bluuebunny/crossref_metadata_2025 huggingface dataset:
Sequences in the range of a vector measure with bounded variation
Authors: Piñeiro Cándido
Published: June 2010

Let X be a Banach space. We consider sequences

(

x
n

)

({x_n})

in X lying in the range of a measure valued in a superspace of X and having bounded variation. Among other results, we prove that G.T. spaces are the only Banach spaces in which those sequences are actually in the range of an

X

∗
∗

{X^{ \ast \ast }}

-valued measure of bounded variation.
Analytic ultradistributions
Authors: Stanković B.
Published: June 2010

A necessary and sufficient condition that an ultradistribution, of Beurling or Roumieu type, which is defined on an open set

Ω
⊂

R

n

\Omega \subset {\mathcal {R}^n}

is a real analytic function is given. This result is applied to different problems.
A reflexive admissible topological group must be locally compact
Authors: Martín Peinador Elena
Published: June 2010

Let G be a reflexive topological group, and

G

∅
^

G\hat \emptyset

its group of characters, endowed with the compact open topology. We prove that the evaluation mapping from

G

∅
^

×
G

G\hat \emptyset \times G

into the torus T is continuous if and only if G is locally compact. This is an analogue of a well-known theorem of Arens on admissible topologies on

C
(
X
)

C(X)

.
Mutually complementary families of 𝑇₁ topologies, equivalence relations and partial orders
Authors: Steprāns Juris , Watson Stephen
Published: June 2010

We examine the maximum sizes of mutually complementary families in the lattice of topologies, the lattice of

T
1

{T_1}

topologies, the semi-lattice of partial orders and the lattice of equivalence relations. We show that there is a family of

κ
\kappa

many mutually complementary partial orders (and thus

T
0

{T_0}

topologies) on

κ
\kappa

and, using this family, build another family of

κ
\kappa

many mutually

T
1

{T_1}

complementary topologies on

κ
\kappa

. We obtain

κ
\kappa

many mutually complementary equivalence relations on any infinite cardinal

κ
\kappa

and thus obtain the simplest proof of a 1971 theorem of Anderson. We show that the maximum size of a mutually

T
1

{T_1}

complementary family of topologies on a set of cardinality

κ
\kappa

may not be greater than

κ
\kappa

unless

ω
>
κ
>

2
c

\omega > \kappa > {2^c}

. We show that it is consistent with and independent of the axioms of set theory that there be

ℵ
2

{\aleph _2}

many mutually

T
1

{T_1}

-complementary topologies on

ω
1

{\omega _1}

using the concept of a splitting sequence. We construct small maximal mutually complementary families of equivalence relations.
Knotted projections of planar graphs
Authors: Taniyama Kouki
Published: June 2010

In this paper we describe a regular projection of a planar graph that is achieved only by knotted embeddings in 3-space. We also give conditions under which any regular projection of such graphs can be achieved by unknotted embeddings.
The power substitution for rings of complex and real functions on compact metric spaces
Authors: Dranishnikov A. N.
Published: June 2010

The weak power substitution property for rings of matrices over the ring of functions on a compact metric space X is given in terms of cohomological dimension. A compactum with the ring of complex functions

C
(
X
)

C(X)

having the following property is constructed: the units of

C
(
X
)

C(X)

are not dense in

C
(
X
)

C(X)

and they are dense among squares.
Measures on product spaces
Authors: Elliott E. O.
Published: June 2010

The theory of regular conditional probability is generalized by replacing a probability measure by a (perhaps non-

σ
\sigma

-finite) outer measure and a resulting measure is obtained on the product space. A Fubini-like theorem is obtained for the integrable functions of this measure and a condition is given for this measure to impart the topological properties of being inner regular and almost Lindelöf to the product space when the component spaces also have these topological properties. Thus some theorems for the Morse-Bledsoe product measure [1] are generalized by methods very similar to those used in their paper on product measures [1].
Inequalities satisfied by entire functions and their derivatives
Authors: Lee Boo-sang , Shah S. M.
Published: June 2010

For a class of entire functions with simple and positive zeros, it is shown that the maximum of the moduli of the first two Taylor coefficients at any point z, dominate all the remaining Taylor coefficients, provided

|

z

|

|z|

is sufficiently large. Further, there is a subclass for which this result holds at every point z.
A noncommutative Hilbert basis theorem and subrings of matrices
Authors: Amitsur S. A.
Published: June 2010

A finitely generated central extension

A
[

u
1

,
…
,

u
k

]

A[{u_1}, \ldots ,{u_k}]

of a commutative noetherian ring A, satisfies the ascending chain condition for ideals P for which

A
[

u
1

,
…
,

u
k

]

/

P

A[{u_1}, \ldots ,{u_k}]/P

can be embedded in matrix rings

M
n

(
K
)

{M_n}(K)

over arbitrary commutative rings K and n bounded. The method of proof leads to an example of a ring R which satisfies the same identities of

M
n

(
K
)

{M_n}(K)

but nevertheless cannot be embedded in any matrix ring over a commutative ring of arbitrary finite order.
Balanced rings and a problem of Thrall
Authors: Camillo Victor P.
Published: June 2010

Balanced ring is defined and related to Thrall’s QF-1 rings. Several theorems are obtained which show that balanced rings enjoy strong homological and chain conditions. The structure of commutative balanced rings is determined. Also, the structure of commutative artinian QF-1 rings is gotten. This is a generalization of a theorem of Floyd.
Markuschevich bases and duality theory
Authors: Johnson William B.
Published: June 2010

Several duality theorems concerning Schauder bases in locally convex spaces have analogues in the theory of Markuschevich bases. For example, a locally convex space with a Markuschevich basis is semireflexive iff the basis is shrinking and boundedly complete. The strong existence Theorem III.1 for Markuschevich bases allows us to show that a separable Banach space is isomorphic to a conjugate space iff it admits a boundedly complete Markuschevich basis, and that a separable Banach space has the metric approximation property iff it admits a Markuschevich basis which is a generalized summation basis in the sense of Kadec.
Finite dimensional inseparable algebras
Authors: Yuan Shuen
Published: June 2010

We determine the structure of finite dimensional algebras which are differentiably simple with respect to a set of higher derivations.
Finitely generated ideals of differentiable functions
Authors: Roth B.
Published: June 2010

In some spaces of differentiable functions, the finitely generated ideals which are closed are characterized in terms of the zeros of the generators. Applications are made to problems of division for distributions.
Koszul resolutions
Authors: Priddy Stewart B.
Published: June 2010

Resolutions, which generalize the classical Koszul resolutions, are constructed for a large class of augmented algebras including the Steenrod algebra and the universal enveloping algebras. For each such algebra

A
A

, an explicit differential algebra

K
¯

∗
(
A
)

\bar K\ast (A)

is described such that (1)

K
¯

∗

(
A
)

\bar K^ \ast (A)

is a small quotient algebra of the cobar complex and (2) the homology of

K
¯

∗

(
A
)

\bar K^ \ast (A)

is the cohomology algebra

H
∗

(
A
)

H ^ \ast (A)

. The resolution of May for restricted Lie algebras in characteristic 2 is retrieved and a simple derivation of the resolution of Kan et al. of the Steenrod algebra is given.
Spectral mapping theorems and perturbation theorems for Browder’s essential spectrum
Authors: Nussbaum Roger D.
Published: June 2010

If

T
T

is a closed, densely defined linear operator in a Banach space, F. E. Browder has defined the essential spectrum of

T
,
ess
⁡
(
T
)

T,\operatorname {ess} (T)

[1]. We derive below spectral mapping theorems and perturbation theorems for Browder’s essential spectrum. If

T
T

is a bounded linear operator and

f
f

is a function analytic on a neighborhood of the spectrum of

T
T

, we prove that

f
(
ess
⁡
(
T
)
)
=
ess
⁡
(
f
(
T
)
)

f(\operatorname {ess} (T)) = \operatorname {ess} (f(T))

. If

T
T

is a closed, densely defined linear operator with nonempty resolvent set and

f
f

is a polynomial, the same theorem holds. For a closed, densely defined linear operator

T
T

and a bounded linear operator

B
B

which commutes with

T
T

, we prove that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="e s s left-parenthesis upper T plus upper B right-parenthesis subset-of-or-equal-to e s s left-parenthesis upper T right-parenthesis plus e s s left-parenthesis upper B right-parenthesis equals left-brace mu plus v colon mu element-of e s s left-parenthesis upper T right-parenthesis comma v element-of e s s left-parenthesis upper B right-parenthesis right-brace">

ess
⁡
(
T
+
B
)
⊆
ess
⁡
(
T
)
+
ess
⁡
(
B
)
=
{
μ
+
v
:
μ
∈
ess
⁡
(
T
)
,
v
∈
ess
⁡
(
B
)
}

\operatorname {ess} (T + B) \subseteq \operatorname {ess} (T) + \operatorname {ess} (B) = \{ \mu + v:\mu \in \operatorname {ess} (T),v \in \operatorname {ess} (B)\}

. By making additional assumptions, we obtain an analogous theorem for

B
B

unbounded.
A formula for semigroups, with an application to branching diffusion processes
Authors: Sawyer Stanley A.
Published: June 2010

A Markov process

P
=
{

x
t

}

P = \{ {x_t}\}

proceeds until a random time

τ
\tau

, where the distribution of

τ
\tau

given

P
P

is

exp
⁡
(
−

ϕ
t

)

\exp ( - {\phi _t})

for finite additive functional

{

ϕ
t

}

\{ {\phi _t}\}

, at which time it jumps to a new position given by a substochastic kernel

K
(

x
τ

,
A
)

K({x_\tau },A)

. A new time

τ
′

\tau ’

is defined, the process again jumps at a time

τ
+

τ
′

\tau + \tau ’

and so forth, producing a new Markov process

P
′

P’

. A formula for the infinitesimal generator of the new process (in terms of the i.g. of the old) is then derived. Using branching processes and local times

{

ϕ
t

}

\{ {\phi _t}\}

, classical solutions of some linear partial differential equations with nonlinear boundary conditions are constructed. Also, conditions are given guaranteeing that a given Markov process is of type

P
′

P’

for some triple

(
P
,
{

ϕ
t

}
,
K
)

(P,\{ {\phi _t}\} ,K)

.
On the generalized Blaschke condition
Authors: Chee P. S.
Published: June 2010

In an earlier paper, the author has shown that the generalized Blaschke condition is satisfied by bounded holomorphic functions in the polydisc or the ball in

C
N

{C^N}

. By essentially the same method, it is shown in the present paper that the same condition is satisfied by larger classes of functions, the Nevanlinna classes.
An abstract nonlinear Cauchy-Kovalevska theorem
Authors: Trèves François
Published: June 2010

A nonlinear version of Ovcyannikov’s theorem is proved. If

F
(
u
,
t
)

F(u,t)

is an analytic function of

t
t

real or complex and of

u
u

varying in a scale of Banach spaces, valued in a scale of Banach spaces, the Cauchy problem

u
t

=
F
(
u
,
t
)
,
u
(
0
)
=

u
0

{u_t} = F(u,t),u(0) = {u_0}

, has a unique analytic solution. This is an abstract version of the Cauchy-Kovalevska theorem which can be applied to equations other than partial-differential, e.g. to certain differential-convolution or, more generally, differential-pseudodifferential equations.
A priori estimates and unique continuation theorems for second order parabolic equations
Authors: Johnson Raymond
Published: June 2010

It is shown that solutions of second-order linear parabolic equations subject to global constraint satisfy an a priori estimate which has among its consequences that if a solution of such an equation vanishes on the characteristic

t
=
T

t = T

and satisfies the global constraint, it vanishes identically.
Inductive definitions and computability
Authors: Grilliot Thomas J.
Published: June 2010

Sets inductively defined with respect to

∏
0

,

Σ
1

{\prod _0},{\Sigma _1}

, (nonmonotonic)

∏
1

{\prod _1}

and

Σ
2

{\Sigma _2}

predicates are characterized in terms of the four chief notions of abstract recursion.
Deformations of formal embeddings of schemes
Authors: Halperin Miriam P.
Published: June 2010

A family of isolated singularities of k-varieties will be here called equisingular if it can be simultaneously resolved to a family of hypersurfaces embedded in nonsingular spaces which induce only locally trivial deformations of pairs of schemes over local artin k-algebras. The functor of locally trivial deformations of the formal embedding of an exceptional set has a versal object in the sense of Schlessinger. When the exceptional set

X
0

{X_0}

is a collection of nonsingular curves meeting normally in a nonsingular surface X, the moduli correspond to Laufer’s moduli of thick curves. When X is a nonsingular scheme of finite type over an algebraically closed field k and

X
0

{X_0}

is a reduced closed subscheme of X, every deformation of

(
X
,

X
0

)

(X,{X_0})

to

k
[
ε
]

k[\varepsilon ]

such that the deformation of

X
0

{X_0}

is locally trivial, is in fact a locally trivial deformation of pairs.
Competitive processes and comparison differential systems
Authors: Ladde G. S.
Published: June 2010

Sufficient conditions are given for stability and nonnegativity of solutions of a system of differential equations, in particular, of comparison differential equations. Finally, it has been shown that the comparison differential equations represent the mathematical models for competitive processes in biological, physical and social sciences.
The translational hull of a topological semigroup
Authors: Hildebrant J. A. , Lawson J. D. , Yeager D. P.
Published: June 2010

This paper is concerned with three aspects of the study of topological versions of the translational hull of a topological semigroup. These include topological properties, applications to the general theory of topological semigroups, and techniques for computing the translational hull. The central result of this paper is that if S is a compact reductive topological semigroup and its translational hull

Ω
(
S
)

\Omega (S)

is given the topology of continuous convergence (which coincides with the topology of pointwise convergence and the compact-open topology in this case), then

Ω
(
S
)

\Omega (S)

is again a compact topological semigroup. Results pertaining to extensions of bitranslations are given, and applications of these together with the central result to semigroup compactifications and divisibility are presented. Techniques for determining the translational hull of certain types of topological semigroups, along with numerous examples, are set forth in the final section.
Parametric perturbation problems in ordinary differential equations
Authors: Hallam Thomas G.
Published: June 2010

The asymptotic behavior of solutions of a nonlinear differential equation that arises through a nonlinear parametric perturbation of a linear system of differential equations is discussed. Fundamental hypotheses include the admissibility of a pair of Banach spaces for the linear system. Conclusions about the behavior of the perturbed system evolve through the behavior of certain manifolds of solutions of the unperturbed linear system. Asymptotic representations are found on a semi-infinite axis

R
+

{R_ + }

and on the real line R. The bifurcation condition, which is shown to be trivial on

R
+

{R_ + }

, plays an essential role for the perturbation problem on R. Illustrations and examples, primarily on the space

L

∞

{{\text {L}}^\infty }

, of the theoretical results are presented.
Asymptotically autonomous multivalued differential equations
Authors: Foti James P.
Published: June 2010

The asymptotic behavior of solutions of the perturbed autonomous multivalued differential equation

x
′

∈
F
(
x
)
+
G
(
t
,
x
)

x’ \in F(x) + G(t,x)

is examined in relation to the behavior of solutions of the autonomous equation

x
′

∈
F
(
x
)

x’ \in F(x)

assuming that all solutions of the latter approach zero as t approaches

∞
\infty

.
Maximal chains of prime ideals in integral extension domains. II
Authors: Ratliff L. J.
Published: June 2010

Four related subjects are investigated: (1) If (L, N) is a locality over a local domain (R, M) such that

N
∩
R
=
M

N \cap R = M

, and if there exists an integral extension domain of L which has a maximal chain of prime ideals of length n (for short, a mcpil n), then there exists an integral extension domain of R which has a mcpil

n
−

trd

L

/

R
+

trd

(
L

/

N
)

/

(
R

/

M
)

n - {\text {trd}}\;L/R + {\text {trd}}(L/N)/(R/M)

. A refinement of the altitude inequality follows from this. (2) A condition for the converse of (1) to hold is given. (3) The class of local domains R such that there exists an integral extension domain of R which has a mcpil n if and only if there exists a mcpil n in R is studied. (4) Two new equivalences for the existence of mcpil n in an integral extension domain of a local domain are given.
A reduction theory for non-self-adjoint operator algebras
Authors: Azoff E. A. , Fong C. K. , Gilfeather F.
Published: June 2010

It is shown that every strongly closed algebra of operators acting on a separable Hilbert space can be expressed as a direct integral of irreducible algebras. In particular, every reductive algebra is the direct integral of transitive algebras. This decomposition is used to study the relationship between the transitive and reductive algebra problems. The final section of the paper shows how to view direct integrals of algebras as measurable algebra-valued functions.
Variation of conformal spheres by simultaneous sewing along several arcs
Authors: McCoy T. L.
Published: June 2010

Let M be a closed Riemann surface of genus zero,

Γ
\Gamma

a tree on M with branches

Γ
j

{\Gamma _j}

, and

p
0

{p_0}

a point of

M
−
Γ

M - \Gamma

. A family of neighboring topological surfaces

M
(
ε
)

M(\varepsilon )

is formed by regarding each

Γ
j

{\Gamma _j}

as a slit with edges

Γ
j
−

\Gamma _j^ -

and

Γ
j
+

\Gamma _j^ +

, and re-identifying p on

Γ

−
j

{\Gamma ^{{ - _j}}}

with

p
+
ε

χ
j

(
p
,
ε
)

p + \varepsilon {\chi _j}(p,\varepsilon )

on

Γ
j
+

\Gamma _j^ +

, with

χ
j

{\chi _j}

vanishing at the endpoints of

Γ
j

{\Gamma _j}

. We assume the

Γ
j

{\Gamma _j}

and

χ
j

{\chi _j}

are such that, under a certain natural choice of uniformizers, the

M
(
ε
)

M(\varepsilon )

are closed Riemann surfaces of genus zero. Then there exists a unique function

f
(
p
,
ε
;

p
0

)

f(p,\varepsilon ;{p_0})

mapping

M
(
ε
)

M(\varepsilon )

conformally onto the complex number sphere, with normalization

f
(

p
0

,
ε
;

p
0

)
=
0
,

f
′

(

p
0

,
ε
;

p
0

)
=
1

f({p_0},\varepsilon ;{p_0}) = 0,f’({p_0},\varepsilon ;{p_0}) = 1

. Under appropriate smoothness hypotheses on

Γ
\Gamma

and the

χ
j

{\chi _j}

, we find the first variation of f as a function of

ε
\varepsilon

. Further, we obtain smoothness results for f as a function of

ε
\varepsilon

. The problem is connected with the study of the extremal schlicht functions; that is, the schlicht mappings of the unit disc corresponding to boundary points of the coefficient bodies.
Uniqueness properties of CR-functions
Authors: Hunt L. R.
Published: June 2010

Let M be a real infinitely differentiable closed hypersurface in X, a complex manifold of complex dimension

n
⩾
2

n \geqslant 2

. The uniqueness properties of solutions to the system

∂
¯

M

u
=
f

{\bar \partial _M}u = f

, where

∂
¯

M

{\bar \partial _M}

is the induced Cauchy-Riemann operator on M, are of interest in the fields of several complex variables and partial differential equations. Since dM is linear, the study of the solution to the equation

∂
¯

M

u
=
0

{\bar \partial _M}u = 0

is sufficient for uniqueness. A

C
∞

{C^\infty }

solution to this homogeneous equation is called a CR-function on M. The main result of this article is that a CR-function is uniquely determined, at least locally, by its values on a real k-dimensional

C
∞

{C^\infty }

generic submanifold

S
k

{S^k}

of M with

k
⩾
n

k \geqslant n

. The facts that

S
k

{S^k}

is generic and

k
⩾
n

k \geqslant n

together form the lower dimensional analogue of the concept of noncharacteristic.
General position of equivariant maps
Authors: Bierstone Edward
Published: June 2010

A natural generic notion of general position for smooth maps which are equivariant with respect to the action of a compact Lie group is introduced. If G is a compact Lie group, and M, N are smooth G-manifolds, then the set of smooth equivariant maps

F
:
M
→
N

F:M \to N

which are in general position with respect to a closed invariant submanifold P of N, is open and dense in the Whitney topology. The inverse image of P, by an equivariant map in general position, is Whitney stratified. The inverse images, by nearby equivariant maps in general position, are topologically ambient isotopic. In the local context, let V, W be linear G-spaces, and

F
:
V
→
W

F:V \to W

a smooth equivariant map. Let

F
1

,
…
,

F
k

{F_1}, \ldots ,{F_k}

be a finite set of homogeneous polynomial generators for the module of smooth equivariant maps, over the ring of smooth invariant functions on V. There are invariant functions

h
1

,
…
,

h
k

{h_1}, \ldots ,{h_k}

such that

F
=
U
∘

F = U \circ

graph h, where graph h is the graph of

h
(
x
)
=
(

h
1

(
x
)
,
…
,

h
k

(
x
)
)

h(x) = ({h_1}(x), \ldots ,{h_k}(x))

, and

U
(
x
,
h
)
=

Σ

i
=
1

k

h
i

F
i

(
x
)

U(x,h) = \Sigma _{i = 1}^k{h_i}{F_i}(x)

. The isomorphism class of the real affine algebraic subvariety

(
U
=
0
)

(U = 0)

of

V
×

R

k

V \times {{\mathbf {R}}^k}

is uniquely determined (up to product with an affine space) by V, W. F is said to be in general position with respect to

0
∈
W

0 \in W

at

0
∈
V

0 \in V

if graph

h
:
V
→
V
×

R

k

h:V \to V \times {{\mathbf {R}}^k}

is transverse to the minimum Whitney stratification of

(
U
=
0
)

(U = 0)

, at

x
∈
V

x \in V

.
Cartan subalgebras of simple Lie algebras
Authors: Wilson Robert Lee
Published: June 2010

Let L be a finite-dimensional simple Lie algebra over an algebraically closed field of characteristic

p
>
7

p > 7

. Let H be a Cartan subalgebra of L, let

L
=
H
+

Σ

γ
∈
Γ

L
γ

L = H + {\Sigma _{\gamma \in \Gamma }}{L_\gamma }

be the Cartan decomposition of L with respect to H, and let

H
¯

\bar H

be the restricted subalgebra of Der L generated by ad H. Let T denote the maximal torus of

H
¯

\bar H

and I denote the nil radical of

H
¯

\bar H

. Then

H
¯

=
T
+
I

\bar H = T + I

. Consequently, each

γ
∈
Γ

\gamma \in \Gamma

is a linear function on H.
On the transformation group of a real hypersurface
Authors: Webster S. M.
Published: June 2010

The group of biholomorphic transformations leaving fixed a strongly pseudoconvex real hypersurface in a complex manifold is a Lie group. In this paper it is shown that the Chern-Moser invariants must vanish if this group is noncompact and the hypersurface is compact. Also considered are transformation groups of flat hypersurfaces and intransitive groups.
The PL Grassmannian and PL curvature
Authors: Levitt Norman
Published: June 2010

A space

G

n
,
k

{\mathcal {G}_{n,k}}

is constructed, together with a block bundle over it, which is analogous to the Grassmannian

G

n
,
k

{G_{n,k}}

in that, given a PL manifold

M
n

{M^n}

as a subcomplex of an affine triangulation of

R

n
+
k

{R^{n + k}}

, there is a natural “Gauss map”

M
n

→

G

n
,
k

{M^n} \to {\mathcal {G}_{n,k}}

covered by a block-bundle map of the PL tubular neighborhood of

M
n

{M^n}

to the block bundle over

G

n
,
k

{G_{n,k}}

. Certain subcomplexes of

G

n
,
k

{G_{n,k}}

are then studied in connection with immersion problems, the chief result being that a connected manifold

M
n

{M^n}

(nonclosed) PL immerses in

R

n
+
k

{R^{n + k}}

satisfying certain “local” conditions if and only if its stable normal bundle is represented by a map to the subcomplex of

G

n
,
k

{G_{n,k}}

corresponding to the condition. An important example of such a condition is a restriction on PL curvature, e.g., nonnegative or nonpositive, PL curvature having been defined by D. Stone.
Subgroups of classical groups generated by long root elements
Authors: Kantor William M.
Published: June 2010

All conjugacy classes of subgroups G of classical groups of characteristic p are determined, which are generated by a conjugacy class of long root elements and satisfy

O
p

(
G
)
⩽

G
′

∩
Z
(
G
)

{O_p}(G) \leqslant G’ \cap Z(G)

.
Degrees of exceptional characters of certain finite groups
Authors: Blau Harvey I.
Published: June 2010

Let G be a finite group whose order is divisible by a prime p to the first power only. Restrictions beyond the known congruences modulo p are shown to hold for the degrees of the exceptional characters of G, under the assumptions that either all

p
′

p’

-elements centralizing a Sylow p-subgroup are in fact central in G and there are at least three conjugacy classes of elements of order p, or that the characters in question lie in the principal p-block. Results of Feit and the author are thereby generalized.
On the existence of nonregular ultrafilters and the cardinality of ultrapowers
Authors: Magidor Menachem
Published: June 2010

Assuming the consistency of huge cardinals, we prove that

ω
3

{\omega _3}

can carry an ultrafilter D such that

ω
1

ω
3

/

D

{\omega _1}^{{\omega _3}}/D

has cardinality

ω
3

{\omega _3}

. (Hence D is not

(

ω
3

,

ω
1

)

({\omega _3},\,{\omega _1})

regular.) Similarly

ω
2

{\omega _2}

can carry an ultrafilter D such that

ω

ω
2

/

D

{\omega ^{{\omega _2}}}/D

has cardinality

ω
2

{\omega _2}

. (Hence D is not

(

ω
2

,

ω
)

({\omega _2},\,\omega )

regular.)
Balanced Cohen-Macaulay complexes
Authors: Stanley Richard P.
Published: June 2010

A balanced complex of type

(

a
1

,
…
,

a
m

)

({a_1},\ldots ,{a_m})

is a finite pure simplicial complex

Δ
\Delta

together with an ordered partition

(

V
1

,
…
,

V
m

)

({V_1},\ldots ,{V_m})

of the vertices of

Δ
\Delta

such that card

(

V
i

∩

F
)

=

a
i

({V_i}\, \cap \,F)\, = \,{a_i}

, for every maximal face F of

Δ
\Delta

. If

b

=

(

b
1

,
…
,

b
m

)

{\mathbf {b}}\, = \,({b_1},\ldots ,{b_m})

, then define

f

b

(
Δ
)

{f_\textbf {b}}(\Delta )

to be the number of

F

∈

Δ

F\, \in \,\Delta

satisfying card

(

V
i

∩

F
)

=

b
i

({V_i}\, \cap \,F)\, = \,{b_i}

. The formal properties of the numbers

f

b

(
Δ
)

{f_\textbf {b}}(\Delta )

are investigated in analogy to the f-vector of an arbitrary simplicial complex. For a special class of balanced complexes known as balanced Cohen-Macaulay complexes, simple techniques from commutative algebra lead to very strong conditions on the numbers

f

b

(
Δ
)

{f_\textbf {b}}(\Delta )

. For a certain complex

Δ
(
P
)

\Delta (P)

coming from a poset P, our results are intimately related to properties of the Möbius function of P.
A decidable fragment of the elementary theory of the lattice of recursively enumerable sets
Authors: Lerman M. , Soare R. I.
Published: June 2010

A natural class of sentences about the lattice of recursively enumerable sets modulo finite sets is shown to be decidable. This class properly contains the class of sentences previously shown to be decidable by Lachlan. New structure results about the lattice of recursively enumerable sets are proved which play an important role in the decision procedure.
Crossed extensions
Authors: Ratcliffe John G.
Published: June 2010

We develop a natural five term exact sequence relating the second and third cohomology of groups. We show that this sequence is the proper framework for the problem of realizing an abstract kernel. As an application, we give an interpretation of the third cohomology of a group in terms of crossed sequences.
The interior operator logic and product topologies
Authors: Sgro Joseph
Published: June 2010

In this paper we present a model theory of the interior operator on product topologies with continuous functions. The main results are a completeness theorem, an axiomatization of topological groups, and a proof of an interpolation and definability theorem.
On special classes of entire functions whose zeros and growth are restricted
Authors: Prather Carl L.
Published: June 2010

The present paper is an investigation of the uniform limits on bounded sets of entire functions of genus

⩽

2
p

\leqslant \,2p

whose zeros are real, or lie in an even number of sectors (or correspondingly on rays) of a certain size, both the number and size depending on p. A characterization of the uniform limits of entire functions of genus

⩽

2
p

\leqslant \,2p

whose zeros lie in these sectors is given.
Equivariant homotopy theory and Milnor’s theorem
Authors: Waner Stefan
Published: June 2010

The foundations of equivariant homotopy and cellular theory are examined; an equivariant Whitehead theorem is proved, and the classical results by Milnor about spaces with the homotopy-type of a CW complex are generalized to the equivariant case. The ambient group G is assumed compact Lie. Further results include equivariant cellular approximation and the procedure for replacement of an arbitrary G-space by a G-CW complex.
Equivariant classifying spaces and fibrations
Authors: Waner Stefan
Published: June 2010

Explicit classifying spaces for equivariant fibrations are constructed using the geometric two-sided bar construction. The constructions are then extended to classify stable equivariant spherical fibrations and equivariant K-theory. The ambient groups is assumed compact Lie.
On oscillatory elliptic equations on manifolds
Authors: Baider A. , Feldman E. A.
Published: June 2010

In this note we investigate the possibility of oscillatory behavior for a second-order selfadjoint elliptic operators on noncompact Riemannian manifolds (M, g). Let A be such an operator which is semibounded below and symmetric on

C
0
∞

(
M
)

⊆

L
2

(
M
,

d
μ
)

C_0^\infty (M)\, \subseteq \,{L^2}(M,\,d\mu )

where

d
μ

d\mu

is a volume element on M. If

φ
\varphi

is a

C
∞

{C^\infty }

function such that

A
φ

=

λ
φ

A\varphi \, = \,\lambda \varphi

, we would naively say that

φ
\varphi

is oscillatory (and by extension

λ
\lambda

is oscillatory if it possesses such an eigenfunction

φ
\varphi

) if

M

−

φ

−
1

(
0
)

M\, - \,{\varphi ^{ - 1}}(0)

has an infinite number of bounded connected components. For technical reasons this is not quite adequate for a definition. However, in §1 we give the usual definition of oscillatory which is a slight generalization of the one above. Let

Λ
0

{\Lambda _0}

be the number below which this phenomenon cannot occur;

Λ
0

{\Lambda _0}

is the oscillatory constant for the operator A. In that A is semibounded and symmetric on

C
0
∞

(
M
)

⊆

L
2

(
M
,

d
μ
)

C_0^\infty (M)\, \subseteq \,{L^2}(M,\,d\mu )

, A has a Friedrichs extension. Let

Λ
c

{\Lambda _c}

be the bottom of the continuous spectrum of the Friedrichs extension of A. Our main result is

Λ
0

=

Λ
c

{\Lambda _0}\, = \,{\Lambda _c}

.
Permutation-partition pairs: a combinatorial generalization of graph embeddings
Authors: Stahl Saul
Published: June 2010

Permutation-partition pairs are a purely combinatorial generalization of graph embeddings. Some parameters are defined here for these pairs and several theorems are proved. These results are strong enough to prove virtually all the known theoretical informaton about the genus parameter as well as a new theorem regarding the genus of the amalgamation of two graphs over three points.
Hermite-Birkhoff interpolation in the 𝑛th roots of unity
Authors: Cavaretta A. S. , Sharma A. , Varga R. S.
Published: June 2010

Consider, as nodes for polynomial interpolation, the nth roots of unity. For a sufficiently smooth function

f
(
z
)

f(z)

, we require a polynomial

p
(
z
)

p(z)

to interpolate f and certain of its derivatives at each node. It is shown that the so-called Pólya conditions, which are necessary for unique interpolation, are in this setting also sufficient.
Principal 2-blocks of the simple groups of Ree type
Authors: Landrock Peter , Michler Gerhard O.
Published: June 2010

The decomposition numbers in characteristic 2 of the groups of Ree type are determined, as well as the Loewy and socle series of the indecomposable projective modules. Moreover, we describe the Green correspondents of the simple modules. As an application of this and similar works on other simple groups with an abelian Sylow 2-subgroup, all of which have been classified apart from those considered in the present paper, we show that the Loewy length of an indecomposable projective module in the principal block of any finite group with an abelian Sylow 2-subgroup of order

2
n

{2^n}

is bounded by

max
{
2
n

+

1
,

2
n

}

\max \{ 2n\, + \,1,\,{2^n}\}

. This bound is the best possible.
Moduli for analytic left algebraic groups
Authors: Magid Andy R.
Published: June 2010

This paper classifies left algebraic group structures on faithfully representable complex analytic groups by establishing the existence of an algebraic variety whose complex points correspond to such structures on a given analytic group.
Higher divided squares in second-quadrant spectral sequences
Authors: Dwyer W. G.
Published: June 2010

The geometric action of the Steenrod algebra on many mod 2 cohomology spectral sequences is complemented by the action of a completely different algebra.
An asymptotic theory for a class of nonlinear Robin problems. II
Authors: Howes F. A.
Published: June 2010

Various asymptotic phenomena exhibited by solutions of singularly perturbed Robin boundary value problems are studied in the case when the right-hand side grows faster than the square of the derivative.
The gluing of maximal ideals—spectrum of a Noetherian ring—going up and going down in polynomial rings
Authors: de Souza Doering Ada Maria , Lequain Yves
Published: June 2010

If

M
1

,

.
.
.

,

M
s

{M_1},\,...\,,\,{M_s}

are maximal ideals of a ring R that have isomorphic residue fields, then they can be “glued” in the sense that a subring D of R with R is integral over D and

M
1

∩

D

=

.
.
.

=

M
s

∩

D

{M_1}\, \cap \,D\, = \,...\, = \,{M_s}\, \cap \,D

can be constructed. We use this gluing process to prove the following result: Given any finite ordered set

B

\mathcal {B}

, there exists a reduced Noetherian ring B and an embedding

ψ
:

B

→

S
p
e
c

B

\psi :\,\mathcal {B}\, \to \,Spec\,B

such that

ψ
\psi

establishes a bijection between the maximal (respectively minimal) elements of

B

\mathcal {B}

and the maximal (respectively minimal) prime ideals of B and such that given any elements

β
′

\beta ’

,

β
\beta

of

B

\mathcal {B}

, there exists a saturated chain of prime ideals of length r between

ψ
(

β
′

)

\psi (\beta ’)

and

ψ
(
β
)

\psi (\beta )

if and only if there exists a saturated chain of length r between

β
′

\beta ’

and

β
\beta

. We also use the gluing process to construct a Noetherian domain A with quotient field L and a Noetherian domain B between A and L such that:

A

↪

B

A\,\hookrightarrow \,B

possesses the Going Up and the Going Down properties,

A
[
X
]

↪

B
[
X
]

A[X]\,\hookrightarrow \,B[X]

is unibranched and

A
[
X
]

↪

B
[
X
]

A[X]\,\hookrightarrow \,B[X]

possesses neither the Going Up nor the Going Down properties.
Second-order equations of fixed type in regions with corners. I
Authors: Sarason Leonard
Published: June 2010

A class of well-posed boundary value problems for second order equations in regions with corners and edges is studied. The boundary condition may involve oblique derivatives, and edge values may enter the graph of the associated Hilbert space operator. Uniqueness of weak solutions and existence of strong solutions is shown.
In-between theorems in uniform spaces
Authors: Preiss D. , Vilímovský J.
Published: June 2010

Necessary and sufficient conditions for the existence of a uniformly continuous function in-between given functions

f

⩾

g

f\, \geqslant \,g

on a uniform space are studied. It appears that the investigation of this problem is closely related to some combinatorial properties of covers and leads to the concept of perfect refinability, the latter being used, e.g., to obtain an intrinsic description of uniform real extensors. Several interesting classes of uniform spaces are characterized by special types of in-between theorems. As examples of applications we show that the usual in-between theorems in topology and their generalizations, as well as some important methods of construction of derivatives of real functions, follow easily from the general results.
The Rayleigh-Schrödinger expansion of the Gibbs state of a classical Heisenberg ferromagnet
Authors: Faris William G.
Published: June 2010

The equilibrium Gibbs state of a classical Heisenberg ferromagnet is a probability measure on an infinite product of spheres. The Kirkwood-Salsburg equations may be iterated to produce a convergent high temperature expansion of this measure about a product measure. Here we show that this expansion may also be obtained as the Rayleigh-Schrödinger expansion of the ground state eigenvector of a differential operator. The operator describes a Markovian time evolution of the ferromagnet.
Chaotic behavior in piecewise continuous difference equations
Authors: Keener James P.
Published: June 2010

A class of piecewise continuous mappings with positive slope, mapping the unit interval into itself is studied. Families of 1-1 mappings depending on some parameter have periodic orbits for most parameter values, but have an infinite invariant set which is a Cantor set for a Cantor set of parameter values. Mappings which are not 1-1 exhibit chaotic behavior in that the asymptotic behavior as measured by the rotation number covers an interval of values. The asymptotic behavior depends sensitively on initial data in that the rotation number is either a nowhere continuous function of initial data, or else it is a constant on all but a Cantor set of the unit interval.
Approximation of 𝐺-maps by maps in equivariant general positions and imbeddings of 𝐺-complexes
Authors: Illman Sören
Published: June 2010

Let G be a finite group. In this paper we consider maps

f
:
P
→
M

f:P \to M

from equivariant polyhedra into equivariant p.l. manifolds. We prove an equivariant general position result which shows how to approximate a given continuous proper equivariant (or isovariant) map

f
:
P
→
M

f:P \to M

by a G-map which is in equivariant general position. We also apply this equivariant general position result to get a general G-imbedding theorem. Applied to the case of G-imbeddings of simplicial G-complexes into euclidean representation space this general G-imbedding theorem gives a result which provides a good hold on the required dimension of the euclidean representation space. For example in the case when

G
=

Z
m

G = {Z_m}

we prove that there exists a representation space

R

r
(
k
,
m
)

(
ρ
)

{{\textbf {R}}^{r(k,m)}}(\rho )

with the property that any k-dimensional simplicial

Z
m

{Z_m}

-complex X admits a proper p.l.

Z
m

{Z_m}

-imbedding into

R

r
(
k
,
m
)

(
ρ
)

{{\textbf {R}}^{r(k,m)}}(\rho )

and we also show that the dimension

r
(
k
,
m
)

r(k,m)

is best possible, i.e., one cannot find a euclidean representation space of lower dimension than

r
(
k
,
m
)

r(k,m)

with the same property as

R

r
(
k
,
m
)

(
ρ
)

{{\textbf {R}}^{r(k,m)}}(\rho )

. Simple explicit expressions for the dimension

r
(
k
,
m
)

r(k,m)

are given. We also consider the case of semi-free actions with a given imbedding of the fixed point set into some euclidean space. Furthermore we show that the p.l. G-imbeddings of equivariant p.l. manifolds into euclidean representation space obtained by our G-imbedding results are in general equivariantly locally knotted although they are locally flat in the ordinary sense. This phenomenon can occur in arbitrarily high codimensions.
Stability of the null solution of parabolic functional inequalities
Authors: Redheffer Ray , Walter Wolfgang
Published: June 2010

Uniqueness and stability theorems are established for coupled systems of parabolic differential equations which may involve a Volterra-type dependence on the past history of the process. We allow retarded or deviating arguments, convolution-type memory terms, and strong coupling. (This means that all the space derivatives up to a given order can occur in all the equations.) Our results for strong coupling depend on the concept of “admissible monomial” which is here introduced for the first time and has no counterpart in the linear case. It is possible for uniqueness to fail in general, but to be restored (relative to a tolerably large class of functions of

(
x
,
t
)

(x,t)

) if a single solution independent of x exists. Another curious feature of these theorems, depending again on the concept of admissible monomial, is that conditions for uniqueness can involve derivatives of order much higher than those occurring in the equation. Examples given elsewhere show that the results are, in various respects, sharp. Thus, the seemingly peculiar hypotheses do not arise from deficient technique, but from the actual behavior of strongly coupled systems. The paper concludes with a new method of dealing with unbounded regions for the difficult case in which the functional occurs in the boundary operator as well as in the differential equation.
Algebras of automorphic forms with few generators
Authors: Wagreich Philip
Published: June 2010

Those finitely-generated Fuchsian groups G for which the graded algebra of automorphic forms A is generated by 2 or 3 elements are classified. In these cases the structure of A is described.
A new result on the convergence of nonhomogeneous stochastic chains
Authors: Mukherjea Arunava
Published: June 2010

Nonhomogeneous stochastic chains with a finite number of states are considered in this paper. Convergence of such chains is established here in terms of strong ergodicity of certain related chains of smaller size. These results are shown to be best possible and extend earlier results of Maksimov. Nonnegative idempotent matrices are also considered.
Holomorphic actions of 𝑆𝑝(𝑛,𝑅) with noncompact isotropy groups
Authors: Rossi Hugo
Published: June 2010

U
(
p
,
q
)

U(p,q)

is a subgroup of

S
p

(
n
,
R
)

{S_p}(n,R)

, for

p
+
q
=
n

p + q = n

.

B
q

=

S
p

(
n
,
r
)

/

U
(
p
,
q
)

{B_q} = {S_p}(n,r)/U(p,q)

is realized as an open subset of the manifold of Lagrangian subspaces of

C

n

×

C

n

{{\mathbf {C}}^n} \times {{\mathbf {C}}^n}

. It is shown that

B
q

{B_q}

carries a

(
p
q
)

(pq)

-pseudoconvex exhaustion function.

B

p
q

=

S
p

(
n
,
r
)

/

U
(
p
)
×
U
(
q
)

{B_{pq}} = {S_p}(n,r)/U(p) \times U(q)

carries two distinct holomorphic structures making the projection to

B
q

{B_q}

,

B
0

{B_0}

holomorphic respectively. The geometry of the correspondence between

B
q

{B_q}

and

B
0

{B_0}

via

B

p
q

{B_{pq}}

is investigated.
Robinson’s consistency theorem in soft model theory
Authors: Mundici Daniele
Published: June 2010

In a soft model-theoretical context, we investigate the properties of logics satisfying the Robinson consistency theorem; the latter is for many purposes the same as the Craig interpolation theorem together with compactness. Applications are given to H. Friedman’s third and fourth problem.
Capacity densities and angular limits of quasiregular mappings
Authors: Vuorinen Matti
Published: June 2010

It is shown that if a bounded quasiregular mapping of the unit ball

B
n

⊂

R
n

{B^n} \subset {R^n}

,

n
⩾
2

n \geqslant 2

, has a limit at

b
∈
∂

B
n

b \in \partial {B^n}

through a set

E
⊂

B
n

E \subset {B^n}

with

b
∈

E
¯

b \in \bar E

, then it has an angular limit at

b
b

provided that

E
E

is contained in an open cone

C
⊂

B
n

C \subset {B^n}

with vertex

b
b

and that

E
E

is thick enough at

b
b

. The thickness condition is expressed in terms of the

n
n

-capacity density.
Representations of functions by derivatives
Authors: Agronsky S. J. , Biskner R. , Bruckner A. M. , Mařík J.
Published: June 2010

Let

Δ
′

\Delta ’

be the class of all derivatives. The main goal of this paper is the investigation of the vector space generated by

Δ
′

\Delta ’

and O’Malley’s class

B
1
∗

B_1^ \ast

; this space is identical with our system

[

Δ
′

]

[\Delta ’]

. We show, in particular, that each approximately continuous function and each approximate derivative belongs to

[

Δ
′

]

[\Delta ’]

and that

[

Δ
′

]

[\Delta ’]

is the system of all functions of the form

g
′

+
h

k
′

g’ + hk’

, where

g
g

,

h
h

and

k
k

are differentiable.
On the contact between complex manifolds and real hypersurfaces in 𝐶³
Authors: Bloom Thomas
Published: June 2010

Let

m
m

be a real

C

∞

{\mathcal {C}^\infty }

hypersurface of an open subset of

C

3

{{\mathbf {C}}^3}

and let

p
∈
M

p \in M

. Let

a
1

(
M
,
p
)

{a^1}(M,p)

denote the maximal order of contact of a one-dimensional complex submanifold of a neighborhood of

p
p

in

C

3

{{\mathbf {C}}^3}

with

M
M

at

p
p

. Let

c
1

(
M
,
p
)

{c^1}(M,p)

denote the

sup
{
m
∈

Z

|

\sup \{ m \in {\mathbf {Z}}|

for all tangential holomorphic vector fields

L
L

with

L
(
p
)
≠
0

L(p) \ne 0

then
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript i 0 Baseline upper L overbar Superscript j 0 Baseline ellipsis upper L Superscript i Super Subscript n Superscript Baseline ModifyingAbove upper L With bar Superscript j Super Subscript n Superscript Baseline left-parenthesis German upper L Subscript upper M Baseline left-parenthesis upper L right-parenthesis right-parenthesis left-parenthesis p right-parenthesis equals 0 right-brace">

L

i
0

L
¯

j
0

…

L

i
n

L
¯

j
n

(

L

M

(
L
)
)
(
p
)
=
0
}

{L^{{i_0}}}{\bar L^{{j_0}}} \ldots {L^{{i_n}}}{\bar L^{{j_n}}}({\mathfrak {L}_M}(L))(p) = 0\}

where

i
0

,
…
,

i
n

;

j
0

,
…
,

j
n

{i_0}, \ldots ,{i_n};{j_0}, \ldots ,{j_n}

are positive integers such that

∑

t
=
0

n

i
t

+

j
t

=
m
−
3

\sum \nolimits _{t = 0}^n {{i_t} + {j_t} = m - 3}

and

L

M

(
L
)

{\mathfrak {L}_M}(L)

denotes the Levi form of

M
M

evaluated on the vector field

L
L

. Theorem. If

M
M

is pseudoconvex near

p
∈
M

p \in M

then

a
1

(
M
,
p
)
=

c
1

(
M
,
p
)

{a^1}(M,p) = {c^1}(M,p)

.
A lattice renorming theorem and applications to vector-valued processes
Authors: Davis William J. , Ghoussoub Nassif , Lindenstrauss Joram
Published: June 2010

A norm,

|

|

|

|

||\;||

, on a Banach space

E
E

is said to be locally uniformly convex if

‖

x
n

‖

→

‖
x
‖

\left \| {{x_n}} \right \| \to \left \| x \right \|

and

‖

x
n

+
x

‖

→
2

‖
x
‖

\left \| {{x_n} + x} \right \| \to 2\left \| x \right \|

implies that

x
n

→
x

{x_n} \to x

in norm. It is shown that a Banach lattice has an (order) equivalent locally uniformly convex norm if and only if the lattice is order continuous. This result is used to reduce convergence theorems for (lattice-valued) positive martingales and submartingales to the scalar case.
Submonotone subdifferentials of Lipschitz functions
Authors: Spingarn Jonathan E.
Published: June 2010

The class of "lowwer-

C
1

{C^1}

" functions, that is functions which arise by taking the maximum of a compactly indexed family of

C
1

{C^1}

functions, is characterized in terms of properties of the generalized subdifferential. A locally Lipschitz function is shown to be lower-

C
1

{C^1}

if and only if its subdifferential is "strictly submonotone". Other properties of functions with "submonotone" subdifferentials are investigated.
Equivariant cofibrations and nilpotency
Authors: Lewis Robert H.
Published: June 2010

Let

f
:
B
→
Y

f:B \to Y

be a cofibration whose cofiber is a Moore space. We give necessary and sufficient conditions for

f
f

to be induced by a map of the desuspension of the cofiber into

B
B

. These conditions are especially simple if

B
B

and

Y
Y

are nilpotent. We obtain some results on the existence of equivariant Moore spaces, and use them to construct examples of noninduced cofibrations between nilpotent spaces. Our machinery also leads to a cell structure proof of the characterization of pre-nilpotent spaces due to Dror and Dwyer [7], and to a simple proof, for finite fundamental group, of the result of Brown and Kahn [4] that homotopy dimension equals simple cohomological dimension in nilpotent spaces.