bluuebunny/crossref_metadata_2025 huggingface dataset:
Mean exit time from a bumpy sphere
Authors: Pinsky Mark A.
Published: June 2010

We find the solution of

Δ
f
=
−
1

\Delta f = - 1

in a deformation of a sphere in

ℜ
d

{\Re ^d}

.
Attouch-Wets convergence and a differential operator for convex functions
Authors: Beer Gerald , Théra Michel
Published: June 2010

The purpose of this note is to characterize Attouch-Wets convergence for sequences of proper lower semicontinuous convex functions defined on a Banach space X in terms of the behavior of an operator

Δ
\Delta

defined on the space of such functions with values in

X
×
R
×

X
∗

X \times R \times {X^ \ast }

, defined by
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Delta left-parenthesis f right-parenthesis equals StartSet left-parenthesis x comma f left-parenthesis x right-parenthesis comma y right-parenthesis colon left-parenthesis x comma y right-parenthesis element-of partial-differential f EndSet">

Δ
(
f
)
=
{
(
x
,
f
(
x
)
,
y
)
:
(
x
,
y
)
∈
∂
f
}

\Delta (f) = \{ (x,f(x),y):(x,y) \in \partial f\}

. We show that

⟨

f
n

⟩

\langle {f_n}\rangle

is Attouch-Wets convergent to f if and only if points of

Δ
(
f
)

\Delta (f)

lying in a fixed bounded set can be uniformly approximated by points of

Δ
(

f
n

)

\Delta ({f_n})

for large n. The operator

Δ
\Delta

is a natural carrier of the Borwein variational principle, which is a key tool in both directions of our proof.
Remarks on the (𝐶,-1)-summability of the distribution of zeros of orthogonal polynomials
Authors: Nevai Paul , Van Assche Walter
Published: June 2010

Given

x
1

>

x
2

>
⋯
>

x
n

{x_1} > {x_2} > \cdots > {x_n}

and

y
1

>

y
2

>
⋯
>

y

n
−
1

{y_1} > {y_2} > \cdots > {y_{n - 1}}

, two interlacing sequences of real numbers, the rectangular diagram for these numbers is a continuous piecewise linear function with slopes

±
1

\pm 1

and with n local minima at the points

x
i

{x_i}

and

n
−
1

n - 1

local maxima at the points

y
j

{y_j}

. Recently, S. Kerov determined the asymptotic behavior of the rectangular diagrams associated with the zeros of two consecutive orthogonal polynomials for which the coefficients in the three-term recurrence relation converge. The purpose of this note is to show how this result of S. Kerov and even some of its generalizations follow directly from certain

(
C
,
−
1
)

(C, - 1)

-summability results on distribution of zeros of orthogonal polynomials proved by us some time ago.
A comparison between Euler and Cesàro methods of summability
Authors: Kuttner B. , Parameswaran M. R.
Published: June 2010

It is well known that there are sequences that are summable by every Cesàro method

C
r

(
r
>
0
)

{C_r}\;(r > 0)

but are not summable by any Euler method

E
p

(
0
>
p
>
1
)

{E_p}\;(0 > p > 1)

. It is proved here that on the other hand there are sequences that are summable by every Euler method

E
p

(
0
>
p
>
1
)

{E_p}\;(0 > p > 1)

but are not summable by any Cesaro method.
Finite rings in varieties with definable principal congruences
Authors: Simons G. E.
Published: June 2010

A variety

V

\mathcal {V}

of rings has definable principal congruences if there is a first-order formula defining principal two-sided ideals for all rings in

V

\mathcal {V}

. Any variety of commutative rings has definable principal congruences, but many non-commutative rings cannot be in a variety with definable principal congruences. We show that a finite ring in a variety with definable principal congruences is a direct product of finite local rings. This result is used to describe the structure of all finite rings R with

J

(
R

)
2

=
0

J{(R)^2} = 0

in a variety with definable principal congruences.
A characterization of normal extensions for subfactors
Authors: Teruya Tamotsu
Published: June 2010

Let

N
⊂
M
⊂
L

N \subset M \subset L

be a tower of factors. If

L
L

is a crossed product

N

⋊
α

G

N{ \rtimes _\alpha }G

of

N
N

by an outer action

α
\alpha

of a finite group

G
G

on

N
N

then it is well known that there exists a subgroup

H
H

of

G
G

such that

M
=
N

⋊

α

|

H

H

M = N{ \rtimes _{{\alpha _{{|_H}}}}}H

. We prove in this paper that

H
H

is a normal subgroup of

G
G

if and only if there exist a finite group

F
F

and an outer action

β
\beta

of

F
F

on

M
M

such that

L
=
M

⋊
β

F

L = M{ \rtimes _\beta }F

.
Indecomposable modules over Nagata valuation domains
Authors: Arnold D. , Dugas M.
Published: June 2010

For a discrete valuation ring R, let

fr

(
R
)

{\text {fr}}(R)

be the supremum of the ranks of indecomposable finite rank torsion-free R-modules. Then

fr

(
R
)
=
1
,
2
,
3

{\text {fr}}(R) = 1,2,3

, or

∞
\infty

. A complete list of indecomposables is given if

fr

(
R
)
≤
3

{\text {fr}}(R) \leq 3

, in which case R is known to be a Nagata valuation domain.
Universal cell-like maps
Authors: Dydak Jerzy , Mogilski Jerzy
Published: June 2010

The main results of the paper are the following: Theorem. Suppose

n
≤
∞

n \leq \infty

. There is a cell-like map

f
:
X
→
Y

f:X \to Y

of complete and separable metric spaces such that

dim
⁡
X
≤
n

\dim X \leq n

, and for any cell-like map

f
′

:

X
′

→

Y
′

f’ :X’ \to Y’

of (complete) separable metric spaces with

dim
⁡

X
′

≤
n

\dim X’ \leq n

there exist (closed) embeddings

i
:

Y
′

→
Y

i:Y’ \to Y

and

j
:

X
′

→

f

−
1

(
i
(

Y
′

)
)

j:X’ \to {f^{ - 1}}(i(Y’ ))

such that

f
j
=
i

f
′

fj = if’

. Corollary. Suppose

n
>
∞

n > \infty

. There is a complete and separable metric space Y such that

dim

Z

Y
≤
n

{\dim _{\mathbf {Z}}}Y \leq n

, and any (complete) separable metric space

Y
′

Y’

with

dim

Z

Y
′

≤
n

{\dim _{\mathbf {Z}}}Y’ \leq n

embeds as a (closed) subset of Y.
Graph spaces and ⊥-free Boolean algebras
Authors: Heindorf Lutz
Published: June 2010

Let X denote an arbitrary second-countable, compact, zero-dimensional space. Our main result says that X is a graph space, i.e., homeomorphic to the space of all complete subgraphs of a suitable graph. We first characterize graph spaces in terms of the Boolean algebras of their clopen subsets. Then it is proved that each countable Boolean algebra has the corresponding property. As a corollary we obtain that X is homeomorphic to the underlying space of a subalgebra of

⟨

2

;
F

⟩
ω

{\langle {\mathbf {2}};F\rangle ^\omega }

, where 2 is the discrete two-point space and F any set of finitary operations on 2 such that neither the negation nor the ternary sum

x
⊕
y
⊕
z

x \oplus y \oplus z

(addition modulo 2) belongs to the clone generated by F.
Singular perturbations of integrodifferential equations in Banach space
Authors: Liu James H.
Published: June 2010

Let

ε
>
0

\varepsilon > 0

and consider
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row epsilon squared u left-parenthesis t semicolon epsilon right-parenthesis plus u prime left-parenthesis t semicolon epsilon right-parenthesis equals upper A u left-parenthesis t semicolon epsilon right-parenthesis plus integral Subscript 0 Superscript t Baseline upper K left-parenthesis t minus s right-parenthesis upper A u left-parenthesis s semicolon epsilon right-parenthesis d s plus f left-parenthesis t semicolon epsilon right-parenthesis comma t greater-than-or-equal-to 0 comma 2nd Row u left-parenthesis 0 semicolon epsilon right-parenthesis equals u 0 left-parenthesis epsilon right-parenthesis comma u prime left-parenthesis 0 semicolon epsilon right-parenthesis equals u 1 left-parenthesis epsilon right-parenthesis comma EndLayout">

ε
2

u
(
t
;
ε
)
+

u
′

(
t
;
ε
)
=
A
u
(
t
;
ε
)
+

∫
0
t

K
(
t
−
s
)
A
u
(
s
;
ε
)

d
s
+
f
(
t
;
ε
)
,

t
≥
0
,

u
(
0
;
ε
)
=

u
0

(
ε
)
,

u
′

(
0
;
ε
)
=

u
1

(
ε
)
,

\begin {array}{*{20}{c}} {{\varepsilon ^2}u(t;\varepsilon ) + u’ (t;\varepsilon ) = Au(t;\varepsilon ) + \int _0^t {K(t - s)Au(s;\varepsilon )\;ds + f(t;\varepsilon ),\quad t \geq 0,} } \\ {u(0;\varepsilon ) = {u_0}(\varepsilon ),\quad u’ (0;\varepsilon ) = {u_1}(\varepsilon ),} \\ \end {array}

\]
and
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="w prime left-parenthesis t right-parenthesis equals upper A w left-parenthesis t right-parenthesis plus integral Subscript 0 Superscript t Baseline upper K left-parenthesis t minus s right-parenthesis upper A w left-parenthesis s right-parenthesis d s plus f left-parenthesis t right-parenthesis t greater-than-or-equal-to 0 comma w left-parenthesis 0 right-parenthesis equals w 0 comma">

w
′

(
t
)
=
A
w
(
t
)
+

∫
0
t

K
(
t
−
s
)
A
w
(
s
)

d
s
+
f
(
t
)

t
≥
0
,
w
(
0
)
=

w
0

,

w’ (t) = Aw(t) + \int _0^t {K(t - s)Aw(s)\,ds + f(t)\quad t \geq 0,w(0) = {w_0},}

\]
in a Banach space X when

ε
→
0

\varepsilon \to 0

. Here A is the generator of a strongly continuous cosine family and a strongly continuous semigroup, and

K
(
t
)

K(t)

is a bounded linear operator for

t
≥
0

t \geq 0

. With some convergence conditions on initial data and

f
(
t
;
ε
)

f(t;\varepsilon )

and smoothness conditions on

K
(
∙
)

K( \bullet )

, we prove that if

ε
→
0

\varepsilon \to 0

, then

u
(
t
;
ε
)
→
w
(
t
)

u(t;\varepsilon ) \to w(t)

in X uniformly for

t
∈
[
0
,
T
]

t \in [0,T]

for any fixed

T
>
0

T > 0

. We will apply this to an equation in viscoelasticity.
Spaces in which the nondegenerate connected sets are the cofinite sets
Authors: Gruenhage Gary
Published: June 2010

Assuming the continuum hypothesis (CH), we construct a perfectly normal space X such that

Y
⊂
X

Y \subset X

is connected and nondegenerate iff

X
∖
Y

X\backslash Y

is finite. We also show that completely regular, as well as countable Hausdorff, examples of this kind can be obtained under axioms weaker than CH, e.g., Martin’s Axiom.
Projectively flat affine surfaces that are not locally symmetric
Authors: Lee Isaac Chaujun
Published: June 2010

By studying affine rotation surfaces (ARS), we prove that any surface affine congruent to

x
2

+
ϵ

y
2

=

z
r

{x^2} + \epsilon {y^2} = {z^r}

or

y
2

=
z
(
x
+
ϵ
z
log
⁡
z
)

{y^2} = z(x + \epsilon z\log z)

is projectively flat but is neither locally symmetric nor an affine sphere, where

ϵ
\epsilon

is 1 or

−
1
,
r
∈

R

−
{
−
1
,
0
,
1
,
2
}

- 1, r \in {\mathbf {R}} - \{ - 1,0,1,2\}

, and

z
>
0

z > 0

. The significance of these surfaces is due to the fact that until now

x
2

+
ϵ

y
2

=

z

−
1

{x^2} + \epsilon {y^2} = {z^{ - 1}}

are the only known surfaces which are projectively flat but not locally symmetric. Although Podestà recently proved the existence of an affine surface satisfying the above italicized conditions, he did not construct any concrete example.
On compactness and Loeb measures
Authors: Aldaz J. M.
Published: June 2010

The purpose of this note is to show that neither a Loeb measure nor the image of a Loeb measure have to be compact, thus answering in the negative two questions of D. Ross.
The strong law of large numbers: a weak-𝑙₂ view
Authors: Heinkel Bernard
Published: June 2010

Let

(

X
k

)

({X_k})

be a sequence of independent, centered, and square integrable real-valued random variables. To that sequence one associates
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="for-all n element-of double-struck upper N comma xi Subscript n Baseline equals double-vertical-bar left-parenthesis 2 Superscript negative n Baseline upper X Subscript k Baseline right-parenthesis comma 2 Superscript n Baseline plus 1 less-than-or-equal-to k less-than-or-equal-to 2 Superscript n plus 1 Baseline double-vertical-bar Subscript 2 comma normal infinity Baseline period">

∀
n
∈

N

,

ξ
n

=

‖

(

2

−
n

X
k

)
,

2
n

+
1
≤
k
≤

2

n
+
1

‖

2
,
∞

.

\forall n \in \mathbb {N},\quad {\xi _n} = {\left \| {({2^{ - n}}{X_k}),\;{2^n} + 1 \leq k \leq {2^{n + 1}}} \right \|_{2,\infty }}.

\]
When there exists

K
≥
1

K \geq 1

such that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript n greater-than-or-equal-to 1 Endscripts upper P Superscript upper K Baseline left-parenthesis xi Subscript n Baseline greater-than c Subscript n Baseline right-parenthesis greater-than plus normal infinity comma">

∑

n
≥
1

P
K

(

ξ
n

>

c
n

)
>
+
∞
,

\sum \limits _{n \geq 1} {{P^K}({\xi _n} > {c_n}) > + \infty ,}

\]
where

(

c
n

)

({c_n})

is a suitable sequence of positive constants, then the strong law of large numbers holds if and only if

(

X
k

/

k
)

({X_k}/k)

converges almost surely to 0.
Sets in the ranges of sums for perturbations of nonlinear 𝑚-accretive operators in Banach spaces
Authors: Kartsatos Athanassios G.
Published: June 2010

Several results are given involving nonlinear range inclusions of the types

B
+
D
⊂

R
(
T
+
C
)

¯

B + D \subset \overline {R(T + C)}

and

int
⁡
(
B
+
D
)
⊂
R
(
T
+
C
)

\operatorname {int} (B + D) \subset R(T + C)

, where B, D are subsets of a real Banach space X, the operator

T
:
X
⊃
D
(
T
)
→

2
X

T:X \supset D(T) \to {2^X}

is at least m-accretive, and the perturbation

C
:
X
⊃
D
(
C
)
→
X

C:X \supset D(C) \to X

is at least compact, or demicontinuous, or m-accretive. Leray-Schauder degree theory is used in most of the results, and extended versions of recent results of Calvert and Gupta, Morales, Reich, and the author are shown to be possible by using mainly homotopies of compact transformations.
Some projective planes of Lenz-Barlotti class I
Authors: Baldwin John T.
Published: June 2010

We construct an infinite projective plane with Lenz-Barlotti class I. Moreover, the plane is almost strongly minimal in a very strong sense: each automorphism of each line extends uniquely to an automorphism of the plane.
Reflexivity of tensor products of linear transformations
Authors: Li Wing Suet , Strouse Elizabeth
Published: June 2010

Let A and B be linear transformations on finite-dimensional Hilbert space. We characterize the reflexivity of

A
⊗
B

A \otimes B

in terms of certain characteristics of A and B.
Large cardinals and small Dowker spaces
Authors: Good Chris
Published: June 2010

We prove that, if there is a model of set-theory which contains no first countable, locally compact, scattered Dowker spaces, then there is an inner model which contains a measurable cardinal.
Linear tame extension operators from closed subvarieties of 𝐶^{𝑑}
Authors: Aytuna Aydın
Published: June 2010

In this note we show that a linear continuous and tame extension operator from the space of analytic functions on a closed irreducible subvariety V of

C

d

{\mathbb {C}^d}

exists if and only if V is an algebraic variety.
The Casselman-Shalika formula for a distinguished model
Authors: Banks William D.
Published: June 2010

Unramified Whittaker functions and their analogues occur naturally in number theory as terms in the Fourier expansions of automorphic forms. Precise information about these functions is useful in many aspects of study, such as in the construction of L-functions. In this paper, the method of Casselman and Shalika is used to derive explicit values for the analogue of the unramified Whittaker function in a distinguished model that arises in connection with quadratic base change.
Cycles in 𝐶^{𝑟}-twists
Authors: Carroll C. R.
Published: June 2010

Let

f
t

,
0
≤
t
≤
1

{f_t},0 \leq t \leq 1

, be a continuous one-parameter family of

C
r

{C^r}

diffeomorphisms of the circle obtained by monotonically twisting away from

f
0

{f_0}

. It is well known that for a dense set of parameter values

t
,

f
t

{t, f_t}

has a periodic orbit. To what extent does the distribution in the circle of these periodic orbits reflect the degree of differentiability r? We show that if
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="r greater-than-or-equal-to 6 comma sup Underscript t Endscripts double-vertical-bar f Subscript t Baseline ring f 0 Superscript negative 1 Baseline double-vertical-bar Subscript upper C Sub Superscript r Subscript Baseline greater-than normal infinity">

r
≥
6
,

sup
t

‖

f
t

∘

f
0

−
1

‖

C
r

>
∞

r \geq 6,{\sup _t}{\left \| {{f_t} \circ f_0^{ - 1}} \right \|_{{C^r}}} > \infty

, and the rotation number of

f
0

{f_0}

is an irrational

α
\alpha

with bounded continued fraction expansion, then periodic orbits corresponding to small values of the parameter t echo the metric structure of

f
0

{f_0}

in the following sense: If the rotation number of the orbit is a convergent of

α
\alpha

, then the orbit divides the circle into intervals of nearly equal

μ
\mu

-measure, where

μ
\mu

is the invariant Borel probability measure of

f
0

{f_0}

. The corresponding result for low differentiability is false.
Holomorphic germs on Tsirelson’s space
Authors: Mujica Jorge , Valdivia Manuel
Published: June 2010

We show that if K is an arbitrary compact subset of the Banach space constructed by Tsirelson, then the space

H

(
K
)

\mathcal {H}(K)

of all holomorphic germs on K, with its natural inductive limit topology, is totally reflexive.
Conditions for a module to be injective and some applications to Hopf algebra duality
Authors: Musson Ian M.
Published: June 2010

We present some simple conditions for a module to be injective in certain situations. Injective modules over bialgebras often have the additional structure of module algebras, and our results can be used to give some explicit examples. In particular, we construct such a module algebra for the quantum group

O
q

(

SL

(
2
)
)

{O_q}({\text {SL}}(2))

. Our results can also be used to describe the Hopf algebra duals of

O
q

(

SL

(
2
)
)

{O_q}({\text {SL}}(2))

and related Hopf algebras.
Application of the operator phase shift in the 𝐿-problem of moments
Authors: Lemnete Luminiţa
Published: June 2010

This note studies more deeply the results obtained in an earlier paper of the author (An operator-valued moment problem, Proc. Amer. Math. Soc. 112 (1991)). It gives a similar condition for the solvability of the L-problem of moments, using the operator phase shift. Based on this, it underlines some of the aspects of the operator phase shift used in the L-problem of moments.
A note on Hermitian operators on function spaces
Authors: Koide Toshiko
Published: June 2010

In this note we shall get concrete expressions of hermitian operators on a closed subspace of

C
(
Ω
)

C(\Omega )

which contains constant functions and separates points of

Ω
\Omega

.
Tempered Boehmians and ultradistributions
Authors: Mikusiński Piotr
Published: June 2010

An extension of the Fourier transform which is a one-to-one continuous mapping from the space of tempered Boehmians onto the space of Schwartz distributions is introduced. This shows that the space of tempered Boehmians can be identified with the space

Z

′

\mathcal {Z}’

of ultradistributions.
A class of Riesz-Fischer sequences
Authors: Reid Russell M.
Published: June 2010

It is proved that if

{

λ
n

}

\{ {\lambda _n}\}

is a sequence of real numbers whose differences are nondecreasing and satisfy

∑

(

λ

k
+
1

−

λ
k

)

−
2

>
∞

\sum {{{({\lambda _{k + 1}} - {\lambda _k})}^{ - 2}} > \infty }

, then the set of complex exponentials

{

e

i

λ
n

x

}

\{ {e^{i{\lambda _n}x}}\}

is a Riesz-Fischer sequence in

L
2

[
−
A
,
A
]

{L_2}[ - A,A]

for every

A
>
0

A > 0

, which is to say that for any positive A, the equations

∫

−
A

A

f
(
x
)

e

i

λ
n

x

d
x
=

c
n

\smallint _{ - A}^Af(x){e^{i{\lambda _n}x}}dx = {c_n}

admit a solution f in

L
2

[
−
A
,
A
]

{L_2}[ - A,A]

for every sequence

{

c
n

}

\{ {c_n}\}

in

ℓ
2

{\ell _2}

. In particular, if

λ
n

=

n
p

{\lambda _n} = {n^p}

, then

{

e

i

λ
n

x

}

\{ {e^{i{\lambda _n}x}}\}

is a Riesz-Fischer sequence when

p
>

1
2

p > \frac {1}{2}

.
Dold manifolds with (𝑍₂)^{𝑘}-action
Authors: Shaker R. J.
Published: June 2010

Actions on Dold manifolds

P
(
m
,

2
k

)

P(m,{2^k})

are constructed to determine the ideals

I

∗
,
k

2
k

\mathcal {I}_{ \ast ,k}^{{2^k}}

of cobordism classes in

N

∗

{\mathcal {N}_ \ast }

containing a representative admitting a

(

Z

2

)
k

{({{\mathbf {Z}}_2})^k}

-action with fixed point set of codimension

2
k

{2^k}

.
Stochastic continuity of random derivations on 𝐻*-algebras
Authors: Villena A. R.
Published: June 2010

In this paper we obtain the continuity of stochastically derivative linear random operators on (nonassociative)

H
∗

{H^ \ast }

-algebras with zero annihilator. Moreover, we investigate the stochastic size of the separating subspace for linear random operators, on

H
∗

{H^ \ast }

-algebras, which have some probability of being derivative.
Banach algebras in which every element is a topological zero divisor
Authors: Bhatt S. J. , Dedania H. V.
Published: June 2010

Every element of a complex Banach algebra

(
A
,

‖
⋅
‖

)

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

is a topological divisor of zero, if at least one of the following holds: (i) A is infinite dimensional and admits an orthogonal basis, (ii) A is a nonunital uniform Banach algebra in which the Silov boundary

∂
A

\partial A

coincides with the Gelfand space

Δ
(
A
)

\Delta (A)

; and (iii) A is a nonunital hermitian Banach

∗
\ast

-algebra with continuous involution. Several algebras of analysis have this property. Examples are discussed to show that (a) neither hermiticity nor

∂
A
=
Δ
(
A
)

\partial A = \Delta (A)

can be omitted, and that (b) in case (ii),

∂
A
=
Δ
(
A
)

\partial A = \Delta (A)

is not a necessary condition.
Functions of conditionally negative type on Kazhdan groups
Authors: Deutsch Annabel , Robertson A. Guyan
Published: June 2010

An explicit bound is given for functions of conditionally negative type on Kazhdan groups, in terms of a set of generators and the corresponding Kazhdan constants. This is used to estimate how far a set in an infinite measure space can be translated by the action of a Kazhdan group. Some estimates are given for Kazhdan constants.
Numerical radius preserving operators on 𝐵(𝐻)
Authors: Chan Jor-Ting
Published: June 2010

Let H be a Hilbert space over

C

\mathbb {C}

and let

B
(
H
)

B(H)

denote the vector space of all bounded linear operators on H. We prove that a linear isomorphism

T
:
B
(
H
)
→
B
(
H
)

T:B(H) \to B(H)

is numerical radius-preserving if and only if it is a multiply of a

C
∗

{C^ \ast }

-isomorphism by a scalar of modulus one.
Castelnuovo regularity and graded rings associated to an ideal
Authors: Johnston Bernard , Katz Daniel
Published: June 2010

We compare the Castelnuovo regularity defined with respect to different homogeneous ideals in a graded ring and use the result we obtain to prove a generalized Goto-Shimoda theorem for ideals of positive height in a Cohen-Macaulay local ring.
The weak convergence of unit vectors to zero in the Hilbert space is the convergence of one-dimensional subspaces in the order topology
Authors: Palko Vladimír
Published: June 2010

In this paper we deal with the (o)-convergence and the order topology in the hilbertian logic

L

(
H
)

\mathcal {L}(H)

of closed subspaces of a separable Hilbert space H. We compare the order topology on

L

(
H
)

\mathcal {L}(H)

with some other topologies. The main result is a theorem which asserts that the weak convergence of a sequence of unit vectors to zero in H is equivalent to the convergence of the sequence of one-dimensional subspaces generated by these vectors to the zero subspace in the order topology on

L

(
H
)

\mathcal {L}(H)

.
Isomorphisms between groups of diffeomorphisms
Authors: Rybicki Tomasz
Published: June 2010

It is known that the group of all diffeomorphisms of a manifold determines uniquely the topological and smooth structure of the manifold itself. We specify a possibly large class of diffeomorphism groups which satisfy this property. In particular, so does the group of contact diffeomorphisms.
On the solutions of the equation 𝑥^{𝑚}+𝑦^{𝑚}-𝑧^{𝑚}=1 in a finite field
Authors: Ke Wen Fong , Kiechle Hubert
Published: June 2010

An explicit formula for the number of solutions of the equation in the title is given when a certain condition, depending only onmand the characteristic of the field, holds.
On the covering and the additivity number of the real line
Authors: Keremedis Kyriakos
Published: June 2010

We show that the real line R cannot be covered by k many nowhere dense sets iff whenever

D
=
{

D
i

:
i
∈
k
}

D = \{ {D_i}:i \in k\}

is a family of dense open sets of R there exists a countable dense set G of R such that

|

G
∖

D
i

|

>
ω

|G\backslash {D_i}| > \omega

for all

i
∈
k

i \in k

. We also show that the union of k meagre sets of the real line is a meagre set iff for every family

D
=
{

D
i

:
i
∈
k
}

D = \{ {D_i}:i \in k\}

of dense open sets of R and for every countable dense set G of R there exists a dense set

Q
⊆
G

Q \subseteq G

such that

|

Q
∖

D

i

|

>
ω

|Q\backslash {D_{i}}| > \omega

for all

i
∈
k

i \in k

.
The minimal normal 𝜇-complete filter on 𝑃_{𝜅}𝜆
Authors: Shioya Masahiro
Published: June 2010

We introduce the closed (resp. strongly closed)

μ
\mu

-unbounded filter

C

F

κ
λ

μ

CF_{\kappa \lambda }^\mu

(resp.

S
C

F

κ
λ

μ

SCF_{\kappa \lambda }^\mu

) for a regular cardinal

μ
≤
κ

\mu \leq \kappa

, which is a

μ
\mu

-complete analog of the closed (resp. strongly closed) unbounded filter on

P
κ

λ

{P_\kappa }\lambda

. We give their simple characterizations for the case

μ
=

ω
1

\mu = {\omega _1}

. We also study generators of

C

F

κ
λ

ν

CF_{\kappa \lambda }^\nu

(resp.

S
C

F

κ
λ

ν

SCF_{\kappa \lambda }^\nu

) over

C

F

κ
λ

μ

CF_{\kappa \lambda }^\mu

(resp.

S
C

F

κ
λ

μ

SCF_{\kappa \lambda }^\mu

) for the case

ω
>
μ
>
ν

\omega > \mu > \nu

.
Dynamics of typical continuous functions
Authors: Lehning Hervé
Published: June 2010

S. J. Agronsky, A. M. Bruckner, and M. Laczkovic have studied the behaviour of the sequence

(

f
n

(
x
)
)

({f^n}(x))

where f is the typical continuous function from the closed unit interval I into itself and x the typical point of I. In particular, they have proved that the typical limit set

ω
(
f
,
x
)

\omega (f,x)

is a Cantor set of Menger-Uryson dimension zero. Using mainly the Tietze extension theorem, we have found a shorter proof of this result which applies to a more general situation. As a matter of fact, we have replaced the closed unit interval by a compact N-dimensional manifold and the Menger-Uryson dimension by the Hausdorff one. We have also proved that, for the typical continuous function f, the function

x
→
ω
(
f
,
x
)

x \to \omega (f,x)

is continuous at the typical point x. It follows that the typical limit set is not a fractal and that, for the typical continuous function f, the sequence

(

f
n

(
x
)
)

({f^n}(x))

is not chaotic.
Oscillatory singular integrals on Hardy spaces associated with Herz spaces
Authors: Lu Shan Zhen , Yang Da Chun
Published: June 2010

In this paper, it is proved that the oscillatory singular integral operators of nonconvolution type are bounded from Hardy spaces associated with Herz spaces to Herz spaces.
A counterexample to access theorems for 𝐶^{∞} functions
Authors: Ortel Marvin
Published: June 2010

We construct a function

f
:

R

2

→

R

f:{\mathbb {R}^2} \to \mathbb {R}

with the following properties: (1) f is of class

∞
\infty

. (2) If

m
∈

R

2

m \in {\mathbb {R}^2}

, then

γ
:
[
0
,
1
]
→

R

2

\gamma :[0,1] \to {\mathbb {R}^2}

exists such that

γ
(
0
)
=
m
,
γ

\gamma (0) = m,\gamma

is continuous, and

f
∘
γ

f \circ \gamma

is strictly increasing on [0, 1]. (3) If

σ
:
[
0
,
1
)
→

R

2

\sigma :[0,1) \to {\mathbb {R}^2}

is continuous and

f
∘
σ

f \circ \sigma

is nondecreasing on [0, 1), then

sup
{

|

σ
(
s
)

|

:
0
≤
s
>
1
}
>
∞

\sup \{ |\sigma (s)|:0 \leq s > 1\} > \infty

.
The stability of Ky Fan’s points
Authors: Tan Kok-Keong , Yu Jian , Yuan Xian-Zhi
Published: June 2010

In this paper, inspired by the work of Fort, the stability of the setF(f)={y∈X:supx∈Xf(x,y)≤0}F(f) = \{ y \in X:{\sup _{x \in X}}f(x,y) \leq 0\}(respectively, the setF(A,f)={y∈A:supx∈Af(x,y)≤0}F(A,f) = \{ y \in A:{\sup _{x \in A}}f(x,y) \leq 0\}) withfvarying (respectively, with bothfandAvarying) is studied whereXis a non-empty compact convex subset of a Hausdorff topological vector space (respectively,Xis a Hausdorff topological space andAis a non-empty compact subset ofX) andf:X×X→Rf:X \times X \to \mathbb {R}is bounded.
Some weakly inner automorphisms of the Cuntz algebras
Authors: Tsui Sze-Kai
Published: June 2010

Let V be an

n
×
n

n \times n

unitary matrix. Then V induces an automorphism

O
V

{O_V}

of

O
∞

{O_\infty }

and

O
n

{O_n}

. It is shown in this paper that

O
V

{O_V}

is weakly inner. Let

F
n

{F_n}

be the UHF

C
∗

{C^ \ast }

-subalgebra of

O
n

{O_n}

and U be a unitary operator in the diagonal maximal abelian

∗
\ast

-subalgebra of

F
n

{F_n}

. Then the automorphism

λ
U

{\lambda _U}

of On defined by

λ
U

(

S
i

)
=

U
∗

S
i

{\lambda _U}({S_i}) = {U^ \ast }{S_i}

, for each generator

S
i

{S_i}

of

O
n

{O_n}

, is weakly inner. Any automorphism conjugate to either one mentioned above is also weakly inner.
Arithmetical conditions on element orders and group structure
Authors: Zhang Ji Ping
Published: June 2010

General results are provided on bounding the number of different prime factors of the order of finite groups in terms of the number for the order of elements.
On the cofinality of the smallest covering of the real line by meager sets. II
Authors: Bartoszyński Tomek , Judah Haim
Published: June 2010

We study the ideal of meager sets and related ideals.
𝑄(𝑡) and 𝑄((𝑡))-admissibility of groups of odd order
Authors: Fein Burton , Schacher Murray
Published: June 2010

Let

Q

(
t
)

\mathbb {Q}(t)

be the rational function field over the rationals,

Q

\mathbb {Q}

, let

Q

(
(
t
)
)

\mathbb {Q}((t))

be the Laurent series field over

Q

\mathbb {Q}

, and let

G

\mathcal {G}

be a group of odd order. We investigate the following question: does there exist a finite-dimensional division algebra D central over

Q

(
t
)

\mathbb {Q}(t)

or

Q

(
(
t
)
)

\mathbb {Q}((t))

which is a crossed product for

G

\mathcal {G}

? If such a D exists,

G

\mathcal {G}

is said to be

Q

(
t
)

\mathbb {Q}(t)

-admissible (respectively,

Q

(
(
t
)
)

\mathbb {Q}((t))

-admissible). We prove that if

G

\mathcal {G}

is

Q

(
(
t
)
)

\mathbb {Q}((t))

-admissible, then

G

\mathcal {G}

is also

Q

(
t
)

\mathbb {Q}(t)

-admissible; we also exhibit a

Q

(
t
)

\mathbb {Q}(t)

-admissible group which is not

Q

(
(
t
)
)

\mathbb {Q}((t))

-admissible.
Carleman inequalities for the Dirac operator and strong unique continuation
Authors: Kim Yonne Mi
Published: June 2010

Using a Carleman inequality, we prove a strong unique continuation theorem for the Schrödinger operator

D
+
V

D + V

, where D is the Dirac operator and V is a potential function in some

L
p

{L^p}

space.
Operator ideals and operator spaces
Authors: Mathes D. Benjamin , Paulsen Vern I.
Published: June 2010

We prove that every full symmetrically normed ideal of operators on a Hilbert space is realizable as the set of completely bounded maps between two homogeneous operator Hilbert spaces, with the c.b. norm equivalent to (but in general not equal to) the symmetric norm. We show that one can have equality of the c.b. norm and the symmetric norm if one leaves the category of operator spaces and passes to a slightly larger category.
Isomorphisms of standard operator algebras
Authors: Šemrl Peter
Published: June 2010

Let X and Y be Banach spaces,

dim
⁡
X
=
∞

\dim X = \infty

, and let

A

\mathcal {A}

and

B

\mathcal {B}

be standard operator algebras on X and Y, respectively. Assume that

ϕ
:

A

→

B

\phi :\mathcal {A} \to \mathcal {B}

is a bijective mapping satisfying
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar phi left-parenthesis upper A upper B right-parenthesis minus phi left-parenthesis upper A right-parenthesis phi left-parenthesis upper B right-parenthesis double-vertical-bar less-than-or-equal-to epsilon comma upper A comma upper B element-of script upper A">

‖

ϕ
(
A
B
)
−
ϕ
(
A
)
ϕ
(
B
)

‖

≤
ε
,
A
,
B
∈

A

\left \| {\phi (AB) - \phi (A)\phi (B)} \right \| \leq \varepsilon ,A,B \in \mathcal {A}

, where

ε
\varepsilon

is a given positive real number (no linearity or continuity of

ϕ
\phi

is assumed). Then

ϕ
\phi

is a spatially implemented linear or conjugate linear algebra isomorphism. In particular,

ϕ
\phi

is continuous.
Regular operator convergence and nonlinear equations involving numerical ranges
Authors: Verma Ram U.
Published: June 2010

Regular operator approximation theory, based on the work of Anselone and Lei (1986), is generalized to the case of strongly accretive operators and applied to nonlinear equations involving the generalized Zarantonello numerical ranges
Kähler Moišezon spaces which are projective algebraic
Authors: Vuono Charles
Published: June 2010

The Moišezon theorem is extended to complex spaces with isolated singularities.
Stolarsky’s inequality with general weights
Authors: Maligranda Lech , Pečarić Josip E. , Persson Lars Erik
Published: June 2010

Recently Stolarsky proved that the inquality
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row with Label left-parenthesis asterisk right-parenthesis EndLabel integral Subscript 0 Superscript 1 Baseline g left-parenthesis x Superscript 1 slash left-parenthesis a plus b right-parenthesis Baseline right-parenthesis d x greater-than-or-equal-to integral Subscript 0 Superscript 1 Baseline g left-parenthesis x Superscript 1 slash a Baseline right-parenthesis d x integral Subscript 0 Superscript 1 Baseline g left-parenthesis x Superscript 1 slash b Baseline right-parenthesis d x EndLayout">

(

∗

)

∫
0
1

g
(

x

1

/

(
a
+
b
)

)

d
x
≥

∫
0
1

g
(

x

1

/

a

)

d
x

∫
0
1

g
(

x

1

/

b

)

d
x

\begin{equation}\tag {$\ast $} \int _0^1 {g({x^{1/(a + b)}})\,dx \geq \int _0^1 {g({x^{1/a}})\,dx\int _0^1 {g({x^{1/b}})\,dx} } } \end{equation}

holds for every

a
,
b
>
0

a,b > 0

and every nonincreasing function on [0, 1] satisfying

0
≤
g
(
u
)
≤
1

0 \leq g(u) \leq 1

. In this paper we prove a weighted version of this inequality. Our proof is based on a generalized Chebyshev inequality. In particular, our result shows that the inequality

(
∗
)

( \ast )

holds for every function g of bounded variation. We also generalize another inequality by Stolarsky concerning the

Γ
\Gamma

-function.
Isomorphisms between endomorphism rings of modules
Authors: Wolfson Kenneth G.
Published: June 2010

We derive a necessary and sufficient condition that an isomorphism between the endomorphism rings of modules be induced by a semi-linear isomorphism of the modules. We require that at least one of the modules contain a non-zero free summand, generalizing work of Xu, who required both modules to be free.
Generalized scalar operators as dilations
Authors: Bercovici Hari , Petrović Srdjan
Published: June 2010

It is shown that polynomially bounded operators on Banach spaces have polynomially bounded dilations which have spectrum in the unit circle and are generalized scalar. The proof also yields a description of all compressions of generalized scalar operators with spectrum in the unit circle.
The lifting of the UKK property from 𝐸 to 𝐶_{𝐸}
Authors: Hsu Yu-Ping
Published: June 2010

In this paper we show that

C
E

{C_E}

, the unitary matrix space associated with the symmetrically normed sequence space E, has the UKK property for the weak operator topology if E has the UKK property for the pointwise convergence topology. We also prove that the quasi-normed space

C
p

=

C

l
p

{C_p} = {C_{{l_p}}}

, for

0
>
p
>
1

0 > p > 1

, has the UKK property for the weak operator topology.
Characteristic functions and products of bounded derivatives
Authors: Maliszewski Aleksander
Published: June 2010

This article is dedicated to the answer to the following question: "Which characteristic functions can be expressed as the product of two or more bounded derivatives?".
Noncrossed product division algebras with a Baer ordering
Authors: Morandi Patrick J. , Sethuraman B. A.
Published: June 2010

Let

n

|

m

n|m

be positive integers with the same prime factors, such that

p
3

|

n

{p^3}|n

for some prime p. We construct a noncrossed product division algebra D with involution

∗
\ast

, of index m and exponent n, such that D possesses a Baer ordering relative to the involution

∗
\ast

. Using similar techniques we construct indecomposable division algebras with involution possessing a Baer ordering.
𝜎-weakly closed modules of certain reflexive operator algebras
Authors: Chen Pei Xin
Published: June 2010

Let

A

\mathcal {A}

be a completely distributive CSL algebra and let M be any

σ
\sigma

-weakly closed

A

\mathcal {A}

-module. We give characterizations of commutant

C
(

A

,
M
)

C(\mathcal {A},M)

of

A

\mathcal {A}

modulo M and AlgLat M. Furthermore, we deal with the relations among

A

,
C
(

A

,
M
)

\mathcal {A},C(\mathcal {A},M)

and AlgLat M.
On the first 𝑛 strongly compact cardinals
Authors: Apter Arthur W.
Published: June 2010

Using techniques of Kimchi and Magidor, we generalize an earlier result and show that it is relatively consistent for the first n strongly compact cardinals to be somewhat supercompact yet not fully supercompact.
On 𝑑-parameter pointwise ergodic theorems in 𝐿₁
Authors: Hasegawa Shigeru , Sato Ryotaro
Published: June 2010

Let

P
1

,
…
,

P
d

{P_1}, \ldots ,{P_d}

be commuting positive linear contractions on

L
1

{L_1}

and let

T
1

,
…
,

T
d

{T_1}, \ldots ,{T_d}

be (not necessarily commuting) linear contractions on

L
1

{L_1}

such that

|

T
i

f

|

≤

P
i

|

f

|

|{T_i}f| \leq {P_i}|f|

for

1
≤
i
≤
d

1 \leq i \leq d

and

f
∈

L
1

f \in {L_1}

. In this paper we prove that if each

P
i

,
1
≤
i
≤
d

{P_i},1 \leq i \leq d

, satisfies the mean ergodic theorem, then the averages
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A Subscript n Baseline left-parenthesis upper T 1 comma ellipsis comma upper T Subscript d Baseline right-parenthesis f equals upper A Subscript n Baseline left-parenthesis upper T 1 right-parenthesis midline-horizontal-ellipsis upper A Subscript n Baseline left-parenthesis upper T Subscript d Baseline right-parenthesis f">

A
n

(

T
1

,
…
,

T
d

)
f
=

A
n

(

T
1

)
⋯

A
n

(

T
d

)
f

{A_n}({T_1}, \ldots ,{T_d})f = {A_n}({T_1}) \cdots {A_n}({T_d})f

, where
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A Subscript n Baseline left-parenthesis upper T Subscript i Baseline right-parenthesis equals n Superscript negative 1 Baseline sigma-summation Underscript k equals 0 Overscript n minus 1 Endscripts upper T Subscript i Superscript k">

A
n

(

T
i

)
=

n

−
1

∑

k
=
0

n
−
1

T
i
k

{A_n}({T_i}) = {n^{ - 1}}\sum \nolimits _{k = 0}^{n - 1} {T_i^k}

, converge a.e. for every

f
∈

L
1

f \in {L_1}

. When

T
1

,
…
,

T
d

{T_1}, \ldots ,{T_d}

commute, we further prove that the

L
1

{L_1}

-norm convergence of the averages

A
n

(

P
1

,
…
,

P
d

)
f

{A_n}({P_1}, \ldots ,{P_d})f

for every

f
∈

L
1

f \in {L_1}

implies the a.e. convergence of the averages

A
n

(

T
1

,
…
,

T
d

)
f

{A_n}({T_1}, \ldots ,{T_d})f

for every

f
∈

L
1

f \in {L_1}

. These improve Çömez and Lin’s ergodic theorem.
Condition ℬ and Baire 1 generalized derivatives
Authors: Darji Udayan B. , Evans Michael J. , O’Malley Richard J.
Published: June 2010

Ordered pairs (F, f) of real-valued functions on [0,1] which satisfy the condition that every perfect set M contains a dense

G
δ

{G_\delta }

set K such that

F
∖
M

F\backslash M

is differentiable to f on K are shown to play a key role in several types of generalized differentiation. In particular, this condition is utilized to prove the equivalence of selective differentiation and various forms of path differentiation under the assumption that the derivatives involved are of Baire class 1, thereby providing an affirmative answer, for Baire 1 selective derivatives, to a question raised in [Trans. Amer. Math. Soc 283 (1984), 97-125].
Skew polynomial extensions of commutative Noetherian Jacobson rings
Authors: Goodearl K. R. , Letzter E. S.
Published: June 2010

The Jacobson condition (i.e., that all prime ideals are semiprimitive) is proved to pass from a commutative noetherian ring R to a skew polynomial ring

R
[
y
;
τ
,
δ
]

R[y;\tau ,\delta ]

, assuming only that

τ
\tau

is an automorphism.
Twisting operations and composite knots
Authors: Teragaito Masakazu
Published: June 2010

Suppose that a composite knot K in

S
3

{S^3}

can be changed to a trivial knot by 1/n-surgery along a trivial loop C. We show that

|

n

|

≤
2

|n| \leq 2

. Moreover, if there is a decomposing sphere of K which meets C in two points, then

|

n

|

≤
1

|n| \leq 1

.
Numerical meshes and covering meshes of approximate inverse systems of compacta
Authors: Watanabe Tadashi
Published: June 2010

Mardešić and Rubin (1989) introduced approximate inverse systems of metric compacta by the conditions

(

A

1

)
∗

−

(

A

3

)
∗

{({\text {A}}1)^ \ast } - {({\text {A}}3)^ \ast }

. Mardešić and Watanabe (1988) introduced approximate inverse systems of topological spaces by the conditions

(

A

1
)
−
(

A

3
)

({\text {A}}1) - ({\text {A}}3)

. In this note we show that any approximate inverse system of metric compacta satisfies

(

A

1
)
−
(

A

3
)

({\text {A}}1) - ({\text {A}}3)

if and only if it satisfies

(

A

1

)
∗

−

(

A

3

)
∗

{({\text {A}}1)^\ast } - {({\text {A}}3)^\ast }

for some matrices (see Theorem 1).
On the composition of transcendental entire and meromorphic functions
Authors: Bergweiler Walter
Published: June 2010

It is proved that

f
(
g
)
−
R

f(g) - R

has infinitely many zeros if f is a transcendental meromorphic, g a transcendental entire, and R a non-constant rational function. The exponent of convergence of the sequence of zeros of

f
(
g
)
−
R

f(g) - R

is also estimated.
Delay differential inclusions with constraints
Authors: Hu Shou Chuan , Papageorgiou Nikolaos S.
Published: June 2010

In this paper we examine functional differential inclusions with memory and state constraints. For the case of time-independent state constraints, we show that the solution set is

R
δ

{R_\delta }

under Carathéodory conditions on the orientor field. For the case of time-dependent state constraints we prove two existence theorems. For this second case, the question of whether the solution set is

R
δ

{R_\delta }

remains open.
A coefficient problem with typically real extremal function
Authors: Konakazawa Seiji
Published: June 2010

Let

Σ

0

\Sigma _{0}

denote the class of univalent functions in

|

z

|

>
1

|z| > 1

, with expansion

f
(
z
)
=
z
+

∑

n
=
1

∞

b
n

z

−
n

f(z) = z + \sum \nolimits _{n = 1}^\infty {{b_n}{z^{ - n}}}

. We show that if the omitted set of an

f
(
z
)
∈

∑
0

f(z) \in {\sum _0}

is on the trajectory arcs of the quadratic differential

−
w
(
w
−
λ
)
d

w
2

- w(w - \lambda )d{w^2}

with

λ
≧
4
(

2

−
1
)

\lambda \geqq 4(\sqrt 2 - 1)

, then

f
(
z
)

f(z)

has real coefficients. From this we can derive the coefficient estimate of

max

Σ

0

R

e
(
−

b
3

−

1
2

b
1
2

+
λ

b
2

)

{\max _{{\Sigma _{0}}}} \mathcal {R}e( - {b_3} - \frac {1}{2}b_1^2 + \lambda {b_2})

.
Formulas for the joint spectral radius of noncommuting Banach algebra elements
Authors: Rosenthal P. , Sołtysiak A.
Published: June 2010

We discuss relations between several formulas for the joint spectral radius of n-tuples of non-commuting Banach algebra elements.
Representing abstract measures by Loeb measures: a generalization of the standard part map
Authors: Aldaz J. M.
Published: June 2010

Loeb measures have been utilized to represent Radon and

τ
\tau

-smooth measures on topological spaces via the standard part map. The purpose of this paper is to show how to extend these results to a nontopological setting.
Morita equivalence of twisted crossed products
Authors: Bui Huu Hung
Published: June 2010

We introduce a natural notion of strong Morita equivalence of twisted actions of a locally compact group on

C
∗

{C^ \ast }

-algebras, and then show that the corresponding twisted crossed products are strongly Morita equivalent. This result is a generalization of the result of Curto, Muhly and Williams concerning strong Morita equivalence of crossed products by actions.
Isoparametric functions and flat minimal tori in 𝐶𝑃²
Authors: Chi Quo-Shin , Jensen Gary R. , Liao Ruijia
Published: June 2010

It is proved that all flat minimal tori in

C

P
2

\mathbb {C}{P^2}

are unitarily congruent to the Clifford torus by studying a certain associated isoparametric function.
Fixed-point sets of autohomeomorphisms of compact 𝐹-spaces
Authors: Hart K. P. , Vermeer J.
Published: June 2010

We investigate fixed-point sets of autohomeomorphisms of compact F-spaces. If the space in question is finite dimensional (in the sense of covering dimension), then the fixed-point set is a P-set; on the other hand there is an infinite-dimensional compact F-space with an involution whose fixed-point set is not a P-set. In addition we show that under CH a closed subset of

ω
∗

{\omega ^ \ast }

is a P-set iff it is the fixed-point set of an autohomeomorphism.
Isomorphisms of lexicographic powers of the reals
Authors: Kuhlmann Salma
Published: June 2010

Given a chain

Γ
\Gamma

, we consider the lexicographic order

R

Γ

{\mathbb {R}^\Gamma }

. If

Δ
\Delta

is a chain such that

R

Γ

≃

R

Δ

{\mathbb {R}^\Gamma } \simeq {\mathbb {R}^\Delta }

, we examine the question of whether necessarily

Γ
≃
Δ

\Gamma \simeq \Delta

. Under an additional hypothesis, we show that

Γ
\Gamma

and

Δ
\Delta

will have the same order types of well ordered subsets. Among other things, this yields an affirmative answer to the above question in the case where

Γ
\Gamma

and

Δ
\Delta

are ordinals.
Complete hypersurfaces with constant mean curvature and nonnegative sectional curvatures
Authors: Hu Ze Jun
Published: June 2010

We classify the complete and non-negatively curved hypersurfaces of constant mean curvature in spaces of constant sectional curvature.
Level crossings of a random polynomial with hyperbolic elements
Authors: Farahmand K.
Published: June 2010

This paper provides an asymptotic estimate for the expected number of K-level crossings of a random hyperbolic polynomial

g
1

cosh
⁡
x
+

g
2

cosh
⁡
2
x
+
⋯
+

g
n

cosh
⁡
n
x

{g_1}\cosh x + {g_2}\cosh 2x + \cdots + {g_n}\cosh nx

, where

g
j

(
j
=
1
,
2
,
…
,
n
)

{g_j}(j = 1,2, \ldots ,n)

are independent normally distributed random variables with mean zero, variance one and K is any constant independent of x. It is shown that the result for

K
=
0

K = 0

remains valid as long as

K
≡

K
n

=
O
(

n

)

K \equiv {K_n} = O(\sqrt n )

.
Dense sets of diagonalizable matrices
Authors: Hartfiel D. J.
Published: June 2010

This paper provides necessary and sufficient conditions for a subspace of matrices to contain a dense set of matrices having distinct eigenvalues. A well-known and useful result in linear algebra is that matrices with distinct eigenvalues are dense in the set of

n
×
n

n \times n

matrices. This result, however, does not hold for subspaces of matrices in general. For example, the subspace
\[

W
=

{

A
:
A
=

[

0

a
m
p
;
0

a

a
m
p
;
0

]

where

a
∈
R

}

W = \left \{ {A:A = \left [ {\begin {array}{*{20}{c}} 0 \hfill & 0 \hfill \\ a \hfill & 0 \hfill \\ \end {array} } \right ]\quad {\text {where}}\;a \in R} \right \}

\]
contains no matrix with distinct eigenvalues. In this paper we give necessary and sufficient conditions for a subspace of matrices to contain a dense set of matrices having distinct eigenvalues. The result is then applied to subspaces of matrices determined by specified 0 patterns.
The multiplicativity of the minimal index of simple 𝐶*-algebras
Authors: Kawakami Satoshi , Watatani Yasuo
Published: June 2010

We show the multiplicativity of the minimal index for simple

C
∗

{C^ \ast }

-algebras. Although our proof is very short and elementary, it is also valid for subfactors, which was first shown by Kosaki and Longo (1992).