bluuebunny/crossref_metadata_2025 huggingface dataset:
Regular polygon solutions of the 𝑁-body problem
Authors: Perko L. M. , Walter E. L.
Published: June 2010

In 1772, Lagrange showed that three masses at the vertices of an equilateral triangle, rotating about their common center of mass with an appropriate angular velocity, describe a periodic solution of the three-body problem. In this paper it is shown that for

N
⩾
4
,
N

N \geqslant 4,N

masses at the vertices of a regular polygon, rotating about their common center of mass with an appropriate angular velocity, describe a periodic solution of the

N
N

-body problem if and only if the masses are equal.
Determinacy with complicated strategies
Authors: Kechris Alexander S.
Published: June 2010

For any class of functions

F

\mathfrak {F}

from

R

{\mathbf {R}}

into

R

,
AD
⁡
(

F

)

{\mathbf {R}},\operatorname {AD}(\mathfrak {F}{\text {)}}

is the assertion that in every two person game on integers one of the two players has a winning strategy in the class

F

\mathfrak {F}

. It is shown, in

Z
F
+
D
C
+
V
=
L
(

R

)

ZF + DC + V = L({\mathbf {R}})

, that for any

F

\mathfrak {F}

of cardinality

>

2

ℵ
0

> {2^{{\aleph _0}}}

(i.e. any

F

\mathfrak {F}

which is a surjective image of

R

{\mathbf {R}}

)

AD
⁡
(

F

)

\operatorname {AD}(\mathfrak {F})

implies AD (the Axiom of Determinacy).
Ergodic actions of the mapping class group
Authors: Masur Howard
Published: June 2010

We prove that the horocyclic flow on the moduli space of a compact Riemann surface is ergodic. We also show that the mapping class group acts ergodically on Thurston’s space of measured foliations.
Spaces with noncoinciding dimensions
Authors: Charalambous M. G.
Published: June 2010

For any given nonnegative integers

l
,
m
,
n

l,m,n

with

max
{
l
,
m
}
⩽
n

\max \{l,m\} \leqslant n

and

n
=
0

n = 0

if

m
=
0

m = 0

, we construct a normal, Hausdorff and separable space

X
X

with

ind
⁡
X
=
l
,
dim
⁡
X
=
m

\operatorname {ind} X = l,\dim X = m

and

ind
⁡
X
=
n

\operatorname {ind} X = n

. We also construct a space

X
n

{X_n}

with

dim
⁡

X
n

=
1

\dim {X_n} = 1

and

ind
⁡

X
n

=
Ind
⁡

X
n

=
n

\operatorname {ind} {X_n} = \operatorname {Ind}{X_n} = n

which is the limit space of an inverse limit sequence of compact, Hausdorff and separable spaces all of whose dimensions are one.
Test modules for projectivity
Authors: Jothilingam P.
Published: June 2010

Let

R
R

be a commutative noetherian local ring with identity. Modules over

R
R

will be assumed to be finitely generated and unitary. A nonzero

R
R

-module

M
M

is said to be a strong test module for projectivity if the condition

Ext
R
1

⁡
(
P
,
M
)
=
(
0
)

\operatorname {Ext}_R^1(P,M) = (0)

, for an arbitrary module

P
P

, implies that

P
P

is projective. This definition is due to Mark Ramras [5]. He proves that a necessary condition for

M
M

to be a strong test module is that depth

M
⩽
1

M \leqslant 1

. This is also easy to see. In this note it is proved that, over a regular local ring, this condition is also sufficient for

M
M

to qualify as a strong test module.
Inequalities relating sectional curvatures of a submanifold to the size of its second fundamental form and applications to pinching theorems for submanifolds
Authors: Howard Ralph , Wei S. Walter
Published: June 2010

The Gauss curvature equation is used to prove inequalities relating the sectional curvatures of a submanifold with the corresponding sectional curvature of the ambient manifold and the size of the second fundamental form. These inequalities are then used to show that if a manifold

M
¯

\overline M

is

δ
\delta

-pinched for some

δ
>

1
4

\delta > \tfrac {1}{4}

, then any submanifold

M
M

of

M
¯

\overline M

that has small enough second fundamental form is

δ
M

{\delta _M}

-pinched for some

δ
M

>

1
4

{\delta _M} > \tfrac {1}{4}

. It then follows from the sphere theorem that the universal covering manifold of

M
M

is a sphere. Some related results are also given.
On successive coefficients of univalent functions
Authors: Hu Ke
Published: June 2010

Let

f
(
z
)
∈
S

f(z) \in S

, that is,

f
(
z
)

f(z)

is analytic and univalent in the unit disk

|
z
|

>
1

\left | z \right | > 1

, normalized by

f
(
0
)
=

f
′

(
0
)
−
1
=
0

f(0) = f’(0) - 1 = 0

. Let

p
p

be real and
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace f left-parenthesis z right-parenthesis slash z right-brace Superscript p Baseline equals 1 plus sigma-summation Underscript n equals 1 Overscript normal infinity Endscripts upper D Subscript n Baseline left-parenthesis p right-parenthesis z Superscript n Baseline period">

{
f
(
z
)

/

z

}
p

=
1
+

∑

n
=
1

∞

D
n

(
p
)

z
n

.

{\{ f(z)/z\} ^p} = 1 + \sum \limits _{n = 1}^\infty {{D_n}(p){z^n}} .

\]
Lucas proved that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue upper D Subscript n Baseline left-parenthesis p right-parenthesis EndAbsoluteValue minus StartAbsoluteValue upper D Subscript n plus 1 Baseline left-parenthesis p right-parenthesis EndAbsoluteValue vertical-bar less-than-or-equal-to upper A n Superscript left-parenthesis t left-parenthesis p right-parenthesis minus 1 right-parenthesis slash 2 Baseline log Superscript 3 slash 2 Baseline n comma n equals 2 comma 3 comma ellipsis comma">

|

D
n

(
p
)

|

−

|

D

n
+
1

(
p
)

|

|

≤
A

n

(
t
(
p
)
−
1
)

/

2

log

3

/

2

n
,

n
=
2
,
3
,
…
,

\left | {{D_n}(p)} \right | - \left | {{D_{n + 1}}(p)} \right |\left | { \leq A{n^{(t(p) - 1)/2}}{{\log }^{3/2}}n,\quad n = 2,3, \ldots ,} \right .

\]
for some absolute constant

A
A

and

t
(
p
)
=

(
2

p

−
1

)
2

t(p) = {(2\sqrt p - 1)^2}

. In this paper we improve

t
(
p
)

t(p)

as follows:
\[

T
(
p
)
=

4
p
−
1

2
p
+
t
(
p
)

t
(
p
)
.

T(p) = \frac {{4p - 1}}{{2p + t(p)}}t(p).

\]
Uniqueness results for groups of measure preserving transformations
Authors: Kallman Robert R.
Published: June 2010

Let

G
G

be the group of measurable, invertible, measure preserving transformations either of the unit inverval or of the line. Then

G
G

has a unique topology in which it is a complete separable metric group.
Hausdorff hypercubes which do not contain arcless continua
Authors: Smith Michel
Published: June 2010

A Hausdorff arc is a compact connected Hausdorff space with exactly two noncut points. The finite product of a Hausdorff arc is called a Hausdorff hypercube. Suppose that

X
X

is a Hausdorff arc which is first countable at none of its points and

n
n

is a positive integer. We show that every nondegenerate subcontinuum of

X
n

{X^n}

contains a Hausdorff arc. Thus

X
n

{X^n}

contains no nondegenerate hereditarily indecomposable continuum.
A further result on extending expansive homeomorphisms
Authors: Wine J. D.
Published: June 2010

In this note we give a necessary and sufficient condition for a selfhomeomorphism defined on an open subset of a compact metric space to be extended to the whole space using the concept of a generator. Two examples of homeomorphic extensions of expansive homeomorphisms are given, one examining the equivalence of the theorem and the other showing that a previous result’s sufficient condition for the extension of expansive homeomorphisms is not necessary.
Nonalgebraic killers of knot groups
Authors: Tsau Chichen M.
Published: June 2010

We show that a knot exists with the property that there exists a killer of the knot group which is not the image of the meridian under any automorphism.
Rational algebraic 𝐾-theory of certain truncated polynomial rings
Authors: Staffeldt R. E.
Published: June 2010

In this paper we derive a formula for rationalized algebraic

K
K

-theory of certain overrings of rings of integers in number fields. Truncated polynomial algebras are examples. Our method is homological calculation which is facilitated by some basic rational homotopy theory and interpreted in terms of the cyclic homology theory of algebras invented by Alain Connes.
Limit theorems for divisor distributions
Authors: Vose Michael D.
Published: June 2010

For a positive integer

N
N

, let

X
N

{X_N}

be a random variable uniformly distributed over the set

{
log
⁡
d
:
d

|

N
}

\{ \log d:d|N\}

. Let

F
N

{F_N}

be the normalized (to have expectation zero and variance one) distribution function for

X
N

{X_N}

. Necessary and sufficient conditions for the convergence of a sequence

F

N
j

{F_{{N_j}}}

of distributions are given. The possible limit distributions are investigated, and the case where the limit distribution is normal is considered in detail.
Construction of a differential equation 𝑦”+𝐴𝑦=0 with solutions having the prescribed zeros
Authors: Shen Li-Chien
Published: June 2010

We show that an entire function

A
(
z
)

A(z)

can be constructed so that the differential equation

y
+
A
y
=
0

y + Ay = 0

has two linearly independent solutions having the prescribed points as their only zeros.
A local kernel property of closed derivations on 𝐶(𝐼×𝐼)
Authors: Nishio Katsuyoshi
Published: June 2010

In this note we show a local behavior of closed derivations on

C

(

[

0
,
1

]

×

[

0
,
1

]

)

C\left ( {\left [ {0,1} \right ] \times \left [ {0,1} \right ]} \right )

, which is essentially different from one-dimensional derivations. Roughly speaking, any closed derivations on

C

(

[

0
,
1

]

×

[

0
,
1

]

)

C\left ( {\left [ {0,1} \right ] \times \left [ {0,1} \right ]} \right )

has a nonconstant kernel locally.
Property (𝐻) in Lebesgue-Bochner function spaces
Authors: Lin Bor-Luh , Lin Pei-Kee
Published: June 2010

We prove that if a Banach space

X
X

has the property (HR) and if

l
1

{l_1}

is not isomorphic to a subspace of

X
X

, then every point on the unit sphere of

X
X

is a denting point of the closed unit ball. We also prove that if

X
X

has the above property, then

L
p

(

μ
,
X

)

{L^p}\left ( {\mu ,X} \right )

,

1
>
p
>
∞

1 > p > \infty

, has the property (H).
Finitely additive supermartingales are differences of martingales and adapted increasing processes
Authors: Armstrong Thomas E.
Published: June 2010

It is shown that any nonnegative bounded supermartingale admits a Doob-Meyer decomposition as a difference of a martingale and an adapted increasing process upon appropriate choice of a reference probability measure which may be only finitely additive.
Enlargements of almost open mappings
Authors: Harte Robin , Mathieu Martin
Published: June 2010

If the enlargement of a bounded linear operator has dense range, then the operator must be almost open.
A finitely additive generalization of Birkhoff’s ergodic theorem
Authors: Ramakrishnan S.
Published: June 2010

A finitely additive generalization of Birkhoff s ergodic theorem is obtained which yields, in particular, strong laws of large numbers in the i.i.d. setting as well as for positive recurrent Markov chains.
𝐹_{𝜎}-set covers of analytic spaces and first class selectors
Authors: Hansell R. W.
Published: June 2010

Let

X
X

be an analytic space (e.g., a complete metric space). We prove that any point-countable

F
σ

{F_\sigma }

-set cover of

X
X

either has

σ
\sigma

-discrete refinement, or else there is a compact subset of

X
X

not covered by any countable subfamily of the cover. It follows that any point-countable

F
σ

{F_\sigma }

-additive family in

X
X

has a

σ
\sigma

-discrete refinement. This is used to show that any weakly

F
σ

{F_\sigma }

-measurable multimap, defined on

X
X

and taking nonempty, closed and separable values in a complete metric space, has a selector of the first Baire class.
Some spectral properties of the perturbed polyharmomic operator
Authors: Eidus Daniel
Published: June 2010

We deal with the polyharmonic operator perturbed by a potential, decreasing at infinity as

|
x
|

−
σ

{\left | x \right |^{ - \sigma }}

. Under some conditions we obtain the absence of eigenvalues in a neighbourhood of the point

z
=
0

z = 0

, the existence of the strong limit and the asymptotic expansion of the corresponding resolvent

R
z

{R_z}

, considered in weighted

L
2

{L^2}

-spaces, as

z
→
0

z \to 0

, where

z
z

is the spectral parameter.
A generalization of slowly varying functions
Authors: Drasin D. , Seneta E.
Published: June 2010

This note establishes that if the main part of the definition of a slowly varying function is relaxed to the requirement that lim

sup

x
→
∞

ψ
(
λ
x
)

/

ψ
(
x
)
>
β
>
∞

{\sup _{x \to \infty }}\psi (\lambda x)/\psi (x) > \beta > \infty

for each

λ
>
0

\lambda > 0

, then

ψ
(
x
)
=
L
(
x
)
θ
(
x
)

\psi (x) = L(x)\theta (x)

, where

L
L

is slowly varying and

θ
\theta

is bounded. This is done by obtaining a representation for the function

ψ
\psi

.
Unimodular matrices in Banach algebra theory
Authors: Corach Gustavo , Larotonda Angel R.
Published: June 2010

Let

A
A

be a ring with 1 and denote by

L
L

(resp.

R
R

) the set of left (resp. right) invertible elements of

A
A

. If

A
A

has an involution *, there is a natural bijection between

L
L

and

R
R

. In general, it seems that there is no such bijection; if

A
A

is a Banach algebra,

L
L

and

R
R

are open subsets of

A
A

, and they have the same cardinality. More generally, we prove that the spaces

U
k

(

A
n

)

{U_k}({A^n})

of

n
×
k

n \times k

-left-invertible matrices and

k

U
(

A
n

)

_kU({A^n})

of

k
×
n

k \times n

-right-invertible matrices are homotopically equivalent. As a corollary, we answer negatively two questions of Rieffel [12].
Sets of 𝑝-powers as irreducible character degrees
Authors: Isaacs I. M.
Published: June 2010

In this paper it is shown that every finite set of powers of the prime

p
p

which contains

p
0

=
1

{p^0} = 1

occurs as the full set of degrees of the irreducible characters of some

p
p

-group.
Frequency entrainment for almost periodic evolution equations
Authors: Murdock James
Published: June 2010

A theorem of Massera stating that periodic solutions of equations are (under a simple hypothesis) entrained is generalized to limit periodic equations and (with a weak definition of entrainment) to almost periodic equations. An error is explained in a stronger result claimed by Cartwright.
An orthonormal basis for 𝐶[0,1] that is not an unconditional basis for 𝐿^{𝑝}[0,1],1<𝑝̸=2
Authors: Zink Robert E.
Published: June 2010

In a recent article, Kazaryan has employed an orthonormal system constructed by Olevskii in order to obtain a negative answer to the following question posed by Ulyanov: Is an orthonormal basis for

C

[

0
,
1

]

C\left [ {0,1} \right ]

necessarily an unconditional basis for each space

L
p

[

0
,
1

]

,
1
>
p
>
∞

{L^p}\left [ {0,1} \right ],1 > p > \infty

? The elements of the Olevskii system, however, are finite linear combinations of Haar functions, and thus, most of them are not continuous on

[

0
,
1

]

\left [ {0,1} \right ]

. For this reason, the example is mildly unsatisfying, since one generally requires the members of a Schauder basis for a given space to belong to that space. In the present work, the author shows that this minute defect can be removed if one modifies the Olevskii system by replacing the Haar functions involved therein with corresponding members of the Franklin system.
On the stability of almost convex functions
Authors: Parnami J. C. , Vasudeva H. L.
Published: June 2010

Let

R

{\mathbf {R}}

denote the set of real numbers and

I
I

an open interval of

R

{\mathbf {R}}

. A function

f
:
I
→
R

f:I \to R

is said to be almost

δ
\delta

-convex iff
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis t x plus left-parenthesis 1 minus t right-parenthesis y right-parenthesis less-than-or-equal-to t f left-parenthesis x right-parenthesis plus left-parenthesis 1 minus t right-parenthesis f left-parenthesis y right-parenthesis plus delta">

f
(
t
x
+
(
1
−
t
)
y
)
≤
t
f
(
x
)
+
(
1
−
t
)
f
(
y
)
+
δ

f(tx + (1 - t)y) \leq tf(x) + (1 - t)f(y) + \delta

holds for all

(
x
,
y
)
∈
I
×
I
∖
N

(x,y) \in I \times I\backslash N

, where

N
⊂
I
×
I

N \subset I \times I

is of measure zero, each

t
∈
[
0
,
1
]

t \in [0,1]

and some

δ
≥
0

\delta \geq 0

. It is proved that such a function is uniformly close to a convex function almost everywhere.
Similarity-invariant continuous functions on ℒ(ℋ)
Authors: Herrero Domingo A.
Published: June 2010

Let

f
:

L

(

H

)
→
X

f:\mathcal {L}(\mathcal {H}) \to X

be a continuous function from the algebra of all bounded linear operators acting on a complex infinite dimensional Hilbert space

H

\mathcal {H}

into a

T
1

{T_1}

-topological space

X
X

. If

f
(
W
A

W

−
1

)
=
f
(
A
)

f(WA{W^{ - 1}}) = f(A)

for all

A
A

in

L

(

H

)

\mathcal {L}(\mathcal {H})

and all invertible

W
W

, then

f
f

is a constant function. The same result is true for a function

f
f

satisfying the above conditions defined on a connected open subset of

L

(

H

)
0

=
{
T
∈

L

(

H

)
:
T

has no normal eigenvalues

\mathcal {L}{(\mathcal {H})_0} = \{ T \in \mathcal {L}(\mathcal {H}):T\,\text {has no normal eigenvalues}

.
Pole- and zero-free regions for analytic continued fractions
Authors: Runckel Hans-J.
Published: June 2010

By using well-known methods of analytic continued fraction theory, various types of zero-free regions are obtained for sequences of polynomials having complex coefficients and being defined by three-term recurrence relations. These results are related to recent investigations by P. Henrici, E. B. Saff and R. S. Varga. As an application, zero-free sectors and stripes in

C

{\mathbf {C}}

are obtained for the Bessel function

J
v

{J_v}

, where

v
v

is complex. Analogous results are obtained for the Lommel polynomials associated with

J
v

{J_v}

.
Pseudofree representations and 2-pseudofree actions on spheres
Authors: Laitinen Erkki , Traczyk Paweł
Published: June 2010

We characterize

1
1

-pseudofree real representations of finite groups. We apply this to show that the representations at fixed points of a

2
2

-pseudofree smooth action of a finite group on a sphere of dimension

⩾
5

\geqslant 5

are topologically equivalent. Moreover with one possible exception, the sphere is

G
G

-homeomorphic to a linear representation sphere.
A remark on the nonuniqueness of tangent cones
Authors: Hutchinson John E. , Meier Michael
Published: June 2010

We give an example of an

n
n

-dimensional varifold

V
V

such that the

n
n

-dimensional density of

V
V

at some point

p
p

equals 1, the

(
n
−
1
)

(n - 1)

density of the first variation at

p
p

equals 0, and

V
V

has nonunique tangent cones at

p
p

. This answers the question implicit in [W. Allard, On the first variation of a varifold, Ann. of Math. (2) 95 (1972), 417-491, §6.5].
Subhomogeneous AF 𝐶*-algebras and their Fubini products. II
Authors: Kye Seung-Hyeok
Published: June 2010

If

C
C

is a nuclear

C
∗

{C^*}

-subalgebra of a

C
∗

{C^*}

-algebra

A
A

, then we have

C
⊗
D
=
(
A
⊗
D
)
∩
(
C
⊗
B
)

C \otimes D = (A \otimes D) \cap (C \otimes B)

for any

C
∗

{C^*}

-algebras

B
B

and

D
D

with

D
⊂
B

D \subset B

. Using this, we show that if

A
A

and

B
B

are AF algebras and

A

⊗
F

B
=
A
⊗
B

A{ \otimes _F}B = A \otimes B

, then either

A
A

or

B
B

must be subhomogeneous.
Most Riesz product measures are 𝐿^{𝑝}-improving
Authors: Ritter David L.
Published: June 2010

A Borel measure

μ
\mu

on a compact abelian group

G
G

is

L
p

{L^p}

-improving if, given

p
>
1

p > 1

, there is a

q
=
q
(
p
,
μ
)
>
p

q = q(p,\mu ) > p

and

a

K
=
K
(
p
,
q
,
μ
)
>
0

{\text {a}}\;K = K(p,q,\mu ) > 0

such that

‖

μ
∗
f

‖

q

≤
K

‖
f
‖

p

{\left \| {\mu * f} \right \|_q} \leq K{\left \| f \right \|_p}

for each

f
f

in

L
p

(
G
)

{L^p}(G)

. Here the

L
p

{L^p}

-improving Riesz product measures on infinite compact abelian groups are characterized by means of their Fourier transforms.
Corps et anneaux de Rolle
Authors: Delon Françoise
Published: June 2010

Brown, Craven and Pelling have proved that if the polynomials over an ordered field

K
K

satisfy Rolle’s theorem, they satisfy it for any ordering on

K
K

. We say that such a field is a Rolle field. We prove that this is a first order property in the language of rings, and that the theory of Rolle fields is decidable. Then we give a common generalisation of these fields and the real closed rings defined by Cherlin and Dickmann: The polynomials over an ordered ring

A
A

satisfy Rolle’s theorem iff

A
A

is the valuation ring of a henselian valued field with Rolle residue field and

m
m

-divisible value group for all odd

m
m

.
The best bound in the 𝐿𝑙𝑜𝑔𝐿 inequality of Hardy and Littlewood and its martingale counterpart
Authors: Gilat David
Published: June 2010

The smallest positive constant

c
c

for which the Hardy and Littlewood [8]

L
log
⁡
L

L\log L

inequality (1)
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M left-parenthesis f right-parenthesis identical-to integral StartFraction d x Over x EndFraction integral Subscript 0 Superscript x Baseline StartAbsoluteValue f EndAbsoluteValue less-than-or-equal-to c left-parenthesis 1 plus integral StartAbsoluteValue f EndAbsoluteValue log Superscript plus Baseline StartAbsoluteValue f EndAbsoluteValue right-parenthesis identical-to c left-parenthesis 1 plus upper L left-parenthesis f right-parenthesis right-parenthesis">

M
(
f
)
≡
∫

d
x

x

∫
0
x

|

f

|

≤
c
(
1
+
∫

|

f

|

log

+

|

f

|

)

≡
c
(
1
+
L
(
f
)
)

M(f) \equiv \int \frac {{dx}}{x}\int _0^x {|f| \leq c(1 + \int |f|{{\log }^ + }|f|)} \quad \equiv c(1 + L(f))

\]
is valid is proved to be the unique positive solution

c
0

{c_0}

of the equation

e

−
c

=

(
c
−
1

)
2

{e^{ - c}} = {(c - 1)^2}

. This settles a question raised by Dubins and Gilat (1978) [6] and, again, more recently, by D. Cox (1984) [3]. Numerically,

c
0

≐
1.478

{c_0} \doteq 1.478

. This should be compared with

c
=
e

(
e
−
1

)

−
1

≐
1.582

c = e{(e - 1)^{ - 1}} \doteq 1.582

, obtained by Doob (1953) [5] in the context of martingale theory and, since then, widely used in the probability literature. Curiously enough, Doob’s coefficient is the best upper bound, but for a slightly different inequality. If only the plus sign is removed from

log
+

⁡

|
f
|

\log ^ + \left | f \right |

in (1), then

c
c

must be at least

e

(
e
−
1

)

−
1

e{(e - 1)^{ - 1}}

for (1), so modified, to be valid. The original inequality (1) is a normalized form of the two-parameter inequality (2)
\[

M
(
f
)
≤
c
L
(
f
)
+
d
,

for all integrable

f
.

M(f) \leq cL(f) + d,\quad {\text {for all integrable}}\quad f.

\]
The set of all ordered pairs

(
c
,
d
)

(c,d)

for which (2) holds is identified as
\[

{
(
c
,
d
)
:
c
>
1
,
d
≥
1
+

e

−
c

/

(
c
−
1
)
}
.

\{ (c,d):c > 1,d \geq 1 + {e^{ - c}}/(c - 1)\} .

\]
Furthermore, for each point on the lower boundary of this set, there is a unique

f
f

(up to null sets) which attains equality in (2).
A theorem on infinite Nielsen extensions
Authors: Halpern Noemi
Published: June 2010

It is shown that every Riemann surface with

n
n

punctures is the infinite Nielsen extension of a surface with

n
n

holes.
Totally real submanifolds with nonnegative sectional curvature
Authors: Ohnita Yoshihiro
Published: June 2010

We prove that an

n
n

-dimensional compact totally real submanifold immersed in an

n
n

-dimensional complex space form with parallel mean curvature vector and nonnegative sectional curvature has parallel second fundamental form. Combining our result and Naitoh’s works we obtain the classification of such submanifolds.
A transfer for compact Lie group actions
Authors: Oliver Robert
Published: June 2010

A short construction of a transfer homomorphism from

H
∗

(
X

/

G
)

{H_ * }(X/G)

to

H
∗

(
X

/

H
)

{H_*}(X/H)

, where

H
⊆
G

H \subseteq G

are compact Lie groups and

X
X

is a

G
G

-CW-complex, is given.
On a connected dense proper subgroup of 𝑅² whose complement is connected
Authors: Maehara Ryuji
Published: June 2010

A simple proof is given to the theorem of F. B. Jones which asserts the existence of such a subgroup of the additive group

R
2

{R^2}

as in the title.
Character values of finite groups as eigenvalues of nonnegative integer matrices
Authors: Chillag David
Published: June 2010

Let

C
1

{C_1}

,

C
2

,
…

{C_2}, \ldots

,

C
k

{C_k}

be the conjugacy classes of the finite group

G
G

and choose

x
i

∈

C
i

{x_i} \in {C_i}

, for

i
=
1

i = 1

,

2
,
…

2, \ldots

,

k
k

. For every complex character

θ
\theta

of

G
G

there is a

k
×
k

k \times k

matrix

M
(
θ
)

M(\theta )

whose entries are nonnegative integers such that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X Superscript negative 1 Baseline upper M left-parenthesis theta right-parenthesis upper X equals diag left-parenthesis theta left-parenthesis x 1 right-parenthesis comma theta left-parenthesis x 2 right-parenthesis comma ellipsis comma theta left-parenthesis x Subscript k Baseline right-parenthesis right-parenthesis">

X

−
1

M
(
θ
)
X
=

diag

(
θ
(

x
1

)
,
θ
(

x
2

)
,
…
,
θ
(

x
k

)
)

{X^{ - 1}}M(\theta )X = {\text {diag}}(\theta ({x_1}),\theta ({x_2}), \ldots ,\theta ({x_k}))

where

X
X

is the character table matrix of

G
G

. Some consequences are shown.
On the singularities of continuous Legendre transforms
Authors: Walter Gilbert G. , Zayed Ahmed I.
Published: June 2010

The analytic properties of continuous Legendre transform

F
(
λ
)

F(\lambda )

of a function

f
(
t
)

f(t)

holomorphic in an elliptical neighborhood of the real interval

[
−
1
,
1
]

[ - 1,1]

are investigated. It is shown to be an entire function of exponential type whose Borel transform

g
(
z
)

g(z)

has a singularity at

z
0

{z_0}

if and only if

f
(
t
)

f(t)

has one at

t
0

{t_0}

where

z
0

=
cosh
⁡

t
0

{z_0} = \cosh {t_0}

. The proof involves a modification of "Hadamard’s argument" on multiplication of singularities. The result may also be interpreted as a statement about the second continuous Legendre transform which gives

f
(
t
)

f(t)

in terms of

F
(
λ
)

F(\lambda )

.
𝑈-embedded subsets of normed linear spaces
Authors: Levy Ronnie , Rice M. D.
Published: June 2010

A subset

S
S

of a metric space

X
X

is

U
U

-embedded in

X
X

if every uniformly continuous function

f
:
S
→
R

f:S \to R

extends to a uniformly continuous function

F
:
X
→
R

F:X \to R

. Thus

U
U

-embedding is the uniform analogue of

C
C

-embedding. The Tietze extension theorem tells us exactly which subsets of metric spaces are

C
C

-embedded. The uniform analogue would tell us exactly which subsets of metric spaces are

U
U

-embedded. In this paper, a characterization of

U
U

-embedded subsets of the Euclidean plane (or any normed linear space) is given.
Whitney levels in 𝐶_{𝑝}(𝑋) are ARs
Authors: Lynch Mark
Published: June 2010

For

X
X

a metric continuum, and

p
∈
X

p \in X

, we show that the Whitney levels in the relative hyperspace

C
p

(
X
)
=
{
K
∈
C
(
X
)

|

p
∈
K
}

{C_p}(X) = \{ K \in C(X)|p \in K\}

are absolute retracts.
A differential equation theoretic interpretation of a geometric result of Hartogs
Authors: Kawai Takahiro
Published: June 2010

A result of Hartogs on the location of singularities of holomorphic functions can be neatly proved by the theory of overdetermined systems of linear differential equations.
Mixing sequences in Hilbert spaces
Authors: Berend Daniel , Bergelson Vitaly
Published: June 2010

A general setup is provided for theorems of the Blum-Hanson type. Notions of strongly and weakly mixing sequences of elements in a Hilbert space are defined, and equivalent characterizations are derived. It turns out that many known generalizations of the Blum-Hanson theorem are special cases of an abstract version which is also suitable for the nonlinear situation.
On comparability in a topos
Authors: Diaconescu Radu
Published: June 2010

While studying the category of "finite" sets associated to a nonstandard model of arithmetic [4], it became apparent that the law of trichotomy plays an important role in that context. The object of this note is to point out the strength of the obvious variants of trichotomy in a general topos. At it turns out even its mildest form (COMP) is quite restrictive, the usual variants (M-COMP, E-COMP) force the topos to be equivalent to a category of sets with AC.
On nilpotency in the Ado-Harish-Chandra theorem on Lie algebra representations
Authors: Block Richard E.
Published: June 2010

Let

L
L

be a finite-dimensional Lie algebra, over an arbitrary field, and regard

L
L

as embedded in its enveloping algebra UL. Theorem. If

K
K

is an ideal of

L
L

and

K
K

is nilpotent of class

q
q

, then for any

r
r

there exists a finite-dimensional representation

ρ
\rho

of

L
L

which vanishes on all products (in UL) of

≥
q
r
+
1

\geq qr + 1

elements of

K
K

and is faithful on the subspace of UL spanned by all products of

≤
r

\leq r

elements of

L
L

. This result sharpens (with respect to nilpotency) the Ado-Iwasawa theorem on the existence of faithful representations and the Harish-Chandra theorem on the existence of representations separating points of UL.
Compact sets of divergence for continuous functions on a Vilenkin group
Authors: Harris David C.
Published: June 2010

Let

G
G

be a Vilenkin group. Let

E
⊂
G

E \subset G

be closed with Haar measure zero. We show there is a continuous function whose Vilenkin-Fourier series diverges at every point in

E
E

.
On infinite-dimensional features of proper and closed mappings
Authors: Sadyrkhanov R. S.
Published: June 2010

We consider some global properties of continuous proper and closed maps acting in infinite-dimensional Fréchet manifolds. These essentially infinite-dimensional features are related to the following questions: 1. When is a closed map proper? 2. When can the "singularity set" of the map, i.e. the subset of the domain of definition where the map is not a local homeomorphism, be deleted? We establish the final answer to the first question and an answer to the second one when the singular set is a countable union of compact sets.
The singular cohomology of the inverse limit of a Postnikov tower is representable
Authors: Dydak Jerzy , Geoghegan Ross
Published: June 2010

Let

X
1

←

X
2

←
⋯

{X_1} \leftarrow {X_2} \leftarrow \cdots

be an inverse sequence of spaces and maps satisfying (i) each

X
n

{X_n}

has the homotopy type of a CW complex, (ii) each

f
n

{f_n}

is a Hurewicz fibration, and (iii) the connectivity of the fiber of

f
n

{f_n}

goes to

∞
\infty

with

n
n

. Let

X
^

\hat X

be the inverse limit of the sequence. It is shown that the natural homomorphism
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove upper H With ˇ Superscript k Baseline left-parenthesis ModifyingAbove upper X With caret comma upper G right-parenthesis right-arrow upper H Superscript k Baseline left-parenthesis ModifyingAbove upper X With caret comma upper G right-parenthesis">

H
ˇ

k

(

X
^

,
G
)
→

H
k

(

X
^

,
G
)

\check {H}^k(\hat {X},G) \to H^k(\hat {X}, G)

(from Čech cohomology to singular cohomology, with ordinary coefficient module

G
G

) is an isomorphism for all

k
k

. It follows that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="limit Underscript right-arrow n Endscripts left-bracket upper X Subscript n Baseline comma upper K left-parenthesis upper G comma k right-parenthesis right-bracket approximately-equals left-bracket ModifyingAbove upper X With caret comma upper K left-parenthesis upper G comma k right-parenthesis right-bracket">

lim

→
n

[

X
n

,
K
(
G
,
k
)
]
≅
[

X
^

,
K
(
G
,
k
)
]

{\lim _{ \to n}}[{X_n},K(G,k)] \cong [\hat X,K(G,k)]

for any Eilenberg- Mac Lane space

K
(
G
,
k
)

K(G,k)

. It is also shown that, except in trivial cases,

X
X

does not have the homotopy type of a CW complex.
Approximate selections and fixed points for upper semicontinuous maps with decomposable values
Authors: Cellina Arrigo , Colombo Giovanni , Fonda Alessandro
Published: June 2010

We prove the existence of continuous approximate selections of upper semicontinuous maps from a separable locally compact metric space

S
S

into the decomposable subsets of

L
1

(
T
,
Z
)

{L^1}(T,Z)

. We then extend a fixed point theorem of Kakutani to upper semicontinuous maps with decomposable values.
Locally compact normal meta-Lindelöf spaces may not be paracompact: an application of uniformization and Suslin lines
Authors: Watson Stephen
Published: June 2010

We show that it is consistent with and independent of the continuum hypothesis (and its negation) that there is a locally compact (perfectly) normal metalindelöf space which is not paracompact. The constructions replace each point in an

ω
\omega

-uniformizable family with a Suslin line.
A remark on singular Calderón-Zygmund theory
Authors: Christ Michael , Stein Elias M.
Published: June 2010

It is shown that in

R

n

{{\mathbf {R}}^n}

the operator
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H f left-parenthesis x right-parenthesis equals p v integral Subscript negative normal infinity Superscript plus normal infinity Baseline f left-parenthesis x 1 minus t comma ellipsis x Subscript n Baseline minus t Superscript n Baseline right-parenthesis t Superscript negative 1 Baseline d t">

H
f

(
x
)

=
p
v

∫

−
∞

+
∞

f

(

x
1

−
t
,
…

x
n

−

t
n

)

t

−
1

d
t

Hf\left ( x \right ) = pv\int _{ - \infty }^{ + \infty } {f\left ( {{x_1} - t, \ldots {x_n} - {t^n}} \right ){t^{ - 1}}dt}

\]
maps

L

(

log
⁡
L

)

L\left ( {\log L} \right )

to weak

L
1

{L^1}

locally. A slight variant of the Calderón-Zygmund procedure provides a new approach to the previously known

L
p

{L^p}

boundedness of

H
,
1
>
p
>
∞

H,1 > p > \infty

. Relatively sharp bounds are obtained as

p
→

1
+

p \to {1^ + }

, and extrapolation produces the result for

L

(

log
⁡
L

)

L\left ( {\log L} \right )

.
Guiding functions and periodic solutions to functional-differential equations
Authors: Fonda Alessandro
Published: June 2010

A new definition of a guiding function for functional differential equations is given, which is sometimes better for applications than the known one by Mawhin. We then prove an existence result for periodic solutions of FDEs related to the new definition.
Perturbations near zero of the leading coefficient of solutions to a nonlinear differential equation
Authors: Komkov Vadim
Published: June 2010

The equation
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartFraction d Over d t EndFraction left-parenthesis a left-parenthesis t right-parenthesis dot psi left-parenthesis x right-parenthesis StartFraction d x Over d t EndFraction right-parenthesis plus f left-parenthesis x right-parenthesis dot StartFraction d x Over d t EndFraction plus c left-parenthesis t right-parenthesis x equals g left-parenthesis t right-parenthesis">

d

d
t

(

a

(
t
)

⋅
ψ

(
x
)

d
x

d
t

)

+
f

(
x
)

⋅

d
x

d
t

+
c

(
t
)

x
=
g

(
t
)

\frac {d}{{dt}}\left ( {a\left ( t \right ) \cdot \psi \left ( x \right )\frac {{dx}}{{dt}}} \right ) + f\left ( x \right ) \cdot \frac {{dx}}{{dt}} + c\left ( t \right )x = g\left ( t \right )

\]
that generalizes the more commonly studied selfadjoint second order equation
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartFraction d Over d t EndFraction left-parenthesis a left-parenthesis t right-parenthesis StartFraction d x Over d t EndFraction right-parenthesis plus c left-parenthesis t right-parenthesis x equals g left-parenthesis t right-parenthesis">

d

d
t

(

a

(
t
)

d
x

d
t

)

+
c

(
t
)

x
=
g

(
t
)

\frac {d}{{dt}}\left ( {a\left ( t \right )\frac {{dx}}{{dt}}} \right ) + c\left ( t \right )x = g\left ( t \right )

\]
occurs in celestial dynamics, in the study of gyroscopic systems, and in other problems of nonlinear mechanics. Using techniques of nonstandard analysis we derive some properties of the "duck"-type cycles for the solutions of this equation.
Invariants for families of Brieskorn varieties
Authors: Lawson Terry
Published: June 2010

Fintushel and Stern have defined invariants for certain homology

3
3

-spheres which, if positive, show that the homology

3
3

-sphere cannot bound a positive definite

4
4

-manifold with no

2
2

-torsion in its first homology. In this note a number-theoretic formula is given for these invariants. It is used to show that all members of certain families of Brieskorn varieties have the same invariants, and hence exhibit the same nonbounding when one of the invariants is positive.
An estimate for the variance of a bounded measurable random variable
Authors: Chawla M. M. , Gopalsamy S.
Published: June 2010

An estimate is provided for the variance of a real-valued essentially bounded measurable random variable in terms of its ess sup and ess inf.
On the Radon-Nikodým property in Jordan triples
Authors: Chu Cho-Ho , Iochum Bruno
Published: June 2010

Given a JBW*-triple

U
U

, we determine when its predual

U
∗

{U_*}

and dual

U
∗

{U^*}

possess the Radon-Nikodým property.
Julia’s lemma and Wolff’s theorem for 𝐽*-algebras
Authors: Włodarczyk Kazimierz
Published: June 2010

Julia’s lemma and Wolff’s theorem are established for (Fréchet-) holomorphic maps of bounded symmetric homogeneous domains in infinite dimensional complex Banach spaces called

J
∗

{J^*}

-algebras.
On a minimax inequality of Ky Fan
Authors: Ha Chung Wei
Published: June 2010

An extension of a minimax inequality of Ky Fan is given. It is then used to generalize to the set-valued setting a fixed point theorem of Ky Fan.
On totally real 3-dimensional submanifolds of the nearly Kaehler 6-sphere
Authors: Dillen F. , Opozda B. , Verstraelen L. , Vrancken L.
Published: June 2010

Let

M
M

be a compact

3
3

-dimensional totally real submanifold of the nearly Kaehler

6
6

-dimensional unit sphere. Let

K
K

be the sectional curvature function of

M
M

. Then, if

K
>
1

/

16

K > 1/16

,

M
M

is a totally geodesic submanifold (and

K
≡
1

K \equiv 1

).
Local cut-points in continuous images of compact ordered spaces
Authors: Maehara Ryuji
Published: June 2010

We prove that if a continuum

X
X

is continuous image of a compact ordered space and if

X
X

is not locally separable at a point

x
x

, then

x
x

lies in the closure of the set of all local cut-points of

X
X

.
The structure of cyclic Lie algebras
Authors: Winter David J.
Published: June 2010

Simple toral rank 1 Lie algebras have been classified in Wilson [8]. This paper is concerned with the structure of a nonsimple toral rank 1 Lie algebra with respect to a specified "toral rank 1" Cartan subalgebra or, equivalently, with the structure of a nonsimple graded Lie algebra where the grading is the cyclic group grading determined by a specific "toral rank 1" Cartan subalgebra. Such graded Lie algebras are called cyclic Lie algebras, to distinguish them from ungraded toral rank 1 Lie algebras and from graded toral rank 1 Lie algebras where the grading is not a cyclic group grading determined by a "toral rank 1" Cartan subalgebra. The structure theorems on cyclic Lie algebras of this paper are established by studying

L
L

in terms of its graded subalgebras and quotient algebras. Their importance is due to the central role which cyclic Lie algebras play in the theory of Lie algebra rootsystems.
On choosing generating sets for ideals
Authors: Nashier Budh
Published: June 2010

For an ideal

I
I

in a ring

R
R

the choice of a generating set with some interesting properties depends on how

I
I

sits inside

R
R

.
Universal vectors for operators on spaces of holomorphic functions
Authors: Gethner Robert M. , Shapiro Joel H.
Published: June 2010

A vector

x
x

in a linear topological space

X
X

is called universal for a linear operator

T
T

on

X
X

if the orbit

{

T
n

x
:
n
≥
0
}

\{ {T^n}x:n \geq 0\}

is dense in

X
X

. Our main result gives conditions on

T
T

and

X
X

which guarantee that

T
T

will have universal vectors. It applies to the operators of differentiation and translation on the space of entire functions, where it makes contact with Pólya’s theory of final sets; and also to backward shifts and related operators on various Hilbert and Banach spaces.
Measurable approximation of a second-order process
Authors: Gill Jelena B.
Published: June 2010

An important problem, having practical as well as theoretical significance, is the problem of determining whether or not a stochastic process has a measurable modification or can be approximated (in the mean square sense) by a second-order process admitting such a modification. It is known [1] that a second-order process has a measurable modification if and only if its covariance function is measurable and its linear space is separable. However, a problem still open is whether sufficient conditions for the existence of a measurable modification can be given in terms of the covariance function only, so that they have a pure analytical form. In this paper we formulate one set of such conditions (Theorem 2, Corollary 2.2) and from that derive a result giving conditions under which a second-order process can be uniformly approximated (in the mean square sense) by a measurable second-order process (Theorem 3).
A criterion for cellularity in a topological 4-manifold
Authors: Repovš Dušan
Published: June 2010

We give a necessary and sufficient condition for a compact set in the interior of a topological

4
4

-manifold to be cellular. This generalizes D. R. McMillan’s cellularity criterion for higher dimensions to dimension four.
A distinguishing example in 𝑘-spaces
Authors: Isbell John
Published: June 2010

Not all locally compact spaces are

k
k

-spaces (that is, in the coreflective hull of the compact Hausdorff spaces).
*-pure subgroups of completely decomposable abelian groups
Authors: Nongxa Loyiso G.
Published: June 2010

In this note we prove that (i) homogeneous

∗
*

-pure subgroups of completely decomposable groups are completely decomposable, (ii)

∗
*

-pure subgroups of finite rank completely decomposable groups are almost completely decomposable. We also characterize those reduced completely decomposable groups

G
G

, with

T
(
G
)

T(G)

satisfying the maximum condition, any

∗
*

-pure subgroup of which is also completely decomposable.
On the dilatation estimates for Beurling-Ahlfors quasiconformal extension
Authors: Tan De Lin
Published: June 2010

Let

μ
(
x
)

\mu (x)

be a

ρ
\rho

-quasisymmetric function. Then the dilatation

K
(
z
)

K(z)

of Beurling-Ahlfors extension with

r
=
1

r = 1

satisfies the inequalitites

K
≤
2
ρ
−
7
(
ρ
−
1
)

/

6
(
ρ
+
1
)

K \leq 2\rho - 7(\rho - 1)/6(\rho + 1)

and

K
>
2
ρ
−
2
+
O
(
1

/

ρ
)

K > 2\rho - 2 + O(1/\rho )

for sufficiently large

ρ
\rho

.
Minimal functions, martingales, and Brownian motion on a noncompact symmetric space
Authors: Taylor J. C.
Published: June 2010

A Brownian motion on

R

n

{{\mathbf {R}}^n}

may be characterized as a process

(

X
t

)

t
⩾
0

{({X_t})_{t \geqslant 0}}

on a probability space

(
Ω
,

F

,
P
)

(\Omega ,\mathfrak {F},P)

such that, for all
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="y element-of bold upper R Superscript d Baseline comma exp left-brace minus left-parenthesis t slash 2 right-parenthesis StartAbsoluteValue EndAbsoluteValue y StartAbsoluteValue EndAbsoluteValue squared plus mathematical left-angle y comma upper X Subscript t Baseline mathematical right-angle right-brace">

y
∈

R

d

,
exp
⁡

{

−
(
t

/

2
)

|

|

y

|

|

2

+

⟨

y
,

X
t

⟩

}

y \in {{\mathbf {R}}^d},\exp \left \{ { - (t/2)||y|{|^2} + \left \langle {y,{X_t}} \right \rangle } \right \}

is a martingale of expectation one. The analogue of this fact is proved for the Brownian motion on a noncompact symmetric space.
Induced universal maps and some hyperspaces with the fixed point property
Authors: Nadler Sam B.
Published: June 2010

For a (metric) continuum

Z
Z

, let

2
Z

{2^Z}

(resp.,

C
(
Z
)

C(Z)

) denote the space of all nonempty compacta (resp., continua) in

Z
Z

with the Hausdorff metric. We prove: (1) If

f
f

is a monotone map of a continuum

X
X

onto a Peano continuum

Y
Y

, then, for any maps

g
:

2
X

→

2
Y

g:{2^X} \to {2^Y}

and

h
:
C
(
X
)
→
C
(
Y
)

h:C(X) \to C(Y)

, there is

A
∈

2
X

A \in {2^X}

and

B
∈
C
(
X
)

B \in C(X)

such that

f
(
A
)
=
g
(
A
)

f(A) = g(A)

and

f
(
B
)
=
h
(
B
)

f(B) = h(B)

. We use (1) to prove: (2) If

X
X

is an inverse limit of dendrites with quasi-monotone bonding maps, then

2
X

{2^X}

and

C
(
X
)

C(X)

have the fixed point property. Thus, we have a proof that for certain indecomposable continua

X
,

2
X

X,{2^X}

has the fixed point property.
Weierstrass weight and degenerations
Authors: Lax R. F.
Published: June 2010

It is shown that as a family of projective smooth curves degenerates to an irreducible Gorenstein curve the Weierstrass weight at a point

P
P

on the limit curve is the sum of the Weierstrass weights at points on the smooth curves converging to

P
P

.
𝐾-theoretic triviality for Rickart 𝐶*-algebras and ℵ₀-continuous regular rings
Authors: Busqué Claudi
Published: June 2010

In this paper we prove that if

R
R

is a purely infinite Rickart

C
∗

{C^*}

-algebra or a purely infinite right

ℵ
0

{\aleph _0}

-continuous regular ring, then

R
R

is an infinite sum ring and hence

K
i

(
R
)
=
0

{K_i}(R) = 0

for all

i
i

.
Regularizing properties of nonlinear semigroups
Authors: Gutman Semion
Published: June 2010

It is known that some classes of

m
m

-accretive operators

A
A

generate Lipschitz continuous semigroups of contractions; that is
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue EndAbsoluteValue upper S left-parenthesis t plus h right-parenthesis x minus upper S left-parenthesis t right-parenthesis x StartAbsoluteValue EndAbsoluteValue less-than-or-slanted-equals upper L left-parenthesis StartAbsoluteValue EndAbsoluteValue x StartAbsoluteValue EndAbsoluteValue right-parenthesis h slash t comma 0 less-than-or-slanted-equals t less-than-or-slanted-equals t plus h less-than-or-slanted-equals upper T comma x element-of ModifyingAbove upper D left-parenthesis upper A right-parenthesis With bar">

|

|

S
(
t
+
h
)
x
−
S
(
t
)
x

|

|

⩽
L
(

|

|

x

|

|

)
h

/

t
,
0
⩽
t
⩽
t
+
h
⩽
T
,
x
∈

D
(
A
)

¯

||S(t + h)x - S(t)x|| \leqslant L(||x||)h/t,0 \leqslant t \leqslant t + h \leqslant T,x \in \overline {D(A)}

. If the underlying Banach spaces

X
X

and

X
∗

{X^*}

are uniformly convex and an

m
m

-accretive operator

B
B

is bounded, we prove, in particular, that the semigroup generated by

A
+
B

A + B

is Hölder continuous. The proof is based on a result on the structure of accretive operators obtained via the Kuratowski-Ryll-Nardzewski Selection Theorem. Also, we consider some applications of these results to the existence of solutions of

u
′

+
A
u
+
B
u
∍
C
u
,
u
(
0
)
=

u
0

u’ + Au + Bu \backepsilon Cu,u(0) = {u_0}

.
Stability and skew-product flows
Authors: Egawa Jirō
Published: June 2010

We consider a skew-product flow with a minimal flow as the basic flow, and we show that, if a bounded solution is positively uniformly stable, then the

ω
\omega

-limit set of it is a minimal set. This is an extension of a result in [2], where it was assumed that the basic flow is equicontinuous.
Reverse Hölder inequalities for spherical harmonics
Authors: Duoandikoetxea Javier
Published: June 2010

We prove that the

L
p

{L^p}

-norm with respect to the normalized Lebesgue measure on the sphere of any spherical harmonic of degree

k
k

is bounded by a constant independent of the dimension times its

L
2

{L^2}

-norm. Several consequences are obtained from this result.
Homoclinic intersections and indecomposability
Authors: Barge Marcy
Published: June 2010

The closure of a one-dimensional unstable manifold of a hyperbolic fixed point of a diffeomorphism having homoclinic points is, under mild assumptions, shown to be an indecomposable continuum. As a result, dynamical systems possessing such behavior cannot be modeled using inverse limits based on any simple space.