bluuebunny/crossref_metadata_2025 huggingface dataset:
Local subgroups of the Monster and odd code loops
Authors: Richardson Thomas M.
Published: June 2012

The main result of this work is an explicit construction of

p
p

-local subgroups of the Monster, the largest sporadic simple group. The groups constructed are the normalizers in the Monster of certain subgroups of order

3

2

3^{2}

,

5

2

5^{2}

, and

7

2

7^{2}

and have shapes
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="3 Superscript 2 plus 5 plus 10 Baseline dot left-parenthesis upper M 11 times upper G upper L left-parenthesis 2 comma 3 right-parenthesis right-parenthesis comma 5 Superscript 2 plus 2 plus 4 Baseline dot upper S 3 times upper G upper L left-parenthesis 2 comma 5 right-parenthesis right-parenthesis comma and 7 Superscript 2 plus 1 plus 2 Baseline dot upper G upper L left-parenthesis 2 comma 7 right-parenthesis">

3

2
+
5
+
10

⋅
(

M

11

×
G
L
(
2
,
3
)
)
,

5

2
+
2
+
4

⋅

S
3

×
G
L
(
2
,
5
)
)
,

and

7

2
+
1
+
2

⋅
G
L
(
2
,
7
)

{3^{2 + 5 + 10}}\cdot ({M_{11}} \times GL(2,3)),\quad {5^{2 + 2 + 4}}\cdot {S_3} \times GL(2,5)),\quad {\text {and}}{7^{2 + 1 + 2}}\cdot GL(2,7)

\]
. These groups result from a general construction which proceeds in three steps. We start with a self-orthogonal code

C
C

of length

n
n

over the field

F

p

{\mathbb {F}_p}

, where

p
p

is an odd prime. The first step is to define a code loop

L
L

whose structure is based on

C
C

. The second step is to define a group

N
N

of permutations of functions from

F

p
2

\mathbb {F}_p^2

to

L
L

. The final step is to show that

N
N

has a normal subgroup

K
K

of order

p
2

{p^2}

. The result of this construction is the quotient group

N

/

K

N/K

of shape

p

2
+
m
+
2
m

(
S
×
G
L
(
2
,
p
)
)

{p^{2 + m + 2m}}(S \times GL(2,p))

, where

m
+
1
=
dim
⁡
(
C
)

m + 1 = \dim (C)

and

S
S

is the group of permutations of

Aut
(
C
)

\text {Aut}(C)

. To show that the groups we construct are contained in the Monster, we make use of certain lattices

Λ
(
C
)

\Lambda (C)

, defined in terms of the code

C
C

. One step in demonstrating this is to show that the centralizer of an element of order

p
p

in

N

/

K

N/K

is contained in the centralizer of an element of order

p
p

in the Monster. The lattices are useful in this regard since a quotient of the automorphism group of the lattice is a composition factor of the appropriate centralizer in the Monster. This work was inspired by a similar construction using code loops based on binary codes that John Conway used to construct a subgroup of the Monster of shape

2

2
+
11
+
22

⋅
(

M

24

×
G
L
(
2
,
2
)
)

{2^{2 + 11 + 22}}\cdot ({M_{24}} \times GL(2,2))

.
Torsion classes and a universal constraint on Donaldson invariants for odd manifolds
Authors: Akbulut Selman , Mrowka Tom , Ruan Yongbin
Published: June 2012

This paper studies the topology of the gauge group and givesmod2\bmod \,2universal relations along Donaldson polynomials of smooth44-manifolds, generalizing Y. Ruan’s previous related result.
The vanishing viscosity method in one-dimensional thermoelasticity
Authors: Chen Gui Qiang , Dafermos Constantine M.
Published: June 2012

The vanishing viscosity method is applied to the system of conservation laws of mass, momentum, and energy for a special class of one-dimensional thermoelastic media that do not conduct heat. Two types of vanishing "viscosity" are considered: Newtonian and artificial, in both cases accompanied by vanishing heat conductivity. It is shown that in either case one can pass to the zero viscosity limit by the method of compensated compactness, provided that velocity and pressure are uniformly bounded. Oscillations in the entropy field may propagate along the linearly degenerate characteristic field but do not affect the compactness of the velocity field or the pressure field. A priori bounds on velocity and pressure are established, albeit only for the case of artificial viscosity.
A right countably sigma-CS ring with ACC or DCC on projective principal right ideals is left Artinian and QF-3
Authors: Huynh Dinh Van
Published: June 2012

A module

M
M

is called a CS module if every submodule of

M
M

is essential in a direct summand of

M
M

. A ring

R
R

is said to be right (countably)

Σ
\Sigma

-CS if any direct sum of (countably many) copies of the right

R
R

-module

R
R

is CS. It is shown that for a right countably

Σ
\Sigma

-CS ring

R
R

the following are equivalent: (i)

R
R

is right

Σ
\Sigma

-CS, (ii)

R
R

has ACC or DCC on projective principal right ideals, (iii)

R
R

has finite right uniform dimension and ACC or DCC holds on projective uniform principal right ideals of

R
R

, (iv)

R
R

is semiperfect. From results of Oshiro [12], [13], under these conditions,

R
R

is left artinian and QF-

3
3

. As a consequence, a ring

R
R

is quasi-Frobenius if it is right countably

Σ
\Sigma

-CS, semiperfect and no nonzero projective right ideals are contained in its Jacobson radical.
Standard Lyndon bases of Lie algebras and enveloping algebras
Authors: Lalonde Pierre , Ram Arun
Published: June 2012

It is well known that the standard bracketings of Lyndon words in an alphabetAAform a basis for the free Lie algebraLie(A){\text {Lie}}(A)generated byAA. Suppose thatg≅Lie(A)/J\mathfrak {g} \cong {\text {Lie}}(A)/Jis a Lie algebra given by a generating setAAand a Lie idealJJof relations. Using a Gröbner basis type approach we define a set of "standard" Lyndon words, a subset of the set Lyndon words, such that the standard bracketings of these words form a basis of the Lie algebrag\mathfrak {g}. We show that a similar approach to the universal enveloping algebrag\mathfrak {g}naturally leads to a Poincaré-Birkhoff-Witt type basis of the enveloping algebra ofg\mathfrak {g}. We prove that the standard words satisfy the property that any factor of a standard word is again standard. Given root tables, this property is nearly sufficient to determine the standard Lyndon words for the complex finite-dimensional simple Lie algebras. We give an inductive procedure for computing the standard Lyndon words and give a complete list of the standard Lyndon words for the complex finite-dimensional simple Lie algebras. These results were announced in [LR].
The Connes spectrum of group actions and group gradings for certain quotient rings
Authors: Osterburg James , Yao Xue
Published: June 2012

Let

H
H

be a finite-dimensional, semisimple Hopf algebra over an algebraically closed field

K
K

where

H
H

is either commutative or cocommutative. We let

A
A

be an

H
H

-module algebra which is semiprime right Goldie. We show that the Connes spectrum of

H
H

acting on

A
A

is the Connes spectrum of

H
H

acting on the classical quotient ring of

A
A

. In our last section, we define a symmetric quotient ring and show that the Connes spectrum of the ring and its quotient ring are the same. Finally, we apply our results to finite group actions and group gradings.
On the tangential interpolation problem for 𝐻₂ functions
Authors: Alpay Daniel , Bolotnikov Vladimir , Peretz Yossi
Published: June 2012

The aim of this paper is to solve a matrix-valued version of the Nevanlinna-Pick interpolation problem for

H
2

{H_2}

functions. We reduce this problem to a Nevanlinna-Pick interpolation problem for Schur functions and obtain a linear fractional transformation which describes the set of all solutions.
Differential identities
Authors: Beauzamy Bernard , Dégot Jérôme
Published: June 2012

We deal here with homogeneous polynomials in many variables and their hypercube representation, introduced in [5]. Associated with this representation there is a norm (Bombieri’s norm) and a scalar product. We investigate differential identities connected with this scalar product. As a corollary, we obtain Bombieri’s inequality (originally proved in [4]), with significant improvements. The hypercube representation of a polynomial was elaborated in order to meet the requests of massively parallel computation on the "Connection Machine" at Etablissement Technique Central de l’Armement; we see here once again (after [3] and [5]) the theoretical power of the model.
Viewing parallel projection methods as sequential ones in convex feasibility problems
Authors: Crombez G.
Published: June 2012

We show that the parallel projection method with variable weights and one variable relaxation coefficient for obtaining a point in the intersection of a finite number of closed convex sets in a given Hilbert space may be interpreted as a semi-alternating sequential projection method in a suitably newly constructed Hilbert space. As such, convergence results for the parallel projection method may be derived from those which may be constructed in the semi-alternating sequential case.
On 𝐶*-algebras associated to the conjugation representation of a locally compact group
Authors: Kaniuth Eberhard , Markfort Annette
Published: June 2012

For a locally compact group

G
G

, let

γ
G

{\gamma _G}

denote the conjugation representation of

G
G

in

L
2

(
G
)

{L^2}(G)

. In this paper we are concerned with nuclearity of

C
∗

{C^*}

-algebras associated to

γ
G

{\gamma _G}

and the question of when these are of bounded representation type.
Groups with no free subsemigroups
Authors: Longobardi P. , Maj M. , Rhemtulla A. H.
Published: June 2012

We look at groups which have no (nonabelian) free subsemigroups. It is known that a finitely generated solvable group with no free subsemigroup is nilpotent-by-finite. Conversely nilpotent-by-finite groups have no free subsemigroups. Torsion-free residually finite-

p
p

groups with no free subsemigroups can have very complicated structure, but with some extra condition on the subsemigroups of such a group one obtains satisfactory results. These results are applied to ordered groups, right-ordered groups, and locally indicable groups.
A covering cocycle which does not grow linearly
Authors: Madden Kathleen M.
Published: June 2012

A cocycle

h
:
X
×

Z
m

→

R
n

h:X \times {Z^m} \to {R^n}

of a

Z
m

{Z^m}

action on a compact metric space, provides an

R
n

{R^n}

suspension flow (analogous to a flow under a function) on a space

X
h

{X_h}

which may not be Hausdorff or even

T
1

{T_1}

. Linear growth of

h
h

guarantees that

X
h

{X_h}

is a Hausdorff space; when

m
=
n

m = n

, linear growth is a consequence of

X
h

{X_h}

being Hausdorff and a covering condition. This paper contains the construction of a cocycle

h
:
X
×
Z
→

R
2

h:X \times Z \to {R^2}

which does not grow linearly yet produces a locally compact Hausdorff space with the covering condition. The

Z
Z

action used in the construction is a substitution minimal set.
Assessing prediction error in autoregressive models
Authors: Zhang Ping , Shaman Paul
Published: June 2012

Assessing prediction error is a problem which arises in time series analysis. The distinction between the conditional prediction error

e
e

and the unconditional prediction error

E
(
e
)

E(e)

has not received much attention in the literature. Although one can argue that the conditional version is more practical, we show in this article that assessing

e
e

is nearly impossible. In particular, we use the correlation coefficient

corr
⁡
(

e
^

,
e
)

\operatorname {corr} (\hat e,e)

, where

e
^

\hat e

is an estimate of

e
e

, as a measure of performance and show that

lim

T
→
∞

T

corr
⁡
(

e
^

,
e
)
=
C

{\lim _{T \to \infty }}\sqrt T \operatorname {corr} (\hat e,e) = C

where

T
T

is the sample size and

C
>
0

C > 0

is some constant. Furthermore, the value of

C
C

is large only when the process is extremely non-Gaussian or nearly nonstationary.
A new measure of growth for countable-dimensional algebras. I
Authors: Hannah John , O’Meara K. C.
Published: June 2012

A new dimension function on countable-dimensional algebras (over a field) is described. Its dimension values lie in the unit interval [0, 1]. Since the free algebra on two generators turns out to have dimension

0
0

(although conceivably some Noetherian algebras might have positive dimension!), this dimension function promises to distinguish among algebras of infinite

G
K

GK

dimension.
Cohomologically symplectic spaces: toral actions and the Gottlieb group
Authors: Lupton Gregory , Oprea John
Published: June 2012

Aspects of symplectic geometry are explored from a homotopical viewpoint. In particular, the question of whether or not a given toral action is Hamiltonian is shown to be independent of geometry. Rather, a new homotopical obstruction is described which detects when an action is Hamiltonian. This new entity, the

λ

α
^

{\lambda _{\hat \alpha }}

-invariant, allows many results of symplectic geometry to be generalized to manifolds which are only cohomologically symplectic in the sense that there is a degree

2
2

cohomology class which cups to a top class. Furthermore, new results in symplectic geometry also arise from this homotopical approach.
The direct decompositions of a group 𝐺 with 𝐺/𝐺’ finitely generated
Authors: Oger Francis
Published: June 2012

We consider the class

C

\mathcal {C}

which consists of the groups

M
M

with

M

/

M
′

M/M’

finitely generated which satisfy the maximal condition on direct factors. It is well known that any

C

\mathcal {C}

-group has a decomposition in finite direct product of indecomposable groups, and that two such decompositions are not necessarily equivalent up to isomorphism, even for a finitely generated nilpotent group. Here, we show that any

C

\mathcal {C}

-group has only finitely many nonequivalent decompositions. In order to prove this result, we introduce, for

C

\mathcal {C}

-groups, a slightly different notion of decomposition, that we call

J
J

-decomposition; we show that this decomposition is necessarily unique. We also obtain, as consequences of the properties of

J
J

-decompositions, several generalizations of results of R. Hirshon. For instance, we have

Z

×
G
≅

Z

×
H

\mathbb {Z} \times G \cong \mathbb {Z} \times H

for any groups

G
G

,

H
H

which satisfy

M
×
G
≅
M
×
H

M \times G \cong M \times H

for a

C

\mathcal {C}

-group

M
M

.
On parametric evolution inclusions of the subdifferential type with applications to optimal control problems
Authors: Papageorgiou Nikolaos S.
Published: June 2012

In this paper we study parametric evolution inclusions of the subdifferential type and their applications to the sensitivity analysis of nonlinear, infinite dimensional optimal control problems. The parameter appears in all the data of the problem, including the subdifferential operator. First we establish several continuity results for the solution multifunction of the subdifferential inclusion. Then we study how these results can be used to examine the sensitivity properties (variational stability) of certain broad classes of nonlinear infinite dimensional optimal control problems. Some examples are worked out in detail, illustrating the applicability of our work. These include obstacle problems (with time varying obstacles), optimal control of distributed parameter systems, and differential variational inequalities.
Residue classes of Lagrangian subbundles and Maslov classes
Authors: Suzuki Haruo
Published: June 2012

For Lagrangian subbundles with singularities in symplectic vector bundles, explicit formulas of relation between their residue classes and Maslov classes outside singularities are obtained. Then a Lagrangian subbundle with singularity is constructed where all possible Maslov classes are nonzero but residue classes vanish for dimension

>
2

> 2

. Moreover, a Lagrangian immersion with singularity is constructed, where the similar property for the associated Maslov classes and residue classes is shown.
Contiguity relations for generalized hypergeometric functions
Authors: Adolphson Alan , Dwork Bernard
Published: June 2012

It is well known that the hypergeometric functions
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="Subscript 2 Baseline upper F 1 left-parenthesis alpha plus-or-minus 1 comma beta comma gamma semicolon t right-parenthesis comma Subscript 2 Baseline upper F 1 left-parenthesis alpha comma beta plus-or-minus 1 comma gamma semicolon t right-parenthesis comma Subscript 2 Baseline upper F 1 left-parenthesis alpha comma beta comma gamma plus-or-minus 1 semicolon t right-parenthesis comma">

2

F
1

(
α
±
1
,
β
,
γ
;
t
)
,

2

F
1

(
α
,
β
±
1
,
γ
;
t
)
,

2

F
1

(
α
,
β
,
γ
±
1
;
t
)
,

_2{F_1}(\alpha \pm 1,\beta ,\gamma ;t),{\quad _2}{F_1}(\alpha ,\beta \pm 1,\gamma ;t),{\quad _2}{F_1}(\alpha ,\beta ,\gamma \pm 1;t),

\]
which are contiguous to

2

F
1

(
α
,
β
,
γ
;
t
)

_2{F_1}(\alpha ,\beta ,\gamma ;t)

, can be expressed in terms of
\[

2

F
1

(
α
,
β
,
γ
;
t
)

and

2

F
1
′

(
α
,
β
,
γ
;
t
)
.

_2{F_1}(\alpha ,\beta ,\gamma ;t)\quad {\text {and}}{\quad _2}F_1^\prime (\alpha ,\beta ,\gamma ;t).

\]
We explain how to derive analogous formulas for generalized hypergeometric functions. Our main point is that such relations can be deduced from the geometry of the cone associated in a recent paper by B. Dwork and F. Loeser to a generalized hypergeometric series.
On the oscillation of differential equations with an oscillatory coefficient
Authors: Harris B. J. , Kong Q.
Published: June 2012

We derive lower bounds for the distance between consecutive zeros of solutions of
\[

(
∗
)

y
"
+
q
(
t
)
y
=
0

( * )\quad y" + q(t)y = 0

\]
when

q
q

takes both positive and negative values. We apply our results to the limit point/limit circle classifications of

(
∗
)

( * )

.
Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d’un groupe réductif 𝑝-adique
Authors: Aubert Anne-Marie
Published: June 2012

We define an involution on the Grothendieck ring of the category of finite length smooth representations of a

p
p

-adic algebraic group, which is a direct analogue Curtis-Alvis duality for finite groups of Lie type. This involution commutes with taking the contragredient, with parabolic induction and, up a few twists, with truncation. It also preserves the irreducible representations up to sign.
Spectral and Fredholm properties of operators in elementary nest algebras
Authors: Barnes Bruce A. , Clauss Jon M.
Published: June 2012

Some spectral and Fredholm properties are proved for linear operators which leave invariant certain nests of closed subspaces.
On a semilinear elliptic Neumann problem with asymmetric nonlinearities
Authors: Gossez J.-P. , Omari P.
Published: June 2012

We consider the Neumann problem (1.1) below. We extend the range of applicability of the sharp nonresonance condition derived in [Go-Om] so as, in particular, allow asymmetric nonlinearities.
Comparison of certain 𝐻^{∞}-domains of holomorphy
Authors: Backlund Ulf
Published: June 2012

We study open sets defined by certain global plurisubharmonic functions in

C

N

{\mathbb {C}^N}

. We examine how the fact that the connected components of the sets are

H
∞

{H^\infty }

-domains of holomorphy is related to the structure of the set of discontinuity points of the global defining functions and to polynomial convexity.
Interpretation of Lavrentiev phenomenon by relaxation: the higher order case
Authors: Belloni Marino
Published: June 2012

We consider integral functionals of the calculus of variations of the form
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F left-parenthesis u right-parenthesis equals integral Subscript 0 Superscript 1 Baseline f left-parenthesis x comma u comma u prime comma ellipsis comma u Superscript left-parenthesis n right-parenthesis Baseline right-parenthesis d x">

F
(
u
)
=

∫
0
1

f
(
x
,
u
,

u
′

,
…
,

u

(
n
)

)
d
x

F(u) = \int \limits _0^1 {f(x,u,u’, \ldots ,{u^{(n)}})dx}

\]
defined for

u
∈

W

n
,
∞

(
0
,
1
)

u \in {W^{n,\infty }}(0,1)

, and we show that the relaxed functional

F
F

with respect to the weak

W

loc

n
,
1

(
0
,
1
)

W_{{\text {loc}}}^{n,1}(0,1)

convergence can be written as
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove upper F With bar left-parenthesis u right-parenthesis equals integral Subscript 0 Superscript 1 Baseline f left-parenthesis x comma u comma u prime comma ellipsis comma u Superscript left-parenthesis n right-parenthesis Baseline right-parenthesis d x plus upper L left-parenthesis u right-parenthesis comma">

F
¯

(
u
)
=

∫
0
1

f
(
x
,
u
,

u
′

,
…
,

u

(
n
)

)
d
x
+
L
(
u
)
,

\overline F (u) = \int \limits _0^1 {f(x,u,u’, \ldots ,{u^{(n)}})dx + L(u),}

\]
where the additional term

L
(
u
)

L(u)

, the Lavrentiev Gap, is explicitly identified in terms of

F
F

.
Singular limit of solutions of 𝑢_{𝑡}=Δ𝑢^{𝑚}-𝐴⋅∇(𝑢^{𝑞}/𝑞) as 𝑞→∞
Authors: Hui Kin Ming
Published: June 2012

We will show that the solutions of

u
t

=
Δ

u
m

−
A
∇
(

u
q

/

q
)

{u_t} = \Delta {u^m} - A\nabla ({u^q}/q)

in
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R Superscript n Baseline times left-parenthesis 0 comma upper T right-parenthesis comma upper T greater-than 0 comma m greater-than 1 comma u left-parenthesis x comma 0 right-parenthesis equals f left-parenthesis x right-parenthesis element-of upper L Superscript 1 Baseline left-parenthesis upper R Superscript n Baseline right-parenthesis intersection upper L Superscript normal infinity Baseline left-parenthesis upper R Superscript n Baseline right-parenthesis">

R
n

×
(
0
,
T
)
,
T
>
0
,
m
>
1
,
u
(
x
,
0
)
=
f
(
x
)
∈

L
1

(

R
n

)
∩

L
∞

(

R
n

)

{R^n} \times (0,T),T > 0,m > 1,u(x,0) = f(x) \in {L^1}({R^n}) \cap {L^\infty }({R^n})

converge weakly in

(

L
∞

(
G
)

)
∗

{({L^\infty }(G))^ * }

for any compact subset

G
G

of

R
n

×
(
0
,
T
)

{R^n} \times (0,T)

as

q
→
∞

q \to \infty

to the solution of the porous medium equation

υ
t

=
Δ

υ
m

{\upsilon _t} = \Delta {\upsilon ^m}

in

R
n

×
(
0
,
T
)

{R^n} \times (0,T)

with

υ
(
x
,
0
)
=
g
(
x
)

\upsilon (x,0) = g(x)

where

g
∈

L
1

(

R
n

)
,
0
⩽
g
⩽
1

g \in {L^1}({R^n}),0 \leqslant g \leqslant 1

, satisfies
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="g left-parenthesis x right-parenthesis plus left-parenthesis g left-parenthesis x right-parenthesis right-parenthesis Subscript x 1 Baseline equals f left-parenthesis x right-parenthesis in script upper D prime left-parenthesis upper R Superscript n Baseline right-parenthesis">

g
(
x
)
+

(
g
(
x
)

)

x
1

=
f
(
x
)

in

D

′

(

R
n

)

g(x) + {(g(x))_{{x_1}}} = f(x)\quad {\text {in}}\quad \mathcal {D}’\left ( {{R^n}} \right )

for some function
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove g With tilde left-parenthesis x right-parenthesis element-of upper L Superscript 1 Baseline left-parenthesis upper R Superscript n Baseline right-parenthesis comma ModifyingAbove g With tilde left-parenthesis x right-parenthesis greater-than-or-slanted-equals 0">

g
~

(
x
)
∈

L
1

(

R
n

)
,

g
~

(
x
)
⩾
0

\tilde {g}(x) \in {L^1}({R^n}),\quad \tilde {g}(x) \geqslant 0

such that

g
(
x
)
=
f
(
x
)
,

g
~

(
x
)
=
0

g(x) = f(x),\quad \tilde {g}(x) = 0

whenever

g
(
x
)
>
1

g(x) > 1

a.e.

x
∈

R
n

x \in {R^n}

. The convergence is uniform on compact subsets of

R
n

×
(
0
,
T
)

if

f
∈

C
0

(

R
n

)

{R^n} \times (0,T)\quad {\text {if}}\quad f \in {C_0}({R^n})

.
Verifiable conditions for openness and regularity of multivalued mappings in Banach spaces
Authors: Jourani A. , Thibault L.
Published: June 2012

This paper establishes verifiable conditions in terms of approximate subdifferentials implying openness and metric regularity of multivalued mappings in Banach spaces. The results are then applied to derive Lagrange multipliers for general nonsmooth vector optimization problems.
Norm estimates for radially symmetric solutions of semilinear elliptic equations
Authors: Kajikiya Ryuji
Published: June 2012

The semilinear elliptic equation

Δ
u
+
f
(
u
)
=
0

\Delta u + f(u) = 0

in

R
n

{R^n}

with the condition

lim

|

x

|

→
∞

u
(
x
)
=
0

{\lim _{|x| \to \infty }}u(x) = 0

is studied, where

n
⩾
2

n \geqslant 2

and

f
(
u
)

f(u)

has a superlinear and subcritical growth at

u
=
±
∞

u = \pm \infty

. For example, the functions
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis u right-parenthesis equals StartAbsoluteValue u EndAbsoluteValue Superscript p minus 1 Baseline u minus u left-parenthesis 1 greater-than p greater-than normal infinity if n equals 2 comma 1 greater-than p greater-than left-parenthesis n plus 2 right-parenthesis slash left-parenthesis n minus 2 right-parenthesis if n greater-than-or-slanted-equals 3 right-parenthesis">

f
(
u
)
=

|

u

|

p
−
1

u
−
u

(
1
>
p
>
∞

if

n
=
2
,

1
>
p
>
(
n
+
2
)

/

(
n
−
2
)

if

n
⩾
3
)

f(u) = |u{|^{p - 1}}u - u\;(1 > p > \infty \;{\text {if}}\;n = 2,\;1 > p > (n + 2)/(n - 2)\;{\text {if}}\;n \geqslant 3)

and

f
(
u
)
=
u
log
⁡

|

u

|

f(u) = u\log |u|

are treated. The

L
2

{L^2}

and

H
1

{H^1}

norm estimates
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C 1 left-parenthesis k plus 1 right-parenthesis Superscript n slash 2 Baseline less-than-or-slanted-equals StartAbsoluteValue EndAbsoluteValue u StartAbsoluteValue EndAbsoluteValue Subscript upper L squared Baseline less-than-or-slanted-equals StartAbsoluteValue EndAbsoluteValue u StartAbsoluteValue EndAbsoluteValue Subscript upper H Sub Superscript 1 Baseline less-than-or-slanted-equals upper C 2 left-parenthesis k plus 1 right-parenthesis Superscript n slash 2">

C
1

(
k
+
1

)

n

/

2

⩽

|

|

u

|

|

L
2

⩽

|

|

u

|

|

H
1

⩽

C
2

(
k
+
1

)

n

/

2

{C_1}{(k + 1)^{n/2}} \leqslant ||u|{|_{{L^2}}} \leqslant ||u|{|_{{H^1}}} \leqslant {C_2}{(k + 1)^{n/2}}

are established for any radially symmetric solution

u
u

which has exactly

k
⩾
0

k \geqslant 0

zeros in the interval

0
⩽

|

x

|

>
∞

0 \leqslant |x| > \infty

. Here

C
1

,

C
2

>
0

{C_1},\;{C_2} > 0

are independent of

u
u

and

k
k

.
The variations of Hodge structure of maximal dimension with associated Hodge numbers ℎ^{2,0}>2 and ℎ^{1,1}=2𝑞+1 do not arise from geometry
Authors: Kasparian Azniv
Published: June 2012

The specified variations are proved to be covered by a bounded contractible domain

Ω
\Omega

. After classifying the analytic boundary components of

Ω
\Omega

with respect to a fixed realization, the group of the biholomorphic automorphisms

Aut

Ω

{\text {Aut}}\Omega

and the

Aut

Ω

{\text {Aut}}\Omega

-orbit structure of

Ω
\Omega

are found explicitly. Then

Ω
\Omega

is shown to admit no quasiprojective arithmetic quotients, whereas the lack of geometrically arising variations, covered by

Ω
\Omega

.
A principle of linearized stability for nonlinear evolution equations
Authors: Kato Nobuyuki
Published: June 2012

We present a principle of linearized stability of stationary solutions to nonlinear evolution equation in Banach spaces. The well-known semilinear case is shown to fit into our framework. Applications to nonlinear population dynamics and to functional differential equations are also considered.
On the conditional expectation and convergence properties of random sets
Authors: Papageorgiou Nikolaos S.
Published: June 2012

In this paper we study random sets, with values in a separable Banach space. First we establish several useful properties of the set-valued conditional expectation and then prove some convergence theorems for set-valued amarts and uniform amarts, using the weak, Kuratowski-Mosco and Hausdorff modes of set convergence.
The connection matrix in Morse-Smale flows. II
Authors: Reineck James F.
Published: June 2012

Given a connection matrix for a Morse-Smale flow on a compact manifold, if there are no periodic orbits of equal or adjacent indices related in the partial order, we show that the periodic orbits can be replaced by doubly connected rest points in such a way that the given connection matrix induces the unique connection matrix for the resulting flow. It follows that for this class of flows, all nonuniqueness in the connection matrix is a consequence of the continuation theorem for connection matrices.
On the classification of (𝑛-𝑘+1)-connected embeddings of 𝑛-manifolds into (𝑛+𝑘)-manifolds in the metastable range
Authors: Liu Rong
Published: June 2012

For an

(
n
−
k
+
1
)

(n - k + 1)

-connected map

f
f

from a connected smooth

n
n

-manifold

M
M

to a connected smooth

(
n
+
k
)

(n + k)

-manifold

V
V

, where

M
M

is closed, we work out the isotopy group

[
M
⊂
V

]
f

{[M \subset V]_f}

in the metastable range

n
⩽
2
k
−
4

n \leqslant 2k - 4

. To prove our results, we develop the Hurewicz-type theorems which provide us with the efficient methods of computing the homology groups with local coefficients from the homotopy groups.
Singular Jacobi forms
Authors: Yang Jae-Hyun
Published: June 2012

We introduce the differential operator

M

g
,
h
,

M

{M_{g,h,\mathcal {M}}}

characterizing singular Jacobi forms. We also characterize singular Jacobi forms by the weight of the associated rational representation of the general linear group. And we provide eigenfunctions of the differential operator

M

g
,
h
,

M

{M_{g,h,\mathcal {M}}}

.
Conformal hypersurfaces with the same Gauss map
Authors: Dajczer Marcos , Vergasta E.
Published: June 2012

In this paper we provide a complete classification of all hypersurfaces of Euclidean space which admit conformal deformations, other than the ones obtained through conformal diffeomorphisms of the ambient space, preserving the Gauss map.
An explicit theory of heights
Authors: Flynn E. V.
Published: June 2012

We consider the problem of explicitly determining the naive height constants for Jacobians of hyperelliptic curves. For genus

>
1

> 1

, it is impractical to apply Hilbert’s Nullstellensatz directly to the defining equations of the duplication law; we indicate how this technical difficulty can be overcome by use of isogenies. The height constants are computed in detail for the Jacobian of an arbitrary curve of genus

2
2

, and we apply the technique to compute generators of

J

(

Q

)

\mathcal {J}(\mathbb {Q})

, the Mordell-Weil group for a selection of rank

1
1

examples.
On the decomposition of Langlands subrepresentations for a group in the Harish-Chandra class
Authors: Garnica-Vigil Eugenio
Published: June 2012

When a group

G
G

is in the Harish-Chandra class, the goal of classifying its tempered representations and the goal of decomposing the Langlands subrepresentation for any of its standard representations are equivalent. The main result of this work is given in Theorem (5.3.5) that consists of a formula for decomposing any Langlands subrepresentation for the group

G
G

. The classification of tempered representations is a consequence of this theorem (Corollary (5.3.6)).
Principally polarized ordinary abelian varieties over finite fields
Authors: Howe Everett W.
Published: June 2012

Deligne has shown that there is an equivalence from the category of ordinary abelian varieties over a finite field

k
k

to a category of

Z

{\mathbf {Z}}

-modules with additional structure. We translate several geometric notions, including that of a polarization, into Deligne’s category of

Z

{\mathbf {Z}}

-modules. We use Deligne’s equivalence to characterize the finite group schemes over

k
k

that occur as kernels of polarizations of ordinary abelian varieties in a given isogeny class over

k
k

. Our result shows that every isogeny class of simple odd-dimensional ordinary abelian varieties over a finite field contains a principally polarized variety. We use our result to completely characterize the Weil numbers of the isogeny classes of two-dimensional ordinary abelian varieties over a finite field that do not contain principally polarized varieties. We end by exhibiting the Weil numbers of several isogeny classes of absolutely simple four-dimensional ordinary abelian varieties over a finite field that do not contain principally polarized varieties.
Periodic orbits for the planar Newtonian three-body problem coming from the elliptic restricted three-body problems
Authors: Llibre Jaume , Saari Donald G.
Published: June 2012

Through the introduction of a new coordinate system followed by a Poincaré compactification, a new relationship is developed to connect the planar three-body problem with the various planar restricted three-body systems. This framework is further used to develop new conditions for the continuation of symmetric periodic orbits from elliptic restricted systems to the full planar three-body problem.
Induced 𝐶*-algebras and Landstad duality for twisted coactions
Authors: Quigg John C. , Raeburn Iain
Published: June 2012

Suppose

N
N

is a closed normal subgroup of a locally compact group

G
G

. A coaction

:
A
→
M
(
A
⊗

C
∗

(
N
)
)

:A \to M(A \otimes {C^ * }(N))

of

N
N

on a

C
∗

{C^ * }

-algebra

A
A

can be inflated to a coaction

δ
\delta

of

G
G

on

A
A

, and the crossed product

A

×
δ

G

A{ \times _\delta }G

is then isomorphic to the induced

C
∗

{C^ * }

-algebra

Ind
N
G

A

×
ϵ

N

\text {Ind}_N^G A{\times _\epsilon }N

. We prove this and a natural generalization in which

A

×
ϵ

N

A{ \times _\epsilon }N

is replaced by a twisted crossed product

A

×

G

/

N

G

A{ \times _{G/N}}G

; in case

G
G

is abelian, we recover a theorem of Olesen and Pedersen. We then use this to extend the Landstad duality of the first author to twisted crossed products, and give several applications. In particular, we prove that if
\[

1
→
N
→
G
→
G

/

N
→
1

1 \to N \to G \to G/N \to 1

\]
is topologically trivial, but not necessarily split as a group extension, then every twisted crossed product

A

×

G

/

N

G

A{ \times _{G/N}}G

is isomorphic to a crossed product of the form

A
×
N

A \times N

.
Heegaard splittings of Seifert fibered spaces with boundary
Authors: Schultens Jennifer
Published: June 2012

We give the classification theorem for Heegaard splittings of fiberwise orientable Seifert fibered spaces with nonempty boundary. A thin position argument yields a reducibility result which, by induction, shows that all Heegaard splittings of such manifolds are vertical in the sense of Lustig-Moriah. Algebraic arguments allow a classification of the vertical Heegaard splittings.
The alternative torus and the structure of elliptic quasi-simple Lie algebras of type 𝐴₂
Authors: Berman Stephen , Gao Yun , Krylyuk Yaroslav , Neher Erhard
Published: June 2012

We present the complete classification of the tame irreducible elliptic quasi-simple Lie algebras of type

A
2

{A_2}

, and in particular, specialize on the case where the coordinates are not associative. Here the coordinates are Cayley-Dickson algebras over Laurent polynomial rings in

ν
⩾
3

\nu \geqslant 3

variables, which we call alternative tori. In giving our classification we need to present much information on these alternative tori and the Lie algebras coordinatized by them.
All finite generalized triangle groups
Authors: Lévai L. , Rosenberger G. , Souvignier B.
Published: June 2012

We complete the classification of those generalized triangle groups that are finite.
Smooth sets for a Borel equivalence relation
Authors: Uzcátegui A. Carlos E.
Published: June 2012

We study some properties of smooth Borel sets with respect to a Borel equivalence relation, showing some analogies with the collection of countable sets from a descriptive set theoretic point of view. We found what can be seen as an analog of the hyperarithmetic points in the context of smooth sets. We generalize a theorem of Weiss from

Z

{\mathbf {Z}}

-actions to actions by arbitrary countable groups. We show that the

σ
\sigma

-ideal of closed smooth sets is

Π
1
1

\Pi _1^1

non-Borel.
The spectrum of the Hodge Laplacian for a degenerating family of hyperbolic three manifolds
Authors: Dodziuk Jozef , McGowan Jeffrey
Published: June 2012

We consider a sequence

(

M
n

)

n
=
1

∞

({M_n})_{n = 1}^\infty

of compact hyperbolic manifolds converging to a complete hyperbolic manifold

M
0

{M_0}

with cusps. The Laplace operator acting on the space of

L
2

{L^2}

differential forms on

M
0

{M_0}

has continuous spectrum filling the half-line

[
0
,
∞
)

[0,\infty )

. One expects therefore that the spectra of this operator on

M
n

{M_n}

accumulate to produce the continuous spectrum of the limiting manifold. We prove that this is the case and obtain a sharp estimate of the rate of accumulation.
Branched circle packings and discrete Blaschke products
Authors: Dubejko Tomasz
Published: June 2012

In this paper we introduce the notion of discrete Blaschke products via circle packing. We first establish necessary and sufficient conditions for the existence of finite branched circle packings. Next, discrete Blaschke products are defined as circle packing maps from univalent circle packings that properly fill

D
=
{
z
:

|
z
|

>
1
}

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

to the corresponding branched circle packings that properly cover

D
D

. It is verified that such maps have all geometric properties of their classical counterparts. Finally, we show that any classical finite Blaschke product can be approximated uniformly on compacta of

D
D

by discrete ones.
Transition time analysis in singularly perturbed boundary value problems
Authors: Dumortier Freddy , Smits Bert
Published: June 2012

The paper deals with the boundary value problem

ε

x
¨

+
x

x
˙

−

x
2

=
0

\varepsilon \ddot x + x\dot x - {x^2} = 0

, with

x
(
0
)
=
A
,
x
(
T
)
=
B

x(0) = A,x(T) = B

for

A
,
B
,
T
>
0

A,B,T > 0

and

ε
>
0

\varepsilon > 0

close to zero. It is shown that for

T
T

sufficiently big, the problem has exactly three solutions, two of which reach negative values. Solutions reaching negative values occur for

T
⩾
T
(
ε
)
>
0

T \geqslant T(\varepsilon ) > 0

and we show that asymptotically for

ε
→
0
,

T
(
ε
)
∼
−

ln

(
ε
)

\varepsilon \to 0,\quad T(\varepsilon ) \sim - {\text {ln}}(\varepsilon )

,

i

.e

.

li

m

ε
→
0

−

T
(
ε
)

ln(

ε

)

=
1

{\text {i}}{\text {.e}}{\text {.}}\quad {\text {li}}{{\text {m}}_{\varepsilon \to 0}} - \frac {{T(\varepsilon )}} {{{\text {ln(}}\varepsilon {\text {)}}}} = 1

. The main tools are transit time analysis in the Liénard plane and normal form techniques. As such the methods are rather qualitative and useful in other similar problems.
Curves in Grassmannians
Authors: Perkinson David
Published: June 2012

Curves in Grassmannians are analyzed using the special structure of the tangent bundle of a Grassmannian, resulting in a theory of inflections or Weierstrass behavior. A duality theorem is established, generalizing the classical duality theorem for projective plane curves. The appendices summarize basic information about principal parts bundles and their application to studying the inflections of curves in projective space.
Characterizations of Bergman spaces and Bloch space in the unit ball of 𝐶ⁿ
Authors: Ouyang Cai Heng , Yang Wei Sheng , Zhao Ru Han
Published: June 2012

In this paper we prove that, in the unit ball

B
B

of

C

n

{{\mathbf {C}}^n}

, a holomorphic function

f
f

is in the Bergman space

L
a
p

(
B
)
,

0
>
p
>
∞

L_a^p(B),\;0 > p > \infty

, if and only if
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Underscript upper B Endscripts vertical-bar ModifyingAbove nabla With tilde f left-parenthesis z right-parenthesis StartAbsoluteValue EndAbsoluteValue squared f left-parenthesis z right-parenthesis vertical-bar Superscript p minus 2 Baseline left-parenthesis 1 minus StartAbsoluteValue z EndAbsoluteValue squared right-parenthesis Superscript n plus 1 Baseline d lamda left-parenthesis z right-parenthesis greater-than normal infinity comma">

∫
B

|

∇
~

f
(
z
)

|

2

|

f
(
z
)

|

p
−
2

(
1
−

|

z

|

2

)

n
+
1

d
λ
(
z
)
>
∞
,

\int _B {|\tilde \nabla } f(z){|^2}|f(z){|^{p - 2}}{(1 - |z{|^2})^{n + 1}}d\lambda (z) > \infty ,

\]
where

∇
~

\tilde \nabla

and

λ
\lambda

denote the invariant gradient and invariant measure on

B
B

, respectively. Further, we give some characterizations of Bloch functions in the unit ball

B
B

, including an exponential decay characterization of Bloch functions. We also give the analogous results for

BMOA
⁡
(
∂
B
)

\operatorname {BMOA} (\partial B)

functions in the unit ball.
Global uniqueness for a two-dimensional semilinear elliptic inverse problem
Authors: Isakov Victor , Nachman Adrian I.
Published: June 2012

For a general class of nonlinear Schrödinger equations

−
Δ
u
+
a
(
x
,
u
)
=
0

- \Delta u + a(x,u) = 0

in a bounded planar domain

Ω
\Omega

we show that the function

a
(
x
,
u
)

a(x,u)

can be recovered from knowledge of the corresponding Dirichlet-to-Neumann map on the boundary

∂
Ω

\partial \Omega

.
Coexistence states and global attractivity for some convective diffusive competing species models
Authors: López-Gómez Julián , Sabina de Lis José C.
Published: June 2012

In this paper we analyze the dynamics of a general competing species model with diffusion and convection. Regarding the interaction coefficients between the species as continuation parameters, we obtain an almost complete description of the structure and stability of the continuum of coexistence states. We show that any asymptotically stable coexistence state lies in aglobal curve ofstable coexistence states and that Hopf bifurcations or secondary bifurcations only may occur from unstable coexistence states. We also characterize whether a semitrivial coexistence state or a coexistence state is a global attractor. The techniques developed in this work can be applied to obtain generic properties of general monotone dynamical systems.
Intertwining operators associated to the group 𝑆₃
Authors: Dunkl Charles F.
Published: June 2012

For any finite reflection group

G
G

on an Euclidean space there is a parametrized commutative algebra of differential-difference operators with as many parameters as there are conjugacy classes of reflections in

G
G

. There exists a linear isomorphism on polynomials which intertwines this algebra with the algebra of partial differential operators with constant coefficients, for all but a singular set of parameter values (containing only certain negative rational numbers). This paper constructs an integral transform implementing the intertwining operator for the group

S
3

{S_3}

, the symmetric group on three objects, for parameter value

⩾

1
2

\geqslant \frac {1} {2}

. The transform is realized as an absolutely continuous measure on a compact subset of

M
2

(

R

)

{M_2}({\mathbf {R}})

, which contains the group as a subset of its boundary. The construction of the integral formula involves integration over the unitary group

U
(
3
)

U(3)

.
𝒜-generators for the Dickson algebra
Authors: Hu’ng Nguyễn H. V. , Peterson Franklin P.
Published: June 2012

Let

D
k

{D_k}

denote the Dickson algebra in

k
k

variables over the field of two elements. We study the problem of determining a minimal set of generators for

D
k

{D_k}

as a module over the Steenrod algebra

A

\mathcal {A}

. This is easy for

k
=
1

k = 1

and

2
2

. In this paper we answer this question for

k
=
3

k = 3

and

4
4

and give techniques which may help solve the problem for general

k
k

.
Uniformisations partielles et critères à la Hurewicz dans le plan
Authors: Lecomte Dominique
Published: June 2012

Résumé: On donne des caractérisations des boréliens potentiellement d’une classe de Wadge donnée, parmi les boréliens à coupes verticales dénombrables d’un produit de deux espaces polonais. Pour ce faire, on utilise des résultats d’uniformisation partielle.
Geometrical evolution of developed interfaces
Authors: de Mottoni Piero , Schatzman Michelle
Published: June 2012

Consider the reaction-diffusion equation in
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R Superscript upper N Baseline times double-struck upper R Superscript plus Baseline colon u Subscript t Baseline minus h squared normal upper Delta u plus phi left-parenthesis u right-parenthesis equals 0 semicolon phi">

R

N

×

R

+

:

u
t

−

h
2

Δ
u
+
φ
(
u
)
=
0
;
φ

{\mathbb {R}^N} \times {\mathbb {R}^ + }:{u_t} - {h^2}\Delta u + \varphi (u) = 0;\varphi

is the derivative of a bistable potential with wells of equal depth and

h
h

is a small parameter. If the initial data has an interface, we give an asymptotic expansion of arbitrarily high order and error estimates valid up to time

O
(

h

−
2

)

O({h^{ - 2}})

. At lowest order, the interface evolves normally, with a velocity proportional to the mean curvature. Soit l’équation de réaction-diffusion dans

R

N

×

R

+

,

u
t

−

h
2

Δ
u
+
φ
(
u
)
=
0

{\mathbb {R}^N} \times {\mathbb {R}^ + },\quad {u_t} - {h^2}\Delta u + \varphi (u) = 0

, avec

φ
\varphi

la dérivée d’un potentiel bistable à puits également profonds et

h
h

un petit paramètre. Pour une condition initiale possédant une interface, on donne un développement asymptotique d’ordre arbitrairement élevé, ainsi que des estimations d’erreur valides jusqu’à un temps en

O
(

h

−
2

)

O({h^{ - 2}})

. A l’ordre le plus bas, l’interface évolue normalement, à une vitesse proportionnelle à la courbure moyenne.
Borrowing strength: a likelihood ratio test for related sparse signals
Authors: Wit Ernst C. , Bakewell David J. G.
Published: June 2012

Motivation: Cancer biology is a field where the complexity of the phenomena battles against the availability of data. Often only a few observations per signal source, i.e. genes, are available. Such scenarios are becoming increasingly more relevant as modern sensing technologies generally have no trouble in measuring lots of channels, but where the number of subjects, such as patients or samples, is limited. In statistics, this problem falls under the heading ‘large p, small n’. Moreover, in such situations the use of asymptotic analytical results should generally be mistrusted.

Results: We consider two cancer datasets, with the aim to mine the activity of functional groups of genes. We propose a hierarchical model with two layers in which the individual signals share a common variance component. A likelihood ratio test is defined for the difference between two collections of corresponding signals. The small number of observations requires a careful consideration of the bias of the statistic, which is corrected through an explicit Bartlett correction. The test is validated on Monte Carlo simulations, which show improved detection of differences compared with other methods. In a leukaemia study and a cancerous fibroblast cell line, we find that the method also works better in practice, i.e. it gives a richer picture of the underlying biology.

Availability: The MATLAB code is available from the authors or on http://www.math.rug.nl/stat/Software.

Contact:  e.c.wit@rug.nl  d.bakewell@liv.ac.uk
Expression of the Human NAD(P)-Metabolizing Ectoenzyme CD38 Compromises Systemic Acquired Resistance inArabidopsis
Authors: Zhang Xudong , Mou Zhonglin
Published: June 2012

Plant systemic acquired resistance (SAR) is a long-lasting, broad-spectrum immune response that is mounted after primary pathogen infection. Although SAR has been extensively researched, the molecular mechanisms underlying its activation have not been completely understood. We have previously shown that the electron carrier NAD(P) leaks into the plant extracellular compartment upon pathogen attack and that exogenous NAD(P) activates defense gene expression and disease resistance in local treated leaves, suggesting that extracellular NAD(P) [eNAD(P)] might function as a signal molecule activating plant immune responses. To further establish the function of eNAD(P) in plant immunity, we tested the effect of exogenous NAD(P) on resistance gene-mediated hypersensitive response (HR) and SAR. We found that exogenous NAD(P) completely suppresses HR-mediated cell death but does not affect HR-mediated disease resistance. Local application of exogenous NAD(P) is unable to induce SAR in distal tissues, indicating that eNAD(P) is not a sufficient signal for SAR activation. Using transgenic Arabidopsis plants expressing the human NAD(P)-metabolizing ectoenzyme CD38, we demonstrated that altering eNAD(P) concentration or signaling compromises biological induction of SAR. This result suggests that eNAD(P) may play a critical signaling role in activation of SAR.