bluuebunny/crossref_metadata_2025 huggingface dataset:
On the convergence of some iteration processes in uniformly convex Banach spaces
Authors: Gwinner J.
Published: June 2010

For the approximation of fixed points of a nonexpansive operator T in a uniformly convex Banach space E the convergence of the Mann-Toeplitz iteration

x

n
+
1

=

α
n

T
(

x
n

)
+
(
1
−

α
n

)

x
n

{x_{n + 1}} = {\alpha _n}T({x_n}) + (1 - {\alpha _n}){x_n}

is studied. Strong convergence is established for a special class of operators T. Via regularization this result can be used for general nonexpansive operators, if E possesses a weakly sequentially continuous duality mapping. Furthermore strongly convergent combined regularization-iteration methods are presented.
Free subgroups of normal subgroups of the multiplicative group of skew fields
Authors: Lichtman A. I.
Published: June 2010

Let D be a skew field,

D
∗

{D^ \ast }

its multiplicative group and

H
◃

D
∗

H \triangleleft {D^ \ast }

. Then H contains a noncyclic free subgroup F, provided that there exists a nonabelian nilpotent-by-finite subgroup G of H.
On genericity and complements of measure zero sets in function spaces
Authors: Rebhuhn D.
Published: June 2010

Generic properties of function spaces have been of particular interest in dynamical systems and singularity theory. The underlying assumption has been that the complement of a dense

G
δ

{G_\delta }

set is sparse enough to be considered unlikely. Nevertheless, in infinite dimensional spaces, even dense

G
δ

{G_\delta }

’s may have measure zero. Since there is no one canonical measure on an infinite dimensional Fréchet space, notions of measure zero have not often been considered. Here we use a notion of Haar measure zero on abelian Polish groups due to Christensen [1]. We show that those sections of a finite dimensional vector bundle over a compact manifold whose jets are transverse to a submanifold of the jet bundle are complements of sets of Haar measure zero.
Uniform asymptotic stability in functional differential equations
Authors: Burton T. A.
Published: June 2010

The classical uniform asymptotic stability result for a system of functional differential equations

(

1

)

x
′

=
F
(
t
,

x
t

)

\begin{equation}\tag {$1$} x’ = F(t,{x_t})\end{equation}

calls for a Liapunov functional

V
(
t
,
ϕ
)

V(t,\phi )

satisfying
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper W left-parenthesis StartAbsoluteValue phi left-parenthesis 0 right-parenthesis EndAbsoluteValue right-parenthesis less-than-or-slanted-equals upper V left-parenthesis t comma phi right-parenthesis less-than-or-slanted-equals upper W 1 left-parenthesis StartAbsoluteValue phi left-parenthesis 0 right-parenthesis EndAbsoluteValue right-parenthesis plus upper W 2 left-parenthesis StartAbsoluteValue EndAbsoluteValue StartAbsoluteValue phi EndAbsoluteValue StartAbsoluteValue EndAbsoluteValue right-parenthesis comma upper V prime Subscript left-parenthesis 1 right-parenthesis Baseline less-than-or-slanted-equals minus upper W 3 left-parenthesis StartAbsoluteValue phi left-parenthesis 0 right-parenthesis EndAbsoluteValue right-parenthesis">

W
(

|

ϕ
(
0
)

|

)
⩽
V
(
t
,
ϕ
)
⩽

W
1

(

|

ϕ
(
0
)

|

)
+

W
2

(

|

|

|

ϕ

|

|

|

)
,

V

(
1
)

′

⩽
−

W
3

(

|

ϕ
(
0
)

|

)

W(|\phi (0)|) \leqslant V(t,\phi ) \leqslant {W_1}(|\phi (0)|) + {W_2}(|||\phi |||),{V’_{(1)}} \leqslant - {W_3}(|\phi (0)|)

, and

|

f
(
t
,

x
t

)

|

|f(t,{x_t})|

bounded for

|

|

|

x
t

|

|

|

|||{x_t}|||

bounded. We show that it is not necessary to require

|

f
(
t
,

x
t

)

|

|f(t,{x_t})|

bounded. Here,

|

|

|

⋅

|

|

|

||| \cdot |||

is the

L
2

{L^2}

-norm.
A characterization of M. W. Wilson’s criterion for nonnegative expansions of orthogonal polynomials
Authors: Micchelli Charles A.
Published: June 2010

Given a nonnegative function

f
(
x
)

f(x)

, M. W. Wilson observed that if
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row with Label left-parenthesis 1 right-parenthesis EndLabel integral Subscript 0 Superscript normal infinity Baseline f left-parenthesis x right-parenthesis upper Q Subscript i Baseline left-parenthesis x right-parenthesis upper Q Subscript j Baseline left-parenthesis x right-parenthesis d mu left-parenthesis x right-parenthesis less-than-or-slanted-equals 0 comma i not-equals j comma EndLayout">

(

1

)

∫
0
∞

f
(
x
)

Q
i

(
x
)

Q
j

(
x
)
d
μ
(
x
)
⩽
0
,

i
≠
j
,

\begin{equation}\int _0^\infty f(x) Q_i(x) Q_j(x)d\mu (x) \leqslant 0,\quad i \ne j, \quad \tag {$1$}\end{equation}

then the polynomials

P
n

(
x
)
,

P
n

(
0
)
=
1

{P_n}(x),{P_n}(0) = 1

, orthogonal relative to

f
(
x
)
d
μ
(
x
)

f(x)d\mu (x)

, have an expansion
\[

P
n

(
x
)
=

∑

k
=
0

n

a

k
n

Q
k

(
x
)

{P_n}(x) = \sum \limits _{k = 0}^n {{a_{kn}}{Q_k}(x)}

\]
with nonnegative coefficients

a

k
n

⩾
0

{a_{kn}} \geqslant 0

where

Q
n

(
x
)
,

Q
n

(
0
)
=
1

{Q_n}(x),{Q_n}(0) = 1

, are orthogonal relative to

d
μ
(
x
)

d\mu (x)

. Recently it was shown that (1) holds for

f
(
x
)
=

x
c

,
0
>
c
>
1

f(x) = {x^c},0 > c > 1

. In this paper we characterize those functions

f
(
x
)

f(x)

for which (1) is valid for all positive measures

d
μ
(
x
)

d\mu (x)

.
Weak* compact convex sets with separable extremal subsets have the Radon-Nikodým property
Authors: Bourgin Richard D.
Published: June 2010

The result stated in the title, as well as several other related results, is derived.
Quasi-similarity of weak contractions
Authors: Wu Pei Yuan
Published: June 2010

Let T be a completely nonunitary (c.n.u.) weak contraction (in the sense of Sz.-Nagy and Foiaş). We show that T is quasi-similar to the direct sum of its

C
0

{C_0}

part and

C

11

{C_{11}}

part. As a corollary, two c.n.u. weak contractions are quasi-similar to each other if and only if their

C
0

{C_0}

parts and

C

11

{C_{11}}

parts are quasi-similar to each other, respectively. We also completely determine when c.n.u. weak contractions and

C
0

{C_0}

contractions are quasi-similar to normal operators.
A generalization of the canonical commutation and anticommutation relations
Authors: Robbins Steven
Published: June 2010

The relation

C
∗

C

C
∗

−

C
∗

=
C

C

∗
2

{C^ \ast }C{C^ \ast } - {C^ \ast } = C{C^{ \ast 2}}

involving a closed densely defined operator C generalizes both the canonical commutation relation of bosons and the canonical anticommutation relation of fermions. It is shown that the operators satisfying this relation can be classified by an index

p
,
p
=
0
,
1
,
2
,
…
,
∞

p,p = 0,1,2, \ldots ,\infty

.
Computable isomorphism invariants for the fundamental group of the complement of a plane projective curve
Authors: Arnold Edward M.
Published: June 2010

The aim of this paper is to attach computable isomorphism invariants to the fundamental groups

π
1

(

P

2

−
c
)

{\pi _1}({{\mathbf {P}}^2} - c)

where c is an irreducible plane projective curve. We use these invariants to distinguish certain of these groups. The vehicle used to obtain these invariants is the free differential calculus of R. Fox.
On the number of lattice points in planar domains
Authors: Tarnopolska-Weiss Marysia
Published: June 2010

Lattice-point estimates are obtained for rotations of planar sets.
A reformulation of 𝑆 and 𝐿
Authors: Roitman Judy
Published: June 2010

We give a combinatorial statement which is equivalent to the existence of an S space, and one equivalent to the existence of an L space, thus verifying the widespread intuition that the problem of S and L is essentially set-theoretic.
Extensions of a theorem of Fuglede and Putnam
Authors: Berberian S. K.
Published: June 2010

The operator equation

A
X
=
X
B

AX = XB

implies

A
∗

X
=
X

B
∗

{A^ \ast }X = X{B^ \ast }

when A and B are normal (theorem of Fuglede and Putnam). If X is of Hilbert-Schmidt class, the assumptions on A and B can be relaxed: it suffices that A and

B
∗

{B^ \ast }

be hyponormal, or that B be invertible with

‖
A
‖

‖

B

−
1

‖

⩽
1

\left \| A \right \|\left \| {{B^{ - 1}}} \right \| \leqslant 1

.
Some spaces related to topological inequalities proven by the Erdős-Rado theorem
Authors: Fleissner William G.
Published: June 2010

The Erdös-Rado theorem is very useful in proving cardinal inequalities in topology. It has been suggested that certain of these inequalities might be strengthened. We note that trees constructed by Jensen and Gregory using various extra axioms of set theory yield several counterexamples to these suggestions; for example, a space

X
,

|

X

|

=

ω
2

,
c
(
X
)
=

ω
1

,
χ
(
X
)
=
ω

X,|X| = {\omega _2},c(X) = {\omega _1},\chi (X) = \omega

, answering a question of Hajnal and Juhász. We consider the apparently similar relation between

|

X

|

,
e
(
X
)

|X|,e(X)

, and

d
Ψ
(
X
)

d\Psi (X)

of Ginsburg and Woods. Using combinatorial consequences of

V
=
L

V = L

, we construct

G
δ

{G_\delta }

tree families, and establish that, assuming

V
=
L

V = L

, an infinite cardinal

κ
\kappa

is weakly compact
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="iff d normal upper Psi left-parenthesis upper X right-parenthesis greater-than kappa comma e Subscript a Baseline left-parenthesis upper X right-parenthesis subset-of kappa imply StartAbsoluteValue upper X EndAbsoluteValue greater-than kappa">

iff

d
Ψ
(
X
)
>
κ
,

e
a

(
X
)
⊂
κ

imply

|

X

|

>
κ

{\text {iff}}\,d\Psi (X) > \kappa ,{e_a}(X) \subset \kappa {\text {imply}}|X| > \kappa

. We consider products of countable chain condition spaces, and show that, using Cohen forcing that (

2
ω

{2^\omega }

can be anything allowed by König’s theorem and there are spaces

X
,
Y
,
c
(
X
)
=
c
(
Y
)
=
ω
,
c
(
X
×
Y
)
=

2
ω

X,Y,c(X) = c(Y) = \omega ,c(X \times Y) = {2^\omega }

). A variation is a space W with the property

c
(

W
n

)
=

ω

n
−
1

c({W^n}) = {\omega _{n - 1}}

.
Resolutions of 𝐻-closed spaces
Authors: Friedler Louis M.
Published: June 2010

It is shown that every Hausdorff space X is the perfect, irreducible, continuous image of a Hausdorff space

X
~

\tilde X

which has a basis with open closures. Further,

w
(

X
~

)
⩽
w
(
X
)

w(\tilde X) \leqslant w(X)

, where

w
(

X
~

)

w(\tilde X)

represents the weight of X, and if X is H-closed then

X
~

\tilde X

is also H-closed. A corollary of this result is that if

f
:
X
→
Y

f:X \to Y

is a continuous map of the H-closed space X onto the semi-regular Hausdorff space Y, then

w
(
Y
)
⩽
w
(
X
)

w(Y) \leqslant w(X)

.
On the relations between some rate-of-growth conditions
Authors: McLaughlin T. G.
Published: June 2010

We discuss the implications and nonimplications between four rate-of-growth properties of sets useful in certain areas of recursion theory; all nonimplications are established within the boolean algebra generated by the recursively enumerable sets.
𝐾-theory and 𝐾-homology relative to a 𝐼𝐼_{∞}-factor
Authors: Raeburn Iain
Published: June 2010

Let X be a compact space and M be a factor of type

I
I

∞

\mathrm {II}_\infty

acting on a separable Hilbert space. Let

K
M

(
X
)

{K_M}(X)

denote the Grothendieck group generated by the semigroup of isomorphism classes of M-vector bundles over X, and, if X is also metric, let

Ext
M

⁡
(
X
)

\operatorname {Ext}^M(X)

denote the group of equivalence classes of extensions of

C
(
X
)

C(X)

relative to M. We show that

K
M

(
X
)

{K_M}(X)

is the direct sum of the even-dimensional Čech cohomology groups of X, and that

Ext
M

⁡
(
X
)

\operatorname {Ext}^M(X)

is the direct product of the odd-dimensional Čech homology groups of X.
Endohomeomorphisms decomposing a space into disjoint copies of a subspace
Authors: O’Callaghan Liam
Published: June 2010

The existence (conjectured by R. Levy in a private communication) of a space X and an endohomeomorphism, f, of

β
X

\beta X

, such that

f
[
X
]
=
β
X
∖
X

f[X] = \beta X\backslash X

is demonstrated. It is shown that if G is one of the topological groups

2

α

,

Q

α

,

R

α

{{\mathbf {2}}^\alpha },{{\mathbf {Q}}^\alpha },{{\mathbf {R}}^\alpha }

or

T

α

{{\mathbf {T}}^\alpha }

, where

ω
>
α

\omega > \alpha

, then G has a dense C-embedded subgroup H and an autohomeomorphism, f, such that G is the union of disjoint sets,

A
0

{A_0}

and

A
1

{A_1}

, where for

{
i
,
j
}
=
{
0
,
1
}
f
[

A
i

]
=

A
j

\{ i,j\} = \{ 0,1\} f[{A_i}] = {A_j}

, and

A
i

{A_i}

is a union of cosets of H.
A generalization of Study’s theorem on convex maps
Authors: Barnard Roger W.
Published: June 2010

Study proved that disks of radius r,

0
>
r
⩽
1

0 > r \leqslant 1

, get mapped onto convex (starlike) sets under all convex (starlike) maps of the unit disk U. Pommerenke and Heins gave a geometric characterization of the subsets of U that get mapped onto convex sets under all convex maps. In this note we give an analytical characterization of the subsets of U that get mapped onto

α
\alpha

-starlike domains under all

α
\alpha

-starlike maps of U for all

α
⩾
0

\alpha \geqslant 0

noting that 0-starlikeness equals starlikeness and 1-starlikeness equals convexity.
The local Hilbert function of a pair of plane curves
Authors: Kothari S. C.
Published: June 2010

Let R be the local ring of a pair of plane curves at a point. In this paper it is proved that the Hilbert function of such a ring changes by at most one at each stage, and it is essentially nonincreasing.
Some properties of asymptotic functions and their applications
Authors: Chan Ling Yau
Published: June 2010

In this paper we give complete characterizations, in terms of Dini numbers and integrals, of positive functions

Φ
(
u
)

\Phi (u)

defined in (0,

∞
\infty

) satisfying the conditions: (i)

Φ
(
u
)

/

u
a

\Phi (u)/{u^a}

is nondecreasing and (ii)

Φ
(
u
)

/

u
b

\Phi (u)/{u^b}

is nonincreasing. By applying these results we obtain necessary and sufficient conditions for power series and trigonometric series to satisfy a certain Lipschitz condition, which include some known results of R. P. Boas, Jr. [1]. We also give complete characterizations of positive functions

Φ
(
u
)

\Phi (u)

defined in

(
−
∞
,
∞
)

( - \infty ,\infty )

satisfying the conditions: (i)

Φ
(
u
)

/

e

a
u

\Phi (u)/{e^{au}}

is nondecreasing and (ii)

Φ
(
u
)

/

e

b
u

\Phi (u)/{e^{bu}}

is nonincreasing.
Symmetric and ordinary differentiation
Authors: Belna C. L. , Evans M. J. , Humke P. D.
Published: June 2010

In 1927, A. Khintchine proved that a measurable symmetrically differentiable function f mapping the real line R into itself is differentiable in the ordinary sense at each point of R except possibly for a set of Lebesgue measure zero. Here it is shown that this exceptional set is also of the first Baire category; even more, it is shown to be a

σ
\sigma

-porous set of E. P. Dolženko.
Every 𝐿_{𝑝} operator is an 𝐿₂ operator
Authors: Johnson W. B. , Jones L.
Published: June 2010

If T is a bounded linear operator on

L
p

(
μ
)
,
1
⩽
p
>
∞
,
μ

{L_p}(\mu ),1 \leqslant p > \infty ,\mu

a probability measure, then, after an appropriate change of density, T acts as a bounded operator on

L
2

{L_2}

.
Spans and intersections of essentially reducing subspaces
Authors: Hoffman Michael J.
Published: June 2010

If P and Q are the projections onto essentially reducing subspaces M and N for an operator, the closed linear span and the intersection of M and N need not be essentially reducing or even essentially invariant. However, they are if

M
+
N

M + N

is closed, in particular if

P
Q
=
Q
P

PQ = QP

or if PQ is compact.
A note on semitopological properties
Authors: Crossley S. Gene
Published: June 2010

The strongly Hausdorff and Urysohn properties of a topological space are shown to be semitopological properties.
Quickly unknotting topological spheres
Authors: Brakes W. R.
Published: June 2010

Locally flat topological sphere and cell pairs of codimension at least three are shown to be unknotted by a simpler method than previously known.
A note on the congruence lattice of a finitely generated algebra
Authors: Rival Ivan , Sands Bill
Published: June 2010

Let

A

\mathfrak {A}

be a finitely generated algebra of finite type. If

θ
\theta

is a congruence relation of

A

\mathfrak {A}

such that

A

/

θ

\mathfrak {A}/\theta

is finite then

θ
\theta

is compact in the lattice

Con

(

A

)

{\text {Con}}(\mathfrak {A})

of all congruence relations of

A

\mathfrak {A}

. Moreover, if

A

\mathfrak {A}

is infinite then there is a congruence relation

θ
\theta

such that

A

/

θ

\mathfrak {A}/\theta

is infinite and

A

/

θ
′

\mathfrak {A}/\theta ’

is finite for every

θ
′

>
θ

\theta ’ > \theta

in

Con

(

A

)

{\text {Con}}(\mathfrak {A})

.
Local properties of quotient analytic spaces
Authors: Takijima Kunio , Tomaru Tadashi
Published: June 2010

Let

T
:=

C

/

Z

ω
1

+

Z

ω
2

T: = {\mathbf {C}}/{\mathbf {Z}}{\omega _1} + {\mathbf {Z}}{\omega _2}

be a complex 1-torus and

E
n

{E_n}

the set of all elliptic functions of order n. Then M. Namba showed that

E
n

{E_n}

is a 2n-dimensional complex manifold. Let

Aut
⁡
T

\operatorname {Aut} T

be the automorphism group of T, then

Aut
⁡
T

\operatorname {Aut} T

is a 1-dimensional compact complex Lie group and the orbit space

E
n

/

Aut

T

{E_n}/{\operatorname {Aut}} T

is an analytic space. In this paper, we shall show that

E
n

/

Aut

T

{E_n}/{\operatorname {Aut}} T

has only rational singularities and if

n
⩾
5
,

E
n

/

Aut

T

n \geqslant 5,{E_n}/{\operatorname {Aut}} T

is rigid.
On the local spectra of seminormal operators
Authors: Clancey Kevin F.
Published: June 2010

Two theorems on the local spectra of seminormal operators are deduced. In the first theorem it is shown that when T is hyponormal any solution of the equation

(
T
−
λ
)
x
(
λ
)
=
x

(T - \lambda )x(\lambda ) = x

on an open set in the plane is necessarily analytic. The second theorem establishes the existence of vectors with small local spectra for a cohyponormal operator with a finite rank self-commutator.
Tensor products and the joint spectrum in Hilbert spaces
Authors: Ceauşescu Zoia , Vasilescu F.-H.
Published: June 2010

Given two complex Hilbert spaces X and Y and two commuting systems of linear continuous operators

a
=
(

a
1

,
…
,

a
n

)

a = ({a_1}, \ldots ,{a_n})

on X and

b
=
(

b
1

,
…
,

b
m

)

b = ({b_1}, \ldots ,{b_m})

on Y, the joint spectrum of the commuting system

(

a
1

⊗
1
,
…
,

a
n

⊗
1
,
1
⊗

b
1

,
…
,
1
⊗

b
m

)

({a_1} \otimes 1, \ldots ,{a_n} \otimes 1,1 \otimes {b_1}, \ldots ,1 \otimes {b_m})

on

X

⊗
¯

Y

X\bar \otimes Y

is expressed by the Cartesian product of the joint spectrum of a with the joint spectrum of b.
Surgery on links containing a cable sublink
Authors: Clark Bradd Evans
Published: June 2010

In this paper it will be shown that there is an upper bound on the genus of any manifold obtained by Dehn surgery on a given torus link. It is also demonstrated that if L is a link in

S
3

{S^3}

with a cable sublink about the knot k, and surgery on at least two components of the sublink cannot be replaced by surgery on k, then the manifold resulting from surgery on L cannot be simply connected.
On the proximinality of compact operators with range in 𝐶(𝑆)
Authors: Mach Jaroslav
Published: June 2010

It is proved that the space of compact operators on X into

C
(
S
)

C(S)

is proximinal in the corresponding space of bounded operators, if X is a Hilbert space, a space

l
p

,
1
>
p
>
+
∞

{l_p},1 > p > + \infty

, or the space

c
0

{c_0}

.
An extremal problem for polynomials with a prescribed zero. II
Authors: Rahman Q. I. , Schmeisser G.
Published: June 2010

Improving upon an earlier estimate it is shown that if

p
n

(
z
)

{p_n}(z)

is a polynomial of degree at most n such that

p
n

(
1
)
=
0

{p_n}(1) = 0

and

max

|

z

|

=
1

|

p
n

(
z
)

|

⩽
1

{\max _{|z| = 1}}|{p_n}(z)| \leqslant 1

, then

|

p
n

(
0
)

|

>
1
−
(
1.03369
)

/

n
+
O
(
1

/

n
2

)

|{p_n}(0)| > 1 - (1.03369)/n + O(1/{n^2})

.
A simpler proof that compact metric spaces are supercompact
Authors: Mills Charles F.
Published: June 2010

We give a simpler proof that every compact metric space is supercompact.
A characterization of prime Noetherian P. I. rings and a theorem of Mori-Nagata
Authors: Braun Amiram
Published: June 2010

Let R be a noetherian prime p.i. ring, C the center of R and

C
¯

\bar C

its normalization. It is proved that R is integral over its center iff

C
¯

\bar C

is a Krull domain. We also give a simple proof for the following theorem [7]: The normalization of a commutative noetherian domain is Krull.
An algebra of functions
Authors: Dahlberg Björn E. J.
Published: June 2010

It is established that the space of logarithmic potentials of

H
1

{H^1}

-functions is closed under multiplication.
A maximum principle for semilinear parabolic systems
Authors: Martin Robert H.
Published: June 2010

We develop a criterion insuring that every component of the solution to a system of semilinear parabolic equations is strictly positive for positive time. This criterion involves the strict (component-wise) positiveness of solutions to a related ordinary differentiable system.
Koebe domains for certain families
Authors: Goodman A. W.
Published: June 2010

The Koebe domain of a family of functions, analytic in the unit disk E, is the largest domain that is contained in

f
(
E
)

f(E)

for every function of the family. In this paper we review some families for which the Koebe domains are known, and find the Koebe domains for some new families.
Analytic properties of cosine operators
Authors: Nelson S. , Triggiani R.
Published: June 2010

Let A be the infinitesimal generator of a strongly continuous cosine operator

C
(
t
)

C(t)

, hence of the analytic semigroup

S
(
t
)

S(t)

, on the Banach space X. It is proved that the set of analytic vectors for

C
(
t
)

C(t)

contains the dense subspace

X
0

=

∪

0
>
t

S
(
t
)
X

{X_0} = { \cup _{0 > t}}S(t)X

, the containment being in general proper.
Extensions relative to a 𝐼𝐼_{∞}-factor
Authors: Cho Sung Je
Published: June 2010

It will be shown that the equivalence classes of

C
∗

{C^\ast }

-algebra extensions of

C
(
X
)

C(X)

relative to a

II
∞

{\text {II}_\infty }

-factor and

Hom
⁡
(

K
~

1

(
X
)
,

R

)

\operatorname {Hom}({\tilde K^1}(X),{\mathbf {R}})

are isomorphic. This provides a proof for the result of Brown, Douglas and Fillmore [5] on the isomorphism between the former group and

Hom
⁡
(

K
~

II

1

(
X
)
,

R

)

\operatorname {Hom}(\tilde K_{{\text {II}}}^1(X),{\mathbf {R}})

.
Self-homotopy equivalences of Postnikov conjugates
Authors: Dror E. , Dwyer W. G. , Kan D. M.
Published: June 2010

The purpose of this note is to generalize a result of Wilkerson [4] and show that the self homotopy equivalences of the Postnikov approximations of a space X determine, in a rather simple manner, simultaneously the self homotopy equivalences of X and the self homotopy equivalences of the Postnikov conjugates of X (i.e. the spaces with the same Postnikov approximations as X).
Pencils of higher derivations of arbitrary field extensions
Authors: Deveney James K. , Mordeson John N.
Published: June 2010

Let L be a field of characteristic

p
≠
0

p \ne 0

. A subfield K of L is Galois if K is the field of constants of a group of pencils of higher derivations on L. Let

F
⊃
K

F \supset K

be Galois subfields of L. Then the group of L over F is a normal subgroup of the group of L over K if and only if

F
=
K
(

L

p
r

)

F = K({L^{{p^r}}})

for some nonnegative integer r. If

L

/

K

L/K

splits as the tensor product of a purely inseparable extension and a separable extension, then the algebraic closure of K in L,

K
¯

\bar K

, is also Galois in L. Given K, for every Galois extension L of K,

K
¯

\bar K

is also Galois in L if and only if

[
K
:

K
p

]
>
∞

[K:{K^p}] > \infty

.
On homomorphisms from algebraic groups to 𝐺𝐿_{𝑛}(𝑍)
Authors: Kambayashi T. , Margrave G.
Published: June 2010

As a rule, there are no nontrivial abstract group homomorphisms from a connected algebraic group to any group devoid of divisible elements. This rule is formulated and proven, and the exceptions to the rule as well as applications of it are discussed.
Remarks on the representation of zero by solutions of differential equations
Authors: Wimp Jet , Colton David
Published: June 2010

Numerical evidence from certain problems arising in optics seems to indicate Fourier-Bessel series which converge to zero in

(
1
−
δ
,
1
]

(1 - \delta ,1]

also converge to zero in

[
1
,
1
+
δ
)

[1,1 + \delta )

, an interval which lies outside the range of orthogonality of the Bessel functions. Here we demonstrate this as a corollary of a result on series of functions which satisfy a general Sturm-Liouville equation.
The stability of the equation 𝑓(𝑥+𝑦)=𝑓(𝑥)𝑓(𝑦)
Authors: Baker John , Lawrence J. , Zorzitto F.
Published: June 2010

It is proved that if f is a function from a vector space to the real numbers satisfying
\[

|

f
(
x
+
y
)
−
f
(
x
)
f
(
y
)

|

>
δ

|f(x + y) - f(x)f(y)| > \delta

\]
for some fixed

δ
\delta

and all x and y in the domain, then f is either bounded or exponential.
Double commutants of 𝐶_{⋅0} contractions. II
Authors: Uchiyama Mitsuru
Published: June 2010

In [13], it was shown that if T is a

C

.
0

C{._0}

contraction with finite defect indices

∞
>

δ

T
∗

>

δ
T

\infty > {\delta _{{T^\ast }}} > {\delta _T}

, then

{
T
}
=
{
ϕ
(
T
)
:
ϕ
∈

H
∞

}

\{ T\} = \{ \phi (T):\phi \in {H^\infty }\}

. In this note we shall extend this result to

∞
⩾

δ

T
∗

>

δ
T

\infty \geqslant {\delta _{{T^\ast }}} > {\delta _T}

and show that

{
T
}

\{ T\}

and

H
∞

{H^\infty }

is isometric isomorphic, and moreover such an operator is reflexive.
On unitary equivalence of representations of 𝐶*-algebras
Authors: Anderson Joel
Published: June 2010

Assuming the continuum hypothesis, there are inequivalent irreducible representations of

B

(

H

)

\mathcal {B}(\mathcal {H})

that are pointwise equivalent.
Pseudocompactness and closed subsets of products
Authors: Joseph James E.
Published: June 2010

This paper contains several new characterizations of arbitrary pseudocompact spaces, i.e. spaces characterized by the property that all continuous real-valued functions on the space are bounded. These characterizations parallel known characterizations of Hausdorff spaces including the useful and well-known result that a space Y is Hausdorff if and only if

ϕ
=
α

\phi = \alpha

whenever

ϕ
\phi

and

α
\alpha

are continuous functions on a common domain into Y which agree on a dense subset of the domain.
Local solvability of left invariant differential operators on the Heisenberg group
Authors: Rothschild Linda Preiss
Published: June 2010

Representation-theoretic criteria are given for the local solvability of left invariant differential operators homogeneous under dilations.
Remarks on the asymptotic behavior of solutions to damped evolution equations in Hilbert space
Authors: Bloom Frederick
Published: June 2010

Lower bounds are derived for the norms of solutions to a class of intitial-value problems associated with the damped evolution equation

u

t
t

+
A

u
t

+
B
u
=
0

{u_{tt}} + A{u_t} + Bu = 0

in Hilbert space. Under appropriate assumptions on the linear operator B it is shown that even in the special strongly damped case where

A
=
Γ
I
,
Γ
>
0

A = \Gamma I,\Gamma > 0

, solutions are bounded away from zero as

t
→
+
∞

t \to + \infty

, even when

Γ
→
+
∞

\Gamma \to + \infty

.
Hyperinvariant subspaces of 𝐶₁₁ contractions
Authors: Wu Pei Yuan
Published: June 2010

For an operator T on a Hilbert space let Hyperlat T denote its hyperinvariant subspace lattice. Assume that T is a completely nonunitary

C

11

{C_{11}}

contraction with finite defect indices. In this note we characterize the elements of Hyperlat T among invariant subspaces for T in terms of their corresponding regular factorizations and show that elements in Hyperlat T are exactly the spectral subspaces of T defined by Sz.-Nagy and Foiaş. As a corollary, if

T
1

,

T
2

{T_1},{T_2}

are two such operators which are quasi-similar to each other, then Hyperlat

T
1

{T_1}

is (lattice) isomorphic to Hyperlat

T
2

{T_2}

.
On two questions of Halmos concerning subspace lattices
Authors: Longstaff W. E. , Rosenthal Peter
Published: June 2010

An example is constructed of a nonreflexive pentagonal lattice of subspaces. It follows that reflexivity is not invariant under lattice isomorphism, even for finite lattices.
Complete bases and Wallman realcompactifications
Authors: Blasco Jose L.
Published: June 2010

We study a particular class of separating nest generated intersection rings on a Tychonoff space X, that we call complete bases. They are characterized by the equality

β
(
υ
(
X
,

D

)
)
=
ω
(
X
,

D

)

\beta (\upsilon (X,\mathcal {D})) = \omega (X,\mathcal {D})

between their associated Wallman spaces. It is proven that for each separating nest generated intersection ring

D

\mathcal {D}

there exists a unique complete base

D

^

\hat {\mathcal {D}}

such that

υ
(
X
,

D

)
=
υ
(
X
,

D

^

)

\upsilon (X,\mathcal {D}) = \upsilon (X,\widehat {\mathcal {D}})

. From this result we obtain a necessary and sufficient condition for the existence of a continuous extension to

υ
(
X
,

D

)

\upsilon (X,\mathcal {D})

of a real-valued function over X. Some applications of these results to certain inverse-closed subalgebras of

C
(
X
)

C(X)

are given.
Homeomorphisms of a surface which act trivially on homology
Authors: Johnson Dennis L.
Published: June 2010

Let

M

\mathfrak {M}

be the mapping class group of a surface of genus

g
⩾
3

g \geqslant 3

, and

I

\mathcal {I}

the subgroup of those classes acting trivially on homology. An infinite set of generators for

I

\mathcal {I}

, involving three conjugacy classes, was obtained by Powell. In this paper we improve Powell’s result to show that

I

\mathcal {I}

is generated by a single conjugacy class and that

[

M

,

I

]
=

I

[\mathfrak {M},\mathcal {I}] = \mathcal {I}

.
A theorem on partially ordered sets of order-preserving mappings
Authors: Duffus Dwight , Wille Rudolf
Published: June 2010

Let P be a partially ordered set and let

P
P

{P^P}

denote the set of all order-preserving mappings of P to P ordered by

f
⩽
g

f \leqslant g

in

P
P

{P^P}

if

f
(
p
)
⩽
g
(
p
)

f(p) \leqslant g(p)

for all

p
∈
P

p \in P

. We prove that if P and Q are finite, connected partially ordered sets and

P
P

≅

Q
Q

{P^P} \cong {Q^Q}

then

P
≅
Q

P \cong Q

.
Modular group algebras of totally projective 𝑝-primary groups
Authors: May Warren
Published: June 2010

Let F be a field of characteristic

p
>
0

p > 0

and let G be a totally projective abelian p-group of countable p-length. If

F
G
≅
F
H

FG \cong FH

for some group H, then it is shown that

G
≅
H

G \cong H

.
Separated 𝐺ₐ-actions
Authors: Magid Andy R.
Published: June 2010

Let X be an open subvariety of an affine variety, i.e. a quasi-affine variety, over an algebraically closed field, and suppose the additive algebraic group

G
a

{G_a}

acts on X. Then a geometric quotient of X by

G
a

{G_a}

exists if and only if every point x of X has a

G
a

{G_a}

-stable open neighborhood U such that the morphism

G
a

×
U
→
U
×
U

{G_a} \times U \to U \times U

which sends (t, u) to (tu, u) has closed image and finite fibres.
Group actions on Q-F-rings
Authors: Pascaud J.-L. , Valette J.
Published: June 2010

Let B be a ring, G a finite group of automorphisms acting on B and

B
G

{B^G}

the fixed subring of B. We give an example of a B which is quasi-Frobenius (Q-F) such that

B
G

{B^G}

is not quasi-Frobenius.
A remark on Schur indices of 𝑝-groups
Authors: Yamada Toshihiko
Published: June 2010

By making use of Hasse’s sum theorem, a simple proof of the following theorem on Schur indices of p-groups is given.
Semiclosed operators in Hilbert space
Authors: Kaufman William E.
Published: June 2010

In a Hilbert space H, an operator C is semiclosed provided that there exists a bounded operator B on H, with range the domain of C, such that CB is bounded. The family of all such operators in H is the smallest family containing all closed operators and itself closed under any one of the following: (1) sums, (2) products, (3) strong limits on domains of closed operators. In fact, every algebraic combination of closed operators in H is the sum of two closed one-to-one operators with the same domain and closed ranges.
Interpolation in 𝐻^{𝑝}-spaces
Authors: Øyma Knut
Published: June 2010

We prove that when we solve the classical interpolation problem in

H
p

{H^p}

, we can also interpolate the first few derivatives at each point. We also study interpolating functions of minimal norm.
An oscillation theorem for characteristic initial value problems for nonlinear hyperbolic equations
Authors: Yoshida Norio
Published: June 2010

The nonlinear hyperbolic operator

L
[
u
]
≡

u

x
y

+
c
(
x
,
y
,
u
)

L[u] \equiv {u_{xy}} + c(x,y,u)

is studied and sufficient conditions are given that all solutions of the characteristic initial value problem for

u
L
[
u
]
⩽
0

uL[u] \leqslant 0

are oscillatory in

(
0
,
∞
)
×
(
0
,
∞
)

(0,\infty ) \times (0,\infty )

.
An addendum to: “On generating distributive sublattices of orthomodular lattices ” [Proc. Amer. Math. Soc. 67 (1977), no. 1, 17–22]
Authors: Greechie Richard J.
Published: June 2010

This addendum provides the details of a computation not presented in [1] but needed for a complete proof that Foulis-Holland sets generate distributive sublattices.
On the rigidity of graded algebras
Authors: Coffee Jane Purcell
Published: June 2010

If

G

\mathcal {G}

is a graded algebra (separated and complete) over a field of characteristic zero and

G

\mathcal {G}

is rigid in the category of algebras, then

G

\mathcal {G}

is rigid in the category of filtered algebras.
Values taken many times by Euler’s phi-function
Authors: Wooldridge Kent
Published: June 2010

Let

b
m

{b_m}

denote the number of integers n such that

ϕ
(
n
)
=
m

\phi (n) = m

, where

ϕ
\phi

is Euler’s function. Erdős has proved that there is a

δ
>
0

\delta > 0

such that

b
m

>

m
δ

{b_m} > {m^\delta }

for infinitely many m. In this paper we show that we may take

δ
\delta

to be any number less than

3
−
2

2

3 - 2\sqrt 2

.
The strongly prime radical
Authors: Nicholson W. K. , Watters J. F.
Published: June 2010

Let R denote a strongly prime ring. An explicit construction is given of the radical in R-mod corresponding to the unique maximal proper torsion theory. This radical is characterized in two other ways analogous to known descriptions of the prime radical in rings. If R is a left Ore domain the radical of a module coincides with the torsion submodule.
Holomorphic sectional curvature of quasisymmetric domains
Authors: Zelow R.
Published: June 2010

It is well known that the holomorphic sectional curvature of a bounded symmetric domain is bounded above by a negative constant. In this paper we show that this is true more generally for a quasi-symmetric Siegel domain, and the proof is based on a formula for the curvature from the author’s thesis. The bounded homogeneous domains are, as is well known, biholomorphic to homogeneous Siegel domains and the bounded symmetric domains are biholomorphic to those quasi-symmetric (homogeneous) Siegel domains that satisfy a certain algebraic identity (which we do not need here).
Alexandroff algebras and complete regularity
Authors: Reynolds George
Published: June 2010

We characterize lattice theoretically the topological notion of complete regularity and study the implications of this characterization in the setting of local lattices (

≡
\equiv

complete distributive lattices).
Edelstein’s contractivity and attractors
Authors: Janos Ludvik , Ko Hwei Mei , Tan Kok Keong
Published: June 2010

In this article an example is constructed to show that Theorem 1.1 of L. Janos [Canad. Math. Bull. 18 (1975), no. 5, 675-678] is false. A proper formulation is obtained as follows. Theorem. If

(
X
,
τ
)

(X,\tau )

is a metrizable topological space,

f
:
X
→
X

f:X \to X

is continuous, and

a
∈
X

a \in X

, then the following statements are equivalent: (1) There exists a metric d compatible with

τ
\tau

such that f is contractive with respect to d and the sequence

(

f
n

(
x
)

)

n
=
1

∞

({f^n}(x))_{n = 1}^\infty

converges to a for every

x
∈
X

x \in X

. (2) The singleton {a} is an attractor for compact subsets under f. Furthermore, under this proper formulation, we show that Theorem 3.2 Janos [Proc. Amer. Math. Soc. 61 (1976), 161-175] and Theorem 2.3 Janos and J. L. Solomon [ibid. 71 (1978), 257-262], where the false Theorem 1.1 in [2] has been quoted in the original proofs, remain valid.
Totally geodesic foliations on 3-manifolds
Authors: Johnson David L. , Whitt Lee B.
Published: June 2010

If M is a compact 3-manifold, it is known that M can be foliated by 2-manifolds. Topological obstructions are given to the geodesibility of such a foliation

F

\mathcal {F}

; that is, to the existence of a Riemannian metric on M making each leaf a totally geodesic submanifold. For example,

π
1

(
M
)

{\pi _1}(M)

must be infinite, and hence the Reeb foliation of

S
3

{S^3}

is not geodesible.
One-sided cluster-set theory in a polydisc
Authors: Childress C. L. , Csordas G. L.
Published: June 2010

In this paper, we develop a technique which reduces the investigation of the boundary behavior of a single function f in

H
∞

(

U
n

)
,
n
>
1

{H^\infty }({U^n}),n > 1

, to the study of the cluster sets of a sequence of functions in

H
∞

(
U
)

{H^\infty }(U)

. We also demonstrate the significance and usefulness of one-sided cluster-set theory.
A characterization of smooth functions defined on a Banach space
Authors: Hain Richard M.
Published: June 2010

A sufficient condition for a function defined on a Banach space to be

C
k

{C^k}

is given. This enables us to characterize the

C
∞

{C^\infty }

functions from one Banach space into another Banach space as those functions that, for each positive integer m, have the property that the composition of the function with each

C
∞

{C^\infty }

function from

R

m

{{\mathbf {R}}^m}

into the domain of the function is

C
∞

{C^\infty }

.
Smooth, compact operators
Authors: Hennefeld Julien
Published: June 2010

It is a result of Holub’s [Math. Ann. 201 (1973), 157-163], that for T a compact operator on a real Hilbert space, T is smooth

⇔

‖

T

x
1

‖

=

‖

T

x
2

‖

=

‖
T
‖

\Leftrightarrow \left \| {T{x_1}} \right \| = \left \| {T{x_2}} \right \| = \left \| T \right \|

for some

‖

x
1

‖

=

‖

x
2

‖

=
1

\left \| {{x_1}} \right \| = \left \| {{x_2}} \right \| = 1

implies

x
1

=
±

x
2

{x_1} = \pm \;{x_2}

. We extend this characterization of smooth, compact operators to a large class of Banach spaces, including

l
p

,

L
p

[
0
,
1
]

{l_p},{L_p}[0,1]

, and

d
(
a
,
p
)

d(a,p)

, with

1
>
p
>
∞

1 > p > \infty

. We show that for this same class of Banach spaces, one dimensional, norm one functionals in

K

(
X

)
∗

K{(X)^\ast }

must be extremal. We also present examples of spaces for which Holub’s condition does not characterize smooth, compact operators.
Uniform closures of Fourier-Stieltjes algebras
Authors: Chou Ching
Published: June 2010

Let H be a closed normal subgroup of a locally compact group G. Assume that f is a continuous function on G such that it is constant on the cosets of H in G and it can be approximated uniformly by coefficient functions of unitary representations of G. We show that f can be approximated uniformly by coefficient functions of representations of G which are lifted from unitary representations of G/H. For abelian G, our theorem is a conjecture of R. B. Burckel.
A two-coloring inequality for Euclidean two-arrangements
Authors: Simmons Gustavus J. , Wetzel John E.
Published: June 2010

We prove that for any properly two-colored arrangement of lines in the Euclidean plane having, say, r red and g green regions with

r
⩾
g

r \geqslant g

, the inequality
\[

r
⩽
2
g
−
2
−

∑
P

(
λ
(
P
)
−
2
)

r \leqslant 2g - 2 - \sum \limits _P {(\lambda (P) - 2)}

\]
holds, where for each point P of intersection of the lines,

λ
(
P
)

\lambda (P)

is the number of lines of the arrangement that contain P. This strengthens recent results of Simmons and Grünbaum.
Explicit quantization of the Kepler manifold
Authors: Blattner Robert J. , Wolf Joseph A.
Published: June 2010

Any representation

π
\pi

of

SO

(
2
,
4
)

{\text {SO}}(2,4)

quantizing the Kepler manifold has the same lowest highest weight as the representation

ν
0

{\nu _0}

in the Sternberg-Wolf description of the

U
(
2
,
2
)

U(2,2)

-restriction of the metaplectic representation of

Sp

(
4
;

R

)

{\text {Sp}}(4;{\mathbf {R}})

. Hence, modulo covering groups,

π
\pi

is unitarily equivalent to

ν
0

{\nu _0}

.
An octic reciprocity law of Scholz type
Authors: Buell Duncan A. , Williams Kenneth S.
Published: June 2010

The authors [3] have conjectured that if p and q are distinct primes satisfying
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p identical-to q identical-to 1 left-parenthesis mod 8 right-parenthesis comma left-parenthesis p slash q right-parenthesis Subscript 4 Baseline equals left-parenthesis q slash p right-parenthesis Subscript 4 Baseline equals plus 1 comma">

p
≡
q
≡
1

(
mod

8
)
,

(
p

/

q

)
4

=

(
q

/

p

)
4

=
+
1
,

p \equiv q \equiv 1\quad \pmod 8,\quad {(p/q)_4} = {(q/p)_4} = + 1,

\]
then
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis StartFraction p Over q EndFraction right-parenthesis Subscript 8 Baseline left-parenthesis StartFraction q Over p EndFraction right-parenthesis Subscript 8 Baseline equals StartLayout Enlarged left-brace 1st Row left-parenthesis StartFraction epsilon Subscript p Baseline Over q EndFraction right-parenthesis Subscript 4 Baseline left-parenthesis StartFraction epsilon Subscript q Baseline Over p EndFraction right-parenthesis Subscript 4 Baseline comma if upper N left-parenthesis epsilon Subscript p q Baseline right-parenthesis equals negative 1 comma 2nd Row left-parenthesis negative 1 right-parenthesis Superscript h left-parenthesis p q right-parenthesis slash 4 Baseline left-parenthesis StartFraction epsilon Subscript p Baseline Over q EndFraction right-parenthesis Subscript 4 Baseline left-parenthesis StartFraction epsilon Subscript q Baseline Over p EndFraction right-parenthesis Subscript 4 Baseline comma if upper N left-parenthesis epsilon Subscript p q Baseline right-parenthesis equals plus 1 comma EndLayout">

(

p
q

)

8

(

q
p

)

8

=

{

(

ε
p

q

)

4

(

ε
q

p

)

4

,

if

N
(

ε

p
q

)
=
−
1
,

(
−
1
)

h
(
p
q
)

/

4

(

ε
p

q

)

4

(

ε
q

p

)

4

,

if

N
(

ε

p
q

)
=
+
1
,

{\left ( {\frac {p}{q}} \right )_8}{\left ( {\frac {q}{p}} \right )_8} = \left \{ {\begin {array}{*{20}{c}} {{{\left ( {\frac {{{\varepsilon _p}}}{q}} \right )}_4}{{\left ( {\frac {{{\varepsilon _q}}}{p}} \right )}_4},\quad {\text {if}}\;N({\varepsilon _{pq}}) = - 1,} \hfill \\ {{{( - 1)}^{h(pq)/4}}{{\left ( {\frac {{{\varepsilon _p}}}{q}} \right )}_4}{{\left ( {\frac {{{\varepsilon _q}}}{p}} \right )}_4},\quad {\text {if}}\;N({\varepsilon _{pq}}) = + 1,} \hfill \\ \end {array} } \right .

\]
where

ε
p

{\varepsilon _p}

is the fundamental unit of

Q
(

p

)
,
N
(

ε

p
q

)

Q(\sqrt p ),N({\varepsilon _{pq}})

denotes the norm of the unit

ε

p
q

{\varepsilon _{pq}}

, and

h
(
p
q
)

h(pq)

is the class number of

Q
(

p
q

)

Q(\sqrt {pq} )

. A proof of this conjecture is given, which makes use of results of Bucher [2].
On relaxation of normality in the Fuglede-Putnam theorem
Authors: Furuta Takayuki
Published: June 2010

An operator means a bounded linear operator on a complex Hilbert space. The familiar Fuglede-Putnam theorem asserts that if A and B are normal operators and if X is an operator such that

A
X
=
X
B

AX = XB

, then

A
∗

X
=
X

B
∗

{A^ \ast }X = X{B^ \ast }

. We shall relax the normality in the hypotheses on A and B. Theorem 1. If A and

B
∗

{B^\ast }

are subnormal and if X is an operator such that

A
X
=
X
B

AX = XB

, then

A
∗

X
=
X

B
∗

{A^ \ast }X = X{B^ \ast }

. Theorem 2. Suppose A, B, X are operators in the Hilbert space H such that

A
X
=
X
B

AX = XB

. Assume also that X is an operator of Hilbert-Schmidt class. Then

A
∗

X
=
X

B
∗

{A^ \ast }X = X{B^ \ast }

under any one of the following hypotheses: (i) A is k-quasihyponormal and

B
∗

{B^ \ast }

is invertible hyponormal, (ii) A is quasihyponormal and

B
∗

{B^\ast }

is invertible hyponormal, (iii) A is nilpotent and

B
∗

{B^\ast }

is invertible hyponormal.
Infinitesimal conditions for the equivariance of morphisms of fibered manifolds
Authors: Kosmann-Schwarzbach Yvette
Published: June 2010

We generalize the usual definition of the Lie derivative to the case of a morphism between fibered manifolds which does not necessarily preserve the base. We prove that the vanishing of the Lie derivatives is a necessary and sufficient condition for the equivariance of a morphism of fibered manifolds under the action of a connected Lie group.
An intuitionistic definition of classical natural numbers
Authors: Lifschitz Vladimir
Published: June 2010

A definition of natural numbers in the theory of species is given which allows us to prove intuitionistically all theorems of classical arithmetic. This provides an alternative to the well-known Gödel negative translation.
A note on an inequality due to Greene
Authors: Das K. M.
Published: June 2010

A simpler proof of the Gronwall type inequality due to Greene for a class of integral systems is presented.
On 𝑝-power central polynomials
Authors: Saltman David J.
Published: June 2010

We show in this note that if

p
2

|

n

{p^2}|n

, p is an odd prime and

U
D
(
Q
,
n
)

UD(Q,n)

is the generic division algebra of degree n over the rational number field, then for

z
∈
U
D
(
Q
,
n
)
,

z
p

z \in UD(Q,n),{z^p}

central implies z is central.
The inaccessible invariant subspaces of certain 𝐶₀ operators
Authors: Daughtry John
Published: June 2010

We extend the Douglas-Pearcy characterization of the inaccessible invariant subspaces of an operator on a finite-dimensional Hilbert space to the cases of algebraic operators and certain

C
0

{C_0}

operators on any Hilbert space. This characterization shows that the inaccessible invariant subspaces for such an operator form a lattice. In contrast to D. Herrero’s recent result on hyperinvariant subspaces, we show that quasisimilar operators in the classes under consideration have isomorphic lattices of inaccessible invariant subspaces.
A note on weakly mixing functions
Authors: Glasner S.
Published: June 2010

Every almost periodic function is the uniform limit of polynomials of weakly mixing functions. If

B

\mathcal {B}

and

F

\mathcal {F}

are uniformly closed translation invariant algebras of purely weakly mixing functions and almost periodic functions respectively, and

A

\mathcal {A}

is the algebra generated by

B

\mathcal {B}

and

F

\mathcal {F}

, then every weakly mixing function in

A

\mathcal {A}

belongs to

B

\mathcal {B}

.
Bornological spaces of non-Archimedean valued functions with the compact-open topology
Authors: Govaerts W.
Published: June 2010

Let F be a field with nontrivial non-Archimedean valuation of rank one and let X be a zero-dimensional Hausdorff space. The vector space

C
(
X
,
F
)

C(X,F)

of all continuous functions from X into F is provided with the compact-open topology c. We prove that

C
(
X
,
F
,
c
)

C(X,F,c)

is bornological if and only if X is a Z-replete space.
Homomorphs of knot groups
Authors: Johnson Dennis
Published: June 2010

A simple proof that every group finitely generated by a single conjugacy class is the quotient of a knot group.
On the Chern classes and the Euler characteristic for nonsingular complete intersections
Authors: Aznar Vicente Navarro
Published: June 2010

It is shown that Hirzebruch’s result on the Chern classes of a complete intersection of nonsingular hypersurfaces in general position in

P

N

(

C

)

{{\mathbf {P}}_N}({\mathbf {C}})

, is also valid for any nonsingular complete intersection. Then relations between Euler characteristic, class and Milnor number are pointed out.
Simple example of nonuniqueness for a dual trigonometric series
Authors: Kelman Robert B.
Published: June 2010

A simple nonzero solution is given for the classic homogeneous dual trigonometric equation having the kernel

{
sin
⁡
(
n
+
1

/

2
)
x
}

\{ \sin (n + 1/2)x\}

. The solution’s rate of growth is minimal.