bluuebunny/crossref_metadata_2025 huggingface dataset:
On left absolutely flat bands
Authors: Bulman-Fleming Sydney , McDowell Kenneth
Published: June 2010

A semigroup

S
S

is called (left, right) absolutely flat if all of its (left, right)

S
S

-sets are flat. Let

S
=
∪
{

S
γ

:
γ
∈
Γ
}

S = \cup \{ {S_\gamma }:\gamma \in \Gamma \}

be the least semilattice decomposition of a band

S
S

. It is known that if

S
S

is left absolutely flat then

S
S

is right regular (that is, each

S
γ

{S_\gamma }

is right zero). In this paper it is shown that, in addition, whenever

α
,
β
∈
Γ
,
α
>
β

\alpha ,\beta \in \Gamma ,\alpha > \beta

, and

F
F

is a finite subset of

S
β

×

S
β

{S_\beta } \times {S_\beta }

, there exists

w
∈

S
α

w \in {S_\alpha }

such that

(
w
u
,
w
v
)
∈

θ
R

(
F
)

(wu,wv) \in {\theta _R}(F)

for all

(
u
,
v
)
∈
F
(

θ
R

(
F
)

(u,v) \in F({\theta _R}(F)

denotes the smallest right congruence on

S
S

containing

F
F

). This condition in fact affords a characterization of left absolute flatness in certain classes of right regular bands (e.g. if

Γ
\Gamma

is a chain, if all chains contained in

Γ
\Gamma

have at most two elements, or if

S
S

is right normal).
Matrix methods and the property of stretchings
Authors: Keagy T. A.
Published: June 2010

D. F. Dawson has proved that if

x
x

is a sequence and

A
A

is a matrix with convergent row sums, then there exist a stretching

z
z

of

x
x

and a row finite matrix

B
B

such that

A
y

Ay

and

B
y

By

converge or diverge together for each stretching

y
y

of

z
z

. An extension of this result is used to answer a question proposed by D. Gaier regarding the conditions necessary for a matrix

A
A

to have the property that if

x
x

is a sequence with finite limit point

t
t

, then

A
A

sums a stretching of

x
x

to

t
t

.
Weakly compact bilinear forms and Arens regularity
Authors: Ülger A.
Published: June 2010

Let

X
X

and

Y
Y

be two Banach spaces. We show that a bounded bilinear form

m
:
X
×
Y
→

C

m:X \times Y \to {\mathbf {C}}

is Arens regular iff it is weakly compact. This result permits us to find very short proofs of some known results as well as some new results. Some of them are: Any

C
∗

{C^*}

-algebra, the disk algebra and the Hardy class

H
∞

{H^\infty }

are Arens regular under every possible product. We also characterize the Arens regularity of certain bilinear mappings.
A generalized capacity and a uniqueness theorem on the dyadic group
Authors: Yoneda Kaoru
Published: June 2010

In this paper we shall introduce a generalized capacity and give a necessary and sufficient condition for a subset of the dyadic group to be a

U
U

-set for a certain class of Walsh series.
On the area of the region where an entire function is greater than one
Authors: Shen Li-Chien
Published: June 2010

Using Carleman’s inequality, we prove that if

f
f

is entire and of finite order

ρ
≥
1

\rho \geq 1

, then
\[

_

r
→
∞

A
(
r
)

r
2

≥

π

2
ρ

,

\_{r \to \infty } \frac {A(r)}{r^2} \geq \frac {\pi }{2\rho },

\]
where

A
(
r
)

A(r)

is the area of the region

{
z
:

|

f
(
z
)

|

≥
1

and

|

z

|

≤
r
}

\{ z:|f(z)| \geq 1\;{\text {and}}\;|z| \leq r\}

.
Invariance of projections in the diagonal of a nest algebra
Authors: Daughtry John
Published: June 2010

The study of operator factorization along commutative subspace lattices which are not nests leads to the investigation of the mapping

ϕ
A

{\phi _A}

which takes an orthogonal projection

Q
Q

in the diagonal of a nest algebra

A

\mathcal {A}

to the projection on the closure of the range of AQ for certain bounded linear operators

A
A

. The purpose of this paper is to demonstrate that if

B
B

is an operator leaving the range of

Q
Q

invariant,

V
V

is an element of the "Larson radical" of

A

,
B
+
V

\mathcal {A},B + V

is invertible,

(
B
+
V

)

−
1

{(B + V)^{ - 1}}

belongs to

A

\mathcal {A}

, and

ϕ

B
+
V

(
Q
)

{\phi _{B + V}}(Q)

is in the diagonal of

A

\mathcal {A}

, then

ϕ
V

(
Q
)
≤
Q

{\phi _V}(Q) \leq Q

. For example, if

V
V

is in the Jacobson radical of

A

\mathcal {A}

and

λ
\lambda

is a nonzero scalar, it follows that

ϕ

λ
I
+
V

(
Q
)
=
Q

{\phi _{\lambda I + V}}(Q) = Q

if and only if

ϕ

λ
I
+
V

(
Q
)

{\phi _{\lambda I + V}}(Q)

belongs to the diagonal of

A

\mathcal {A}

. Examples of the applications to operator factorization and unitary equivalence of sets of projections are given.
Cyclic vectors in 𝐴^{-∞}
Authors: Brown Leon , Korenblum Boris
Published: June 2010

If

f
f

is in

A

−
p

{A^{ - p}}

, then

f
f

is cyclic in

A

−
∞

{A^{ - \infty }}

if and only if

f
f

is cyclic in every

A

−
q

(
q

 > 

p
)

{A^{ - q}}(q{\text { > }}p)

. An analogous result holds for the Bergman spaces

B
p

{B^p}

. In this note we apply the theory developed in [2 and 3] to explain the relationship between cyclic vectors in

A

−
∞

{A^{ - \infty }}

and

A

−
p

{A^{ - p}}

or

B
p

{B^p}

.
Conformally natural extension of vector fields from 𝑆ⁿ⁻¹ to 𝐵ⁿ
Authors: Earle Clifford J.
Published: June 2010

Up to multiplication by a constant there is exactly one conformally natural continuous linear map from the space of continuous vector fields on

S

n
−
1

{S^{n - 1}}

to the space of continuous vector fields on

B
n

{B^n}

.
On the sphere conjecture of Birkhoff
Authors: Jerrard Richard
Published: June 2010

Birkhoff’s sphere conjecture, now known to be false, says that if

f
f

is a measure preserving homeomorphism of

S
2

{S^2}

with the poles

N
N

and

S
S

fixed, and with no other periodic points, then

f
f

is topologically conjugate to an irrational rotation of

S
2

{S^2}

. In this setting we say that

D
⊂

S
2

D \subset {S^2}

is maximal for

f
f

if

f

(
D
)

∩
D
=
∅

f\left ( D \right ) \cap D = \emptyset

and

D
D

is maximal with respect to that property. Also,

f
f

is

2
2

-small if for any circular ball

B
B

such that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis upper B right-parenthesis intersection upper B equals normal empty-set comma f Superscript negative 1 Baseline left-parenthesis upper B right-parenthesis intersection f left-parenthesis upper B right-parenthesis equals normal empty-set">

f

(
B
)

∩
B
=
∅
,

f

−
1

(
B
)

∩
f

(
B
)

=
∅

f\left ( B \right ) \cap B = \emptyset ,{f^{ - 1}}\left ( B \right ) \cap f\left ( B \right ) = \emptyset

also. Theorem. Any

f
f

as above and also

2
2

-small has a maximal set

D
D

which is an open ball; its boundary contains

N
N

and

S
S

and is locally connected, and the area of

D
D

is an irrational fraction of the area of

S
2

{S^2}

. This theorem gives another way of looking at the maps involved in the Birkhoff conjecture.
Rings graded by polycyclic-by-finite groups
Authors: Chin William , Quinn Declan
Published: June 2010

We use the duality between group gradings and group actions to study polycyclic-by-finite group-graded rings. We show that, for such rings, graded Noetherian implies Noetherian and relate the graded Krull dimension to the Krull dimension. In addition we find a bound on the length of chains of prime ideals not containing homogeneous elements when the grading group is nilpotent-by-finite. These results have suitable corollaries for strongly group-graded rings. Our work extends several results on skew group rings, crossed products and group-graded rings.
A counterexample to the nodal domain conjecture and a related semilinear equation
Authors: Lin Chang Shou , Ni Wei-Ming
Published: June 2010

In this paper we first establish a nonuniqueness result for a semilinear Dirichlet problem of which the nonlinearity is of super-critical growth. We then apply this result to construct a Schrödinger operator on a domain

Ω
\Omega

such that the second eigenfunctions of this operator (with zero Dirichlet boundary data) have their nodal sets completely contained in the interior of the domain

Ω
\Omega

.
Strongly commuting selfadjoint operators and commutants of unbounded operator algebras
Authors: Schmüdgen Konrad
Published: June 2010

Let

A
1

{A_1}

and

A
2

{A_2}

be (unbounded) selfadjoint operators on a Hilbert space

H

\mathcal {H}

which commute on a dense linear subspace of

H

\mathcal {H}

. To conclude that

A
1

{A_1}

and

A
2

{A_2}

strongly commute, additional assumptions are necessary. Two propositions which contain such additional conditions are proved in §1. In §2 we define different commutants of unbounded operator algebras (form commutant, weak unbounded commutant, strong unbounded commutant) and we discuss the relations between them and their bounded parts. In §3 we construct a selfadjoint

∗

{*}

-representation of the polynomial algebra in two variables for which the form commutant is different from the weak unbounded commutant.
Expansion of discrete and closure-preserving families
Authors: Mizokami Takemi
Published: June 2010

In this paper, we define the classes of

d
d

-IP-expandable spaces and IP-expandable spaces, and study their properties and relations with orthocompact spaces and nonarchimedean quasi-metrizable spaces.
Two questions on Heegaard diagrams of 𝑆³
Authors: Montesinos José María
Published: June 2010

We review some of the methods that have been used to recognize

S
3

{S^3}

from a Heegaard diagram. We propose a revision of these methods and examine their failure for manifolds different from

S
3

{S^3}

.
Multinomial probabilities, permanents and a conjecture of Karlin and Rinott
Authors: Bapat R. B.
Published: June 2010

The probability density function of a multiparameter multinomial distribution can be expressed in terms of the permanent of a suitable matrix. This fact and certain results on conditionally negative definite matrices are used to prove a conjecture due to Karlin and Rinott.
Embeddings of the maximal quotient ring of a von Neumann regular ring into its completion with respect to a rank function
Authors: Vogel Annie
Published: June 2010

Let

R
R

be a commutative von Neumann regular ring. A pseudorank function on

R
R

is characterized by a probability measure on the spectrum of

R
R

. We exhibit two commutative von Neumann regular rings

R
R

and

R
′

R’

with the same spectrum

S
S

, and two rank functions

N
N

and

N
′

N’

on

R
R

and

R
′

R’

, corresponding to the same probability measure on

S
S

, and such that the maximal right quotient ring

Q

max

(
R
)

{Q_{\max }}(R)

embeds in the

N
N

-completion

R
¯

\bar R

of

R
R

while

Q

max

(

R
′

)

{Q_{\max }}(R’)

does not embed in

R
′

¯

\overline {R’}

.
Normal representations of Banach Jordan triple systems
Authors: Barton T. J. , Dang T. , Horn G.
Published: June 2010

Some new techniques in the representation theory of Banach Jordan triple systems (i.e., JB*-triples) are developed. These are applied to prove a Kaplansky density theorem and to show that JBW*-triples decompose into special and exceptional parts.
Interpolation and factorization of operators
Authors: Bloom Steven , Vignati Anita Tabacco , Vignati Marco
Published: June 2010

We apply the complex method of interpolation to families of infinite-dimensional, separable Hilbert spaces, and obtain a detailed description of the structure of the interpolation spaces, by means of a unique "extremal" operator-valued, analytic function. We use these interpolation techniques to give a different proof, under weaker assumptions, of a theorem of A. Devinatz concerning the factorization of positive, infinite-rank, operator-valued functions.
A note on pseudoconvexity and proper holomorphic mappings
Authors: Lin E. B. , Wong B.
Published: June 2010

In this paper we discuss some connections between proper holomorphic mappings between domains in

C

n

{{\mathbf {C}}^n}

and the boundary behaviors of certain canonical invariant metrics. A compactness theorem has been proved. This generalizes slightly an earlier result proved by the second author.
Jones’ braid-plat formula and a new surgery triple
Authors: Birman Joan S. , Kanenobu Taizo
Published: June 2010

A link

L
β

(

2
k
,
n
−
2
k

)

{L_\beta }\left ( {2k,n - 2k} \right )

is defined by a type

(

2
k
,
n
−
2
k

)

\left ( {2k,n - 2k} \right )

pairing of an

n
n

-braid

β
\beta

if the first

2
k

2k

strands are joined up as in a plat and the remaining

n
−
2
k

n - 2k

as in a closed braid. The main result is a formula for the Jones polynomials of

L
β

(

2
k
,
n
−
2
k

)

{L_\beta }\left ( {2k,n - 2k} \right )

, valid for all

k
,
0
⩽
2
k
⩽
n

k,0 \leqslant 2k \leqslant n

, which generalizes and relates earlier results of Jones for the cases

n
=
0

n = 0

and

2
k

2k

.
A rational torsion invariant
Authors: Ewing John , Löffler Peter , Pedersen Erik Kjaer
Published: June 2010

We show that for spaces with rational cohomology an exterior algebra on odd dimensional generators, one can define a torsion invariant which is a rational number. This may be interpreted as an absolute version of the multiplicative Euler characteristic associated to a rational homotopy equivalence.
A product expansion in 𝑝-adic and other non-Archimedean fields
Authors: Knopfmacher Arnold , Knopfmacher John
Published: June 2010

An algorithm is introduced and shown to lead to a unique infinite product representation for a given

p
p

-adic integer

A
A

with leading coefficient 1 as a product
\[

A
=

∏

n
=
1

∞

(
1
+

b
n

p

r
n

)

A = \prod \limits _{n = 1}^\infty {(1 + {b_n}{p^{{r_n}}})}

\]
where

1
≤

b
n

≤
p
−
1
,

r
n

∈

N

1 \leq {b_n} \leq p - 1,{r_n} \in {\mathbf {N}}

and

r

n
+
1

>

r
n

{r_{n + 1}} > {r_n}

. The degree of approximation by the natural number

(
1
+

b
1

p

r
1

)
⋯
(
1
+

b
n

p

r
n

)

(1 + {b_1}{p^{{r_1}}}) \cdots (1 + {b_n}{p^{{r_n}}})

is also considered. In addition we derive similar representations for elements of arbitrary complete non-Archimedean fields with discrete valuations.
Mordell-Weil groups of generic abelian varieties in the unitary case
Authors: Silverberg Alice
Published: June 2010

The generic fibre of a fibre system of polarized abelian varieties with level structure, and with endomorphism structure coming from a CM-field, is defined over the function field of the moduli space for the abelian varieties. We prove that the points on this generic abelian variety which are defined over the function field of the moduli space form a finite group. The methods of proof generalize those of Mordell- Weil groups of generic abelian varieties, Invent. Math. 81 (1985), 71-106, to which this paper is a sequel.
Note on multiplicity
Authors: Katz Daniel
Published: June 2010

Let

(
R
,
M
)

(R,M)

be a local ring with infinite residue field and

I
=
(

x
1

,
…
,

x
d

)
R

I = ({x_1}, \ldots ,{x_d})R

an ideal generated by a system of parameters. It is shown that the multiplicity of

I
I

equals the multiplicity of

I
T

IT

where
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T equals upper R overTilde left-bracket x 1 slash x Subscript d Baseline comma ellipsis comma x Subscript d minus 1 Baseline slash x Subscript d Baseline right-bracket Subscript upper M ModifyingAbove upper R With tilde left-bracket x 1 slash x Sub Subscript d Subscript comma ellipsis comma x Sub Subscript d minus 1 Subscript slash x Sub Subscript d Subscript right-bracket">

T
=

R
~

[

x
1

/

x
d

,
…
,

x

d
−
1

/

x
d

]

M

R
~

[

x
1

/

x
d

,
…
,

x

d
−
1

/

x
d

]

T = \tilde R{[{x_1}/{x_d}, \ldots ,{x_{d - 1}}/{x_d}]_{M\tilde R[{x_1}/{x_d}, \ldots ,{x_{d - 1}}/{x_d}]}}

\]
and

R
~

=
R

/

(
0
:

x
d
N

)
,
N

\tilde R = R/(0:x_d^N),N

large.
Singular foliation 𝐶*-algebras
Authors: Sheu Albert Jeu-Liang
Published: June 2010

A way to construct

C
∗

{C^*}

-algebras from the so-called singular foliations is proposed, which generalizes Connes’ construction of

C
∗

{C^*}

-algebras of regular foliations. A certain desired property is shown to hold for such

C
∗

{C^*}

-algebras and some connection with the boundary behavior of pseudodifferential operators is indicated.
An application of Baumslag-Solitar non-Hopfian groups to finitary automorphisms
Authors: Caserta Francesco
Published: June 2010

It is shown that finitary automorphisms, as distinct from those described as special, do not possess good hereditary properties on subgroups.
Is there a point of 𝜔* that sees all others?
Authors: Hindman Neil
Published: June 2010

If the cardinal

c
c

of the continuum is singular and

p
p

is an ultrafilter on

ω
\omega

of character

c
c

, then there is an ultrafilter

q
q

on

ω
\omega

which is not comparable to

p
p

in the Rudin-Keisler order.
Congruences associated with DOL-schemes
Authors: Petrich Mario , Thierrin Gabriel
Published: June 2010

For a DOL-scheme

(
X
,
φ
)

(X,\varphi )

, where

X
X

is a finite alphabet and

φ
\varphi

is an endomorphism of

X
∗

{X^*}

, we study the properties of the congruence

φ
¯

\bar \varphi

induced by

φ
\varphi

in terms of the properties of

X
∗

φ

{X^*}\varphi

. We prove that every submonoid of

X
∗

{X^*}

has a disjunctive subset (for any

X
X

) and deduce that

φ
¯

\bar \varphi

is a syntactic congruence. As special cases, we consider the conditions on

φ
\varphi

which are equivalent to

φ
¯

\bar \varphi

being perfect or uniquely perfect or linear. The latter is introduced in the paper together with a ramification.
Filtrations and Noetherian symbolic blow-up rings
Authors: Schenzel Peter
Published: June 2010

For a one-dimensional prime ideal in a local Noetherian ring it is characterized when the symbolic blow-up ring is an algebra of finite type. More generally, for a filtration of ideals of a local Noetherian ring there is a necessary and sufficient condition for the corresponding Rees ring to be a Noetherian ring. Applications concern asymptotic prime divisors and the analytic spread.
Measures invariant under local homeomorphisms
Authors: Ross David
Published: June 2010

Suppose

X
X

is a compact Hausdorff space, and

G
G

is a set of local homeomorphisms of

X
X

; sufficient conditions are given for the existence of a

G
G

-invariant Borel probability measure

P
P

on

X
X

. The result generalizes theorems of Mycielski and Steinlage. The proof is an application of the "Loeb measure" construction from nonstandard analysis.
An unusual monotonicity theorem with applications
Authors: Malý J. , Preiss D. , Zajíček L.
Published: June 2010

In the article an unusual monotonicity theorem is proved. It easily implies some usual monotonicity theorems which deal with preponderant and symmetrical derivatives. We also obtain some results concerning one-sided densities of arbitrary linear sets, which are closely related to an O’Malley theorem.
4-planar geodesic Kaehler immersions into a complex projective space
Authors: Pak Jin Suk , Sakamoto Kunio
Published: June 2010

If

f
f

is a proper

4
4

-planar geodesic Kaehler immersion of a connected complete Kaehler manifold

M
n

(
n
≥
2
)

{M^n}(n \geq 2)

into

C

P
m

(
c
)

C{P^m}(c)

, then

M
n

=
C

P
n

(
c

/

4
)

{M^n} = C{P^n}(c/4)

and

f
f

is equivalent to the 4th Veronese map.
Thurston norm and taut branched surfaces
Authors: Sterba-Boatwright B. D.
Published: June 2010

Let

x
x

denote the Thurston norm on

H
2

(
N
;

R

)

{H_2}(N;{\mathbf {R}})

, where

N
N

is a closed, oriented, irreducible, atoroidal three-manifold

N
N

. U. Oertel defined a taut oriented branched surface to be a branched surface with the property that each surface it carries is incompressible and

x
x

-minimizing for the (nontrivial) homology class it represents. Given

φ
\varphi

, a face of the

x
x

-unit sphere in

H
2

(
N
;

R

)

{H_2}(N;{\mathbf {R}})

, Oertel then asks: is there a taut oriented branched surface carrying surfaces representing every integral homology class projecting to

φ
\varphi

? In this article, an example is constructed for which the answer is negative.
Quotients of tangential 𝑘-blocks
Authors: Whittle Geoffrey
Published: June 2010

A tangential

k
k

-block over

G
F
(
q
)

GF(q)

is a simple matroid representaba over

G
F
(
q
)

GF(q)

with critical exponent

k
+
1

k + 1

for which every proper loopless minor has critical exponent at most

k
k

. Such matroids are of central importance in the critical problem of Crapo and Rota. In this paper we provide sufficient conditions for a quotient of a tangential

k
k

-block over

G
F
(
q
)

GF(q)

to be also a tangential

k
k

-block over

G
F
(
q
)

GF(q)

. This enables us to show that there exist rank

r
r

supersolvable tangential

k
k

-blocks over

G
F
(
q
)

GF(q)

exactly when

q
k

≥
r
≥
k
+
1

{q^k} \geq r \geq k + 1

.
A converse to a residual finiteness theorem of G. Baumslag
Authors: Shirvani M.
Published: June 2010

It is shown that if at least two of the factor groups of a nontrivial amalgamated free product

G
G

satisfy nontrivial identities, then a special form of the profinite closure of the associated subgroups is necessary (as well as sufficient) for the residual finiteness of

G
G

. An example shows that the necessity no longer holds if only one of the factor groups satisfies an identity.
A remark on inherent differentiability
Authors: Freedman Michael H. , He Zheng-Xu
Published: June 2010

Harrison’s analysis of

C
r

{C^r}

-diffeomorphisms which are not conjugate to

C
s

{C^s}

-diffeomorphisms for

s
>
r
>
0

s > r > 0

is extended to dimension = 4. Also topological conjugacy may be generalized to an arbitrary change of differentiable structure. Combining these statements yields: for any smooth manifold of dimension

≥
2

\geq 2

there is a

C
r

{C^r}

-diffeomorphism which is not a

C
s

{C^s}

-diffeomorphism w.r.t. any smooth structure.
Radii problems for sections of convex functions
Authors: Silverman Herb
Published: June 2010

A classical theorem of Szegö states that the sections

f
n

(
z
)
=
z
+

∑

k
=
2

n

a
k

z
k

{f_n}(z) = z + \sum \nolimits _{k = 2}^n {{a_k}{z^k}}

of a convex function

f
(
z
)
=
z
+

∑

k
=
2

∞

a
k

z
k

f(z) = z + \sum \nolimits _{k = 2}^\infty {{a_k}{z^k}}

must be convex for

|
z
|

>

1
4

\left | z \right | > \frac {1}{4}

. We determine disks

|
z
|

>

r
n

\left | z \right | > {r_n}

in which

f
n

{f_n}

is starlike and starlike of a positve order. Our proofs rely on some properties of convolutions.
Large automorphism groups of hyperelliptic Klein surfaces
Authors: Bujalance E. , Etayo J. J.
Published: June 2010

In this paper we study the groups of automorphisms of all hyperelliptic bordered Klein surfaces of genus

p
>
3

p > 3

having at least

4
(
p
−
1
)

4(p - 1)

automorphisms.
Reduction of a matrix depending on parameters to a diagonal form by addition operations
Authors: Vaserstein L. N.
Published: June 2010

It is shown that any

n
n

by

n
n

matrix with determinant 1 whose entries are real or complex continuous functions on a finite dimensional normal topological space can be reduced to a diagonal form by addition operations if and only if the corresponding homotopy class is trivial, provided that

n
≠
2

n \ne 2

for real-valued functions; moreover, if this is the case, the number of operations can be bounded by a constant depending only on

n
n

and the dimension of the space. For real functions and

n
=
2

n = 2

, we describe all spaces such that every invertible matrix with trivial homotopy class can be reduced to a diagonal form by addition operations as well as all spaces such that the number of operations is bounded.
Karp’s theorem in acoustic scattering theory
Authors: Colton David , Kirsch Andreas
Published: June 2010

Karp’s Theorem states that if the far field pattern corresponding to the scattering of a time harmonic plane acoustic wave by a sound-soft cylinder is of the form

F
0

(
k
;
θ
−
α
)

{F_0}(k;\theta - \alpha )

where

k
k

is the wave number,

θ
\theta

the angle of observation and

α
\alpha

the angle of incidence of the plane wave, then the cylinder must be circular. A new proof is given of this result and extended to the cases of scattering by a sound-hard obstacle and an inhomogeneous medium.
Weak* convergence in higher duals of Orlicz spaces
Authors: Leung Denny H.
Published: June 2010

It is shown that the spaces

(

Σ
⊕
E

)

l
∞

(
Γ
)

{\left ( {\Sigma \oplus E} \right )_{{l^\infty }(\Gamma )}}

are Grothendieck spaces for a class of Banach lattices

E
E

which includes the Orlicz spaces with weakly sequentially complete duals.
The symmetric derivation basis measure and the packing measure
Authors: Meinershagen Sandra
Published: June 2010

The packing measure as defined by S. J. Taylor for continuous, monotone functions

h
h

and the measure generated by the symmetric derivation basis measure using

h
h

are shown here to be the same for subsets of the real line.
The one-radius theorem is not true for bounded real-analytic functions
Authors: Izuchi K.
Published: June 2010

There exists a bounded real-analytic function on the unit ball which does not satisfy Rudin’s one-radius theorem.
Asymptotic behavior of a class of nonlinear differential equations of 𝑛th order
Authors: Kong Qingkai
Published: June 2010

In this paper we obtain a result of the asymptotic behavior of the

n
n

th order equation

u

(
n
)

+
f
(
t
,
u
,

u
′

,
…
,

u

(
n
−
1
)

)
=
0

{u^{(n)}} + f(t,u,u’, \ldots ,{u^{(n - 1)}}) = 0

under some assumptions. For

n
=
2

n = 2

and

f
(
t
,
u
,

u
′

)
≡
f
(
t
,
u
)

f(t,u,u’) \equiv f(t,u)

, it revises the result given by Jingcheng Tong, which is not true in general.
Growth properties of 𝑝th means of potentials in the unit ball
Authors: Gardiner S. J.
Published: June 2010

Let

v
v

be a potential in the unit ball of

R

n

{{\mathbf {R}}^n}

, and

M

p

(
v
;
r
)

{\mathcal {M}_p}(v;r)

be its

p
p

th order mean over the sphere of radius

r
r

centred at the origin. It is shown that, as

r
→
1
−

r \to 1 -

, the function
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis r right-parenthesis equals left-parenthesis 1 minus r right-parenthesis Superscript left-parenthesis n minus 1 right-parenthesis left-parenthesis 1 minus 1 slash p right-parenthesis Baseline script upper M Subscript p Baseline left-parenthesis v semicolon r right-parenthesis">

f
(
r
)
=

(
1
−
r

)

(
n
−
1
)
(
1
−
1

/

p
)

M

p

(
v
;
r
)

f(r) = {(1 - r)^{(n - 1)(1 - 1/p)}}{\mathcal {M}_p}(v;r)

has limit 0 when

1
≤
p

 > 

(
n
−
1
)

/

(
n
−
2
)

1 \leq p{\text { > }}(n - 1)/(n - 2)

, and has lower limit 0 when

n
≥
3

n \geq 3

and

(
n
−
1
)

/

(
n
−
2
)
≤
p

 > 

(
n
−
1
)

/

(
n
−
3
)

(n - 1)/(n - 2) \leq p{\text { > }}(n - 1)/(n - 3)

. This extends a result of Stoll, who showed that, when

n
=
2

n = 2

and

p
=
+
∞
,
lim

inf

r
→
1
−

f
(
r
)
=
0

p = + \infty ,\lim {\inf _{r \to 1 - }}f(r) = 0

. Examples are given to show that the theorems presented are best possible.
On Sullivan’s invariant measure problem
Authors: Bunce L. J. , Wright J. D. Maitland
Published: June 2010

Sullivan has posed an invariant measure problem for which a positive answer is very plausible. It also seems highly plausible that hyperfinite AW*-factors are injective. Surprisingly, it turns out that one of these problems must have a negative solution. Specifically we show that either the hyperfinite Takenouchi-Dyer factor is not injective, or no

G
G

-invariant category measure exists for any free, ergodic action of a countable nonamenable group

G
G

on a perfect Polish space.
The nonimbeddability of real hypersurfaces in spheres
Authors: Faran James J.
Published: June 2010

It is shown that there exist real analytic real hypersurfaces in

C

n

{{\mathbf {C}}^n}

which cannot be locally holomorphically imbedded in any finite dimensional sphere

S

2
N
−
1

⊂

C

2
N

{S^{2N - 1}} \subset {{\mathbf {C}}^{2N}}

.
Partitioner-representable algebras
Authors: Frankiewicz R. , Zbierski P.
Published: June 2010

We give a simple proof of the theorem of Baumgartner and Weese on representability of Boolean algebras. We also show that the representability of

P

(

ω
1

)

P\left ( {{\omega _1}} \right )

implies the existence of a relative

Q
3

{Q_3}

-set.
Extension of random contractions
Authors: Myjak J. , Zygadlewicz W.
Published: June 2010

Let

Ω
\Omega

be a measurable space. Let

X
X

and

Y
Y

be separable Hilbert spaces and let

D
D

be a subset of

X
X

. Then every random contraction

f
:
Ω
×
D
→
Y

f:\Omega \times D \to Y

can be extended to a random contraction defined on all

Ω
×
X

\Omega \times X

. This statement remains true if

Ω
\Omega

is a complete measurable space,

X
X

and

Y
Y

are separable metric spaces and the pair

(
X
,
Y
)

(X,Y)

has the Kirszbraun intersection property.
Common fixed points for commuting and compatible maps on compacta
Authors: Jungck Gerald
Published: June 2010

Compatible maps—a generalization of commuting maps—are characterized in terms of coincidence points, and common fixed point theorems for compatible maps and commuting maps on compact metric spaces are obtained.
Elementary divisor theorem for noncommutative PIDs
Authors: Guralnick Robert M. , Levy Lawrence S. , Odenthal Charles
Published: June 2010

We prove that, over a PID, if two matrices

A

{\mathbf {A}}

and

B

{\mathbf {B}}

have the same size, present isomorphic modules and have rank

≥
2

\geq 2

, then

A

{\mathbf {A}}

is equivalent to

B

{\mathbf {B}}

. This answers a question raised by Nakayama in 1938. Our solution makes use of a number of facts about the algebraic

K
K

-theory of noetherian rings.
Grothendieck groups of algebras with nilpotent annihilators
Authors: Auslander Maurice , Reiten Idun
Published: June 2010

Let

R
R

be a commutative noetherian ring and

i
:
R
→
Λ

i:R \to \Lambda

an

R
R

-algebra such that

Λ
\Lambda

is a finitely generated

R
R

-module. Then the annihilator of

Λ
\Lambda

in

R
R

is nilpotent if and only if the cokernel of the induced map of Grothendieck groups

i
∗

:

K
0

(
mod
Λ
)

{i^*}:{K_0}(\bmod \Lambda )

is a torsion group.
Nonstandard methods for families of 𝜏-smooth probability measures
Authors: Landers Dieter , Rogge Lothar
Published: June 2010

For families of

τ
\tau

-smooth probability measures we give nonstandard characterizations of uniform

τ
\tau

-smoothness, uniform tightness, uniform pretightness, and relative compactness in the weak topology. We apply these characterizations to obtain two important theorems of probability theory: A theorem of Topsøe and a theorem of Prohorov.
Factorization of measures and normal conditional distributions
Authors: Maitra A. , Ramakrishnan S.
Published: June 2010

Let

(
Y
,

C

,
Q
)

(Y,\mathcal {C},Q)

be a probability space. If every probability measure

R
R

on

B

1

⊗

C

{\mathcal {B}^1} \otimes \mathcal {C}

with marginal

Q
Q

on

Y
Y

admits a factorization, where

B

1

{\mathcal {B}^1}

is the Borel

σ
\sigma

-field on the real line,

Q
Q

must be perfect. Conversely if

Q
Q

is perfect and

C

\mathcal {C}

is

ℵ
1

{\aleph _1}

-generated, then (a) for any measure

R
R

on

A

⊗

C

\mathcal {A} \otimes \mathcal {C}

with marginal

Q
Q

, where

A

\mathcal {A}

is any

σ
\sigma

-field of subsets of a set

X
X

, there is a factorization; (b) for every tail-like sub-

σ
\sigma

-field

D

\mathcal {D}

of

C

\mathcal {C}

, there is a normal conditional distribution given

D

\mathcal {D}

. In special cases of interest, normal conditional distributions, satisfying additional desirable properties, are shown to exist.
A characterization of Artinian rings whose endomorphism rings have finite global dimension
Authors: Zacharia Dan
Published: June 2010

We prove that if

Λ
\Lambda

is a left artinian ring having the property that for every idempotent

e
e

, the ring

e
Λ
e

e\Lambda e

has finite global dimension then

Λ
\Lambda

is a quotient of an hereditary artinian ring.
Singular measures with spectral gaps
Authors: Lyons Russell
Published: June 2010

We show that every Borel measure on the circle whose Fourier spectrum has lacunary-type gaps annihilates every

H
H

-set.
The initial value problem for a degenerate wave equation
Authors: Kannai Y. , Kiro S.
Published: June 2010

The Cauchy problem for a degenerate wave equation, for which the spatial part is essentially a hypoelliptic sum of squares, is solved via a suitable modification of the standard Hilbert space approach for the usual problem.
The Kobayashi and Bergman metrics on generalized Thullen domains
Authors: Hahn K. T. , Pflug P.
Published: June 2010

A comparison theorem of the Kobayashi metric and the Bergman metric is obtained on generalized Thullen domains in

C

2

{{\mathbf {C}}^2}

. This theorem is then used to obtain a lower estimate for the Kobayashi metric. It is noted that the lower estimate obtained is best possible.
Zonoids with minimal volume-product—a new proof
Authors: Gordon Y. , Meyer M. , Reisner S.
Published: June 2010

A new and simple proof of the following result is given: The product of the volumes of a symmetric zonoid

A
A

in

R

n

{{\mathbf {R}}^n}

and of its polar body is minimal if and only if

A
A

is the Minkowski sum of

n
n

segments.
Universally catenarian domains of 𝐷+𝑀 type
Authors: Anderson David F. , Dobbs David E. , Kabbaj Salah , Mulay S. B.
Published: June 2010

Let

T
T

be a domain of the form

K
+
M

K + M

, where

K
K

is a field and

M
M

is a maximal ideal of

T
T

. Let

D
D

be a subring of

K
K

and let

R
=
D
+
M

R = D + M

. It is proved that if

K
K

is algebraic over

D
D

and both

D
D

and

T
T

are universally catenarian, then

R
R

is universally catenarian. The converse holds if

K
K

is the quotient field of

D
D

. As a consequence, we construct for each

n
>
2

n > 2

, an

n
n

-dimensional universally catenarian domain which does not belong to any previously known class of universally catenarian domains.
Exact embedding functors and left coherent rings
Authors: Fuller Kent R. , Hutchinson George
Published: June 2010

Let

R
R

and

S
S

be rings with unit. Suppose

P
P

is a free

R
R

-module on

β
\beta

generators, where

β
\beta

is an infinite cardinal number not smaller than the cardinality of

R
R

, and

T
T

is the ring of endomorphisms

End
⁡

(
R

P
)

\operatorname {End}{(_R}P)

. Theorem. If

R
R

is left coherent and there exists an exact embedding functor

F
:
R
−
Mod
→
S
−
Mod

F:R - \operatorname {Mod} \to S - \operatorname {Mod}

, then

S

F

(
R

)
R

_SF{(R)_R}

is a bimodule such that

F

(
R

)
R

F{(R)_R}

is faithfully flat. Theorem. If

F
:
R
−
Mod
→
S
−
Mod

F:R - \operatorname {Mod} \to S - \operatorname {Mod}

is an exact embedding functor, then

R

P
T

_R{P_T}

is a bimodule such that

R

P

_RP

is a projective generator (inducing an exact embedding Hom functor from

R
−
Mod

R - \operatorname {Mod}

into

T
−
Mod

T - \operatorname {Mod}

,) and

S

F

(
T

)
T

_SF{(T)_T}

is a bimodule such that

F

(
T

)
T

F{(T)_T}

is faithfully flat (inducing an exact embedding tensor product functor

S

F
(
T
)

⊗
T

_SF(T){ \otimes _T}

— from

T
−
Mod

T - \operatorname {Mod}

into

S
−
Mod

S - \operatorname {Mod}

.) Theorem. There exists an exact embedding functor

R
−
Mod
→
S
−
Mod

R - \operatorname {Mod} \to S - \operatorname {Mod}

iff there exists an

S
S

-module

N
N

and a unit-preserving ring monomorphism

h
:
End
⁡

(
R

P
)
→
End
⁡

(
S

N
)

h:\operatorname {End}{(_R}P) \to \operatorname {End}{(_S}N)

of their endomorphism rings, such that

h
h

preserves and reflects exact pairs of endomorphisms.
A structure theorem for simple transcendental extensions of valued fields
Authors: Matignon Michel , Ohm Jack
Published: June 2010

The fundamental inequality for a finite algebraic extension of a valued field relates the degree of the extension to the ramification indices and residue degrees, and of primary importance is the question of when this inequality becomes equality. An analogous question for simple transcendental extensions is treated here as an application of a fundamental structure theorem for such extensions.
Comparison theorems for causal functional-differential equations
Authors: McNabb Alex , Weir Graham
Published: June 2010

Weak and strong comparison theorems are proved for causal functional differential equations
A new proof of Sonine’s formula
Authors: Stempak Krzysztof
Published: June 2010

We give a new proof of an old integral formula due to Sonine in which the Bessel functions are involved. By considering the Banach algebra of radial functions on

R

n

,
n
≥
2

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

, we observe that Sonine’s formula is valid for all positive integers. Next, a complex function theory argument is applied to obtain the validity of the formula for all complex parameters

z
z

with Re

z
>
0

z > 0

.
Differentiability of distance functions and a proximinal property inducing convexity
Authors: Giles J. R.
Published: June 2010

In a normed linear space

X
X

, consider a nonempty closed set

K
K

which has the property that for some

r
>
0

r > 0

there exists a set of points

x
0

∈
X
∖
K
,
d
(

x
0

K
)
>
r

{x_0} \in X\backslash K,d({x_0}K) > r

, which have closest points

p
(

x
0

)
∈
K

p({x_0}) \in K

and where the set of points
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x 0 minus r left-parenthesis left-parenthesis x 0 minus p left-parenthesis x 0 right-parenthesis right-parenthesis slash StartAbsoluteValue EndAbsoluteValue x 0 minus p left-parenthesis x 0 right-parenthesis StartAbsoluteValue EndAbsoluteValue right-parenthesis">

x
0

−
r
(
(

x
0

−
p
(

x
0

)
)

/

|

|

x
0

−
p
(

x
0

)

|

|

)

{x_0} - r(({x_0} - p({x_0}))/||{x_0} - p({x_0})||)

is dense in

X
∖
K

X\backslash K

. If the norm has sufficiently strong differentiability properties, then the distance function

d
d

generated by

K
K

has similar differentiability properties and it follows that, in some spaces,

K
K

is convex.
The argument of an extremal dilatation
Authors: Ortel Marvin , Smith Wayne
Published: June 2010

Suppose

κ
\kappa

is the complex dilatation of an extremal quasiconformal homeomorphism of the unit disk onto itself. Then, except in special cases, the width of the set of arguments of

κ
\kappa

must strictly exceed

π
\pi

.
Oscillatory solutions for certain delay-differential equations
Authors: Seifert George
Published: June 2010

The existence of oscillatory solutions for a certain class of scalar first order delay-differential equations is proved. An application to a delay logistic equation arising in certain models for population variation of a single specie in a constant environment with limited resources for growth is considered.
A characterization of the generalized Veronese surfaces
Authors: Itoh Takehiro
Published: June 2010

We prove that compact

m
m

-regular minimal surfaces in a sphere are generalized Veronese surfaces if the Gaussian curvature satisfies an inequality.
Invariant subspaces for algebras of subnormal operators. II
Authors: Thomson James E.
Published: June 2010

We continue our study of hyperinvariant subspaces for rationally cyclic subnormal operators. We establish a connection between hyperinvariant subspaces and weak-star continuous point evaluations on the commutant.
An elementary proof of a result on Λ(𝑝) sets
Authors: Hare Kathryn E.
Published: June 2010

We give an elementary proof of the fact that a subset of the dual of a compact abelian group which is a

Λ
(
p
)

\Lambda (p)

set for some

1
≤
p
>
2

1 \leq p > 2

is a

Λ
(
p
+
ε
)

\Lambda (p + \varepsilon )

set for some

ε
>
0

\varepsilon > 0

, and extend this result to

Λ
(
p
)

\Lambda (p)

sets for

0
>
p
>
1

0 > p > 1

.
The first Dirichlet eigenvalue and radius of a geodesic ball
Authors: Bang Seung-Jin
Published: June 2010

We give certain relation between the first Dirichlet eigenvalue and radius of a geodesic ball in a connected, compact

n
n

-dimensional Riemannian globally symmetric space of rank one.
The Wiener lemma and cocycles
Authors: Rychlik Marek Ryszard
Published: June 2010

We give a sufficient and necessary condition for a function with its values in the unit circle to be a multiplicative coboundary. This theorem generalizes the following result of Veech [1]. Let

T
:

T

→

T

T:{\mathbf {T}} \to {\mathbf {T}}

be a rotation of the unit circle

T

{\mathbf {T}}

by an irrational angle

θ
\theta

. Let

F
:

T

→

T

F:{\mathbf {T}} \to {\mathbf {T}}

be a measurable function. Then

F
F

is a multiplicative coboundary iff
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Underscript bold upper T Endscripts upper F left-parenthesis x right-parenthesis upper F left-parenthesis upper T x right-parenthesis midline-horizontal-ellipsis upper F left-parenthesis upper T Superscript n minus 1 Baseline x right-parenthesis d mu left-parenthesis x right-parenthesis right-arrow 1 comma as double-vertical-bar n theta double-vertical-bar right-arrow 0 comma">

∫

T

F
(
x
)
F
(
T
x
)
⋯
F
(

T

n
−
1

x
)
d
μ
(
x
)
→
1
,

as 

‖

n
θ

‖

→
0
,

\int _{\mathbf {T}} {F(x)F(Tx) \cdots F({T^{n - 1}}x)d\mu (x) \to 1,\quad {\text {as }}\left \| {n\theta } \right \| \to 0,}

\]
where

‖

n
θ

‖

\left \| {n\theta } \right \|

is the distance of

n
θ

n\theta

from integers and

μ
\mu

is the Haar measure.
Small spaces which “generate” large spaces
Authors: Comfort W. W.
Published: June 2010

Let

S
_

\underline S

denote the class of Tychonoff spaces. For

X
∈

S
_

X \in \underline S

and

C
_

⊆

S
_

\underline C \subseteq \underline S

, we say that

X
X

generates large

C
_

\underline C

-spaces if for every cardinal

α
\alpha

there is

Y
∈

S
_

Y \in \underline S

such that

Y
∈

C
_

,
X
⊆
Y

Y \in \underline C, X \subseteq Y

, and every

Z
∈

C
_

Z \in \underline {C}

with

X
⊆
Z
⊆
Y

X \subseteq Z \subseteq Y

satisfies

|

Z

|

>
α

|Z| > \alpha

. For classes

C
_

\underline C

which satisfy certain mild and natural conditions, we show for each

X
∈

S
_

X \in \underline S

that

X
X

generates large

C
_

\underline C

-spaces iff there is no weakly free

C
_

\underline C

-space over

X
X

—i.e., no space

Y
Y

such that

X
⊆
Y
⊆
C

X \subseteq Y \subseteq C

and every continuous

f
:
X
→
Z
∈

C
_

f:X \to Z \in \underline C

extends to a continuous function

f
¯

:
Y
→
Z

\bar f:Y \to Z

. Among the classes

C
_

⊆

S
_

\underline C \subseteq \underline S

which satisfy these conditions for every

X
∉

C
_

X \notin \underline C

are the class of pseudocompact Tychonoff spaces and the class of almost compact (= absolutely

C
∗

{C^*}

-embedded) Tychonoff spaces.
Inequalities for 𝛼-optimal partitioning of a measurable space
Authors: Legut Jerzy
Published: June 2010

An

α
\alpha

-optimal partition

{

A
i
∗

}

i
=
1

n

\{ A_i^ * \} _{i = 1}^n

of a measurable space according to

n
n

nonatomic probability measures

{

μ
i

}

i
=
1

n

\{ {\mu _i}\} _{i = 1}^n

is defined. A two-sided inequality for

ν
∗

=
min

α
i

−
1

μ
i

(

A
i
∗

)

{\nu ^ * } = \min \alpha _i^{ - 1}{\mu _i}(A_i^ * )

is given. This estimation generalizes and improves a result of Elton et al. [3].
Cofinal families of compacta in separable metric spaces
Authors: van Engelen Fons
Published: June 2010

We show that if

X
X

is a

Π
1
1

\Pi _1^1

-set, then the family of compact subsets of

X
X

contains a cofinal (w.r.t. inclusion) subset of cardinality

d

{\mathbf {d}}

; the same is true if

X
X

is

Π
3
1

\Pi _3^1

, under strong set-theoretic hypotheses.
A note on Jacobson rings and polynomial rings
Authors: Ferrero Miguel , Parmenter Michael M.
Published: June 2010

As is well known, if

R
R

is a ring in which every prime ideal is an intersection of primitive ideals, the same is true of

R
[
X
]

R[X]

. The purpose of this paper is to give a general theorem which shows that the above result remains true when many other classes of prime ideals are considered in place of primitive ideals.
Some Fourier-Stieltjes coefficients revisited
Authors: Reese Sylvester
Published: June 2010

We give a new proof of a result of R. Salem: The Fourier-Stieltjes coefficients of certain strictly increasing singular functions do not vanish at infinity.
Minimal models of nilmanifolds
Authors: Hasegawa Keizo
Published: June 2010

In this paper we first determine minimal models of nilmanifolds associated with given rational nilpotent Lie algebras. Then we study some properties of nilmanifolds through their associated Lie algebras and minimal models. In particular, we will see that a minimal model of a nilmanifold is formal if and only if it is a torus, and thus a non-toral nilmanifold has no complex structure which is birationally isomorphic to a Kähler manifold.
Euclidean metric and flat metric outside a compact set
Authors: Innami Nobuhiro
Published: June 2010

We investigate to what extent there is the gap between Euclidean metrics and flat metrics outside a compact set in complete Riemannian planes.
An application of Hadamard-Lévy’s theorem to a scalar initial value problem
Authors: Rădulescu Sorin , Rădulescu Marius
Published: June 2010

A global inversion theorem due to Hadamard and Lévy is applied to a Volterra integral operator acting in a space of continuous functions to obtain a one-sided criterion for global existence and uniqueness of a scalar initial value problem.
Oscillation theorems for second order nonlinear differential equations
Authors: Wong James S. W.
Published: June 2010

Oscillation criteria for the second-order nonlinear differential equation

x
+
a

(
t
)

|
x
|

y

sgn
⁡
x
=
0

γ
≠
1

x + a\left ( t \right ){\left | x \right |^y}\operatorname {sgn} x = 0\,\gamma \ne 1

, are studied where the coefficient

a

(
t
)

a\left ( t \right )

is not assumed to be non-negative. New proofs are given to theorems of Butler, and extend earlier results of the author.
Torsion units in alternative loop rings
Authors: Goodaire Edgar G. , Polcino Milies César
Published: June 2010

Let

Z

L

{\mathbf {Z}}L

denote the integral alternative loop ring of a finite loop

L
L

. If

L
L

is an abelian group, a well-known result of

G

{\text {G}}

. Higman says that

±
g
,
g
∈
L

\pm g,g \in L

are the only torsion units (invertible elements of finite order) in

Z

L

{\mathbf {Z}}L

. When

L
L

is not abelian, another obvious source of units is the set

±

γ

−
1

g
γ

\pm {\gamma ^{ - 1}}g\gamma

of conjugates of elements of

L
L

by invertible elements in the rational loop algebra

Q

L

{\mathbf {Q}}L

. H. Zassenhaus has conjectured that all the torsion units in an integral group ring are of this form. In the alternative but not associative case, one can form potentially more torsion units by considering conjugates of conjugates

γ

1

−
1

(

γ
2

−
1

g

γ
2

)

γ
1

\gamma _{^1}^{ - 1}\left ( {\gamma _2^{ - 1}g{\gamma _2}} \right ){\gamma _1}

and so forth. In this paper we prove that every torsion unit in an alternative loop ring over

Z

{\mathbf {Z}}

is

±
\pm

a conjugate of a conjugate of a loop element.
A characterization of the Veronese surface
Authors: Ballico Edoardo
Published: June 2010

Here we prove a slight modification of a conjecture of Beltrametti-Sommese proving that the Veronese surface and a general intersection of 3 quadrics are the only smooth surfaces of

C
P

5

{\mathbf {CP}^5}

which are

2
2

-spanned.
A semigroup treatment of a one-dimensional nonlinear parabolic equation
Authors: Serizawa Hisamitsu
Published: June 2010

In this paper we study the existence, uniqueness and differentiability of solutions (in a certain generalized sense) for the nonlinear parabolic equation
\[

u
t

=

u

x
x

−
F
(
u
,

u
x

)
(
0
>
x
>
1
,
t
>
0
)
,

{u_t} = {u_{xx}} - F(u,{u_x})(0 > x > 1,t > 0),

\]
under the maximal monotone boundary conditions:
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis negative 1 right-parenthesis Superscript i Baseline u Subscript x Baseline left-parenthesis t comma i right-parenthesis element-of beta Subscript i Baseline left-parenthesis u left-parenthesis t comma i right-parenthesis right-parenthesis comma t greater-than 0 comma i equals 0 comma 1 period">

(
−
1

)
i

u
x

(
t
,
i
)
∈

β
i

(
u
(
t
,
i
)
)
,
t
>
0
,
i
=
0
,
1.

{( - 1)^i}{u_x}(t,i) \in {\beta _i}(u(t,i)),t > 0,i = 0,1.

\]
𝑀-groups with Sylow towers
Authors: Gunter Elsa L.
Published: June 2010

Let

G
G

be a finite group, all of whose irreducible complex characters are induced from linear characters. Suppose that

G
G

has a normal series of Hall subgroups

G
i

◃
G

{G_i} \triangleleft G

such that

G
0

=
1
,

G
n

=
G

{G_0} = 1,{G_n} = G

, and

|

G
i

:

G

i
−
1

|

\left | {{G_i}:{G_{i - 1}}} \right |

is a power of a prime, for each

i
=
1
,
…
,
n

i = 1, \ldots ,n

. If

N
N

is a normal subgroup of

G
G

, then every irreducible complex character of

N
N

is induced from a linear character.