bluuebunny/crossref_metadata_2025 huggingface dataset:
Human Ether-à-go-go–related Gene K+ Channel Gating Probed with Extracellular Ca2+
Authors: Johnson J.P. , Mullins Franklin M. , Bennett Paul B.
Published: July 2002

Human ether-à-go-go–related gene (HERG) encoded K+ channels were expressed in Chinese hamster ovary (CHO-K1) cells and studied by whole-cell voltage clamp in the presence of varied extracellular Ca2+ concentrations and physiological external K+. Elevation of external Ca2+ from 1.8 to 10 mM resulted in a reduction of whole-cell K+ current amplitude, slowed activation kinetics, and an increased rate of deactivation. The midpoint of the voltage dependence of activation was also shifted +22.3 ± 2.5 mV to more depolarized potentials. In contrast, the kinetics and voltage dependence of channel inactivation were hardly affected by increased extracellular Ca2+. Neither Ca2+ screening of diffuse membrane surface charges nor open channel block could explain these changes. However, selective changes in the voltage-dependent activation, but not inactivation gating, account for the effects of Ca2+ on Human ether-à-go-go–related gene current amplitude and kinetics. The differential effects of extracellular Ca2+ on the activation and inactivation gating indicate that these processes have distinct voltage-sensing mechanisms. Thus, Ca2+ appears to directly interact with externally accessible channel residues to alter the membrane potential detected by the activation voltage sensor, yet Ca2+ binding to this site is ineffective in modifying the inactivation gating machinery.
Fraction of the Dark Current Carried by Ca2+ through Cgmp-Gated Ion Channels of Intact Rod and Cone Photoreceptors
Authors: Ohyama Tsuyoshi , Hackos David H. , Frings Stephan , Hagen Volker , Kaupp U. Benjamin , Korenbrot Juan I.
Published: July 2002

The selectivity for Ca2+ over Na+, PCa/PNa, is higher in cGMP-gated (CNG) ion channels of retinal cone photoreceptors than in those of rods. To ascertain the physiological significance of this fact, we determined the fraction of the cyclic nucleotide–gated current specifically carried by Ca2+ in intact rods and cones. We activated CNG channels by suddenly (<5 ms) increasing free 8Br-cGMP in the cytoplasm of rods or cones loaded with a caged ester of the cyclic nucleotide. Simultaneous with the uncaging flash, we measured the cyclic nucleotide–dependent changes in membrane current and fluorescence of the Ca2+-binding dye, Fura-2, also loaded into the cells. The ratio of changes in fura-2 fluorescence and the integral of the membrane current, under a restricted set of experimental conditions, is a direct measure of the fractional Ca2+ flux. Under normal physiological salt concentrations, the fractional Ca2+ flux is higher in CNG channels of cones than in those of rods, but it differs little among cones (or rods) of different species. Under normal physiological conditions and for membrane currents ≤200 pA, the Ca2+ fractional flux in single cones of striped bass was 33 ± 2%, and 34 ± 6% in catfish cones. Under comparable conditions, the Ca2+ fractional flux in rod outer segments of tiger salamander was 21 ± 1%, and 14 ± 1% in catfish rods. Fractional Ca2+ flux increases as extracellular Ca2+ rises, with a dependence well described by the Michaelis-Menten equation. KCa, the concentration at which Ca2+ fractional flux is 50% was 1.98 mM in bass cones and 4.96 mM in tiger salamander rods. Because Ca2+ fractional flux is higher in cones than in rods, light flashes that generate equal photocurrents will cause a larger change in cytoplasmic Ca2+ in cones than in rods.
Polarized Signaling via Purinoceptors in Normal and Cystic Fibrosis Airway Epithelia
Authors: Paradiso Anthony M. , Ribeiro Carla M.P. , Boucher Richard C.
Published: July 2002

Airway epithelia are confronted with distinct signals emanating from the luminal and/or serosal environments. This study tested whether airway epithelia exhibit polarized intracellular free calcium (Ca2+i) and anion secretory responses to 5′ triphosphate nucleotides (ATP/UTP), which may be released across both barriers of these epithelia. In both normal and cystic fibrosis (CF) airway epithelia, mucosal exposure to ATP/UTP increased Ca2+i and anion secretion, but both responses were greater in magnitude for CF epithelia. In CF epithelia, the mucosal nucleotide–induced response was mediated exclusively via Ca2+i interacting with a Ca2+-activated Cl− channel (CaCC). In normal airway epithelia (but not CF), nucleotides stimulated a component of anion secretion via a chelerythrine-sensitive, Ca2+-independent PKC activation of cystic fibrosis transmembrane conductance regulator. In normal and CF airway epithelia, serosally applied ATP or UTP were equally effective in mobilizing Ca2+i. However, serosally applied nucleotides failed to induce anion transport in CF epithelia, whereas a PKC-regulated anion secretory response was detected in normal airway epithelia. We conclude that (1) in normal nasal epithelium, apical/basolateral purinergic receptor activation by ATP/UTP regulates separate Ca2+-sensitive and Ca2+-insensitive (PKC-mediated) anion conductances; (2) in CF airway epithelia, the mucosal ATP/UTP-dependent anion secretory response is mediated exclusively via Ca2+i; and (3) Ca2+i regulation of the Ca2+-sensitive anion conductance (via CaCC) is compartmentalized in both CF and normal airway epithelia, with basolaterally released Ca2+i failing to activate CaCC in both epithelia.
Water Permeability of Asymmetric Planar Lipid Bilayers
Authors: Krylov Andrey V. , Pohl Peter , Zeidel Mark L. , Hill Warren G.
Published: July 2002

To understand how plasma membranes may limit water flux, we have modeled the apical membrane of MDCK type 1 cells. Previous experiments demonstrated that liposomes designed to mimic the inner and outer leaflet of this membrane exhibited 18-fold lower water permeation for outer leaflet lipids than inner leaflet lipids (Hill, W.G., and M.L. Zeidel. 2000. J. Biol. Chem. 275:30176–30185), confirming that the outer leaflet is the primary barrier to permeation. If leaflets in a bilayer resist permeation independently, the following equation estimates single leaflet permeabilities: 1/PAB = 1/PA + 1/PB (Eq. l), where PAB is the permeability of a bilayer composed of leaflets A and B, PA is the permeability of leaflet A, and PB is the permeability of leaflet B. Using for the MDCK leaflet–specific liposomes gives an estimated value for the osmotic water permeability (Pf) of 4.6 × 10−4 cm/s (at 25°C) that correlated well with experimentally measured values in intact cells. We have now constructed both symmetric and asymmetric planar lipid bilayers that model the MDCK apical membrane. Water permeability across these bilayers was monitored in the immediate membrane vicinity using a Na+-sensitive scanning microelectrode and an osmotic gradient induced by addition of urea. The near-membrane concentration distribution of solute was used to calculate the velocity of water flow (Pohl, P., S.M. Saparov, and Y.N. Antonenko. 1997. Biophys. J. 72:1711–1718). At 36°C, Pf was 3.44 ± 0.35 × 10−3 cm/s for symmetrical inner leaflet membranes and 3.40 ± 0.34 × 10−4 cm/s for symmetrical exofacial membranes. From , the estimated permeability of an asymmetric membrane is 6.2 × 10−4 cm/s. Water permeability measured for the asymmetric planar bilayer was 6.7 ± 0.7 × 10−4 cm/s, which is within 10% of the calculated value. Direct experimental measurement of Pf for an asymmetric planar membrane confirms that leaflets in a bilayer offer independent and additive resistances to water permeation and validates the use of .
Martin’s Axiom does not imply perfectly normal non-archimedean spaces are metrizable
Authors: Qiao Yuan-Qing
Published: July 2002

In this paper we prove that in various models of Martin’s Axiom there are perfectly normal, non-metrizable non-archimedean spaces of

ℵ
2

\aleph _2

.
Compactifying sufficiently regular covering spaces of compact 3-manifolds
Authors: Myers Robert
Published: July 2002

In this paper it is proven that if the group of covering translations of the covering space of a compact, connected,

P

2

\mathbf {P}^2

-irreducible 3-manifold corresponding to a non-trivial, finitely-generated subgroup of its fundamental group is infinite, then either the covering space is almost compact or the subgroup is infinite cyclic and has normalizer a non-finitely-generated subgroup of the rational numbers. In the first case additional information is obtained which is then used to relate Thurston’s hyperbolization and virtual bundle conjectures to some algebraic conjectures about certain 3-manifold groups.
Statistical extensions of some classical Tauberian theorems
Authors: Fridy J. , Khan M.
Published: July 2002

Hardy’s well-known Tauberian theorem for Cesàro means says that if the sequence

x
x

satisfies

lim
C
x
=
L

\lim Cx = L

and

Δ

x
k

=
O
(
1

/

k
)

\Delta x_k = O (1/k)

, then

lim
x
=
L

\lim x = L

. In this paper it is shown that the hypothesis

lim
C
x
=
L

\lim Cx = L

can be replaced by the weaker assumption of the statistical limit: st-lim

C
x
=
L

Cx = L

, i.e., for every

ϵ
>
0

\epsilon >0

,
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="limit n Superscript negative 1 Baseline StartAbsoluteValue StartSet k less-than-or-equal-to n colon StartAbsoluteValue left-parenthesis upper C x right-parenthesis Subscript k Baseline minus upper L EndAbsoluteValue greater-than-or-equal-to epsilon EndSet EndAbsoluteValue equals 0">

lim

n

−
1

|

{
k
≤
n
:

|

(
C
x

)
k

−
L

|

≥
ϵ
}

|

=
0

\lim n^{-1} | \{ k \leq n: | ( Cx)_k - L | \geq \epsilon \} | = 0

. Similarly, the “one-sided” Tauberian theorem of Landau and Schmidt’s Tauberian theorem for the Abel method are extended by replacing

lim
C
x

\lim Cx

and

lim
A
x

\lim Ax

with st-lim

C
x

Cx

and st-lim

A
x

Ax

, respectively. The Hardy-Littlewood Tauberian theorem for Borel summability is also extended by replacing

lim
t

(
B
x

)
t

=
L

\lim _t (Bx)_t=L

, where

t
t

is a continuous parameter, with

lim
n

(
B
x

)
n

=
L

\lim _n (Bx)_n =L

, and further replacing it by

(

B

∗

)

(B^{*})

-st-lim

B

∗

x
=
L

B^{*} x =L

, where

B

∗

B^{*}

is the Borel matrix method.
Morita equivalence and Pedersen ideals
Authors: Ara Pere
Published: July 2002

We show that twoC∗C^{*}-algebras are strongly Morita equivalent if and only if their Pedersen ideals are Morita equivalent as rings with involution.
A Helson-Lowdenslager-deBranges Theorem in 𝐿²
Authors: Paulsen Vern , Singh Dinesh
Published: July 2002

This paper presents a generalization of the invariant subspace theorem of Helson and Lowdenslager along the lines of de Branges’ generalization of Beurling’s theorem.
Weyl’s theorem holds for algebraically hyponormal operators
Authors: Han Young Min , Lee Woo
Published: July 2002

In this note it is shown that if

T
T

is an “algebraically hyponormal" operator, i.e.,

p
(
T
)

p(T)

is hyponormal for some nonconstant complex polynomial

p
p

, then for every

f
∈
H
(
σ
(
T
)
)

f\in H(\sigma (T))

, Weyl’s theorem holds for

f
(
T
)

f(T)

, where

H
(
σ
(
T
)
)

H(\sigma (T))

denotes the set of analytic functions on an open neighborhood of

σ
(
T
)

\sigma (T)

.
Iteration processes for approximating fixed points of operators of monotone type
Authors: Feng Gu
Published: July 2002

In this paper, the unique fixed points of multi-valued and single-valued operators of monotone type are approximated by Ishikawa and Mann iteration processes with errors in real Banach spaces. The operators may not satisfy the Lipschitzian conditions. The results presented improve and extend some recent results.
Seiberg-Witten invariants for manifolds diffeomorphic outside a circle
Authors: Vidussi Stefano
Published: July 2002

In this paper we prove that simple type four manifolds withb2+>1b_{2}^{+}>1which are diffeomorphic outside a point or outside a wedge of circles have the same Seiberg-Witten invariants, excluding the use of these invariants to detect eventual inequivalent smooth structures.
A normal countably compact not absolutely countably compact space
Authors: Pavlov Oleg
Published: July 2002

We construct an example of a normal countably compact not absolutely countably compact space. We also prove that every hereditarily normal countably compact space is absolutely countably compact and suggest a method for construction of hereditarily normal spaces without property

(
a
)

(a)

.
Sur l’inégalité de Poincaré, à support compact, pour un ou plusieurs champs de vecteurs
Authors: Derridj Makhlouf
Published: July 2002

Nous démontrons, dans cette note, une inégalité de type Poincaré pour un ou plusieurs champs de vecteurs

{

X
j

}

j
=
1
,
…
,
r

,
r
≥
1

\{X_j\}_{j = 1 ,\dotsc ,r}, r \geq 1

, et des fonctions régulières à support contenu dans un voisinage d’une hypersurface

S
S

, sous une hypothèse naturelle de contact entre

S
S

et la famille

{

X
j

}

\{ X_j \}

. La constante intervenant dans cette inégalité est précisément reliée à l’épaisseur du voisinage autour de

S
S

et à l’ordre du contact entre

S
S

et

{

X
j

}

\{ X_j \}

.
On algebraic polynomials with random coefficients
Authors: Farahmand K.
Published: July 2002

The expected number of real zeros and maxima of the curve representing algebraic polynomial of the form
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a 0 StartBinomialOrMatrix n minus 1 Choose 0 EndBinomialOrMatrix Superscript 1 slash 2 plus a 1 StartBinomialOrMatrix n minus 1 Choose 1 EndBinomialOrMatrix Superscript 1 slash 2 Baseline x plus a 2 StartBinomialOrMatrix n minus 1 Choose 2 EndBinomialOrMatrix Superscript 1 slash 2 Baseline x squared plus midline-horizontal-ellipsis plus a Subscript n minus 1 Baseline StartBinomialOrMatrix n minus 1 Choose n minus 1 EndBinomialOrMatrix Superscript 1 slash 2 Baseline x Superscript n minus 1">

a
0

(

n
−
1

0

)

1

/

2

+

a
1

(

n
−
1

1

)

1

/

2

x
+

a
2

(

n
−
1

2

)

1

/

2

x
2

+
⋯
+

a

n
−
1

(

n
−
1

n
−
1

)

1

/

2

x

n
−
1

a_0\binom {n-1}{0}^{1/2}+a_1\binom {n-1}{1}^{1/2}x +a_2\binom {n-1}{2}^{1/2}x^2+\cdots +a_{n-1}\binom {n-1}{n-1}^{1/2}x^{n-1}

where

a

j

,
j
=
0
,
1
,
2
,
…
,
n
−
1

a_{j}, j= 0, 1, 2, \ldots , n-1

, are independent standard normal random variables, are known. In this paper we provide the asymptotic value for the expected number of maxima which occur below a given level. We also show that most of the zero crossings of the curve representing the polynomial are perpendicular to the

x
x

axis. The results show a significant difference in mathematical behaviour between our polynomial and the random algebraic polynomial of the form

a

0

+

a

1

x
+

a

2

x

2

+
⋯
+

a

n
−
1

x

n
−
1

a_{0}+a_{1}x +a_{2}x^{2}+\cdots +a_{n- 1}x^{n-1}

which was previously the most studied.
The Kanenobu-Miyazawa conjecture and the Vassiliev-Gusarov skein modules based on mixed crossings
Authors: Przytycki Józef , Taniyama Kouki
Published: July 2002

We show that a Brunnian link of

n
n

components and the

n
n

component trivial link share the same first

n
−
1

n-1

coefficients of the Jones-Conway (Homflypt) polynomial (answering the question of Kanenobu and Miyazawa). We prove also the similar result for the Kauffman polynomial of Brunnian links. We place our solution in the context of Vassiliev-Gusarov skein modules based on mixed singular crossings.
An addition theorem for the color number
Authors: Aarts Jan , Fokkink Robbert
Published: July 2002

There is a close relation between the color number of a continuous map

f
:
X
→
X

f\colon X \to X

without fixed points and the topological dimension. If 

f
f

is an involution, the color number is also related to the co-index. An addition theorem for the color number is established thus underscoring the interrelations between color number, dimension and co-index.
Noncommutative complex analysis and Bargmann-Segal multipliers
Authors: Rochberg Richard , Weaver Nik
Published: July 2002

We state several equivalent noncommutative versions of the Cauchy-Riemann equations and characterize the unbounded operators on

L

2

(

R

)

L^{2}(\mathbf {R})

which satisfy them. These operators arise from the creation operator via a functional calculus involving a class of entire functions, identified by Newman and Shapiro, which act as unbounded multiplication operators on Bargmann-Segal space.
Polynomial approximation on three-dimensional real-analytic submanifolds of 𝐂ⁿ
Authors: Anderson John , Izzo Alexander , Wermer John
Published: July 2002

It was once conjectured that if

A
A

is a uniform algebra on its maximal ideal space

X
X

and if each point of

X
X

is a peak point for

A
A

, then

A
=
C
(
X
)

A = C(X)

. This peak point conjecture was disproved by Brian Cole in 1968. However, it was recently shown by Anderson and Izzo that the peak point conjecture does hold for uniform algebras generated by smooth functions on smooth two-manifolds with boundary. Although the corresponding assertion for smooth three-manifolds is false, we establish a peak point theorem for real-analytic three-manifolds with boundary.
On the intersection of two-parameter mean value families
Authors: Alzer Horst , Ruscheweyh Stephan
Published: July 2002

We determine all means which are in the intersection of two multivariable two-parameter mean value families. These families were introduced by C. Gini (1938) and K.B. Stolarsky (1975).
Weak Harnack’s Inequality for non-negative solutions of elliptic equations with potential
Authors: Mohammed Ahmed
Published: July 2002

We present an alternative and shorter proof to a weak Harnack inequality for non-negative solutions of divergence structure elliptic equations with potentials from the Kato class.
New examples of non–slice, algebraically slice knots
Authors: Livingston Charles
Published: July 2002

For

n
>
1

n >1

, if the Seifert form of a knotted

2
n
−
1

2n-1

–sphere

K
K

in

S

2
n
+
1

S^{2n+ 1}

has a metabolizer, then the knot is slice. Casson and Gordon proved that this is false in dimension three. However, in the three–dimensional case it is true that if the metabolizer has a basis represented by a strongly slice link, then

K
K

is slice. The question has been asked as to whether it is sufficient that each basis element is represented by a slice knot to assure that

K
K

is slice. For genus one knots this is of course true; here we present genus two counterexamples.
Isolated points and essential components of composition operators on 𝐻^{∞}
Authors: Hosokawa Takuya , Izuchi Keiji , Zheng Dechao
Published: July 2002

We consider the topological space of all composition operators on the Banach algebra of bounded analytic functions on the unit disk. We obtain a function theoretic characterization of isolated points and show that each isolated composition operator is essentially isolated.
Primary decomposition: Compatibility, independence and linear growth
Authors: Yao Yongwei
Published: July 2002

For finitely generated modules

N
⊊
M

N \subsetneq M

over a Noetherian ring

R
R

, we study the following properties about primary decomposition: (1) The Compatibility property, which says that if

Ass
⁡
(
M

/

N
)
=
{

P
1

,

P
2

,
…
,

P
s

}

\operatorname {Ass} (M/N)=\{ P_1, P_2, \dots , P_s\}

and

Q
i

Q_i

is a

P
i

P_i

-primary component of

N
⊊
M

N \subsetneq M

for each

i
=
1
,
2
,
…
,
s

i=1,2,\dots ,s

, then

N
=

Q
1

∩

Q
2

∩
⋯
∩

Q
s

N =Q_1 \cap Q_2 \cap \cdots \cap Q_s

; (2) For a given subset

X
=
{

P
1

,

P
2

,
…
,

P
r

}
⊆
Ass
⁡
(
M

/

N
)

X=\{ P_1, P_2, \dots , P_r \} \subseteq \operatorname {Ass}(M/N)

,

X
X

is an open subset of

Ass
⁡
(
M

/

N
)

\operatorname {Ass}(M/N)

if and only if the intersections
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Q 1 intersection upper Q 2 intersection midline-horizontal-ellipsis intersection upper Q Subscript r Baseline equals upper Q prime 1 intersection upper Q prime 2 intersection midline-horizontal-ellipsis intersection upper Q prime Subscript r">

Q
1

∩

Q
2

∩
⋯
∩

Q
r

=

Q
1
′

∩

Q
2
′

∩
⋯
∩

Q
r
′

Q_1 \cap Q_2\cap \cdots \cap Q_r= Q_1’ \cap Q_2’ \cap \cdots \cap Q_r’

for all possible

P
i

P_i

-primary components

Q
i

Q_i

and

Q
i
′

Q_i’

of

N
⊊
M

N\subsetneq M

; (3) A new proof of the ‘Linear Growth’ property, which says that for any fixed ideals

I
1

,

I
2

,
…
,

I
t

I_1, I_2, \dots , I_t

of

R
R

there exists a

k
∈

N

k \in \mathbb N

such that for any

n
1

,

n
2

,
…
,

n
t

∈

N

n_1, n_2, \dots , n_t \in \mathbb N

there exists a primary decomposition of

I
1

n
1

I
2

n
2

⋯

I
t

n
t

M
⊂
M

I_1^{n_1}I_2^{n_2}\cdots I_t^{n_t}M \subset M

such that every

P
P

-primary component

Q
Q

of that primary decomposition contains

P

k
(

n
1

+

n
2

+
⋯
+

n
t

)

M

P^{k(n_1+n_2+\cdots +n_t)}M

.
An automatic adjoint theorem and its applications
Authors: Wu Junde , Lu Shijie
Published: July 2002

In this paper, we prove the following automatic adjoint theorem: For any sequence spaces

E
(
X
)

E(X)

and

F
(
Y
)

F(Y)

, if

E
(
X
)

E(X)

has the signed-weak gliding hump property and

A
A

is an infinite matrix which transforms

E
(
X
)

E(X)

into

F
(
Y
)

F(Y)

, then the transpose matrix

A
′

A’

of

A
A

transforms

F
(
Y

)
β

F(Y)^\beta

into

E
(
X

)
β

E(X)^\beta

, and for any

x
∈
E
(
X
)

x\in E(X)

and

T
∈
F
(
Y

)
β

T\in F(Y)^\beta

,

[
A
x
,
T
]
=
[
x
,

A
′

T
]

[Ax,T]=[x,A’T]

. That is, the adjoint operator of

A
A

automatically exists and is just the transpose matrix

A
′

A’

of

A
A

. From the theorem we obtain a class of infinite matrix topological algebras

(
λ
,
μ
)

(\lambda ,\mu )

, and prove also a

λ
\lambda

-multiplier convergence theorem of Orlicz-Pettis type. The theorem improves substantially the famous Stiles’ Orlicz-Pettis theorem.
On functions that are trivial cocycles for a set of irrationals. II
Authors: Baggett Lawrence , Medina Herbert , Merrill Kathy
Published: July 2002

Two results are obtained about the topological size of the set of irrationals for which a given function is a trivial cocycle. An example of a continuous function which is a coboundary with non-

L
1

L^1

cobounding function is constructed.
Polynomial rings over Goldie-Kerr commutative rings II
Authors: Faith Carl
Published: July 2002

An overlooked corollary to the main result of the stated paper (Proc. Amer. Math. Soc. 120 (1994), 989–993) is that any Goldie ring

R
R

of Goldie dimension 1 has Artinian classical quotient ring

Q
Q

, hence is a Kerr ring in the sense that the polynomial ring

R
[
X
]

R[X]

satisfies the

a
c
c

acc

on annihilators

(
=
a
c
c
⊥
)

(=acc \bot )

. More generally, we show that a Goldie ring

R
R

has Artinian

Q
Q

when every zero divisor of

R
R

has essential annihilator (in this case

Q
Q

is a local ring; see Theorem

1
′

1^\prime

). A corollary to the proof is Theorem 2: A commutative ring

R
R

has Artinian

Q
Q

iff

R
R

is a Goldie ring in which each element of the Jacobson radical of

Q
Q

has essential annihilator. Applying a theorem of Beck we show that any

a
c
c
⊥

acc \bot

ring

R
R

that has Noetherian local ring

R
p

R_p

for each associated prime

P
P

is a Kerr ring and has Kerr polynomial ring

R
[
X
]

R[X]

(Theorem 5).
Algebraic difference between 𝑝-classes of an H*-algebra
Authors: Molnár Lajos
Published: July 2002

We show that there do not exist surjective ring homomorphisms between different

p
p

-classes of an infinite-dimensional H*-algebra.
A proportional Dvoretzky-Rogers factorization result
Authors: Giannopoulos A.
Published: July 2002

If

X
X

is an

n
n

-dimensional normed space and

ε
∈
(
0
,
1
)

\varepsilon \in (0,1)

, there exists

m
≥
(
1
−
ε
)
n

m\geq (1-\varepsilon )n

, such that the formal identity

i

2
,
∞

:

l
2
m

→

l
∞
m

i_{2,\infty }\colon l^m_2\to l^m_\infty

can be written as

i

2
,
∞

=
α
∘
β
,
β
:

l
2
m

→
X
,
α
:
X
→

l
∞
m

i_{2,\infty }=\alpha \circ \beta ,\beta \colon l^m_2\to X,\alpha \colon X\to l^m_\infty

, with

‖
α
‖
⋅
‖
β
‖
≤
c

/

ε

\|\alpha \|\cdot \|\beta \|\leq c/\varepsilon

. This is proved as a consequence of a Sauer-Shelah type theorem for ellipsoids.
Congruence lattices of algebras— the signed labelling
Authors: Seif S.
Published: July 2002

For an arbitrary algebra

A

\mathbf {A}

a new labelling, called the signed labelling, of the Hasse diagram of

Con
⁡

A

\operatorname {Con}\mathbf {A}

is described. Under the signed labelling, each edge of the Hasse diagram of

Con
⁡

A

\operatorname {Con}\mathbf {A}

receives a label from the set

{
+
,
−
}

\{+,-\}

. The signed labelling depends completely on a subset of the unary polynomials of

A

\mathbf {A}

and its inspiration comes from semigroup theory. For finite algebras, the signed labelling complements the labelled congruence lattices of tame congruence theory (TCT). It provides a different kind of information about those algebras than the TCT labelling particularly with regard to congruence semimodularity. The main result of this paper shows that the congruence lattice of any algebra

A

\mathbf {A}

admits a natural join congruence, denoted

≈
+

\approx _+

, such that

Con
⁡

A

/

≈
+

\operatorname {Con} \mathbf {A}/\approx _+

satisfies the semimodular law. In an application of that result, it is shown that for a regular semigroup

S

\mathbf {S}

, for which

J

=

D

\mathcal {J}=\mathcal {D}

in

H

(

S

)

\mathbf {H}(\mathbf {S})

,

≈
+

\approx _+

is actually a lattice congruence,

≈
+

\approx _+

coincides with

U
U

, and

Con
⁡

S

/

U

\operatorname {Con} \mathbf {S}/U

(
=
Con
⁡

S

/

≈
+

)

(=\operatorname {Con}\mathbf {S}/\approx _+)

satisfies the semimodular law.
The identical equation in 𝜓-products
Authors: Sitaramaiah V. , Subbarao M.
Published: July 2002

In Bull. Amer. Math. Soc. 36 (1930), 762–772, R. Vaidyanatha- swamy established a remarkable identity valid for any multiplicative arithmetic function and involving Dirichlet convolution. D. H. Lehmer (Trans. Amer. Math. Soc. 33 (1931), 945–952) introduced a very general class of arithmetical convolutions, called

ψ
\psi

-products, which include the well-known Dirichlet products, Eckford Cohen’s unitary convolutions, and in fact Narkiewicz’s so-called regular

A
A

-convolutions. In this paper, we establish an identical equation valid for multiplicative arithmetic functions and Lehmer’s

ψ
\psi

-convolutions which yields, as special cases, all known identical equations valid for the Dirichlet and unitary convolutions, besides establishing identical equations for several new convolutions.
On results of Czubiak-Gundersen and Osgood-Yang
Authors: Yi Hong-Xun
Published: July 2002

This paper studies the problem of uniqueness of entire functions that share real zeros and real ones. An example is provided to show that a result of Czubiak and Gundersen is not completely correct. Results in this paper correct the result of Czubiak and Gundersen, and also correct a result of Osgood and Yang.
Trace theorems for holomorphic semigroups and the second order Cauchy problem
Authors: El-Mennaoui O. , Keyantuo V.
Published: July 2002

We use the theory of boundary values (also called traces) of holomorphic semigroups as developed by Boyadzhiev-deLaubenfels (1993) and El-Mennaoui (1992) to study the second order Cauchy problem for certain generators of holomorphic semigroups. Our results contain in particular the result of Hieber (Math. Ann. 291 (1991), 1–16) for the Laplace operator on

L
p

(

R

N

)

L^p(\mathbb R^N)

.
Completely positive module maps and completely positive extreme maps
Authors: Tsui Sze-kai
Published: July 2002

Let

A
,
B

A,B

be unital

C
∗

C^*

-algebras and

P
∞

(
A
,
B
)

P_\infty (A,B)

be the set of all completely positive linear maps of

A
A

into

B
B

. In this article we characterize the extreme elements in

P
∞

(
A
,
B
,
p
)

P_\infty (A,B,p)

,

p
=
Φ
(
1
)

p=\Phi (1)

for all

Φ
∈

P
∞

(
A
,
B
,
p
)

\Phi \in P_\infty (A,B,p)

, and pure elements in

P
∞

(
A
,
B
)

P_\infty (A,B)

in terms of a self-dual Hilbert module structure induced by each

Φ
\Phi

in

P
∞

(
A
,
B
)

P_\infty (A,B)

. Let

P
∞

(
B
(
H
)

)
R

P_\infty (B(H))_R

be the subset of

P
∞

(
B
(
H
)
,
B
(
H
)
)

P_\infty (B(H), B(H))

consisting of

R
R

-module maps for a von Neumann algebra

R
⊆
B
(

H

)

R\subseteq B(\mathbb {H})

. We characterize normal elements in

P
∞

(
B
(
H
)

)
R

P_\infty (B(H))_R

to be extreme. Results here generalize various earlier results by Choi, Paschke and Lin.
On the uniqueness problem of harmonic quasiconformal mappings
Authors: Hanbai Wei
Published: July 2002

In this paper, we give an affirmative answer to Sheretov’s problem on the uniqueness of harmonic mappings and improve the unique minimal mapping theorem of Reich and Strebel. Meanwhile, we also solve a problem posed by Reich and obtain the uniqueness theorem on related weight functions.
Factorization theorems for Hardy spaces of the bidisc, 0<𝑝≤1
Authors: Lin Ing-Jer
Published: July 2002

A factorization theorem is proved in the Hardy spaces

H
p

H^p

of the bi-upper half plane,

0
>
p
≤
1

0>p\le 1

. The proof is based on some fundamental work of Chang-Fefferman on atomic decompositions of

H
p

H^p

.
On the dimension of infinite covers
Authors: Dwyer W. , Stolz S. , Taylor L.
Published: July 2002

We prove the following theorem and some generalizations.

Theorem. Let

X
X

be a connected CW complex which satisfies Poincaré duality of dimension

n
≥
4

n\ge 4

. For any subgroup

H
H

of

π
1

(
X
)

\pi _1(X)

, let

X
H

X_H

denote the cover of

X
X

corresponding to

H
H

. If

H
H

has infinite index in

π
1

(
X
)

\pi _1(X)

, then

X
H

X_H

is homotopy equivalent to an

(
n
−
1
)

(n-1)

-dimensional CW complex.
Weighted inequalities for the maximal geometric mean operator
Authors: Yin Xiangrong , Muckenhoupt Benjamin
Published: July 2002

For nonnegative Borel measures

μ
\mu

on

R
1

R^1

and for the maximal geometric mean operator

G
f

G_f

, we characterize the weight pairs

(
w
,
v
)

(w,v)

for which

G
f

G_f

is of weak type

(
p
,
p
)

(p,p)

and of strong type

(
p
,
p
)

(p,p)

,

0
>
p
>
∞

0>p>\infty

. No doubling conditions are needed. We also note that a previously published different characterization for the strong type inequality for

G
f

G_f

has an incorrect proof.
Generalized interpolation in a multiply connected region
Authors: Bercovici Hari , Zucchi Adele
Published: July 2002

In this paper we extend to the case of multiply connected regions the famous result of Sarason concerning the characterization of operators commuting with the compression of the unilateral shift on

H

2

H^{2}

to a co-invariant subspace.
A topological characterization of linearity for quasi-traces
Authors: Bunce L. , Wright J.
Published: July 2002

Let

A

\mathcal A

be a

C
∗

C^\ast

-algebra, and let

μ
\mu

be a (local) quasi-trace on

A

\mathcal A

. Then

μ
\mu

is linear if, and only if, the restriction of

μ
\mu

to the closed unit ball of

A

\mathcal A

is uniformly weakly continuous.
Generalized contraction mapping principle and differential equations in probabilistic metric spaces
Authors: Chang S. , Lee B. , Cho Y. , Chen Y. , Kang S. , Jung J.
Published: July 2002

A new generalized contraction mapping principle in probabilistic metric spaces is obtained. As an application, we utilize this principle to prove the existence theorems of solutions to differential equations in probabilistic metric spaces. All the results presented in this paper are new.
Rational nodal curves with no smooth Weierstrass points
Authors: Garcia Arnaldo , Lax R.
Published: July 2002

Let

X
X

denote the rational curve with

n
+
1

n+1

nodes obtained from the Riemann sphere by identifying 0 with

∞
\infty

and

ζ
j

\zeta ^j

with

−

ζ
j

-\zeta ^j

for

j
=
0
,
1
,
…
,
n
−
1

j=0,1,\dots ,n-1

, where

ζ
\zeta

is a primitive

(
2
n
)

(2n)

th root of unity. We show that if

n
n

is even, then

X
X

has no smooth Weierstrass points, while if

n
n

is odd, then

X
X

has

2
n

2n

smooth Weierstrass points.
𝑝-sequentiality and 𝑝-Fréchet-Urysohn property of Franklin compact spaces
Authors: Garcia-Ferreira S. , Malykhin V.
Published: July 2002

Franklin compact spaces defined by maximal almost disjoint families of subsets of

ω
\omega

are considered from the view of its

p
p

-sequentiality and

p
p

-Fréchet-Urysohn-property for ultrafilters

p
∈

ω
∗

p\in \omega ^*

. Our principal results are the following: CH implies that for every

P
P

-point

p
∈

ω
∗

p\in \omega ^*

there are a Franklin compact

p
p

-Fréchet-Urysohn space and a Franklin compact space which is not

p
p

-Fréchet-Urysohn; and, assuming CH, for every Franklin compact space there is a

P
P

-point

q
∈

ω
∗

q\in \omega ^*

such that it is not

q
q

-Fréchet-Urysohn. Some new problems are raised.
Some characterizations of 𝐶(ℳ)
Authors: Bishop Christopher
Published: July 2002

We show that a function

f
f

on the unit disk extends continuously to

M

\mathcal M

, the maximal ideal space of

H
∞

(

D

)

H^\infty (\mathbb D)

iff it is uniformly continuous (in the hyperbolic metric) and close to constant on the complementary components of some Carleson contour.
On nonlinear 𝑛-widths
Authors: Dung Dinh , Thanh Vu
Published: July 2002

For characterization of best nonlinear approximation, DeVore, Howard, and Micchelli have recently suggested the nonlinear

n
n

-width

δ
n

(
W
,
X
)

\delta _n(W,X)

of a subset

W
W

in a normed linear space

X
X

. We proved by a topological method that for

δ
n

(
W
,
X
)

\delta _n(W,X)

and the well-known Aleksandrov

n
n

-width

a
n

(
W
,
X
)

a_n(W,X)

in a Banach space

X
X

the following inequalities hold:
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="delta Subscript 2 n plus 1 Baseline left-parenthesis upper W comma upper X right-parenthesis less-than-or-equal-to a Subscript n Baseline left-parenthesis upper W comma upper X right-parenthesis less-than-or-equal-to delta Subscript n Baseline left-parenthesis upper W comma upper X right-parenthesis">

δ

2
n
+
1

(
W
,
X
)
≤

a
n

(
W
,
X
)
≤

δ
n

(
W
,
X
)

\delta _{2n+1}(W,X)\le a_n(W,X)\le \delta _n(W,X)

. Let

K

p
,
θ

α

K_{p,\theta }^{\alpha }

be the unit ball of Besov space

B

p
,
θ

α

,

α
>
0
,

1
≤
p
,
θ
≤
∞

B_{p,\theta }^{\alpha },\quad \alpha >0,\quad 1\le p,\theta \le \infty

, of multivariate periodic functions. Then for approximation in

L
q

,

1
≤
q
≤
∞

L_q,\quad 1\le q\le \infty

, with some restriction on

p
,
q

p,q

and

α
\alpha

, we established the asymptotic degree of these

n
n

-widths:
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a Subscript n Baseline left-parenthesis upper K Subscript p comma theta Superscript alpha Baseline comma upper L Subscript q Baseline right-parenthesis almost-equals delta Subscript n Baseline left-parenthesis upper K Subscript p comma theta Superscript alpha Baseline comma upper L Subscript q Baseline right-parenthesis almost-equals n Superscript negative alpha">

a
n

(

K

p
,
θ

α

,

L
q

)
≈

δ
n

(

K

p
,
θ

α

,

L
q

)
≈

n

−
α

a_n(K_{p,\theta }^{\alpha },L_q)\approx \delta _n(K_{p,\theta }^{\alpha }, L_q)\approx n^{-\alpha }

.
Mean theoretic approach to the grand Furuta inequality
Authors: Fujii Masatoshi , Kamei Eizaburo
Published: July 2002

Very recently, Furuta obtained the grand Furuta inequality which is a parameteric formula interpolating the Furuta inequality and the Ando-Hiai inequality as follows : If

A
≥
B
≥
0

A \ge B \ge 0

and

A
A

is invertible, then for each

t
∈
[
0
,
1
]

t \in [0,1]

,
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F Subscript p comma t Baseline left-parenthesis upper A comma upper B comma r comma s right-parenthesis equals upper A Superscript negative r slash 2 Baseline left-brace upper A Superscript r slash 2 Baseline left-parenthesis upper A Superscript negative t slash 2 Baseline upper B Superscript p Baseline upper A Superscript negative t slash 2 Baseline right-parenthesis Superscript s Baseline upper A Superscript r slash 2 Baseline right-brace Superscript StartFraction 1 minus t plus r Over left-parenthesis p minus t right-parenthesis s plus r EndFraction Baseline upper A Superscript negative r slash 2">

F

p
,
t

(
A
,
B
,
r
,
s
)
=

A

−
r

/

2

{

A

r

/

2

(

A

−
t

/

2

B

p

A

−
t

/

2

)

s

A

r

/

2

}

1
−
t
+
r

(
p
−
t
)
s
+
r

A

−
r

/

2

\begin{equation*}F_{p,t}(A,B,r,s) = A^{-r/2}\{A^{r/2}(A^{-t/2}B^{p}A^{-t/2})^{s}A ^{r/2}\}^{\frac {1-t+r}{(p-t)s+r}}A^{-r/2} \end{equation*}

is a decreasing function of both

r
r

and

s
s

for all

r
≥
t
,
 
p
≥
1

r \ge t, ~p \ge 1

and

s
≥
1

s \ge 1

. In this note, we employ a mean theoretic approach to the grand Furuta inequality. Consequently we propose a basic inequality, by which we present a simple proof of the grand Furuta inequality.
Support cones and convexity of sets in ℝⁿ
Authors: Huotari Robert , Shi Junning
Published: July 2002

We discuss several metric characterizations of convexity of sets in non-smooth finite-dimensional Banach spaces. We describe a setting in which convexity is equivalent to the rotation-invariance of various properties, including almost convexity, radial continuity of the metric projection, and Chebyshevity. One of the tools used is a generalization of norm-smoothness which involves support cones of the unit ball.
Locally injective maps in o-minimal structures without poles are surjective
Authors: Lewenberg Adam
Published: July 2002

Iff:Rm→Rmf:\mathbf R^m\to \mathbf R^mis continuous and locally injective, thenffis in fact surjective and a homeomorphism, providedffis definable in an o-minimal expansion without poles of the ordered additive group of real numbers; ‘without poles’ means that every one-variable definable function is locally bounded. Some general properties of definable maps in o-minimal expansions of ordered abelian groups without poles are also established.
Paracompact subspaces in the box product topology
Authors: Nyikos Peter , Piatkiewicz Leszek
Published: July 2002

In 1975 E. K. van Douwen showed that if

(

X
n

)

n
∈
ω

( X_n )_{ n \in \omega }

is a family of Hausdorff spaces such that all finite subproducts

∏

n
>
m

X
n

\prod _{ n > m } X_n

are paracompact, then for each element

x
x

of the box product

◻

n
∈
ω

X
n

\square _{n \in \omega } X_n

the

σ
\sigma

-product
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma left-parenthesis x right-parenthesis equals StartSet y element-of white medium square upper X Subscript n Baseline colon StartSet n element-of omega colon x left-parenthesis n right-parenthesis not-equals y left-parenthesis n right-parenthesis EndSet is finite EndSet">

σ
(
x
)
=
{
y
∈

◻

n
∈
ω

X
n

:
{
n
∈
ω
:
x
(
n
)
≠
y
(
n
)
}
 is finite
}

\sigma ( x ) = \{ y \in \square _{n \in \omega } X_n : \{ n \in \omega : x (n) \neq y (n) \} \text { is finite} \}

is paracompact. He asked whether this result remains true if one considers uncountable families of spaces. In this paper we prove in particular the following result: Theorem Let

κ
\kappa

be an infinite cardinal number, and let

(

X

α

)

α
∈
κ

( X_{\alpha } )_{\alpha \in \kappa }

be a family of compact Hausdorff spaces. Let

x
∈

◻

=

◻

α
∈
κ

X
α

x \in \square = \square _{\alpha \in \kappa } X_\alpha

be a fixed point. Given a family

R

\mathcal {R}

of open subsets of

◻

\square

which covers

σ
(
x
)

\sigma ( x )

, there exists an open locally finite in

◻

\square

refinement

S

\mathcal {S}

of

R

\mathcal {R}

which covers

σ
(
x
)

\sigma ( x )

. We also prove a slightly weaker version of this theorem for Hausdorff spaces with “all finite subproducts are paracompact" property. As a corollary we get an affirmative answer to van Douwen’s question.
Growth series for the commutator subgroup
Authors: Pollicott Mark , Sharp Richard
Published: July 2002

In this paper we study growth series associated to commutator subgroups of surface groups. We conclude that these growth series are not rational.
A degree estimate for subdivision surfaces of higher regularity
Authors: Reif Ulrich
Published: July 2002

Subdivision algorithms can be used to construct smooth surfaces from control meshes of arbitrary topological structure. In contrast to tangent plane continuity, which is well understood, very little is known about the generation of subdivision surfaces of higher regularity. This work presents a degree estimate for piecewise polynomial subdivision surfaces saying that curvature continuity is possible only if the bi-degree

d
d

of the patches satisfies

d
≥
2
k
+
2

d \ge 2k+2

, where

k
k

is the order of smoothness on the regular part of the surface. This result applies to any stationary or non-stationary scheme consisting of masks of arbitrary size provided that some generic symmetry and regularity assumptions are fulfilled.
On purely inseparable extensions 𝐾[𝑋,𝑌]/𝐾[𝑋’,𝑌’] and their generators
Authors: Daigle D.
Published: July 2002

Let

k

\mathbf {k}

be a field of characteristic

p
>
0

p>0

and

R
=

k

[
X
,
Y
]

R=\mathbf {k} [X,Y]

a polynomial algebra in two variables. By a

p
p

-generator of

R
R

we mean an element

u
u

of

R
R

for which there exist

v
∈
R

v\in R

and

n
≥
0

n\ge 0

such that

k

[
u
,
v
]
⊇

R

p
n

\mathbf {k} [u,v]\supseteq R^{p^n}

. We also define a

p
p

-line of

R
R

to mean any element

u
u

of

R
R

whose coordinate ring

R

/

u
R

R/uR

is that of a

p
p

-generator. Then we prove that if

u
∈
R

u\in R

is such that

u
−
T

u-T

is a

p
p

-line of

k

(
T
)
[
X
,
Y
]

\mathbf {k} (T)[X,Y]

(where

T
T

is an indeterminate over

R
R

), then

u
u

is a

p
p

-generator of

R
R

. This is analogous to the well-known fact that if

u
∈
R

u\in R

is such that

u
−
T

u-T

is a line of

k

(
T
)
[
X
,
Y
]

\mathbf {k} (T)[X,Y]

, then

u
u

is a variable of

R
R

. We also prove that if

u
u

is a

p
p

-line of

R
R

for which there exist

ϕ
∈
qt
⁡
R

\phi \in \operatorname {qt} R

and

n
≥
0

n\ge 0

such that

k

(
u
,
ϕ
)
⊇

R

p
n

\mathbf {k} (u,\phi )\supseteq R^{p^n}

, then

u
u

is in fact a

p
p

-generator of

R
R

.
Separating versus strictly separating vectors
Authors: Azoff Edward , Ding Lifeng , Wogen Warren
Published: July 2002

Let

S
S

be a linear manifold of Banach space operators which is closed in the strong operator topology. Existence of a disjoint pair of separating vectors does not guarantee reflexivity of

S
S

, but

S
S

must be reflexive if one of these vectors is strictly separating.

S
S

must also be reflexive if all non–zero linear combinations of some independent pair of vectors strictly separate

S
S

.
Weighted composition operators on Hilbert spaces of vector-valued functions
Authors: Hornor William , Jamison James
Published: July 2002

In this paper we investigate criterion for the hyponormality, cohyponormality, and normality of weighted composition operators acting on Hilbert spaces of vector-valued functions.
A note on Miller’s theorem about maps out of classifying spaces
Authors: McGibbon C.
Published: July 2002

Let

X
X

be a connected infinite loop space whose fundamental group is a torsion group and let

Y
Y

be a finite nilpotent

C
W

CW

-complex. The main result of this paper is that the space of based maps from

X
X

to the profinite completion of

Y
Y

is weakly contractible.
A new proof of Masser’s vanishing theorem
Authors: Nishioka Kumiko
Published: July 2002

We give a simple proof of Masser’s vanishing theorem, which is important in investigating the algebraic independence of the values of Mahler functions.
A cocycle theorem with an application to Rosenthal sets
Authors: Schwartz Peter
Published: July 2002

For certain Markov operators

T
T

we show that bounded cocycles with respect to

T
T

are coboundaries. This result is applied to show that certain translation invariant subspaces of functions on the unit circle have unexpected regularity properties.
𝐾-invariant Kaehler structures on 𝐾_{𝐂}/𝐍 and the associated line bundles
Authors: Chuah Meng-Kiat
Published: July 2002

Let

K
K

be a compact semi-simple Lie group, and let

N
N

be a maximal unipotent subgroup of the complexified group

K

C

K_{ \mathbf {C}}

. In this paper, we classify all the

K
K

-invariant Kaehler structures on

K

C

/

N

K_{ \mathbf {C}}/N

. For each Kaehler structure

ω
\omega

, let

L

{ \mathbf {L}}

be the line bundle with connection whose curvature is

ω
\omega

. We then study the holomorphic sections of

L

{ \mathbf {L}}

, which constitute a

K
K

-representation space.
𝐶(𝐾,𝐴) and 𝐶(𝐾,𝐻^{∞}) have the Dunford-Pettis property
Authors: Contreras Manuel , Díaz Santiago
Published: July 2002

Denote by

X
X

either the disc algebra

A
A

, or the space

H

∞

H^{\infty }

of bounded analytic functions on the disc, or any of their even duals. Then

C
(
K
,
X
)

C(K,X)

has the Dunford-Pettis property.
On the set of all continuous functions with uniformly convergent Fourier series
Authors: Ki Haseo
Published: July 2002

In this article we calculate the exact location in the Borel hierarchy ofUCF,UCF,the set of all continuous functions on the unit circle with uniformly convergent Fourier series. It turns out to be completeFσδ.F_{\sigma \delta }.Also we prove that anyGδσG_{\delta \sigma }set that includesUCFUCFmust contain a continuous function with divergent Fourier series.
A quick proof of the classification of simple real Lie algebras
Authors: Knapp A.
Published: July 2002

Élie Cartan’s classification of the simple Lie algebras over

R

\mathbb {R}

is derived quickly from some structure theory over

R

\mathbb {R}

and the classification over

C

\mathbb {C}

.
Union and tangle
Authors: Nakanishi Yasutaka
Published: July 2002

Shibuya proved that any union of two nontrivial knots without local knots is a prime knot. In this note, we prove it in a general setting. As an application, for any nontrivial knot, we give a knot diagram such that a single unknotting operation on the diagram cannot yield a diagram of a trivial knot.
Locally solvable factors of varieties
Authors: Kearnes Keith
Published: July 2002

We give necessary and sufficient local conditions, which are easy to check, for a locally finite variety

V

\mathcal {V}

to decompose as the product of a locally solvable subvariety

U

\mathcal {U}

and a subvariety

W

\mathcal {W}

which has type set disjoint from the type set of

U

\mathcal {U}

.
On Voiculescu’s double commutant theorem
Authors: Berger C. , Coburn L.
Published: July 2002

For a separable infinite-dimensional Hilbert space

H
H

, we consider the full algebra of bounded linear transformations

B
(
H
)

B(H)

and the unique non-trivial norm-closed two-sided ideal of compact operators

K

\mathcal K

. We also consider the quotient

C
∗

C^*

-algebra

C

=
B
(
H
)

/

K

\mathcal C=B(H)/\mathcal K

with quotient map
\[

π
:
B
(
H
)
→

C

.

\pi \colon B(H)\to \mathcal C.

\]
For

A

\mathcal A

any

C
∗

C^*

-subalgebra of

C

\mathcal C

, the relative commutant is given by

A

′

=
{
C
∈

C

:
C
A
=
A
C

\mathcal A’=\{C\in \mathcal C\colon CA=AC

for all

A
A

in

A

}

\mathcal A\}

. It was shown by D. Voiculescu that, for

A

\mathcal A

any separable unital

C
∗

C^*

-subalgebra of

C

\mathcal C

,

(VDCT)

A

=

A

.

\begin{equation*} \mathcal A=\mathcal A.\tag {VDCT} \end{equation*}

In this note, we exhibit a non-separable unital

C
∗

C^*

-subalgebra

A

0

\mathcal A_0

of

C

\mathcal C

for which (VDCT) fails.
Conormal differential forms of an analytic germ
Authors: Gassler Robert
Published: July 2002

A differential form vanishing on the tangent space at smooth points of a reduced embedded analytic germ is called conormal. To prove that a conormal one–form of a hypersurface vanishes at its singularities, we state a Bertini–type theorem.
Uncountably many 𝐶⁰ conformally distinct Lorentz surfaces and a finiteness theorem
Authors: Smyth Robert
Published: July 2002

This paper describes an uncountable family of Lorentz surfaces realized as rectangular regions in the Minkowski 2-planeE12E^2_1. A simpleC0C^0conformal invariant is defined which assigns a different real value to each Lorentz surface in the family. While these surfaces provide uncountably manyC0C^0conformally distinct, bounded, convex subsets ofE12E^2_1which are each symmetric about a properly embedded timelike curve and about a properly embedded spacelike curve, it is shown that there are only 21C0C^0conformally distinct, bounded, convex subsets ofE12E^2_1which are symmetric about some null line.