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3  The Convolution Sum $\sum_{m Alaca, Ay\c{s}e; Alaca, \c{S}aban; Williams, Kenneth S. 

15  The Duality Problem for the Class of AMCompact Operators on Banach Lattices Aqzzouz, Belmesnaoui; Nouira, Redouane; Zraoula, Larbi
We prove the converse of a
theorem of Zaanen about the duality problem of
positive AMcompact operators.


21  A Remark on Extensions of CR Functions from Hyperplanes Baracco, Luca
In the characterization of the range of the Radon transform, one
encounters the problem of the holomorphic extension of functions
defined on $\R^2\setminus\Delta_\R$ (where $\Delta_\R$ is the diagonal
in $\R^2$) and which extend as ``separately holomorphic" functions of
their two arguments. In particular, these functions extend in fact to $\C^2\setminus
\Delta_\C$ where $\Delta_\C$ is the complexification of
$\Delta_\R$. We take this theorem from the integral geometry and put
it in the more natural context of the CR geometry where it accepts an
easier proof and a more general statement. In this new setting it
becomes a variant of the celebrated ``edge of the wedge" theorem of
Ajrapetyan and Henkin.


26  Hin\v cin's Theorem for Multiplicative Free Convolution Belinschi, S. T.; Bercovici, H.
Hin\v cin proved that any limit law, associated with a triangular
array of infinitesimal random variables, is infinitely divisible.
The analogous result for additive free convolution was proved earlier by
Bercovici and Pata.
In this paper we will prove corresponding results for the multiplicative
free convolution of measures definded on the unit circle and on the
positive halfline.


32  On Linear Independence of a Certain Multivariate Infinite Product Choi, Stephen; Zhou, Ping
Let $q,m,M \ge 2$ be positive integers and
$r_1,r_2,\dots ,r_m$ be positive rationals and
consider the following $M$ multivariate infinite products
\[
F_i = \prod_{j=0}^\infty ( 1+q^{(Mj+i)}r_1+q^{2(Mj+i)}r_2+\dots +
q^{m(Mj+i)}r_m)
\]
for $i=0,1,\dots ,M1$.
In this article, we study the linear independence of these infinite products.
In particular, we obtain a lower bound for the dimension of the vector space
$\IQ F_0+\IQ F_1 +\dots + \IQ F_{M1} + \IQ$ over $\IQ$ and show that
among these $M$ infinite products, $F_0, F_1,\dots ,F_{M1}$, at least
$\sim M/m(m+1)$ of them are irrational for fixed $m$ and $M \rightarrow
\infty$.


47  The Minimal Number of ThreeTerm Arithmetic Progressions Modulo a Prime Converges to a Limit Croot, Ernie
How few threeterm arithmetic progressions can a
subset $S \subseteq \Z_N := \Z/N\Z$ have if $S \geq \upsilon N$
(that is, $S$ has density at least $\upsilon$)?
Varnavides %\cite{varnavides}
showed that this number of arithmetic progressions is at
least $c(\upsilon)N^2$ for sufficiently large integers $N$.
It is well known that determining good lower bounds for
$c(\upsilon)> 0$ is at the same level of depth as Erd\" os's famous
conjecture about whether a subset $T$ of the naturals where
$\sum_{n \in T} 1/n$ diverges, has a $k$term arithmetic progression
for $k=3$ (that is, a threeterm arithmetic progression).


57  A Note on Integer Symmetric Matrices and Mahler's Measure Dobrowolski, Edward
We find a lower bound on the absolute value of the discriminant of
the minimal polynomial of an integral symmetric matrix and apply
this result to find a lower bound on Mahler's measure of related
polynomials and to disprove a conjecture of D. Estes and R. Guralnick.


60  F{\o}lner Nets for Semidirect Products of Amenable Groups Janzen, David
For unimodular semidirect products of locally compact amenable
groups $N$ and $H$, we show that one can always construct a
F{\o}lner net of the form $(A_\alpha \times B_\beta)$ for $G$, where
$(A_\alpha)$ is a strong form of F{\o}lner net for $N$ and
$(B_\beta)$ is any F{\o}lner net for $H$. Applications to the
Heisenberg and Euclidean motion groups are provided.


67  RearrangementInvariant Functionals with Applications to Traces on Symmetrically Normed Ideals Kalton, Nigel; Sukochev, Fyodor
We present a construction of singular rearrangement
invariant functionals on Marcinkiewicz function/operator spaces.
The functionals constructed differ from all previous examples in
the literature in that they fail to be symmetric. In other words,
the functional $\phi$ fails the condition that if $x\pprec y$
(HardyLittlewoodPolya submajorization) and $0\leq x,y$, then
$0\le \phi(x)\le \phi(y).$ We apply our results to singular traces
on symmetric operator spaces (in particular on
symmetricallynormed ideals of compact operators), answering
questions raised by Guido and Isola.


81  Homotopy Formulas for Cyclic Groups Acting on Rings Kassel, Christian
The positive cohomology groups of a finite group acting on a ring
vanish when the ring has a norm one element. In this note we give
explicit homotopies on the level of cochains when the group is cyclic,
which allows us to express any cocycle of a cyclic group
as the coboundary of an explicit cochain.
The formulas in this note are closely related to the effective problems considered in previous joint work
with Eli Aljadeff.


86  The Numerical Range of 2Dimensional Krein Space Operators Nakazato, Hiroshi; Bebiano, Natália; Providência, Jo\ ao da
The tracial numerical range of operators on a $2$dimensional
Krein space is investigated. Results in the vein
of those obtained in the context of Hilbert
spaces are obtained.


100  Dynamical Zeta Function for Several Strictly Convex Obstacles Petkov, Vesselin
The behavior of the dynamical zeta function $Z_D(s)$ related to
several strictly convex disjoint obstacles is similar to that of the
inverse $Q(s) = \frac{1}{\zeta(s)}$ of the Riemann zeta function
$\zeta(s)$. Let $\Pi(s)$ be the series obtained from $Z_D(s)$ summing
only over primitive periodic rays. In this paper we examine the
analytic singularities of $Z_D(s)$ and $\Pi(s)$ close to the line $\Re
s = s_2$, where $s_2$ is the abscissa of absolute convergence of the
series obtained by the second iterations of the primitive periodic
rays. We show that at least one of the functions $Z_D(s), \Pi(s)$
has a singularity at $s = s_2$.


114  Zero Cycles on a Twisted Cayley Plane Petrov, V.; Semenov, N.; Zainoulline, K.
Let $k$ be a field of characteristic not $2,3$.
Let $G$ be an exceptional simple algebraic group over $k$
of type $\F$, $^1{\E_6}$ or $\E_7$ with trivial Tits algebras.
Let $X$ be a projective $G$homogeneous variety.
If $G$ is of type $\E_7$, we assume in addition
that the respective
parabolic subgroup is of type $P_7$.
The main result of the paper says that
the degree map on the group of zero cycles of $X$
is injective.


125  Explicit Real Cubic Surfaces PoloBlanco, Irene; Top, Jaap
The topological classification of smooth real
cubic surfaces is
recalled and compared to the classification in terms of
the number of real lines and of real tritangent planes,
as obtained
by L.~Schl\"afli in 1858.
Using this, explicit examples of
surfaces of every possible type are given.


134  Numerical Semigroups Having a Toms Decomposition Rosales, J. C.; Garc\'{\i}aSánchez, P. A.
We show that the class of system proportionally modular numerical semigroups
coincides with the class of numerical semigroups having a Toms
decomposition.


140  First Variations of the Best Sobolev Trace Constant with Respect to the Domain Rossi, Julio D.
In this paper we study the best constant of the Sobolev trace
embedding $H^{1}(\Omega)\to L^{2}(\partial\Omega)$, where $\Omega$
is a bounded smooth domain in $\RR^N$. We find a formula for the
first variation of the best constant with respect to the domain.
As a consequence, we prove that the ball is a critical domain when
we consider deformations that preserve volume.


146  SteppingStone Model with Circular Brownian Migration Zhou, Xiaowen
In this paper we consider the steppingstone model on a circle with
circular Brownian migration. We first point out a connection between
Arratia flow on the circle and the marginal distribution of this
model. We then give a new representation for the steppingstone
model using Arratia flow and circular coalescing Brownian motion.
Such a representation enables us to carry out some explicit
computations. In particular, we find the distribution for the first
time when there is only one type
left across the circle.


161  Wirtinger's Inequalities on Time Scales Agarwal, Ravi P.; OteroEspinar, Victoria; Perera, Kanishka; Vivero, Dolores R.
This paper is devoted to the study of Wirtingertype
inequalities for the Lebesgue $\Delta$integral on an arbitrary time scale $\T$.
We prove a general inequality for a class of absolutely continuous
functions on closed subintervals of an adequate subset of $\T$.
By using this expression and by assuming that $\T$ is bounded,
we deduce that
a general inequality is valid for every absolutely continuous function on $\T$
such that its $\Delta$derivative belongs to $L_\Delta^2([a,b)\cap\T)$ and at most it vanishes
on the boundary of $\T$.


172  Consecutive Large Gaps in Sequences Defined by Multiplicative Constraints Alkan, Emre; Zaharescu, Alexandru
In this paper we obtain quantitative results on the occurrence of
consecutive large gaps between $B$free numbers, and consecutive
large gaps between nonzero Fourier coefficients of a class of
newforms without complex multiplication.


182  Group Gradings on Associative Algebras with Involution Bahturin, Y. A.; Giambruno, A.
In this paper we describe the group gradings by a finite abelian
group $G$ of the matrix algebra $M_n(F)$ over an algebraically
closed field $F$ of characteristic different from 2, which respect
an involution (involution gradings). We also describe, under
somewhat heavier restrictions on the base field, all $G$gradings on
all finitedimensional involution simple algebras.


195  Boundedness from Below of Composition Operators on $\alpha$Bloch Spaces Chen, Huaihui; Gauthier, Paul
We give a necessary and sufficient condition for a composition
operator on an $\alpha$Bloch space with $\alpha\ge 1$ to be bounded below.
This extends a known result for the Bloch space due to P. Ghatage,
J. Yan, D. Zheng, and H. Chen.


205  On Gâteaux Differentiability of Pointwise Lipschitz Mappings Duda, Jakub
We prove that for every function $f\from X\to Y$,
where $X$ is a separable Banach space and $Y$ is a Banach space
with RNP, there exists a set $A\in\tilde\mcA$ such that $f$ is
G\^ateaux differentiable at all $x\in S(f)\setminus A$, where
$S(f)$ is the set of points where $f$ is pointwiseLipschitz.
This improves a result of Bongiorno. As a corollary,
we obtain that every $K$monotone function on a separable Banach space
is Hadamard differentiable outside of a set belonging to $\tilde\mcC$;
this improves a result due to Borwein and Wang.
Another corollary is that if $X$ is Asplund, $f\from X\to\R$ cone monotone,
$g\from X\to\R$ continuous convex, then there exists a point in $X$, where $f$ is Hadamard
differentiable and $g$ is Fr\'echet differentiable.


217  A Multivalued Nonlinear System with the Vector $p$Laplacian on the SemiInfinity Interval Filippakis, Michael E.; Papageorgiou, Nikolaos S.
We study a second order nonlinear system driven by the vector
$p$Laplacian, with a multivalued nonlinearity and defined on
the positive time semiaxis $\mathbb{R}_+.$ Using degree
theoretic techniques we solve an auxiliary mixed boundary value
problem defined on the finite interval $[0,n]$ and then via a
diagonalization method we produce a solution for the original
infinite timehorizon system.


229  Existence of Solutions to Poisson's Equation Hanley, Mary
Let $\Omega$ be a domain in $\mathbb R^n$ ($n\geq 2$). We find a
necessary and sufficient topological condition on $\Omega$ such
that, for any measure $\mu$ on $\mathbb R^n$, there is a function $u$
with specified boundary conditions that satisfies the Poisson
equation $\Delta u=\mu$ on $\Omega$ in the sense of distributions.


236  Kolmogorov, Linear and PseudoDimensional Widths of Classes of $s$Monotone Functions in $\mathbb{L}_p$, $0 Konovalov, Victor N.; Kopotun, Kirill A.
Let $B_p$ be the unit ball in $\mathbb{L}_p$, $0<p<1$, and let $\Delta^s_+$,
$s\in\N$, be the set of all $s$monotone functions on a finite
interval $I$, \ie, $\Delta^s_+$ consists of all functions $x \colon I
\mapsto \R$ such that the divided differences $[x; t_0,\dots,t_s]$ of
order $s$ are nonnegative for all choices of $(s+1)$ distinct points
$t_0,\dots,t_s \in I$. For the classes $\Delta^s_+ B_p := \Delta^s_+
\cap B_p$, we obtain exact orders of Kolmogorov, linear and
pseudodimensional widths in the spaces $\Lq$, $0<q<p<1$:
$$
d_n (\Delta^s_+ B_p)^{\psd}_{\Lq} \asymp
d_n (\Delta^s_+ B_p)^{\kol}_{\Lq} \asymp
d_n (\Delta^s_+ B_p)^{\lin}_{\Lq} \asymp n^{s}.
$$


249  On the Inner Radius of a Nodal Domain Mangoubi, Dan
Let $M$ be a closed Riemannian manifold.
We consider the inner radius of a nodal domain for a large eigenvalue $\lambda$.
We give upper and lower bounds on the inner radius of the type
$C/\lambda^\alpha(\log\lambda)^\beta$. Our proof is based on
a local behavior of eigenfunctions discovered by Donnelly and
Fefferman and a Poincar\'{e} type inequality proved by Maz'ya.
Sharp lower bounds are known
only in dimension two. We give an account of this case too.


261  On the Classification of Rational Quantum Tori and the Structure of Their Automorphism Groups Neeb, KarlHermann
An $n$dimensional quantum torus is a twisted group algebra of the
group $\Z^n$. It is called rational if all invertible commutators are roots
of unity. In the present note we describe a normal form for rational
$n$dimensional quantum
tori over any field. Moreover, we show that for
$n = 2$ the natural exact sequence
describing the automorphism group of the quantum torus splits over any
field.


283  The NoetherLefschetz Theorem Via Vanishing of Coherent Cohomology Ravindra, G. V.
We prove that for a generic hypersurface in $\mathbb P^{2n+1}$ of degree at
least $2+2/n$, the $n$th Picard number is one. The proof is algebraic
in nature and follows from certain coherent cohomology vanishing.


291  Group Algebras with Minimal Strong Lie Derived Length Spinelli, Ernesto
Let $KG$ be a noncommutative strongly Lie solvable group algebra of a
group $G$ over a field $K$ of positive characteristic $p$. In this
note we state necessary and sufficient conditions so that the
strong Lie derived length of $KG$ assumes its minimal value, namely
$\lceil \log_{2}(p+1)\rceil $.


298  The Kostrikin Radical and the Invariance of the Core of Reduced Extended Affine Lie Algebras Tocón, Maribel
In this paper we prove that the Kostrikin radical of an extended affine Lie algebra of
reduced type coincides with the center of its core, and use this characterization to get a typefree
description of the core of such algebras. As a consequence we get that the core of an extended affine
Lie algebra of reduced type is invariant under the automorphisms of the algebra.


310  Relative Homotopy in Relational Structures Witbooi, P. J.
The homotopy groups of a finite partially ordered set (poset) can be
described entirely in the context of posets, as shown in a paper by
B. Larose and C. Tardif.
In this paper we describe the relative version of such a
homotopy theory, for pairs $(X,A)$ where $X$ is a poset and $A$ is a
subposet of $X$. We also prove some theorems on the relevant version
of the notion of weak homotopy equivalences for maps of pairs of such
objects. We work in the category of reflexive binary relational
structures which contains the posets as in the work of Larose and
Tardif.


321  Quantum Multiple Construction of Subfactors Asaeda, Marta
We construct the quantum $s$tuple subfactors for an AFD II$_{1}$
subfactor with finite index and depth, for an arbitrary natural number
$s$. This is a generalization of the quantum multiple subfactors by
Erlijman and Wenzl, which in turn generalized the quantum double
construction of a subfactor for the case that the original subfactor
gives rise to a braided tensor category. In this paper we give a
multiple construction for a subfactor with a weaker condition than
braidedness of the bimodule system.


334  Value Distribution of the Riemann Zeta Function AscahCoallier, I.; Gauthier, P. M.
In this note, we give a new short proof of the fact, recently
discovered by Ye, that all (finite) values are equidistributed by
the Riemann zeta function.


337  Differences between Perfect Powers Bennett, Michael A.
We apply the hypergeometric method of Thue and Siegel to prove
that if $a$ and $b$ are positive integers, then the inequality $
0 < a^x  b^y  < \frac{1}{4} \, \max \{ a^{x/2}, b^{y/2} \}$
has at most a single solution in positive integers $x$ and $y$.
This essentially sharpens a classic result of LeVeque.


348  The Reconstruction Property in Banach Spaces and a Perturbation Theorem Casazza, Peter G.; Christensen, Ole
Perturbation theory is a fundamental tool in Banach space theory.
However, the applications of the classical results
are limited by the fact that they force the
perturbed sequence to be equivalent to the given sequence.
We will develop
a more general perturbation theory that does not force equivalence of the
sequences.


359  Real Hypersurfaces in Complex Space Forms with Reeb Flow Symmetric Structure Jacobi Operator Cho, Jong Taek; Ki, UHang
Real hypersurfaces in a complex space form whose structure
Jacobi operator is symmetric along the Reeb flow are studied. Among
them, homogeneous real hypersurfaces of type $(A)$ in a complex
projective or hyperbolic space are characterized as those whose structure
Jacobi operator commutes with the shape operator.


372  Picard's Iterations for Integral Equations of Mixed Hammerstein Type Ezquerro, J. A.; Hernández, M. A.
A new semilocal convergence result for the Picard method is presented,
where the main required condition in the contraction mapping principle is relaxed.


378  Cyclic Vectors in Some Weighted $L^p$ Spaces of Entire Functions Izuchi, Kou Hei
In this paper,
we generalize a result recently obtained by the author.
We characterize the cyclic vectors in $\Lp$.
Let $f\in\Lp$ and $f\poly$ be contained in the space.
We show that $f$ is nonvanishing if and only if $f$ is cyclic.


386  Positive Solutions of the FalknerSkan Equation Arising in the Boundary Layer Theory Lan, K. Q.; Yang, G. C.
The wellknown FalknerSkan equation is one of the most important
equations in laminar boundary layer theory and is used to describe
the steady twodimensional flow of a slightly viscous
incompressible fluid past wedge shaped bodies of angles related to
$\lambda\pi/2$, where $\lambda\in \mathbb R$ is a parameter
involved in the equation. It is known that there exists
$\lambda^{*}<0$ such that the equation with suitable boundary
conditions has at least one positive solution for each $\lambda\ge
\lambda^{*}$ and has no positive solutions for
$\lambda<\lambda^{*}$. The known numerical result shows
$\lambda^{*}=0.1988$. In this paper, $\lambda^{*}\in
[0.4,0.12]$ is proved analytically by establishing a singular
integral equation which is equivalent to the FalknerSkan
equation. The equivalence result
provides new techniques to study properties and existence of solutions of
the FalknerSkan equation.


399  Linear Equations with Small Prime and Almost Prime Solutions Meng, Xianmeng
Let $b_1, b_2$ be any integers such that
$\gcd(b_1, b_2)=1$ and $c_1b_1<b_2\leq c_2b_1$, where
$c_1, c_2$ are any given positive constants. Let $n$ be any
integer satisfying $\{gcd(n, b_i)=1$, $i=1,2$. Let $P_k$ denote
any integer with no more than $k$ prime factors, counted according
to multiplicity. In this paper, for almost all $b_2$, we prove (i)
a sharp lower bound for $n$ such that the equation $b_1p+b_2m=n$
is solvable in prime $p$ and almost prime $m=P_k$, $k\geq 3$
whenever both $b_i$ are positive, and (ii) a sharp upper bound for the
least solutions $p, m$ of the above equation whenever $b_i$ are
not of the same sign, where $p$ is a prime and $m=P_k, k\geq 3$.


406  Condensed and Strongly Condensed Domains Mimouni, Abdeslam
This paper deals with the concepts of condensed and strongly condensed
domains. By definition, an integral domain $R$ is condensed
(resp. strongly condensed) if each pair of ideals $I$ and $J$ of $R$,
$IJ=\{ab/a \in I, b \in J\}$ (resp. $IJ=aJ$ for some $a \in I$ or
$IJ=Ib$ for some $b \in J$). More precisely, we investigate the
ideal theory of condensed and strongly condensed domains in
Noetherianlike settings, especially Mori and strong Mori domains and
the transfer of these concepts to pullbacks.


413  Big Ramsey Degrees and Divisibility in Classes of Ultrametric Spaces Thé, L. Nguyen Van
Given a countable set $S$ of positive reals, we study
finitedimensional Ramseytheoretic properties of the countable
ultrametric Urysohn space $\textbf{Q} _S$ with distances in $S$.


424  Noncommutative Symmetric Bessel Functions Novelli, JeanChristophe; Thibon, JeanYves
The consideration of tensor products of $0$Hecke algebra modules
leads to natural analogs of the Bessel $J$functions in the algebra
of noncommutative symmetric functions. This provides a simple explanation
of various combinatorial properties of Bessel functions.


439  On the Maximal Spectrum of Semiprimitive Multiplication Modules Samei, Karim
An $R$module $M$ is called a multiplication module if for each
submodule $N$ of $M$, $N=IM$ for some ideal $I$ of $R$. As
defined for a commutative ring $R$, an $R$module $M$ is said to be
semiprimitive if the intersection of maximal submodules of $M$ is
zero. The maximal spectra of a semiprimitive multiplication
module $M$ are studied. The isolated points of $\Max(M)$ are
characterized algebraically. The relationships among the maximal
spectra of $M$, $\Soc(M)$ and $\Ass(M)$ are studied. It is shown
that $\Soc(M)$ is exactly the set of all elements of $M$ which
belongs to every maximal submodule of $M$ except for a finite
number. If $\Max(M)$ is infinite, $\Max(M)$ is a onepoint
compactification of a discrete space if and only if $M$ is Gelfand and for
some maximal submodule $K$, $\Soc(M)$ is the intersection of all
prime submodules of $M$ contained in $K$. When $M$ is a
semiprimitive Gelfand module, we prove that every intersection
of essential submodules of $M$ is an essential submodule if and only if
$\Max(M)$ is an almost discrete space. The set of uniform
submodules of $M$ and the set of minimal submodules of $M$
coincide. $\Ann(\Soc(M))M$ is a summand submodule of $M$ if and only if
$\Max(M)$ is the union of two disjoint open subspaces $A$ and
$N$, where $A$ is almost discrete and $N$ is dense in itself. In
particular, $\Ann(\Soc(M))=\Ann(M)$ if and only if $\Max(M)$ is almost
discrete.


448  Stability of Biharmonic Legendrian Submanifolds in Sasakian Space Forms Sasahara, Toru
Biharmonic maps are defined as critical points of the bienergy.
Every harmonic map is a stable biharmonic map.
In this article, the stability of nonharmonic
biharmonic Legendrian submanifolds in Sasakian space forms is discussed.


460  On Primitive Ideals in Graded Rings Smoktunowicz, Agata
Let $R=\bigoplus_{i=1}^{\infty}R_{i}$ be a graded nil ring. It is shown
that primitive ideals in $R$ are homogeneous. Let
$A=\bigoplus_{i=1}^{\infty}A_{i}$ be a graded nonPI justinfinite
dimensional algebra and let $I$ be a prime ideal in $A$. It is shown
that either $I=\{0\}$ or $I=A$. Moreover, $A$ is either primitive or
Jacobson radical.


467  Coupled Vortex Equations on Complete Kähler Manifolds Wang, Yue
In this paper, we first investigate the Dirichlet
problem for coupled vortex equations. Secondly, we give existence
results for solutions of the coupled vortex equations on a class
of complete noncompact K\"ahler manifolds which include
simplyconnected strictly negative curved manifolds, Hermitian
symmetric spaces of noncompact type and strictly pseudoconvex
domains equipped with the Bergmann metric.


481  Universal Inner Functions on the Ball Bayart, Frédéric
It is shown that given any sequence of automorphisms $(\phi_k)_k$ of the
unit ball $\bn$ of $\cn$ such that $\\phi_k(0)\$ tends to $1$,
there exists an inner function
$I$ such that the family of ``nonEuclidean translates"
$(I\circ\phi_k)_k$ is locally uniformly dense in the unit ball of
$H^\infty(\bn)$.


487  Laplace Transform Type Multipliers for Hankel Transforms Betancor, Jorge J.; Mart\'{\i}nez, Teresa; Rodr\'{\i}guezMesa, Lourdes
In this paper we establish that Hankel multipliers
of Laplace transform type are bounded from $L^p(w)$ into itself
when $1<p<\infty$, and from $L^1(w)$ into $L^{1,\infty }(w)$,
provided that $w$ is in the Muckenhoupt class $A^p$ on $((0,\infty),\,dx)$.


497  Expected Norms of ZeroOne Polynomials Borwein, Peter; Choi, KwokKwong Stephen; Mercer, Idris
Let $\cA_n = \big\{ a_0 + a_1 z + \cdots + a_{n1}z^{n1} : a_j \in \{0, 1 \
} \big\}$, whose elements are called \emf{zeroone polynomials}
and correspond naturally to the $2^n$ subsets of $[n] := \{ 0, 1,
\ldots, n1 \}$. We also let $\cA_{n,m} = \{ \alf(z) \in \cA_n :
\alf(1) = m \}$, whose elements correspond to the ${n \choose m}$
subsets of~$[n]$ of size~$m$, and let $\cB_n = \cA_{n+1} \setminus
\cA_n$, whose elements are the zeroone polynomials of degree
exactly~$n$.


508  A Result in Surgery Theory Cavicchioli, Alberto; Spaggiari, Fulvia
We study the topological $4$dimensional surgery problem
for a closed connected orientable
topological $4$manifold $X$ with vanishing
second homotopy and $\pi_1(X)\cong A * F(r)$, where $A$ has
one end and $F(r)$ is the free group of rank $r\ge 1$.
Our result is related to a theorem of Krushkal and Lee, and
depends on the validity of the Novikov conjecture for
such fundamental groups.


519  The Effective Cone of the Kontsevich Moduli Space Coskun, Izzet; Harris, Joe; Starr, Jason
In this paper we prove that the cone of effective divisors on the
Kontsevich moduli spaces of stable maps, $\Kgnb{0,0}(\PP^r,d)$,
stabilize when $r \geq d$. We give a complete characterization of the
effective divisors on $\Kgnb{0,0}(\PP^d,d)$. They are nonnegative
linear combinations of boundary divisors and the divisor of maps with
degenerate image.


535  On the Simple $\Z_2$homotopy Types of Graph Complexes and Their Simple $\Z_2$universality Csorba, Péter
We prove that the neighborhood complex $\N(G)$,
the box complex $\B(G)$, the homomorphism complex
$\Hom(K_2,G)$and the Lov\'{a}sz complex $\L(G)$ have the
same simple $\Z_2$homotopy type in the sense of
Whitehead. We show that these graph complexes
are simple $\Z_2$universal.


545  $C^{\ast}$Algebras Associated with MauldinWilliams Graphs Ionescu, Marius; Watatani, Yasuo
A MauldinWilliams graph $\mathcal{M}$ is a generalization of an
iterated function system by a directed graph. Its invariant set $K$
plays the role of the selfsimilar set. We associate a $C^{*}$algebra
$\mathcal{O}_{\mathcal{M}}(K)$ with a MauldinWilliams graph $\mathcal{M}$
and the invariant set $K$, laying emphasis on the singular points.
We assume that the underlying graph $G$ has no sinks and no sources.
If $\mathcal{M}$ satisfies the open set condition in $K$, and $G$
is irreducible and is not a cyclic permutation, then the associated
$C^{*}$algebra $\mathcal{O}_{\mathcal{M}}(K)$ is simple and purely
infinite. We calculate the $K$groups for some examples including the
inflation rule of the Penrose tilings.


561  Expansion of the Riemann $\Xi$ Function in MeixnerPollaczek Polynomials Kuznetsov, Alexey
In this article we study in detail the expansion of the Riemann
$\Xi$ function in MeixnerPollaczek polynomials. We obtain explicit
formulas, recurrence relation and asymptotic expansion for the
coefficients and investigate the zeros of the partial sums.


570  Amsterdam Properties of $C_p(X)$ Imply Discreteness of $X$ Lutzer, D. J.; Mill, J. van; Tkachuk, V. V.
We prove, among other things, that if $C_p(X)$ is
subcompact in the sense of de Groot, then the space $X$ is
discrete. This generalizes a series of previous results on
completeness properties of function spaces.


579  Guessing with Mutually Stationary Sets Matet, Pierre
We use the mutually stationary sets of Foreman and Magidor
as a tool to establish the validity of the twocardinal version
of the diamond principle in some special cases.


584  On Tensor Products of Polynomial Representations Purbhoo, Kevin; Willigenburg, Stephanie van
We determine the necessary and sufficient combinatorial
conditions for which the tensor product of two irreducible polynomial
representations of $\GL(n,\mathbb{C})$ is isomorphic to another.
As a consequence we discover families of LittlewoodRichardson
coefficients that are nonzero, and a condition on Schur nonnegativity.


593  Chasing Silver Ros{\l}anowski, Andrzej; Stepr\={a}ns, Juris
We show
that limits of CS iterations of the $n$Silver forcing notion have the
$n$localization property.


604  The Invariant Subspace Problem for NonArchimedean Banach Spaces {\'S}liwa, Wies{\l}aw
It is proved that every infinitedimensional
nonarchimedean Banach space of countable type admits a linear
continuous operator without a nontrivial closed invariant
subspace. This solves a problem stated by A.~C.~M. van Rooij and
W.~H. Schikhof in 1992.


618  Vanishing Theorems in Colombeau Algebras of Generalized Functions Valmorin, V.
Using a canonical linear embedding of the algebra
${\mathcal G}^{\infty}(\Omega)$ of Colombeau generalized functions in the space of
$\overline{\C}$valued $\C$linear maps on the space
${\mathcal D}(\Omega)$ of smooth functions with compact support, we give vanishing
conditions for functions and linear integral operators of class
${\mathcal G}^\infty$. These results are then applied to the zeros of holomorphic
generalized functions in dimension greater than one.


627  Summation of Series over Bourget Functions Vidanovi\'{c}, Mirjana V.; Tri\v{c}kovi\'{c}, Slobodan B.; Stankovi\'{c}, Miomir S.
In this paper we derive formulas for summation of series involving
J.~Bourget's generalization of Bessel functions of integer order, as
well as the analogous generalizations by H.~M.~Srivastava. These series are
expressed in terms of the Riemann $\z$ function and Dirichlet
functions $\eta$, $\la$, $\b$, and can be brought into closed form in
certain cases, which means that the infinite series are represented
by finite sums.


637  Author Index  Index des auteurs CJM
No abstract.

