bluuebunny/crossref_metadata_2025 huggingface dataset:
TRIBUTES TO JOHN HOPE FRANKLIN:
Authors: Gates Henry Louis
Published: June 2010

When I was twenty, I decided to hitchhike across the African continent, more or less following the line of the Equator, from the Indian Ocean to the Atlantic. I packed only one pair of sandals and one pair of jeans to make room for the three hefty books I had decided to read from cover to cover: Don Quixote, Moby Dick, and From Slavery to Freedom, by John Hope Franklin. I read the latter—the black and white bound third edition of the book—while recovering from a severe bout of amoebic dysentery sailing down the Congo River. It became such a valued reference for me that I kept it, for years, in the bookcase at my bedside.
TRIBUTES TO JOHN HOPE FRANKLIN
Authors: Saville Julie
Published: June 2010

Long before I had the pleasure of making his acquaintance in person, John Hope Franklin's writings were a vital presence in my academic life. His books were some of the earliest sign posts that I encountered when I first ventured into the new and unfamiliar territory of the historian. The Free Negro in North Carolina was critical to the framework of my first research paper in graduate school. The Militant South was required reading in C. Vann Woodward's reading and discussion seminar in Southern history. I turned to Reconstruction: After the Civil War hoping that it would help me put limits to the deepening puzzles of Reconstruction. But perhaps none of these works—important as they are—has influenced the historical imagination as profoundly as what is undoubtedly his most widely read work, From Slavery to Freedom: A History of Negro Americans, first published in 1947. It kept me company over an anxious winter when I prepared for oral exams. I adopted its fifth edition as required reading in the first course that I taught as a graduate student. Known to general and academic readers alike, From Slavery to Freedom does not recount the progressive unfolding of an emancipatory project, even though its title early named what has become a theme central to analysis of the historical experiences of African Americans in the United States. Instead, it locates the emergence of a distinctively brittle racial regime in the United States within the complex contradictions of modern freedom that were set in motion by Atlantic slavery and the slave trade. “It was forces let loose by the Renaissance and the Commercial Revolution,” he writes, “that created the modern institution of slavery and the slave trade” (Franklin 1947, p. 43; 1980, p. 31). There are thus no postwar echoes of NATO triumphalism in Franklin's conception of Atlantic modernity:
A study to evaluate the provision of psychosocial supervision within an Early Intervention team
Authors: Neil Sandra T. , Nothard Sarah , Glentworth David , Stewart Elaine
Published: June 2010

Psychosocial Interventions (PSIs) and PSI supervision underpin the delivery of early interventions for people experiencing psychosis. Early Intervention (EI) teams are relatively new in the NHS and there is currently a lack of empirical research into PSI supervision in this area. This study aimed to elicit staff views of PSI supervision and to identify any unmet supervision needs within a newly developed EI team in the UK. Semi-structured interviews were conducted with 16 multidisciplinary team members. Descriptive statistics and a thematic analysis were used to analyse the responses. The different types of supervision available to team members, gaps in the provision of PSI supervision and aspects that supervisees found helpful and unhelpful about PSI supervision are discussed as are ideas for improving the provision of PSI supervision in EI teams. The limitations of the study and ideas for further research are also outlined.
Interannual variability of mid‐tropospheric CO2 from Atmospheric Infrared Sounder
Authors: Jiang Xun , Chahine Moustafa T. , Olsen Edward T. , Chen Luke L. , Yung Yuk L.
Published: June 2010

Atmospheric Infrared Sounder (AIRS) offers a unique opportunity to investigate the variability of mid‐tropospheric CO2 over the entire globe. In this paper, we use AIRS data to examine the interannual variability of CO2 and find significant correlations between AIRS mid‐tropospheric CO2 and large‐scale atmospheric dynamics. During El Niño events, mid‐tropospheric CO2 over the central Pacific Ocean is enhanced whereas it is reduced over the western Pacific Ocean as a result of the change in the Walker circulation. The variation of AIRS CO2 in the high latitudes of the northern hemisphere is closely related to the strength of the northern hemispheric annular mode. These results contribute to a better understanding of the influence of large‐scale dynamics on tracer distributions.
Temporary Focal Cerebral Ischemia Results in Swollen Astrocytic End-Feet That Compress Microvessels and Lead to Focal Cortical Infarction
Authors: Ito Umeo , Hakamata Yoji , Kawakami Emiko , Oyanagi Kiyomitsu
Published: June 2010

We examined the mechanisms underlying the abrupt onset of the focal infarction in disseminated selective neuronal necrosis (DSNN) after temporary ischemia. Stroke-positive animals were selected according to their stroke-index score during the first 10 minutes after left carotid occlusion performed twice at a 5-hour interval. The animals were euthanized at various times after the second ischemia. Light- and electron-microscopical studies were performed chronologically on the coronal-cut surface of the cerebral cortex at the chiasmatic level, where focal infarction evolved in the maturing DSNN. We counted the number of neurons, astrocytes, and astrocytic processes (APs); measured the areas of end-feet and astrocytes; and counted the numbers of obstructed microvessels and carbon-black-suspension-perfused microvessels (CBSPm). Between 0.5 and 5 hours after ischemia, DSNN matured, with the numbers of degenerated and dead neurons increasing, and those of APs cut-ends decreasing; whereas the area of the end-feet and the numbers of obstructed microvessels increased and those of CBSPm decreased. At 12 and 24 hours after ischemia, the infarction evolved, with the area of end-feet and astrocytic number decreased; whereas the numbers of obstructed microvessels decreased and the CBSPm number increased. The focal infarction evolved by temporary microvascular obstruction because of compression by swollen end-feet.
Spatial and temporal pattern of alpine grassland condition and its response to human activities in Northern Tibet, China
Authors: Gao Q. Z. , Wan Y. F. , Li Y. , Qin X. B. , Jiangcun W. , Xu H. M.
Published: June 2010

The trend in condition of alpine grasslands from 1981 to 2004 in different topographic regions and with different intensities of human activity in Northern Tibet was analysed by using remote sensing data and geographic information system techniques. The results of this study showed that the condition of the alpine grasslands in 2004 varied throughout Northern Tibet. The changes in condition over this period of most of the alpine grasslands (76.7%) were without any significant trend, whereas a larger portion of the remaining area showed significant recovery then underwent significant degradation. Where significant degradation did occur it was mostly on the steeper slopes whereas significant recovery was mostly on the flatter areas (<1° slope). As a result of strong solar radiation, high temperature, drying effects and more grazing activities, alpine grasslands on the sunny slopes had a greater potential for degradation. The special geographic location of Northern Tibet (with an average elevation of 4500 m.a.s.l.) means that alpine grasslands are mostly confined to an elevation ranging from 4500 to 5500 m, where both human and grazing activities were mostly migratory from 1981 to 2004. As a result, by far the majority of the alpine grasslands (90.4%) had either no significant degradation or some or significant recovery between 1981 and 2004. A greater proportion of alpine grasslands at high elevations (above 5000 m) had a significant trend of degradation than at lower elevations. The negative impact of residential areas on alpine grassland condition was smaller than that of roads.
Deformation theory of subspaces in a Riemann space
Authors: Hlavatý V.
Published: June 2010

This paper deals with the infinitesimal transformation (2,1) of a family (

V
m

V_m

) of subspaces

V
m

V_m

in a Riemann space. In §§1–4 the transformation (2,1) is applied on internal objects of a

V
m

V_m

, while in §§5 and 6 the characteristic mixed tensors

K

a
r

…

a
1

v

K_{a_r\dots a_1}^v

(cf. the equation (1,2; 4)) of a

V
m

V_m

are investigated with respect to (2,1). Finally, some applications of the theory are given in §§7 and 8. In particular the statement expressed by the equation (8,10)b is the generalization of the well known Levi-Civita result for

m
=
1

m = 1

, while the statement expressed by the equation (8,10)c generalizes the classical result (for

m
=
1

m = 1

,

n
=
2

n = 2

) by Jacobi.
The algebra of log-summable functions
Authors: Etter Daniel O.
Published: June 2010

The space

L
0

{L_0}

consists of measurable functions

f
f

on

[
0
,
1
]

[0,1]

such that

log
⁡
(
1
+

|

f
(
x
)

|

)

\log (1 + |f(x)|)

is summable on

[
0
,
1
]

[0,1]

, with functions equal almost everywhere identified. The integral defines a quasinorm on

L
0

{L_0}

. With this quasinorm,

L
0

{L_0}

becomes a complete quasinormed linear space, the topology of which is not locally bounded. The quasinorm is plurisubharmonic (subharmonic on one-dimensional complex manifolds).

L
0

{L_0}

is closed under multiplication, and multiplication is continuous. Inversion is not continuous, and the group of invertible elements is not open. There are no proper closed maximal ideals. The resolvent

(
λ
−
f

)

−
1

{(\lambda - f)^{ - 1}}

may exist for all complex

λ
\lambda

, but it cannot be entire.
A class of non-noetherian domains
Authors: Huckaba James A.
Published: June 2010

A new class of non-noetherian domains, called

β
\beta

-domains, are characterized in the first part of this paper. The second part is concerned with deciding when the intersection of a

β
\beta

-domain with a valuation ring is again a

β
\beta

-domain.
Decomposability of finitely presented modules
Authors: Warfield R. B.
Published: June 2010

It is proved that a commutative ring with

1
1

has the property that every finitely presented module is a summand of a direct sum of cyclic modules if and only if it is locally a generalized valuation ring. A Noetherian ring has this property if and only if it is a direct product of a finite number of Dedekind domains and an Artinian principal ideal ring. Any commutative local ring which is not a generalized valuation ring has finitely presented indecomposable modules requiring arbitrarily large numbers of generators.
Examples of nonnormal seminormal operators whose spectra are not spectral sets
Authors: Clancey Kevin F.
Published: June 2010

An example is given of a nonnormal seminormal operator on a Hilbert space whose spectrum is thin (in the sense of von Neumann) and is therefore not a spectral set. It is shown that every nonnormal subnormal operator is the limit of a sequence of hyponormal and nonsubnormal operators.
Extending partial permutation matrices
Authors: Lindner Charles C.
Published: June 2010

Let

M
1

,

M
2

,
⋯
,

M
s

{M_1},\;{M_2}, \cdots ,\;{M_s}

be

n
×
n

n \times n

arrays such that in each

M
i

{M_i}

, each cell is either empty or occupied by a

1
1

. It is shown that if

M
1

+

M
2

+
⋯
+

M
s

{M_1} + {M_2} + \cdots + {M_s}

contains only

1
1

’s, the totality of

1
1

’s is less than or equal to

n
−
1

n - 1

, and the

1
1

’s are in different rows and columns, then the

M
i

{M_i}

’s can be completed to permutation matrices

M
1
′

,
⋯
,

M
s
′

M_1’ , \cdots ,M_s’

so that

M
1
′

+
⋯
+

M
s
′

M_1’ + \cdots + M_s’

is a

(
0
,

1
)

(0,\;1)

-matrix.
Class number in constant extensions of elliptic function fields
Authors: Leitzel James R. C.
Published: June 2010

For

F

/

K

F/K

a function field of genus one having the finite field

K
K

as field of constants and

E
E

the constant extension of degree

n
n

we give explicitly the class number of the field

E
E

as a polynomial expression in terms of the class number of

F
F

and the order of the field

K
K

. Applications are made to determine the degree of a constant extension

E
E

necessary to have a predetermined prime

p
p

occur as a divisor of the class number of the field

E
E

.
Automorphisms of countable primary abelian groups
Authors: Hill Paul
Published: June 2010

It is proved that the automorphism group

A
A

of a countable primary abelian group

G
G

is transitive on certain subsets of subgroups of

G
G

. One such subset of subgroups in case

G
G

is without elements of infinite height is the collection of all basic subgroups of

G
G

with a fixed corank, finite or infinite.
A property of torsion-free modules over left Ore domains
Authors: Van de Water Arthur
Published: June 2010

It is well known that for an integral domain

A
A

, the property that a module is divisible if and only if it is injective is equivalent to the property that

A
A

is a Dedekind domain. In this paper, it is shown that if

A
A

is a left Ore domain, then a torsion-free left

A
A

-module is divisible if and only if it is injective.
A real analogue of the Gel′fand-Neumark theorem
Authors: Ono Tamio
Published: June 2010

Let

A
A

be a real Banach

∗

^{\ast }

-algebra enjoying the following three conditions:
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue EndAbsoluteValue x Superscript asterisk Baseline x StartAbsoluteValue EndAbsoluteValue equals StartAbsoluteValue EndAbsoluteValue x Superscript asterisk Baseline StartAbsoluteValue EndAbsoluteValue StartAbsoluteValue EndAbsoluteValue x StartAbsoluteValue EndAbsoluteValue comma upper S p x Superscript asterisk Baseline x greater-than-over-equals 0">

|

|

x

∗

x

|

|

=

|

|

x

∗

|

|

|

|

x

|

|

,

S
p

x

∗

x
≧
0

||{x^{\ast }}x|| = ||{x^{\ast }}||\;||x||,\;Sp{x^{\ast }}x \geqq 0

, and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue EndAbsoluteValue x Superscript asterisk Baseline StartAbsoluteValue EndAbsoluteValue equals StartAbsoluteValue EndAbsoluteValue x StartAbsoluteValue EndAbsoluteValue left-parenthesis x element-of upper A right-parenthesis">

|

|

x

∗

|

|

=

|

|

x

|

|

(
x
∈
A
)

||{x^{\ast }}|| = ||x||\;(x \in A)

. It is shown, after Ingelstam, Palmer, and Behncke, as a real analogue of the Gelfand-Neumark theorem, that

A
A

is isometrically

∗

^{\ast }

-isomorphic onto a real

C

∗

{C^{\ast }}

-algebra acting on a suitable real (or complex) Hilbert space. The converse is obvious.
The structure and asymptotic behavior of polynomially compact operators
Authors: Gilfeather Frank
Published: June 2010

A. R. Bernstein and A. Robinson proved that every polynomially compact operator in Hilbert space has nontrivial invariant subspaces. This paper gives a structure theorem for these operators. We show that a polynomially compact operator is the finite sum of translates of operators which have the property that a finite power of the operator is compact. Furthermore, the spectrum of polynomially compact operators is completely described. Conditions are given to determine the weak and strong asymptotic behavior of a polynomially compact contraction in Hilbert space.
Complete continuity of the inverse of a positive symmetric operator.
Authors: Fink James P.
Published: June 2010

Let

A
A

be a symmetric positive definite linear transformation defined on a dense subset of a Hilbert space

H
H

, and let

H
A

{H_A}

. be the Hilbert space completion of the domain of

A
A

with respect to the inner product

(
u
,
v

)
A

=
(
A
u
,
v
)

{(u,v)_A} = (Au,v)

. It is shown that the inverse of

A
A

is completely continuous on

H
A

{H_A}

if and only if it is completely continuous on

H
H

.
A note on Moufang Veblen-Wedderburn systems
Authors: Narayana Rao M. L.
Published: June 2010

The purpose of this note is to show that a Veblen-Wedderburn system with multiplicative Moufang identity is a near field if its dimension

d
d

over its kern does not exceed

7
7

.
On the stable homotopy of quaternionic and complex projective spaces.
Authors: Segal David M.
Published: June 2010

Let the image in

H

4
k

(

QP
∞

:
Z
)
=
Z

{H_{4k}}({\operatorname {QP} ^\infty }:Z) = Z

of stable homotopy under the Hurewicz homomorphism be

h
(
k
)
⋅
Z

h(k) \cdot Z

. Using the Adams spectral sequence for the

2
2

-primary stable homotopy of quaternionic and complex projective spaces it is shown that

h
(
k
)

h(k)

is

(
2
k
)
!

(2k)!

if

k
k

is even and is

(
2
k
)
!

/

2

(2k)!/2

if

k
k

is odd.
A generalization of Zariski’s main theorem
Authors: Evans E. Graham
Published: June 2010

This note extends techniques of Peskine and Zariski to prove a generalization of Zariski’s Main Theorem which allows infinite integral extensions of finitely generated rings.
An infinite integral involving Meijer 𝐺-function
Authors: Arora K. L. , Kulshreshtha K.
Published: June 2010

In this note an infinite integral involving Meijer

G
G

-function and confluent hypergeometric functions is evaluated. Some particular cases of this integral are also discussed. The method used is based on operational calculus.
The Jacobson radical of the endomorphism ring of a projective module.
Authors: Ware R. , Zelmanowitz J.
Published: June 2010

In a recently published paper [3], the elements of the Jacobson radical of a ring of row-finite matrices over an arbitrary ring

R
R

are characterized as those matrices with entries in the Jacobson radical of

R
R

which have a vanishing set of column ideals. In this paper, the characterization is extended to include the endomorphism ring of an arbitrary projective module. In the process we offer a greatly simplified proof of the theorem for row-finite matrices.
Another summable 𝐶_{Ω}-group
Authors: Cutler Doyle O.
Published: June 2010

An example is given of a

p
p

-primary Abelian group

G
G

having the following properties:

G
G

is summable; the length of

G
G

is

Ω
\Omega

; the

α
\alpha

th Ulm invariant of

G
G

is one for all

α
>
Ω

\alpha > \Omega

; if

α
>
Ω

\alpha > \Omega

, any

p
α

G

{p^\alpha }G

-high subgroup of

G
G

is countable;

G

/

p
α

G

G/{p^\alpha }G

is countable for all

α
>
Ω

\alpha > \Omega

; and

G
G

is not

p
β

{p^\beta }

-projective for any ordinal

β
\beta

.
Approximating residual sets by strongly residual sets
Authors: Moran D. A.
Published: June 2010

Let

M
M

be a closed topological manifold,

R
R

residual in

M
M

, and

N
N

any neighborhood of

R
R

in

M
M

. The fulfillment by

R
R

of a certain local separation property in

M
M

implies that there exists a topological spine

R
′

R’

of

M
M

such that

N
⊃

R
′

⊃
R

N \supset R’ \supset R

. (Topological spine = strongly residual set.) This local separation property is satisfied whenever

R
R

is an

ANR
\operatorname {ANR}

, or when

dim
⁡
R
≦
dim
⁡
M
−
2

\dim R \leqq \dim M - 2

.
An embedding theorem for homeomorphisms of the closed disc
Authors: Jones Gary D.
Published: June 2010

If

f
f

is an orientation preserving self-homeomorphism of the closed disc

D
D

with the property that if

x
,
y
∈
D
−
N

x,y \in D - N

, where the set of fixed points

N
N

is finite and contained in

D
−
int
⁡
D

D - \operatorname {int} D

, then there exists an arc

A
⊂
D
−
N

A \subset D - N

joining

x
x

and

y
y

such that

f
n

(
A
)

{f^n}(A)

tends to a fixed point as

n
→
±
∞

n \to \pm \infty

, then it is shown that

f
f

can be embedded in a continuous flow on

D
D

.
On the free product of two groups with an amalgamated subgroup of finite index in each factor
Authors: Karrass A. , Solitar D.
Published: June 2010

Let

G
=
(
A
∗
B
;
U
)

G = (A \ast B;U)

where

U
U

is finitely generated and of finite index

≠
1

\ne 1

in both

A
A

and

B
B

. We prove that

G
G

is a finite extension of a free group iff

A
A

and

B
B

are both finite. In particular, this answers in the negative a question of W. Magnus as to whether or not

G
G

can be free. Analogous results are obtained for tree products and HNN groups.
On the semisimplicity of twisted group algebras
Authors: Passman D. S.
Published: June 2010

In this paper we make a number of simple observations on the question of the semisimplicity of twisted group algebras. The results are based for the most part on certain results known for algebraically closed fields and on the behavior of the Jacobson Radical under field extension.
Semiuniform spaces and topological homeomorphism groups
Authors: Fuller R. V.
Published: June 2010

A well-known sufficient condition that a group of homeomorphisms,

H
H

, from a topological space

X
X

onto itself be a topological group relative to the topology of pointwise convergence is that

X
X

be uniformizable and

H
H

be equicontinuous. In this paper we prove an analogous condition in which the space

X
X

is assumed to be only regular instead of completely regular (uniformizable). This is accomplished by means of the concepts of semiuniformity and semiequicontinuity introduced here.
An approximation theorem for \overline∂-closed forms of type (𝑛,𝑛-1)
Authors: Weinstock Barnet M.
Published: June 2010

Let

D
D

be a bounded open set in

C
n

{C^n}

with smooth boundary. Then every closed form of type

(
n
,
n
−
1
)

(n,n - 1)

which is

C
∞

{C^\infty }

on

D
¯

\bar D

can be approximated uniformly on

D
¯

\bar D

by

(
n
,
n
−
1
)

(n,n - 1)

forms which are closed in a neighborhood of

D
¯

\bar D

. If

C
n

−
D

{C^n} - D

is connected these forms can be chosen to be closed in

C
n

{C^n}

. This is applied to prove that a continuous function on the connected boundary of a bounded domain in

C
n

{C^n}

admits a holomorphic extension to the interior if and only if it is a weak solution of the tangential Cauchy-Riemann equations.
On the stability of the functional equation 𝜑[𝑓(𝑥)]=𝑔(𝑥)𝜑(𝑥)+𝐹(𝑥)
Authors: Brydak Dobiesław
Published: June 2010

This paper gives results on the stability of the solutions of

φ
[
f
(
x
)
]
=
g
(
x
)
φ
(
x
)
+
F
(
x
)

\varphi [f(x)] = g(x)\varphi (x) + F(x)

where

f
,
g

f,g

and

F
F

are given functions and

φ
\varphi

is unknown.
Operators from Banach spaces to complex interpolation spaces
Authors: Williams Vernon
Published: June 2010

Given a closed linear operator

A
A

with dense domain in a Banach space

X
X

, M. Schechter [4] utilized the Lebesgue integral to construct a family of bounded linear operators from

X
X

to the Calderón complex interpolation space

(
X
,
D
(
A
)

)
8

{(X,D(A))_8}

[2], where

D
(
A
)

D(A)

, the domain of

A
A

in

X
X

, is a Banach space under the norm
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue EndAbsoluteValue x StartAbsoluteValue EndAbsoluteValue Subscript upper D left-parenthesis upper A right-parenthesis Baseline equals StartAbsoluteValue EndAbsoluteValue x StartAbsoluteValue EndAbsoluteValue plus StartAbsoluteValue EndAbsoluteValue upper A x StartAbsoluteValue EndAbsoluteValue period">

|

|

x

|

|

D
(
A
)

=

|

|

x

|

|

+

|

|

A
x

|

|

.

||x|{|_{D(A)}} = ||x|| + ||Ax||.

\]
In this paper we utilize the complex functional calculus, which provides a more natural setting, to construct a similar family of operators. At the same time we achieve a strengthening of the Schechter result, for in the proof of our theorem we make no use of the adjoint

A
∗

{A^ \ast }

of

A
A

and consequently do not require the domain of

A
A

to be dense in

X
X

. A completely analogous procedure would permit the removal from the Schechter theorem, referred to above, of the hypothesis that the domain of

A
A

is dense in

X
X

.
Some results on expansive mappings
Authors: Williams Richard K.
Published: June 2010

In this paper, expansive mappings are seen as generalizations of expansive homeomorphisms, and known theorems are generalized. The nonexistence of expansive functions on the open unit interval is proven, and a new example of an expansive homeomorphism on the open unit disk is given. Finally, a method for constructing expansive homeomorphisms from expansive mappings is given.
Generalized balayage and a Radon-Nikodým theorem
Authors: Herbert D. J.
Published: June 2010

A simplified proof is given of Doob’s result that a balayage ordered collection of probability measures on a compact Hausdorff space

K
K

yields a

K
K

-valued supermartingale with the measures as marginal distributions. The proof shows further connections with martingale convergence theory.
Concerning product integrals and exponentials
Authors: Davis W. P. , Chatfield J. A.
Published: June 2010

Suppose

S
S

is a linearly ordered set,

N
N

is the set of real numbers,

G
G

is a function from

S
×
S

S \times S

to

N
N

, and all integrals are of the subdivision-refinement type. We show that if

∫
a
b

G
2

=
0

\int _a^b {{G^2} = 0}

and either integral exists, then the other exists and

a
∏

b

(
1
+
G
)
=
exp
⁡

∫
a
b

G

a\prod {^b(1 + G) = \exp \int _a^b G }

. We also show that the bounded variation of

G
G

is neither necessary nor sufficient for

∫
a
b

G
2

\int _a^b {{G^2}}

to be zero.
Pseudo-uniform convexity of 𝐻¹ in several variables
Authors: Hoffmann Laurence D.
Published: June 2010

A convergence theorem of D. J. Newman for the Hardy space

H
1

{H^1}

is generalized to several complex variables. Specifically, in both

H
1

{H^1}

of the polydisc and

H
1

{H^1}

of the ball, weak convergence, together with convergence of norms, is shown to imply norm convergence. As in Newman’s work, approximation of

L
1

{L^1}

by

H
1

{H^1}

is also considered. It is shown that every function in

L
1

{L^1}

of the torus, (or in

L
1

{L^1}

of the boundary of the ball), has a best

H
1

{H^1}

-approximation which, in several variables, need not be unique.
An infinite class of irreducible homology 3-spheres
Authors: Gross Jonathan L.
Published: June 2010

A class of irreducible homology

3
3

-spheres is obtained by pasting together complements of torus knots. Representations of the fundamental groups of these homology

3
3

-spheres into symmetric groups are then used to distinguish the members of an infinite subclass.
An equivalent form of Lévy’s axiom schema
Authors: Jorgensen Murray
Published: June 2010

A generalized notion of ordinal inaccessibility is defined. A characterization of this notion in terms of normal ordinal functions yields as a consequence that a schema analogous to a form of Tarski’s Axiom of Inaccessible Cardinals is equivalent to Lévy’s axiom schema under the axiom of choice.
The Künneth formula and abelian monoids
Authors: Meyer Jean-Pierre
Published: June 2010

A proof is given, of the Künneth formula for ordinary cohomology, using the theory of abelian monoids.
Higher homotopy commutativity and extension of maps
Authors: Williams F. D.
Published: June 2010

Let

X
X

denote the cartesian product of based spaces,

X
=

X
1

×
⋯
×

X
n

X = {X_1} \times \cdots \times {X_n}

, and

A
=

X
1

∨
⋯
∨

X
n

A = {X_1} \vee \cdots \vee {X_n}

, the subspace consisting of their one-point union. Further, let

g
:
A
→
Y

g:A \to Y

be a map, for

Y
Y

any based space. This article develops a criterion for the extendibility of

g
g

to a map

G
:
X
→
Y

G:X \to Y

. The criterion is in terms of higher products which live in the Pontryagin ring of

Ω
Y

\Omega Y

, the loop space of

Y
Y

.
A comparision theorem for Hamiltonian vector fields
Authors: Weinstein Alan , Marsden Jerrold
Published: June 2010

The question of completeness of Hamiltonian systems is investigated for a class of potentials not necessarily bounded below. The result generalizes previous work of W. Gordon and D. Ebin.
On the completeness of Hamiltonian vector fields
Authors: Gordon William B.
Published: June 2010

Sufficient conditions are given for a hamiltonian vector field to be complete which involve bounds on the potential or its gradient.
The spectral radius of a direct integral of operators
Authors: Chow T. R.
Published: June 2010

The purpose of this paper is to give a formula for computing the spectral radius of a direct integral of operators from the numerical radius of its integrand. The direct sum of operators is a special case of our theorem. An example is given where our theorem cannot be applied.
The automorphism group of a finite metacyclic 𝑝-group
Authors: Davitt Richard M.
Published: June 2010

In this paper it is shown that if

G
G

is a finite non-Abelian metacyclic

p
p

-group,

p
≠
2

p \ne 2

, then the order of

G
G

divides the order of the automorphism group of

G
G

.
The nonexistence of maximum solutions of Volterra integral equations.
Authors: Gollwitzer H. E. , Hager R. A.
Published: June 2010

It has been claimed for some time that the scalar Volterra integral equation of the second kind has a maximum solution under rather mild hypotheses. We present and discuss a counterexample to this claim.
Uniqueness of generators of principal ideals in rings of continuous functions
Authors: Canfell M. J.
Published: June 2010

Let

a
R

aR

denote the principal right ideal generated in a ring

R
R

by an element

a
a

. Kaplansky has raised the question: If

a
R
=
b
R

aR = bR

, are

a
a

and

b
b

necessarily right associates? In this note we show that for rings of continuous functions the answer is affirmative if and only if the underlying topological space is zero-dimensional. This gives an algebraic characterization of the topological concept “zero-dimensional". By extending the notion of uniqueness of generators of principal ideals we are able to give an algebraic characterization of the concept “

n
n

-dimensional".
Some 𝑝-adic versions of Polya’s theorem on integer valued analytic functions
Authors: Hilliker D. L. , Straus E. G.
Published: June 2010

It is shown that functions whose values at the positive integers lie in a fixed algebraic number field with exponential growth restrictions on the conjugates and common denominators of these values must be polynomials if they can be represented by functions which are analytic in sufficiently large disks of

p
p

-adic planes.
Rings with the contraction property
Authors: Wickless William J.
Published: June 2010

A ring

R
R

(not necessarily commutative or with unit) has the contraction property iff every ideal of every subring of

R
R

is a contracted ideal. It is shown that

R
R

is a primitive ring with the contraction property iff

R
R

is an absolutely algebraic field. This result, together with the fact that the Jacobson Radical of a ring with the contraction property is nil, shows that a nil semisimple ring with the contraction property is a subdirect sum of absolutely algebraic fields (and is therefore commutative). It is shown that if

R
R

is a torsion free nil ring with the contraction property then

R
2

=
(
0
)

{R^2} = (0)

. It follows that any torsion free ring with the contraction property is the extension of a zero ring and a subdirect sum of absolutely algebraic fields. Also, if

R
R

is a nil ring with the contraction property then

R
2

{R^2}

is torsion as an additive group.
𝐶^{∞}-functions need not be bimeasurable
Authors: Darst R. B.
Published: June 2010

A real valued

C
∞

{C^\infty }

-function

f
f

is constructed on the interval

I
=
[
0
,
1
]

I = [0,1]

such that some Borel subsets of

I
I

are mapped by

f
f

onto non-Borel sets.
Projective modules as fiber bundles
Authors: Evans E. Graham
Published: June 2010

Projective modules over real affine rings,

R
R

, with compact real points,

X
X

, can be considered as fiber bundles over

X
X

by tensoring with the real valued continuous functions on

X
X

. This induces a map

f
:

K
0

(
R
)
→

K
0

(
X
)

f:{K_0}(R) \to {K^0}(X)

, In this article the kernel of

f
f

is determined and an example with nonzero kernel is given.
A note on extensions of free groups by torsion groups
Authors: Hill Paul
Published: June 2010

Under the assumption of the continuum hypothesis, a torsion free group

G
G

is constructed that is the extension of a free group

F
F

by a reduced primary group

T
T

such that

G
G

cannot be embedded in a product of

Z
Z

’s. In particular,

G
G

is not free. This settles a question raised by Griffith.
On the univalence of a certain integral
Authors: Merkes E. P. , Wright D. J.
Published: June 2010

We consider the function

g
(
z
)
=

∫
0
z

[
f
(
t
)

/

t

]
α

d
t

g(z) = \smallint _0^z{[f(t)/t]^\alpha }dt

for

f
f

in the classes of convex, starlike, and close-to-convex univalent functions, and we determine precisely which values of

α
\alpha

yield a close-to-convex function

g
g

.
A new characterization of Dedekind domains
Authors: Johnson E. W. , Lediaev J. P.
Published: June 2010

In this note it is shown that a Noetherian ring

R
R

is a Dedekind domain if every maximal ideal

M
M

of

R
R

satisfies the cancellation law: if

A
A

and

B
B

are nonzero ideals of

R
R

and

M
A
=
M
B

MA = MB

, then

A
=
B

A = B

.
Minimal nonnilpotent solvable Lie algebras
Authors: Stitzinger Ernest L.
Published: June 2010

We shall say that a solvable Lie algebra

L
L

is a minimal nonnilpotent Lie algebra if

L
L

is nonnilpotent but all proper subalgebras of

L
L

are nilpotent. It is shown here that if

L
L

is a minimal nonnilpotent Lie algebra, then

L
L

is the vector space direct sum of

A
A

and

F
F

where

A
A

is an ideal in

L
,
F

L,F

is a one-dimensional subalgebra of

L
L

, either

A
A

is a minimal ideal of

L
L

or the center of

A
A

coincides with the derived algebra,

A
′

A’

, of

A
A

and in either case

F
F

acts irreducibly on

A

/

A
′

A/A’

.
Solution of the Hughes problem for finite 𝑝-groups of class 2𝑝-2.
Authors: Macdonald I. D.
Published: June 2010

In this paper the Hughes conjecture for finite

p
p

-groups is proved in the case of groups which are nilpotent of class

2
p
−
2

2p - 2

.
Compact totally ℋ ordered semigroups
Authors: Carruth J. H. , Clark C. E.
Published: June 2010

Compact totally

H

\mathcal {H}

ordered semigroups are characterized. Each such semigroup is abelian and is, in fact, a closed subsemigroup of an

I
I

-semigroup. Several questions are posed about (algebraic) semigroups which are naturally totally (quasi-) ordered.
Pseudo-complements in posets
Authors: Venkatanarasimhan P. V.
Published: June 2010

In this paper a theory of pseudo-complements is developed for posets (partially ordered sets). The concepts of ideal and semi-ideal are introduced for posets and a few results about them are obtained. These results together with known results about pseudo-complements in distributive lattices lead to the main results. It is proved that if in a pseudo-complemented semilattice or dual semilattice every element is normal, then it is a Boolean algebra. Using this result new proofs for two known theorems are obtained. The existence of maximal ideals in posets is established and it is shown that the dual ideal of dense elements of a poset with 0 is the product of all the maximal dual ideals.
Representations of 𝑙-groups by almost-finite quotient maps
Authors: Chambless Donald A.
Published: June 2010

There are numerous existing methods of embedding an archimedean lattice group into a space of extended-real-valued continuous functions defined on a topological space. In this paper the topological space is constructed using the hull-kernel topology and some prime subgroups of a certain extension of the given group, and the representing functions are described as certain quotient maps. The resulting representation essentially coincides with earlier representations given by B. Vulih and by S. J. Bernau.
Simple zeros of solutions of 𝑛𝑡ℎ-order linear differential equations
Authors: Kim W. J.
Published: June 2010

Let the

n
n

th-order linear differential equation

L
y
=
0

Ly = 0

have a nontrivial solution with

n
n

zeros (counting multiplicities) on an interval

[
α
,
β
]

[\alpha ,\beta ]

. A condition under which

L
y
=
0

Ly = 0

has a solution with

n
n

simple zeros on

[
α
,
β
]

[\alpha ,\beta ]

is established. Also, a new proof is given for a known result concerning an interval of the type

[
α
,
β
)

[\alpha ,\beta )

.
On the perturbability of the asymptotic manifold of a perturbed system of differential equations
Authors: Ladas G. , Lakshmikantham V. , Leela S.
Published: June 2010

We investigate the asymptotic relationship between the solutions of a linear differential system and its perturbed system. Our results depend upon a known result of F. Brauer on asymptotic equilibrium. We also study the asymptotic manifold of solutions of the nonlinear system generated by the solutions of the corresponding linear system.
A product integral representation for an evolution system
Authors: Herod J. V.
Published: June 2010

This paper provides a product integral representation for a nonlinear evolution system. The representation is valid for expansive systems and provides an analysis in the nonexpansive case which is different from ones previously discovered.
On a conjecture of A. J. Hoffman
Authors: Zaks Joseph
Published: June 2010

A

3
3

-polytope

P
P

and four closed convex sets

C
1

,
⋯
,

C
4

{C_1}, \cdots ,{C_4}

in

P
P

are described, having the following property: every line which meets

P
P

meets at least one of the

C
i

{C_i}

’s, and for every collection of polytopes

D
1

,
⋯
,

D
4

{D_1}, \cdots ,{D_4}

, with

D
i

⊆

C
i

{D_i} \subseteq {C_i}

for all

1
≦
i
≦
4

1 \leqq i \leqq 4

, there exists a line which meets

P
P

and misses all of the

D
i

{D_i}

’s. This is a counterexample to a conjecture of A. J. Hoffman.
Embedding of complete Moore spaces
Authors: Creede Geoffrey D.
Published: June 2010

The purpose of this paper is to give necessary and sufficient conditions for Moore spaces to be complete in terms of embeddings in bicompact spaces.
The functional equation of some Dirichlet series
Authors: Berndt Bruce C.
Published: June 2010

The functional equation for two classes of Dirichlet series is established. These Dirichlet series involve primitive characters and can be regarded as generalizations of Dirichlet’s L-functions or of Epstein’s zeta-functions. One class is also a generalization of some series studied by Stark.
Integral ring extensions and prime ideals of infinite rank
Authors: Heinzer William
Published: June 2010

An example is constructed showing that for an integral ring extension

R
⊂
T

R \subset T

, and a prime ideal

P
P

of

R
R

having infinite rank, it can happen that in

T
T

each prime ideal lying over

P
P

has finite rank.
𝑝.𝑝. rings and finitely generated flat ideals
Authors: Jøndrup Søren
Published: June 2010

In this note all rings considered are associative with an identity element 1 and all modules are unital left modules. It is shown that a commutative ring

R
R

has principal ideals projective if and only if

R
[
X
]

R[X]

has the same property. Furthermore it is proved that a ring

R
R

has all

n
n

-generated left ideals flat if and only if all

n
n

-generated right ideals are flat. In the last part of this note we will prove the following results: Fix

n
≧
1

n \geqq 1

. Then there exists a ring

R
R

such that all

n
n

-generated left ideals are projective, in particular, flat, while there exists a nonflat

(
n
+
1
)

(n + 1)

-generated left ideal.
On the conjugacy of injectors
Authors: Chambers Graham A.
Published: June 2010

In their paper, Injektoren endlicher auflösbarer Gruppen, Fischer, Gaschütz and Hartley ask the following question. If

F

\mathfrak {F}

is a normal subgroup closed class of groups and if

G
G

is a finite solvable group which possesses

F

\mathfrak {F}

-injectors, is it true that any two

F

\mathfrak {F}

-injectors of

G
G

are conjugate in

G
G

? A partial answer is given. It is proven that if

G
G

has

p
p

-length 1 for each prime

p
p

, then the answer to this question is yes.
On continuability of solutions of second order differential equations.
Authors: Burton T. , Grimmer R.
Published: June 2010

An equation (1)

x
+
a
(
t
)
f
(
x
)
=
0

x + a(t)f(x) = 0

together with some generalizations are considered. We give necessary and sufficient conditions in order that (1) have solutions which are not continuable in a certain fashion whenever

a
(
t
)

a(t)

becomes negative.
Right 𝐿𝐶𝑀 domains
Authors: Beauregard Raymond A.
Published: June 2010

A right LCM domain is a not necessarily commutative integral domain with unity in which the intersection of any two principal right ideals is again principal. The principal result deals with right LCM domains that satisfy an additional mild hypothesis; for such rings (which include right HCF domains and weak Bezout domains) it is shown that each prime factorization of an element is unique up to order of factors and projective factors. Projectivity is an equivalence relation that reduces to the relation of “being associates” in commutative rings and reduces to similarity in weak Bezout domains.
Annihilators of modules with a finite free resolution
Authors: Vasconcelos Wolmer V.
Published: June 2010

Let A be a commutative ring and let E be an A-module with a finite free resolution (see below for definition). Extending results known previously for noetherian rings, it is shown that

ann

(
E
)
=
annihilator

{\text {ann}}(E)=\text {annihilator}

of E is trivial if and only if the Euler characteristic of

E
=
χ
(
E
)
>
0

E = \chi (E) > 0

; in addition, if

χ
(
E
)
=
0
,

ann

(
E
)

\chi (E) = 0,{\text {ann}}(E)

is dense (i.e.

ann

(

ann

(
E
)
)
=
0

{\text {ann}}({\text {ann}}(E)) = 0

). Also, a local ring is constructed with its maximal ideal with a finite free resolution but consisting exclusively of zero-divisors and thus, contrary to the noetherian case, one does not always have a nonzero divisor in

ann

(
E
)

{\text {ann}}(E)

if

χ
(
E
)
=
0

\chi (E) = 0

. Finally, if E has a finite resolution by (f.g.) projective modules it turns out that

ann

(

ann

(
E
)
)

{\text {ann}}({\text {ann}}(E))

is generated by an idempotent element.
A note on the Blum-Hanson theorem
Authors: Jones Lee , Kuftinec Velimir
Published: June 2010

Let T be a linear contraction on an arbitrary Hilbert space. We prove that the weak convergence of the sequence

{

T
n

x
}

\{ {T^n}x\}

implies the strong convergence of the averages of the sequences

{

T

k
i

x
}

\{ {T^{{k_i}}}x\}

for all strictly increasing sequences

{

k
i

}

\{ {k_i}\}

of positive integers.
Tame polyhedra in wild cells and spheres
Authors: Sher R. B.
Published: June 2010

It is shown that each arc on a disk D in

E
4

{E^4}

can be homeomorphically approximated by an arc in D which is tame in

E
4

{E^4}

. Some applications of this are given. Also, we construct an everywhere wild

(
n
−
1
)

(n - 1)

-sphere in

E
n

,
n
≧
3

{E^n},n \geqq 3

, each of whose arcs is tame in

E
n

{E^n}

.
Some radical properties of 𝑠-rings
Authors: Rich Michael
Published: June 2010

The class of s-rings includes as a proper subset the classes of associative, alternative, Lie, Jordan, and standard rings. It is shown that in any s-ring R the prime radical of R coincides with the Baer lower radical of R. Relationships between the prime radical and certain other radicals are also given.
The Gronwall inequality for weighted integrals
Authors: Wright F. M. , Klasi M. L. , Kennebeck D. R.
Published: June 2010

The objective of this paper is to establish a Gronwall inequality for the weighted refinement integral

[
F
,
(

w
1

,

w
2

,

w
3

)
]

∫
a
b

f
(
t
)
d
g
(
t
)

[F,({w_1},{w_2},{w_3})]\smallint _a^bf(t)dg(t)

. This result generalizes a recent result by W. W. Schmaedeke and G. R. Sell for the mean sigma integral and the interior refinement integral. The proof in this paper is based on the one given by Schmaedeke and Sell but is shorter and simpler. B. W. Helton has established a product integral representation for a Gronwall inequality for the refinement integral

(
L
R
)

∫
a
b

(
f
H
+
f
G
)

(LR)\smallint _a^b(fH + fG)

. Helton’s result contains the result here for the special case where

w
1

{w_1}

and

w
3

{w_3}

are nonnegative real numbers such that

w
1

+

w
3

=
1

{w_1} + {w_3} = 1

. The ideas used here are considerably less complicated than those used by Helton. J. V. Herod has established a Gronwall inequality for linear Stieltjes integrals working with a linear function

J
[
f
]

J[f]

that is more general than the linear function

J
[
f
]
=
(
L
R
)

∫
a
b

(
f
H
+
f
G
)

J[f] = (LR)\smallint _a^b(fH + fG)

considered by Helton.
Note on Salié’s sum
Authors: Williams Kenneth S.
Published: June 2010

It is shown in a very simple way that an exponential sum (involving the Legendre symbol) considered by Salié is the sum of two Gauss sums.
On categories of quotients
Authors: Klein Aaron
Published: June 2010

We construct a category of quotients over a category satisfying a condition similar to the Ore condition. Addition of quotients is briefly discussed.
Locally finite self-interchange graphs
Authors: Schwartz Benjamin L. , Beineke Lowell W.
Published: June 2010

Graphs isomorphic to their interchanges are studied. Using prior results of more special cases, plus one new concept, it is possible to characterize all locally finite self-interchange graphs, finite and infinite, connected and disconnected, with loops and parallel edges admitted. All solutions are shown to be component-unions of graphs from six easily described classes.
Geometrical realization of combinatorial geometries
Authors: Mason J. H.
Published: June 2010

A method of depicting combinatorial geometries geometrically is used to construct examples of small combinatorial geometries which arise as subsets of a vector space over division rings restricted by their characteristic.
A holomorphic function having a discontinuous inverse
Authors: Suffridge T. J.
Published: June 2010

An example is given of a function

f
f

which is holomorphic in the open unit ball of

l
∞

{l^\infty }

and which extends in a natural way to the closed unit ball. The extended function gives a one-toone correspondence of the closed ball with itself but the inverse function fails to be continuous on the image of the open ball under the map

f
f

.
𝐻-spaces which are co-𝐻-spaces
Authors: West Robert W.
Published: June 2010

It is shown that a space, having the homotopy type of a CW complex of finite type, admitting both

H
H

-space and co-

H
H

-space structures must have the homotopy type of a point or an

n
n

-sphere for

n
=
1

n = 1

, 3 or 7.
An embedding theorem for commutative lattice-ordered domains
Authors: Steinberg Stuart A.
Published: June 2010

In a recent paper Conrad and Dauns have shown that a finitely-rooted lattice-ordered field

R
R

, in which multiplication by a positive special element is a lattice homomorphism, can be embedded in a formal power series

l
l

-field with real coefficients, provided that the value group of

R
R

is torsion-free. In this note it is shown that their theorem is true when

R
R

is a commutative integral domain.
Dirichlet 𝐿-functions and primitive characters
Authors: Apostol Tom M.
Published: June 2010

It is well known that a Dirichlet

L
L

-function

L
(
s
,
χ
)

L(s,\chi )

has a functional equation if the character

χ
\chi

is primitive. This note proves the converse result. That is, if

L
(
s
,
χ
)

L(s,\chi )

satisfies the usual functional equation then

χ
\chi

is primitive.
The distribution of absolutely irreducible polynomials in several indeterminates
Authors: Fredman M. L.
Published: June 2010

Asymptotic formulas are derived for the distribution of absolutely irreducible polynomials in two indeterminates over finite fields. A pair of inversion formulas is presented which yield exact formulas relating the distributions of irreducible and absolutely irreducible polynomials.
Products of uncountably many 𝑘-spaces
Authors: Noble N.
Published: June 2010

It is shown that if a product of nonempty spaces is a

k
k

-space then for each infinite cardinal

n

\mathfrak {n}

some product of all but

n

\mathfrak {n}

of the factors has each

n

\mathfrak {n}

-fold subproduct

n

−

ℵ
0

\mathfrak {n} - {\aleph _0}

-compact (each

n

\mathfrak {n}

-fold open cover has a finite subcover). An example is given, for each regular

n

\mathfrak {n}

, of a space

X
X

which is not

n

−

ℵ
0

\mathfrak {n} - {\aleph _0}

-compact (so

X

n

+

{X^{{\mathfrak {n}^ + }}}

is not a

k
k

-space) for which

X

n

{X^\mathfrak {n}}

is a

k
k

-space.