bluuebunny/crossref_metadata_2025 huggingface dataset:
Orthocompactness in infinite product spaces
Authors: Kemoto Nobuyuki , Yajima Yukinobu
Published: July 2010

In this paper, we prove the following results for an infinite product space

X
=

∏

α
∈
κ

X
α

X = \prod \nolimits _{\alpha \in \kappa } {{X_\alpha }}

. (1) If a dense subspace of

X
X

is orthocompact, then it is

κ
\kappa

-metacompact. (2) Assume that all finite subproducts of

X
X

are hereditarily orthocompact. If a subspace of

X
X

is

κ
\kappa

-metacompact, then it is orthocompact.
Lifting vector-valued meromorphic functions in infinite dimensions
Authors: Khue Nguyen Van , Nga Nguyen Thu
Published: July 2010

It is shown that the lifting problem for Fréchet-valued meromorphic functions on open subsets of a (DFN)-space has a solution.
A sufficient condition for surfaces in 3-manifolds to have unique prime decompositions
Authors: Motto Michael
Published: July 2010

In 1975, Suzuki proved that prime decompositions of closed, connected surfaces in

S
3

{S^3}

are unique up to ambient isotopy if the surface bounds a

3
3

-manifold whose factors under the prime decomposition all have incompressible boundary. This paper extends this result to surfaces in more general

3
3

-manifolds, when there is a prime decomposition for which every factor of the surface is incompressible on one side.
Optimal programs and their price characterization in a multisector growth model with uncertainty
Authors: Papageorgiou Nikolaos S.
Published: July 2010

In this paper we examine a nonstationary multisector growth model with uncertainty in which future utilities are discounted. First we establish the existence of strongly optimal programs emanating from a given initial capital stock. Then we show that this optimal program

x
^

\hat x

is sustained by a system of prices

p
^

\hat p

so that the pair

[

x
^

,

p
^

]

[\hat x,\hat p]

is competitive and a strong transversality condition holds. We also show that competitiveness and transversality imply optimality.
On the size of finite Sidon sequences
Authors: Chen Sheng
Published: July 2010

Let

h
≥
2

h \geq 2

be an integer. A set of positive integers B is called a

B
h

{B_h}

-sequence, or a Sidon sequence of order h, if all sums

a
1

+

a
2

+
⋯
+

a
h

{a_1} + {a_2} + \cdots + {a_h}

, where

a
i

∈
B
(
i
=
1
,
2
,
…
,
h
)

{a_i} \in B (i = 1,2, \ldots ,h)

, are distinct up to rearrangements of the summands. Let

F
h

(
n
)

{F_h}(n)

be the size of the maximum

B
h

{B_h}

-sequence contained in

{
1
,
2
,
…
,
n
}

\{ 1,2, \ldots ,n\}

. We prove that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F Subscript 2 r minus 1 Baseline left-parenthesis n right-parenthesis less-than-or-equal-to left-parenthesis left-parenthesis r factorial right-parenthesis squared n right-parenthesis Superscript 1 slash left-parenthesis 2 r minus 1 right-parenthesis Baseline plus upper O left-parenthesis n Superscript 1 slash left-parenthesis 4 r minus 2 right-parenthesis Baseline right-parenthesis period">

F

2
r
−
1

(
n
)
≤

(

(
r
!

)
2

n

)

1

/

(
2
r
−
1
)

+
O
(

n

1

/

(
4
r
−
2
)

)
.

{F_{2r - 1}}(n) \leq {({(r!)^2}n)^{1/(2r - 1)}} + O({n^{1/(4r - 2)}}).

\]
Isolated orbits of the adjoint action and area-minimizing cones
Authors: Kerckhove Michael
Published: July 2010

Using a criterion of Lawlor, it is shown that the cone over an isolated orbit of the adjoint action of

SU

(
n
)

{\text {SU}}(n)

on the unit sphere in the vector space of traceless n-by- n Hermitian symmetric matrices is area-minimizing for

n
>
2

n > 2

. Likewise, the cone over an isolated orbit of the adjoint action of

SO

(
n
)

{\text {SO}}(n)

is shown to be area-minimizing for

n
>
3

n > 3

.
An example of a quantum group: the twisted 𝑆𝑝_{𝑞}(2)
Authors: Paolucci A.
Published: July 2010

We investigate the structure of the quantum symplectic group

Sp
⁡
(
2
)

\operatorname {Sp}(2)

and give an explicit form for the fundamental representation. We prove that this group is a deformation of the classical compact group

Sp
⁡
(
2
)

\operatorname {Sp}(2)

by showing that it is equivalent to the Reshetikhin, Takhtajan, Faddeev quantum

Sp
⁡
(
2
)

\operatorname {Sp}(2)

.
𝑖-convexity of manifolds with real projective structures
Authors: Choi Suhyoung
Published: July 2010

We compare the notion of higher-dimensional convexity, as defined by Carrière, for real projective manifolds with the existence of hemispheres. We show that if an i-convex real projective manifold M of dimension n for an integer i with

0
>
i
>
n

0 > i > n

has an i-dimensional hemisphere, then M is projectively homeomorphic to

S

n

/

Γ

{{\mathbf {S}}^n}/\Gamma

where

Γ
\Gamma

is a finite subgroup of

O
(
n
+
1
,

R

)

O(n + 1,{\mathbf {R}})

acting freely on

S

n

{{\mathbf {S}}^n}

.
Ricci curvature and a criterion for simple-connectivity on the sphere
Authors: Chuaqui Martin
Published: July 2010

From the recent work of Osgood and Stowe on the Schwarzian derivative for conformal maps between Riemannian manifolds we derive a sharp sufficient condition for a domain on the sphere to be simply-connected. We show further that a less restrictive form of the condition yields a uniform lower bound for the length of closed geodesics.
Packing measure as a gauge variation
Authors: Edgar G. A.
Published: July 2010

Meinershagen noted that (in the line) the fractal packing measure of Tricot and Taylor can be considered to be a Henstock-Thomson gauge variation ("method III") for an appropriate choice of derivation basis and set function. We show that this point of view remains interesting in a general metric space.
On the number of operations in a clone
Authors: Berman Joel , Kisielewicz Andrzej
Published: July 2010

A clone C on a set A is a set of operations on A containing the projection operations and closed under composition. A combinatorial invariant of a clone is its

p
n

{p_n}

-sequence

⟨

p
0

(
C
)
,

p
1

(
C
)
,
…
⟩

\langle {p_0}(C),{p_1}(C), \ldots \rangle

, where

p
n

(
C
)

{p_n}(C)

is the number of essentially n-ary operations in C. We investigate the links between this invariant and structural properties of clones. It has been conjectured that the

p
n

{p_n}

-sequence of a clone on a finite set is either eventually strictly increasing or is bounded above by a finite constant. We verify this conjecture for a large family of clones. A special role in our work is played by totally symmetric operations and totally symmetric clones. We show that every totally symmetric clone on a finite set has a bounded

p
n

{p_n}

-sequence and that it is decidable if a clone is totally symmetric.
Matrix transformations of power series
Authors: Borwein David , Jakimovski Amnon
Published: July 2010

We consider the sequence of transforms

(

g
n

)

({g_n})

of a power series

∑

n
=
0

∞

a
n

z
n

\sum \nolimits _{n = 0}^\infty {{a_n}{z^n}}

given by

g
n

(
z
)
:=

∑

k
=
0

∞

b

n
k

a
k

z
k

{g_n}(z): = \sum \nolimits _{k = 0}^\infty {{b_{nk}}{a_k}{z^k}}

. We establish necessary and sufficient conditions on the matrix

(

b

n
k

)

({b_{nk}})

for the sequence

(

g
n

)

({g_n})

to converge uniformly on compact subsets of the disk

D
P

:=
{
z
:

|

z

|

>
P
}

{D_P}: = \{ z:|z| > P\}

to a function holomorphic on

D
P

{D_P}

.
Quotient rings of Noetherian module finite rings
Authors: Chatters A. W. , Hajarnavis C. R.
Published: July 2010

Let R be a Noetherian ring which is a finite module over its centre C. We obtain a necessary and sufficient condition for R to have a full quotient ring. We also show that when such a quotient ring does exist, it is obtained by inverting those elements of C which are regular in R.
𝐻^{𝑝} estimates for bi-invariant operators on compact Lie groups
Authors: Fan Da Shan , Xu Zeng Fu
Published: July 2010

The main purpose of this paper is to extend to compact Lie groups a Hörmander multiplier theorem concerning translation invariant operators on Hardy spaces

H
p

,
0
>
p
≤
1

{H^p},0 > p \leq 1

.
Cohomology of nilpotent subalgebras of affine Lie algebras
Authors: Fialowski A.
Published: July 2010

We compute the cohomology of the maximal nilpotent Lie algebra of an affine Lie algebra

g

^

\hat {\mathfrak {g}}

with coefficients in modules of functions on the circle with values in a representation space of

g

\mathfrak {g}

. These modules are not highest weight modules and are somewhat similar to the adjoint representation.
Support theorems for totally geodesic Radon transforms on constant curvature spaces
Authors: Kurusa Árpád
Published: July 2010

We prove a relation between the k-dimensional totally geodesic Radon transforms on the various constant curvature spaces using the geodesic correspondence between the spaces. Then we use this relation to obtain improved support theorems for these transforms.
On the distance of the Riemann-Liouville operator from compact operators
Authors: Opic Bohumír
Published: July 2010

We consider generalized Hardy operators
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T f left-parenthesis x right-parenthesis equals integral Subscript a Superscript x Baseline phi left-parenthesis x comma y right-parenthesis f left-parenthesis y right-parenthesis d y comma x element-of left-parenthesis a comma b right-parenthesis subset-of double-struck upper R comma">

T
f
(
x
)
=

∫
a
x

φ
(
x
,
y
)
f
(
y
)

d
y
,

x
∈
(
a
,
b
)
⊂

R

,

Tf(x) = \int _a^x {\varphi (x,y)f(y)\;dy,\quad x \in (a,b) \subset \mathbb {R},}

\]
acting between two weighted Lebesgue spaces

X
=

L
p

(
a
,
b
;
v
)

X = {L^p}(a,b;v)

and

Y
=

L
q

(
a
,
b
;
w
)
,
1
>
p
≤
q
>
∞

Y = {L^q}(a,b;w), 1 > p \leq q > \infty

, and present lower and upper bounds on the distance of T from the space of all compact linear operators P,

P
:
X
→
Y

P:X \to Y

. The conditions on the kernel

φ
(
x
,
y
)

\varphi (x,y)

are patterned in such a way that the above mentioned class of operators T contains the Riemann-Liouville fractional operators of orders equal to or greater than one.
A characterization of the exponential distribution involving absolute differences of i.i.d. random variables
Authors: Stadje W.
Published: July 2010

A probability measure

μ
\mu

on

[
0
,
∞
)

[0,\infty )

is said to have property H if for independent random variables

X
1

{X_1}

and

X
2

{X_2}

distributed according to

μ
\mu

the absolute difference

|

X
1

−

X
2

|

|{X_1} - {X_2}|

has the same distribution. Continuing previous work of Puri and Rubin we characterize the set of all distributions having property H.
Compact perturbations of Fredholm 𝑛-tuples
Authors: Gelca Răzvan
Published: July 2010

Let T be an operator on a Hilbert space. We show that the pair (T, T) can be perturbed to an invertible pair if and only if T is Fredholm of index zero. We also exhibit a large class of Fredholm n-tuples acting on a Banach space which cannot be perturbed by finite rank operators to invertible ones.
Cesàro means of Fourier transforms and multipliers on 𝐿¹(𝑅)
Authors: Giang Dăng Vũ , Móricz Ferenc
Published: July 2010

We prove that the Cesàro mean

σ
\sigma

of a multiplier

λ
\lambda

on

L
1

(

R

)

{L^1}({\mathbf {R}})

is also a multiplier on

L
1

(

R

)

{L^1}({\mathbf {R}})

. In the particular cases when (i)

λ
\lambda

is odd, we prove that

σ
\sigma

is the Fourier transform of an odd function in the Hardy space

H
1

(

R

)

{H^1}({\mathbf {R}})

, and (ii)

λ
\lambda

is even, we give a necessary and sufficient condition in order that

σ
\sigma

be a Fourier transform of an even function in

L
1

(

R

)

{L^1}({\mathbf {R}})

. As a corollary, we obtain a nontrivial condition for

λ
\lambda

in order to be a multiplier on

L
1

(

R

)

{L^1}({\mathbf {R}})

; namely,
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Subscript 0 Superscript normal infinity Baseline StartAbsoluteValue StartFraction 1 Over t EndFraction integral Subscript 0 Superscript t Baseline left-brace lamda left-parenthesis xi right-parenthesis minus lamda left-parenthesis negative xi right-parenthesis right-brace d xi EndAbsoluteValue StartFraction d t Over t EndFraction greater-than normal infinity period">

∫
0
∞

|

1
t

∫
0
t

{
λ
(
ξ
)
−
λ
(
−
ξ
)
}

d
ξ

|

d
t

t

>
∞
.

\int _0^\infty {\left | {\frac {1}{t}\int _0^t {\{ \lambda (\xi ) - \lambda ( - \xi )\} \,d\xi } } \right |} \frac {{dt}}{t} > \infty .

\]
We also prove Hardy type inequalities for multipliers and Hilbert transforms.
Absolute summability factors of type (𝑋,𝑌)
Authors: Mishra K. N.
Published: July 2010

In Theorem 1 a set of sufficient conditions is investigated for the summability factor of type
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="theta Subscript n Baseline element-of left-parenthesis StartAbsoluteValue upper N overbar comma q EndAbsoluteValue Subscript k Baseline comma StartAbsoluteValue upper N overbar comma p EndAbsoluteValue Subscript k Baseline right-parenthesis comma k greater-than-or-equal-to 1">

θ
n

∈
(

|

N
¯

,
q

|

k

,

|

N
¯

,
p

|

k

)
,
k
≥
1

{\theta _n} \in (|\bar N ,q{|_k},|\bar N ,p{|_k}),k \geq 1

. In the special case when

k
=
1

k = 1

three different sets of necessary and sufficient conditions are established in Theorem 2 for the factor

θ
n

{\theta _n}

. Various known and some new results are also deduced as special cases.
Twist-roll spun knots
Authors: Teragaito Masakazu
Published: July 2010

We study 2-knots obtained from 1-knots by a combination of twist-spinning and roll-spinning and ask whether they are nontrivial. It is proved that, under a certain assumption, the resulting 2-knot is always nontrivial when the 1-knot is not a torus knot, making use of the Cyclic Surgery Theorem.
Real Banach Jordan triples
Authors: Dang Truong C. , Russo Bernard
Published: July 2010

A theory of real Jordan triples and real bounded symmetric domains in finite dimensions was developed by Loos. Upmeier has proposed a definition of a real

J

B
∗

J{B^ \ast }

-triple in arbitrary dimensions. These spaces include real

C
∗

{C^ \ast }

-algebras and

J

B
∗

J{B^\ast }

-triples considered as vector spaces over the reals and have the property that their open unit balls are real bounded symmetric domains. This, together with the observation that many of the more recent techniques in Jordan theory rely on functional analysis and algebra rather than holomorphy, suggests that it may be possible to develop a real theory and to explore its relationship with the complex theory. In this paper we employ a Banach algebraic approach to real Banach Jordan triples. Because of our recent observation on commutative

J

B
∗

J{B^\ast }

-triples (see §2), we can now propose a new definition of a real

J

B
∗

J{B^\ast }

-triple, which we call a

J
∗

B

{J^\ast }B

-triple. Our

J
∗

B

{J^\ast }B

-triples include real

C
∗

{C^\ast }

-algebras and complex

J

B
∗

J{B^\ast }

-triples. Our main theorem is a structure theorem of Gelfand-Naimark type for commutative

J
∗

B

{J^\ast }B

-triples.
Exotic smoothings of hyperbolic manifolds which do not support pinched negative curvature
Authors: Farrell F. T. , Jones L. E.
Published: July 2010

Constructed in this note are examples of topological manifolds M supporting at least two distinct smooth structures

M

1

{\mathcal {M}_1}

and

M

2

{\mathcal {M}_2}

, where

M

1

{\mathcal {M}_1}

is a complete, finite volume, real hyperbolic manifold, while

M

2

{\mathcal {M}_2}

cannot support a complete, finite volume, pinched negatively curved Riemannian metric.
A necessary condition for an elliptic element to belong to a uniform tree lattice
Authors: Liu Ying-Sheng
Published: July 2010

Let

X
X

be a universal cover of a finite connected graph,

G
=
Aut
⁡
(
X
)

G = \operatorname {Aut} (X)

, and

Γ
\Gamma

a group acting discretely and cocompactly on

X
X

, i.e., a uniform lattice on

X
X

. We give a necessary condition for an elliptic element of

G
G

to belong to a uniform lattice or to the commensurability group. By using this condition, we construct some explicit examples.
Some geometric properties of spaces associated with multiple stable integrals
Authors: Szulga Jerzy
Published: July 2010

We investigate properties of vector lattices of multiply integrable functions with respect to a symmetric stable process.
Sums and products of cyclic operators
Authors: Wu Pei Yuan
Published: July 2010

It is proved that every bounded linear operator on a complex separable Hilbert space is the sum of two cyclic operators. For the product, we show that an operator T is the product of finitely many cyclic operators if and only if the kernel of

T
∗

{T^ \ast }

is finite-dimensional. More precisely, if dim ker

T
∗

≤
k
(
2
≤
k
>
∞
)

{T^ \ast } \leq k(2 \leq k > \infty )

, then T is the product of at most

k
+
2

k + 2

cyclic operators. We conjecture that in this case at most k cyclic operators would suffice and verify this for some special classes of operators.
On 4-manifolds with finitely dominated covering spaces
Authors: Hillman Jonathan A.
Published: July 2010

We show that if the universal covering space

M
~

\widetilde {M}

of a closed 4-manifold

M
M

is finitely dominated then either

M
M

is aspherical, or

M
~

\tilde M

is homotopy equivalent to

S
2

{S^2}

or

S
3

{S^3}

, or

π
1

(
M
)

{\pi _1}(M)

is finite. We also give a criterion for a closed 4-manifold to be homotopy equivalent to one which fibres over the circle.
On the homology of complements of arrangements of subspaces and spheres
Authors: Hu Yi
Published: July 2010

We prove that the Goresky-MacPherson combinatorial formula for the homology of the complement of affine subspaces in Euclidean spaceRn{\mathbb {R}^n}holds for much more general "mixed" arrangements of subspaces and spheres.
On smooth and analytic disks in 𝐂² with common boundary
Authors: Kim Kang-Tae
Published: July 2010

We construct explicitly a real analytic embedded real two-dimensional disk in

C

2

{{\mathbf {C}}^2}

totally real except at exactly one elliptic complex tangent point, which shares the common boundary with an analytic disk in the same

C

2

{{\mathbf {C}}^2}

, but does not contain this analytic disk in its envelope of holomorphy. The same proof further yields an explicit example of a holomorphic re-embedding of the standard two-sphere into

C

2

{{\mathbf {C}}^2}

in such a way that the new embedding shows some exceptional properties: It bounds a real three-dimensional Levi flat cell in

C

2

{{\mathbf {C}}^2}

foliated by analytic disks, which is not polynomially convex. In particular, this new embedding of the standard two-sphere cannot be a subset of any compact strongly pseudoconvex surface in

C

2

{{\mathbf {C}}^2}

or a subset of any strongly pseudoconvex graph in

C

2

{{\mathbf {C}}^2}

in the sense of Bedford and Gaveau.
On constructing fields corresponding to the 𝐴̃_{𝑛}’s of Mestre for odd 𝑛
Authors: Swallow John R.
Published: July 2010

An isomorphism is given between the trace bilinear form of Mestre’s

A
n

{A_n}

extensions over

Q

(
t
)

\mathbb {Q}(t)

and a certain quadratic form over

Q

\mathbb {Q}

with base field lifted to

Q

(
t
)

\mathbb {Q}(t)

. This reduces the problem of constructing

A
~

n

{\tilde A_n}

extensions from Mestre’s

A
n

{A_n}

’s to that of diagonalizing certain forms over

Q

\mathbb {Q}

. The result expands a result of Schneps.
Cellular strings on polytopes
Authors: Billera L. J. , Kapranov M. M. , Sturmfels B.
Published: July 2010

The complex of cellular strings with respect to a generic linear functional on a d-dimensional convex polytope has the homotopy type of the

(
d
−
2
)

(d - 2)

-sphere. This result was conjectured in a special case by H.-J. Baues.
One-sided ideals and derivations of prime rings
Authors: Brešar Matej
Published: July 2010

The action of derivations on right ideals of prime rings is considered.
The volume of a hyperbolic 3-manifold with Betti number 2
Authors: Culler Marc , Shalen Peter B.
Published: July 2010

If

M
M

is a closed orientable hyperbolic

3
3

-manifold with first Betti number

2
2

then the volume of

M
M

exceeds

0.34
0.34

.
On quadratic residues and nonresidues in difference sets modulo 𝑚
Authors: Fabrykowski J.
Published: July 2010

Let

m
>
1

m > 1

, and consider a set

A

=
{

a
i

}

\mathcal {A} = \{ {a_i}\}

of residues modulo m such that

a
i

{a_i}

and

a
i

−

a
j

{a_i} - {a_j}

for all i and j with

i
≠
j

i \ne j

are quadratic residues (nonresidues) modulo m. We investigate the estimation of the maximal cardinality of such a set

A

\mathcal {A}

for various moduli m.
Support theorems for Radon transforms on higher rank symmetric spaces
Authors: Gonzalez Fulton , Quinto Eric Todd
Published: July 2010

We prove support theorems for Radon transforms with real-analytic measures on horocycles in higher rank symmetric spaces. The microlocal analysis is more difficult than for rank one, but we prove a generalization of Helgason’s support theorem and a theorem that is new even in the classical case.
An extremal problem for polynomials
Authors: Erëmenko A. , Lempert L.
Published: July 2010

Let

f
(
z
)
=

z
n

+
⋯

f(z) = {z^n} + \cdots

be a polynomial such that the level set

E
=
{
z
:

|

f
(
z
)

|

≤
1
}

E = \{ z:|f(z)| \leq 1\}

is connected. Then
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="max left-brace right-brace colon vertical-bar vertical-bar of ff prime left-parenthesis right-parenthesis z colon element-of element-of zE less-than-or-equal-to 2 Superscript left-parenthesis 1 slash n right-parenthesis minus 1 Baseline n squared">

max
{

|

f
′

(
z
)

|

:
z
∈
E
}
≤

2

(
1

/

n
)
−
1

n
2

\max \{ |f’ (z)|:z \in E\} \leq {2^{(1/n) - 1}}{n^2}

, and this estimate is the best possible.
Schur’s double centralizer theorem for triangular Hopf algebras
Authors: Cohen Miriam , Fischman Davida , Westreich Sara
Published: July 2010

Let (H, R) be a triangular Hopf algebra and let V be a finite-dimensional representation of H. Following Manin we imitate the standard algebraic constructions in order to define the relativized notions of R-universal enveloping algebras of R-Lie algebras and the R-Lie algebra

gl
R

(
V
)

{\text {gl}_R}(V)

. Using Majid’s "bosonization" theorem and the above we prove an R-analogue of Schur’s double centralizer theorem.
On the 𝐾-groups of certain 𝐶*-algebras used in 𝐸-theory
Authors: Nagy Gabriel
Published: July 2010

Let A be a

C

∗

{{\text {C}}^ \ast }

-algebra. We denote by

A
∞

{A_\infty }

the quotient of the

C

∗

{{\text {C}}^ \ast }

-algebra of bounded continuous functions

[
1
,
∞
)
→
A

[1,\infty ) \to A

by the ideal of the functions which vanish at

∞
\infty

. We show that the the canonical map

A
→

A
∞

A \to {A_\infty }

gives an isomorphism between K-groups, provided that A is stable.
The existence of flat covers
Authors: Belshoff Richard , Enochs Edgar E. , Xu Jin Zhong
Published: July 2010

We show that over a right coherent ring all pure injective left modules have flat covers. Then using recent work of Auslander and Buchweitz we show that left modules of finite flat dimension over right coherent rings also have flat covers.
A converse of the volume-mean-value property for invariantly harmonic functions
Authors: Bruna Joaquim , Detraz Jacqueline
Published: July 2010

It is shown that the balls are the only domains having the mean value property with respect to the invariantly harmonic functions in the unit ball of

C

n

{\mathbb {C}^n}

.
Factorization of positive cones of order 𝑛 of von Neumann algebras
Authors: Miura Yasuhide
Published: July 2010

In this paper we shall consider the factorization of positive cones of order

n
n

of a von Neumann algebra. Namely, we shall show the existence of a

∗

{\ast }

-subalgebra inducing the positive cone of order

n
n

of a von Neumann algebra.
Surfaces of constant mean curvature 1 in 𝐻³ and algebraic curves on a quadric
Authors: Small A. J.
Published: July 2010

We show that there exists a natural correspondence between holomorphic curves in

P

SL

(
2
,

C

)

\mathbb {P}{\text {SL}}(2,\mathbb {C})

that are null with respect to the Cartan-Killing metric, and holomorphic curves on

P

1

×

P

1

{\mathbb {P}_1} \times {\mathbb {P}_1}

. This correspondence derives from classical osculation duality between curves in

P

3

{\mathbb {P}_3}

and its dual,

P

3
∗

\mathbb {P}_3^ \ast

. Thus, via Bryant’s correspondence, surfaces of constant mean curvature 1 in the 3-dimensional hyperbolic space of curvature

−
1

- 1

, are studied in terms of complex geometry: in particular, ’Weierstrass representation formulae’ for such surfaces are derived.
A correspondence theorem for modules over Hopf algebras
Authors: Bergen Jeffrey
Published: July 2010

Let H be a finite-dimensional Hopf algebra. We prove that if M is a faithful H-module and if

H
1

≠

H
2

{H_1} \ne {H_2}

are sub-Hopf algebras of H, then

M

H
1

≠

M

H
2

{M^{{H_1}}} \ne {M^{{H_2}}}

, where

M

H
1

{M^{{H_1}}}

and

M

H
2

{M^{{H_2}}}

are the invariants in M under the respective actions of

H
1

{H_1}

and

H
2

{H_2}

. We also show that if

H
1

≠

H
2

{H_1} \ne {H_2}

, then

H
1

{H_1}

and

H
2

{H_2}

have different left integrals. Both of these results rely heavily on the freeness theorem of Nichols-Zoeller.
A general formula for fundamental solutions of linear partial differential equations with constant coefficients
Authors: May Gerhard
Published: July 2010

In this note we present a formula which furnishes particular fundamental solutions of linear partial differential equations with constant coefficients. Our construction extends an explicit formula of König (to appear) after the procedure of Malgrange (1955-1956). The crucial point is that he works with equations rather than with estimations as in the classical proof of the Malgrange-Ehrenpreis theorem. Following his ideas, we obtain fundamental solutions which are regular in the sense of Hörmander (1983); they are of basic importance. Our formula is as explicit as the zeros of a polynomial in one variable are explicit as functions of the coefficients.
Characterizations of bounded sets in spaces of ultradistributions
Authors: Pilipović Stevan
Published: July 2010

We characterize bounded sets in ultradistributions spaces
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper D Subscript upper L Sub Superscript t Subscript Superscript prime left-parenthesis upper M Super Subscript p Superscript right-parenthesis Baseline comma t element-of left-bracket 1 comma normal infinity right-bracket comma upper S Superscript prime left-brace upper M Super Subscript p Superscript right-brace">

D

L
t

′

(

M
p

)

,

t
∈
[
1
,
∞
]
,

S

′

{

M
p

}

\mathcal {D}_{{L^t}}^{’({M_p})},\,t \in [1,\infty ],\,S{’^{\{ {M_p}\} }}

, and

S

′

(

M
p

)

S{’^{({M_p})}}

and bounded sets and convergent sequences in

D

′

(

M
p

)

\mathcal {D}{’^{({M_p})}}

and

D

′

{

M
p

}

\mathcal {D}{’^{\{ {M_p}\} }}

via the convolution by corresponding test functions. The structural theorems for

D

L
t

′

{

M
p

}

\mathcal {D}_{{L^t}}^{’\{ {M_p}\} }

and

D
~

L
t

′

{

M
p

}

,

t
∈
[
1
,
∞
]

\widetilde D_{{L^t}}^{’\{ {M_p}\} },\;t \in [1,\infty ]

, are also given.
On uniqueness sets for areally mean 𝑝-valent functions
Authors: Villamor Enrique
Published: July 2010

We study the sets of uniqueness of areally mean p-valent functions in the unit disc. Namely, if

f
(
z
)

f(z)

is in this class and has the same angular limit in a set E on the boundary of the unit disc, we prove that if p is small compared to the size of E then

f
(
z
)

f(z)

is constant. We then construct an areally mean p-valent function which shows that some condition on the size of the set E must be imposed.
Correspondence theorems for nondegenerate modules and their endomorphism rings
Authors: Zhou Zheng Ping
Published: July 2010

Let

R

U

_RU

be a left R-module whose Morita context is nondegenerate and

S
=

End

(
U
)

S = {\text {End}}(U)

. We show the following: (1) There is a projectivity (that is, an order-preserving bijection) between the complement submodules of

R

U

_RU

and the complement left ideals of S; (2) S is a left CS ring if and only if

R

U

_RU

is a CS module; (3) S is a Baer and left CS ring if and only if

R

U

_RU

is a nonsingular and CS module. Special cases include some earlier works.
Mean value inequalities
Authors: Clarke F. H. , Ledyaev Yu. S.
Published: July 2010

We prove a new type of mean value theorem, one in which the functional differences are estimated in multiple directions simultaneously.
An operator bound related to Feynman-Kac formulae
Authors: Jefferies Brian
Published: July 2010

Those Fourier matrix multiplier operators which are convolutions with respect to a matrix valued measure are characterised in terms of an operator bound. As an application, the finite-dimensional distributions of the process associated with Dirac equation are shown to be unbounded on the algebra of cylinder sets.
On the Jacobian of the Klein curve
Authors: Prapavessi Despina T.
Published: July 2010

Its is known that the Jacobian J of the Klein curve is isogenous to

E

3

{{\mathbf {E}}^3}

for a certain elliptic curve E. We compute explicit equations for E and prove that J is in fact isomorphic to

E

3

{{\mathbf {E}}^3}

. We also identify the subgroup of J generated by the image of the Weierstrass points of the curve under an Albanese embedding, and we show that it is isomorphic to

Z

/

2

Z

×

(

Z

/

7

Z

)
3

{\mathbf {Z}}/2{\mathbf {Z}} \times {({\mathbf {Z}}/7{\mathbf {Z}})^3}

.
Hyperplane sections of linearly normal curves
Authors: Ballico E.
Published: July 2010

A particular case of the results proved here is that a general set of d points in

P

r
−
1

(
k
)

{{\mathbf {P}}^{r - 1}}(k)

is not the hyperplane section of a linearly normal, locally complete intersection curve in

P

r

(
k
)

{{\mathbf {P}}^r}(k)

if

r
≥
6
,
d
≥
max
(
15
,
r
+
3
)

r \geq 6,d \geq \max (15,r + 3)

, and the characteristic of k is zero.
An example concerning the Yosida-Hewitt decomposition of finitely additive measures
Authors: Hensgen Wolfgang
Published: July 2010

Let

λ
\lambda

be Lebesgue measure on the Lebesgue

σ
\sigma

-algebra

L

\mathcal {L}

of

I
:=
]
0
,
1
[

I:=]0,1[

. The author gives an example of a purely finitely additive measure

φ
:

L

→
[
0
,
1
]

\varphi :\mathcal {L} \to [0,1]

vanishing on

λ
\lambda

-null sets such that

∫
f

d
φ
=
∫
f

d
λ

\smallint f\,d\varphi = \smallint f\,d\lambda

for every bounded continuous function f on I

(
f
∈

C
b

(
I
)
)

(f \in {C_b}(I))

. Consequently,

λ
−
φ
∈

L
∞

(
λ

)
′

\lambda - \varphi \in {L^\infty }(\lambda )’

annihilates

C
b

(
I
)

{C_b}(I)

and is not purely finitely additive, contrary to an assertion of Yosida and Hewitt.
On the ramification theory of regular schemes
Authors: Luo Zhao Hua
Published: July 2010

We prove a fundamental theorem on the ramification of morphisms of regular schemes, extending Dedekind’s theorem of different.
A note on the Lickorish-Millett-Turaev formula for the Kauffman polynomial
Authors: Przytycki Józef H.
Published: July 2010

We use the idea of expressing a nonoriented link as a sum of all oriented links corresponding to the link to present a short proof of the Lickorish-Millett-Turaev formula for the Kauffman polynomial at

z
=
−
a
−

a

−
1

z = - a - {a^{ - 1}}

. Our approach explains the observation made by Lickorish and Millett that the formula is the generating function for the linking number of a sublink of the given link with its complementary sublink.
𝐿^{𝑝}-boundedness of the Hilbert transform and maximal function associated to flat plane curves
Authors: Ziesler S.
Published: July 2010

We give a sufficient condition for the Hilbert transform and maximal function associated to a flat plane convex curve

Γ
(
t
)
=
(
t
,
γ
(
t
)
)

\Gamma (t) = (t,\gamma (t))

to be bounded on

L
p

,
1
>
p
>
∞

{L^p},1 > p > \infty

. Our result includes the previously known sufficient conditions, i.e.,

γ
′

\gamma ’

doubling or h, defined by

h
(
t
)
=
t

γ
′

(
t
)
−
γ
(
t
)
,
t
>
0

h(t) = t\gamma ’(t) - \gamma (t),t > 0

, infinitesimally doubling, as special cases.
Crossed products by semigroups of endomorphisms and the Toeplitz algebras of ordered groups
Authors: Adji Sriwulan , Laca Marcelo , Nilsen May , Raeburn Iain
Published: July 2010

Let

Γ
+

{\Gamma ^ + }

be the positive cone in a totally ordered abelian group

Γ
\Gamma

. We construct crossed products by actions of

Γ
+

{\Gamma ^ + }

as endomorphisms of

C
∗

{C^ \ast }

-algebras, and give criteria which ensure a given representation of the crossed product is faithful. We use this to prove that the

C
∗

{C^\ast }

-algebras generated by two semigroups V,

W
:

Γ
+

→
B
(
H
)

W:{\Gamma ^ + } \to B(H)

of nonunitary isometries are canonically isomorphic, thus giving a new, self-contained proof of a theorem of Murphy, which includes earlier results of Coburn and Douglas.
An inverse mapping theorem for set-valued maps
Authors: Dontchev A. L. , Hager W. W.
Published: July 2010

We prove that certain Lipschitz properties of the inverse

F

−
1

{F^{ - 1}}

of a set-valued map F are inherited by the map

(
f
+
F

)

−
1

{(f + F)^{ - 1}}

when f has vanishing strict derivative.
A 𝑞-beta integral on the unit circle and some biorthogonal rational functions
Authors: Al-Salam Waleed A. , Ismail Mourad E. H.
Published: July 2010

In this paper we first consider a pair of polynomial sets which are biorthogonal on the unit circle with respect to a complex weight function. We then show how the biorthogonality of this pair of polynomial sets implies aq-beta integral which in turn leads to a pair of biorthogonal rational functions. Finally we show that the asymptotics for these pairs of rational functions exhibit qualitative properties reminiscent of the Szegö theory for orthogonal polynomials.
Multiplicative subgroups of finite index in a division ring
Authors: Turnwald Gerhard
Published: July 2010

If

G
G

is a subgroup of finite index

n
n

in the multiplicative group of a division ring

F
F

then

G
−
G
=
F

G - G = F

or

|

F

|

>

(
n
−
1

)
4

+
4
n

|F| > {(n - 1)^4} + 4n

. For infinite

F
F

this is derived from the Hales-Jewett theorem. If

|

F

|

>

(
n
−
1

)
2

|F| > {(n - 1)^2}

and

−
1

- 1

is a sum of elements of

G
G

then every element of

F
F

has this property; the bound

(
n
−
1

)
2

{(n - 1)^2}

is optimal for infinitely many

n
n

.
On supportless convex sets in incomplete normed spaces
Authors: Fonf V. P.
Published: July 2010

It is proved that every incomplete separable normed space

M
M

contains a closed bounded convex set

W
W

such that the closed linear span of

W
W

coincides with

M
M

and

W
W

contains no weakly supported points. This theorem answers a question of Klee and a question of Borwein and Tingley.
Locally uniformly continuous functions
Authors: Izzo Alexander J.
Published: July 2010

It is shown that on every infinite-dimensional separable normed space there exist continuous real-valued functions that are nowhere locally uniformly continuous. An explicit example of such a function on

l
p

(
1
≤
p
>
∞
)

{l^p}\;(1 \leq p > \infty )

is given. It is also shown that every continuous real-valued function on a metric space can be approximated uniformly by locally uniformly continuous functions.
A symmetry property of the Fréchet derivative
Authors: Mathias Roy
Published: July 2010

Let

A
A

and

B
B

be

n
×
n

n \times n

matrices. We show that the matrix representing the linear transformation
\[

X
↦

(
A
X
B
+
B
X
A

)
T

X \mapsto {(AXB + BXA)^T}

\]
(which is from the space of

n
×
n

n \times n

matrices to itself) with respect to the usual basis is symmetric and show a similar symmetry property for the Fréchet derivative of a function

f
(
X
)
=

∑

i
=
0

∞

a
i

X
i

f(X) = \sum \nolimits _{i = 0}^\infty {{a_i}{X^i}}

defined on the space of

n
×
n

n \times n

matrices.
An adjoint characterization of the category of sets
Authors: Rosebrugh Robert , Wood R. J.
Published: July 2010

If a category B with Yoneda embedding

Y
:

B

→

C
A
T

(

B

op

,

s
e
t

)

Y:{\mathbf {B}} \to {\mathbf {CAT}}({{\mathbf {B}}^{{\text {op}}}},{\mathbf {set}})

has an adjoint string,

U
⊣
V
⊣
W
⊣
X
⊣
Y

U \dashv V \dashv W \dashv X \dashv Y

, then B is equivalent to set.
Harnack-type inequalities for evolution equations
Authors: Auchmuty Giles , Bao David
Published: July 2010

Here we derive Harnack inequalities for nonnegative solutions of the porous medium equation and the p-diffusion equation. The method applies to functions obeying certain a priori evolution inequalities. The proofs are based on optimizing inequalities for the convective derivative of the function along a path.
On regularity conditions for random fields
Authors: Bradley Richard C.
Published: July 2010

Indexed by the integer lattice of dimension at least two, there exists a nondegenerate strictly stationary random field which is one-dependent with respect to "lattice-halfspaces" but which is also measurable with respect to its own tail sigma-field.
Ideals of operators strictly singular on subspaces
Authors: Meyer Michael J.
Published: July 2010

For each set

Ω
\Omega

of cardinality at most

2
ω

{2^\omega }

, we give an easy construction of Banach spaces X, such that the algebra

B

(
X
)

\mathcal {B}(X)

of all bounded linear operators on X contains a lattice of closed ideals, which is order isomorphic with respect to inclusion to the full power set of

Ω
\Omega

.
On weighted Sobolev interpolation inequalities
Authors: Chua Seng-Kee
Published: July 2010

We obtain some weighted Sobolev interpolation inequalities on

R

n

{\mathbb {R}^n}

and domains satisfying the Boman chain condition for doubling weights satisfying a weighted Poincaré inequality.
Commutators as powers in free products of groups
Authors: Comerford Leo P. , Edmunds Charles C. , Rosenberger Gerhard
Published: July 2010

The ways in which a nontrivial commutator can be a proper power in a free product of groups are identified.
Polynomial rings over Goldie-Kerr commutative rings
Authors: Faith Carl
Published: July 2010

All rings in this paper are commutative, and

acc
⁡
⊥

\operatorname {acc} \bot

(resp.,

acc

⊕

\operatorname {acc} \, \oplus

) denotes the acc on annihilators (resp., on direct sums of ideals). Any subring of an

acc
⁡
⊥

\operatorname {acc} \bot

ring, e.g., of a Noetherian ring, is an

acc
⁡
⊥

\operatorname {acc} \bot

ring. Together,

acc
⁡
⊥

\operatorname {acc} \bot

and

acc

⊕

\operatorname {acc} \, \oplus

constitute the requirement for a ring to be a Goldie ring. Moreover, a ring

R
R

is Goldie iff its classical quotient ring

Q
Q

is Goldie. A ring

R
R

is a Kerr ring (the appellation is for J. Kerr, who in 1990 constructed the first Goldie rings not Kerr) iff the polynomial ring

R
[
x
]

R[x]

has

acc
⁡
⊥

\operatorname {acc} \bot

(in which case

R
R

must have

acc
⁡
⊥

\operatorname {acc} \bot

). By the Hilbert Basis theorem, if

S
S

is a Noetherian ring, then so is

S
[
x
]

S[x]

; hence, any subring

R
R

of a Noetherian ring is Kerr. In this note, using results of Levitzki, Herstein, Small, and the author, we show that any Goldie ring

R
R

such that

Q
=

Q
c

(
R
)

Q = {Q_c}(R)

has nil Jacobson radical (equivalently, the nil radical of

R
R

is an intersection of associated prime ideals) is Kerr in a very strong sense:

Q
Q

is Artinian and, hence, Noetherian (Theorems 1.1 and 2.2). As a corollary we prove that any Goldie ring

A
A

that is algebraic over a field

k
k

is Artinian, and, hence, any order

R
R

in

A
A

is a Kerr ring (Theorem 2.5 and Corollary 2.6). The same is true of any algebra

A
A

over a field

k
k

of cardinality exceeding the dimension of

A
A

(Corollary 2.7). Other Kerr rings are: reduced

acc
⁡
⊥

\operatorname {acc} \bot

rings and valuation rings with

acc
⁡
⊥

\operatorname {acc} \bot

(see 3.3 and 3.4).
Free normal complements and the unit group of integral group rings
Authors: Jespers Eric
Published: July 2010

It is shown that there are only four finite groups G with the property that G has a nonabelian free normal complement in the unit group of the integral group ZG.
Reducible Hilbert scheme of smooth curves with positive Brill-Noether number
Authors: Keem Changho
Published: July 2010

In this paper we demonstrate various reducible examples of the scheme

I

d
,
g
,
r

′

\mathcal {I}{’ _{d,g,r}}

of smooth curves of degee d and genus g in

P

r

{\mathbb {P}^r}

with positive Brill-Noether number. An example of a reducible

I

d
,
g
,
r

′

\mathcal {I}{’ _{d,g,r}}

with positive

ρ
(
d
,
g
,
r
)

\rho (d,g,r)

, namely, the example

I

2
g
−
8
,
g
,
g
−
8

′

,

\mathcal {I}{’ _{2g - 8,g,g - 8}},

, has been known to some people and seems to have first appeared in the literature in Eisenbud and Harris, Irreducibility of some families of linear series with Brill-Noether number

−
1

-1

, Ann. Sci. École Norm. Sup. (4) 22 (1989), 33-53. The purpose of this paper is to add a wider class of examples to the list of such reducible examples by using general k-gonal curves. We also show that

I

d
,
g
,
r

′

\mathcal {I}{’ _{d,g,r}}

is irreducible for the range of

d
≥
2
g
−
7

d \geq 2g - 7

and

g
−
d
+
r
≤
0

g - d + r \leq 0

.
Wandering domains for infinitely renormalizable diffeomorphisms of the disk
Authors: Bonatti Christian , Gambaudo Jean-Marc , Lion Jean-Marie , Tresser Charles
Published: July 2010

Denjoy’s theorem and counter-example for circle maps have counterparts for infinitely renormalizable diffeomorphisms of the 2-disk.
Fixed point theorem for nonexpansive semigroup on Banach space
Authors: Takahashi Wataru , Jeong Doo Hoan
Published: July 2010

Let C be a nonempty closed convex subset of a uniformly convex Banach space, and let S be a semitopological semigroup such that

RUC

(
S
)

{\text {RUC}}(S)

has a left invariant submean. Then we prove a fixed point theorem for a continuous representation of S as nonexpansive mappings on C.
Nonunimodality of graded Gorenstein Artin algebras
Authors: Boij Mats , Laksov Dan
Published: July 2010

We give an explicit expression for the Hilbert function of a large class of graded Gorenstein Artin algebras and give a criterion for this function to be unimodal. As a result we obtain an abundance of graded Gorenstein Artin algebras with nonunimodal Hilbert function.
Purely inseparable extensions of 𝑘[𝑋,𝑌]
Authors: Daigle D.
Published: July 2010

Let k be a field of characteristic

p
>
0

p > 0

and R a polynomial ring in two variables over k. Define weak variable of R to mean an element u of R such that

u
−
λ

u - \lambda

is irreducible for each

λ
∈

k

\lambda \in {\mathbf {k}}

and such that

R

p
n

⊆

k

[
u
,
v
]

{R^{{p^n}}} \subseteq {\mathbf {k}}[u,v]

for some

v
∈
R

v \in R

and some integer

n
≥
0

n \geq 0

. Given a weak variable u of R, consider all

v
∈
R

v \in R

such that

R

p
n

⊆

k

[
u
,
v
]

{R^{{p^n}}} \subseteq {\mathbf {k}}[u,v]

for some n; if one of these v is "absolutely smaller" than u (roughly,

deg
X

v
>

deg
X

u

{\deg _X}v > {\deg _X}u

for all coordinate systems (X, Y) of R), we call it an R-companion of u. The main result gives a connection between the structure of a purely inseparable extension

R
⊃
A

R \supset A

, where A is a polynomial ring in two variables, and whether or not there exists a companion for each u in a suitable set of weak variables of R.
Path properties for 𝑙^{∞}-valued Gaussian processes
Authors: Csörgő Miklós , Lin Zheng Yan , Shao Qi Man
Published: July 2010

We prove moduli of continuity results for

l
∞

{l^\infty }

-valued Gaussian processes in general, as well as for

l
∞

{l^\infty }

-valued Ornstein-Uhlenbeck processes in particular.
Some estimates of Kobayashi metric in the normal direction
Authors: Fu Siqi
Published: July 2010

In this paper, we study the behavior of the Kobayashi metric in the normal direction near a Levi-pseudoconvex boundary point of a smoothly bounded domain without assuming global pseudoconvexity. As a corollary, we obtain a characterization of pseudoconvexity by the rate of the growth of the Kobayashi metric in the normal direction.
Reflection and weakly collectionwise Hausdorff spaces
Authors: LaBerge Tim , Landver Avner
Published: July 2010

We show that

◻

(
θ
)

\square (\theta )

implies that there is a first countable

>
θ

> \theta

-collectionwise Hausdorff space that is not weakly

θ
\theta

-collectionwise Hausdorff. We also show that in the model obtained by Levy collapsing a weakly compact (supercompact) cardinal to

ω
2

{\omega _2}

, first countable

ℵ
1

{\aleph _1}

-collectionwise Hausdorff spaces are weakly

ℵ
2

{\aleph _2}

-collectionwise Hausdorff (weakly collectionwise Hausdorff). In the last section we show that assuming

E
θ
ω

E_\theta ^\omega

, a certain

θ
\theta

-family of integer-valued functions exists and that in the model obtained by Levy collapsing a supercompact cardinal to

ω
2

{\omega _2}

, these families do not exist.
Surfaces minimizing area plus length of singular curves
Authors: Morgan Frank
Published: July 2010

We give the first existence and regularity results on surfaces minimizing area plus length of singular curves, as in energy-minimizing interfaces in materials.
Countable size nonmetrizable spaces which are stratifiable and 𝜅-metrizable
Authors: Sakai Masami
Published: July 2010

K. Tamano asked the following question. Is a stratifiable space metrizable if it is

κ
\kappa

-metrizable? To answer this question, we show that the class of stratifiable

κ
\kappa

-metrizable spaces is much wider than that of metrizable spaces. In fact, we describe two very distinct classes of countable, stratifiable

κ
\kappa

-metrizable spaces which are not metrizable. One of them has no nontrivial convergent sequence. The other is bisequential but not a w-space. In addition, we give a characterization of

κ
\kappa

-metrizability of countable spaces defined by the Cantor tree and note a topological property of monotonically normal

κ
\kappa

-metrizable spaces.
A large Π¹₂ set, absolute for set forcings
Authors: Friedman Sy D.
Published: July 2010

We show how to obtain, by class-forcing over L, a set of reals X which is large in

L
(
X
)

L(X)

and has a

Π
2
1

\Pi _2^1

definition valid in all set-generic extensions of

L
(
X
)

L(X)

. As a consequence we show that it is consistent for the Perfect Set Property to hold for

Σ
2
1

\Sigma _2^1

sets yet fail for some

Π
2
1

\Pi _2^1

set. Also it is consistent for the perfect set property to hold for

Σ
2
1

\Sigma _2^1

sets and for there to be a long

Π
2
1

\Pi _2^1

well-ordering. These applications (necessarily) assume the consistency of an inaccessible cardinal.
Geometric properties, minimax inequalities, and fixed point theorems on convex spaces
Authors: Park Sehie , Bae Jong Sook , Kang Hoo Kyung
Published: July 2010

Using a selection theorem, we obtain a very general Ky Fan type geometric property of convex sets and apply it to the existence of maximizable quasiconcave functions, new minimax inequalities, and fixed point theorems for upper hemicontinuous multifunctions. Our results generalize works of Ha, Fan, Jiang, Himmelberg, and many others.
How long does it take for a gas to fill a porous container?
Authors: Cortázar Carmen , Elgueta Manuel
Published: July 2010

Let us consider the problem

u
t

(
x
,
t
)
=
Δ

u
m

(
x
,
t
)

{u_t}(x,t) = \Delta {u^m}(x,t)

for

(
x
,
t
)
∈
D
×
[
0
,
+
∞
)
,
u
(
x
,
0
)
=

u
0

(
x
)

(x,t) \in D \times [0, + \infty ),u(x,0) = {u_0}(x)

for

x
∈
D

x \in D

, and

(
∂

u
m

/

∂
n
)
(
x
,
t
)
=
h
(
x
,
t
)

(\partial {u^m}/\partial n)(x,t) = h(x,t)

for

(
x
,
t
)
∈
∂
D
×
[
0
,
+
∞
)

(x,t) \in \partial D \times [0, + \infty )

. Here we assume

D
⊂

R
N

,
m
>
1
,

u
0

≥
0

D \subset {R^N},m > 1,{u_0} \geq 0

, and

h
≥
0

h \geq 0

. It is well known that solutions to this problem have the property of finite speed propagation of the perturbations. By this we mean that if z is an interior point of D and exterior to the support of

u
0

{u_0}

, then there exists a time

T
(
z
)
>
0

T(z) > 0

so that

u
(
z
,
t
)
=
0

u(z,t) = 0

for

t
>
T
(
z
)

t > T(z)

and

u
(
z
,
t
)
>
0

u(z,t) > 0

for

t
>
T
(
z
)

t > T(z)

. In this note we give, in an elementary way, an upper bound for

T
(
z
)

T(z)

for the case of bounded convex domains and in the case of a half space.
The compact neighborhood extension property and local equi-connectedness
Authors: Nhu Nguyen To , Sakai Katsuro
Published: July 2010

It is shown that any

σ
\sigma

-compact metrizable space is an AR (ANR) if and only if it is (locally) equi-connected and has the compact (neighborhood) extension property.