bluuebunny/crossref_metadata_2025 huggingface dataset:
On regular semigroups and their multiplication
Authors: Grillet Pierre Antoine
Published: July 2010

A method is given for the construction of regular semigroups in terms of groups and partially ordered sets. This describes any regular semigroup S and its multiplication by means of triples

(

i
,

g
,

λ

)

\left ( {i,\,g,\,\lambda } \right )

with

i

∈

S

/

R

i\, \in \,S/{\mathcal {R}}

,

λ

∈

S

/

L

\lambda \, \in \,S/{\mathcal {L}}

and g in the Schützenberger group of the corresponding

D

{\mathcal {D}}

-class. It is shown that the multiplication on S is determined by certain simple products. Furthermore the associativity of these simple products implies associativity of the entire multiplication.
On modular functions in characteristic 𝑝
Authors: Li Wen Ch’ing Winnie
Published: July 2010

Let

k

=

F

q

(
T
)

k\, = \,{{\textbf {F}}_q}\left ( T \right )

be a function field of one variable over a finite field

F

q

{{\textbf {F}}_q}

. For a nonzero polynomial

A

∈

F

q

[
T
]

A\, \in \,{{\textbf {F}}_q}\left [ T \right ]

one can define the modular group

Γ

(
A
)

\Gamma \left ( A \right )

. In this paper, we continue a theme introduced by Weil, and study the

λ
\lambda

-harmonic modular functions for

Γ

(
A
)

\Gamma \left ( A \right )

. The main purpose of this paper is to give a natural definition of

λ
\lambda

-harmonic Eisenstein series for

Γ

(
A
)

\Gamma \left ( A \right )

so that we obtain a decomposition theory of

λ
\lambda

-harmonic modular functions, analogous to the classical results of Hecke. That is, we prove
\[

Modular

Function

 = 

Eisenstein

series

⊕

Cusp Functions

.

{\text {Modular}}\,{\text {Function}}\,{\text { = }}\,{\text {Eisenstein}}\,{\text {series}}\, \oplus \,{\text {Cusp Functions}}{\text {.}}

\]
Moreover, the dimension of the space generated by

λ
\lambda

-harmonic Eisenstein series for

Γ

(
A
)

\Gamma \left ( A \right )

is equal to the number of cusps of

Γ

(
A
)

\Gamma \left ( A \right )

, and so is independent of

λ
\lambda

. For the definition of

λ
\lambda

-harmonic Eisenstein series and the proof of decomposition theory, we consider two cases: (i)

λ

≠

±
2

q

\lambda \, \ne \, \pm 2\sqrt q

and (ii)

λ

=

±
2

q

\lambda \, = \, \pm 2\sqrt q

, separately. Case (i) is treated in the usual way. Case (ii), being a “degenerate” case, is more interesting and requires more complicated analysis.
Hardy spaces of close-to-convex functions and their derivatives
Authors: Holland Finbarr , Twomey John B.
Published: July 2010

Let

f
(
z
)
=

∑
1
∞

a
n

z
n

f(z) = \sum \nolimits _1^\infty {{a_n}} {z^n}

be close-to-convex on the unit disc. It is shown that (a) if

λ
>
0

\lambda > 0

, then f belongs to the Hardy space

H
λ

{H^\lambda }

if and only if

∑

n

λ
−
2

|

a
n

|

λ

{\sum {{n^{\lambda - 2}}\left | {{a_n}} \right |} ^\lambda }

is finite and that (b) if

0
>
λ
>
1

0 > \lambda > 1

, then

f
′

∈

H
λ

f’ \in {H^\lambda }

if and only if either

∑

n

2
λ
−
2

|

a
n

|

λ

\sum {{n^{2\lambda - 2}}} {\left | {{a_n}} \right |^\lambda }

or, equivalently,

∫
0
1

M
λ

(
r
,

f
′

)

d
r

\int _0^1 {{M^\lambda }(r,f’)} dr

is convergent. It is noted that the first of these results does not extend to the full class of univalent functions and that the second is best possible in a number of different senses.
Dense subgroups of Lie groups. II
Authors: Zerling David
Published: July 2010

Let G be a dense analytic subgroup of an analytic group L. Then G contains a maximal (CA) closed normal analytic suhgroup M and a closed abelian subgroup

A
=
Z
(
G
)
×
E

A = Z(G) \times E

, where E is a closed vector subgroup of G, such that

G
=
M
⋅
A

G = M \cdot A

,

M
∩
A
=
Z
(
G
)

M \cap A = Z(G)

,

M
¯

=
M
⋅

Z
(
G
)

¯

\overline M = M \cdot \overline {Z(G)}

, and

L
=
M
⋅

A
¯

L = M \cdot \overline A

. We also indicate the extent to which a (CA) analytic group is uniquely determined by its center and a dense analytic subgroup.
Rational subspaces of induced representations and nilmanifolds
Authors: Penney R.
Published: July 2010

Recently, Auslander and Brezin developed a technique of distinguishing between certain unitarily equivalent irreducible subspaces of

L
2

{L^2}

of the Heisenberg nilmanifold. In this paper we extend the Auslander-Brezin technique to arbitrary induced representations of arbitrary locally compact groups. We then return to nilmanifolds, showing that the existence of a “nice” theory of distinguished subspaces is equivalent to the existence of square integrable representations for the group.
Parabolic function spaces with mixed norm
Authors: Gopala Rao V. R.
Published: July 2010

The spaces

H

α
p

\mathcal {H}_\alpha ^p

of parabolic Bessel potentials were introduced by B. F. Jones and R. J. Bagby. We prove a Sobolev-type imbedding theorem for

H

α

p
1

,

p
2

\mathcal {H}_\alpha ^{{p_1},{p_2}}

(multinormed versions of

H

α
p

\mathcal {H}_\alpha ^p

) when

α
\alpha

is a positive integer k,

1
>

p
1

1 > {p_1}

,

p
2

>
∞

{p_2} > \infty

. In particular this theorem holds for

W

2
l
,
l

p

W_{2l,l}^p

, since

H

2
l

p

≡

W

2
l
,
l

p

\mathcal {H}_{2l}^p \equiv W_{2l,l}^p

. We use the concepts of parabolic Riesz transforms and half-time derivatives introduced by us elsewhere.
Some metric properties of piecewise monotonic mappings of the unit interval
Authors: Wong Sherman
Published: July 2010

In this note, the result of Lasota and Yorke on the existence of invariant measures for piecewise

C
2

{C^2}

functions is extended to a larger class of piecewise continuous functions. Also the result of Li and Yorke on the existence of ergodic measures for piecewise

C
2

{C^2}

functions is extended for the above class of functions.
Rational fibrations, minimal models, and fibrings of homogeneous spaces
Authors: Halperin Stephen
Published: July 2010

Sullivan’s theory of minimal models is used to study a class of maps called rational fibrations, which contains most Serre fibrations. It is shown that if the total space has finite rank and the fibre has finite dimensional cohomology, then both fibre and base have finite rank. This is applied to prove that certain homogeneous spaces cannot be the total space of locally trivial bundles. In addition two main theorems are proved which exhibit a close relation between the connecting homomorphism of the long exact homotopy sequence, and certain properties of the cohomology of fibre and base.
Undecidable existential problems for addition and divisibility in algebraic number rings
Authors: Lipshitz L.
Published: July 2010

Existential formulas involving addition and divisibility are shown to be undecidable in the ring of integers of a real quadratic extension of the rationals. A weaker result is proved for extensions of higher degree.
Symmetrized separable convex programming
Authors: McLinden L.
Published: July 2010

The duality model for convex programming studied recently by E. L. Peterson is analyzed from the viewpoint of perturbational duality theory. Relationships with the traditional Lagrangian model for ordinary programming are explored in detail, with particular emphasis placed on the respective dual problems, Kuhn-Tucker vectors, and extremality conditions. The case of homogeneous constraints is discussed by way of illustration. The Slater existence criterion for optimal Lagrange multipliers in ordinary programming is sharpened for the case in which some of the functions are polyhedral. The analysis generally covers nonclosed functions on general spaces and includes refinements to exploit polyhedrality in the finite-dimensional case. Underlying the whole development are basic technical facts which are developed concerning the Fenchel conjugate and preconjugate of the indicator function of an epigraph set.
Distribution of eigenvalues of a two-parameter system of differential equations
Authors: Faierman M.
Published: July 2010

In this paper two simultaneous Sturm-Liouville systems are considered, the first defined for the interval

0

⩽

x
1

⩽

1

0\, \leqslant \,{x_1}\, \leqslant \,1

, the second for the interval

0

⩽

x

2

⩽

1

0\, \leqslant \,{x_{2\,}}\, \leqslant \,1

, and each containing the parameters

λ
\lambda

and

μ
\mu

. Denoting the eigenvalues and eigenfunctions of the simultaneous systems by

(

λ

j
,
k

,

μ

j
,
k

)

({\lambda _{j,k}},{\mu _{j,k}})

and

ψ

j
,
k

(

x

1
,

x
2

)

{\psi _{j,k}}({x_{1,}}{x_2})

, respectively,

j
,

k

=

0
,

1
,

…

j,\,k\, = \,0,\,1,\, \ldots \,

, asymptotic methods are employed to derive asymptotic formulae for these expressions, as

j
+
k
→
∞

j + k \to \infty

when

(
j
,

k
)

(j,\,k)

is restricted to lie in a certain sector of the

(
x
,

y
)

(x,\,y)

-plane. These results constitute a further stage in the development of the theory related to the behaviour of the eigenvalues and eigenfunctions of multiparameter Sturm-Liouville systems and answer an open question concerning the uniform boundedness of the

ψ

j
,
k

(

x
1

,

x
2

)

{\psi _{j,k}}\,({x_1},\,{x_2})

.
Thickenings of CW complexes of the form 𝑆^{𝑚}∪_{𝛼}𝑒ⁿ
Authors: Cooke George
Published: July 2010

Necessary conditions are given for the existence of a thickening of

S
m

∪
α

e
n

{S^m}\,{ \cup _\alpha }\,{e^n}

in codimension k. I give examples of such complexes requiring arbitrarily large codimension in order to thicken. Sufficient conditions are given for the existence of a tractable thickening in codimension

k

+

1

k\, + \,1

. The methods used include the study of the reduced product space of a pair of CW complexes.
A consistent consequence of AD
Authors: Bull E. L. , Kleinberg E. M.
Published: July 2010

We are concerned with the existence of a normal measure concentrating on the

ω
\omega

-closed unbounded sets. We strengthen the known result that the axiom of choice implies no such measure exists. It is shown that the existence of these measures is consistent (relative to a large cardinal). In particular,

ℵ
2

{\aleph _2}

may admit exactly two normal measures: one which contains the

ω
\omega

-closed unbounded sets and the other, the

ℵ
1

{\aleph _1}

-closed unbounded sets. This property of

ℵ
2

{\aleph _2}

is a well-known consequence of AD.
Coxeter functors without diagrams
Authors: Auslander Maurice , Platzeck María Inés , Reiten Idun
Published: July 2010

The first part of this paper is devoted to a generalization of the notion of partial Coexeter functor from diagrams to certain types of artin rings and artin algebras. The rest of the paper is devoted to a discussion of the connection between the various Coxeter functors which exist for diagrams as well as for artin rings and artin algebras.
Modeloids. I
Authors: Benda Miroslav
Published: July 2010

If A is a set and Â is the collection of finite nonrepeating sequences of its elements then a modeloid E on A is an equivalence relation on Â which preserves length, is hereditary, and is invariant under the action of permutations. The pivotal operation on modeloids is the derivative. The theory of this operation turns out to be very rich with connections leading to diverse branches of mathematics. For example, in §3 we associate an action space with a modeloid and in §5 we characterize the action spaces which are associated with the basic modeloids, i.e., those which are derivatives of themselves. What emerges is a kind of stability for the action space. We then show that action spaces with this stability can be approximated by finite actions and, subject to certain requirements, this approximation is unique (see Proposition 5.7). Algebraically, the countable basic modeloids correspond to closed subgroups of the symmetric groups. This and the study of automorphisms of modeloids let us show, without any algebra, that the only nontrivial normal subgroups of the finite (

(

⩾

5

)

\left ( { \geqslant \,\,5} \right )

) symmetric groups are the alternating groups. The last section gives, hopefully, credence to the thesis that the essence of model theory is the study of modeloids.
Ultrafiltres à la façon de Ramsey
Authors: Daguenet-Teissier Maryvonne
Published: July 2010

Let

β

N

\beta {\text {N}}

be the set of ultrafilters on N;

U

∈
β

N

{\mathcal {U}} \in \beta {\text {N}}

is “absolu” [6] (Ramsey [4]) if all its free images by continuous maps

β

N

→
β

N

\beta {\text {N}} \to \beta {\text {N}}

are isomorphic. We study here a weaker Ramsey-like property, which implies the existence of fiber products

D

⊗

E

D

(

⊗

E

k

D

)

\mathcal {D} \otimes {_E}\mathcal {D}\left ( { \otimes _\textbf {E}^k\mathcal {D}} \right )

extending the usual product

D

⊗

D

(

⊗

k

D

)

{\mathcal {D}} \otimes {\mathcal {D}}\left ( {{ \otimes ^{k}}{\mathcal {D}}} \right )

. This can be translated in the language of model-theory on the one hand as the existence of repeated almagamated sums and on the other hand by some properties of sets of indiscernibles associated with ultrafilters having this property (§5). We show that the class of ultrafilters we study strictly contains the class of Ramsey ultrafilters (§1) and is (§2) strictly (§3) contained in the class of p-point ultrafilters [9] ("

δ
\delta

-stables” [6]) and contains the free images of its elements (§4). In §2 we also give a characterization of p-point ultrafilters in terms of the product

⊗
k

D

{ \otimes ^k}{\mathcal {D}}

. In §3 we show the link with weakly Ramsey ultrafilters of Blass [3] and more generally we study ultrafilters

D

{\mathcal {D}}

on N having only a finite number

i

(

D

)

i\left ( {\mathcal {D}} \right )

of free images up to isomorphism and such that

#
τ

−
1

(

D

,

D

)

=
2
i

(

D

)

+
1

\# \tau {^{ - 1}}\left ( {{\mathcal {D}},{\mathcal {D}}} \right ) = 2i\left ( {\mathcal {D}} \right ) + 1

, where

#

τ

−
1

(

D

,

D

)

\# {\tau ^{ - 1}}\left ( {{\mathcal {D}},{\mathcal {D}}} \right )

is the number of ultrafilters on

N

2

{{\text {N}}^2}

finer than the filter generated by

(

D
×
D

)

\left ( {D \times D} \right )

with

D
∈

D

D \in {\mathcal {D}}

.
A nonunitary pairing of polarizations for the Kepler problem
Authors: Rawnsley J. H.
Published: July 2010

The half-form pairing of two polarizations of the Kepler manifold is found and shown to define a bounded linear isomorphism of the two Hilbert spaces, but is not unitary.
Defining Lagrangian immersions by phase functions
Authors: Lees J. Alexander
Published: July 2010

In order to analyze the singularities of the solutions of certain partial differential equations, Hörmander, in his paper on Fourier integral operators, extends the method of stationary phase by introducing the class of nondegenerate phase functions. Each phase function, in turn, defines a lagrangian submanifold of the cotangent bundle of the manifold which is the domain of the corresponding differential operator. Given a lagrangian submanifold of a cotangent bundle, when is it globally defined by a nondegenerate phase function? A necessary and sufficient condition is here found to be the vanishing of two topological obstructions; one in the cohomology and the other in the k-theory of the given lagrangian submanifold.
Orthogonal polynomials defined by a recurrence relation
Authors: Nevai Paul G.
Published: July 2010

R. Askey has conjectured that if a system of orthogonal polynomials is defined by the three term recurrence relation
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x p Subscript n minus 1 Baseline left-parenthesis x right-parenthesis equals StartFraction gamma Subscript n minus 1 Baseline Over gamma Subscript n Baseline EndFraction p Subscript n Baseline left-parenthesis x right-parenthesis plus alpha Subscript n minus 1 Baseline p Subscript n minus 1 Baseline left-parenthesis x right-parenthesis plus StartFraction gamma Subscript n minus 2 Baseline Over gamma Subscript n minus 1 Baseline EndFraction p Subscript n minus 2 Baseline left-parenthesis x right-parenthesis">

x

p

n

−

1

(
x
)

=

γ

n

−

1

γ

n

p
n

(
x
)

+

α

n

−

1

p

n

−

1

(
x
)

+

γ

n

−

2

γ

n

−

1

p

n

−

2

(
x
)

x{p_{n\, - \,1}}\left ( x \right )\, = \,\frac {{{\gamma _{n\, - \,1}}}} {{{\gamma _{n\,}}}}\,{p_n}\left ( x \right )\, + \,{\alpha _{n\, - \,1}}{p_{n\, - \,1}}\left ( x \right )\, + \,\frac {{{\gamma _{n\, - \,2}}}} {{{\gamma _{n\, - \,1}}}}\,{p_{n\, - \,2}}\left ( x \right )

\]
and
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="alpha Subscript n Baseline equals StartFraction left-parenthesis negative 1 right-parenthesis Superscript n Baseline Over n EndFraction const plus upper O left-parenthesis StartFraction 1 Over n squared EndFraction right-parenthesis comma">

α
n

=

(
−
1
)

n

n

const

 + 

O

(

1

n
2

)

,

{\alpha _n}\, = \,\frac {{{{( - 1)}^n}}} {n}\,{\text {const}}\,{\text { + }}O\left ( {\frac {1} {{{n^2}}}} \right ),

\]

\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartFraction gamma Subscript n Baseline Over gamma Subscript n plus 1 Baseline EndFraction equals one half plus StartFraction left-parenthesis negative 1 right-parenthesis Superscript n Baseline Over n EndFraction const plus upper O left-parenthesis StartFraction 1 Over n squared EndFraction right-parenthesis comma">

γ
n

γ

n
+
1

=

1
2

+

(
−
1
)

n

n

const

 + 

O

(

1

n
2

)

,

\frac {{{\gamma _n}}} {{{\gamma _{n + 1}}}}\, = \,\frac {1} {2}\, + \,\frac {{{{( - 1)}^n}}} {n}\,{\text {const}}\,{\text { + }}O\left ( {\frac {1} {{{n^2}}}} \right ),

\]
then the logarithm of the absolutely continuous portion of the corresponding weight function is integrable. The purpose of this paper is to prove R. Askey’s conjecture and solve related problems.
Uniformly continuous functionals on the Fourier algebra of any locally compact group
Authors: Lau Anthony To Ming
Published: July 2010

Let

G
G

be any locally compact group. Let

V
N
(
G
)

VN(G)

be the von Neumann algebra generated by the left regular representation of

G
G

. We study in this paper the closed subspace

U
B
C
(

G
^

)

UBC(\hat {G})

of

V
N
(
G
)

VN(G)

consisting of the uniformly continuous functionals as defined by E. Granirer. When

G
G

is abelian,

U
B
C
(

G
^

)

UBC(\hat {G})

is precisely the bounded uniformly continuous functions on the dual group

G
^

\hat {G}

. We prove among other things that if

G
G

is amenable, then the Banach algebra

U
B
C
(

G
^

)
∗

UBC(\hat {G})^\ast

(with the Arens product) contains a copy of the Fourier-Stieltjes algebra in its centre. Furthermore,

U
B
C
(

G
^

)
∗

UBC(\hat {G})^\ast

is commutative if and only if

G
G

is discrete. We characterize

W
(

G
^

)

W(\hat {G})

, the weakly almost periodic functionals, as the largest subspace

X
X

of

V
N
(
G
)

VN(G)

for which the Arens product makes sense on

X
∗

X^*

and

X
∗

X^*

is commutative. We also show that if

G
G

is amenable, then for certain subspaces

Y
Y

of

V
N
(
G
)

VN(G)

which are invariant under the action of the Fourier algebra

A
(
G
)

A(G)

, the algebra of bounded linear operators on

Y
Y

commuting with the action of

A
(
G
)

A(G)

is isometric and algebra isomorphic to

X
∗

X^*

for some

X
⊆
U
B
C
(

G
^

)

X \subseteq UBC(\hat {G})

.
Complete characterization of functions which act, via superposition, on Sobolev spaces
Authors: Marcus Moshe , Mizel Victor J.
Published: July 2010

Given a domain

Ω
⊂

R
N

\Omega \subset {R_N}

and a Borel function

h
:

R
m

→
R

h:\,{R_m} \to R

, conditions on h are sought ensuring that for every m-tuple of functions

u
i

{u_i}

belonging to the first order Sobolev space

W

1
,
p

(
Ω
)

{W^{1,p}}(\Omega )

, the function

h
(

u
1

(
⋅
)
,
…
,

u
m

(
⋅
)
)

h({u_1}( \cdot ), \ldots ,{u_m}( \cdot ))

will belong to a first order Sobolev space

W

1
,
r

(
Ω
)

{W^{1,r}}(\Omega )

,

1
⩽
r
⩽
p
>
∞

1 \leqslant r \leqslant p > \infty

.In this paper conditions are found which are both necessary and sufficient in order that h have the above property. This result is based on a characterization obtained here for those Borel functions

g
:

R
m

×

(

R
N

)
m

→
R

g:\,{R_m} \times {({R_N})_m} \to R

satisfying the requirement that for every m-tuple of functions

u
i

∈

W

1
,
p

(
Ω
)

{u_i} \in {W^{1,p}}(\Omega )

the function
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="g left-parenthesis u 1 left-parenthesis dot right-parenthesis comma ellipsis comma u Subscript m Baseline left-parenthesis dot right-parenthesis comma nabla u 1 left-parenthesis dot right-parenthesis comma ellipsis comma nabla u Subscript m Baseline left-parenthesis dot right-parenthesis right-parenthesis">

g
(

u
1

(
⋅
)
,
…
,

u
m

(
⋅
)
,
∇

u
1

(
⋅
)
,
…
,
∇

u
m

(
⋅
)
)

g({u_1}( \cdot ), \ldots ,{u_m}( \cdot ),\nabla {u_1}( \cdot ), \ldots ,\nabla {u_m}( \cdot ))

belongs to

L
r

(
Ω
)

{L^r}(\Omega )

. A needed result on the measurability of the set of

R
k

{R_k}

-Lebesgue points of a function on

R
N

{R_N}

is presented in an appendix.
Wall manifolds
Authors: Stong R. E.
Published: July 2010

In the calculation of the oriented cobordism ring, it is standard to consider so-called Wall manifolds, for which the first Stiefel-Whitney class is the reduction of an integral class. This paper studies the Wall-type structures in the equivariant case.
On a sufficient condition for proximity
Authors: Lau Ka Sing
Published: July 2010

A closed subspace M in a Banach space X is called U-proximinal if it satisfies:
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis 1 plus rho right-parenthesis upper S intersection left-parenthesis upper S plus upper M right-parenthesis subset-of-or-equal-to upper S plus epsilon left-parenthesis rho right-parenthesis left-parenthesis upper S intersection upper M right-parenthesis">

(
1
+
ρ
)
S
∩
(
S
+
M
)
⊆
S
+
ε
(
ρ
)
(
S
∩
M
)

(1 + \rho )S \cap (S + M) \subseteq S + \varepsilon (\rho )(S \cap M)

, for some positive valued function

ε
(
ρ
)

\varepsilon (\rho )

,

ρ
>
0

\rho > 0

, and

ε
(
ρ
)
→
0

\varepsilon (\rho ) \to 0

as

ρ

→

0

\rho \, \to \, 0

, where S is the closed unit ball of X. One of the important properties of this class of subspaces is that the metric projections are continuous. We show that many interesting subspaces are U-proximinal, for example, the subspaces with the 2-ball property (semi M-ideals) and certain subspaces of compact operators in the spaces of bounded linear operators.
Statically tame periodic homeomorphisms of compact connected 3-manifolds. I. Homeomorphisms conjugate to rotations of the 3-sphere
Authors: Moise Edwin E.
Published: July 2010

Let f be a homeomorphism of the 3-sphere onto itself, of finite period n, and preserving orientation. Suppose that the fixed-point set F of f is a tame 1-sphere. It is shown that (1) the 3-sphere has a triangulation

K
(

S

3

)

K({{\textbf {S}}^3})

such that F forms a subcomplex of

K
(

S

3

)

K({{\textbf {S}}^3})

and f is simplicial relative to

K
(

S

3

)

K({{\textbf {S}}^3})

. Suppose also that F is unknotted. It then follows that (2) f is conjugate to a rotation.
Inductive construction of homogeneous cones
Authors: Dorfmeister Josef
Published: July 2010

A method is explained how to construct all homogeneous cones in a unique way out of lower dimensional ones. The infinitesimal automorphisms of such a cone and its associated left-symmetric algebras are described in terms of the lower dimensional constituents of the cone. It is characterized when a homogeneous cone is self-dual or a sum of homogeneous cones.
On an extremal property of Doob’s class
Authors: Hwang J. S.
Published: July 2010

Recently, we have solved a long open problem of Doob (1935). To introduce the result proved here, we say that a function

f
(
z
)

f(z)

belongs to Doob’s class D, if

f
(
z
)

f(z)

is analytic in the unit disk U and has radial limit zero at an endpoint of some arc R on the unit circle such that

lim

inf

n
→
∞

|

f
(

P
n

)

|

\operatorname {lim} \,{\operatorname {inf} _{n \to \infty }}\,\left | {f({P_n})} \right |

, where

{

P
n

}

\{ {P_n}\}

is an arbitrary sequence of points in U tending to an arbitrary interior point of R. With this definition, our main result is the following extremal property of Doob’s class. Theorem.

inf

f
∈
D

‖
f
‖

=

2

/

e

{\operatorname {inf} _{f \in D}}\left \| f \right \|\, = \,{2 /e}

, where
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar f double-vertical-bar equals sup Underscript z element-of upper U Endscripts left-parenthesis 1 minus StartAbsoluteValue z EndAbsoluteValue squared right-parenthesis StartAbsoluteValue f prime left-parenthesis z right-parenthesis EndAbsoluteValue">

‖
f
‖

=

sup

z
∈
U

(
1

−

|

z

|

2

)

|

f
′

(
z
)

|

\left \| f \right \|\, = \,{\sup _{z \in U}}(1\, - |z{|^2})|f’(z)|

.
Multiplications on cohomology theories with coefficients
Authors: Martin Alvin Frank
Published: July 2010

Araki and Toda have considered the existence and classification of multiplications on generalized cohomology theories with coefficients in the category of finite CW-complexes. We consider the same matters for representable cohomology theories in a category of stable CW-spectra, such as that constructed by Adams. We obtain similar, and in certain instances stronger, results than Araki and Toda, with methods of proof that are often simpler and more straightforward.
Difference equations over locally compact abelian groups
Authors: Edgar G. A. , Rosenblatt J. M.
Published: July 2010

A homogeneous linear difference equation with constant coefficients over a locally compact abelian group G is an equation of the form

Σ

j

=

1

n

c
j

f
(

t
j

x
)

=

0

\Sigma _{j\, = \,1}^n {{c_j}f({t_j}x)\, = \,0}

which holds for all

x

∈

G

x\, \in \,G

where

c
1

,
…
,

c
n

{c_1}, \ldots ,\,{c_n}

are nonzero complex scalars,

t
1

,

…

,

t
n

{t_1},\, \ldots \,,\,{t_n}

are distinct elements of G, and f is a complex-valued function on G. A function f has linearly independent translates precisely when it does not satisfy any nontrivial linear difference equation. The locally compact abelian groups without nontrivial compact subgroups are exactly the locally compact abelian groups such that all nonzero

f

∈

L
p

(
G
)

f\, \in \,{L_p}(G)

with

1

⩽

p

⩽

2

1\, \leqslant \,p\, \leqslant \,2

have linearly independent translates. Moreover, if G is the real line or, more generally, if G is

R
n

{R^n}

and the difference equation has a characteristic trigonometric polynomial with a locally linear zero set, then the difference equation has no nonzero solutions in

C
0

(
G
)

{C_0}(G)

and no nonzero solutions in

L
p

(
G
)

{L_p}(G)

for

1

⩽

p

>

∞

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

. But if G is some

R
n

{R^n}

for

n

⩾

2

n\, \geqslant \,2

and the difference equation has a characteristic trigonometric polynomial with a curvilinear portion of its zero set, then there will be nonzero

C
0

(

R
n

)

{C_0}({R^n})

solutions and even nonzero

L
p

(

R
n

)

{L_p}({R^n})

solutions for

p

>

2
n

/

(
n
−
1
)

p\, > \,2n/(n - 1)

. These examples are the best possible because if

1

⩽
p

>

2
n

/

(
n
−
1
)

1\, \leqslant p\, > \,2n/(n - 1)

, then any nonzero function in

L
p

(

R
n

)

{L_p}({R^n})

has linearly independent translates. Also, the solutions to linear difference equations over the circle group can be simply described in a fashion which an example shows cannot be extended to all compact abelian groups.
Generic sets and minimal 𝛼-degrees
Authors: Chong C. T.
Published: July 2010

A non-

α
\alpha

-recursive subset G of an admissible ordinal

α
\alpha

is of minimal

α
\alpha

-degree if every set of strictly lower

α
\alpha

-degree than that of G is

α
\alpha

-recursive. We give a characterization of regular sets of minimal

α
\alpha

-degree below

0
′

0’

via the notion of genericity. We then apply this to outline some ’minimum requirements’ to be satisfied by any construction of a set of minimal

ℵ
ω
L

\aleph _\omega ^L

-degree below

0
′

0’

.
Analytic extensions and selections
Authors: Globevnik J.
Published: July 2010

Let G be a closed subset of the closed unit disc in C, let F be a closed subset of the unit circle of measure 0 and let

Φ
\Phi

map G into the class of all open subsets of a complex Banach space X. Under suitable additional assumptions on

Φ
\Phi

we prove that given any continuous function

f
:

F
→
X

f:\,F \to X

satisfying

f
(
z
)

∈

closure(

Φ
(
z
)
)

(
z

∈

F

∩

G
)

f(z)\, \in \,{\text {closure(}}\Phi (z))\,(z\, \in \,F\, \cap \,G)

there exists a continuous function f from the closed unit disc into X, analytic in the open unit disc, which extends f and satisfies

f
~

(
z
)

∈

Φ
(
z
)

(
z

∈

G

−

F
)

\tilde f(z)\, \in \,\Phi (z)\,(z\, \in \,G\, - \,F)

. This enables us to generalize and sharpen known dominated extension theorems for the disc algebra.
Cell-like 0-dimensional decompositions of 𝑆³ are 4-manifold factors
Authors: Daverman R. J. , Row W. H.
Published: July 2010

The main result is the title theorem asserting that if G is any upper semicontinuous decomposition of

S
3

{S^3}

into cell-like sets which is 0-dimensional, in the sense that the image of the nondegenerate elements in

S
3

/

G

{S^3}/G

is 0-dimensional, then

G

×

S
1

G\, \times \,{S^1}

is shrinkable, and

(

S
3

/

G

)

×

S
1

\left ( {{S^3}/G} \right )\, \times \,{S^1}

is homeomorphic to

S
3

×

S
1

{S^3}\, \times \,{S^1}

.
Constructing framed 4-manifolds with given almost framed boundaries
Authors: Kaplan Steve J.
Published: July 2010

Two methods are presented for constructing framed 4-manifolds with given almost framed boundaries. The main tools are the “moves” of Kirby’s calculus of framed links. A new description is given for the

μ
\mu

-in-variant of a knot and this description is used to study almost framed 3-manifolds.
Selection theorems for 𝐺_{𝛿}-valued multifunctions
Authors: Srivastava S. M.
Published: July 2010

In this paper we establish under suitable conditions the existence of measurable selectors for

G
δ

{G_\delta }

-valued multifunctions. In particular we prove that a measurable partition of a Polish space into

G
δ

{G_\delta }

sets admits a Borel selector.
Analogs of Clifford’s theorem for polycyclic-by-finite groups
Authors: Lorenz Martin
Published: July 2010

Let P be a primitive ideal in the group algebra

K
[
G
]

K[G]

of the polycyclic group G and let N be a normal subgroup of G. We show that among the irreducible right

K
[
G
]

K[G]

-modules with annihilator P there exists at least one, V, such that the restricted

K
[
N
]

K[N]

-module

V
N

{V_N}

is completely reducible, a sum of G-conjugate simple

K
[
N
]

K[N]

-submodules. Various stronger versions of this result are obtained. We also consider the action of G on the factor

K
[
N
]

/

P
∩
K
[
N
]

K[N]/P \cap K[N]

and show that, in case K is uncountable, any ideal I of

K
[
N
]

K[N]

satisfying

∩

g
∈
G

I
g

=

P

∩

K
[
N
]

{ \cap _{g \in G}}{I^g}\, = \,P\, \cap \,K[N]

is contained in a primitive ideal Q of

K
[
N
]

K[N]

with

∩

g
∈
G

I
g

=

P

∩

K
[
N
]

{ \cap _{g \in G}}{I^g}\, = \,P\, \cap \,K[N]

.
Critical mappings of Riemannian manifolds
Authors: Bleecker David D.
Published: July 2010

We consider maps, from one Riemannian manifold to another, which are critical for all invariantly defined functionals on the space of maps. There are many such critical mappings, perhaps too numerous to suitably classify, although a characterization of sorts is provided. They are proven to have constant rank, with the image being a homogeneous minimal submanifold of the target manifold. Critical maps need not be Riemannian submersions onto their images. Also, there are homogeneous spaces for which the identity map is not critical. Many open problems remain.
The Dirichlet norm and the norm of Szegő type
Authors: Saitoh Saburou
Published: July 2010

Let S be a smoothly bounded region in the complex plane. Let

g
(
z
,
t
)

g(z,t)

denote the Green’s function of S with pole at t. We show that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-integral Underscript upper S Endscripts StartAbsoluteValue f prime left-parenthesis z right-parenthesis EndAbsoluteValue squared d x d y less-than-or-slanted-equals one half integral Underscript partial-differential upper S Endscripts StartAbsoluteValue f prime left-parenthesis z right-parenthesis EndAbsoluteValue squared left-parenthesis StartFraction partial-differential g left-parenthesis z comma t right-parenthesis Over partial-differential n Subscript z Baseline EndFraction right-parenthesis Superscript negative 1 Baseline StartAbsoluteValue d z EndAbsoluteValue">

∬
S

|

f
′

(
z
)

|

2

d
x

d
y

⩽

1
2

∫

∂
S

|

f
′

(
z
)

|

2

(

∂
g
(
z
,
t
)

∂

n
z

)

−
1

|

d
z

|

\iint _S {|f’(z){|^2}\,dx\,dy\, \leqslant \,\frac {1}{2}\int _{\partial S} {|f’(z){|^2}{{\left ( {\frac {{\partial g(z,t)}} {{\partial {n_z}}}} \right )}^{ - 1}}|dz|} }

\]
holds for any analytic function

f
(
z
)

f(z)

on

S

∪

∂
S

S\, \cup \,\partial S

. This curious inequality is obtained as a special case of a much more general result.
Twisted sums of sequence spaces and the three space problem
Authors: Kalton N. J. , Peck N. T.
Published: July 2010

In this paper we study the following problem: given a complete locally bounded sequence space Y, construct a locally bounded space Z with a subspace X such that both X and

Z

/

X

Z/X

are isomorphic to Y, and such that X is uncomplemented in Z. We give a method for constructing Z under quite general conditions on Y, and we investigate some of the properties of Z. In particular, when Y is

l
p

(
1

>

p

>

∞
)

{l_p}\,(1\, > \,p\, > \,\infty )

, we identify the dual space of Z, we study the structure of basic sequences in Z, and we study the endomorphisms of Z and the projections of Z on infinite-dimensional subspaces.
CR functions and tube manifolds
Authors: Kazlow M.
Published: July 2010

Various generalizations of Bochner’s theorem on the extension of holomorphic functions over tube domains are considered. It is shown that CR functions on tubes over connected, locally closed, locally starlike subsets of

R

n

{\textbf {R}^n}

uniquely extend to CR functions on almost all of the convex hull of the tube set. A CR extension theorem on maximally stratified real submanifolds of

C

n

{\textbf {C}^n}

is proven. The above two theorems are used to show that the CR functions (resp. CR distributions) on tubes over a fairly general class of submanifolds of

R

n

{\textbf {R}^n}

uniquely extend to CR functions (CR distributions) on almost all of the convex hull.
Necessary conditions for the convergence of cardinal Hermite splines as their degree tends to infinity
Authors: Goodman T. N. T.
Published: July 2010

Let

S

n
,
s

{\mathcal {S}_{n,s}}

denote the class of cardinal Hermite splines of degree n having knots of multiplicity S at the integers. In this paper we show that if

f
n

→

f

{f_n}\, \to \,f

uniformly on R, where

f
n

∈

S

i

n
,
s

i
n

→

∞

{f_n}\, \in \,{\mathcal {S}_{{i_{n,s}}}}\,{i_n}\, \to \,\infty

as

n

→

∞

n\, \to \,\infty

, and f is bounded, then f is the restriction to R of an entire function of exponential type

⩽

S

\leqslant \,S

. In proving this result, we need to derive some extremal properties of certain splines

E

n
,
s

∈

S

n
,
s

{\mathcal {E}_{n,s}}\, \in \,{\mathcal {S}_{n,s}}

, in particular that

|

|

E

n
,
s

|

|

∞

||{\mathcal {E}_{n,s}}|{|_\infty }

minimises

|

|

S

|

|

∞

||S|{|_\infty }

over

S

∈

S

n
,
s

S\, \in \,{\mathcal {S}_{n,s}}

with
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue EndAbsoluteValue upper S Superscript left-parenthesis n right-parenthesis Baseline StartAbsoluteValue EndAbsoluteValue Subscript normal infinity Baseline equals StartAbsoluteValue EndAbsoluteValue script upper E Subscript n comma s Superscript left-parenthesis n right-parenthesis Baseline StartAbsoluteValue EndAbsoluteValue Subscript normal infinity">

|

|

S

(
n
)

|

|

∞

=

|

|

E

n
,
s

(
n
)

|

|

∞

||{S^{(n)}}|{|_\infty }\, = \,||\mathcal {E}_{n,s}^{(n)}|{|_\infty }

.
Stability theory for functional-differential equations
Authors: Burton T. A.
Published: July 2010

We consider a system of functional differential equations

x
′

(
t
)

=

F

(
t
,

x
(
⋅
)
)

x’\,(t)\, = \,\mathcal {F}\,(t,\,x( \cdot ))

, together with a Liapunov functional

V

(
t
,

x
(
⋅
)
)

\mathcal {V}\,(t,\,x( \cdot ))

with

V

′

⩽

0

\mathcal {V}’\, \leqslant \,0

. Most classical results require that

F

\mathcal {F}

be bounded for

x
(
⋅
)

x( \cdot )

bounded and that

F

\mathcal {F}

depend on

x
(
s
)

x(s)

only for

t

−

α
(
t
)

⩽

s

⩽

t

t\, - \,\alpha (t)\, \leqslant \,s\, \leqslant \,t

where

α
\alpha

is a bounded function in order to obtain stability properties. We show that if there is a function

H
(
t
,

x
)

H(t,\,x)

whose derivative along

x
′

(
t
)

=

F

(
t
,

x
(
⋅
)
)

x’\,(t)\, = \,\mathcal {F}\,(t,\,x( \cdot ))

is bounded above, then those requirements can be eliminated. The derivative of H may take both positive and negative values. This extends the classical theorem on uniform asymptotic stability, gives new results on asymptotic stability for unbounded delays and unbounded

F

\mathcal {F}

, and it improves the standard results on the location of limit sets for ordinary differential equations.
Markov cell structures for expanding maps in dimension two
Authors: Farrell F. T. , Jones L. E.
Published: July 2010

Let

f
:

M
2

→

M
2

f:\,{M^2}\, \to \,{M^2}

be an expanding self-immersion of a closed 2-manifold, then for some positive integer n,

f
n

{f^n}

leaves invariant a cell structure on

M
2

{M^2}

. A similar result is true when M is a branched 2-manifold.
Global analysis on PL-manifolds
Authors: Teleman Nicolae
Published: July 2010

The paper deals mainly with combinatorial structures; in some cases we need refinements of combinatorial structures. Riemannian metrics are defined on any combinatorial manifold M. The existence of distance functions and of Riemannian metrics with “constant volume density” implies smoothing. A geometric realization of

PL

(
m
)

/O

(
m
)

{\text {PL}}\left ( m \right ){\text {/O}}\left ( m \right )

is given in terms of Riemannian metrics. A graded differential complex

Ω

∗

(
M
)

{\Omega ^ {\ast } }( M )

is constructed: it appears as a subcomplex of Sullivan’s complex of piecewise differentiable forms. In the complex

Ω

∗

(
M
)

{\Omega ^{\ast }}( M )

the operators

d
d

,

∗
\ast

,

δ
\delta

,

Δ
\Delta

are defined. A Rellich chain of Sobolev spaces is presented. We obtain a Hodge-type decomposition theorem, and the Hodge homomorphism is defined and studied. We study also the combinatorial analogue of the signature operator.
The analytic continuation of the discrete series. II
Authors: Wallach Nolan R.
Published: July 2010

This is the second in a series of papers on the analytic continuation of the holomorphic discrete series. In this paper necessary and sufficient conditions for unitarizability are given in the case of line bundles. The foundations for the vector valued case are begun.
Molecular Diagnostic Assay for Detection of the Butternut Canker Pathogen Sirococcus clavigignenti-juglandacearum
Authors: Broders K. D. , Boland G. J.
Published: July 2010

Butternut canker, caused by the fungal pathogen Sirococcus clavigignenti-juglandacearum, is present throughout the range of butternut (Juglans cinerea) and is the primary cause for its decline. A quick and reliable method for identification of S. clavigignenti-juglandacearum would provide a valuable tool for the detection of the pathogen on propagative material to avoid spread, as well as assist studies targeted at the epidemiology of this pathogen, in particular the dissemination of the pathogen by seeds of the butternut. The objective of this study was to develop a diagnostic assay to detect S. clavigignenti-juglandacearum in butternut plant tissue. The primers were developed using an alignment of internal transcribed spacer (ITS) sequences from isolates of S. clavigignenti-juglandacearum and several closely related species. These primers were tested on J. cinerea, 48 isolates of S. clavigignenti-juglandacearum recovered from diseased trees, and 26 species of other fungi recovered from butternut tissue. The primers amplified a product from the DNA of all isolates of S. clavigignenti-juglandacearum, detected its DNA at a concentration as low as 1 pg/μl, and detected the pathogen at a concentration of 1 × 103 spore/ml. The primers developed in this study will be a valuable tool for the detection of S. clavigignenti-juglandacearum present on butternut seeds, and as a rapid diagnostic tool for early detection of the pathogen on butternut trees.
Multiplex Real-Time PCR Assays for the Identification of the Potato Cyst and Tobacco Cyst Nematodes
Authors: Nakhla Mark K. , Owens Kristina J. , Li Wenbin , Wei Gang , Skantar Andrea M. , Levy Laurene
Published: July 2010

TaqMan primer-probe sets were developed for the detection and identification of potato cyst nematodes (PCNs) Globodera pallida and G. rostochiensis using two-tube, multiplex real-time polymerase chain reaction (PCR). One tube contained a primer-probe set specific for G. pallida (pale potato cyst nematode) multiplexed with another primer-probe set specific for G. rostochiensis (golden potato cyst nematode). A second tube consisted of the G. pallida-specific primer-probe set multiplexed with a primer-probe set specific for G. tabacum (the morphologically similar tobacco cyst nematode). This internal transcribed spacer rDNA-based system was specific for the Globodera spp. of interest and successfully identified several populations of PCN. This rapid, sensitive, and specific quantitative PCR assay presents a useful tool for PCN regulatory response and management programs.
Identification of the Phytoplasma Associated with Wheat Blue Dwarf Disease in China
Authors: Wu Yunfeng , Hao Xingan , Li Zhengnan , Gu Peiwen , An Fengqui , Xiang Jianye , Wang Haini , Luo Zhaopeng , Liu Junjun , Xiang Yu
Published: July 2010

Wheat blue dwarf disease (WBD) was first reported in China in the 1960s. It has caused severe losses on several occasions in winter wheat (Triticum aestivum) in northwestern China, and the nature of the pathogenic agent has been unknown. Here we have shown that WBD was caused by a 16SrI-C phytoplasma transmitted by Psammotettix striatus. This finding was based on molecular diagnostics, insect transmission trials, and host-range determination. Portions of the 16S rRNA and ribosomal protein (rp) genes, rpsS (rps19), rplV (rpl22), and rpsC (rps3), were amplified from DNA samples of WBD-infected wheat seedlings by polymerase chain reaction (PCR) utilizing phytoplasma specific primer pairs. The nucleotide sequences of these amplicons showed high identity to these genes from phytoplasma strains in the aster yellows group (16SrI). Pairwise nucleotide sequence identities of WBD 16S rDNA compared to representative genes of 16SrI group strains ranged from 98.9 to 99.9%, whereas compared to 17 other phytoplasma groups (16SrII to 16SrXVIII), sequence identity ranged from 88.6 to 96.0%. Similarly, the sequence identities of rps19, rpl22, and rps3 between WBD and 16SrI group strains varied from 96.6 to 99.7%, but only 60.3 to 65% between WBD and other phytoplasma groups. Phylogenetic analyses were carried out on sequences from 16S rRNA and ribosomal protein genes (rps19, rpl22, and rps3), respectively, and both results indicated that WBD phytoplasma was a member of the 16SrI group and most closely related to subgroup 16SrI-C. WBD-infected P. striatus were present in wheat fields with WBD, and phytoplasma infection was verified by PCR detection followed by DNA sequencing. Insect transmission trials confirmed that P. striatus transmitted the WBD phytoplasmal agent from infected wheat to healthy wheat seedlings and seven other different plant species in the greenhouse. A survey of various weed species near WBD-infected wheat fields found 10 plant species in seven families to be positive for the presence of WBD phytoplasma.
Genetic and Pathological Diversity AmongXanthomonasStrains Responsible for Bacterial Spot on Tomato and Pepper in the Southwest Indian Ocean Region
Authors: Hamza A. A. , Robène-Soustrade I. , Jouen E. , Gagnevin L. , Lefeuvre P. , Chiroleu F. , Pruvost O.
Published: July 2010

Bacterial spot of tomato and pepper, a major problem in tropical climates, can be caused by several Xanthomonas genospecies. We examined the genetic and pathological diversity of a collection of 72 strains from the southwest Indian Ocean region as part of a regional research and development program to update inventories of agricultural pests and pathogens. Xanthomonas euvesicatoria, X. perforans, X. gardneri, and X. vesicatoria were identified in our strain collection. The identification of strains at the species level was consistently achieved by amplified fragment length polymorphism (AFLP) and multilocus sequence analysis (MLSA). Overall, X. euvesicatoria was the species recovered prevalently. MLSA data based on four housekeeping genes identified two to three sequence types per genospecies. It suggested that sequence variations primarily consisted of synonymous mutations, although a recombination event spanning several hundred nucleotides was detected for some strains of X. euvesicatoria on the atpD gene coding for the F1-F0-ATPase β subunit. The pathogenicity of strains was consistent with data found in the literature. Some pathological variations were primarily observed among strains identified as X. euvesicatoria. This study provides the first ever comprehensive description of the status of Xanthomonas species that cause bacterial spot of tomato and pepper in the southwest Indian Ocean region.
Effect of QoI Fungicides on Colonization and Sporulation of Monilinia fructicola on Peach Fruit and Blossom Blight Cankers
Authors: Burnett A. L. , Lalancette N. , McFarland K. A.
Published: July 2010

Three studies were conducted to examine the curative activity of azoxystrobin, trifloxystrobin, and pyraclostrobin + boscalid against Monilinia fructicola, causal agent of brown rot on peach. In the first study, ‘Autumnglo’ peach trees were treated with each of the three fungicides both before and after fruit inoculation. In the second study, the effects of fungicide active ingredient, rate/volume, and inoculation timing were examined on inoculated ‘Suncrest’ peach fruit. Results of these studies showed that sporulating area, on average across all treatments, was reduced by 15.9, 42.4, and 0.4% for azoxystrobin, trifloxystrobin, and pyraclostrobin + boscalid, respectively. In any single treatment, trifloxystrobin provided the greatest benefit with two consecutive sprays, reducing sporulating area by 53 to 60%. In contrast to sporulation activity, the three fungicides exhibited less of an inhibitory effect on fruit colonization. When applied at maximum labeled rates in the various treatments, azoxystrobin, trifloxystrobin, and pyraclostrobin + boscalid reduced colony growth, on average, by 12.3, 7.5, and 7.4%, respectively. Because the pathogen was inoculated into the mesocarp, this low level of activity against colonization may be due to a lack of deeper systemic movement of the fungicides into fruit tissue. In the final study, the three fungicides were examined for their antisporulant activity on blossom blight twig cankers. Unlike results observed on fruit, significant reductions in spore production on cankers were observed for all three fungicides. Azoxystrobin, trifloxystrobin, and pyraclostrobin + boscalid provided 56, 71, and 53% reductions, respectively, in the number of conidia produced per unit canker length. Overall results of these studies indicated that quinone outside inhibitor fungicides, in addition to their known protectant activity, also possess varying levels of curative activity against M. fructicola. In particular, trifloxystrobin demonstrated good antisporulant activity on both fruit infections and cankers.