bluuebunny/crossref_metadata_2025 huggingface dataset:
Representation functions of sequences in additive number theory
Authors: Nathanson Melvyn B.
Published: June 2010

Let

A

\mathcal {A}

be a set of nonnegative integers, and let

r
2

A

(
n
)

r_2^\mathcal {A}(n)

denote the number of representations of n in the form

n
=

a
i

+

a
j

n = {a_i} + {a_j}

with

a
i

,

a
j

∈

A

{a_i},{a_j} \in \mathcal {A}

. The set

A

\mathcal {A}

is periodic if

a
∈

A

a \in \mathcal {A}

implies

a
+
m
∈

A

a + m \in \mathcal {A}

for some

m
⩾
1

m \geqslant 1

and all

a
>
N

a > N

. It is proved that if

A

\mathcal {A}

is not periodic, then for every set

B

≠

A

\mathcal {B} \ne \mathcal {A}

there exist infinitely many n such that

r
2

A

(
n
)
≠

r
2

B

(
n
)

r_2^\mathcal {A}(n) \ne r_2^\mathcal {B}(n)

. Moreover, all pairs of periodic sets

A

\mathcal {A}

and

B

\mathcal {B}

are constructed that satisfy

r
2

A

(
n
)
=

r
2

B

(
n
)

r_2^\mathcal {A}(n) = r_2^\mathcal {B}(n)

for all but finitely many n.
Antipodal manifolds in compact symmetric spaces of rank one
Authors: Tirao Juan Alfredo
Published: June 2010

Let M be a compact Riemannian globally symmetric space of rank one. A theorem due to Helgason states that the antipodal manifold

A
x

{A_x}

of a point

x
∈
M

x \in M

is again a symmetric space of rank one. We compute the multiplicities of the restricted roots of

A
x

{A_x}

from those of M, obtaining a very convenient way to determine

A
x

{A_x}

.
The deterministic Itô-belated integral is equivalent to the Lebesgue integral
Authors: Darst R. B. , McShane E. J.
Published: June 2010

Let [a, b) be a bounded half-open interval in the real numbers R. Denote by

I

=

I

[
a
,
b
)

\mathcal {I} = \mathcal {I}[a,b)

and

L

=

L

[
a
,
b
)

\mathcal {L} = \mathcal {L}[a,b)

the sets of functions

f
:
R
→
R

f:R \to R

that are Itô-belated and Lebesgue integrable on [a, b). It is known that

L

⊂

I

\mathcal {L} \subset \mathcal {I}

, so the assertion in the title is substantiated by showing that

I

⊂

L

\mathcal {I} \subset \mathcal {L}

in the sequel.
A theorem of Beurling and Tsuji is best possible
Authors: Yamashita Shinji
Published: June 2010

We shall show that Beurling-Tsuji’s theorem (see Theorem A) is, in a sense, best possible. For each pair

a
,
b
∈
(
0
,
+
∞
)

a, b \in (0, + \infty )

there exists a function f holomorphic in

{

|

z

|

>
1
}

\{ |z| > 1\}

such that the Euclidean area of the Riemannian image of each non-Euclidean disk of non-Euclidean radius a, is bounded by b, and such that f has finite angular limit nowhere on the unit circle.
Positively curved complex submanifolds immersed in a complex space form
Authors: Itoh Takehiro
Published: June 2010

The author gives the partial solution for the conjecture; a Kaehler submanifold in a complex space form of constant holomorphic sectional curvature 1 is totally geodesic if ever its holomorphic sectional curvature is greater than

1
2

\frac {1}{2}

.
A Korovkin-type theorem in locally convex spaces
Authors: Flösser Hans-O.
Published: June 2010

Let E be a locally convex M-space,

∅
≠
M

\emptyset \ne M

a subset. The universal Korovkin-closure of M as well as the sequentially or stationary defined Korovkin-closures coincide with the space of M-harmonic elements and with the uniqueness closure of M.
Lattice properties of integral operators
Authors: Lessner Lawrence
Published: June 2010

In this paper we are concerned with linear operators

K
:
L
→
M

K:L \to M

, where L is a Riesz subspace of measurable, finite a.e. functions and M is the class of all measurable, finite a.e. functions defined by

k
(
x
,
y
)

k(x,y)

is a measurable kernel. It will be shown that the class

I
[
L
,
M
]

I[L,M]

of all such integral operators is a Dedekind complete Riesz space, an ideal and a band in the space of order bounded linear maps

T
:
L
→
M

T:L \to M

.
Representing a closed operator as a quotient of continuous operators
Authors: Kaufman William E.
Published: June 2010

The closed operators in a Hilbert space H are characterized as quotients

A

B

−
1

A{B^{ - 1}}

of continuous operators on H such that the vector sum

A
∗

(
H
)
+

B
∗

(
H
)

{A^\ast }(H) + {B^\ast }(H)

is closed. This leads to the function

Γ
(
A
)
=
A

(
1
−

A
∗

A

)

−
1

/

2

\Gamma (A) = A{(1 - {A^\ast }A)^{ - 1/2}}

, which is shown to map the strictly contractive operators on H reversibly onto the closed densely-defined operators, so as to preserve the selfadjoint and nonnegative conditions.
On the existence of dense analytic subgroups
Authors: Zerling David
Published: June 2010

The purpose of this paper is to establish a necessary and sufficient condition for a connected Lie group to contain a proper dense connected Lie subgroup.
Homoclinic points of mappings of the interval
Authors: Block Louis
Published: June 2010

Let f be a continuous map of a closed interval I into itself. A point

x
∈
I

x \in I

is called a homoclinic point of f if there is a peridoic point p of f such that

x
≠
p
,
x

x \ne p,x

is in the unstable manifold of p, and p is in the orbit of x under

f
n

{f^n}

, where n is the period of p. It is shown that f has a homoclinic point if and only if f has a periodic point whose period is not a power of 2. Furthermore, in this case, there is a subset X of I and a positive integer n, such that

f
n

(
X
)
=
X

{f^n}(X) = X

and there is a topological semiconjugacy of

f
n

:
X
→
X

{f^n}:X \to X

onto the full (one-sided) shift on two symbols.
On the covering dimension of subspaces of product of Sorgenfrey lines
Authors: Fora Ali A.
Published: June 2010

Let S denote the Sorgenfrey line. Then the following results are proved in this paper: (i) If X is a nonempty subspace of

S

ℵ
0

{S^{{\aleph _0}}}

, then

dim
⁡
X
=
0

\dim X = 0

. (ii) For any nonempty separable space

X
⊂

S

ℵ
0

,
dim
⁡

X
m

=
0

X \subset {S^{{\aleph _0}}},\dim {X^m} = 0

for any cardinal m.
Metrizability of compact sets and continuous selections
Authors: Mägerl G.
Published: June 2010

It is shown that, in two of Michael’s theorems on continuous selections, the condition that the range of the correspondence under consideration be metrizable is not only essential (as known through several counterexamples), but in some sense also necessary. This yields a characterization of metrizability for compact spaces and compact convex sets by means of continuous selections.
A topological note on the Adams spectral sequence based on Morava’s 𝐾-theory
Authors: Yagita Nobuaki
Published: June 2010

In this note, we compute the Hopf algebra

K

(
n

)
∗

(
K
(
n
)
)

K{(n)_ \ast }(K(n))

and consider the Adams spectral sequence of

K

(
n

)
∗

(
−
)

K{(n)_ \ast }( - )

theory.
A lower bound on the number of vertices of a graph
Authors: Kane V. G. , Mohanty S. P.
Published: June 2010

In this note, we derive a lower bound for the number of vertices of a graph in terms of its diameter, d, connectivity k and minimum degree

ρ
\rho

which is sharper than that of Watkins [1] by an amount

2
(
ρ
−
k
)

2(\rho - k)

.
Partitions into chains of a class of partially ordered sets
Authors: Metropolis N. , Rota Gian-Carlo , Strehl Volker , White Neil
Published: June 2010

Let a cube of side k in

R

n

{{\mathbf {R}}^n}

be dissected into

k
n

{k^n}

unit cubes. The collection of all affine subspaces of

R

n

{{\mathbf {R}}^n}

determined by the faces of the unit cubes forms a lattice

L
(
n
,
k
)

L(n,k)

when ordered by inclusion. We explicitly construct a Dilworth partition into chains of

L
(
n
,
k
)

L(n,k)

.
Higher order analogues to the tangential Cauchy-Riemann equations for real submanifolds of 𝐶ⁿ with C.R. singularity
Authors: Harris Gary Alvin
Published: June 2010

An infinite succession of higher order operators are developed for real

C

∞

{\mathcal {C}^\infty }

submanifolds of

C
n

{C^n}

, with possible C.R. singularity, which reduce to the tangential Cauchy-Riemann operator in the case of a C.R. submanifold. Certain known holomorphic approximation and extension results for C.R. submanifolds are then “extended” to the non-C.R. case.
Some remarks on functions of Λ-bounded variation
Authors: Perlman S. , Waterman D.
Published: June 2010

It is shown that if a

Λ

BV

\Lambda {\text {BV}}

function has no external saltus, then its total

Λ
\Lambda

-variation is independent of its values at points of discontinuity, and a function which is equal to the given function at points of continuity cannot have a lesser total

Λ
\Lambda

-variation. Necessary and sufficient conditions are determined for one

Λ

BV

\Lambda {\text {BV}}

space to contain another and for two spaces to be identical.
Morita equivalence of simple Noetherian rings
Authors: Stafford J. T.
Published: June 2010

We show that a simple Noetherian ring of finite global dimension and Krull dimension one is Morita equivalent to a domain.
Geometric estimation of the solution to 𝑥+𝑇𝑥=0 for unbounded densely defined monotone operator 𝑇 in Hilbert space
Authors: Williamson T. E.
Published: June 2010

In recent papers R. Bruck and J. C. Dunn have given convergent schemes for approximating the solution p of

x
+
T
x
=
f

x + Tx = f

for T a monotone mapping on a Hilbert space, with T locally bounded. The present paper derives a geometric fact and uses this in a direct manner to give a scheme applicable to densely defined T. The scheme is computable with decreasing error estimates without any assumptions of boundedness. The convergence of the scheme to the solution p is proven under the weak condition that

‖

x
n

+
T

x
n

‖

\left \| {{x_n} + T{x_n}} \right \|

grow no faster than

n

1

/

2

{n^{1/2}}

.
Separation by finite sets in connected, continuous images of ordered compacta
Authors: Treybig L. B.
Published: June 2010

In this paper we answer a question of Mardešić by showing that if the points x and y lie in a continuum M which is the continuous image of a compact ordered space, but x and y lie in no metric subcontinuum of M, then x and y are separated in M by a finite set.
Multifunctions and cluster sets
Authors: Joseph James E.
Published: June 2010

In this article the notion of cluster set-which has been extensively studied within the framework of real and analytic function theory and to some extent for arbitrary functions between arbitrary topological spaces-is investigated for multifunctions. We generalize the notion of cluster set, extend and generalize some results for cluster sets of functions, and offer some results for multifunctions which are new for functions. In the last section, several compactness generalizations are characterized in terms of multifunctions and cluster sets.
Almost all 1-set contractions have a fixed point
Authors: Butler G. J.
Published: June 2010

The 1-set contractions and strict set contractions of a bounded, closed, convex subset C of a Banach space X are generalizations of the nonexpansive mappings and the Banach contractions of C, defined in terms of the measure of noncompactness of bounded subsets of X. Vidossich has shown that “almost all” nonexpansive mappings of C into itself have fixed points. In this note we establish a similar generic result for the 1-set contractions of C.
On the fundamental groups of negatively curved manifolds with finite volume
Authors: Goto Midori S.
Published: June 2010

We will prove that if M is a complete, simply connected riemannian manifold with sectional curvature K,

a
⩽
K
>
0

a \leqslant K > 0

, for

a
>
0

a > 0

and

Γ
\Gamma

a properly discontinuous group of isometries of M acting freely on M with volume

(
M

/

Γ
)

(M/\Gamma )

finite, then

M

/

Γ

M/\Gamma

is compact if and only if

Γ
\Gamma

consists of hyperbolic elements.
A nonshrinkable decomposition of 𝑆ⁿ determined by a null sequence of cellular sets
Authors: Daverman Robert J.
Published: June 2010

The result derived is one of existence: there is a decomposition of the n-sphere

S
n

(
n
⩾
5
)

{S^n}(n \geqslant 5)

into points and a null sequence of cellular sets that is not shrinkable. In one form the implicit example leads to a nonmanifold decomposition space closely allied with the nonmanifold “dogbone” space developed by W. T. Eaton.
A PI-algebra which is not PI when an inverse is adjoined
Authors: Indik Robert A.
Published: June 2010

An example is produced of an algebra, embedded in

2
×
2

2 \times 2

matrices over a field, which is not PI when an element’s inverse is formally adjoined. This example is used to show that the generic

2
×
2

2 \times 2

matrices, a domain, has the same property.
A condition equivalent to the solvability of the endomorphism problem for free groups
Authors: Edmunds Charles C.
Published: June 2010

To solve the endomorphism problem for a word W involving n generators of a free group F, it suffices to solve the problem assuming that the images of W involve no more than n generators.
Weak 𝑞-rings with zero singular ideal
Authors: Mohamed Saad , Singh Surjeet
Published: June 2010

A ring R is called a (right) wq-ring if every right ideal not isomorphic to

R
R

{R_R}

is quasi-injective. The main result proved is the following: Let R be a ring with zero singular ideal, then R is a wq-ring if and only if either R is a q-ring, or

R
=

[

0

a
m
p
;
D

D

a
m
p
;
D

]

R = \left [\begin {smallmatrix}0&D\\D&D\end {smallmatrix}\right ]

for some division ring D, or R is such that every right ideal not isomorphic to

R
R

{R_R}

is completely reducible.
Hille-Wintner type comparison theorems for second-order ordinary differential equations
Authors: Butler G. J.
Published: June 2010

Apart from the Sturm theorem, some of the most useful comparison theorems in second-order ordinary linear differential equations are the Taam-Hille-Wintner theorems. In this note we obtain an extension of these theorems to more general nonlinear equations and incidentially settle an open question for the linear case.
An extreme point in 𝐻^{∞}(𝑈²)
Authors: Riesenberg Nathaniel R.
Published: June 2010

In this paper an example of a function

f
∈

H
∞

(

U
2

)

f \in {H^\infty }({U^2})

with

‖
f
‖

∞

=
1

{\left \| f \right \|_\infty } = 1

and
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Underscript upper T squared Endscripts log left-parenthesis 1 minus StartAbsoluteValue f Superscript asterisk Baseline left-parenthesis z right-parenthesis EndAbsoluteValue right-parenthesis d m greater-than negative normal infinity comma z element-of upper T squared comma">

∫

T
2

log
⁡
(
1
−

|

f
∗

(
z
)

|

)
d
m
>
−
∞
,

z
∈

T
2

,

\int _{{T^2}} {\log (1 - |{f^ \ast }(z)|)dm > - \infty ,\quad z \in {T^2}} ,

\]
yet f is an extreme point in the unit ball of

H
∞

{H^\infty }

, is given. For functions

f
∈

H
∞

(

U
1

)

f \in {H^\infty }({U^1})

that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Underscript upper T Endscripts log left-parenthesis 1 minus StartAbsoluteValue f Superscript asterisk Baseline left-parenthesis z right-parenthesis EndAbsoluteValue right-parenthesis d m equals negative normal infinity comma z element-of upper T comma">

∫
T

log
⁡
(
1
−

|

f
∗

(
z
)

|

)
d
m
=
−
∞
,

z
∈
T
,

\int _T {\log (1 - |{f^ \ast }(z)|)dm = - \infty ,\quad z \in T,}

\]
is both necessary and sufficient for f to be an extreme point in

H
∞

{H^\infty }

.
Deformability of a submanifold in a Euclidean space whose image by the Gauss map is fixed
Authors: Muto Yosio
Published: June 2010

In the present paper, deformations of an immersion of an m-dimensional manifold M in Euclidean n-space

R
n

{R^n}

such that the Gauss image is fixed pointwise are studied. We call such deformations admissible deformations. The main theorem gives a necessary and sufficient condition for an immersed manifold to admit nontrivial admissible deformations.
Excess and conjugation in the Steenrod algebra
Authors: Gallant Andrew M.
Published: June 2010

Some formulas concerning conjugation are generalized to certain sub-Hopf-algebras of the Steenrod algebra. A number-theoretic result enables explicit computation of the excess for a certain family of Milnor basis elements. Finally, a family of self-conjugate elements is produced.
Some extensions of the Brock-Carlitz identity
Authors: Cohen M. E. , Sun H. S.
Published: June 2010

The paper deals with a number of generalizations of an identity first introduced by Brock, and subsequently investigated in some detail by Carlitz. The theorem presented in this paper not only extends the formulas of Carlitz, but also shows that a multi-dimensional function satisfies the identity. A result is also deduced regarding the positive nature of the recurrence relation.
Stable range in 𝐴𝑊* algebras
Authors: Handelman David
Published: June 2010

We show all finite

A

W
∗

A{W^\ast }

algebras (and somewhat more general

C
∗

{C^\ast }

algebras) satisfy a stronger property than having 1 in their stable range.
Most similarity orbits are strongly dense
Authors: Hadwin D. W. , Nordgren E. A. , Radjavi Heydar , Rosenthal Peter
Published: June 2010

It is shown that the strong and weak closures of the similarity orbit of an operator on a Banach space always coincide, and a simple characterization of these closures is given. Whenever an operator is not the sum of a scalar and a finite rank operator, its similarity orbit is strongly dense in the set of all bounded linear operators.
The uniqueness class for the Cauchy problem for pseudoparabolic equations
Authors: Rundell William
Published: June 2010

It is shown that the class of functions satisfying

|

u
(
x
,
t
)

|

⩽
M

e

α

|

x

|

|u(x,t)| \leqslant M{e^{\alpha |x|}}

forms a uniqueness class for the Cauchy problem for pseudoparabolic equations. The surprising fact is that, unlike the case of parabolic equations, the constant

α
\alpha

is not arbitrary but depends on the coefficients of the equation.
Ideals of finite codimension in 𝐶[0,1] and 𝐿¹(𝑅)
Authors: Warner C. Robert , Whitley Robert
Published: June 2010

We characterize the ideals of finite codimension in

C
[
0
,
1
]

C[0,1]

and

L
1

(
R
)

{L^1}(R)

.
Tensor products of division rings and finite generation of subfields
Authors: Resco Richard , Small Lance W. , Wadsworth Adrian R.
Published: June 2010

Let D be a division algebra over a field k. It is shown that if

D

⊗
k

D
0

D{ \otimes _k}{D^0}

is Noetherian, then every commutative subfield of D containing k is finitely generated over k. This theorem applies to

D
n

{D_n}

, the quotient division algebra of the nth Weyl algebra, and also to a number of other standard examples of nonalgebraic division algebras.
A multiplier theorem for analytic functions of slow mean growth
Authors: Matheson A.
Published: June 2010

Multipliers into

l
q

{l^q}

spaces are characterized for certain spaces of functions analytic in the unit disk whose p-means

(
0
>
p
⩽
1
)

(0 > p \leqslant 1)

do not grow too rapidly.
Local compactness and simple extensions of discrete spaces
Authors: Herrlich H. , Kannan V. , Rajagopalan M.
Published: June 2010

Hereditarily locally compact spaces are characterized as those locally compact spaces which are simple extensions of discrete spaces.
The distribution of modular representations into blocks
Authors: Burry David W.
Published: June 2010

The p-modular representations of a finite group that are induced from a p-subgroup are investigated. A series of three results describing how these representations are distributed into p-blocks are presented. Several applications are discussed, including the result that there are a finite number of indecomposable p-modular representations (up to equivalence) in a p-block of a group if and only if its defect group is cyclic.
Permutation groups with projective unitary subconstituents
Authors: Weiss Richard
Published: June 2010

Let

Γ
\Gamma

be a finite directed graph with vertex set

V
(
Γ
)

V(\Gamma )

and edge set

E
(
Γ
)

E(\Gamma )

and let G be a subgroup of

aut

(
Γ
)

{\operatorname {aut}}(\Gamma )

which we assume to act transitively on both

V
(
Γ
)

V(\Gamma )

and

E
(
Γ
)

E(\Gamma )

. Suppose that for some prime power q, the stabilizer

G
(
x
)

G(x)

of a vertex x induces on both

{
y

|

(
x
,
y
)
∈
E
(
Γ
)
}

\{ y|(x,y) \in E(\Gamma )\}

and

{
w

|

(
w
,
x
)
∈
E
(
Γ
)
}

\{ w|(w,x) \in E(\Gamma )\}

a group lying between

P
S
U
(
3
,

q
2

)

PSU(3,{q^2})

and

P
Γ
U
(
3
,

q
2

)

P\Gamma U(3,{q^2})

. It is shown that if G acts primitively on

V
(
Γ
)

V(\Gamma )

, then for each edge (x, y), the subgroup of

G
(
x
)

G(x)

fixing every vertex in

{
w

|

(
x
,
w
)

\{ w|(x,w)

or

(
y
,
w
)
∈
E
(
Γ
)
}

(y,w) \in E(\Gamma )\}

is trivial.
On Beurling’s theorem for locally compact groups
Authors: Weit Yitzhak
Published: June 2010

Beurling’s Theorem in spectral analysis of bounded functions on the real line is generalized to a class of semidirect products of locally compact abelian groups.
A direct summand in 𝐻*(𝑀𝑂⟨8⟩,𝑍₂)
Authors: Bahri A. P. , Mahowald M. E.
Published: June 2010

H
∗

(
M
O
⟨
8
⟩
,

Z
2

)

{H^\ast }(MO\langle 8\rangle ,{Z_2})

as a module over the Steenrod algebra is shown to have a direct summand

A

/

/

A
2

⋅
U

A//{A_2} \cdot U

.
The closed socle of an Azumaya algebra
Authors: DeMeyer F. R.
Published: June 2010

If R is a Noetherian ring and A is an Azumaya algebra over R then an ideal

H
(
A
)

H(A)

in R, called the closed socle of A, is defined and it is shown that

H
(
A
)

H(A)

is independent of the representative A in the Brauer group of R. When R is a domain, the behavior of

H
(
A
)

H(A)

under localization and passage to the quotient field is studied, and

H
(
A
)

H(A)

is calculated when R is the affine ring of a real curve.
Complete intersections in 𝐶ⁿ and 𝑅²ⁿ
Authors: Vitulli Marie A.
Published: June 2010

When

C

n

{{\mathbf {C}}^n}

is identified with

R

2
n

{{\mathbf {R}}^{2n}}

in the usual way, algebraic varieties over the complex numbers give rise to varieties over the reals. We ask when a (strict) complete intersection in

C

n

{{\mathbf {C}}^n}

yields a (strict) complete intersection in

R

2
n

{{\mathbf {R}}^{2n}}

. If the original variety V is connected, a necessary and sufficient condition that its image be a complete intersection is that V be irreducible. We give examples that show that without the connectedness assumption the conclusion is false. In the course of proving this result we give an algebraic analogue of a result by Ephraim on germs of complex and the corresponding real analytic varieties. As our methods apply to varieties over the algebraic closure of an arbitrary real closed field the paper is written in this more general setting.
Some transformations of basic hypergeometric series and their applications
Authors: Jain V. K.
Published: June 2010

Using Bailey’s transformation, relations between basic and basic bilateral hypergeometric series are obtained. Some interesting special cases, like identities of Rogers-Ramanujan type, summation theorems for particular basic bilateral hypergeometric series

2

ψ
2

_2{\psi _2}

, are also discussed.
Fixed points and stationary points of dissipative multivalued maps
Authors: Aubin Jean-Pierre , Siegel Jerrold
Published: June 2010

Fixed or stationary points of multivalued maps are seen to exist in the presence of various entropy functions for the map. Generalizations of the Banach-Picard and Caristi fixed point theorems are presented.
Averaging a representation over a subgroup
Authors: Burckel R. B.
Published: June 2010

The purpose of this note is to extend a well-known technique for getting a representation of a quotient group from one of the original group. This is usually done by “integrating” coefficient functions of the representation over the subgroup, i.e., by applying some mean to them. Hence amenability hypotheses are usually made. None are needed here because the relevant coefficient functions belong to the algebra of weakly almost periodic functions (Eberlein [3]), which is always amenable (Ryll-Nardzewski [5]).
A Hurewicz-type theorem for approximate fibrations
Authors: Coram D. S. , Duvall P. F.
Published: June 2010

This paper concerns conditions on point inverses which insure that a mapping between locally compact, separable, metric ANR’s is an approximate fibration. Roughly a mapping is said to be

π
i

{\pi _i}

-movable [respectively,

H
i

{H_i}

-movable] provided that nearby fibers include isomorphically into mutual neighborhoods on

π
i

{\pi _i}

[resp.

H
i

{H_i}

]. An earlier result along this line is that

π
i

{\pi _i}

-movability for all i implies that a mapping is an approximate fibration. The main result here is that for a

U

V
1

U{V^1}

mapping,

π
i

{\pi _i}

-movability for

i
⩽
k
−
1

i \leqslant k - 1

plus

H
k

{H_k}

- and

H

k
+
1

{H_{k + 1}}

-movability imply

π
k

{\pi _k}

-movability of the mapping. Hence a

U

V
1

U{V^1}

mapping which is

H
i

{H_i}

-movable for all i is an approximate fibration. Also, if a

U

V
1

U{V^1}

mapping is

π
i

{\pi _i}

-movable for

i
⩽
k

i \leqslant k

and k is at least as large as the fundamental dimension of any point inverse, then it is an approximate fibration. Finally, a

U

V
1

U{V^1}

mapping

f
:

M
m

→

N
n

f:{M^m} \to {N^n}

between manifolds is an approximate fibration provided that f is

π
i

{\pi _i}

-movable for all

i
⩽
max
{
m
−
n
,

1
2

(
m
−
1
)
}

i \leqslant \max \{ m - n,\tfrac {1}{2}(m - 1)\}

.
Algebraic deformations and triple cohomology
Authors: Fox Thomas F.
Published: June 2010

The fundamental theorems of algebraic deformation theory are shown to hold in the context of enriched triple cohomology. This unifies and generalizes the classical theory.
An asymptotic formula for the Taylor coefficients of automorphic forms
Authors: Wolpert Scott
Published: June 2010

An asymptotic estimate for the lattice of a Fuchsian group with quotient of finite area is discussed. The estimate is used to obtain an asymptotic formula for the Taylor coefficients of holomorphic automorphic forms.
Vector-valued inequalities for Fourier series
Authors: De Francia José L. Rubio
Published: June 2010

Denoting by

S
∗

{S^\ast }

the maximal partial sum operator of Fourier series, we prove that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S Superscript asterisk Baseline left-parenthesis f 1 comma f 2 comma ellipsis comma f Subscript k Baseline comma ellipsis right-parenthesis equals left-parenthesis upper S Superscript asterisk Baseline f 1 comma upper S Superscript asterisk Baseline f 2 comma ellipsis comma upper S Superscript asterisk Baseline f Subscript k Baseline comma ellipsis right-parenthesis">

S
∗

(

f
1

,

f
2

,
…
,

f
k

,
…
)
=
(

S
∗

f
1

,

S
∗

f
2

,
…
,

S
∗

f
k

,
…
)

{S^\ast }({f_1},{f_2}, \ldots ,{f_k}, \ldots ) = ({S^\ast }{f_1},{S^\ast }{f_2}, \ldots ,{S^\ast }{f_k}, \ldots )

is a bounded operator from

L
p

(

l
r

)

{L^p}({l^r})

to itself,

1
>
p
,
r
>
∞

1 > p,r > \infty

. Thus, we extend the theorem of Carleson and Hunt on pointwise convergence of Fourier series to the case of vector valued functions. We give also an application to the rectangular convergence of double Fourier series.
An invariant subspace lattice of order type 𝜔+𝜔+1
Authors: Harrison K. J. , Longstaff W. E.
Published: June 2010

An example is given of a bounded linear operator on a Hilbert space whose lattice of invariant subspaces is totally ordered and is of order-type

ω
+
ω
+
1

\omega + \omega + 1

.
The efficiency of an algorithm of integer programming: a probabilistic analysis
Authors: Lifschitz Vladimir
Published: June 2010

A simple algorithm for solving the knapsack problem is shown to lead to examining, on the average, around

e

2

n

{e^{2\sqrt n }}

vectors out of

2
n

{2^n}

.
Elliptic functions and nonexistence of complete minimal surfaces of certain type
Authors: Chen Chi Cheng
Published: June 2010

It is proved that any complete minimal surfaces in

R

n

(
n
⩾
3
)

{{\mathbf {R}}^n}(n \geqslant 3)

with total curvature

−
4
π

- 4\pi

is conformally equivalent to the complex plane or the punctured plane, just like the case in

R

3

{{\mathbf {R}}^3}

.
Sets with fixed point property for isometric mappings
Authors: Lau Anthony To Ming
Published: June 2010

A subset K of a Banach space E is said to have the fixed point property for isometric mappings (f. p. p.) if there exists z in K such that

U
(
z
)
=
z

U(z) = z

for each isometric mapping U from K onto K. We prove that any bounded closed subsets of E with uniform relative normal structure have the f. p. p. We also prove that if E is either

B

(
H
)

\mathcal {B}(H)

(bounded operators on a Hilbert space H) or

l
∞

(
X
)

{l_\infty }(X)

(bounded functions on X), then E is finite dimensional if and only if each

w
e
a
k

∗

\mathrm {weak}^*

-compact convex subset of E has the f. p. p. This is also equivalent to the convex set of (normal) states on E having the f. p. p.
Property 𝐿 and asymptotic abelianness for 𝑊*-algebras
Authors: Sarian Edward
Published: June 2010

(i) Let

A

\mathcal {A}

be a finite

W
∗

W^*

-algebra acting on a separable Hilbert space and having no abelian direct summand. If

A

\mathcal {A}

is asymptotically abelian, then

A

\mathcal {A}

has property L. (ii) Let

A

\mathcal {A}

be a finite

W
∗

W^*

-algebra acting on a separable Hilbert space. Then

A

⊗
B
(
h
)
,
h

\mathcal {A} \otimes B(h), h

a separable infinite dimensional Hilbert space, is not asymptotically abelian. (iii) Type

I
I

∞

W
∗

\mathrm {II}_\infty W^*

-algebras are not asymptotically abelian. (iv) Noncommutative type I

W
∗

W^*

-algebras are not asymptotically abelian. (v) The type III factor

B

=

P

⊗

A

(
G
)

\mathcal {B} = \mathcal {P} \otimes \mathcal {A}(G)

is not asymptotically abelian.

B

\mathcal {B}

produces uncountably many nonisomorphic nonasymptotically abelian factors of type III and establishes an example of a purely infinite factor that has property L but is not asymptotically abelian.
Absolutely FG spaces
Authors: Stone A. H.
Published: June 2010

This paper gives characterizations of (a) the Hausdorff spaces that are the intersection of an open set and a closed set in every Hausdorff space containing them, (b) the spaces all of whose subspaces have the property in (a). The last extends a theorem of Herrlich, Kannan and Rajagopalan on hereditarily locally compact spaces.
The stability of de Rham currents
Authors: Puta Mircea
Published: June 2010

The purpose of this short note is to give a theorem concerning the action of the diffeomorphism group of a smooth manifold on the space of de Rham currents.
Asymptotic prime divisors and analytic spreads
Authors: McAdam Stephen
Published: June 2010

Let I be an ideal in a Noetherian domain R, and let Î be the integral closure of I. Let

A
^

∗

(
I
)
=

Ass

(
R

/

I
^

n

)

{\hat A^ \ast }(I) = {\text {Ass}}(R/{\hat I^n})

for n large (it being known that for large n this set does not vary with n). Suppose that R satisfies the altitude formula. Then it is shown that

P
∈

A
^

∗

(
I
)

P \in {\hat A^ \ast }(I)

if and only if height

P
=
l
(

I
P

)

P = l({I_P})

, the analytic spread of

I
P

{I_P}

.
Finite groups and invariant solutions to one-dimensional Plateau problems
Authors: Bindschadler David
Published: June 2010

Let G be a finite group of isometries acting on a complete Riemannian manifold. Suppose that B is a 0-dimensional boundary which is G-invariant. If the order of G divides the product of the cardinality of the orbit and the density of B at each point, then a G-invariant absolutely length minimizing integral current with boundary B can be constructed.
Rationally varying polarizing subalgebras in nilpotent Lie algebras
Authors: Corwin Lawrence , Greenleaf Frederick P.
Published: June 2010

Let

N

\mathfrak {N}

be a nilpotent Lie algebra, with (vector space) dual

N

∗

{\mathfrak {N}^{*}}

. We construct a map

l
↦

M

l

l \mapsto {\mathfrak {M}_l}

from a Zariski-open subset of

N

∗

{\mathfrak {N}^{*}}

to the set of subalgebras of

N

\mathfrak {N}

such that

M

l

{\mathfrak {M}_l}

varies rationally with

l
l

,

M

l

{\mathfrak {M}_l}

is polarizing for

l
l

,

(

Ad

x
)

M

l

=

M

l
′

(

l
′

=

A

d

∗

x
⋅
l
)

({\text {Ad}}x){\mathfrak {M}_l} = {\mathfrak {M}_{l’}}(l’ = {\text {A}}{{\text {d}}^ {*} }x \cdot l)

for all

x
∈
N

x \in N

, and

u
n

k
∞

(
l
)
⊆

M

l

⊆
u
n

k
∞

(
l
)

un{k_\infty }(l) \subseteq {\mathfrak {M}_l} \subseteq un{k_\infty }(l)

, where

u
n

k
∞

(
l
)

un{k_\infty }(l)

and

u
n

k
∞

(
l
)

un{k_\infty }(l)

are the canonical subalgebras introduced by R. Penney.
Integral identities of norms and characterization of inner product spaces
Authors: Stanojević Časlav V. , Suchanek Ana M.
Published: June 2010

Integral identities of norms over compact groups are used to characterize inner product spaces. These integral identities also generalize the Penico-Stanojević [1] integral form of the parallelogram law.
Some properties of closed 1-forms on a special Riemannian manifold
Authors: Tsagas Gr.
Published: June 2010

Let

M
M

be a compact Riemannian manifold whose sectional curvature is strictly negative; then every closed

1
1

-form on

M
M

has a singularity.
Multipliers of group algebras of vector-valued functions
Authors: Tewari U. B. , Dutta M. , Vaidya D. P.
Published: June 2010

Let

G
G

be a locally compact abelian group and

X
X

be a Banach space. Let

L
1

(
G
,
X
)

{L^1}(G,X)

be the Banach space of

X
X

-valued Bochner integrable functions on

G
G

. We prove that the space of bounded linear translation invariant operators of

L
1

(
G
,
X
)

{L^1}(G,X)

can be identified with

L
(
X
,
M
(
G
,
X
)
)

L(X,M(G,X))

, the space of bounded linear operators from

X
X

into

M
(
G
,
X
)

M(G,X)

where

M
(
G
,
X
)

M(G,X)

is the space of

X
X

-valued regular, Borel measures of bounded variation on

G
G

. Furthermore, if

A
A

is a commutative semisimple Banach algebra with identity of norm 1 then

L
1

(
G
,
A
)

{L^1}(G,A)

is a Banach algebra and we prove that the space of multipliers of

L
1

(
G
,
A
)

{L^1}(G,A)

is isometrically isomorphic to

M
(
G
,
A
)

M(G,A)

. It also follows that if dimension of

A
A

is greater than one then there exist translationinvariant operators of

L
1

(
G
,
A
)

{L^1}(G,A)

which are not multipliers of

L
1

(
G
,
A
)

{L^1}(G,A)

.
A generalized pressing-down lemma and isocompactness
Authors: Scott Brian M.
Published: June 2010

A topological generalization of the Pressing-Down Lemma (= Neumer’s Theorem) is formulated and proved. It is shown that this result implies several recent results on isocompactness due to Worrell and Wicke.
The word problem and related results for graph product groups
Authors: Horadam K. J.
Published: June 2010

A graph product is the fundamental group of a graph of groups. Amongst the simplest examples are HNN groups and free products with amalgamation. The torsion and conjugacy theorems are proved for any group presented as a graph product. The graphs over which some graph product has a solvable word problem are characterised. Conditions are then given for the solvability of the word and order problems and also for the extended word problem for cyclic subgroups of any graph product. These results generalise the known ones for HNN groups and free products with amalgamation.
On extending characters
Authors: Milnes Paul
Published: June 2010

Amplifying modestly on recent work of R. W. Henrichs, we indicate that, while the impossibility of extending a continuous character

ψ
\psi

on a subgroup

H
H

of a topological group

G
G

to a character on

G
G

is often due to algebraic problems, the impossibility of extending

ψ
\psi

to a continuous positive definite function on

G
G

can often be viewed as a problem with uniform continuity.
A characterization of the contact Lie algebras
Authors: Gregory Thomas B.
Published: June 2010

We classify the simple finite-dimensional irreducible graded Lie algebras over an algebraically closed field of characteristic

p
>
5

p > 5

which have the form
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Subscript negative 2 Baseline circled-plus upper L Subscript negative 1 Baseline circled-plus upper L 0 circled-plus upper L 1 circled-plus midline-horizontal-ellipsis circled-plus upper L Subscript k Baseline comma k greater-than-or-slanted-equals 3">

L

−
2

⊕

L

−
1

⊕

L
0

⊕

L
1

⊕
⋯
⊕

L
k

,
k
⩾
3

{L_{ - 2}} \oplus {L_{ - 1}} \oplus {L_0} \oplus {L_1} \oplus \cdots \oplus {L_k},k \geqslant 3

, where

L
0

{L_0}

is classical and reductive. We show that any such Lie algebra must be a Lie algebra of the contact series of Lie algebras of Cartan type by showing how the constraints imposed by the hypotheses force the existence of a highest-weight vector in

L

−
1

{L_{ - 1}}

for the representation of

L
0

{L_0}

in

L

−
1

{L_{ - 1}}

induced by the adjoint representation of

L
L

in itself. The existence of this highest-weight vector enables us to conclude that the above-mentioned representation is restricted.

L
L

can then be determined by appeal to an earlier classification theorem.
Totally real Klein bottles in 𝐶²
Authors: Rudin Walter
Published: June 2010

It is proved that

C

2

{{\mathbf {C}}^2}

contains totally real compact submanifolds that are nonorientable, being homeomorphic to a Klein bottle.
The sequential stability index and certain spaces of affine functions
Authors: Jellett F.
Published: June 2010

A theorem of J. M. Anderson and J. E. Jayne on the existence of uniformly closed linear subspaces of the space

C
1

(
X
)

{C^1}(X)

of bounded Baire-

1
1

functions on the compact Hausdorff space

X
X

having specified sequential stability index

α
>
Ω

\alpha > \Omega

is here adapted and extended to yield similar theorems for certain spaces of Baire-affine functions defined on a compact Choquet simplex.
The Bockstein and the Adams spectral sequences
Authors: May J. P. , Milgram R. J.
Published: June 2010

We show that, above the appropriate "vanishing line", the Adams spectral sequence of a connective spectrum can be read off from its Bockstein spectral sequence.
When are proper subgroups of LCA groups contained in maximal ones?
Authors: Khan M. A.
Published: June 2010

In this note we determine (1) the class of LCA groups for which every proper closed subgroup is contained in a maximal subgroup, (2) the class of LCA groups for which every proper dense subgroup is contained in a maximal subgroup, and (3) the class for which every proper subgroup is contained in a maximal one. We also determine when both an LCA group and its dual have these properties.
The spectrum of vector bundle flows with invariant subbundles
Authors: Swanson R. C.
Published: June 2010

A vector bundle flow

(

Φ
t

,

ϕ
t

)

({\Phi ^t},{\phi ^t})

on the vector bundle

E
E

over a compact metric space

M
M

induces a one-parameter group

{

Φ
t
#

}

\{ \Phi _t^\# \}

of bounded operators acting on the continuous sections of

E
E

, with infinitesimal generator

L
L

. An example is given by the tangent flow

(
T

ϕ
t

,

ϕ
t

)

(T{\phi ^t},{\phi ^t})

, if

ϕ
t

{\phi ^t}

is a flow on a smooth manifold. In this article, the spectrum of the generator

L
L

is used to study the exponential growth rates of bundle trajectories in the neighborhood of a fixed invariant subbundle, e.g. the tangent bundle of a submanifold of

M
M

. Auxiliary normal and tangential spectra are introduced, and their relationship and fine structure are explored.
On immersions of 𝑘-manifolds in (2𝑘-1)-manifolds
Authors: Li B. H. , Peterson F. P.
Published: June 2010

Let

f
:

M
k

→

N

2
k
−
1

f:{M^k} \to {N^{2k - 1}}

. We prove that

f
f

is homotopic to an immersion.
Pedersen ideal and group algebras
Authors: Hartmann Klaus
Published: June 2010

For a locally compact

T
2

{T_2}

group

G
G

which has an open subgroup of polynomial growth (e.g.,

G
G

a group that has a compact neighbourhood invariant under inner automorphisms or

G
G

a compact extension of a locally compact nilpotent group) the intersection of the Pedersen ideal of the group

C
∗

{C^ * }

-algebra with

L
1

(
G
)

{L^1}(G)

is dense in

L
1

(
G
)

{L^1}(G)

(Theorem 1). For groups with small invariant neighbourhoods this intersection is the smallest dense ideal of

L
1

(
G
)

{L^1}(G)

, and it consists exactly of those

f
∈

L
1

(
G
)

f \in {L^1}(G)

whose "Fourier transform" vanishes outside some (closed) quasicompact subset of

G
^

\hat G

(Theorem 3); the Pedersen ideal of

C
∗

(
G
)

{C^ * }(G)

is described as the set of all

a
∈

C
∗

(
G
)

a \in {C^ * }(G)

for which

{

π
∈

G
^

:
π
(
a
)
≠
0

}

\left \{ {\pi \in \hat G:\pi (a) \ne 0} \right \}

is contained in some (closed) quasicompact subset of

G
^

\hat G

(Theorem 2).
Characterization of (𝑟,𝑠)-adjacency graphs of complexes
Authors: Gardner Marianne , Harary Frank
Published: June 2010

The

(
r
,
s
)

(r,s)

-adjacency graph of a simplicial complex

K
K

has been defined as the graph whose nodes are the

r
r

-cells of

K
K

with adjacency whenever there is incidence with a common

s
s

-cell. The

(
r
,
s
)

(r,s)

-adjacency graphs for

r
>
s

r > s

have been characterized by graph coverings by Dewdney and Harary generalizing the result of Krausz for line-graphs

(
r
=
1
,
s
=
0
)

(r = 1,s = 0)

. We now complete the characterization by handling the case

r
>
s

r > s

.
An invariant for continuous factors of Markov shifts
Authors: Kitchens Bruce
Published: June 2010

Let

Σ
A

{\Sigma _A}

and

Σ
B

{\Sigma _B}

be subshifts of finite type with Markov measures

(
p
,
P
)

(p,P)

and

(
q
,
Q
)

(q,Q)

. It is shown that if there is a continuous onto measure-preserving factor map from

Σ
A

{\Sigma _A}

to

Σ
B

{\Sigma _B}

, then the block of the Jordan form of

Q
Q

with nonzero eigenvalues is a principal submatrix of the Jordan form of

P
P

. If

Σ
A

{\Sigma _A}

and

Σ
B

{\Sigma _B}

are irreducible with the same topological entropy, then the same relationship holds for the matrices

A
A

and

B
B

. As a consequence,

ζ
B

(
t
)

/

ζ
A

(
t
)

{\zeta _B}(t)/{\zeta _A}(t)

, the ratio of the zeta functions, is a polynomial. From this it is possible to construct a pair of equalentropy subshifts of finite type that have no common equal-entropy continuous factor of finite type, and a strictly sofic system that cannot have an equal-entropy subshift of finite type as a continuous factor.
The Riemann integral in constructive mathematics
Authors: Spring David
Published: June 2010

A suitable Riemann integral in one variable is developed for use in constructive mathematics.
Continuity of best approximants
Authors: Landers D. , Rogge L.
Published: June 2010

Let

C
n

{C_n}

,

n
∈

N

n \in {\mathbf {N}}

, be

Φ
\Phi

-closed lattices in an Orlicz-space

L
Φ

(
Ω
,

A

,
μ
)

{L_\Phi }(\Omega , \mathcal {A}, \mu )

and assume that

C
n

{C_n}

increases or decreases to a

Φ
\Phi

-closed lattice

C
∞

{C_\infty }

. Let

f
n

{f_n}

,

n
∈

N

n \in {\mathbf {N}}

, be

A

\mathcal {A}

-measurable real valued functions with

f
n

→
f
μ

{f_n} \to f\mu

-a.e. and

sup

|

f
n

|

∈

L
Φ

\sup |{f_n}| \in {L_\Phi }

. If

g
n

{g_n}

is a best

Φ
\Phi

-approximant of

f
n

{f_n}

in

C
n

{C_n}

it is shown that

lim
_

n
∈

N

g
n

{\underline {\lim } _{n \in {\mathbf {N}}}}{g_n}

and

lim
¯

n
∈

N

g
n

{\overline {\lim } _{n \in {\mathbf {N}}}}{g_n}

are best

Φ
\Phi

-approximants of

f
f

in

C
∞

{C_\infty }

.
The image of the Ahlfors function
Authors: Minda David
Published: June 2010

Let

Ω
\Omega

denote a maximal region on the Riemann sphere for bounded holomorphic functions and

p
∈
Ω

p \in \Omega

. We present a class of examples to show that the complement in the unit disk of the image of the Ahlfors function for

Ω
\Omega

and

p
p

can be a fairly general discrete subset of the unit disk.
A monotonic property for the zeros of ultraspherical polynomials
Authors: Laforgia Andrea
Published: June 2010

It is shown that

λ

x

n
,
k

(
λ
)

\lambda x_{n,k}^{(\lambda )}

increases as

λ
\lambda

increases for

0
>
λ
>
1
,
k
=
1
,
2
,
…
,

[

n
2

]

0 > \lambda > 1,k = 1,2, \ldots ,\left [ {\tfrac {n}{2}} \right ]

, where

x

n
,
k

(
λ
)

x_{n,k}^{(\lambda )}

is the

k

th

k{\text {th}}

positive zero of ultraspherical polynomial

P
n

(
λ
)

(
x
)

P_n^{(\lambda )}(x)

.
A note on a lemma of Shelah concerning stationary sets
Authors: Mekler Alan H. , Pelletier Donald H. , Taylor Alan D.
Published: June 2010

Let

κ
\kappa

be an infinite cardinal, let

I
I

be a nonprincipal ideal on

κ
\kappa

and let

I
+

=
{
X
⊆
κ
:
X
∉
I
}

{I^ + } = \{ X \subseteq \kappa :X \notin I\}

.

S
(
I
)

S(I)

is the following property of ideals: for every

A
∈

I
+

A \in {I^ + }

and every pair of functions

f
,
g

f,g

from

A
A

into

κ
\kappa

such that, for every

α
∈
A

\alpha \in A

,

f
(
a
)
≠
g
(
α
)

f(a) \ne g(\alpha )

, there exists a set

B
⊆
A

B \subseteq A

with

B
∈

I
+

B \in {I^ + }

such that

f
B
∩
g
B
=
∅

fB \cap gB = \emptyset

. We prove that

S
(
I
)

S(I)

holds for every weakly selective ideal

I
I

on any infinite cardinal

κ
\kappa

(including

κ
=
ω

\kappa = \omega

), and that

S
(
I
)

S(I)

holds for every

κ
\kappa

-complete ideal on

κ
\kappa

iff

κ
\kappa

is not strongly inaccessible.
A split action associated with a compact transformation group
Authors: Schwartzman Sol
Published: June 2010

We associate with an effective action of a compact connected Lie group as a pathwise connected space

X
X

a split action of a quotient group

G

/

K

G/K

on the quotient space

X

/

K

X/K

. One application of the main theorem states that if

X
X

is a compact oriented manifold whose principal cohomology class is a cup product of one-dimensional classes then the action of

G
G

on

X
X

splits. We prove this in the differentiate case; the topological case has since been dealt with by Schultz.
Converging factors for continued fractions 𝐾(𝑎_{𝑛}/1), 𝑎_{𝑛}→0
Authors: Gill John
Published: June 2010

Converging factors for continued fractions

K
(

a
n

/

1
)

K({a_n}/1)

are used to enhance convergence either by accelerating the convergence process or by altering the region of convergence if the

a
n

{a_n}

’s are functions of a complex variable. The first results concerning the use of converging factors to accelerate convergence in the important case

a
n

→
0

{a_n} \to 0

are presented in this paper.
On the explicit form of the density of Brownian excursion local time
Authors: Hooghiemstra G.
Published: June 2010

Let

W
_

0
+

(
t
)

\underline W _0^ + (t)

,

0
⩽
t
⩽
1

0 \leqslant t \leqslant 1

, denote Brownian excursion and let

l
_

0
+

(
υ
)

\underline {l} _0^ + (\upsilon )

,

υ
⩾
0

\upsilon \geqslant 0

, be its local time at level

υ
\upsilon

. Starting from a representation of the density of

l
_

0
+

(
υ
)

\underline {l} _0^ + (\upsilon )

as a complex integral we derive an explicit form of this density, written as an infinite series involving the

n
n

-fold convolution of known densities. Finally the result is used as an alternative check of Knight’s result on the same topic.
An inequality for trigonometric polynomials
Authors: Harris Lawrence A.
Published: June 2010

Our purpose is to obtain in an elementary way a sharp estimate on the derivative of a trigonometric polynomial of degree

⩽
n

\leqslant n

at a point

θ
\theta

when the trigonometric polynomial has a known bound at the Chebyshev points and at

θ
\theta

.
Construction of fixed points for asymptotically nonexpansive mappings
Authors: Passty Gregory B.
Published: June 2010

In uniformly convex Banach spaces with Fréchet differentiable norms (e.g.

L
p

{L^p}

,

1
>
p
>
∞

1 > p > \infty

), fixed points for asymptotically nonexpansive mappings are constructed as weak limits of iterates of the mappings themselves or of related mappings.
A nonvariational second order elliptic operator with singular elliptic measure
Authors: Modica Luciano , Mortola Stefano , Salsa Sandro
Published: June 2010

We exhibit an example which proves that the elliptic measure for a second-order operator of the form

Σ

i
,
j
=
1

n

a

i
j

D

i
j

2

\Sigma _{i,j = 1}^n{a_{ij}}D_{ij}^2

with continuous coefficients can be singular with respect to the surface measure on the boundary of a smooth two-dimensional domain.