bluuebunny/crossref_metadata_2025 huggingface dataset:
On invertible bimodules and automorphisms of noncommutative rings
Authors: Guralnick Robert M. , Montgomery Susan
Published: June 2012

In this article, we attempt to generalize the result that for a commutative ring

R
R

the outer automorphism group of

R
R

-automorphisms of

M
n

(
R
)

{M_n}(R)

is abelian of exponent

n
n

. It is shown that a slightly weaker stable version of the result is still valid for affine semiprime noetherian pi rings. We also show that the automorphism group of an affine commutative domain of positive dimension acts faithfully on the spectrum of the domain. We investigate other questions involving bimodules and automorphisms and extend a result of Smith on the first Weyl algebra as a fixed ring.
Local asymptotic distribution of zeros of orthogonal polynomials
Authors: Totik Vilmos , Ullman Joseph L.
Published: June 2012

Converse results, which state a relation (inequality) for measures from that on their logarithmic potentials, are applied to local density of zeros of orthogonal polynomials when the measure of orthogonality is a general one with compact support. It will be shown that if the measure is sufficiently thick on a part of its support, then on that part the density of the zeros will be at least as large as the equilibrium measure of the support. A corresponding upper estimate on the distribution of the zeros will also be proved. All of our estimates are sharp, and they localize several well-known results.
On convergence and closedness of multivalued martingales
Authors: Wang Zhen Peng , Xue Xing Hong
Published: June 2012

In this paper, various convergence theorems and criteria of closedness of multivalued martingales, submartingales, and supermartingales are proved.
The hexagonal packing lemma and Rodin Sullivan conjecture
Authors: Aharonov Dov
Published: June 2012

The Hexagonal Packing Lemma of Rodin and Sullivan [6] states that

s
n

→
0

{s_n} \to 0

as

n
→
∞

n \to \infty

. Rodin and Sullivan conjectured that

s
n

=
O
(
1

/

n
)

{s_n} = O(1/n)

. This has been proved by Z-Xu He [2]. Earlier, the present author proved the conjecture under some additional restrictions [1]. In the following we are able to remove these restrictions, and thus give an alternative proof of the RS conjecture. The proof is based on our previous article [1]. It is completely different from the proof of He, and it is mainly based on discrete potential theory, as developed by Rodin for the hexagonal case [4].
Witt equivalence of global fields. II. Relative quadratic extensions
Authors: Szymiczek Kazimierz
Published: June 2012

This paper explores the consequences of the Hasse Principle for Witt equivalence of global fields in the case of relative quadratic extensions. We are primarily interested in generating the Witt equivalence classes of quadratic extensions of a given number field, and we study the structure of the class, the number of classes, and the structure of the set of classes. Along the way, we reprove several results obtained earlier in the absolute case of the rational ground field, giving unified and short proofs based on the Hasse Principle.
The Selberg trace formula for 𝑆𝐿(3,𝑍)\𝑆𝐿(3,𝑅)/𝑆𝑂(3,𝑅)
Authors: Wallace D. I.
Published: June 2012

In this paper we compute the trace formula for

S
L
(
3
,

Z

)

SL(3,\mathbb {Z})

in detail and refine it to a greater extent than has previously been done. We show that massive cancellation occurs in the parabolic terms, leading to a far simpler formula than had been thought possible.
Powers of ideals generated by quadratic sequences
Authors: Raghavan K.
Published: June 2012

Huneke’s conjecture that weak d-sequences generate ideals of quadratic type is proved. The proof suggests the definition of quadratic sequences, which are more general than weak d-sequences yet simpler to define and handle, in addition to being just as useful. We extend the theory of d-sequences and weak d-sequences to quadratic sequences. Results of Costa on sequences of linear type are generalized. An example of a two-dimensional local domain in which every system of parameters is a d-sequence in some order but which nevertheless fails to be Buchsbaum is given. A criterion is established for when equality holds in Burch’s inequality for an ideal generated by a quadratic sequence.
𝔉-categories and 𝔉-functors in the representation theory of Lie algebras
Authors: Cox Ben
Published: June 2012

The fields of algebra and representation theory contain abundant examples of functors on categories of modules over a ring. These include of course Horn, Ext, and Tor as well as the more specialized examples of completion and localization used in the setting of representation theory of a semisimple Lie algebra. In this article we let

a

\mathfrak {a}

be a Lie subalgebra of a Lie algebra

g

\mathfrak {g}

and

Γ
\Gamma

be a functor on some category of

a

\mathfrak {a}

-modules. We then consider the following general question: For a

g

\mathfrak {g}

-module E what hypotheses on

Γ
\Gamma

and E are sufficient to insure that

Γ
(
E
)

\Gamma (E)

admits a canonical structure as a

g

\mathfrak {g}

-module? The article offers an answer through the introduction of the notion of

F

\mathfrak {F}

-categories and

F

\mathfrak {F}

-functors. The last section of the article treats various examples of this theory.
Le théorème de Fermat-Goss
Authors: Denis Laurent
Published: June 2012

The analogue of the Fermat equation and of the Fermat conjecture is studied by Goss [G], on the rational function fields in characteristic

p
>
0

p > 0

. We prove here that this equation has no nontrivial solutions. When

q
=
2

q = 2

, the method uses the canonical height on the t-module constructed in [D]. This method also gives finiteness theorems for some generalization of the Fermat equation in higher dimension.
On realization of Björner’s “continuous partition lattice” by measurable partitions
Authors: Haiman Mark D.
Published: June 2012

Björner [1] showed how a construction by von Neumann of examples of continuous geometries can be adapted to construct a continuous analogue of finite partition lattices. Björner’s construction realizes the continuous partition lattice abstractly, as a completion of a direct limit of finite lattices. Here we give an alternative construction realizing a continuous partition lattice concretely as a lattice of measurable partitions. This new lattice contains the Björner lattice and shares its key properties. Furthermore its automorphism group is the full automorphism group

(
mod

0
)

\pmod 0

of the unit interval with Lebesgue measure, whereas, as we show, the Björner lattice possesses only a proper subgroup of these automorphisms.
Operator semigroups for functional-differential equations with delay
Authors: Ruess W. M. , Summers W. H.
Published: June 2012

We show that a strongly continuous operator semigroup can be associated with the functional differential delay equation (FDE)
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout Enlarged left-brace 1st Row 1st Column x prime left-parenthesis t right-parenthesis plus a x left-parenthesis t right-parenthesis plus upper B x left-parenthesis t right-parenthesis small-contains-as-member upper F left-parenthesis x Subscript t Baseline right-parenthesis comma 2nd Column a m p semicolon t greater-than-or-equal-to 0 2nd Row 1st Column x vertical-bar Subscript double-struck upper R Sub Superscript minus Subscript Baseline equals phi element-of upper E 2nd Column a m p semicolon EndLayout">

{

x
′
(
t
)
+
a
x
(
t
)
+
B
x
(
t
)
∍
F
(

x
t

)
,

a
m
p
;

t
≥
0

x

|

R

−

=
φ
∈
E

a
m
p
;

\left \{ {\begin {array}{*{20}{c}} {x\prime (t) + ax(t) + Bx(t) \backepsilon F({x_t}),} \hfill & {t \geq 0} \hfill \\ {x{|_{{\mathbb {R}^ - }}} = \varphi \in E} \hfill & {} \hfill \\ \end {array} } \right .

\]
under local conditions which give wide latitude to those subsets of the state space

X
X

and initial data space

E
E

, respectively, where (a) the (generally multivalued) operator

B
⊆
X
×
X

B \subseteq X \times X

is defined and accretive, and (b) the historyresponsive function

F
:
D
(
F
)
⊆
E
→
X

F:D(F) \subseteq E \to X

is defined and Lipschitz continuous. The associated semigroup is then used to investigate existence and uniqueness of solutions to (FDE). By allowing the domain of the solution semigroup to be restricted according to specific local properties of

B
B

and

F
F

, moreover, our methods automatically lead to assertions on flow invariance. We illustrate our results through applications to the Goodwin oscillator and a single species population model.
Scattering theory for semilinear wave equations with small data in two space dimensions
Authors: Tsutaya Kimitoshi
Published: June 2012

We study scattering theory for the semilinear wave equation

u

t
t

−
Δ
u
=

|

u

|

p
−
1

u

{u_{tt}} - \Delta u = |u{|^{p - 1}}u

in two space dimensions. We show that if

p
>

p
0

=
(
3
+

17

)

/

2

p > {p_0} = (3 + \sqrt {17} )/2

, the scattering operator exists for smooth and small data. The lower bound

p
0

{p_0}

of p is considered to be optimal (see Glassey [6, 7], Schaeffer [18]). Our result is an extension of the results by Strauss [19], Klainerman [10], and Mochizuki and Motai [14, 15]. The construction of the scattering operator for small data does not follow directly from the proofs in [7, 13, 20 and 22] concerning the global existence of solutions for the Cauchy problem of the above equation with small initial data given at

t
=
0

t = 0

in two space dimensions, because we have to consider the integral equation with unbounded integral region associated to the above equation:
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u left-parenthesis x comma t right-parenthesis equals u 0 Superscript minus Baseline left-parenthesis x comma t right-parenthesis plus StartFraction 1 Over 2 pi EndFraction integral Subscript negative normal infinity Superscript t Baseline integral Underscript StartAbsoluteValue x minus y EndAbsoluteValue less-than-or-equal-to t minus s Endscripts StartFraction left-parenthesis StartAbsoluteValue u EndAbsoluteValue Superscript p minus 1 Baseline u right-parenthesis left-parenthesis y comma s right-parenthesis Over StartRoot left-parenthesis t minus s right-parenthesis squared minus StartAbsoluteValue x minus y EndAbsoluteValue squared EndRoot EndFraction d y d s comma">

u
(
x
,
t
)
=

u
0
−

(
x
,
t
)
+

1

2
π

∫

−
∞

t

∫

|

x
−
y

|

≤
t
−
s

(

|

u

|

p
−
1

u
)
(
y
,
s
)

(
t
−
s
)

2

−

|

x
−
y

|

2

d
y

d
s
,

u(x,t) = u_0^ - (x,t) + \frac {1}{{2\pi }}\int _{ - \infty }^t {\int _{|x - y| \leq t - s} {\frac {{(|u{|^{p - 1}}u)(y,s)}}{{\sqrt {{{(t - s)}^2} - |x - y{|^2}} }}dy\;ds,} }

\]
for

t
∈
R

t \in R

, where

u
0
−

(
x
,
t
)

u_0^ - (x,t)

is a solution of

u

t
t

−
Δ
u
=
0

{u_{tt}} - \Delta u = 0

which

u
(
x
,
t
)

u(x,t)

approaches asymptotically as

t
→
−
∞

t \to - \infty

. The proof of the basic estimate for the above integral equation is more difficult and complicated than that for the Cauchy problem of

u

t
t

−
Δ
u
=

|

u

|

p
−
1

u

{u_{tt}} - \Delta u = |u{|^{p - 1}}u

in two space dimensions.
Homoclinic loop and multiple limit cycle bifurcation surfaces
Authors: Perko L. M.
Published: June 2012

This paper establishes the existence and analyticity of homoclinic loop bifurcation surfaces

H

\mathcal {H}

and multiplicity-two, limit cycle bifurcation surfaces

C

\mathcal {C}

for planar systems depending on two or more parameters; it determines the side of

H

\mathcal {H}

or

C

\mathcal {C}

on which limit cycles occur; and it shows that if

H

\mathcal {H}

and

C

\mathcal {C}

intersect, then typically they do so at a flat contact.
Lattice-ordered algebras that are subdirect products of valuation domains
Authors: Henriksen Melvin , Larson Suzanne , Martinez Jorge , Woods R. G.
Published: June 2012

An f-ring (i.e., a lattice-ordered ring that is a subdirect product of totally ordered rings) A is called an SV-ring if

A

/

P

A/P

is a valuation domain for every prime ideal P of A . If M is a maximal

ℓ
\ell

-ideal of A, then the rank of A at M is the number of minimal prime ideals of A contained in M , rank of A is the sup of the ranks of A at each of its maximal

ℓ
\ell

-ideals. If the latter is a positive integer, then A is said to have finite rank, and if

A
=
C
(
X
)

A = C(X)

is the ring of all real-valued continuous functions on a Tychonoff space, the rank of X is defined to be the rank of the f-ring

C
(
X
)

C(X)

, and X is called an SV-space if

C
(
X
)

C(X)

is an ST-ring. X has finite rank k iff k is the maximal number of pairwise disjoint cozero sets with a point common to all of their closures. In general f-rings these two concepts are unrelated, but if A is uniformly complete (in particular, if

A
=
C
(
X
)

A = C(X)

) then if A is an SV-ring then it has finite rank. Showing that this latter holds makes use of the theory of finite-valued lattice-ordered (abelian) groups. These two kinds of rings are investigated with an emphasis on the uniformly complete case. Fairly powerful machinery seems to have to be used, and even then, we do not know if there is a compact space X of finite rank that fails to be an SV-space.
A homotopy invariance theorem in coarse cohomology and 𝐾-theory
Authors: Higson Nigel , Roe John
Published: June 2012

We introduce a notion of homotopy which is appropriate to the coarse geometry and topology studied by the second author in [7]. We prove the homotopy invariance of coarse cohomology, and of the K-theory of the

C
∗

{C^\ast }

-algebra associated to a coarse structure on a space. We apply our homotopy invariance results to show that if M is a Hadamard manifold then the inverse of the exponential map at any point 0 induces an isomorphism between the K-theory groups of the

C
∗

{C^\ast }

-algebras associated to M and its tangent space at 0 (see Theorem 7.9). This result is consistent with a coarse version of the Baum-Connes conjecture.
A differential operator for symmetric functions and the combinatorics of multiplying transpositions
Authors: Goulden I. P.
Published: June 2012

By means of irreducible characters for the symmetric group, formulas have previously been given for the number of ways of writing permutations in a given conjugacy class as products of transpositions. These formulas are alternating sums of binomial coefficients and powers of integers. Combinatorial proofs are obtained in this paper by analyzing the action of a partial differential operator for symmetric functions.
Geometry of 2-step nilpotent groups with a left invariant metric. II
Authors: Eberlein Patrick
Published: June 2012

We obtain a partial description of the totally geodesic submanifolds of a 2-step, simply connected nilpotent Lie group with a left invariant metric. We consider only the case that N is nonsingular; that is,

ad

ξ
:

N

→

Z

{\text {ad}}\xi :\mathcal {N} \to \mathcal {Z}

is surjective for all elements

ξ
∈

N

−

Z

\xi \in \mathcal {N} - \mathcal {Z}

, where

N

\mathcal {N}

denotes the Lie algebra of N and

Z

\mathcal {Z}

denotes the center of

N

\mathcal {N}

. Among other results we show that if H is a totally geodesic submanifold of N with

dim
⁡
H
≥
1
+
dim
⁡

Z

\dim H \geq 1 + \dim \mathcal {Z}

, then H is an open subset of

g

N
∗

g{N^\ast }

, where g is an element of H and

N
∗

{N^\ast }

is a totally geodesic subgroup of N. We find simple and useful criteria that are necessary and sufficient for a subalgebra

N

∗

{\mathcal {N}^\ast }

of

N

\mathcal {N}

to be the Lie algebra of a totally geodesic subgroup

N
∗

{N^\ast }

. We define and study the properties of a Gauss map of a totally geodesic submanifold H of N. We conclude with a characterization of 2-step nilpotent Lie groups N of Heisenberg type in terms of the abundance of totally geodesic submanifolds of N.
Univalent functions and the Pompeiu problem
Authors: Garofalo Nicola , Segàla Fausto
Published: June 2012

In this paper we prove a result on the Pompeiu problem. If the Schwarz function

Φ
\Phi

of the boundary of a simply-connected domain

Ω
⊂

R

2

\Omega \subset {\mathbb {R}^2}

extends meromorphically into a certain portion

E
E

of

Ω
\Omega

with a pole at some point

z
0

∈
E

{z_0} \in E

, then

Ω
\Omega

has the Pompeiu property unless

Φ
\Phi

is a Möbius transformation, in which case

Ω
\Omega

is a disk.
Finitely generated Kleinian groups in 3-space and 3-manifolds of infinite homotopy type
Authors: Potyagaĭlo L.
Published: June 2012

We prove the existence of a finitely generated Kleinian group

N
⊂
S

O
+

(
1
,
4
)

N \subset S{O_ + }(1,4)

acting freely on an invariant component

Ω
⊂

S
3

\Omega \subset {S^3}

without parabolic elements such that the fundamental group

π
1

(
Ω

/

N
)

{\pi _1}(\Omega /N)

is not finitely generated. Moreover, N is a finite index subgroup of a Kleinian group

N
0

{N_0}

which has infinitely many conjugacy classes of elliptic elements.
Minimal torsion in isogeny classes of elliptic curves
Authors: Ross Raymond
Published: June 2012

Let K be a field finitely generated over its prime field, and let

w
(
K
)

w(K)

denote the number of roots of unity in K. If K is of characteristic 0, then there is an integer D, divisible only by those primes dividing

w
(
K
)

w(K)

, such that for any elliptic curve

E

/

K

E/K

without complex multiplication over K, there is an elliptic curve

E
′

/

K

E\prime /K

isogenous to E such that

E
′

(
K

)

tors

E\prime {(K)_{{\text {tors}}}}

is of order dividing D. In case K admits a real embedding, we show

D
=
2

D = 2

, and a nonuniform result is proved in positive characteristic.
Commutator theory without join-distributivity
Authors: Lipparini Paolo
Published: June 2012

We develop Commutator Theory for congruences of general algebraic systems (henceforth called algebras) assuming only the existence of a ternary term

d
d

such that

d
(
a
,
b
,
b
)
[
α
,
α
]
a
[
α
,
α
]
d
(
b
,
b
,
a
)

d(a,b,b)[\alpha ,\alpha ]a[\alpha ,\alpha ]d(b,b,a)

, whenever

α
\alpha

is a congruence and

a
α
b

a\alpha b

. Our results apply in particular to congruence modular and

n
n

-permutable varieties, to most locally finite varieties, and to inverse semigroups. We obtain results concerning permutability of congruences, abelian and solvable congruences, connections between congruence identities and commutator identities. We show that many lattices cannot be embedded in the congruence lattice of algebras satisfying our hypothesis. For other lattices, some intervals are forced to be abelian, and others are forced to be nonabelian. We give simplified proofs of some results about the commutator in modular varieties, and generalize some of them to single algebras having a modular congruence lattice.
Differential equations for symmetric generalized ultraspherical polynomials
Authors: Koekoek Roelof
Published: June 2012

We look for differential equations satisfied by the generalized Jacobi polynomials

{

P
n

α
,
β
,
M
,
N

(
x
)

}

n
=
0

∞

\{ P_n^{\alpha ,\beta ,M,N}(x)\} _{n = 0}^\infty

which are orthogonal on the interval

[
−
1
,
1
]

[- 1,1]

with respect to the weight function
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartFraction normal upper Gamma left-parenthesis alpha plus beta plus 2 right-parenthesis Over 2 Superscript alpha plus beta plus 1 Baseline normal upper Gamma left-parenthesis alpha plus 1 right-parenthesis normal upper Gamma left-parenthesis beta plus 1 right-parenthesis EndFraction left-parenthesis 1 minus x right-parenthesis Superscript alpha Baseline left-parenthesis 1 plus x right-parenthesis Superscript beta Baseline plus upper M delta left-parenthesis x plus 1 right-parenthesis plus upper N delta left-parenthesis x minus 1 right-parenthesis comma">

Γ
(
α
+
β
+
2
)

2

α
+
β
+
1

Γ
(
α
+
1
)
Γ
(
β
+
1
)

(
1
−
x

)
α

(
1
+
x

)
β

+
M
δ
(
x
+
1
)
+
N
δ
(
x
−
1
)
,

\frac {{\Gamma (\alpha + \beta + 2)}}{{{2^{\alpha + \beta + 1}}\Gamma (\alpha + 1)\Gamma (\beta + 1)}}{(1 - x)^\alpha }{(1 + x)^\beta } + M\delta (x + 1) + N\delta (x - 1),

\]
where

α
>
−
1

\alpha > - 1

,

β
>
−
1

\beta > - 1

,

M
≥
0

M \geq 0

, and

N
≥
0

N \geq 0

. In the special case that

β
=
α

\beta = \alpha

and

N
=
M

N = M

we find all differential equations of the form
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript i equals 0 Overscript normal infinity Endscripts c Subscript i Baseline left-parenthesis x right-parenthesis y Superscript left-parenthesis i right-parenthesis Baseline left-parenthesis x right-parenthesis equals 0 comma y left-parenthesis x right-parenthesis equals upper P Subscript n Superscript alpha comma alpha comma upper M comma upper M Baseline left-parenthesis x right-parenthesis comma">

∑

i
=
0

∞

c
i

(
x
)

y

(
i
)

(
x
)
=
0
,

y
(
x
)
=

P
n

α
,
α
,
M
,
M

(
x
)
,

\sum \limits _{i = 0}^\infty {{c_i}(x){y^{(i)}}(x) = 0,\quad y(x) = P_n^{\alpha ,\alpha ,M,M}(x),}

\]
where the coefficients

{

c
i

(
x
)

}

i
=
1

∞

\{ {c_i}(x)\} _{i = 1}^\infty

are independent of the degree n. We show that if

M
>
0

M > 0

only for nonnegative integer values of

α
\alpha

there exists exactly one differential equation which is of finite order

2
α
+
4

2\alpha + 4

. By using quadratic transformations we also obtain differential equations for the polynomials

{

P
n

α
,
±
1

/

2
,
0
,
N

(
x
)

}

n
=
0

∞

\{ P_n^{\alpha , \pm 1/2,0,N}(x)\} _{n = 0}^\infty

for all

α
>
−
1

\alpha > - 1

and

N
≥
0

N \geq 0

.
𝑞-Hermite polynomials, biorthogonal rational functions, and 𝑞-beta integrals
Authors: Ismail M. E. H. , Masson D. R.
Published: June 2012

We characterize the solutions of the indeterminate moment problem associated with the continuousqq-Hermite polynomials whenq>1q > 1in terms of their Stieltjes transforms. The extremal measures are found explicitly. An analog of the Askey-Wilson integral is evaluated. It involves integrating a kernel, similar to the Askey-Wilson kernel, against any solution of theqq-Hermite moment problem, provided that certain integrability conditions hold. This led to direct evaluation of severalqq-beta integrals and their discrete analogs as well as a generalization of Bailey’s6ψ6{}_6{\psi _6}, sum containing infinitely many parameters. A system of biorthogonal rational functions is also introduced.
The profile near blowup time for solution of the heat equation with a nonlinear boundary condition
Authors: Hu Bei , Yin Hong-Ming
Published: June 2012

This paper studies the blowup profile near the blowup time for the heat equation

u
t

=
Δ
u

{u_t} = \Delta u

with the nonlinear boundary condition

u
n

=

u
p

{u_n} = {u^p}

on

∂
Ω
×
[
0
,
T
)

\partial \Omega \times [0,T)

. Under certain assumptions, the exact rate of the blowup is established. It is also proved that the blowup will not occur in the interior of the domain. The asymptotic behavior near the blowup point is also studied.
A measure theoretical subsequence characterization of statistical convergence
Authors: Miller Harry I.
Published: June 2012

The concept of statistical convergence of a sequence was first introduced by H. Fast. Statistical convergence was generalized by R. C. Buck, and studied by other authors, using a regular nonnegative summability matrix

A
A

in place of

C
1

{C_1}

. The main result in this paper is a theorem that gives meaning to the statement:

S
=
{

s
n

}

S = \{ {s_n}\}

converges to

L
L

statistically

(
T
)

(T)

if and only if "most" of the subsequences of

S
S

converge, in the ordinary sense, to

L
L

. Here

T
T

is a regular, nonnegative and triangular matrix. Corresponding results for lacunary statistical convergence, recently defined and studied by J. A. Fridy and C. Orhan, are also presented.
The structure of Mackey functors
Authors: Thévenaz Jacques , Webb Peter
Published: June 2012

Mackey functors are a framework having the common properties of many natural constructions for finite groups, such as group cohomology, representation rings, the Burnside ring, the topological

K

{\text {K}}

-theory of classifying spaces, the algebraic

K

{\text {K}}

-theory of group rings, the Witt rings of Galois extensions, etc. In this work we first show that the Mackey functors for a group may be identified with the modules for a certain algebra, called the Mackey algebra. The study of Mackey functors is thus the same thing as the study of the representation theory of this algebra. We develop the properties of Mackey functors in the spirit of representation theory, and it emerges that there are great similarities with the representation theory of finite groups. In previous work we had classified the simple Mackey functors and demonstrated semisimplicity in characteristic zero. Here we consider the projective Mackey functors (in arbitrary characteristic), describing many of their features. We show, for example, that the Cartan matrix of the Mackey algebra may be computed from a decomposition matrix in the same way as for group representations. We determine the vertices, sources and Green correspondents of the projective and simple Mackey functors, as well as providing a way to compute the Ext groups for the simple Mackey functors. We parametrize the blocks of Mackey functors and determine the groups for which the Mackey algebra has finite representation type. It turns out that these Mackey algebras are direct sums of simple algebras and Brauer tree algebras. Throughout this theory there is a close connection between the properties of the Mackey functors, and the representations of the group on which they are defined, and of its subgroups. The relationships between these representations are exactly the information encoded by Mackey functors. This observation suggests the use of Mackey functors in a new way, as tools in group representation theory.
Functional rotation numbers for one-dimensional maps
Authors: Blokh A. M.
Published: June 2012

We introduce functional rotation numbers and sets for one-dimensional maps (we call them

f
f

-rotation numbers and sets) and deduce some of their properties (density of

f

{\text {f}}

-rotation numbers of periodic points in the

f

{\text {f}}

-rotation set, conditions for the connectedness of the

f

{\text {f}}

-rotation set) from the spectral decomposition theorem for one-dimensional maps.
The structure of MFD shock waves for rectilinear motion in some models of plasma
Authors: Hesaaraki Mahmoud
Published: June 2012

The mathematical question of the existence of structure for "fast", "slow" and "intermediate" MFD shock waves in the case of rectilinear motion in some model of plasma is stated in terms of a six-dimensional system of ordinary differential equations, which depends on five viscosity parameters. In this article we shall show that this system is gradient-like. Then by using the Conley theory we prove that the fast and the slow shocks always possess structure. Moreover, the intermediate shocks do not admit structure. Some limiting cases for singular viscosities are investigated. In particular, we show how the general results in the classical one fluid MHD theory are obtained when "the plasma viscosities"

β
\beta

and

χ
\chi

tend to zero.
When do the upper Kuratowski topology (homeomorphically, Scott topology) and the co-compact topology coincide?
Authors: Dolecki Szymon , Greco Gabriele H. , Lechicki Alojzy
Published: June 2012

A topology is called consonant if the corresponding upper Kuratowski topology on closed sets coincides with the co-compact topology, equivalently if each Scott open set is compactly generated. It is proved that Čechcomplete topologies are consonant and that consonance is not preserved by passage to

G
δ

{G_\delta }

-sets, quotient maps and finite products. However, in the class of the regular spaces, the product of a consonant topology and of a locally compact topology is consonant. The latter fact enables us to characterize the topologies generated by some

Γ
\Gamma

-convergences.
Automorphism group schemes of basic matrix invariants
Authors: Waterhouse William C.
Published: June 2012

For

3
⩽
k
>
n
,

let

E
k

(
X
)

3 \leqslant k > n,\quad {\text {let}}\quad {E_k}(X)

be the polynomial in

n
2

{n^2}

variables defined by

det

(
X
+
λ
I
)
=
∑

E
k

(
X
)

λ

n
−
k

{\text {det}}(X + \lambda I) = \sum {{E_k}(X){\lambda ^{n - k}}}

. Let

R
R

be a ring containing a field of characteristic

p
⩾
0

p \geqslant 0

. If

p
p

does not divide

n
−
k
+
1

n - k + 1

, the invertible linear transformations on matrices preserving

E
k

(
X
)

{E_k}(X)

up to scalars are (in essence) just the obvious ones arising from scaling, similarities, and transposition. If the power

p
s

{p^s}

dividing

n
−
k
+
1

n - k + 1

is greater than

k
k

, then we have these elements times maps of the form

X
↦
X
+
f
(
X
)
I

X \mapsto X + f(X)I

. When smaller powers

p
s

{p^s}

divide

n
−
k
+
1

n - k + 1

, the group scheme is like the first with an infinitesimal part of the second. One corollary is that every division algebra of finite dimension

n
2

>
4

{n^2} > 4

over its center carries a canonical cubic form that determines it up to antiisomorphism.
On the cohomology of Γ_{𝑝}
Authors: Xia Yining
Published: June 2012

Let

Γ
g

{\Gamma _g}

denote the mapping class group of genus

g
g

. In this paper, we calculate

p
p

-torsion of Farrell cohomology

H
^

∗

(

Γ
p

)

{\widehat {H}^*}({\Gamma _p})

for any odd prime

p
p

.
On permutations of lacunary intervals
Authors: Hare Kathryn E. , Klemes Ivo
Published: June 2012

Let

{

I
j

}

\{ {I_j}\}

be an interval partition of the integers and consider the Littlewood-Paley type square function

S
(
f
)
=

(
∑

|

f
j

|

2

)

1

/

2

S(f) = {(\sum {\left | {{f_j}} \right |^2})^{1/2}}

where

f
^

j

=

f
^

χ

I
j

{\hat f_j} = \hat f\chi {I_j}

. We prove that if the lengths

ℓ
(

I
j

)

\ell ({I_j})

of the intervals

I
j

{I_j}

satisfy

ℓ
(

I

j
+
1

)

/

ℓ
(

I
j

)
→
∞

\ell ({I_{j + 1}})/\ell ({I_j}) \to \infty

, then

‖

S
(
f
)

‖

p

≈

‖
f
‖

p

{\left \| {S(f)} \right \|_p} \approx {\left \| f \right \|_p}

for

1
>
p
>
∞

1 > p > \infty

. As these intervals need not be adjacent, such partitions can be thought of as permutations of lacunary intervals. This work generalizes the specific partition considered in a previous paper [H2]. We conjecture that it suffices to assume

ℓ
(

I

j
+
1

)

/

ℓ
(

I
j

)
⩾
λ
>
1

\ell ({I_{j + 1}})/\ell ({I_j}) \geqslant \lambda > 1

, and we also conjecture a necessary and sufficient condition.
On some subalgebras of 𝐵(𝑐₀) and 𝐵(𝑙₁)
Authors: Cass F. P. , Gao J. X.
Published: June 2012

For a non-reflexive Banach space

X
X

and

w
∈

X

∗

∗

w \in {X^{{\ast }{\ast }}}

, two families of subalgebras of
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper B left-parenthesis upper X right-parenthesis comma normal upper Gamma Subscript w Baseline equals left-brace upper T element-of upper B left-parenthesis upper X right-parenthesis vertical-bar upper T Superscript asterisk asterisk Baseline w equals k w for some k element-of double-struck upper C right-brace">

B
(
X
)
,

Γ
w

=
{
T
∈
B
(
X
)

|

T

∗

∗

w
=
k
w

for some

k
∈

C

} 

B(X),\;{\Gamma _w} = \{ T \in B(X)|{T^{{\ast }{\ast }}}w = kw\;{\text {for some}}\;k \in \mathbb {C}{\text {\} }}

, and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Omega Subscript w Baseline equals StartSet upper T element-of upper B left-parenthesis upper X right-parenthesis vertical-bar upper T Superscript asterisk asterisk Baseline w element-of w circled-plus ModifyingAbove upper X With caret EndSet">

Ω
w

=
{
T
∈
B
(
X
)

|

T

∗

∗

w
∈
w
⊕

X
^

}

{\Omega _w} = \{ T \in B(X)|{T^{{\ast }{\ast }}}w \in w \oplus \hat X\}

for

w
∈

X

∗

∗

∖

X
^

w \in {X^{{\ast }{\ast }}}\backslash \hat X

with

Ω
w

=
B
(
X
)

{\Omega _w} = B(X)

for

w
∈

X
^

w \in \hat X

, were defined originally by Wilansky. We consider

X
=

c
0

X = {c_0}

and

X
=

l
1

X = {l_1}

and investigate relationships between the subalgebras for different

w
∈

X

∗

∗

w \in {X^{{\ast }{\ast }}}

. We prove in the case of

c
0

{c_0}

that, for

w
∈

X

∗

∗

∖

X
^

w \in {X^{{\ast }{\ast }}}\backslash \hat X

, all

Γ
w

{\Gamma _w}

’s are isomorphic and all

Ω
w

{\Omega _w}

’s are isomorphic. For

X
=

l
1

X = {l_1}

, where it is known that not all

Γ
w

{\Gamma _w}

’s are isomorphic and not all

Ω
w

{\Omega _w}

’s are isomorphic, we show, surprisingly, that subalgebras associated with a Dirac measure on

β

N

∖

N

\beta \mathbb {N}\backslash \mathbb {N}

, regarded as a functional on

l
1

∗

l_1^{\ast }

, are isomorphic to those associated with some Banach limit (i.e., a translation invariant extended limit). We also obtain a representation for the operators in the subalgebras

{
∩

Γ
f

|

f

is a Banach limit

}

\{ \cap {\Gamma _f}|f\;{\text {is a Banach limit}}\}

and

{
∩

Ω
f

|

f

is a Banach limit

}

\{ \cap {\Omega _f}|f\;{\text {is a Banach limit}}\}

of

B
(

l
1

)

B({l_1})

.
Cyclic Sullivan-de Rham forms
Authors: Allday Christopher
Published: June 2012

For a simplicial set

X
X

the Sullivan-de Rham forms are defined to be the simplicial morphisms from

X
X

to a simplicial rational commutative graded differential algebra (cgda)

∇
\nabla

. However

∇
\nabla

is a cyclic cgda in a standard way. And so, when

X
X

is a cyclic set, one has a cgda of cyclic morphisms from

X
X

to

∇
\nabla

. It is shown here that the homology of this cgda is naturally isomorphic to the rational cohomology of the orbit space of the geometric realization

|
X
|

\left | X \right |

with its standard circle action. In addition, a cyclic cgda

∇
C

\nabla C

is introduced; and it is shown that the homology of the cgda of cyclic morphisms from

X
X

to

∇
C

\nabla C

is naturally isomorphic to the rational equivariant (Borel construction) cohomology of

|
X
|

\left | X \right |

.
Shadow forms of Brasselet-Goresky-MacPherson
Authors: Bendiffalah Belkacem
Published: June 2012

Brasselet, Goresky and MacPherson constructed an explicit morphism, providing a De Rham isomorphism between the intersection homology of a singular variety

X
X

and the cohomology of some complex of differential forms, called "shadow forms" and generalizing Whitney forms, on the smooth part of

X
X

. The coefficients of shadow forms are integrals of Dirichlet type. We find an explicit formula for them; from that follows an alternative proof of Brasselet, Goresky and MacPherson’s theorem. Next, we give a duality formula and a product formula for shadow forms and construct the correct algebra structure, for which shadow forms yield a morphism.
Triangles of groups
Authors: Chermak Andrew
Published: June 2012

Given a certain commutative diagram of groups and monomorphisms, does there necessarily exist a group in which the given diagram is essentially a diagram of subgroups and inclusions? In general, the answer is negative, but J. Corson, and Gersten and Stallings have shown that in the case of a "non-spherical triangle" of groups the answer is positive. This paper improves on these results by weakening the non-sphericality requirement.
Minimization problems for noncoercive functionals subject to constraints
Authors: Vy Khoi Le , Schmitt Klaus
Published: June 2012

We consider noncoercive functionals on a reflexive Banach space and establish minimization theorems for such functionals on smooth constraint manifolds. These results in turn yield critical point theorems for certain classes of homogeneous functionals. Several applications to the study of boundary value problems for quasilinear elliptic equations are included.
Kazhdan-Lusztig conjecture for generalized Kac-Moody algebras. II. Proof of the conjecture
Authors: Naito Satoshi
Published: June 2012

Generalized Kac-Moody algebras were introduced by Borcherds in the study of Conway and Norton’s moonshine conjectures for the Monster sporadic simple group. In this paper, we prove the Kazhdan-Lusztig conjecture for generalized Kac-Moody algebras under a certain mild condition, by using a generalization (to the case of generalized Kac-Moody algebras) of Jantzen’s character sum formula. Our (main) formula generalizes the celebrated result for the case of Kac-Moody algebras, and describes the characters of irreducible highest weight modules over generalized Kac-Moody algebras in terms of the "extended" Kazhdan-Lusztig polynomials.
𝑒-invariants and finite covers. II
Authors: Smith Larry
Published: June 2012

Let

M
~

↓
M

\widetilde {M} \downarrow M

be a finite covering of closed framed manifolds. By the Pontrijagin-Thom construction both

M
~

\widetilde {M}

and

M
M

define elements in the stable homotopy ring of spheres

π
∗
s

\pi _*^s

. Associated to

M
~

\widetilde {M}

and

M
M

are their

e
e

invariants

e
L

(

M
~

)

{e_L}(\widetilde {M})

,

e
L

(
M
)
∈

Q

/

Z

{e_L}(M) \in \mathbb {Q}/\mathbb {Z}

. If

N
~

↓
N

\widetilde {N} \downarrow N

is a finite covering of closed oriented manifolds, then there is a related invariant

I
Δ

(

N
~

↓
N
)
∈

Q

{I_\Delta }(\widetilde {N} \downarrow N) \in \mathbb {Q}

of the diffeomorphism class of the covering. In a previous paper we examined the relation between these invariants. We reduced the determination of

e
L

(

M
~

)
−
p

e
L

(
M
)

{e_L}(\widetilde {M}) - p{e_L}(M)

, as well as

I
Δ

(

N
~

↓
N
)

{I_\Delta }(\widetilde {N} \downarrow N)

, for a

p
p

-fold cover, to the evaluation of certain sums of roots of unity. In this sequel we show how the invariant theory of the cyclic group

Z

/

p

\mathbb {Z}/p

may be used to evaluate these rums. For example we obtain
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript StartLayout 1st Row zeta Superscript p Baseline equals 1 2nd Row zeta not-equals 1 EndLayout Endscripts StartFraction left-parenthesis 1 plus zeta right-parenthesis left-parenthesis 1 plus zeta Superscript negative 1 Baseline right-parenthesis Over left-parenthesis 1 minus zeta right-parenthesis left-parenthesis 1 minus zeta Superscript negative 1 Baseline right-parenthesis EndFraction equals StartFraction left-parenthesis p minus 1 right-parenthesis left-parenthesis p minus 2 right-parenthesis Over 3 EndFraction">

∑

ζ
p

=
1

ζ
≠
1

(
1
+
ζ
)
(
1
+

ζ

−
1

)

(
1
−
ζ
)
(
1
−

ζ

−
1

)

=

(
p
−
1
)
(
p
−
2
)

3

\sum _{\substack {\zeta ^p = 1\\\zeta \ne 1}} \frac {(1 + \zeta )(1 + \zeta ^{-1})}{(1 - \zeta )(1 - \zeta ^{-1})} = \frac {(p - 1)(p - 2)}{3}

\]
which may be used to determine the value of

I
Δ

{I_\Delta }

in degrees congruent to

3
3

mod

2
(
p
−
1
)

\mod 2(p - 1)

for odd primes

p
p

.
Global surjectivity of submersions via contractibility of the fibers
Authors: Rabier Patrick J.
Published: June 2012

We give a sufficient condition for a

C
1

{C^1}

submersion

F
:
X
→
Y

F:X \to Y

,

X
X

and

Y
Y

real Banach spaces, to be surjective with contractible fibers

F

−
1

(
y
)

{F^{ - 1}}(y)

. Roughly speaking, this condition "interpolates" two well-known but unrelated hypotheses corresponding to the two extreme cases: Hadamard’s criterion when

Y
≃
X

Y \simeq X

and

F
F

is a local diffeomorphism, and the Palais-Smale condition when

Y
=

R

Y = \mathbb {R}

. These results may be viewed as a global variant of the implicit function theorem, which unlike the local one does not require split kernels. They are derived from a deformation theorem tailored to fit functionals with a norm-like nondifferentiability.
Orthogonal calculus
Authors: Weiss Michael
Published: June 2012

Orthogonal calculus is a calculus of functors, similar to Goodwillie’s calculus. The functors in question take finite dimensional real vector spaces (with an inner product) to pointed spaces. Prime example:

F
(
V
)
=
B
O
(
V
)

F(V) = BO(V)

, where

O
(
V
)

O(V)

is the orthogonal group of

V
V

. In this example, and in general, first derivatives in the orthogonal calculus reproduce and generalize much of the theory of Stiefel-Whitney classes. Similarly, second derivatives in the orthogonal calculus reproduce and generalize much of the theory of Pontryagin classes.
Finite Group Actions on Siegel Modular Spaces
Authors: Lai K. F. , Lee Ronnie
Published: June 2012

The theory of nonabelian cohomology is used to show that the set of fixed points of a finite group acting on a Siegel modular space is a union of Shimura varieties
DiNuP: a systematic approach to identify regions of differential nucleosome positioning
Authors: Fu Kai , Tang Qianzi , Feng Jianxing , Liu X. Shirley , Zhang Yong
Published: June 2012

Motivation: With the rapid development of high-throughput sequencing technologies, the genome-wide profiling of nucleosome positioning has become increasingly affordable. Many future studies will investigate the dynamic behaviour of nucleosome positioning in cells that have different states or that are exposed to different conditions. However, a robust method to effectively identify the regions of differential nucleosome positioning (RDNPs) has not been previously available.

Results: We describe a novel computational approach, DiNuP, that compares nucleosome profiles generated by high-throughput sequencing under various conditions. DiNuP provides a statistical P-value for each identified RDNP based on the difference of read distributions. DiNuP also empirically estimates the false discovery rate as a cutoff when two samples have different sequencing depths and differentiate reliable RDNPs from the background noise. Evaluation of DiNuP showed it to be both sensitive and specific for the detection of changes in nucleosome location, occupancy and fuzziness. RDNPs that were identified using publicly available datasets revealed that nucleosome positioning dynamics are closely related to the epigenetic regulation of transcription.

Availability and implementation: DiNuP is implemented in Python and is freely available at http://www.tongji.edu.cn/~zhanglab/DiNuP.

Contact:  yzhang@tongji.edu.cn

Supplementary Information:  Supplementary data are available at Bioinformatics online.
RNA Silencing and Plant Viral Diseases
Authors: Wang Ming-Bo , Masuta Chikara , Smith Neil A. , Shimura Hanako
Published: June 2012

RNA silencing plays a critical role in plant resistance against viruses, with multiple silencing factors participating in antiviral defense. Both RNA and DNA viruses are targeted by the small RNA-directed RNA degradation pathway, with DNA viruses being also targeted by RNA-directed DNA methylation. To evade RNA silencing, plant viruses have evolved a variety of counter-defense mechanisms such as expressing RNA-silencing suppressors or adopting silencing-resistant RNA structures. This constant defense–counter defense arms race is likely to have played a major role in defining viral host specificity and in shaping viral and possibly host genomes. Recent studies have provided evidence that RNA silencing also plays a direct role in viral disease induction in plants, with viral RNA-silencing suppressors and viral siRNAs as potentially the dominant players in viral pathogenicity. However, questions remain as to whether RNA silencing is the principal mediator of viral pathogenicity or if other RNA-silencing-independent mechanisms also account for viral disease induction. RNA silencing has been exploited as a powerful tool for engineering virus resistance in plants as well as in animals. Further understanding of the role of RNA silencing in plant–virus interactions and viral symptom induction is likely to result in novel anti-viral strategies in both plants and animals.
Identification and Prevalence of Botrytis spp. from Blackberry and Strawberry Fields of the Carolinas
Authors: Li Xingpeng , Fernández-Ortuño Dolores , Chai Wenxuan , Wang Fei , Schnabel Guido
Published: June 2012

Gray mold disease of blackberry and strawberry is caused by Botrytis cinerea and B. caroliniana in the southeastern United States. In this study, methods to distinguish both species were established and their prevalence was determined in commercial blackberry and strawberry fields. Using DNA from B. cinerea and B. caroliniana reference strains, a species-differentiating polymerase chain reaction (PCR) amplification was developed that amplified G3PDH gene fragments of two different sizes depending on the species. The PCR is performed with three primers (two species-differentiating forward primers and one universal reverse primer) and amplified a 238-bp product from B. cinerea and a 536-bp fragment from B. caroliniana reference isolates. A total of 400 Botrytis isolates were collected from 6 commercial blackberry and 11 strawberry fields of the Carolinas and identified to the species level by the new PCR method. Both Botrytis spp. were identified in blackberry and strawberry fields, but B. caroliniana was less common than B. cinerea. Only 33 of 202 isolates from blackberry fields were identified as B. caroliniana, and the majority of these isolates came from two fields in South Carolina. Only 1 of 198 isolates from strawberries was identified as B. caroliniana, and this isolate was found in central North Carolina. B. cinerea but not B. caroliniana isolates sporulated on potato dextrose agar and Kings medium B. Our results show that B. cinerea and B. caroliniana coexist in at least some commercial blackberry and strawberry fields of the Carolinas, with B. cinerea being the more prevalent species.
Biological invasions and the acoustic niche: the effect of bullfrog calls on the acoustic signals of white-banded tree frogs
Authors: Both Camila , Grant Taran
Published: June 2012

Invasive species are known to affect native species in a variety of ways, but the effect of acoustic invaders has not been examined previously. We simulated an invasion of the acoustic niche by exposing calling native male white-banded tree frogs (
Hypsiboas albomarginatus
) to recorded invasive American bullfrog (
Lithobates catesbeianus
) calls. In response, tree frogs immediately shifted calls to significantly higher frequencies. In the post-stimulus period, they continued to use higher frequencies while also decreasing signal duration. Acoustic signals are the primary basis of mate selection in many anurans, suggesting that such changes could negatively affect the reproductive success of native species. The effects of bullfrog vocalizations on acoustic communities are expected to be especially severe due to their broad frequency band, which masks the calls of multiple species simultaneously.
Anthony Trafford James. 6 March 1922 — 7 December 2006
Authors: Gurr Michael
Published: June 2012

A. T . (‘Tony’) James first came to scientific prominence in the 1950s while working with A. J. P. Martin at the Medical Research Council’s National Institute for Medical Research, London, for demonstrating the practicality of gas–liquid chromatography. This technique enabled the separation and analysis of complex mixtures of closely related volatile compounds down to microgram amounts. The method was rapidly taken up by research laboratories and industrial organizations worldwide. James himself used the technique to study lipid biosynthesis, first in plants and later in animal tissues; he established at the Unilever Research Laboratory Colworth House one of the premier lipid biochemistry groups in the world. As his administrative and managerial duties increased, he established himself as a leader in UK science policy, being an advocate for the better funding of biological research through his work for several research councils.
Tensorial Minkowski functionals of triply periodic minimal surfaces
Authors: Mickel Walter , Schröder-Turk Gerd E. , Mecke Klaus
Published: June 2012

A fundamental understanding of the formation and properties of a complex spatial structure relies on robust quantitative tools to characterize morphology. A systematic approach to the characterization of average properties of anisotropic complex interfacial geometries is provided by integral geometry which furnishes a family of morphological descriptors known as tensorial Minkowski functionals. These functionals are curvature-weighted integrals of tensor products of position vectors and surface normal vectors over the interfacial surface. We here demonstrate their use by application to non-cubic triply periodic minimal surface model geometries, whose Weierstrass parametrizations allow for accurate numerical computation of the Minkowski tensors.