bluuebunny/crossref_metadata_2025 huggingface dataset:
André permutations, lexicographic shellability and the 𝑐𝑑-index of a convex polytope
Authors: Purtill Mark
Published: June 2012

The

c
d

cd

-index of a polytope was introduced by Fine; it is an integer valued noncommutative polynomial obtained from the flag-vector. A result of Bayer and Fine states that for any integer "flag-vector," the existence of the

c
d

cd

-index is equivalent to the holding of the generalized Dehn-Sommerville equations of Bayer and Billera for the flag-vector. The coefficients of the

c
d

cd

-index are conjectured to be nonnegative. We show a connection between the

c
d

cd

-index of a polytope

P

\mathcal {P}

and any

C
L

CL

-shelling of the lattice of faces of

P

\mathcal {P}

; this enables us to prove that each André polynomial of Foata and Schützenberger is the

c
d

cd

-index of a simplex. The combinatorial interpretation of this

c
d

cd

-index can be extended to cubes, simplicial polytopes, and some other classes (which implies that the

c
d

cd

-index has nonnegative coefficients for these polytopes). In particular, we show that any polytope of dimension five or less has a positive

c
d

cd

-index.
A subcategory of TOP
Authors: Dow Alan , Watson Stephen
Published: June 2012

We consider the smallest class of topological spaces which contains the converging sequence and which is closed under the operations of taking arbitrary sums, quotients and finite products. We show that if there is a model of set-theory in which there is a measurable cardinal then there is a model in which this class does not contain all topological spaces. In addition, we prove that it is consistent that this class does contain all topological spaces—in fact much more, a large cardinal is needed to produce a model of set theory in which this class is proper.
Subvarieties of moduli space determined by finite groups acting on surfaces
Authors: Ries John F. X.
Published: June 2012

Suppose the finite group

G
G

acts as orientation preserving homeomorphisms of the oriented surface

S
S

of genus

g
g

. This determines an irreducible subvariety

M

g

[
G
]

\mathcal {M}_g^{[G]}

of the moduli space

M

g

{\mathcal {M}_g}

of Riemann surfaces of genus

g
g

consisting of all surfaces with a group

G
1

{G_1}

of holomorphic homeomorphisms of the same topological type as

G
G

. This family is determined by an equivalence class of epimorphisms

ψ
\psi

from a Fuchsian group

Γ
\Gamma

to

G
G

whose kernel is isomorphic to the fundamental group of

S
S

. To examine the singularity of

M

g

{\mathcal {M}_g}

along this family one needs to know the full automorphism group of a generic element of

M

g

[
G
]

\mathcal {M}_g^{[G]}

. In

§
2

\S 2

we show how to compute this from

ψ
\psi

. Let

M

g
G

\mathcal {M}_g^G

denote the locus of all Riemann surfaces of genus

g
g

whose automorphism group contains a subgroup isomorphic to

G
G

. In

§
3

\S 3

we show that the irreducible components of this subvariety do not necessarily correspond to the families above, that is, the components cannot be put into a one-to-one correspondence with the topological actions of

G
G

. In

§
4

\S 4

we examine the actions of

G
G

on the spaces of holomorphic

k
k

-differentials and on the first homology. We show that when

G
G

is not cyclic, the characters of these actions do not necessarily determine the topological type of the action of

G
G

on

S
S

.
The weighted Hardy’s inequality for nonincreasing functions
Authors: Stepanov Vladimir D.
Published: June 2012

The purpose of this paper is to give an alternative proof of recent results of M. Arino and B. Muckenhoupt [1] and E. Sawyer [8], concerning Hardy’s inequality for nonincreasing functions and related applications to the boundedness of some classical operators on general Lorentz spaces. Our approach will extend the results of [1,8] to the values of the parameters which are inaccessible by the methods of these papers.
Mountain impasse theorem and spectrum of semilinear elliptic problems
Authors: Tintarev Kyril
Published: June 2012

This paper studies a minimax problem for functionals in Hilbert space in the form of

G
(
u
)
=

1
2

ρ

|

|

u

|

|

2

−
g
(
u
)

G(u) = \frac {1} {2}\rho ||u|{|^2} - g(u)

, where

g
(
u
)

g(u)

is Fréchet differentiable with weakly continuous derivative. If

G
G

has a "mountain pass geometry" it does not necessarily have a critical point. Such a case is called, in this paper, a "mountain impasse". This paper states that in a case of mountain impasse, there exists a sequence

u
j

∈
H

{u_j} \in H

such that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="g prime left-parenthesis u Subscript j Baseline right-parenthesis equals rho Subscript j Baseline u Subscript j Baseline comma rho Subscript j Baseline right-arrow rho comma StartAbsoluteValue EndAbsoluteValue u Subscript j Baseline StartAbsoluteValue EndAbsoluteValue right-arrow normal infinity comma">

g
′
(

u
j

)
=

ρ
j

u
j

,

ρ
j

→
ρ
,

|

|

u
j

|

|

→
∞
,

g\prime ({u_j}) = {\rho _j}{u_j},\quad {\rho _j} \to \rho ,||{u_j}|| \to \infty ,

\]
and

G
(

u
j

)

G({u_j})

approximates the minimax value from above. If
\[

γ
(
t
)
=

sup

|

|

u

|

|

2

=
t

g
(
u
)

\gamma (t) = \sup \limits _{||u|{|^2} = t} \;g(u)

\]
and
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper J 0 equals left-parenthesis 2 inf Underscript t 2 greater-than t 1 greater-than 0 Endscripts StartFraction gamma left-parenthesis t 2 right-parenthesis minus gamma left-parenthesis t 1 right-parenthesis Over t 2 minus t 1 EndFraction comma 2 sup Underscript t 2 greater-than t 1 greater-than 0 Endscripts StartFraction gamma left-parenthesis t 2 right-parenthesis minus gamma left-parenthesis t 1 right-parenthesis Over t 2 minus t 1 EndFraction right-parenthesis comma">

J
0

=

(

2

inf

t
2

>

t
1

>
0

γ
(

t
2

)
−
γ
(

t
1

)

t
2

−

t
1

,
2

sup

t
2

>

t
1

>
0

γ
(

t
2

)
−
γ
(

t
1

)

t
2

−

t
1

)

,

{J_0} = \left ( {2\inf \limits _{{t_2} > {t_1} > 0} \frac {{\gamma ({t_2}) - \gamma ({t_1})}} {{{t_2} - {t_1}}},2\sup \limits _{{t_2} > {t_1} > 0} \frac {{\gamma ({t_2}) - \gamma ({t_1})}} {{{t_2} - {t_1}}}} \right ),

\]
then

g
′
(
u
)
=
ρ
u

g\prime (u) = \rho u

has a nonzero solution

u
u

for a dense subset of

ρ
∈

J
0

\rho \in {J_0}

.
Supercuspidal representations and the theta correspondence. II. 𝑆𝐿(2) and the anisotropic 𝑂(3)
Authors: Manderscheid David
Published: June 2012

A parametrization is given of the local theta correspondence attached to the reductive dual pair

(

SL

2

(
F
)
,

O

(
F
)
)

({\text {SL}}_2(F),\;{\text {O}}(F))

where

F
F

is a nonarchimedean local field of odd residual characteristic and

O

{\text {O}}

is the orthogonal group of a ternary quadratic form which is anisotropic over

F
F

. The parametrization is in terms of inducing data. Various lattice models of the oscillator representation are used.
Zeta regularized products
Authors: Quine J. R. , Heydari S. H. , Song R. Y.
Published: June 2012

If

λ
k

{\lambda _k}

is a sequence of nonzero complex numbers, then we define the zeta regularized product of these numbers,

∏
k

λ
k

\prod \nolimits _k {{\lambda _k}}

, to be

exp
⁡
(
−
Z
′
(
0
)
)

\exp ( - Z\prime (0))

where

Z
(
s
)
=

∑

k
=
0

∞

λ
k

−
s

Z(s) = \sum \nolimits _{k = 0}^\infty {\lambda _k^{ - s}}

. We assume that

Z
(
s
)

Z(s)

has analytic continuation to a neighborhood of the origin. If

λ
k

{\lambda _k}

is the sequence of positive eigenvalues of the Laplacian on a manifold, then the zeta regularized product is known as

det
′
Δ

\det \prime \Delta

, the determinant of the Laplacian, and

∏
k

(

λ
k

−
λ
)

\prod \nolimits _k {({\lambda _k} - \lambda )}

is known as the functional determinant. The purpose of this paper is to discuss properties of the determinant and functional determinant for general sequences of complex numbers. We discuss asymptotic expansions of the functional determinant as

λ
→
−
∞

\lambda \to - \infty

and its relationship to the Weierstrass product. We give some applications to the theory of Barnes’ multiple gamma functions and elliptic functions. A new proof is given for Kronecker’s limit formula and the product expansion for Barnes’ double Stirling modular constant.
Martin and end compactifications for non-locally finite graphs
Authors: Cartwright Donald I. , Soardi Paolo M. , Woess Wolfgang
Published: June 2012

We consider a connected graph, having countably infinite vertex set

X
X

, which is permitted to have vertices of infinite degree. For a transient irreducible transition matrix

P
P

corresponding to a nearest neighbor random walk on

X
X

, we study the associated harmonic functions on

X
X

and, in particular, the Martin compactification. We also study the end compactification of the graph. When the graph is a tree, we show that these compactifications coincide; they are a disjoint union of

X
X

, the set of ends, and the set of improper vertices—new points associated with vertices of infinite degree. Other results proved include a solution of the Dirichlet problem in the context of the end compactification of a general graph. Applications are given to, e.g., the Cayley graph of a free group on infinitely many generators.
Analyse quasi-sure et l’estimation du noyau de la chaleur pour temps petit
Authors: Fang Shizan
Published: June 2012

The Ito functional can be redefined out of a slim set by the natural way. Quasi-sure analysis is used to deal with the heat kernel asymptotic problems.
On complete manifolds of nonnegative 𝑘th-Ricci curvature
Authors: Shen Zhong Min
Published: June 2012

In this paper we establish some vanishing and finiteness theorems for the topological type of complete open riemannian manifolds under certain positivity conditions for curvature. Key tools are comparison techniques and Morse Theory of Busemann and distance functions.
Homogeneity for open partitions of pairs of reals
Authors: Feng Qi
Published: June 2012

We prove a partition theorem for analytic sets of reals, namely, if

A
⊆

R

A \subseteq \mathbb {R}

is analytic and

[
A

]
2

=

K
0

∪

K
1

{[A]^2} = {K_0} \cup {K_1}

with

K
0

{K_0}

relatively open, then either there is a perfect

0
0

-homogeneous subset or

A
A

is a countable union of

1
1

-homogeneous subsets. We also show that such a partition property for coanalytic sets is the same as that each uncountable coanalytic set contains a perfect subset. A two person game for this partition property is also studied. There are some applications of such partition properties.
Characterization of automorphisms on the Barrett and the Diederich-Fornæss worm domains
Authors: Chen So-Chin
Published: June 2012

In this paper we show that every automorphism on either the Barrett or the Diederich-Fornaess worm domains is given by a rotation in

w
w

-variable. In particular, any automorphism on either one of these two domains can be extended smoothly up to the boundary.
A Frobenius characterization of rational singularity in 2-dimensional graded rings
Authors: Fedder Richard
Published: June 2012

A ring

R
R

is said to be

F
F

-rational if, for every prime

P
P

in

R
R

, the local ring

R
P

{R_P}

has the property that every system of parameters ideal is tightly closed (as defined by Hochster-Huneke). It is proved that if

R
R

is a

2
2

-dimensional graded ring with an isolated singularity at the irrelevant maximal ideal

m
m

, then the following are equivalent: (1)

R
R

has a rational singularity at

m
m

. (2)

R
R

is

F
F

-rational. (3)

a
(
R
)
>
0

a(R) > 0

. Here

a
(
R
)

a(R)

(as defined by Goto-Watanabe) denotes the least nonvanishing graded piece of the local cohomology module

H
m

(
R
)

{H_m}(R)

. The proof of this result relies heavily on the properties of derivations of

R
R

, and suggests further questions in that direction; paradigmatically, if one knows that

D
(
a
)

D(a)

satisfies a certain property for every derivation

D
D

, what can one conclude about the original ring element

a
a

?
When Cantor sets intersect thickly
Authors: Hunt Brian R. , Kan Ittai , Yorke James A.
Published: June 2012

The thickness of a Cantor set on the real line is a measurement of its "size". Thickness conditions have been used to guarantee that the intersection of two Cantor sets is nonempty. We present sharp conditions on the thicknesses of two Cantor sets which imply that their intersection contains a Cantor set of positive thickness.
The Gorensteinness of the symbolic blow-ups for certain space monomial curves
Authors: Goto Shiro , Nishida Koji , Shimoda Yasuhiro
Published: June 2012

Let

p

=

p

(

n
1

,

n
2

,

n
3

)

{\mathbf {p}} = {\mathbf {p}}({n_1},{n_2},{n_3})

denote the prime ideal in the formal power series ring

A
=
k
[
[
X
,
Y
,
Z
]
]

A = k[[X,Y,Z]]

over a field

k
k

defining the space monomial curve

X
=

T

n
1

X = {T^{{n_1}}}

,

Y
=

T

n
2

Y = {T^{{n_2}}}

, and

Z
=

T

n
3

Z = {T^{{n_3}}}

with

GCD

(

n
1

,

n
2

,

n
3

)
=
1

{\text {GCD}}({n_1},{n_2},{n_3}) = 1

. Then the symbolic Rees algebras

R
s

(

p

)
=

⊕

n
≥
0

p

(
n
)

{R_s}({\mathbf {p}}) = { \oplus _{n \geq 0}}{{\mathbf {p}}^{(n)}}

are Gorenstein rings for the prime ideals

p

=

p

(

n
1

,

n
2

,

n
3

)

{\mathbf {p}} = {\mathbf {p}}({n_1},{n_2},{n_3})

with

min
{

n
1

,

n
2

,

n
3

}
=
4

\min \{ {n_1},{n_2},{n_3}\} = 4

and

p

=

p

(
m
,
m
+
1
,
m
+
4
)

{\mathbf {p}} = {\mathbf {p}}(m,m + 1,m + 4)

with

m
≠
9
,
13

m \ne 9,13

. The rings

R
s

(

p

)

{R_s}({\mathbf {p}})

for

p

=

p

(
9
,
10
,
13
)

{\mathbf {p}} = {\mathbf {p}}(9,10,13)

and

p

=

p

(
13
,
14
,
17
)

{\mathbf {p}} = {\mathbf {p}}(13,14,17)

are Noetherian but non-Cohen-Macaulay, if

ch

k
=
3

\operatorname {ch}\,k = 3

.
Bass numbers of local cohomology modules
Authors: Huneke Craig L. , Sharp Rodney Y.
Published: June 2012

Let

A
A

be a regular local ring of positive characteristic. This paper is concerned with the local cohomology modules of

A
A

itself, but with respect to an arbitrary ideal of

A
A

. The results include that all the Bass numbers of all such local cohomology modules are finite, that each such local cohomology module has finite set of associated prime ideals, and that, whenever such a local cohomology module is Artinian, then it must be injective. (This last result had been proved earlier by Hartshorne and Speiser under the additional assumptions that

A
A

is complete and contains its residue field which is perfect.) The paper ends with some low-dimensional evidence related to questions about whether the analogous statements for regular local rings of characteristic

0
0

are true.
Singular integral operators on 𝐶¹ manifolds
Authors: Lewis Jeff E. , Selvaggi Renata , Sisto Irene
Published: June 2012

We show that the kernel of a singular integral operator is real analytic in

R

n

∖
{
0
}

{{\mathbf {R}}^n}\backslash \{ 0\}

iff the symbol [Fourier transform] is real analytic in

R

n

∖
{
0
}

{{\mathbf {R}}^n}\backslash \{ 0\}

. The singular integral operators with continuous coefficients and real analytic kernels (symbols) form an operator algebra with the usual symbolic calculus. The symbol is invariantly defined under

C
1

{C^1}

changes of coordinates.
Harmonic analysis and ultracontractivity
Authors: Cowling Michael , Meda Stefano
Published: June 2012

Let

(

T
t

)

t
>
0

{({T_t})_{t > 0}}

be a symmetric contraction semigroup on the spaces

L
p

(
M
)

(
1
≤
p
≤
∞
)

{L^p}(M)\;(1 \leq p \leq \infty )

, and let the functions

ϕ
\phi

and

ψ
\psi

be "regularly related". We show that

(

T
t

)

t
>
0

{({T_t})_{t > 0}}

is

ϕ
\phi

-ultracontractive, i.e., that

(

T
t

)

t
>
0

{({T_t})_{t > 0}}

satisfies the condition
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar upper T Subscript t Baseline f double-vertical-bar Subscript normal infinity Baseline less-than-or-equal-to upper C phi left-parenthesis t right-parenthesis Superscript negative 1 Baseline double-vertical-bar f double-vertical-bar Subscript 1">

‖

T
t

f

‖

∞

≤
C
ϕ

(
t

)

−
1

‖
f
‖

1

{\left \| {{T_t}f} \right \|_\infty } \leq C\phi {(t)^{ - 1}}{\left \| f \right \|_1}

for all

f
f

in

L
1

(
M
)

{L^1}(M)

and all

t
t

in

R

+

{{\mathbf {R}}^ + }

, if and only if the infinitesimal generator

G

\mathcal {G}

has Sobolev embedding properties, namely,
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar psi left-parenthesis script upper G right-parenthesis Superscript negative alpha Baseline f double-vertical-bar Subscript q Baseline less-than-or-equal-to upper C double-vertical-bar f double-vertical-bar Subscript p">

‖

ψ

(

G

)

−
α

f

‖

q

≤
C

‖
f
‖

p

{\left \| {\psi {{(\mathcal {G})}^{ - \alpha }}f} \right \|_q} \leq C{\left \| f \right \|_p}

for all

f
f

in

L
p

(
M
)

{L^p}(M)

, whenever

1
>
p
>
q
>
∞

1 > p > q > \infty

and

α
=
1

/

p
−
1

/

q

\alpha = 1/p - 1/q

. We establish some new spectral multiplier theorems and maximal function estimates. In particular, we give sufficient conditions on

m
m

for

m
(

G

)

m(\mathcal {G})

to map

L
p

(
M
)

{L^p}(M)

to

L
q

(
M
)

{L^q}(M)

, and for the example where there exists

μ
\mu

in

R

+

{{\mathbf {R}}^ + }

such that

ϕ
(
t
)
=

t
μ

\phi (t) = {t^\mu }

for all

t
t

in

R

+

{{\mathbf {R}}^ + }

, we give conditions which ensure that the maximal function

sup

t
>
0

|

t
α

T
t

f
(
∙
)

|

{\sup _{t > 0}}|{t^\alpha }{T_t}f( \bullet )|

is bounded.
Classification of singularities for blowing up solutions in higher dimensions
Authors: Velázquez J. J. L.
Published: June 2012

Consider the Cauchy problem (P)\[<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout Enlarged left-brace 1st Row 1st Column u Subscript t Baseline minus normal upper Delta u equals u Superscript p Baseline 2nd Column a m p semicolon when x element-of double-struck upper R Superscript upper N Baseline comma 3rd Column a m p semicolon t greater-than 0 comma upper N greater-than-or-equal-to 1 comma 2nd Row 1st Column u left-parenthesis x comma 0 right-parenthesis equals u 0 left-parenthesis x right-parenthesis 2nd Column a m p semicolon when x element-of double-struck upper R Superscript upper N Baseline comma 3rd Column a m p semicolon EndLayout">{ut−Δu=upamp;whenx∈RN,amp;t>0,N≥1,u(x,0)=u0(x)amp;whenx∈RN,amp;\left \{ {\begin {array}{*{20}{c}} {{u_t} - \Delta u = {u^p}} \hfill & {{\text {when}}\;x \in {\mathbb {R}^N},} \hfill & {t > 0,N \geq 1,} \hfill \\ {u(x,0) = {u_0}(x)} \hfill & {{\text {when}}\;x \in {\mathbb {R}^N},} \hfill & {} \hfill \\ \end {array} } \right .\]wherep>1p > 1, andu0(x){u_0}(x)is a continuous, nonnegative and bounded function. It is known that, under fairly general assumptions onu0(x){u_0}(x), the unique solution of(P)({\text {P}}),u(x,t)u(x,t), blows up in a finite time, by which we mean that\[<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="limit sup Underscript t up-arrow upper T Endscripts left-parenthesis sup Underscript x element-of double-struck upper R Superscript upper N Baseline Endscripts u left-parenthesis x comma t right-parenthesis right-parenthesis equals plus normal infinity period">limsupt↑T(supx∈RNu(x,t))=+∞.\lim \sup \limits _{t \uparrow T} \left ( {\sup \limits _{x \in {\mathbb {R}^N}} \;u(x,t)} \right ) = + \infty .\]In this paper we shall assume thatu(x,t)u(x,t)blows up atx=0x = 0,t=T>+∞t = T > + \infty, and derive the possible asymptotic behaviours ofu(x,t)u(x,t)as(x,t)→(0,T)(x,t) \to (0,T), under general assumptions on the blow-up rate.
Uniform algebras generated by holomorphic and pluriharmonic functions
Authors: Izzo Alexander J.
Published: June 2012

It is shown that if

f
1

,
…
,

f
n

{f_1}, \ldots ,{f_n}

are pluriharmonic on

B
n

{B_n}

(the open unit ball in

C

n

)

{\mathbb {C}^n})

and

C
1

{C^1}

on

B
¯

n

{\bar B_n}

, and the

n
×
n

n \times n

matrix

(
∂

f
j

/

∂

z
¯

k

)

(\partial {f_j}/\partial {\bar z_k})

is invertible at every point of

B
n

{B_n}

, then the norm-closed algebra generated by the ball algebra

A
(

B
¯

n

)

A({\bar B_n})

and

f
1

,
…
,

f
n

{f_1}, \ldots ,{f_n}

is equal to

C
(

B
¯

n

)

C({\bar B_n})

. Extensions of this result to more general strictly pseudoconvex domains are also presented.
Regularity properties of solutions to transmission problems
Authors: Escauriaza Luis , Seo Jin Keun
Published: June 2012

We show that the gradients of solutions to certain elliptic and parabolic transmission problems with internal Lipschitz boundary and constant coefficients at each side of the internal boundary are square integrable along the internal boundary.
On property I for knots in 𝑆³
Authors: Zhang Xingru
Published: June 2012

This paper deals with the question of which knot surgeries on

S
3

{S^3}

can yield

3
3

-manifolds homeomorphic to, or with the same fundamental group as, the Poincaré homology

3
3

-sphere.
Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions
Authors: Mordukhovich Boris
Published: June 2012

We consider some basic properties of nonsmooth and set-valued mappings (multifunctions) connected with open and inverse mapping principles, distance estimates to the level sets (metric regularity), and a locally Lipschitzian behavior. These properties have many important applications to various problems in nonlinear analysis, optimization, control theory, etc., especially for studying sensitivity and stability questions with respect to perturbations of initial data and parameters. We establish interrelations between these properties and prove effective criteria for their fulfillment stated in terms of robust generalized derivatives for multifunctions and nonsmooth mappings. The results obtained provide complete characterizations of the properties under consideration in a general setting of closed-graph multifunctions in finite dimensions. They ensure new information even in the classical cases of smooth single-valued mappings as well as multifunctions with convex graphs.
Optimal natural dualities
Authors: Davey B. A. , Priestley H. A.
Published: June 2012

The authors showed previously that for each of the varieties

B

n

(
3
≤
n
>
ω
)

{{\mathbf {B}}_n}(3 \leq n > \omega )

of pseudocomplemented distributive lattices there exists a natural duality given by a set of

p
(
n
)
+
3

p(n) + 3

binary algebraic relations, where

p
(
n
)

p(n)

denotes the number of partitions of

n
n

. This paper improves this result by establishing that an optimal set of

n
+
3

n + 3

of these relations suffices. This is achieved by the use of "test algebras": it is shown that redundancy among the relations of a duality for a prevariety generated by a finite algebra may be decided by testing the duality on the relations, qua algebras.
The geometry of Julia sets
Authors: Aarts Jan M. , Oversteegen Lex G.
Published: June 2012

The long term analysis of dynamical systems inspired the study of the dynamics of families of mappings. Many of these investigations led to the study of the dynamics of mappings on Cantor sets and on intervals. Julia sets play a critical role in the understanding of the dynamics of families of mappings. In this paper we introduce another class of objects (called hairy objects) which share many properties with the Cantor set and the interval: they are topologically unique and admit only one embedding in the plane. These uniqueness properties explain the regular occurrence of hairy objects in pictures of Julia sets—hairy objects are ubiquitous. Hairy arcs will be used to give a complete topological description of the Julia sets of many members of the exponential family.
Basic constructions in the 𝐾-theory of homotopy ring spaces
Authors: Schwänzl R. , Vogt R. M.
Published: June 2012

Using the language of category theory and universal algebra we formalize the passage from the permutative category of finitely generated free

R
R

-modules to the algebraic

K
K

-theory

K
R

KR

of

R
R

and thus make it applicable to homotopy ring spaces. As applications we construct a Waldhausen type of algebraic

K
K

-theory for arbitrary homotopy ring spaces, show its equivalence with constructions of May and Steiner, prove its Morita invariance and show that the algebraic

K
K

-theory

K
X

KX

of an

E
∞

{E_\infty }

ring

X
X

is itself an

E
∞

{E_\infty }

ring. Finally we investigate the monomial map

Q
(
B

X
+
∗

)
→
K
X

Q(BX_ + ^\ast ) \to KX

.
Characteristic cycles of discrete series for 𝑅-rank one groups
Authors: Chang Jen-Tseh
Published: June 2012

We determine the characteristic cycles of the discrete series representations for connected

R

\mathbb {R}

-rank one linear groups. The computation is made through the moment maps; we determine their fibers and the cohomology in question case by case. The multiplicity of the discrete series, in terms of their Harish-Chandra parameters, is given by recursive formulae; for groups of type

A
A

and

B
B

closed formulae are obtained.
Minimal models and degenerations of surfaces with Kodaira number zero
Authors: Crauder Bruce , Morrison David R.
Published: June 2012

For Ueno’s degenerations of abelian surfaces and for analytic flowerpot degenerations of surfaces with Kodaira number zero, we find analytically

Q

\mathbb {Q}

-factorial terminal minimal models. All contractions, singularities and flips are given by explicit geometric constructions.
Noetherian properties of skew polynomial rings with binomial relations
Authors: Gateva-Ivanova Tatiana
Published: June 2012

In this work we study standard finitely presented associative algebras over a fixed field K. A restricted class of skew polynomial rings with quadratic relations considered in an earlier work of M. Artin and W. Schelter will be studied. We call them binomial skew polynomial algebras. We establish necessary and sufficient conditions for such an algebra to be a Noetherian domain.
Amenable relations for endomorphisms
Authors: Hawkins J. M.
Published: June 2012

We give necessary and sufficient conditions for an endomorphism to admit an equivalent invariant

σ
\sigma

-finite measure in terms of a generalized Perron-Frobenius operator. The assumptions are that the endomorphism is nonsingular (preserves sets of measure zero), conservative, and finite-to-1. We study two orbit equivalence relations associated to an endomorphism, and their connections to nonsingularity, ergodicity, and exactness. We also discuss Radon-Nikodym derivative cocycles for the relations and the endomorphism, and relate these to the Jacobian of the endomorphism.
Graphs with the circuit cover property
Authors: Alspach Brian , Goddyn Luis , Zhang Cun Quan
Published: June 2012

A circuit cover of an edge-weighted graph (G, p) is a multiset of circuits in G such that every edge e is contained in exactly

p
(
e
)

p(e)

circuits in the multiset. A nonnegative integer valued weight vector p is admissible if the total weight of any edge-cut is even, and no edge has more than half the total weight of any edge-cut containing it. A graph G has the circuit cover property if (G, p) has a circuit cover for every admissible weight vector p. We prove that a graph has the circuit cover property if and only if it contains no subgraph homeomorphic to Petersen’s graph. In particular, every 2-edge-connected graph with no subgraph homeomorphic to Petersen’s graph has a cycle double cover.
A variational principle in Kreĭn space
Authors: Binding Paul , Najman Branko
Published: June 2012

A variational characterization, involving a max-inf of the Rayleigh quotient, is established for certain eigenvalues of a wide class of definitizable selfadjoint operators Q in a Krein space. The operator Q may have continuous spectrum and nonreal and nonsemisimple eigenvalues; in particular it may have embedded eigenvalues. Various applications are given to selfadjoint linear and quadratic eigenvalue problems with weak definiteness assumptions.
Microlocal analysis of some isospectral deformations
Authors: Marhuenda F.
Published: June 2012

We study the microlocal structure of the examples of isospectral deformations of Riemannian manifolds given by D. DeTurck and C. Gordon in [DeT-Gl]. The Schwartz kernel of the intertwining operators considered by them may be written as an oscillatory integral with a singular phase function and product type amplitude. In certain instances, we identify them as belonging to the space of Fourier integral operators associated with various pairwise intersecting Lagrangians. After formulating a class of operators incorporating the most relevant features of the operators above, we establish a composition calculus for this class and show that is not necessary to introduce new Lagrangians in the composition.
Holomorphic motions and Teichmüller spaces
Authors: Earle C. J. , Kra I. , Krushkal′ S. L.
Published: June 2012

We prove an equivariant form of Slodkowski’s theorem that every holomorphic motion of a subset of the extended complex plane

C

^

\hat {\mathbb {C}}

extends to a holomorphic motion of

C

^

\widehat {\mathbb {C}}

. As a consequence we prove that every holomorphic map of the unit disc into Teichmüller space lifts to a holomorphic map into the space of Beltrami forms. We use this lifting theorem to study the Teichmüller metric.
Entropy solutions for diffusion-convection equations with partial diffusivity
Authors: Escobedo M. , Vázquez J. L. , Zuazua Enrike
Published: June 2012

We consider the Cauchy problem for the following scalar conservation law with partial viscosity
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u Subscript t Baseline equals normal upper Delta Subscript x Baseline u plus partial-differential Subscript y Baseline left-parenthesis f left-parenthesis u right-parenthesis right-parenthesis comma left-parenthesis x comma y right-parenthesis element-of bold upper R Superscript upper N Baseline comma t greater-than 0 period">

u
t

=

Δ
x

u
+

∂
y

(
f
(
u
)
)
,

(
x
,
y
)
∈

R

N

,
t
>
0.

{u_t} = {\Delta _x}u + {\partial _y}(f(u)),\quad (x,y) \in {{\mathbf {R}}^N},t > 0.

\]
The existence of solutions is proved by the vanishing viscosity method. By introducing a suitable entropy condition we prove uniqueness of solutions. This entropy condition is inspired by the entropy criterion introduced by Kruzhkov for hyperbolic conservation laws but it takes into account the effect of diffusion.
Groups and fields interpretable in separably closed fields
Authors: Messmer Margit
Published: June 2012

We prove that any infinite group interpretable in a separably closed field F of finite Eršov-invariant is definably isomorphic to an F-algebraic group. Using this result we show that any infinite field K interpretable in a separably closed field F is itself separably closed; in particular, in the finite invariant case K is definably isomorphic to a finite extension of F.
On the solvability of systems of inclusions involving noncompact operators
Authors: Nistri P. , Obukhovskiĭ V. V. , Zecca P.
Published: June 2012

We consider the solvability of a system
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout Enlarged left-brace 1st Row y element-of ModifyingAbove upper F With bar left-parenthesis x comma y right-parenthesis comma 2nd Row x element-of ModifyingAbove upper G With bar left-parenthesis x comma y right-parenthesis EndLayout">

{

y
∈

F
¯

(
x
,
y
)
,

x
∈

G
¯

(
x
,
y
)

\left \{ {\begin {array}{*{20}{c}} {y \in \bar F(x,y),} \\ {x \in \bar G(x,y)} \\ \end {array} } \right .

\]
of set-valued maps in two different cases. In the first one, the map

(
x
,
y
)
−
∘

F
¯

(
x
,
y
)

(x,y) - \circ \bar F(x,y)

is supposed to be closed graph with convex values and condensing in the second variable and

(
x
,
y
)
−
∘

G
¯

(
x
,
y
)

(x,y) - \circ \bar G(x,y)

is supposed to be a permissible map (i.e. composition of an upper semicontinuous map with acyclic values and a continuous, single-valued map), satisfying a condensivity condition in the first variable. In the second case

F
¯

\bar F

is as before with compact, not necessarily convex, values and

G
¯

\bar G

is an admissible map (i.e. it is composition of upper semicontinuous acyclic maps). In the latter case, in order to apply a fixed point theorem for admissible maps, we have to assume that the solution set

x
−
∘
S
(
x
)

x - \circ S(x)

of the first equation is acyclic. Two examples of applications of the abstract results are given. The first is a control problem for a neutral functional differential equation on a finite time interval; the second one deals with a semilinear differential inclusion in a Banach space and sufficient conditions are given to show that it has periodic solutions of a prescribed period.
On a two-dimensional elliptic problem with large exponent in nonlinearity
Authors: Ren Xiaofeng , Wei Juncheng
Published: June 2012

A semilinear elliptic equation on a bounded domain in

R
2

{R^2}

with large exponent in the nonlinear term is studied in this paper. We investigate positive solutions obtained by the variational method. It turns put that the constrained minimizing problem possesses nice asymptotic behavior as the nonlinear exponent, serving as a parameter, gets large. We shall prove that

c
p

{c_p}

, the minimum of energy functional with the nonlinear exponent equal to p, is like

(
8
π
e

)

1

/

2

p

−
1

/

2

{(8\pi e)^{1/2}}{p^{ - 1/2}}

as p tends to infinity. Using this result, we shall prove that the variational solutions remain bounded uniformly in p. As p tends to infinity, the solutions develop one or two peaks. Precisely the solutions approach zero except at one or two points where they stay away from zero and bounded from above. Then we consider the problem on a special class of domains. It turns out that the solutions then develop only one peak. For these domains, the solutions enlarged by a suitable quantity behave like a Green’s function of

−
Δ

- \Delta

. In this case we shall also prove that the peaks must appear at a critical point of the Robin function of the domain.
Minimal displacement of points under holomorphic mappings and fixed point properties for unions of convex sets
Authors: Kuczumow Tadeusz , Reich Simeon , Stachura Adam
Published: June 2012

Let D be an open convex bounded subset of a complex Banach space

(
X
,

‖
⋅
‖

)

(X,\left \| \cdot \right \|)

, and let C be the union of a finite number of closed convex sets lying strictly inside D. Using the Kuratowski measure of noncompactness with respect to the Kobayashi distance in D, we first show that if

f
:
D
→
D

f:D \to D

is a holomorphic mapping which leaves C invariant, and if the Lefschetz number

λ
(

f

|

C

)
≠
0

\lambda ({f_{|C}}) \ne 0

, then

inf
{

‖

x
−
f
(
x
)

‖

:
x
∈
C
}
=
0

\inf \{ \left \| {x - f(x)} \right \|:x \in C\} = 0

. We then deduce several new fixed point theorems for holomorphic and nonexpansive mappings.
Structural instability of exponential functions
Authors: Ye Zhuan
Published: June 2012

We first prove some equivalent statements on J-stability of families of critically finite entire functions. Then, with these in hand, a conjecture concerning stability of the family of exponential functions is affirmatively answered in some cases.
First- and second-order necessary conditions for control problems with constraints
Authors: Páles Zsolt , Zeidan Vera
Published: June 2012

Second-order necessary conditions are developed for an abstract nonsmooth control problem with mixed state-control equality and inequality constraints as well as a constraint of the form

G
(
x
,
u
)
∈
Γ

G(x,u) \in \Gamma

, where

Γ
\Gamma

is a closed convex set of a Banach space with nonempty interior. The inequality constraints

g
(
s
,
x
,
u
)
⩽
0

g(s,x,u) \leqslant 0

depend on a parameter

s
s

belonging to a compact metric space

S
S

. The equality constraints are split into two sets of equations

K
(
x
,
u
)
=
0

K(x,u) = 0

and

H
(
x
,
u
)
=
0

H(x,u) = 0

, where the first equation is an abstract control equation, and

H
H

is assumed to have a full rank property in

u
u

. The objective function is

max

t
∈
T

f
(
t
,
x
,
u
)

{\max _{t \in T}}f(t,x,u)

where

T
T

is a compact metric space,

f
f

is upper semicontinuous in

t
t

and Lipschitz in

(
x
,
u
)

(x,u)

. The results are in terms of a function

σ
\sigma

that disappears when the parameter spaces

T
T

and

S
S

are discrete. We apply these results to control problems governed by ordinary differential equations and having pure state inequality constraints and control state equality and inequality constraints. Thus we obtain a generalization and extension of the existing results on this problem.
𝐹-regularity, test elements, and smooth base change
Authors: Hochster Melvin , Huneke Craig
Published: June 2012

This paper deals with tight closure theory in positive characteristic. After a good deal of preliminary work in the first five sections, including a treatment of

F
F

-rationality and a treatment of

F
F

-regularity for Gorenstein rings, a very widely applicable theory of test elements for tight closure is developed in

§
6

\S 6

and is then applied in

§
7

\S 7

to prove that both tight closure and

F
F

-regularity commute with smooth base change under many circumstances (where "smooth" is used to mean flat with geometrically regular fibers). For example, it is shown in

§
6

\S 6

that for a reduced ring

R
R

essentially of finite type over an excellent local ring of characteristic

p
p

, if

c
c

is not in any minimal prime of

R
R

and

R
c

{R_c}

is regular, then

c
c

has a power that is a test element. It is shown in

§
7

\S 7

that if

S
S

is a flat

R
R

-algebra with regular fibers and

R
R

is

F
F

-regular then

S
S

is

F
F

-regular. The general problem of showing that tight closure commutes with smooth base change remains open, but is reduced here to showing that tight closure commutes with localization.
On the oblique derivative problem for diffusion processes and diffusion equations with Hölder continuous coefficients
Authors: Tsuchiya Masaaki
Published: June 2012

On a

C
2

{C^2}

-domain in a Euclidean space, we consider the oblique derivative problem for a diffusion equation and assume the coefficients of the diffusion and boundary operators are Hölder continuous. We then prove the uniqueness of diffusion processes and fundamental solutions corresponding to the problem. For the purpose, obtaining a stochastic representation of some solutions to the problem plays a key role; in our situation, a difficulty arises from the absence of a fundamental solution with

C
2

{C^2}

-smoothness up to the boundary. It is overcome by showing some stability of a fundamental solution and a diffusion process, respectively, under approximation of the domain. In particular, the stability of the fundamental solution is verified through construction: it is done by applying the parametrix method twice to a parametrix with explicit expression.
Inverse theorems for subset sums
Authors: Nathanson Melvyn B.
Published: June 2012

Let

A
A

be a finite set of integers. For

h
⩾
1

h \geqslant 1

, let

S
h

(
A
)

{S_h}(A)

denote the set of all sums of

h
h

distinct elements of

A
A

. Let

S
(
A
)

S(A)

denote the set of all nonempty sums of distinct elements of

A
A

. The direct problem for subset sums is to find lower bounds for

|

S
h

(
A
)

|

|{S_h}(A)|

and

|

S
(
A
)

|

|S(A)|

in terms of

|

A

|

|A|

. The inverse problem for subset sums is to determine the structure of the extremal sets

A
A

of integers for which

|

S
h

(
A
)

|

|{S_h}(A)|

and

|

S
(
A
)

|

|S(A)|

are minimal. In this paper both the direct and the inverse problem for subset sums are solved.
Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions
Authors: Mischaikow Konstantin , Smith Hal , Thieme Horst R.
Published: June 2012

From the work of C. Conley, it is known that the omega limit set of a precompact orbit of an autonomous semiflow is a chain recurrent set. Here, we improve a result of L. Markus by showing that the omega limit set of a solution of an asymptotically autonomous semiflow is a chain recurrent set relative to the limiting autonomous semiflow. In the special case that there is a Lyapunov function for the limiting semiflow, sufficient conditions are given for an omega limit set of the asymptotically autonomous semiflow to be contained in a level set of the Lyapunov function.
A constructive proof of the Poincaré-Birkhoff theorem
Authors: Li Yong , Lin Zheng Hua
Published: June 2012

In this paper, with the use of the homotopy method, a constructive proof of the Poincaré-Birkhoff theorem is given. This approach provides a global method for finding fixed points of area-preserving maps and periodic solutions of Duffing equations.
Rates of eigenvalues on a dumbbell domain. Simple eigenvalue case
Authors: Arrieta José M.
Published: June 2012

We obtain the first term in the asymptotic expansion of the eigenvalues of the Laplace operator in a typical dumbbell domain in

R

2

{\mathbb {R}^2}

. This domain consists of two disjoint domains

Ω
L

{\Omega ^L}

,

Ω
R

{\Omega ^R}

joined by a channel

R
ε

{R_\varepsilon }

of height of the order of the parameter

ε
\varepsilon

. When an eigenvalue approaches an eigenvalue of the Laplacian in

Ω
L

∪

Ω
R

{\Omega ^L} \cup {\Omega ^R}

, the order of convergence is

ε
\varepsilon

, while if the eigenvalue approaches an eigenvalue which comes from the channel, the order is weaker:

ε

|

ln

ε

|

\varepsilon \left | {{\text {ln}}\varepsilon } \right |

. We also obtain estimates on the behavior of the eigenfunctions.
𝐿^{𝑝} theory of differential forms on manifolds
Authors: Scott Chad
Published: June 2012

In this paper, we establish a Hodge-type decomposition for the

L
p

{L^p}

space of differential forms on closed (i.e., compact, oriented, smooth) Riemannian manifolds. Critical to the proof of this result is establishing an

L
p

{L^p}

estimate which contains, as a special case, the

L
2

{L^2}

result referred to by Morrey as Gaffney’s inequality. This inequality helps us show the equivalence of the usual definition of Sobolev space with a more geometric formulation which we provide in the case of differential forms on manifolds. We also prove the

L
p

{L^p}

boundedness of Green’s operator which we use in developing the

L
p

{L^p}

theory of the Hodge decomposition. For the calculus of variations, we rigorously verify that the spaces of exact and coexact forms are closed in the

L
p

{L^p}

norm. For nonlinear analysis, we demonstrate the existence and uniqueness of a solution to the

A
A

-harmonic equation.
Local uniqueness in the inverse conductivity problem with one measurement
Authors: Alessandrini G. , Isakov V. , Powell J.
Published: June 2012

We prove local uniqueness of a domain

D
D

entering the conductivity equation

div

(
(
1
+
χ
(
D
)
)
∇
u
)
=
0

{\text {div}}((1 + \chi (D))\nabla u) = 0

in a bounded planar domain

Ω
\Omega

given the Cauchy data for

u
u

on a part of

∂
Ω

\partial \Omega

. The main assumption is that

∇
u

\nabla u

has zero index on

∂
Ω

\partial \Omega

which is easy to guarantee by choosing special boundary data for

u
u

. To achieve our goals we study index of critical points of

u
u

on

∂
Ω

\partial \Omega

.
𝐿^{𝑝} spectra of pseudodifferential operators generating integrated semigroups
Authors: Hieber Matthias
Published: June 2012

Consider the

L
p

{L^p}

-realization

O

p

p

(
a
)

{\text {O}}{{\text {p}}_p}(a)

of a pseudodifferential operator with symbol

a
∈

S

ρ
,
0

m

a \in S_{\rho ,0}^m

having constant coefficients. We show that for a certain class of symbols the spectrum of

O

p

p

(
a
)

{\text {O}}{{\text {p}}_p}(a)

is independent of

p
p

. This implies that

O

p

p

(
a
)

{\text {O}}{{\text {p}}_p}(a)

generates an

N
N

-times integrated semigroup on

L
p

(

R

n

)

{L^p}({\mathbb {R}^n})

for a certain

N
N

if and only if

ρ
(

O

p

p

(
a
)
)
≠
∅

\rho ({\text {O}}{{\text {p}}_p}(a)) \ne \emptyset

and the numerical range of

a
a

is contained in a left half-plane. Our method allows us also to construct examples of operators generating integrated semigroups on

L
p

(

R

n

)

{L^p}({\mathbb {R}^n})

if and only if

p
p

is sufficiently close to

2
2

.
Mean value property and subdifferential criteria for lower semicontinuous functions
Authors: Aussel Didier , Corvellec Jean-Noël , Lassonde Marc
Published: June 2012

We define an abstract notion of subdifferential operator and an associated notion of smoothness of a norm covering all the standard situations. In particular, a norm is smooth for the Gâteaux (Fréchet, Hadamard, Lipschitz-smooth) subdifferential if it is Gâteaux (Fréchet, Hadamard, Lipschitz) smooth in the classical sense, while on the other hand any norm is smooth for the Clarke-Rockafellar subdifferential. We then show that lower semicontinuous functions on a Banach space satisfy an Approximate Mean Value Inequality with respect to any subdifferential for which the norm is smooth, thus providing a new insight on the connection between the smoothness of norms and the subdifferentiability properties of functions. The proof relies on an adaptation of the "smooth" variational principle of Borwein-Preiss. Along the same vein, we derive subdifferential criteria for coercivity, Lipschitz behavior, conemonotonicity, quasiconvexity, and convexity of lower semicontinuous functions which clarify, unify and extend many existing results for specific subdifferentials.
The zero-sets of the radial-limit functions of inner functions
Authors: Belna Charles L. , Berman Robert D. , Colwell Peter , Piranian George
Published: June 2012

A set

E
E

on the unit circle is the zero-set of the radial-limit function of some inner function if and only if

E
E

is a countable intersection of

F
σ

{F_\sigma }

-sets of measure

0
0

.
The structure of the reverse Hölder classes
Authors: Cruz-Uribe David , Neugebauer C. J.
Published: June 2012

In this paper we study the structure of the class of functions

(
R

H
s

)

(R{H_s})

which satisfy the reverse Hölder inequality with exponent

s
>
1

s > 1

. To do so we introduce a new operator, the minimal operator, which is analogous to the Hardy-Littlewood maximal operator, and a new class of functions,

(
R

H
∞

)

(R{H_\infty })

, which plays the same role for

(
R

H
s

)

(R{H_s})

that the class

(

A
1

)

({A_1})

does for the

(

A
p

)

({A_p})

classes.
Wiman-Valiron theory in two variables
Authors: Fenton P. C.
Published: June 2012

Inequalities are obtained for the coefficients of the Taylor series of an entire function of two complex variables and used to obtain an inequality for the maximum modulus of the function in terms of the maximum term of the series.
Quasilinear elliptic equations with VMO coefficients
Authors: Palagachev Dian K.
Published: June 2012

Strong solvability and uniqueness in Sobolev space

W

2
,
n

(
Ω
)

{W^{2,n}}(\Omega )

are proved for the Dirichlet problem
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace Subscript u equals phi on partial-differential normal upper Omega period Superscript a Super Superscript i j Superscript left-parenthesis x comma u right-parenthesis upper D Super Subscript i j Superscript u plus b left-parenthesis x comma u comma upper D u right-parenthesis equals 0 a period e period normal upper Omega">

{

u
=
φ

on

∂
Ω
.

a

i
j

(
x
,
u
)

D

i
j

u
+
b
(
x
,
u
,
D
u
)
=
0

a

.e

.

Ω

\left \{ {_{u = \varphi \quad {\text {on}}\partial \Omega .}^{{a^{ij}}(x,u){D_{ij}}u + b(x,u,Du) = 0\quad {\text {a}}{\text {.e}}{\text {.}}\Omega }} \right .

\]
It is assumed that the coefficients of the quasilinear elliptic operator satisfy Carathéodory’s condition, the

a

i
j

{a^{ij}}

are

V

M

O

V\, M\, O

functions with respect to

x
x

, and structure conditions on

b
b

are required. The main results are derived by means of the Aleksandrov-Pucci maximum principle and Leray-Schauder’s fixed point theorem via a priori estimate for the

L

2
n

{L^{2n}}

-norm of the gradient.