bluuebunny/crossref_metadata_2025 huggingface dataset:
Asymptotic nonbases which are not subsets of maximal asymptotic nonbases
Authors: Hennefeld Julien
Published: June 2010

Let A be a set of positive integers. If all but a finite number of the positive integers can be written as a sum of h elements of A, then A is called an asymptotic basis of order h. Otherwise, A is called an asymptotic nonbasis of order h. For each

h
⩾
2

h \geqslant 2

, we construct an asymptotic nonbasis of order h which is not a subset of a maximal asymptotic nonbasis of order h.
On a theorem of Furstenberg and the structure of topologically ergodic measures
Authors: Pakula Lewis , Sine Robert
Published: June 2010

An almost everywhere convergence theorem for topologically ergodic measures stated by Furstenberg for homeomorphisms is extended to Markov operators on

C
(
X
)

C(X)

with compact Hausdörff state space. A structure theorem for topologically ergodic measures is obtained in the compact metric case again in the more general setting of Markov operators.
Sticky arcs in 𝐸ⁿ (𝑛≥4)
Authors: Wright David G.
Published: June 2010

Let A and B be arcs in

E
3

{E^3}

, Euclidean 3-space. Then A can be “slipped” off B; i.e., there exists a homeomorphism of

E
3

{E^3}

onto itself, arbitrarily close to the identity, such that

h
(
A
)
∩
B
=
∅

h(A) \cap B = \emptyset

. The purpose of this note is to show that arcs in

E
n

(
n
⩾
4
)

{E^n}(n \geqslant 4)

do not always enjoy this property. The examples depend heavily on a recent result of McMillan.
Deformations of a two-generator purely inseparable field of exponent 1
Authors: Callahan Francis P.
Published: June 2010

This paper gives a discussion of the algebraic deformations of a two-generator purely inseparable field of exponent 1, this being the simplest field having noncommutative deformations. It gives a necessary condition for a 2-cocycle to be integrable and, if it is allowed to adjoin a single separable element to the groundfield, also a sufficient condition for a 2-cocycle to be integrable. The method used is to study certain skew symmetric biderivations associated with the field.
Maximal quotient rings of prime group algebras
Authors: Hannah John , O’Meara K. C.
Published: June 2010

It is shown that a prime nonsingular group algebra KG, where G is a group whose conjugacy classes are countable, has for its maximal right quotient ring either a full linear ring or a simple directly infinite ring. In the case where G is also locally finite only the second type can occur.
The derivative of the atomic function is not in 𝐵^{2/3}
Authors: Belna Charles L. , Muckenhoupt Benjamin
Published: June 2010

H. A. Allen and C. L. Belna have shown that the derivative of the atomic function

A
(
z
)
=
exp
⁡
[
(
z
+
1
)

/

(
z
−
1
)
]

A(z) = \exp [(z + 1)/(z - 1)]

is in

B
p

{B^p}

for

0
>
p
>
2

/

3

0 > p > 2/3

, where

B
p

{B^p}

is the containing Banach space for the Hardy class

H
p

(
0
>
p
>
1
)

{H^p}(0 > p > 1)

. Here we show that

A
′

(
z
)

A’(z)

does not belong to any of the other

B
p

{B^p}

spaces.
Maximal subalgebras of central separable algebras
Authors: Racine M. L.
Published: June 2010

Let A be a central separable algebra over a commutative ring R. A proper R-subalgebra of A is said to be maximal if it is maximal with respect to inclusion. Theorem. Any proper subalgebra of A is contained in a maximal one. Any maximal subalgebra B of A contains a maximal ideal

m

A

\mathfrak {m}A

of A,

m

\mathfrak {m}

a maximal ideal of R, and

B

/

m

A

B/\mathfrak {m}A

is a maximal subalgebra of the central simple

R

/

m

R/\mathfrak {m}

algebra

A

/

m

A

A/\mathfrak {m}A

. More intrinsic characterizations are obtained when R is a Dedekind domain.
The modular group-ring of a finite 𝑝-group
Authors: Johnson D. L.
Published: June 2010

For a finite p-group G and the field k of p elements, we investigate the embedding of G in the group

G
∗

{G^\ast }

of elements of the group-ring kG having coefficient-sum equal to 1. Of particular interest is the question of when G has a normal complement in

G
∗

{G^\ast }

, for in this case simple proofs can be given for a number of diverse known results.
A characterization of the Pedersen ideal of 𝐶𝐷0(𝑇,𝐵₀(𝐻)) and a counter-example
Authors: Gillette R. M. , Taylor D. C.
Published: June 2010

Let T be a locally compact Hausdorff space, H a complex Hilbert space, and A the

C
∗

{C^\ast }

-algebra

C
0

(
T
,

B
0

(
H
)
)

{C_0}(T,{B_0}(H))

. Let

A
0

{A_0}

be the Pedersen ideal of A and

J
A

{J_A}

the two-sided ideal of A consisting of all x having compact support, for which

sup
{
dim
⁡
x
(
t
)
:
t
∈
T
}
>
∞

\sup \{ \dim x(t):t \in T\} > \infty

. It is known that

A
0

⊆

J
A

{A_0} \subseteq {J_A}

, and equality has been conjectured by Pedersen. We give a new characterization of

A
0

{A_0}

which enables us to show that the conjecture is false.
Approximability of the inverse of an operator
Authors: Feintuch Avraham
Published: June 2010

Let A be an invertible operator on a complex Hilbert space

H

\mathcal {H}

. A necessary and sufficient condition is given for

A

−
1

{A^{ - 1}}

to be a weak limit of polynomials in A.
Diophantine sets over 𝑍[𝑇]
Authors: Denef J.
Published: June 2010

Let

Z

[
T
]

{\mathbf {Z}}[T]

be the ring of polynomials with integer coefficients. We prove that every recursively enumerable subset of

Z

[
T
]

{\mathbf {Z}}[T]

is diophantine over

Z

[
T
]

{\mathbf {Z}}[T]

. This extends a theorem of Davis and Putnam which states that every recursively enumerable subset of Z is diophantine over

Z

[
T
]

{\mathbf {Z}}[T]

.
Stable equivalence of uniserial rings
Authors: Fuller K. R. , Haack J. , Hullinger H.
Published: June 2010

It is well known that two basic rings are Morita equivalent if and only if they are isomorphic. Here it is shown that local uniserial rings are stably equivalent in the sense of M. Auslander and I. Reiten in case they are isomorphic modulo certain powers of their radicals. In particular, two commutative local uniserial rings of Loewy length n are stably equivalent if and only if they are isomorphic modulo the [n/2]th power of their radicals.
A cross section theorem and an application to 𝐶*-algebras
Authors: Kallman Robert R. , Mauldin R. D.
Published: June 2010

The purpose of this note is to prove a cross section theorem for certain equivalence relations on Borel subsets of a Polish space. This theorem is then applied to show that cross sections always exist on countably separated Borel subsets of the dual of a separable

C
∗

{C^ \ast }

-algebra.
Orthogonal decomposition of isometries in a Banach space
Authors: Faulkner G. D. , Huneycutt J. E.
Published: June 2010

In this paper the Wold decomposition theorem is proved for a class of isometries in smooth reflexive Banach spaces. The class in particular contains all isometries of

L
p

(
μ
)

{L^p}(\mu )

spaces for arbitrary measures

μ
\mu

.
A class of differential fields with minimal differential closures
Authors: Singer Michael F.
Published: June 2010

We give examples of differential fields which are not differentially closed but which become differentially closed when one adjoins

−
1

\sqrt { - 1}

; differential fields whose differential closures are therefore minimal.
On a result of Osborn
Authors: Wene G. P.
Published: June 2010

The structure of certain semiprimitive rings with involution

∗
\ast

is determined by imposing conditions on the set of

∗
\ast

-symmetric elements and limiting the number of orthogonal

∗
\ast

-symmetric idempotents.
A note on differentiable functions
Authors: Fleissner Richard J. , Foran James
Published: June 2010

This paper provides a proof that the class of those real functions f for which there exists a change of variable g so that

f
∘
g

f \circ g

is differentiable coincides with the class of continuous functions which are of generalized bounded variation in the restricted sense.
A univalent function nowhere semiconformal on the unit circle
Authors: Yamashita Shinji
Published: June 2010

We shall construct a function f holomorphic and univalent in the open unit disk such that f is not semiconformal at any point of the unit circle. It is also shown that f may be extended quasiconformally to the whole extended plane.
An algebra norm on 𝑙² whose restriction to 𝑙¹ is the usual 𝑙¹-norm
Authors: Esterle Jean
Published: June 2010

Let

p
1

{p_1}

, and

p
2

{p_2}

be two real numbers such that

p
2

⩾

p
1

⩾
1

{p_2} \geqslant {p_1} \geqslant 1

. We prove that there exists an algebra norm on

l

p
2

{l^{{p_2}}}

which extends the

l

p
1

{l^{{p_1}}}

-norm if and only if

p
2

⩽
2

p
1

{p_2} \leqslant 2{p_1}

.
Quasitriangular matrices
Authors: Dombrowski J.
Published: June 2010

It is shown that there exist quasitriangular operators which cannot be represented as quasitriangular matrices.
A note on Kellogg’s uniqueness theorem for fixed points
Authors: Talman Louis A.
Published: June 2010

In 1975, R. B. Kellogg gave a condition guaranteeing uniqueness for the fixed point whose existence is insured by the Schauder Theorem. In this note, we indicate how to extend Kellogg’s result to the class of k-set-contractions.
Compact 𝜎-metric Hausdorff spaces are sequential
Authors: Ostaszewski A. J.
Published: June 2010

It is shown that a locally countably compact, regular

T
2

{T_2}

space which may be covered by a countable number of metrizable subspaces is sequential.
Another realcompact, 0-dimensional, non-𝑁-compact space
Authors: Broverman Samuel
Published: June 2010

A refinement of the topology of the plane is constructed which is locally compact, locally countable, 0-dimensional, realcompact, but not N-compact.
A generalization of the Nagumo uniqueness criterion
Authors: Gard Thomas C.
Published: June 2010

The classical Nagumo criterion for uniqueness of solutions of the initial value problem

x
′

=
F
(
t
,
x
)
,
x
(

t
0

)
=

x
0

x’ = F(t,x),x({t_0}) = {x_0}

, assumes continuity of F as well as a modulus of continuity condition involving

1

/

t

1/t

. Recently, it has been shown that

1

/

t

1/t

can be replaced by

α

/

t

\alpha /t

, for

α
>
1

\alpha > 1

, or by

1

/

t
2

1/{t^2}

provided that the continuity condition on F is suitably modified; in each case it is required that

F
(
t
,
x
)

F(t,x)

at least approach a limit at a certain minimal rate as

(
t
,
x
)

(t,x)

tends to the initial value. In this note we extend both of these results, and in so doing, clarify the relationship between the two types of conditions needed.
Note on Brewer’s character sum
Authors: Williams Kenneth S.
Published: June 2010

A very short proof is given of the result
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript x equals 0 Overscript p minus 1 Endscripts left-parenthesis StartFraction left-parenthesis x plus 2 right-parenthesis left-parenthesis x squared minus 2 right-parenthesis Over p EndFraction right-parenthesis equals 0 comma">

∑

x
=
0

p
−
1

(

(
x
+
2
)
(

x
2

−
2
)

p

)

=
0
,

\sum \limits _{x = 0}^{p - 1} {\left ( {\frac {{(x + 2)({x^2} - 2)}}{p}} \right )} = 0,

\]
if

p
≡
5

p \equiv 5

or

7

(
mod

8
)

7 \pmod 8

.
Commutative perfect 𝑄𝐹-1 rings
Authors: Tachikawa Hiroyuki
Published: June 2010

If R is a commutative artinian ring, then it is known that every finitely generated faithful R-module is balanced (i.e. has the double centralizer property) if and only if R is a quasi-Frobenius ring. In this note, constructing new nonbalanced modules we prove that the assumption on R to be artinian can be replaced by the weaker condition that R is perfect.
A note on nonunitary principal series representations
Authors: Kraljević Hrvoje
Published: June 2010

It is proven in a rather elementary way that any nonunitary principal series representation of a semisimple Lie group G is of finite length, having as a trivial consequence that the set of infinitesimal equivalence classes of quasisimple irreducible representations of G with a given infinitesimal character is finite.
Extremal holomorphic imbeddings between the ball and polydisc
Authors: Alexander H.
Published: June 2010

The following problem of Fornaess and Stout is considered: Find, among all polydiscs imbedded in the unit ball, the one which contains the largest ball centered at the origin.
Hypergeometric functions of 2×2 matrix argument are expressible in terms of Appel’s functions 𝐹₄
Authors: Koornwinder Tom , Sprinkhuizen-Kuyper Ida
Published: June 2010

It is proved that the hypergeometric function of

2
×
2

2 \times 2

matrix argument is expressible as a solution of the partial differential equations for Appell’s function

F
4

{F_4}

. As a result the first-mentioned function can be written as a sum of two

F
4

{F_4}

-functions.
La deuxième conjecture de Hirschfeld-Żelazko pour les algèbres de Banach est fausse
Authors: Aupetit Bernard
Published: June 2010

We prove that there exists a noncommutative complex Banach algebra with no quasi-nilpotents elements such that the spectrum function is continuous for the Hausdorff metric.
A nondesuspension theorem for stunted real projective spaces
Authors: Davis Donald M. , Mahowald Mark
Published: June 2010

For certain stunted projective spaces P and positive integers n, it is shown that P cannot be homotopy equivalent to the n-fold suspension of some other complex.
On the homology of weighted homogeneous manifolds
Authors: Wang Kai
Published: June 2010

In this note we produce a formula for the rank of the homology groups of weighted homogeneous manifolds which is derived from Milnor and Orlik’s formula. However, our formula is easier to compute if the weights have many repetitions.
On Darboux’s lemma
Authors: Samelson Hans
Published: June 2010

We resurrect Carathéodory’s proof of Darboux’s lemma (normal form

Σ
d

p
i

d

q
i

\Sigma d{p_i}d{q_i}

for a nondegenerate closed 2-form). The proof is simple and straightforward (after eliminating unnecessary steps) and deserves to be better known. It involves, not surprisingly, the canonical differential equations of Hamilton-Jacobi theory.
Markov partitions are not smooth
Authors: Bowen Rufus
Published: June 2010

The boundaries of the sets in a Markov partition for linear Anosov diffeomorphisms of

T
3

{T^3}

cannot be smooth.
Norm conditions on resolvents of similarities of Hilbert space operators and applications to direct sums and integrals of operators
Authors: Gilfeather Frank
Published: June 2010

Similarities of an operator T are determined so that on certain sets the norm of the resolvents of the similarity satisfy bounding conditions independent of T. The results are applied to show that direct sums and integrals of operators are quasi-similar to operators with spectrum depending only on the spectrum of the summands.
Position of compact hypersurfaces of the 𝑛-sphere
Authors: Wason James R.
Published: June 2010

Let

S
n

{S^n}

be the Euclidean sphere of dimension n. Let p and q be antipodal points on

S
n

{S^n}

, and, for nonnegative h, let

C
(
p
,
h
)
,

C
(
q
,
h
)

C(p,h),\;C(q,h)

be the hyperspheres of constant mean curvature h centered at p and q, respectively. Then any closed hypersurface in

S
n

{S^n}

with mean curvature bounded by h must have a point in the ’tropical’ region bounded by

C
(
p
,
h
)

C(p,h)

and

C
(
q
,
h
)

C(q,h)

.
On the reflection principle in several complex variables
Authors: Webster S. M.
Published: June 2010

The edge-of-the-wedge theorem is used to extend a biholomorphic map across a nondegenerate real analytic boundary in

C

n

{{\mathbf {C}}^n}

under some differentiability assumption at the boundary.
Neighborhoods of the diagonal and strong normality properties
Authors: Shapiro H. L. , Smith F. A.
Published: June 2010

We define the concept of n-even and

ℵ
0

{\aleph _0}

-even covers and show their relationship to collectionwise normality and normality.
The solution of 3𝑦²±2ⁿ=𝑥³
Authors: Rabinowitz Stanley
Published: June 2010

The diophantine equation

(

∗

)

3

y
2

+

2
n

γ
=

x
3

,

with

γ
=
±
1

\begin{equation}\tag {$\ast $} \quad 3{y^2} + {2^n}\gamma = {x^3},\quad {\text {with}}\;\gamma = \pm 1\end{equation}

is solved.
Nice sets of multi-indices
Authors: Madych W. R. , Szeptycki P.
Published: June 2010

Finite sets, A, of n-tuples for which
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis normal upper Sigma Subscript alpha element-of upper A Baseline left-parenthesis product Underscript j equals 1 Overscript n Endscripts StartAbsoluteValue x Subscript j Baseline EndAbsoluteValue Superscript alpha Super Subscript j Superscript Baseline right-parenthesis right-parenthesis Superscript negative p Baseline comma p greater-than 0">

(

Σ

α
∈
A

(

∏

j
=
1

n

|

x
j

|

α
j

)

)

−
p

,
p
>
0

{({\Sigma _{\alpha \in A}}(\prod _{j = 1}^n|{x_j}{|^{{\alpha _j}}}))^{ - p}},p > 0

, is integrable over

R
n

{R^n}

are given a simple characterization. Applications to certain Fourier multiplier theorems are mentioned.
Extension of Privaloff’s theorem to ultraspherical expansions
Authors: Fryant Allan J.
Published: June 2010

Privaloff’s theorem which relates the boundary continuity of

Re
⁡
(
f
)

\operatorname {Re} (f)

to that of f, f analytic on a disk, is extended to ultraspherical expansions.
Bounded sections on a Riemann surface
Authors: Pranger Walter
Published: June 2010

Let X denote a hyperbolic Riemann surface,

ζ
\zeta

a unitary line bundle, and

H
∞

(
ζ
)

{H^\infty }(\zeta )

the Banach space of bounded holomorphic sections of

ζ
\zeta

. If, for a given point

ξ
\xi

in X, the norm of the evaluation functional on

H
∞

(
ζ
)

{H^\infty }(\zeta )

varies continuously with the bundle

ζ
\zeta

, then it is shown that the space of bounded holomorphic sections is dense in the space of holomorphic sections for every unitary line bundle.
Quasi-expectations and amenable von Neumann algebras
Authors: Bunce John W. , Paschke William L.
Published: June 2010

A quasi-expectation of a

C
∗

{C^ \ast }

-algebra A on a

C
∗

{C^\ast }

-subalgebra B is a bounded linear projection

Q
:
A
→
B

Q:A \to B

such that

Q
(
x
a
y
)
=
x
Q
(
a
)
y
∀
x
,
y
∈
B
,
a
∈
A

Q(xay) = xQ(a)y \forall x,y \in B,a \in A

. It is shown that if M is a von Neumann algebra of operators on Hilbert space H for which there exists a quasi-expectation of

B
(
H
)

B(H)

on M, then there exists a projection of norm one of

B
(
H
)

B(H)

on M, i.e. M is injective. Further, if M is an amenable von Neumann subalgebra of a von Neumann algebra N, then there exists a quasi-expectation of N on

M
′

∩
N

M’ \cap N

. These two facts yield as an immediate corollary the recent result of A. Connes that all amenable von Neumann algebras are injective.
The corona theorem as an operator theorem
Authors: Schubert C. F.
Published: June 2010

We provide a short proof of a theorem of W. B. Arveson in operator theory. The conclusion of this theorem is the same as that of the Corona Theorem but the hypotheses are operator theoretic. Our proof yields an exact value for the constant involved. We also comment on this theorem as a new approximation problem.
A fixed point theorem and attractors
Authors: Janos Ludvik , Solomon J. L.
Published: June 2010

We investigate attractors for compact sets by considering a certain quotient space. The following theorem is included. Let

f
:
G
→
G

f:G \to G

, G a closed convex subset of a Banach space, f a mapping satisfying (i) there exists

M
⊂
G

M \subset G

which is an attractor for compact sets under f; (ii) the family

{

f
n

}

n
=
1

∞

\{ {f^n}\} _{n = 1}^\infty

is equicontinuous. Then f has a fixed point.
Brauer groups of linear algebraic groups with characters
Authors: Magid Andy R.
Published: June 2010

Let G be a connected linear algebraic group over an algebraically closed field of characteristic zero. Then the Brauer group of G is shown to be

C
×

(

Q

/

Z

)

(
n
)

C \times {({\mathbf {Q}}/Z)^{(n)}}

where C is finite and

n
=
d
(
d
−
1
)

/

2

n = d(d - 1)/2

, with d the Z-rank of the character group of G. In particular, a linear torus of dimension d has Brauer group

(

Q

/

Z

)

(
n
)

{({\mathbf {Q}}/Z)^{(n)}}

with n as above.
A counterexample in the theory of finite groups
Authors: Sibley David A.
Published: June 2010

Suppose G is a finite group and p and q are distinct odd primes. Let

χ
\chi

be an irreducible character of G and x and y be a p-element and a q-element of G such that

χ
(
x
)
,
χ
(
y
)

\chi (x),\chi (y)

are both irrational. In this situation it is known that G contains an element of order pq. John Thompson has asked whether y must commute with some conjugate of x. We show by example that this need not be the case.
A note on the disintegration of measures
Authors: Berberian S. K.
Published: June 2010

Complements to a theorem of Bourbaki on the disintegration of measures on separated topological spaces.
On a classification of plane domains for Hardy classes
Authors: Kobayashi Shōji
Published: June 2010

For every positive nubmer p, let

O
p

{O_p}

denote the class of plane domains W for which the Hardy class

H
p

(
W
)

{H_p}(W)

contains no nonconstant functions, and

O
p
−

=
∪
{

O
q

:
0
>
q
>
p
}

O_p^ - = \cup \{ {O_q}:0 > q > p\}

. In this paper it is proved that

O
p

{O_p}

strictly contains

O
p
−

O_p^ -

if

p
⩾
1

p \geqslant 1

.
Applications of Andrews’ basic Lauricella transformation
Authors: Bressoud D. M.
Published: June 2010

We view Andrews’ transformation for the fourth basic Lauricella function as a multiple summation analog of Heine’s fundamental transformation for

2

ϕ
1

_2{\phi _1}

. This leads to multiple summation analogs of several classical q-series identities, and a new proof of a recent partition theorem.
Oscillation criteria for second-order differential systems
Authors: Ahmad Shair , Travis C. C.
Published: June 2010

Sufficient conditions for the oscillation of solutions to the differential system

X
(
t
)
+
A
(
t
)
X
(
t
)
=
0

X(t) + A(t)X(t) = 0

are established which are valid when the matrix A is not symmetric. An example is given to demonstrate that a condition known to be sufficient for the oscillation of solutions when A is symmetric is not valid in the nonsymmetric case.
Homomorphisms of lattices of continuous functions
Authors: Mena R. , Roth B.
Published: June 2010

We prove that for Y a compact Hausdorff space, every lattice homomorphism from

C
(
Y
)

C(Y)

to

C
(
X
)

C(X)

which takes each constant function on Y to the same function on X is linear.
The Lebesgue decomposition theorem for partially ordered semigroup-valued measures
Authors: Pavlakos Panaiotis K.
Published: June 2010

The present paper is concerned with partially ordered semigroup-valued measures. Below are given generalizations of the classical Lebesgue Decomposition Theorem. These results can be applied to Stone or

W
∗

{W^ \ast }

algebra-valued positive measures (cf. [3], [12], [13], [14]).
A generalization of a theorem of Tatchell
Authors: Singh Niranjan
Published: June 2010

Necessary and sufficient conditions for

Σ

a
n

ε
n

\Sigma {a_n}{\varepsilon _n}

to be summable

|

A
,

λ
n

|

|A,{\lambda _n}|

, whenever

Σ

a
n

\Sigma {a_n}

is convergent, have been obtained. The sufficiency part of this result has also been improved.
Codimension two submanifolds of positive curvature
Authors: Moore John Douglas
Published: June 2010

In this note it is proven that a compact connected n-dimensional Riemannian manifold of positive curvature, isometrically immersed in

(
n
+
2
)

(n + 2)

-dimensional Euclidean space, is a homotopy sphere if

n
⩾
3

n \geqslant 3

; hence it is homeomorphic to a sphere if

n
⩾
5

n \geqslant 5

.
On the notion of 𝑛-cardinality
Authors: Przymusiński Teodor C.
Published: June 2010

In this paper we introduce and investigate the notion of n-cardinality, which turned out to be useful in constructions involving product spaces and has a number of interesting applications.
Positive derivations on partially ordered linear algebra with an order unit
Authors: Dai Taen Yu , DeMarr Ralph
Published: June 2010

We show that the range of a positive derivation on a Dedekind

σ
\sigma

-complete partially ordered linear algebra with an order unit is a set of generalized nilpotents. With additional assumptions on the algebra, we show that the algebra has an important property similar to a property of the algebra of upper triangular matrices.
An identity on algebras over a Hopf algebra
Authors: Papastavridis Stavros
Published: June 2010

Let A be a connected Hopf algebra which has an associative comultiplication

ψ
:
A
→
A
⊗
A

\psi :A \to A \otimes A

. Let

χ
:
A
→
A

\chi :A \to A

be the canonical conjugation on A. Let M be a graded algebra over the Hopf algebra A. If

x
,
y
∈
M
,
ψ
(
a
)
=
Σ

a
′

⊗
a

x,y \in M,\psi (a) = \Sigma a’ \otimes a

, then we have the identity
\[

a
x
⋅
y
=
Σ

(
−
1

)

deg
⁡
x
⋅
deg
⁡
a

a
′

(
x
⋅
χ
(
a
)
y
)
.

ax \cdot y = \Sigma {( - 1)^{\deg x \cdot \deg a}}a’(x \cdot \chi (a)y).

\]
On the absolute convergence of lacunary Fourier series
Authors: Patadia J. R.
Published: June 2010

Let

f
∈
L
[
−
π
,
π
]

f \in L[ - \pi ,\pi ]

be

2
π

2\pi

-periodic. Noble [6] posed the following problem: if the fulfillment of some property of a function f on the whole interval

[
−
π
,
π
]

[ - \pi ,\pi ]

implies certain conclusions concerning the Fourier series

σ
(
f
)

\sigma (f)

of f, then what lacunae in

σ
(
f
)

\sigma (f)

guarantees the same conclusions when the property is fulfilled only locally? Applying the more powerful methods of approach to this kind of problems, originally developed by Paley and Wiener [7], the absolute convergence of a certain lacunary Fourier series is studied when the function f satisfies some hypothesis in terms of either the modulus of continuity or the modulus of smoothness of order l considered only at a fixed point of

[
−
π
,
π
]

[ - \pi ,\pi ]

. The results obtained here are a kind of generalization of the results due to Patadia [8].
On strongly exposing functionals
Authors: Borwein J. M.
Published: June 2010

Let K be a weakly compact convex set. The recent result of Lau that its strongly exposing functionals form a dense

G
δ

{G_\delta }

is here proved by a modification of Lindenstrauss’s proof that K is the closed convex hull of its strongly exposed points.
The Carathéodory extension theorem for vector valued measures
Authors: Kupka Joseph
Published: June 2010

This paper comprises three advertisements for a known theorem which, the author believes, deserves the title of the Carathéodory extension theorem for vector valued premeasures. Principal among these is a short and transparent proof of Porcelli’s criterion for the weak convergence of a sequence in the Banach space of bounded finitely additive complex measures defined on an arbitrary field, and equipped with the total variation norm. Also, a characterization of the so-called Carathéodory Extension Property is presented, and there is a brief discussion of the relevance of this material to stochastic integration.
A class of mappings containing all continuous and all semiconnected mappings
Authors: Kohli J. K.
Published: June 2010

A function

f
:
X
→
Y

f:X \to Y

is called s-continuous if for each

x
∈
X

x \in X

and each open set V containing

f
(
x
)

f(x)

and having connected complement there is an open set U containing x such that

f
(
U
)
⊂
V

f(U) \subset V

. In this paper basic properties of s-continuous functions are studied; conditions on domain and/or range implying continuity of s-continuous functions are obtained which generalize recent theorems of Jones, Lee and Long on semiconnected functions. Improvements of recent results of Hagan, Kohli and Long concerning the continuity of certain connected functions follow as a consequence. Also characterizations of semilocally connected spaces in terms of s-continuous functions are obtained.
On the homotopy groups of one point union with a bouquet of circles
Authors: Berstein I. , Dror E.
Published: June 2010

This note points out some properties of the higher homotopy groups of

X
∨
K
(
π
,
1
)

X \vee K(\pi ,1)

as modules over

π
\pi

.
Two theorems on the mapping class group of a surface
Authors: Powell Jerome
Published: June 2010

The mapping class group of a closed surface of genus

⩾
3

\geqslant 3

is perfect. An infinite set of generators is given for the subgroup of maps that induce the identity on homology.
Maximal residue difference sets modulo 𝑝
Authors: Buell Duncan A. , Williams Kenneth S.
Published: June 2010

Let

p
≡
1

(
mod

4
)

p \equiv 1 \pmod 4

be a prime. A residue difference set modulo p is a set

S
=
{

a
i

}

S = \{ {a_i}\}

of integers

a
i

{a_i}

such that

(

a
i

p

)
=
+
1

(\frac {{{a_i}}}{p}) = + 1

and

(

a
i

−

a
j

p

)
=
+
1

(\frac {{{a_i} - {a_j}}}{p}) = + 1

for all i and j with

i
≠
j

i \ne j

, where

(

n
p

)

(\frac {n}{p})

is the Legendre symbol modulo p. Let

m
p

{m_p}

be the cardinality of a maximal such set S. The authors estimate the size of

m
p

{m_p}

.
Prime elements and prime sequences in polynomial rings
Authors: Davis Edward D.
Published: June 2010

The central question of this note concerns the existence of prime elements in polynomial rings. In it are established for polynomial rings over arbitrary noetherian rings—insofar as is generally possible—certain results concerning bases for maximal ideals, well known for polynomial rings over fields and principal ideal domains. These results may be interpreted geometrically as theorems about normal (and especially smooth) closed points on ruled schemes.
A counterexample in the factorization of Banach space operators
Authors: Bouldin Richard
Published: June 2010

A counterexample is given which completes the Banach space generalization of a theorem of R. G. Douglas concerning the factorization of Hilbert space operators.
A note on stable equivalence and Nakayama algebras
Authors: Reiten Idun
Published: June 2010

Two artin algebras

Λ
\Lambda

and

Λ
′

\Lambda ’

are said to be stably equivalent if the categories of finitely generated modules modulo projective for

Λ
\Lambda

and

Λ
′

\Lambda ’

are equivalent categories. If

Λ
′

\Lambda ’

is stably equivalent to a Nakayama (i.e. generalized uniserial) algebra

Λ
\Lambda

, we prove that

Λ
\Lambda

and

Λ
′

\Lambda ’

have the same number of nonprojective simple modules. And if

Λ
\Lambda

and

Λ
′

\Lambda ’

are stably equivalent indecomposable Nakayama algebras where each indecomposable projective module has length at least 3, then

Λ
\Lambda

and

Λ
′

\Lambda ’

have the same admissible sequences.
Almost every quasinilpotent Hilbert space operator is a universal quasinilpotent
Authors: Herrero Domingo A.
Published: June 2010

Let Q be a quasinilpotent operator acting on a complex separable infinite dimensional Hilbert space; then either

Q
k

{Q^k}

is compact for some positive integer k, or the closure of the similarity orbit of Q contains every quasinilpotent operator. Analogous results are shown to be true for the Calkin algebra and for nonseparable Hilbert spaces. For the nonseparable case, the analogous result is true for the closed bilateral ideal

J

\mathcal {J}

, strictly larger than the ideal of compact operators, if and only if

J

\mathcal {J}

is not the ideal associated with an

ℵ
0

{\aleph _0}

-regular limit cardinal. For the ideal of compact operators, the problem remains open.
Crumpled cubes that are not highly complex
Authors: Daverman Robert J.
Published: June 2010

It is proved that any crumpled n-cube

C
,
n
⩾
5

C,n \geqslant 5

, whose wildness is contained in an

(
n
−
2
)

(n - 2)

-manifold S in Bd C must be of Type 2, which is to say that its wildness, though possibly complicated, is not incredibly complicated.
A bound on solutions of linear integer equalities and inequalities
Authors: von zur Gathen Joachim , Sieveking Malte
Published: June 2010

Consider a system of linear equalities and inequalities with integer coefficients. We describe the set of rational solutions by a finite generating set of solution vectors. The entries of these vectors can be bounded by the absolute value of a certain subdeterminant. The smallest integer solution of the system has coefficients not larger than this subdeterminant times the number of indeterminates. Up to the latter factor, the bound is sharp.
An internal and an external characterization of convergence spaces in which adherences of filters are closed
Authors: Lowen-Colebunders Eva
Published: June 2010

The purpose of this note is to give necessary and sufficient conditions for a convergence space (X, q) such that for every filter on X its adherence is a closed subset of (X, q). An internal characterization of this property is given by weakening the diagonal condition of Kowalsky. An external characterization is given using a hyperspace structure on the collection of all closed subsets of the given space. It will be shown that a convergence space has closed adherences if and only if the hyperspace is compact.
Poincaré series of modules over local rings
Authors: Levin Gerson
Published: June 2010

There is a well known conjecture, originally made by Kaplansky, that the Poincaré series

P
R
M

(
z
)

P_R^M(z)

of a finitely generated module M over a local ring R is a rational function. Two reductions of this conjecture are made, one to the case where M is artinian (for a fixed R) and the other to the case where R is artinian.
On Robinson’s 1\over2 conjecture
Authors: Barnard Roger W.
Published: June 2010

In 1947, R. Robinson conjectured that if f is in S, i.e. a normalized univalent function on the unit disk, then the radius of univalence of

[
z
f
(
z
)

]
′

/

2

[zf(z)]’/2

is at least

1
2

\tfrac {1}{2}

. He proved in that paper that it was at least .38. The conjecture has been shown to be true for most of the known subclasses of S. This author shows through use of the Grunski inequalities, that the minimum lower bound over the class S lies between .49 and .5.
Curvature of product 3-manifolds
Authors: Wason James R.
Published: June 2010

Let M be a compact product 3-manifold without boundary. Let g be a Riemannian metric on M. If g has everywhere nonpositive sectional curvature, then g is locally diffeomorphic to a product metric. The proof is by the method of pseudoframes.
A pseudo differential operator which shifts the wave front set
Authors: Parenti Cesare , Rodino Luigi
Published: June 2010

The note concerns pseudo differential operators in the classes

L

ρ
,
1

m

,
0
>
ρ
⩽
1

L_{\rho ,1}^m,0 > \rho \leqslant 1

. These operators are pseudo-local, but they can displace the wave front set of distributions, as we show by means of an example in

L

1
,
1

0

L_{1,1}^0

.
Leray-Schauder principles for condensing multivalued mappings in topological linear spaces
Authors: Schöneberg Rainald
Published: June 2010

By establishing the existence of an equivalent fixed point problem it is shown without any recourse to degree theory or to the theory of homotopy-extension-theorems that all fixed point theorems of Leray-Schauder type for condensing (single- or multi-valued) mappings in topological linear spaces can immediately be deduced from the corresponding fixed point theorems of Schauder type.
Antisymmetry and contractive representations of function algebras
Authors: Szymański Waclław
Published: June 2010

In the present paper the antisymmetry of the image of a function algebra under its contractive representation is characterized. A complete solution of this problem is obtained for subnormal contractive representations. Some applications, in particular, to the von Neumann functional calculus, are given.
Boolean algebras without nontrivial onto endomorphisms exist in every uncountable cardinality
Authors: Loats James , Rubin Matatyahu
Published: June 2010

We prove, assuming ZFC, that for every uncountable cardinal

λ
\lambda

, there is a Boolean algebra of cardinality

λ
\lambda

, without onto endomorphisms other than the identity.
The Milnor number of some isolated complete intersection singularities with 𝐶*-action
Authors: Randell Richard
Published: June 2010

We compute the Milnor number of isolated complete intersection singularities defined by weighted homogeneous polynomials of the same type. We use this result to compute the characteristic polynomial of a certain monodromy and thus obtain some information about the link of the singularity. We also discuss the question of when such a complete intersection with specified weights exists.
Fixed points of sequences of locally expansive maps
Authors: Rosen Harvey
Published: June 2010

A stability theorem for fixed points of a uniformly convergent sequence of open, locally expansive maps is obtained.
Two results relating nilpotent spaces and cofibrations
Authors: Lewis Robert H.
Published: June 2010

We first prove a Blakers-Massey Theorem for nilpotent spaces: If (X, A) is an n-connected,

n
⩾
1

n \geqslant 1

, pair of nilpotent spaces, then under suitable conditions the map

π
∗

(
X
,
A
)
→

π
∗

X

/

A

{\pi _ \ast }(X,A) \to {\pi _ \ast }X/A

is an isomorphism in dimension

n
+
1

n + 1

and an epimorphism in dimension

n
+
2

n + 2

. Next, we dualize the well-known fact that if the total space of a fibration is nilpotent, so is the fiber. Our dual theorem can be used to construct new examples of finite nilpotent CW complexes.
On splitting in finite groups
Authors: Wright C. R. B.
Published: June 2010

A splitting criterion due to Šemetkov yields complements to residual normal subgroups in finite solvable groups, as well as splitting conditions for nonsolvable groups.
Hypoellipticity in the complexes of pseudodifferential operators
Authors: Kim Jongsik
Published: June 2010

Sufficient conditions for the pseudodifferential operator defined on a complex to be hypoelliptic are investigated.
Analytic multipliers of the Radon transform
Authors: Peters James V.
Published: June 2010

We define the Radon transform over the real and complex domain, and list some of its simplest properties. For the complex domain

C

n

{{\mathbf {C}}^n}

, a theorem of the Paley-Wiener type is obtained to determine the support of a continuous, integrable function from its Radon transform. The construction requires defining an associated function of the Radon transform for each

z
∈

C

n

z \in {{\mathbf {C}}^n}

. The support of the function is then obtained via analytic multipliers of the associated functions.
Skew-products with simple approximations
Authors: Whitman P. N.
Published: June 2010

Conditions are given in order that the cartesian product of two measure-preserving invertible transformations admits an approximation. A class of skew-product transformations is defined and conditions are given for a member of this class to admit a simple approximation.
The hyperinvariant subspace lattice of a contraction of class 𝐶.₀
Authors: Wu Pei Yuan
Published: June 2010

It is shown that if T is a

C

⋅
0

{C_{ \cdot 0}}

contraction with finite defect indices, then Hyperlat T is (lattice) generated by those subspaces which are either

ker
⁡
ψ
(
T
)

\ker \psi (T)

or ran

ran

ξ
(
T
)

¯

\overline {{\text {ran}}\;\xi (T)}

, where

ψ
\psi

and

ξ
\xi

are scalar-valued inner functions.
Parovičenko’s characterization of 𝛽𝜔-𝜔 implies CH
Authors: van Douwen Eric K. , van Mill Jan
Published: June 2010

Parovičenko characterized

β
ω
−
ω

\beta \omega - \omega

(dually: the field of subsets of

ω
\omega

modulo the finite sets) under CH. We show that his characterization implies CH.
On the central limit theorem in 𝐹-spaces
Authors: Helm Werner E.
Published: June 2010

In this note we improve the known result on the integrability of F-norms with respect to Gaussian measures and obtain a Central Limit Theorem for probability measures on arbitrary separable F-spaces.
Souslin dendrons
Authors: van Mill J. , Wattel E.
Published: June 2010

A dendron is a continuum in which every two distinct points have a separation point. We call a dendron X a Souslin dendron provided that X satisfies the countable chain condition, is not separable and has the additional property that every countable subset of X is contained in a metrizable subcontinuum of X. We prove that the existence of a Souslin line is equivalent to the existence of a Souslin dendron. In addition, each Souslin dendron is a continuous image of some Souslin continuum.
Immersions of semianalytic spaces
Authors: Wells G. S.
Published: June 2010

It is proved that

d
:

Imm

(
V
,
M
)
→
L

d:{\text {Imm}}(V,M) \to L

is a weak homotopy equivalence, where

Imm

(
V
,
M
)

{\text {Imm}}(V,M)

denotes the space of smooth immersions of a compact semianalytic space V into a manifold M, L denotes the space of continuous bundle maps, linear and injective on each fibre, from the Zariski tangent bundle of V to the tangent bundle of M, and d is the differential. This generalizes the Haefliger-Poenaru-Hirsch-Smale immersion theory for compact manifolds.
Bornological spaces of non-Archimedean valued functions with the point-open topology
Authors: Govaerts W.
Published: June 2010

F denotes a nontrivially non-Archimedean valued field with rank one, X an ultraregular space and

C
(
X
,
F
,
p
)

C(X,F,p)

is the vector space

C
(
X
,
F
)

C(X,F)

of all continuous functions from X into F with the topology p of pointwise convergence. We show that

C
(
X
,
F
,
p
)

C(X,F,p)

is a bornological space if and only if X is a Z-replete space. Also, some results are found concerning the compact-open topology c and we make a comparison with that case as studied by Bachman, Beckenstein, Narici and Warner.
Fibered stable compacta have finite homotopy type
Authors: Geoghegan Ross
Published: June 2010

It is proved that a fibered compact metric space having the shape of a CW complex has the homotopy type of that complex, and that its Wall obstruction to finiteness is zero.
Group actions on homology quaternionic projective planes
Authors: Weintraub Steven H.
Published: June 2010

A class of

Z

p

{{\mathbf {Z}}_p}

-actions, resembling well-known actions on the quaternionic projective plane, is defined and studied. The existence of such actions on a closed homology quaternionic projective plane is shown to imply numerical restrictions on the manifold’s Pontrjagin classes. One consequence is that for

p
=
3

p = 3

, or 5, infinitely many smooth manifolds of this type admit no smooth

Z

p

{{\mathbf {Z}}_p}

-actions.
Symmetric graphs with projective subconstituents
Authors: Weiss Richard
Published: June 2010

Let

Γ
\Gamma

be a finite, undirected, connected graph and G a subgroup of

aut

(
Γ
)

{\operatorname {aut}}(\Gamma )

acting transitively on the vertex set of

Γ
\Gamma

such that the stabilizer

G
(
x
)

G(x)

in G of a vertex x contains a normal subgroup which induces a permutation group on the set of vertices adjacent to x isomorphic to

P
S
L
(
n
,
q
)

PSL(n,q)

with

n
⩾
3

n \geqslant 3

. A bound for

|

G
(
x
)

|

|G(x)|

depending only on n and q is shown to exist under certain conditions.
Pseudo-similarity for matrices over a field
Authors: Hartwig R. E. , Hall F. J.
Published: June 2010

We call two square matrices A and B (over a ring) pseudo-similar, if matrices

X
,

X
−

,

X
=

X,{X^ - },{X^ = }

exist, such that

X
−

A
X
=
B
,
X
B

X
=

A
,
X

X
−

X
=
X

{X^ - }AX = B,XB{X^ = }A,X{X^ - }X = X

and

X

X
=

X
=
X

X{X^ = }X = X

. We show that if A and B have the same dimension and if the ring is a field, then pseudo-similarity implies similarity, and hence that pseudo-similarity is an equivalence relation.
Cohomological triviality by spectral methods
Authors: Martínez Juan José
Published: June 2010

In this note, the spectral sequence of a group extension is used to obtain a direct proof of the twins’ criterion for cohomological triviality of modules over a finite group, stated in its strong form.
A generalization of the Riesz-Herglotz theorem on representing measures
Authors: Loeb Peter A.
Published: June 2010

A simple construction is given that obtains maximal representing measures for positive harmonic functions on a domain W as the

w
e
a
k

∗

\mathrm {weak}^*

limits of finite sums of point masses on

[
0
,
+
∞

]
W

{[0, + \infty ]^W}

. This new standard result, new even for the unit disk, is established for very general elliptic differential equations and domains, in fact, for a Brelot harmonic space, using nonstandard analysis.
Capacity and equidistribution for holomorphic maps from 𝐶² to 𝐶²
Authors: Molzon Robert E.
Published: June 2010

The relationship between equidistribution for holomorphic maps and sets of capacity zero are investigated.
A bound for decompositions of 𝑚-convex sets whose LNC points lie in a hyperplane
Authors: Breen Marilyn
Published: June 2010

A set S in

R
d

{R^d}

is said to be m-convex,

m
⩾
2

m \geqslant 2

, if and only if for every m points in S, at least one of the line segments determined by these points lies in S. Let S denote a closed m-convex set in

R
d

{R^d}

, and assume that the set of lnc points of S lies in a hyperplane. Then S is a union of

f
(
m
)

f(m)

or fewer convex sets, where f is defined inductively as follows:

f
(
2
)
=
1
,
f
(
3
)
=
2

f(2) = 1,f(3) = 2

, and

f
(
m
)
=
f
(
m
−
2
)
+
3

f(m) = f(m - 2) + 3

for

m
⩾
4

m \geqslant 4

. Moreover, for

d
⩾
3

d \geqslant 3

, an example reveals that the best bound is no lower than

g
(
m
)

g(m)

, where

g
(
m
)
=
f
(
m
)

g(m) = f(m)

for

2
⩽
m
⩽
5

2 \leqslant m \leqslant 5

and for

m
=
7

m = 7

, and

g
(
m
)
=
g
(
m
−
3
)
+
4

g(m) = g(m - 3) + 4

otherwise.
Nonhomogeneity of products of preimages and 𝜋-weight
Authors: van Douwen Eric K.
Published: June 2010

We prove a general nonhomogeneity result which implies among others (1) if X is a homogeneous Hausdorff space, then

|

X

|

⩽

2

π
(
X
)

|X| \leqslant {2^{\pi (X)}}

; (2) no power of

β
(
ω
)
−
ω

\beta (\omega ) - \omega

, or of

β
Q
−
Q

\beta Q - Q

or of

β
R
−
R

\beta R - R

is homogeneous.
On Baker’s finite basis theorem for congruence distributive varieties
Authors: Burris Stanley
Published: June 2010

This paper contains the simplest, most direct proof of Baker’s Theorem to date together with an easy argument which shows how to find an exponential bound on the number of variables needed in a finite basis.
Expansions associated with nonselfadjoint boundary value problems
Authors: Carlson Robert
Published: June 2010

Eigenfunction expansions are given for a class of non-self-adjoint boundary-value problems. The results apply to systems of ordinary differential equations, some of whose coefficients may be arbitrary bounded Hilbert space operators.
On a theorem of Duren, Shapiro and Shields
Authors: Yamashita Shinji
Published: June 2010

We shall show that, an extension of the theorem of Duren, Shapiro and Shields on the univalence of a function f holomorphic in the unit disk D, still remains of significance, if the power

α
∈
(
0
,
1
)

\alpha \in (0,1)

in
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sup Underscript z element-of upper D Endscripts left-parenthesis 1 minus StartAbsoluteValue z EndAbsoluteValue squared right-parenthesis Superscript alpha Baseline StartAbsoluteValue f left-parenthesis z right-parenthesis slash f prime left-parenthesis z right-parenthesis EndAbsoluteValue">

sup

z
∈
D

(
1
−

|

z

|

2

)
α

|

f
(
z
)

/

f
′

(
z
)

|

{\sup _{z \in D}}{(1 - |z{|^2})^\alpha }|f(z)/f’(z)|

\]
is small enough.
On univalent functions convex in one direction
Authors: Goodman A. W. , Saff E. B.
Published: June 2010

Let

f
(
z
)
=
z
+

Σ
2
∞

a
k

z
k

f(z) = z + \Sigma _2^\infty {a_k}{z^k}

be analytic and univalent in the unit disk

E
:

|

z

|

>
1

E:|z| > 1

and map the disk onto a domain which is convex in the direction of the imaginary axis. We show by example that for

2

−
1
>
r
>
1

\sqrt 2 - 1 > r > 1

, the function

f
(
z
)

f(z)

need not map the disk

|

z

|

>
r

|z| > r

onto a domain convex in the direction of the imaginary axis. We also find the largest domain contained in

f
(
E
)

f(E)

for every normalized

f
(
z
)

f(z)

that maps E onto a domain convex in the direction of the imaginary axis.
On Weyl fractional calculus
Authors: Raina R. K. , Koul C. L.
Published: June 2010

The Weyl fractional calculus is applied in developing the Laplace transform of

t
q

f
(
t
)

{t^q}f(t)

, for all values of q. Also, a generalized Taylor’s formula in Weyl fractional calculus is established. The results are then used in deriving a certain generating function for the H-function of Fox.