(V)

.
Computability and noncomputability in classical analysis
Authors: Pour-El Marian Boykan , Richards Ian
Published: June 2010

This paper treats in a systematic way the following question: which basic constructions in real and complex analysis lead from the computable to the noncomputable, and which do not? The topics treated include: computability for

C
n

{C^n}

,

C
∞

{C^\infty }

, real analytic functions, Fourier series, and Fourier transforms. A final section presents a more general approach via "translation invariant operators". Particular attention is paid to those processes which occur in physical applications. The approach to computability is via the standard notion of recursive function from mathematical logic.
Differentiable group actions on homotopy spheres. III. Invariant subspheres and smooth suspensions
Authors: Schultz Reinhard
Published: June 2010

A linear action of an abelian group on a sphere generally contains a large family of invariant linear subspheres. In this paper the problem of finding invariant subspheres for more general smooth actions on homotopy spheres is considered. Classification schemes for actions with invariant subspheres are obtained; these are formally parallel to the classifications discussed in the preceding paper of this series. The realizability of a given smooth action as an invariant codimension two subsphere is shown to depend only on the ambient differential structure and an isotopy invariant. Applications of these results to specific cases are given; for example, it is shown that every exotic

10
10

-sphere admits a smooth circle action.
Unital 𝑙-prime lattice-ordered rings with polynomial constraints are domains
Authors: Steinberg Stuart A.
Published: June 2010

It is shown that a unital lattice-ordered ring in which the square of every element is positive must be a domain provided the product of two nonzero

l
l

-ideals is nonzero. More generally, the same conclusion follows if the condition

a
2

⩾
0

{a^2} \geqslant 0

is replaced by

p
(
a
)
⩾
0

p(a) \geqslant 0

for suitable polynomials

p
(
x
)

p(x)

; and if it is replaced by

f
(
a
,
b
)
⩾
0

f(a,b) \geqslant 0

for suitable polynomials

f
(
x
,
y
)

f(x,y)

one gets an

l
l

-domain. It is also shown that if

a
∧
b
=
0

a \wedge b = 0

in a unital lattice-ordered algebra which satisfies these constraints, then the

l
l

-ideals generated by

a
b

ab

and

b
a

ba

are identical.
Some conjectures on elliptic curves over cyclotomic fields
Authors: Goldfeld D. , Viola C.
Published: June 2010

We give conjectures for the mean values of Hasse-Weil type

L
L

-functions over cyclotomic fields. In view of the Birch-Swinnerton-Dyer conjectures, this translates to interesting arithmetic information.
The derived functors of the primitives for 𝐵𝑃_{∗}(Ω𝑆²ⁿ⁺¹)
Authors: Bendersky Martin
Published: June 2010

Formulas for the Hopf invariant, and the

P
P

map in the Novikov double suspension sequence are derived. The formulas allow an effective inductive computation of the

E
2

{E_2}

-term of the unstable Adams-Novikov spectral sequence. The

3
3

primary

E
2

{E_2}

-term through the

54
54

stem is displayed.
The splitting of 𝐵𝑂⟨8⟩∧𝑏𝑜 and 𝑀𝑂⟨8⟩∧𝑏𝑜
Authors: Davis Donald M.
Published: June 2010

Let

B
O

⟨
8
⟩

BO\left \langle 8 \right \rangle

denote the classifying space for vector bundles trivial on the

7
7

-skeleton, and

M
O

⟨
8
⟩

MO\left \langle 8 \right \rangle

the associated Thom spectrum. It is proved that, localized at

2
2

,

B
O

⟨
8
⟩

∧

b
o

BO\left \langle 8 \right \rangle \wedge \,bo

and

M
O

⟨
8
⟩

∧

b
o

MO\left \langle 8 \right \rangle \wedge \,bo

split as a wedge of familiar spectra closely related to

b
o

bo

, where

b
o

bo

is the spectrum for connective

K
O

KO

-theory.
Weighted norm inequalities for the Fourier transform
Authors: Muckenhoupt Benjamin
Published: June 2010

Given

p
p

and

q
q

satisfying

1
>
p
⩽
q
>
∞

1 > p \leqslant q > \infty

, sufficient conditions on nonnegative pairs of functions

U
,
V

U,V

are given to imply
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-bracket integral Subscript upper R Superscript n Baseline Superscript Baseline StartAbsoluteValue ModifyingAbove f With caret left-parenthesis x right-parenthesis EndAbsoluteValue Superscript q Baseline upper U left-parenthesis x right-parenthesis d x right-bracket Superscript 1 slash q Baseline less-than-or-slanted-equals c left-bracket integral Subscript upper R Superscript n Baseline Superscript Baseline StartAbsoluteValue f left-parenthesis x right-parenthesis EndAbsoluteValue Superscript p Baseline upper V left-parenthesis x right-parenthesis d x right-bracket Superscript 1 slash p Baseline comma">

[

∫

R
n

|

f
^

(
x
)

|

q

U
(
x
)

d
x

]

1

/

q

⩽
c

[

∫

R
n

|

f
(
x
)

|

p

V
(
x
)

d
x

]

1

/

p

,

{\left [ {\int _{{R^n}}^{} {|\hat f(x){|^q}U(x)\,dx}} \right ]^{1/q}} \leqslant c{\left [ {\int _{{R^n}}^{} {|f(x){|^p}V(x)\,dx}} \right ]^{1/p}},

\]
where

f
^

\hat f

denotes the Fourier transform of

f
f

, and

c
c

is independent of

f
f

. For the case

q
=

p
′

q = p’

the sufficient condition is that for all positive

r
r

,
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-bracket integral Underscript upper U left-parenthesis x right-parenthesis greater-than upper B r Endscripts upper U left-parenthesis x right-parenthesis d x right-bracket left-bracket integral Underscript upper V left-parenthesis x right-parenthesis greater-than r Superscript p minus 1 Baseline Endscripts upper V left-parenthesis x right-parenthesis Superscript negative 1 slash left-parenthesis p minus 1 right-parenthesis Baseline d x right-bracket less-than-or-slanted-equals upper A comma">

[

∫

U
(
x
)
>
B
r

U
(
x
)

d
x

]

[

∫

V
(
x
)
>

r

p
−
1

V

(
x
)

−
1

/

(
p
−
1
)

d
x

]

⩽
A
,

\left [ {\int _{U(x) > Br} {U(x)\;dx}} \right ]\left [ {\int _{V(x) > {r^{p - 1}}} {V{{(x)}^{- 1/(p - 1)}}\;dx}} \right ] \leqslant A,

\]
where

A
A

and

B
B

are positive and independent of

r
r

. For

q
≠

p
′

q \ne p’

the condition is more complicated but also is invariant under rearrangements of

U
U

and

V
V

. In both cases the sufficient condition is shown to be necessary if the norm inequality holds for all rearrangements of

U
U

and

V
V

. Examples are given to show that the sufficient condition is not necessary for a pair

U
,
V

U,V

if the norm inequality is assumed only for that pair.
Discrete series characters and Fourier inversion on semisimple real Lie groups
Authors: Herb Rebecca A.
Published: June 2010

Let

G
G

be a semisimple real Lie group. Explicit formulas for discrete series characters on noncompact Cartan subgroups are given. These formulas are used to give a simple formula for the Fourier transform of orbital integrals of regular semisimple orbits.
Relative genus theory and the class group of 𝑙-extensions
Authors: Cornell Gary
Published: June 2010

The structure of the relative genus field is used to study the class group of relative

l
l

-extensions. Application to class field towers of cyclic

l
l

-extensions of the rationals are given.
Extension of Wiener’s Tauberian identity and multipliers on the Marcinkiewicz space
Authors: Lau Ka-Sing
Published: June 2010

This is a continuation of the work of Bertrandias, Lee and Lau on Wiener’s generalized harmonic analysis. Among the other results, we extend Wiener’s Tauberian identity to cover a larger class of functions; we characterize the multipliers on the Marcinkiewicz space

M

2

{\mathcal {M}^2}

, and we obtain a Tauberian theorem on

M

2

{\mathcal {M}^2}

with full generality.
Asymptotic behaviour and propagation properties of the one-dimensional flow of gas in a porous medium
Authors: Vázquez Juan Luis
Published: June 2010

The one-dimensional porous media equation

u
t

=

(

u
m

)

x
x

{u_t} = {({u^m})_{xx}}

,

m
>
1

m > 1

, is considered for

x
∈
R

x \in R

,

t
>
0

t > 0

with initial conditions

u
(
x
,
0
)
=

u
0

(
x
)

u(x,0) = {u_0}(x)

integrable, nonnegative and with compact support. We study the behaviour of the solutions as

t
→
∞

t \to \infty

proving that the expressions for the density, pressure, local velocity and interfaces converge to those of a model solution. In particular the first term in the asymptotic development of the free-boundary is obtained.
The symmetric derivative
Authors: Larson Lee
Published: June 2010

It is shown that all symmetric derivatives belong to Baire class one, and a condition characterizing all measurable symmetrically differentiable functions is presented. A method to find a well-behaved primitive for any finite symmetric derivative is introduced, and several of the standard theorems of differential calculus are extended to include the symmetric derivative.
Ambiently universal sets in 𝐸ⁿ
Authors: Wright David G.
Published: June 2010

For each closed set

X
X

in

E
n

{E^n}

of dimension at most

n
−
3

n - 3

, we show that

X
X

fails to be ambiently universal with respect to Cantor sets in

E
n

{E^n}

; i.e., we find a Cantor set

Y
Y

in

E
n

{E^n}

so that for any self-homeomorphism

h
h

of

E
n

{E^n}

,

h
(
Y
)

h(Y)

is not contained in

X
X

. This result answers a question posed by H. G. Bothe and completes the understanding of ambiently universal sets in

E
n

{E^n}

.
Strongly Cohen-Macaulay schemes and residual intersections
Authors: Huneke Craig
Published: June 2010

This paper studies the local properties of closed subschemes

Y
Y

in Cohen-Macaulay schemes

X
X

such that locally the defining ideal of

Y
Y

in

X
X

has the property that its Koszul homology is Cohen-Macaulay. Whenever this occurs

Y
Y

is said to be strongly Cohen-Macaulay in

X
X

. This paper proves several facts about such embeddings, chiefly with reference to the residual intersections of

Y
Y

in

X
X

. The main result states that any residual intersection of

Y
Y

in

X
X

is again Cohen-Macaulay.
Bi-interpretable groups and lattices
Authors: Jambu-Giraudet M.
Published: June 2010

A large class of

0
-
2

0\text {-}2

transitive lattice-ordered groups is finitely axiomatizable as a class of groups and as a class of lattices. In each model, the group structure and the lattice structure plus one parameter are bi-interpretable, sometimes up to duality only. A characterization of lattice-automorphisms of the structures is also given.
Inverting the half-jump
Authors: Homer S. , Sacks G. E.
Published: June 2010

Assume

β
\beta

is weakly admissible over

0
0

and

0

1

/

2

{0^{1\,/\,2}}

. It follows that the

β
\beta

-recursively enumerable degrees are dense. In addition each

β
\beta

-recursively enumerable degree above

0

1

/

2

{0^{1\,/\,2}}

is the half-jump of some tamely

β
\beta

-recursively enumerable degree below

0

1

/

2

{0^{1\,/\,2}}

.
The structure of rings with faithful nonsingular modules
Authors: Zelmanowitz J. M.
Published: June 2010

It is shown that the existence of a faithful nonsingular uniform module characterizes rings which have a full linear maximal quotient ring. New information about the structure of these rings is obtained and their maximal quotient rings are constructed in an explicit manner. More generally, rings whose maximal quotient rings are finite direct sums of full linear rings are characterized by the existence of a faithful nonsingular finite dimensional module.
The Gauss-Lucas theorem and Jensen polynomials
Authors: Craven Thomas , Csordas George
Published: June 2010

A characterization is given of the sequences

{

γ
k

}

k
=
0

∞

\{ {\gamma _k}\}_{k = 0}^\infty

with the property that, for any complex polynomial

f
(
z
)
=
Σ

a
k

z
k

f(z) = \Sigma \,{a_k}{z^k}

and convex region

K
K

containing the origin and the zeros of

f
f

, the zeros of

Σ

γ
k

a
k

z
k

\Sigma \,{\gamma _k}{a_k}{z^k}

again lie in

K
K

. Many applications and related results are also given. This work leads to a study of the Taylor coefficients of entire functions of type

I
\text {I}

in the Laguerre-Pólya class. If the power series of such a function is given by

Σ

γ
k

z
k

/

k
!

\Sigma \,{\gamma _k}{z^k}/k!

and the sequence

{

γ
k

}

\{ {\gamma _k}\}

is positive and increasing, then the sequence satisfies an infinite collection of strong conditions on the differences, namely

Δ
n

γ
k

⩾
0

{\Delta ^n}{\gamma _k} \geqslant 0

for all

n
n

,

k
k

.
The coordinatization of Arguesian lattices
Authors: Day Alan , Pickering Douglas
Published: June 2010

We show that the auxiliary planar ternary ring of an

n
n

-frame in an Arguesian lattice,

n
⩾
3

n \geqslant 3

, is indeed an associative ring with unit. The addition of two weak necessary conditions allows us to coordinatize a hyperplane of this

n
n

-frame. This generalizes the classical work of von Neumann, Baer-Inaba, Jónsson and Jónsson-Monk.
Almost everywhere summability on nilmanifolds
Authors: Hulanicki Andrzej , Jenkins Joe W.
Published: June 2010

Let

G
G

be a stratified, nilpotent Lie group and let

L
L

be a homogeneous sublaplacian on

G
G

. Let

E
(
λ
)

E(\lambda )

denote the spectral resolution of

L
L

on

L
2

(
G
)

{L^2}(G)

. Given a function

K
K

on

R

+

\mathbf {R}^+

, define the operator

T
K

{T_K}

on

L
2

(
G
)

{L^2}(G)

by

T
k

f
=

∫
0
∞

K
(
λ
)

d
E
(
λ
)

f

{T_k}f = \int _0^\infty \, {K(\lambda )\;dE(\lambda )\,f}

. Sufficient conditions on

K
K

to imply that

T
K

{T_K}

is bounded on

L
1

(
G
)

{L^1}(G)

and the maximal operator
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K Superscript asterisk Baseline phi left-parenthesis x right-parenthesis equals sup Underscript t greater-than 0 Endscripts StartAbsoluteValue upper T Subscript upper K Sub Subscript t Subscript Baseline phi left-parenthesis x right-parenthesis EndAbsoluteValue">

K

∗

φ
(
x
)
=

sup

t
>
0

|

T

K
t

φ
(
x
)

|

K^{\ast } \varphi (x) = \sup _{t > 0}|{T_{K_t}}\varphi (x)|

(where

K
t

(
λ
)
=
K
(
t
λ
)

{K_t}(\lambda ) = K(t\lambda )

) is of weak type

(
1
,
1
)

(1,1)

are given. Picking a basis

e
0

,

e
1

,
…

{e_0},{e_1},\ldots

of

L
2

(
G

/

Γ
)

{L^2}(G/\Gamma )

(

Γ
\Gamma

being a discrete cocompact subgroup of

G
G

) consisting of eigenfunctions of

L
L

, we obtain almost everywhere and norm convergence of various summability methods of
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Sigma left-parenthesis phi comma e Subscript j Baseline right-parenthesis e Subscript j Baseline comma phi element-of upper L Superscript p Baseline left-parenthesis upper G slash normal upper Gamma right-parenthesis comma 1 less-than-or-slanted-equals p greater-than normal infinity">

Σ
(
φ
,

e
j

)

e
j

,
φ
∈

L
p

(
G

/

Γ
)
,
1
⩽
p
>
∞

\Sigma (\varphi ,{e_j}){e_j},\varphi \in {L^p}(G/\Gamma ), 1 \leqslant p > \infty

.
An inequality with applications in potential theory
Authors: Korenblum Boris , Thomas Edward
Published: June 2010

An analytic inequality (announced previously) is proved and a certain monotonicity condition is shown to be essential for its validity, contrary to an earlier conjecture. Then, a generalization of the inequality, which takes into account the extent of nonmonotonicity, is established.
The invariant subspace structure of nonselfadjoint crossed products
Authors: Solel Baruch
Published: June 2010

Let

L

\mathcal {L}

be the von Neumann algebra crossed product determined by a finite von Neumann algebra

M
M

and a trace preserving

∗

^{\ast }

-automorphism

α
\alpha

of

M
M

. We study the invariant subspace structure of the subalgebra

L

+

{\mathcal {L}_ + }

of

L

\mathcal {L}

consisting of those operators whose spectrum with respect to the dual automorphism group on

L

\mathcal {L}

is nonnegative. We investigate the conditions for two invariant subspaces

M

1

{\mathcal {M}_1}

, and

M

2

{\mathcal {M}_2}

(with

Q

1

,

Q
2

{Q_{1}},{Q_2}

the corresponding orthogonal projections) to satisfy

Q
1

=

R
υ

Q
2

R
υ

∗

{Q_1} = {R_\upsilon }\,{Q_2}\,R_\upsilon ^{\ast }

for some partial isometry

R

υ

{R_{\upsilon }}

in

L

′

\mathcal {L}’

. We use this analysis to find the general form of a

σ
\sigma

-weakly closed subalgebra of

L

\mathcal {L}

that contains

L

+

{\mathcal {L}_ + }

.
A convergence theory for saddle functions
Authors: Attouch Hédy , Wets Roger J.-B.
Published: June 2010

We develop a convergence theory called epi/hypo-convergence, for bivariate functions that essentially implies the convergence of their saddle points. We study the properties of this limiting process in particular. We characterize the limit functions associated to any collection of bivariate functions and obtain a compactness theorem for the space of saddle functions. Even when restricted to the univariate case, the results generalize those known for epi-convergence. In particular, we show that the analysis of the convergence process via Yosida approximates must not be restricted to the convex case.
Highly connected embeddings in codimension two
Authors: Szczepanski Susan
Published: June 2010

In this paper we study semilocal knots over

f
f

into

ξ
\xi

, that is, embeddings of a manifold

N
N

into

E
(
ξ
)

E(\xi )

, the total space of a

2
2

-disk bundle over a manifold

M
M

, such that the restriction of the bundle projection

p
:
E
(
ξ
)
→
M

p:E(\xi ) \to M

to the submanifold

N
N

is homotopic to a normal map of degree one,

f
:
N
→
N

f:N \to N

. We develop a new homology surgery theory which does not require homology equivalences on boundaries and, in terms of these obstruction groups, we obtain a classification (up to cobordism) of semilocal knots over

f
f

into

ξ
\xi

. In the simply connected case, the following geometric consequence follows from our classification. Every semilocal knot of a simply connected manifold

M
#
K

M\# K

in a bundle over

M
M

is cobordant to the connected sum of the zero section of this bundle with a semilocal knot of the highly connected manifold

K
K

into the trivial bundle over a sphere.
Diffusion dependence of the FitzHugh-Nagumo equations
Authors: Collins Clyde
Published: June 2010

We investigate the behavior of the solutions of
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row u Subscript t Baseline equals u Subscript x x Baseline minus alpha u minus v plus f left-parenthesis u right-parenthesis comma 2nd Row v Subscript t Baseline equals eta v Subscript x x Baseline plus sigma u minus gamma v comma EndLayout">

u
t

=

u

x

x

−
α

u
−
v
+
f
(
u
)
,

v
t

=
η

v

x

x

+
σ

u
−
γ
v
,

\begin {array}{*{20}{c}} {{u_t} = {u_{x\,x}} - \alpha \,u - v + f(u),} \\ {{v_t} = \eta \,{v_{x\,x}} + \sigma \,u - \gamma v,} \\ \end {array}

\]
as

η
\eta

tends to zero from above.
Correction to: “The stable geometric dimension of vector bundles over real projective spaces” [Trans. Amer. Math. Soc. 268 (1981), no. 1, 39–61; MR0628445 (83c:55006)]
Authors: Davis Donald M. , Gitler Sam , Mahowald Mark
Published: June 2010

The theory of

b
o

bo

-resolutions as utilized in The stable geometric dimension of vector bundles over real projective spaces did not give adequate care to the

K

Z

2

K{{\mathbf {Z}}_2}

’s occurring at each stage of the resolution. This restricts somewhat the set of integers

e
e

for which we can prove that the geometric dimension of vector bundles of order

2
e

{2^e}

on large real projective spaces is precisely

2

e
+
δ

2\,e + \delta

.
Weighted norm inequalities for strongly singular convolution operators
Authors: Chanillo Sagun
Published: June 2010

We derive sharp function estimates for convolution operators whose kernels are more singular than Calderon-Zygmund kernels. This leads to weighted norm inequalities. Weighted weak

(
1
,
1
)

(1,1)

results are also proved. All the results obtained are in the context of

A
p

{A_p}

weights.
Homologically homogeneous rings
Authors: Brown K. A. , Hajarnavis C. R.
Published: June 2010

In this paper we study the structure of a right Noetherian ring

R
R

of finite right global dimesion integral over a central subring

C
C

and satisfying the following condition: if

V
,
W

V,W

are irreducible right

R
R

-modules with

r
C

(
V
)
=

r
C

(
W
)

{r_C}(V) = {r_C}(W)

then

pr

dim
⁡
(
V
)
=
pr

dim
⁡
(
W
)

\operatorname {pr}\, \dim (V) = \operatorname {pr}\, \dim (W)

.
Nonlinear stability of asymptotic suction
Authors: Miklavčič Milan
Published: June 2010

The semigroup approach to the Navier-Stokes equation in halfspace is used to prove that the stability of the asymptotic suction velocity profile is determined by the eigenvalues of the classical Orr-Sommerfeld equation. The usual obstacle, namely, that the corresponding linear operator contains

0
0

in the spectrum is removed with the use of weighted spaces.
Inducible periodic homeomorphisms of tree-like continua
Authors: Toledo Juan A.
Published: June 2010

In this paper we prove that every periodic homeomorphism on a tree-like continuum can be strongly induced on an inverse sequence composed of a certain kind of graph that we call “bellows”. We introduce the concepts of “#-graph” of a periodic homeomorphism and of “perfect” homeomorphism. A theorem concerning the parallel inducing of two periodic homeomorphisms having orbit spaces with the same multiplicity structure is also proved. The results are related to conjugacy and to the pseudo-arc.