bluuebunny/crossref_metadata_2025 huggingface dataset:
On the alternating projections theorem and bivariate stationary stochastic processes
Authors: Salehi Habib
Published: June 2010

In this paper we shall first use the theorem of von Neumann on alternating projections to obtain an algorithm for finding the projection of an element x in a Hilbert space

H

\mathcal {H}

onto the subspace spanned by

H

\mathcal {H}

-valued orthogonally scattered measures

ξ
1

{\xi _1}

and

ξ
2

{\xi _2}

. We then specialize this algorithm to the case that

ξ
1

{\xi _1}

and

ξ
2

{\xi _2}

are the canonical measures of the components of a bivariate stationary stochastic process (SP), and thereby get an algorithm for finding the best linear predictor in the time domain.
Inseparable Galois theory of exponent one
Authors: Yuan Shuen
Published: June 2010

An exponent one inseparable Galois theory for commutative ring extensions of prime characteristic

p
≠
0

p \ne 0

is given in this paper.
Embeddings in division rings
Authors: Dauns John
Published: June 2010

A method for embedding a certain class of integral domains in division rings is devised. Integral domains

A
A

are constructed with a generalized valuation into a (noncommutative) totally ordered semigroup that need not be discrete. Then the multiplicative semigroup

A
∖
{
0
}

A\backslash \{ 0\}

is expressed as an inverse limit of semigroups each of which is embeddable in a group. Thus

A
∖
{
0
}

A\backslash \{ 0\}

can be embedded in a group

G
G

. The main problem is to introduce addition on

G
G

in order that

G
G

becomes a division ring by the use of eventually commuting maps of inverse limits.
A diophantine problem on groups. I
Authors: Baker R. C.
Published: June 2010

The following theorem of H. Weyl is generalised to the context of locally compact abelian groups. Theorem. Let

λ
1

>

λ
2

>

λ
3

⋯

{\lambda _1} > {\lambda _2} > {\lambda _3} \cdots

be a sequence such that, for some

c
>
0
,
ε
>
0
,

λ

n
+
k

−

λ
n

≧
c

c > 0,\varepsilon > 0,{\lambda _{n + k}} - {\lambda _n} \geqq c

whenever

k
≧
n

/

(
log
⁡
n

)

1
+
ε

(
n
=
1
,
2
,
…
)

k \geqq n/{(\log n)^{1 + \varepsilon }}(n = 1,2, \ldots )

. Then for almost all real

u
u

the sequence

λ
1

u
,

λ
2

u
,
…
,

λ
n

u

(
mod

1
)

{\lambda _1}u,{\lambda _2}u, \ldots ,{\lambda _n}u\pmod 1

is uniformly distributed.
Theorems of Krein-Milman type for certain convex sets of operators.
Authors: Morris P. D. , Phelps R. R.
Published: June 2010

Let

M
M

be a real (or complex) Banach space and

C
(
Y
)

C(Y)

the space of continuous real (or complex) functions on the compact Hausdorff space

Y
Y

. The unit ball of the space of bounded operators from

M
M

into

C
(
Y
)

C(Y)

is shown to be the weak operator (or equivalently, strong operator) closed convex hull of its extreme points, provided

Y
Y

is totally disconnected, or provided

M
∗

{M^ \ast }

is strictly convex. These assertions are corollaries to more general theorems, most of which have valid converses. In the case

M
=
C
(
X
)

M = C(X)

, similar results are obtained for the positive normalized operators. Analogous results are obtained for the unit ball of the space of compact operators (this time in the operator norm topology) from

M
M

into

C
(
Y
)

C(Y)

.
An exponential limit formula for nonlinear semigroups
Authors: Mermin Joel L.
Published: June 2010

In recent papers, many writers have developed the theory of semigroups of operators generated by nonlinear accretive operators. In the present paper, we construct this semigroup by means of an exponential limit formula, and then use this means of obtaining the semigroup to prove an approximation theorem that is a direct generalization of the Kato-Trotter theorem for linear semigroups.
Elements with trivial centralizer in wreath products
Authors: Kappe Wolfgang P. , Parker Donald B.
Published: June 2010

Groups with self-centralizing elements have been investigated in recent papers by Kappe, Konvisser and Seksenbaev. In particular, if

G
=
A
wr
B

G = A\text {wr} B

is a wreath product some necessary and some sufficient conditions have been given for the existence of self-centralizing elements and for

G
=

⟨

S
G

⟩

G = \left \langle {{S_G}} \right \rangle

, where

S
G

{S_G}

is the set of self-centralizing elements. In this paper

S
G

{S_G}

and the set

R
G

{R_G}

of elements with trivial centralizer are determined both for restricted and unrestricted wreath products. Based on this the size of

⟨

S
G

⟩

\left \langle {{S_G}} \right \rangle

and

⟨

R
G

⟩

\left \langle {{R_G}} \right \rangle

is found in some cases, in particular if

A
A

and

B
B

are

p
p

-groups or if

B
B

is not periodic.
Dual spaces of weighted spaces
Authors: Summers W. H.
Published: June 2010

The topological duals of a large class of weighted spaces of continuous functions are characterized as spaces of Radon measures which can be factored into a product of a weight function and a bounded Radon measure. We next obtain a representation for a base for the equicontinuous subsets of these dual spaces and for the extremal points of the members of this base. Finally, among other applications, these ideas make possible an extension of the representation theorem for biequicontinuous completed tensor products of weighted spaces obtained by the author in an earlier paper.
Bounded and compact vectorial Hankel operators
Authors: Page Lavon B.
Published: June 2010

Operators

H
H

satisfying

S
∗

H
=
H
S

{S^ \ast }H = HS

where

S
S

is a unilateral shift on Hilbert space are called Hankel operators. For a fixed shift

S
S

of arbitrary multiplicity the Banach spaces of bounded Hankel operators and of compact Hankel operators are described, and it is shown that the former is always the second dual of the latter. Representations for bounded and for compact Hankel operators are given in a standard function space model.
Finite groups with quasi-dihedral and wreathed Sylow 2-subgroups.
Authors: Alperin J. L. , Brauer Richard , Gorenstein Daniel
Published: June 2010

The primary purpose of this paper is to give a complete classification of all finite simple groups with quasi-dihedral Sylow 2-subgroups. We shall prove that any such group must be isomorphic to one of the groups

L
3

(
q
)

{L_3}(q)

with

q
≡
−
1

(
mod

4
)
,

U
3

(
q
)

q \equiv - 1 \pmod 4,{U_3}(q)

with

q
≡
1

(
mod

4
)

q \equiv 1 \pmod 4

, or

M

11

{M_{11}}

. We shall also carry out a major portion of the corresponding classification of simple groups with Sylow 2-subgroups isomorphic to the wreath product of

Z

2
n

{Z_{{2^n}}}

and

Z
2

,
n
≧
2

{Z_2},n \geqq 2

.
Polynomial approximation on compact manifolds and homogeneous spaces
Authors: Ragozin David L.
Published: June 2010

We prove several theorems which relate the smoothness of a function,

f
f

, defined on a compact

C
∞

{C^\infty }

-submanifold of a Euclidean space to the rate at which the error in the best uniform approximation to

f
f

by polynomials of degree at most

n
n

tends to zero.
Noncommutative Jordan algebras of capacity two
Authors: Smith Kirby C.
Published: June 2010

Let

J
J

be a noncommutative Jordan algebra with 1. If

J
J

has two orthogonal idempotents

e
e

and

f
f

such that

1
=
e
+
f

1 = e + f

and such that the Peirce

1
1

-spaces of each are Jordan division rings, then

J
J

is said to have capacity two. We prove that a simple noncommutative Jordan algebra of capacity two is either a Jordan matrix algebra, a quasi-associative algebra, or a type of quadratic algebra whose plus algebra is a Jordan algebra determined by a nondegenerate symmetric bilinear form.
Characteristic subgroups of lattice-ordered groups
Authors: Byrd Richard D. , Conrad Paul , Lloyd Justin T.
Published: June 2010

Characteristic subgroups of anll-group are those convexll-subgroups that are fixed by eachll-automorphism. Certain sublattices of the lattice of all convexll-subgroups determine characteristic subgroups which we call socles. Various socles of anll-group are constructed and this construction leads to some structure theorems. The concept of a shifting subgroup is introduced and yields results relating the structure of anll-group to that of the lattice of characteristic subgroups. Interesting results are obtained when thell-group is characteristically simple. We investigate the characteristic subgroups of the vector lattice of real-valued functions on a root system and determine those vector lattices in which everyll-ideal is characteristic. The automorphism group of the vector lattice of all continuous real-valued functions (almost finite real-valued functions) on a topological space (a Stone space) is shown to be a splitting extension of the polar preserving automorphisms by the ring automorphisms. This result allows us to construct characteristically simple vector lattices. We show that self-injective vector lattices exist and that an archimedean self-injective vector lattice is characteristically simple. It is proven that eachll-group can be embedded as anll-subgroup of an algebraically simplell-group. In addition, we prove that each representable (abelian)ll-group can be embedded as anll-subgroup of a characteristically simple representable (abelian)ll-group.
Engulfing continua in an 𝑛-cell
Authors: Tondra Richard J.
Published: June 2010

In this paper it is shown that there exist open connected subsets

D
1

,

D
2

{D_1},{D_2}

, and

D
3

{D_3}

of an

n
n

-cell

E
E

such that, if

C
C

is any proper compact connected subset of

E
E

and

C
⊂
U
,
U

C \subset U,U

open, then there exists a homeomorphism

h
h

of

E
E

onto itself such that

C
⊂
h
(

D
i

)
⊂
U

C \subset h({D_i}) \subset U

for some

i
,
1
≦
i
≦
3

i,1 \leqq i \leqq 3

.
Regular identities in lattices
Authors: Padmanabhan R.
Published: June 2010

An algebraic system

A

=
⟨
A
;
+
,
∘
⟩

\mathfrak {A} = \langle A; + , \circ \rangle

is called a quasilattice if the two binary operations + and

∘
\circ

are semilattice operations such that the natural partial order relation determined by + enjoys the substitution property with respect to

∘
\circ

and vice versa. An identity “

f
=
g

f = g

” in an algebra is called regular if the set of variables occurring in the polynomial

f
f

is the same as that in

g
g

. It is called

n
n

-ary if the number of variables involved in it is at the most

n
n

. In this paper we show that the class of all quasilattices is definable by means of ternary regular lattice identities and that these identities span the set of all regular lattice identities and that the arity of these defining equations is the best possible. From these results it is deduced that the class of all quasilattices is the smallest equational class containing both the class of all lattices and the class of all semilattices in the lattice of all equational classes of algebras of type

⟨
2
,
2
⟩

\langle 2,2\rangle

and that the lattice of all equational classes of quasilattices is distributive.
Some analytic varieties in the polydisc and the Müntz-Szasz problem in several variables
Authors: Hellerstein Simon
Published: June 2010

For

1
≦

p
1

>

p
2

>
∞

1 \leqq {p_1} > {p_2} > \infty

and

n
≧
2

n \geqq 2

it is shown that there exists a sequence of monomials

{

∏

j
=
1

n

S
j
λ

m
j
}

\{ \prod _{j = 1}^nS_j^\lambda mj\}

with

λ

m
j

∼
m

{\lambda _{mj}} \sim m

for each

j
=
1
,
…
,
n

j = 1, \ldots ,n

whose linear span is dense in

L

p
1

(

I
n

)

{L^{{p_1}}}({I^n})

but not in

L

p
2

(

I
n

)

{L^{{p_2}}}({I^n})

(

I
n

{I^n}

is the Cartesian product of

n
n

copies of the closed unit interval

[
0
,
1
]

[0, 1]

). Construction of the examples is via duality, making use of suitable analytic varieties in the polydisc.
Noncommutative Jordan rings
Authors: McCrimmon Kevin
Published: June 2010

Heretofore most investigations of noncommutative Jordan algebras have been restricted to algebras over fields of characteristic

≠
2

\ne 2

in order to make use of the passage from a noncommutative Jordan algebra

A

\mathfrak {A}

to the commutative Jordan algebra

A

+

{\mathfrak {A}^ + }

with multiplication

x
⋅
y
=

1
2

(
x
y
+
y
x
)

x \cdot y = \frac {1}{2}(xy + yx)

. We have recently shown that from an arbitrary noncommutative Jordan algebra

A

\mathfrak {A}

one can construct a quadratic Jordan algebra

A

+

{\mathfrak {A}^ + }

with a multiplication

U
x

y
=
x
(
x
y
+
y
x
)
−

x
2

y
=
(
x
y
+
y
x
)
x
−
y

x
2

{U_x}y = x(xy + yx) - {x^2}y = (xy + yx)x - y{x^2}

, and that these quadratic Jordan algebras have a theory analogous to that of commutative Jordan algebras. In this paper we make use of this passage from

A

\mathfrak {A}

to

A

+

{\mathfrak {A}^ + }

to derive a general structure theory for noncommutative Jordan rings. We define a Jacobson radical and show it coincides with the nil radical for rings with descending chain condition on inner ideals; semisimple rings with d.c.c. are shown to be direct sums of simple rings, and the simple rings to be essentially the familiar ones. In addition we obtain results, which seem to be new even in characteristic

≠
2

\ne 2

, concerning algebras without finiteness conditions. We show that an arbitrary simple noncommutative Jordan ring containing two nonzero idempotents whose sum is not 1 is either commutative or quasiassociative.
On representations of the group 𝑆𝑈(𝑛,1)
Authors: Kraljević Hrvoje
Published: June 2010

A natural bijection is established between the set of equivalence classes of irreducible unitary representations of the group

G
=
S
U
(
n
,
1
)

G = SU(n,1)

, which are not induced from a proper parabolic subgroup, and the set of equivalence classes of irreducible representations of a maximal compact subgroup.
Every weak proper homotopy equivalence is weakly properly homotopic to a proper homotopy equivalence
Authors: Edwards David A. , Hastings Harold M.
Published: June 2010

We prove that every weak proper homotopy equivalence of

σ
\sigma

-compact, locally compact Hausdorff spaces is weakly properly homotopic to a proper homotopy equivalence.
Reductivity and the automorphism group of locally compact groups
Authors: Lee Dong Hoon
Published: June 2010

In this paper, we study reductivity of locally compact groups and its effect on the automorphism group and generalize the classical results on the automorphism group of analytic semisimple groups on the one hand and of compact groups on the other.
Absolute Tauberian constants for Cesàro means of a function
Authors: Sherif Soraya
Published: June 2010

This paper is concerned with introducing two estimates of the forms
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F less-than-or-slanted-equals upper C upper A Subscript k Baseline left-parenthesis alpha right-parenthesis comma upper F less-than-or-slanted-equals upper D upper B Subscript k Baseline left-parenthesis alpha right-parenthesis comma left-parenthesis alpha greater-than 0 right-parenthesis">

F
⩽
C

A
k

(
α
)
,
F
⩽
D

B
k

(
α
)
,
(
α
>
0
)

F \leqslant C{A_k}(\alpha ),F \leqslant D{B_k}(\alpha ),(\alpha > 0)

, where
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F equals integral Subscript 0 Superscript normal infinity Baseline StartAbsoluteValue d left-brace f left-parenthesis alpha x right-parenthesis minus sigma Subscript k Baseline left-parenthesis x right-parenthesis right-brace EndAbsoluteValue comma sigma Subscript k Baseline left-parenthesis x right-parenthesis">

F
=

∫
0
∞

|

d
{
f
(
α
x
)
−

σ
k

(
x
)
}

|

,

σ
k

(
x
)

F = \smallint _0^\infty {|d\{ f(\alpha x) - {\sigma _k}(x)\} |,{\sigma _k}(x)}

denote the Cesàro transform of order k of the function

f
(
x
)
=

∫
0
x

g
(
t
)

d
t
,
g
(
t
)

f(x) = \smallint _0^x {g(t)\;dt,g(t)}

is a function of bounded variation in every finite interval of

t
⩾
0
,

A
k

(
α
)
,

B
k

(
α
)

t \geqslant 0,{A_k}(\alpha ),{B_k}(\alpha )

are absolute Tauberian constants,
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C equals integral Subscript 0 Superscript normal infinity Baseline StartAbsoluteValue d left-brace t g left-parenthesis t right-parenthesis right-brace EndAbsoluteValue greater-than normal infinity comma upper D equals integral Subscript 0 Superscript normal infinity Baseline StartAbsoluteValue d left-brace phi left-parenthesis t right-parenthesis right-brace EndAbsoluteValue greater-than normal infinity">

C
=

∫
0
∞

|

d
{
t
g
(
t
)
}

|

>
∞
,
D
=

∫
0
∞

|

d
{
ϕ
(
t
)
}

|

>
∞

C = \smallint _0^\infty {|d\{ tg(t)\} | > \infty ,D = \smallint _0^\infty {|d\{ \phi (t)\} | > \infty } }

and

ϕ
(
t
)
=

t

−
1

∫
0
t

u
g
(
u
)
d
u

\phi (t) = {t^{ - 1}}\smallint _0^t {ug(u)du}

. The constants

A
k

(
α
)
,

B
k

(
α
)

{A_k}(\alpha ),{B_k}(\alpha )

will be determined.
Quasi-similar models for nilpotent operators
Authors: Apostol C. , Douglas R. G. , Foiaş C.
Published: June 2010

Every nilpotent operator on a complex Hilbert space is shown to be quasi-similar to a canonical Jordan model. Further, the para-reflexive operators are characterized generalizing a result of Deddens and Fillmore.
Maximal chains of prime ideals in integral extension domains. I
Authors: Ratliff L. J. , McAdam S.
Published: June 2010

Let (R, M) be a local domain, let k be a positive integer, and let Q be a prime ideal in

R
k

=
R
[

X
1

,
…
,

X
k

]

{R_k} = R[{X_1}, \ldots ,{X_k}]

such that

M

R
k

⊂
Q

M{R_k} \subset Q

. Then the following statements are equivalent: (1) There exists an integral extension domain of R which has a maximal chain of prime ideals of length n. (2) There exists a minimal prime ideal z in the completion of R such that depth

z
=
n

z = n

. (3) There exists a minimal prime ideal w in the completion of

(

R
k

)
Q

{({R_k})_Q}

such that depth

w
=
n
+
k
−

depth

Q

w = n + k - {\text {depth}}\;Q

. (4) There exists an integral extension domain of

(

R
k

)
Q

{({R_k})_Q}

which has a maximal chain of prime ideals of length

n
+
k
−

depth

Q

n + k - {\text {depth}}\;Q

. (5) There exists a maximal chain of prime ideals of length

n
+
k
−

depth

Q

n + k - {\text {depth}}\;Q

in

(

R
k

)
Q

{({R_k})_Q}

. (6) There exists a maximal chain of prime ideals of length

n
+
1

n + 1

in

R

[

X
1

]

(
M
,

X
1

)

R{[{X_1}]_{(M,{X_1})}}

.
Conjugate points of vector-matrix differential equations
Authors: Lewis Roger T.
Published: June 2010

The system of equations
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript k equals 0 Overscript n Endscripts left-parenthesis negative 1 right-parenthesis Superscript n minus k Baseline left-parenthesis upper P Subscript k Baseline left-parenthesis x right-parenthesis y Superscript left-parenthesis n minus k right-parenthesis Baseline left-parenthesis x right-parenthesis right-parenthesis Superscript left-parenthesis n minus k right-parenthesis Baseline equals 0 left-parenthesis 0 less-than-or-slanted-equals x greater-than normal infinity right-parenthesis">

∑

k
=
0

n

(
−
1
)

n
−
k

(

P
k

(
x
)

y

(
n
−
k
)

(
x
)

)

(
n
−
k
)

=
0

(
0
⩽
x
>
∞
)

\sum \limits _{k = 0}^n {{{( - 1)}^{n - k}}{{\left ( {{P_k}(x){y^{(n - k)}}(x)} \right )}^{(n - k)}}} = 0\quad (0 \leqslant x > \infty )

\]
is considered where the coefficients are real, continuous, symmetric matrices, y is a vector, and

P
0

(
x
)

{P_0}(x)

is positive definite. It is shown that the well-known quadratic functional criterion for existence of conjugate points for this system can be further utilized to extend results of the associated scalar equation to the vector-matrix case, and in some cases the scalar results are also improved. The existence and nonexistence criteria for conjugate points of this system are stated in terms of integral conditions on the eigenvalues or norms of the coefficient matrices.
On the dimension of left invariant means and left thick subsets
Authors: Klawe Maria
Published: June 2010

IfSis a left amenable semigroup, letdim⁡⟨Ml(S)⟩\dim \langle Ml(S)\rangledenote the dimension of the set of left invariant means onS. Theorem.If S is left amenable, thendim⁡⟨Ml(S)⟩=n>∞\dim \langle Ml(S)\rangle = n > \inftyif and only if S contains exactly n disjoint finite left ideal groups. This result was proved by Granirer forScountable or left cancellative. Moreover, whenSis infinite, left amenable, and either left or right cancellative, we show thatdim⁡⟨Ml(S)⟩\dim \langle Ml(S)\rangleis at least the cardinality ofS. An application of these results shows that the radical of the second conjugate algebra ofl1(S){l_1}(S)is infinite dimensional whenSis a left amenable semigroup which does not contain a finite ideal.
The asymptotic behavior of the first eigenvalue of differential operators degenerating on the boundary
Authors: Devinatz Allen , Friedman Avner
Published: June 2010

When L is a second order ordinary or elliptic differential operator, the principal eigenvalue for the Dirichlet problem and the corresponding principal (positive) eigenfunction u are known to exist and u is unique up to normalization. If further L has the form
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="epsilon normal upper Sigma a Subscript i j Baseline partial-differential squared slash partial-differential x Subscript i partial-differential x Subscript i plus normal upper Sigma b Subscript i Baseline partial-differential slash partial-differential x Subscript i">

ε
Σ

a

i
j

∂
2

/

∂

x
i

∂

x
i

+
Σ

b
i

∂

/

∂

x
i

\varepsilon \Sigma {a_{ij}}{\partial ^2}/\partial {x_i}\partial {x_i} + \Sigma {b_i}\partial /\partial {x_i}

then results are known regarding the behavior of the principal eigenvalue

λ
=

λ
ε

\lambda = {\lambda _\varepsilon }

as

ε
↓
0

\varepsilon \downarrow 0

. These results are very sharp in case the vector

(

b
i

)

({b_i})

has a unique asymptotically stable point in the domain

ω
\omega

where the eigenvalue problem is considered. In this paper the case where L is an ordinary differential operator degenerating on the boundary of

ω
\omega

is considered. Existence and uniqueness of a principal eigenvalue and eigenfunction are proved and results on the behavior of

λ
ε

{\lambda _\varepsilon }

as

ε
↓
0

\varepsilon \downarrow 0

are established.
The weakly coupled Yukawa₂ field theory: cluster expansion and Wightman axioms
Authors: Cooper Alan , Rosen Lon
Published: June 2010

We prove convergence of the Glimm-Jaffe-Spencer cluster expansion for the weakly coupled Yukawa model in two dimensions, thereby verifying the Wightman axioms including a positive mass gap.
A partial surface variation for extremal schlicht functions
Authors: McCoy T. L.
Published: June 2010

Let a topological sphere be formed from

|

z

|

⩽
1

|z| \leqslant 1

by dissecting the circumference into finitely many pairs

(

I
j

,

I
j
′

)

({I_j},{I’_j})

of disjoint arcs, identifying

I
j

{I_j}

and

I
j
′

{I’_j}

in opposite directions and making further identifications among the endpoints. If there exists a meromorphic function

Q
(
z
)

Q(z)

, real and non-negative on

|

z

|

=
1

|z| = 1

and satisfying certain consistency conditions with respect to the dissection (given in detail in our Introduction), then one forms a Q-polygon by using the element of length i

d
s
=

Q
(
z
)

d
z

/

z

ds = \sqrt {Q(z)} \;dz/z

to effect the metric identification of the pairs

I
j

,

I
j
′

{I_j},{I’_j}

. In a natural way, Q-polygons become Riemann surfaces, thus can be mapped conformally onto the number sphere. When Q is of the form

Q
(
z
)
=

Σ

j
=
−
N

N

B
j

z
j

Q(z) = \Sigma _{j = - N}^N{B_j}{z^j}

, then the corresponding mapping functions, suitably normalized, become the extremal schlicht functions for the coefficient body

V

N
+
1

{V_{N + 1}}

[3, p. 120]. Suppose that for a given dissection of

|

z

|

=
1

|z| = 1

there is a family

Q
(
z
,
t
)

Q(z,t)

of consistent meromorphic functions. For Q sufficiently smooth as a function of

ε
\varepsilon

, we study the variation of the corresponding normalized mapping functions

f
(
p
,
ε
)

f(p,\varepsilon )

, using results of [2], and show smoothness of f as a function of

ε
\varepsilon

. Specializing Q to the form above, we deduce the existence of smooth submanifolds of

∂

V

N
+
1

\partial {V_{N + 1}}

and obtain a variational formula for the extremal schlicht functions corresponding to motion along these submanifolds.
The porous medium equation in one dimension
Authors: Knerr Barry F.
Published: June 2010

We consider a second order nonlinear degenerate parabolic partial differential equation known as the porous medium equation, restricting our attention to the case of one space variable and to the Cauchy problem where the initial data are nonnegative and have compact support consisting of a bounded interval. Solutions are known to have compact support for each fixed time. In this paper we study the lateral boundary, called the interface, of the support

P
[
u
]

P[u]

of the solution in

R
1

×
(
0
,
T
)

{R^1} \times (0,T)

. It is shown that the interface consists of two monotone Lipschitz curves which satisfy a specified differential equation. We then prove results concerning the behavior of the interface curves as t approaches zero and as t approaches infinity, and prove that the interface curves are strictly monotone except possibly near

t
=
0

t = 0

. We conclude by proving some facts about the behavior of the solution in

P
[
u
]

P[u]

.
Convergence of random processes without discontinuities of the second kind and limit theorems for sums of independent random variables
Authors: Grinblat L. Š.
Published: June 2010

Let

ξ
1

(
t
)
,
…
,

ξ
n

(
t
)
,
…

{\xi _1}(t), \ldots ,{\xi _n}(t), \ldots

and

ξ
(
t
)

\xi (t)

be random processes on the interval [0, 1], without discontinuities of the second kind. A. V. Skorohod has given necessary and sufficient conditions under which the distribution of

f
(

ξ
n

(
t
)
)

f({\xi _n}(t))

converges to the distribution of

f
(
ξ
(
t
)
)

f(\xi (t))

as

n
→
∞

n \to \infty

for any functional f continuous in the Skorohod metric. In the following we shall consider only stochastically right-continuous processes without discontinuities of the second kind, i.e., processes such that the space X of their sample functions is the space of all right-continuous functions

x
(
t
)
(
0
⩽
t
⩽
1
)

x(t)(0 \leqslant t \leqslant 1)

without discontinuities of the second kind. For a set

T
=
{

t
1

,
…

t
n

,
…
}
⊂
[
0
,
1
]

T = \{ {t_1}, \ldots {t_n}, \ldots \} \subset [0,1]

the metric

ρ
T

{\rho _T}

is defined on X as in 2.3. The metric

ρ
T

{\rho _T}

defines on the X the minimal topology in which all functional continuous in Skorohod’s metric and also the functional
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x left-parenthesis t 1 minus 0 right-parenthesis comma x left-parenthesis t 1 right-parenthesis comma ellipsis comma x left-parenthesis t Subscript n Baseline minus 0 right-parenthesis comma x left-parenthesis t Subscript n Baseline right-parenthesis comma ellipsis">

x
(

t
1

−
0
)
,
x
(

t
1

)
,
…
,
x
(

t
n

−
0
)
,
x
(

t
n

)
,
…

x({t_1} - 0),x({t_1}), \ldots ,x({t_n} - 0),x({t_n}), \ldots

are continuous. We will give necessary and sufficient conditions under which the distribution of

f
(

ξ
n

(
t
)
)

f({\xi _n}(t))

converges to the distribution of

f
(
ξ
(
t
)
)

f(\xi (t))

as

n
→
∞

n \to \infty

for any completely continuous functional f, i.e. for any functional f which is continuous in any of the metrics

ρ
T

{\rho _T}

defined in 2.3.
Circle-preserving functions of spheres
Authors: Gibbons Joel , Webb Cary
Published: June 2010

Suppose a function of the standard sphere

S
2

{S^2}

into the standard sphere

S

2
+
m

{S^{2 + m}}

,

m
⩾
0

m \geqslant 0

, sends every circle into a circle but is not a circlepreserving bijection of

S
2

{S^2}

. Then the image of the function must lie in a five-point set or, if it contains more than five points, it must lie in a circle together with at most one other point. We prove the local version of this theorem together with a generalization to n dimensions. In the generalization, the significance of 5 is replaced by

2
n
+
1

2n + 1

. There is also proved a 3-dimensional result in which, compared to the n-dimensional theorem, we are allowed to weaken the structure assumed on the image set of the function.
Uniquely arcwise connected plane continua have the fixed-point property
Authors: Hagopian Charles L.
Published: June 2010

This paper contains a solution to a fixed-point problem of G. S. Young [17, p. 884] and R. H. Bing [4, Question 4, p. 124]. Let M be an arcwise connected plane continuum that does not contain a simple closed curve. We prove that every continuous function of M into M has a fixed point.
The Bergman norm and the Szegő norm
Authors: Saitoh Saburou
Published: June 2010

Let G denote an arbitrary bounded regular region in the plane and

H
2

(
G
)

{H_2}\left ( G \right )

the analytic Hardy class on G with index 2. We show that the generalized isoperimetric inequality
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row StartFraction 1 Over pi EndFraction double-integral Underscript upper G Endscripts StartAbsoluteValue phi left-parenthesis z right-parenthesis psi left-parenthesis z right-parenthesis EndAbsoluteValue squared d x d y less-than-or-slanted-equals StartFraction 1 Over 2 pi EndFraction integral Underscript partial-differential upper G Endscripts StartAbsoluteValue phi left-parenthesis z right-parenthesis EndAbsoluteValue squared StartAbsoluteValue d z EndAbsoluteValue StartFraction 1 Over 2 pi EndFraction integral Underscript partial-differential upper G Endscripts StartAbsoluteValue psi left-parenthesis z right-parenthesis EndAbsoluteValue squared StartAbsoluteValue d z EndAbsoluteValue left-parenthesis z equals x plus i y right-parenthesis EndLayout">

1
π

∬
G

|

φ

(
z
)

ψ

(
z
)

|

2

d
x

d
y

⩽

1

2
π

∫

∂
G

|
φ
(
z
)
|

2

|
d
z
|

1

2
π

∫

∂
G

|
ψ
(
z
)
|

2

|
d
z
|

(
z

=

x

+

i
y
)

\begin{multline} \frac {1}{\pi }\,\iint \limits _G {{{\left | {\varphi \left ( z \right )\psi \left ( z \right )} \right |}^{2\,}}dx\,dy\,\, \leqslant }\,\frac {1}{{2\pi }}\,\int _{\partial G}{{{\left | \varphi (z) \right |}^{2}}}\left | dz \right |\,\frac {1}{2\pi }\,\int _{\partial G}{{{\left | \psi (z) \right |}^{2}}\,\left | dz \right |}\,\,\,\,\,\,\,(z\,=\,x\,+\,iy) \end{multline}

holds for any

φ
\varphi

and

ψ

∈

H
2

(
G
)

\psi \, \in \,{H_2}\left ( G \right )

. We also determine necessary and sufficient conditions for equality.
Extensions, restrictions, and representations of states on 𝐶*-algebras
Authors: Anderson Joel
Published: June 2010

In the first three sections the question of when a pure state g on a

C

∗

{C^{\ast }}

-subalgebra B of a

C

∗

{C^{\ast }}

-algebra A has a unique state extension is studied. It is shown that an extension f is unique if and only if inf

‖

b

(

a

−

f

(
a
)

1

)

b

‖

=

0

\left \| {b\left ( {a\, - \,f\left ( a \right )1} \right )b} \right \|\, = \,0

for each a in A, where the inf is taken over those b in B such that

0

⩽

b

⩽

1

0\, \leqslant \,b\, \leqslant \,1

and

g
(
b
)
=
1

g(b) = 1

. The special cases where B is maximal abelian and/or

A

=

B

(
H
)

A\, = \,B\left ( H \right )

are treated in more detail. In the remaining sections states of the form

T
↦

lim

u

(

T

x
α

,

x
α

)

T \mapsto \lim \limits _{\mathcal {u}} \left ( {T{x_\alpha },\,{x_\alpha }} \right )

, where

{

x
α

}

α

∈

κ

\left \{ {{x_\alpha }} \right \}{\,_{\alpha \, \in \,\kappa }}

is a set of unit vectors in H and

u

\mathcal {u}

is an ultrafilter are studied.
Equivariant 𝐺-structure on versal deformations
Authors: Rim Dock S.
Published: June 2010

Let

X
0

{X_0}

be an algebraic variety, and

(
χ
,

Σ
)

(\chi ,\,\Sigma )

its versal deformation. Now let G be an affine algebraic group acting algebraically on

X
0

{X_0}

. It gives rise to a definite linear G-action on the tangent space of

Σ
\Sigma

. In this paper we establish that if G is linearly reductive then there is an equivariant G-action on

(
χ
,
Σ
)

(\chi ,\Sigma )

which induces given G-action on the special fibre

X
0

{X_0}

and its linear G-action on the tangent space of the formal moduli

Σ
\Sigma

. Furthermore, such equivariant G-structure is shown to be unique up to noncanonical isomorphism.
On the oscillatory behavior of singular Sturm-Liouville expansions
Authors: Shaw J. K.
Published: June 2010

A singular Sturm-Liouville operator

L
y

=

−
(
P

y
′

)
′

+

Q
y

Ly\, =\, - (Py’)’\, +\, Qy

, defined on an interval

[
0
,

b

∗

)

[0,b^{\ast })

of regular points, but singular at

b

∗

b^{\ast }

, is considered. Examples are the Airy equation on

[
0
,
∞
)

[0,\infty )

and the Legendre equation on

[
0
,
1
)

[0,1)

. A mode of oscillation of the successive iterates

f
(
t
)

f(t)

,

(
L
f
)
(
t
)

(Lf)(t)

,

(

L
2

f
)
(
t
)
,

…

({L^2}f)(t),\, \ldots

of a smooth function f is assumed, and the resulting influence on f is studied. The nature of the mode is that for a fixed integer

N

⩾

0

N\, \geqslant \, 0

, each iterate

(

L
k

f
)
(
t
)

({L^k}f)(t)

shall have on

(
0
,

b

∗

)

(0,b^{\ast })

exactly N sign changes which are stable, in a certain sense, as k varies. There is quoted from the literature the main characterization of such functions f which additionally satisfy strong homogeneous endpoint conditions at 0 and

b

∗

b^{\ast }

. An extended characterization is obtained by weakening the conditions of f at 0 and

b

∗

b^{\ast }

. The homogeneous endpoint conditions are replaced by a summability condition on the values, or limits of values, of f at 0 and

b

∗

b^{\ast }

.
Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms
Authors: Kaplan Aroldo
Published: June 2010

We introduce a class of nilpotent Lie groups which arise naturally from the notion of composition of quadratic forms, and show that their standard sublaplacians admit fundamental solutions analogous to that known for the Heisenberg group.
Derivation alternator rings with idempotent
Authors: Hentzel Irvin R. , Smith Harry F.
Published: June 2010

A nonassociative ring is called a derivation alternator ring if it satisfies the identities
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis y z comma x comma x right-parenthesis equals y left-parenthesis z comma x comma x right-parenthesis plus left-parenthesis y comma x comma x right-parenthesis z comma left-parenthesis x comma x comma y z right-parenthesis equals y left-parenthesis x comma x comma z right-parenthesis plus left-parenthesis x comma x comma y right-parenthesis z">

(
y
z
,

x
,

x
)

=

y
(
z
,

x
,

x
)

+

(
y
,

x
,

x
)
z
,

(
x
,

x
,

y
z
)

=

y
(
x
,

x
,

z
)

+

(
x
,

x
,

y
)
z

(yz,\,x,\,x)\, = \,y(z,\,x,\,x)\, + \,(y,\,x,\,x)z,\,(x,\,x,\,yz)\, = \,y(x,\,x,\,z)\, + \,(x,\,x,\,y)z

and

(
x
,

x
,

x
)

=
0

(x,\,x,\,x)\, = 0

. Let R be a prime derivation alternator ring with idempotent

e
≠
1

e \ne 1

and characteristic

≠
2

\ne 2

. If R is without nonzero nil ideals of index 2, then R is alternative.
Cyclic extensions of parafree groups
Authors: Wong Peng Choon
Published: June 2010

Let

1

→

F

→

G

→

T

→

1

1\, \to \,F\, \to \,G\, \to \,T\, \to \,1

be a short exact sequence where F is parafree and T is infinite cyclic. We examine some properties of G when

F

/

F
′

F/F’

is a free ZT-module. Here

F
′

F’

is the commutator subgroup of F and ZT is the integral group ring of T. In particular, we show G is parafree and

γ
n

F

/

γ

n
+
1

F

{\gamma _n}F/{\gamma _{n + 1}}F

is a free ZT-module for every

n
⩾
1

n \geqslant 1

(where

γ
n

F

{\gamma _n}F

is the nth term of the lower central series of F).
Affine connections and defining functions of real hypersurfaces in 𝐶ⁿ
Authors: Luk Hing Sun
Published: June 2010

The affine connection and curvature introduced by Tanaka on a strongly pseudoconvex real hypersurface are computed explicitly in terms of its defining function. If Fefferman’s defining function is used, then the Ricci form is shown to be a function multiple of the Levi form. The factor is computable by Fefferman’s algorithm and its positivity implies the vanishing of certain cohomology groups (of the

∂
¯

b

{\bar \partial _b}

complex) in the compact case.
Approximately finite-dimensional 𝐶*-algebras and Bratteli diagrams
Authors: Lazar A. J. , Taylor D. C.
Published: June 2010

We determine properties of an AF algebra by observing the characteristics of its diagram. In particular, we characterize AF algebras that are liminal, postliminal, antiliminal and with continuous trace; moreover, we characterize liminal AF algebras with Hausdorff spectrum. Some elementary examples of AF algebras with certain desired properties are constructed by using these characterizations.
On Harish-Chandra’s 𝜇-function for 𝑝-adic groups
Authors: Silberger Allan J.
Published: June 2010

The Harish-Chandra

μ
\mu

-function is, up to known constant factors, the Plancherel’s measure associated to an induced series of representations. In this paper we show that, when the series is induced from special representations lifted to a parabolic subgroup, the

μ
\mu

-function is a quotient of translated

μ
\mu

-functions associated to series induced from supercuspidal representations. It is now known, in both the real and p-adic cases, that the

μ
\mu

-function is always an Euler factor.
Harmonically induced representations on nilpotent Lie groups and automorphic forms on nilmanifolds
Authors: Penney Richard C.
Published: June 2010

It is shown that the irreducible “discrete series” representations of certain nilpotent Lie groups may be realized in square integrable

∂
¯

\bar \partial

cohomology spaces. This theory is applied to obtain a concept of automorphic forms on nilmanifolds which generalizes the niltheta functions of Cartier and Auslander-Tolimieri. We also use the automorphic cohomology to solve certain holomorphic difference equations on

C

n

{{\textbf {C}}^n}

.
Extending combinatorial piecewise linear structures on stratified spaces. II
Authors: Anderson Douglas R. , Hsiang Wu Chung
Published: June 2010

Let X be a stratified space and suppose that both the complement of the n-skeleton and the n-stratum have been endowed with combinatorial piecewise linear (PL) structures. In this paper we investigate the problem of “fitting together” these separately given PL structures to obtain a single combinatorial PL structure on the complement of the

(
n

−

1
)

(n\, - \,1)

-skeleton. The first main result of this paper reduces the geometrically given “fitting together” problem to a standard kind of obstruction theory problem. This is accomplished by introducing a tangent bundle for the n-stratum and using immersion theory to show that the “fitting together” problem is equivalent to reducing the structure group of the tangent bundle of the n-stratum to an appropriate group of PL homeomorphisms. The second main theorem describes a method for computing the homotopy groups arising in the obstruction theory problem via spectral sequence methods. In some cases, the spectral sequences involved are fairly small and the first few differentials are described. This paper is an outgrowth of earlier work by the authors on this problem.
Disconjugacy and integral inequalities
Authors: Clausing Achim
Published: June 2010

The basic data in this paper are a disconjugate differential operator and an associated two-point boundary value problem. These define in a natural way a cone of functions satisfying a differential inequality with respect to the operator. By using a result of P. W. Bates and G. B. Gustafson on the monotonicity properties of Green’s kernels it is shown that such a cone has a compact convex base which is a Bauer simplex. This result is used to derive a variety of integral inequalities which include known inequalities of Frank and Pick, Levin and Steckin, Karlin and Ziegler, as well as several new ones.
A separation theorem for Σ¹₁ sets
Authors: Louveau Alain
Published: June 2010

In this paper, we show that the notion of Borel class is, roughly speaking, an effective notion. We prove that if a set A is both

∏
ξ
0

\prod _\xi ^0

and

Δ
1
1

\Delta _1^1

, it possesses a

Π
ξ
0

\Pi _\xi ^0

-code which is also

Δ
1
1

\Delta _1^1

. As a by-product of the induction used to prove this result, we also obtain a separation result for

Σ
1
1

\Sigma _1^1

sets: If two

Σ
1
1

\Sigma _1^1

sets can be separated by a

Π
ξ
0

\Pi _\xi ^0

set, they can also be separated by a set which is both

Δ
1
1

\Delta _1^1

and

Π
ξ
0

\Pi _\xi ^0

. Applications of these results include a study of the effective theory of Borel classes, containing separation and reduction principles, and an effective analog of the Lebesgue-Hausdorff theorem on analytically representable functions. We also give applications to the study of Borel sets and functions with sections of fixed Borel class in product spaces, including a result on the conservation of the Borel class under integration.
Algebras of Fourier transforms with closed restrictions
Authors: Wells Benjamin B.
Published: June 2010

Let G denote a compact abelian group and let B denote a Banach subalgebra of A, the algebra of complex-valued functions on G whose Fourier series is absolutely convergent. If B contains the constant functions, separates the points of G, and if the restriction algebra,

B
(
E
)

B(E)

, is closed in

A
(
E
)

A(E)

for every closed subset E of G, then

B
=
A

B = A

.
On the Wall finiteness obstruction for the total space of certain fibrations
Authors: Munkholm Hans J. , Pedersen Erik Kjaer
Published: June 2010

The problem of computing the Wall finiteness obstruction for the total space of a fibration

p
:

E

→

B

p:\,E\, \to \,B

in terms of that for the base and homological data of the fiber has been considered by D. R. Anderson and by E. K. Pedersen and L. R. Taylor. We generalize their results and show how the problem is related to the algebraically defined transfer map
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi Superscript asterisk Baseline colon upper K 0 left-parenthesis bold upper Z pi 1 left-parenthesis upper B right-parenthesis right-parenthesis right-arrow upper K 0 left-parenthesis bold upper Z pi 1 left-parenthesis upper E right-parenthesis right-parenthesis">

φ

∗

:

K
0

(

Z

π
1

(
B
)
)

→

K
0

(

Z

π
1

(
E
)
)

{\varphi ^{\ast }}:\,{K_0}({\textbf {Z}}{\pi _1}(B))\, \to \,{K_0}({\textbf {Z}}{\pi _1}(E))

,

φ

=

p

∗

:

π
1

(
E
)

→

π
1

(
B
)

\varphi \, = \,{p_{\ast }}:\,{\pi _1}(E)\, \to \,{\pi _1}(B)

, whenever the latter is defined.
Canonical embeddings
Authors: Morrow J. , Rossi H.
Published: June 2010

In this paper the authors compare the embedding of a compact Riemann surface in its tangent bundle to the embedding as the diagonal in the product. These embeddings are proved to be first, but not second, order equivalent. The embedding of a hyperelliptic curve in its tangent bundle is described in an explicit way. Although it is not possible to be so explicit in the other cases, it is shown that in all cases, if the Riemann surface R has genus greater than two, then the blowdown of the zero section of the tangent bundle and the blowdown of the diagonal in the product have the same Hilbert polynomial.
The asymptotic behavior of gas in an 𝑛-dimensional porous medium
Authors: Friedman Avner , Kamin Shoshana
Published: June 2010

Consider the flow of gas in an n-dimensional porous medium with initial density

u
0

(
x
)

⩾

0

{u_0}(x)\, \geqslant \,0

. The density

u
(
x
,

t
)

u(x,\,t)

then satisfies the nonlinear degenerate parabolic equation

u
t

=

Δ

u
m

{u_t}\, = \,\Delta {u^m}

where

m

>

1

m\, > \,1

is a physical constant. Assuming that

I

≡

∫

u
0

(
x
)

d
x

>

∞

I\, \equiv \,\int {\,{u_0}(x)} dx\, > \,\infty

it is proved that

u
(
x
,

t
)

u(x,\,t)

behaves asymptotically, as

t

→

∞

t\, \to \,\infty

, like the special (explicitly given) solution

V
(

|

x

|

,

t
)

V(|x|,\,t)

which is invariant by similarity transformations and which takes the initial values

δ
(
x
)
I

(
δ
(
x
)

=

\delta (x)I\,(\delta (x)\, = \,

the Dirac measure) in the distribution sense.
On a relation between ̃𝑆𝐿₂ cusp forms and cusp forms on tube domains associated to orthogonal groups
Authors: Rallis S. , Schiffmann G.
Published: June 2010

We use the decomposition of the discrete spectrum of the Weil representation of the dual reductive pair

(

S
L

~

2

,

O
(
Q
)
)

({\tilde {SL}_2},\;O(Q))

to construct a generalized Shimura correspondence between automorphic forms on

O
(
Q
)

O(Q)

and

S

L
2

~

\widetilde {S{L_2}}

. We prove a generalized Zagier identity which gives the relation between Fourier coefficients of modular forms on

S

L
2

~

\widetilde {S{L_2}}

and

O
(
Q
)

O(Q)

. We give an explicit form of the lifting between

S

L
2

~

\widetilde {S{L_2}}

and

O
(
n
,
2
)

O(n,2)

in terms of Dirichlet series associated to modular forms. For the special case

n
=
3

n = 3

, we construct certain Euler products associated to the lifting between

S

L
2

S{L_2}

and

S

p

2

≅
O
(
3
,
2
)

{\text {S}}{{\text {p}}_2} \cong O(3,2)

(locally).
On the prevalence of horseshoes
Authors: Young Lai Sang
Published: June 2010

In this paper the symbolic dynamics of several differentiable systems are investigated. It is shown that many well-known dynamical systems, including Axiom

A

{\text {A}}

systems, piecewise monotonic maps of the interval, the Lorenz attractor and Abraham-Smale examples, have inside them subsystems conjugate to subshifts of finite type. These subsystems have hyperbolic structures and hence are stable. They can also be chosen to have entropy arbitrarily close to that of the ambient system.
The Hewitt realcompactification of products
Authors: Ohta Haruto
Published: June 2010

For a completely regular Hausdorff space

X
X

,

υ
X

\upsilon X

denotes the Hewitt realcompactification of

X
X

. Given a topological property

P

\mathcal {P}

of spaces, our interest is in characterizing the class

R

(

P

)

\mathcal {R}(\mathcal {P})

of all spaces

X
X

such that

υ
(
X
×
Y
)
=
υ
X
×
υ
Y

\upsilon (X \times Y) = \upsilon X \times \upsilon Y

holds for each

P

\mathcal {P}

-space

Y
Y

. In the present paper, we obtain such characterizations in the case that

P

\mathcal {P}

is locally compact and in the case that

P

\mathcal {P}

is metrizable.
The lattice of closed congruences on a topological lattice
Authors: Clinkenbeard Dennis J.
Published: June 2010

Our primary objectives are: (1) if

L
L

is a lattice endowed with a topology making both the meet and join continuous then (i) the natural map which associates a congruence with the smallest topologically closed congruence containing it preserves finite meets and arbitrary joins; (ii) the lattice of such closed congruences is a complete Brouwerian lattice; (2) if

L
L

is a topological (semi) lattice with the unit interval as a (semi) lattice homomorphic image then the lattice of closed (semi) lattice congruences has no compatible Hausdorff topology.