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3  Carmichael Numbers with a Square Totient Banks, W. D.
Let $\varphi$ denote the Euler function. In this paper, we show that
for all large $x$ there are more than $x^{0.33}$ Carmichael numbers
$n\le x$ with the property that $\varphi(n)$ is a perfect square. We
also obtain similar results for higher powers.


9  On the Spectrum of an $n!\times n!$ Matrix Originating from Statistical Mechanics Chassé, Dominique; SaintAubin, Yvan
Let $R_n(\alpha)$ be the $n!\times n!$ matrix whose matrix elements
$[R_n(\alpha)]_{\sigma\rho}$, with $\sigma$ and $\rho$ in the
symmetric group $\sn$, are $\alpha^{\ell(\sigma\rho^{1})}$ with
$0<\alpha<1$, where $\ell(\pi)$ denotes the number of cycles in $\pi\in
\sn$. We give the spectrum of $R_n$ and show that the ratio of the
largest eigenvalue $\lambda_0$ to the second largest one (in absolute
value) increases as a positive power of $n$ as $n\rightarrow \infty$.


18  Harmonicity of Holomorphic Maps Between Almost Hermitian Manifolds Chinea, Domingo
In this paper we study holomorphic maps between almost Hermitian
manifolds. We obtain a new criterion for the harmonicity of such
holomorphic maps, and we deduce some applications to horizontally
conformal holomorphic submersions.


28  Right and Left Weak Approximation Properties in Banach Spaces Choi, Changsun; Kim, Ju Myung; Lee, Keun Young
New necessary and sufficient conditions are established for Banach
spaces to have the approximation property; these conditions are
easier to check than the known ones. A shorter proof of a result
of Grothendieck is presented, and some properties of a weak
version of the approximation property are addressed.


39  A Representation Theorem for Archimedean Quadratic Modules on $*$Rings Cimpri\v{c}, Jakob
We present a new approach to noncommutative real algebraic geometry
based on the representation theory of $C^\ast$algebras.
An important result in commutative real algebraic geometry is
Jacobi's representation theorem for archimedean quadratic modules
on commutative rings.
We show that this theorem is a consequence of the
GelfandNaimark representation theorem for commutative $C^\ast$algebras.
A noncommutative version of GelfandNaimark theory was studied by
I. Fujimoto. We use his results to generalize
Jacobi's theorem to associative rings with involution.


53  Cusp Forms Like $\Delta$ Cummins, C. J.
Let $f$ be a squarefree integer and denote by $\Gamma_0(f)^+$ the
normalizer of $\Gamma_0(f)$ in $\SL(2,\R)$. We find the analogues of
the cusp form $\Delta$ for the groups $\Gamma_0(f)^+$.


63  Small Zeros of Quadratic Forms Avoiding a Finite Number of Prescribed Hyperplanes Dietmann, Rainer
We prove a new upper bound for the smallest zero $\mathbf{x}$
of a quadratic form over a number field with the additional
restriction that $\mathbf{x}$ does not lie in a finite number of $m$ prescribed
hyperplanes. Our bound is polynomial in the height of the quadratic
form, with an exponent depending only on the number of variables but
not on $m$.


66  Huber's Theorem for Hyperbolic Orbisurfaces Dryden, Emily B.; Strohmaier, Alexander
We show that for compact orientable hyperbolic orbisurfaces, the
Laplace spectrum determines the length spectrum as well as the
number of singular points of a given order. The converse also holds, giving
a full generalization of Huber's theorem to the setting of
compact orientable hyperbolic orbisurfaces.


72  A SAGBI Basis For $\mathbb F[V_2\oplus V_2\oplus V_3]^{C_p}$ Duncan, Alexander; LeBlanc, Michael; Wehlau, David L.
Let $C_p$ denote the cyclic group of order $p$, where $p \geq 3$ is
prime. We denote by $V_n$ the indecomposable $n$ dimensional
representation of $C_p$ over a field $\mathbb F$ of characteristic
$p$. We compute a set of generators, in fact a SAGBI basis, for
the ring of invariants $\mathbb F[V_2 \oplus V_2 \oplus V_3]^{C_p}$.


84  Hartogs' Theorem on Separate Holomorphicity for Projective Spaces Gauthier, P. M.; Zeron, E. S.
If a mapping of several complex variables into projective space is
holomorphic in each pair of variables, then it is globally
holomorphic.


87  Holomorphic 2Forms and Vanishing Theorems for GromovWitten Invariants Lee, Junho
On a compact K\"{a}hler manifold $X$ with a holomorphic 2form
$\a$, there is an almost complex structure associated with $\a$. We
show how this implies vanishing theorems for the GromovWitten
invariants of $X$. This extends the approach used by Parker and
the author for K\"{a}hler surfaces to higher dimensions.


95  Matrix Valued Orthogonal Polynomials on the Unit Circle: Some Extensions of the Classical Theory Miranian, L.
In the work presented below the classical subject of orthogonal
polynomials on the unit
circle is discussed in the matrix setting. An explicit matrix
representation of the matrix valued orthogonal polynomials in terms of
the moments of the measure is presented. Classical recurrence
relations are revisited using the matrix representation of the
polynomials. The matrix expressions for the kernel polynomials and the
ChristoffelDarboux formulas are presented for the first time.


105  Generalized Eigenfunctions and a Borel Theorem on the Sierpinski Gasket Okoudjou, Kasso A.; Rogers, Luke G.; Strichartz, Robert S.
We prove there exist exponentially decaying generalized eigenfunctions
on a blowup of the Sierpinski gasket with boundary. These are used
to show a Boreltype theorem, specifically that for a prescribed jet
at the boundary point there is a smooth function having that jet.


117  On the Rational Points of the Curve $f(X,Y)^q = h(X)g(X,Y)$ Poulakis, Dimitrios
Let $q = 2,3$ and $f(X,Y)$, $g(X,Y)$, $h(X)$ be polynomials with
integer coefficients. In this paper we deal with the curve
$f(X,Y)^q = h(X)g(X,Y)$, and we show that under some favourable
conditions it is possible to determine all of its rational points.


127  The Erd\H{o}sRado Arrow for Singular Cardinals Shelah, Saharon
We prove in ZFC that if $\cf(\lambda)>\aleph_0$ and
$2^{\cf (\lambda)}<\lambda$, then $\lambda \rightarrow
(\lambda,\omega+1)^2$.


132  On Projectively Flat $(\alpha,\beta)$metrics Shen, Zhongmin
The solutions to Hilbert's Fourth Problem in the regular case
are projectively flat Finsler metrics. In this paper,
we consider the socalled $(\alpha,\beta)$metrics defined by a
Riemannian metric $\alpha$ and a $1$form $\beta$, and find a
necessary and sufficient condition for such metrics to be projectively
flat in dimension $n \geq 3$.


145  $2$Clean Rings Wang, Z.; Chen, J. L.
A ring $R$ is said to be $n$clean if every
element can be written as a sum of an idempotent and $n$ units.
The class of these rings contains clean rings and $n$good rings
in which each element is a sum of $n$ units. In this paper, we
show that for any ring $R$, the endomorphism ring of a free
$R$module of rank at least 2 is $2$clean and that the ring $B(R)$
of all $\omega\times \omega$ row and columnfinite matrices over
any ring $R$ is $2$clean. Finally, the group ring $RC_{n}$ is
considered where $R$ is a local ring.


154  A Big Picard Theorem for Holomorphic Maps into Complex Projective Space Ye, Yasheng; Ru, Min
We prove a big Picard type extension theorem for holomorphic maps
$f\from XA \rightarrow M$, where $X$ is a complex manifold,
$A$ is an analytic subvariety of $X$, and $M$ is the complement of the
union of a set of hyperplanes in ${\Bbb P}^n$ but is not
necessarily hyperbolically imbedded in ${\Bbb P}^n$.


161  A New Tautological Relation in $\overline{\mathcal{M}}_{3,1}$ via the Invariance Constraint Arcara, D.; Lee, Y.P.
A new tautological relation of $\overline{\mathcal{M}}_{3,1}$ in codimension 3
is derived and proved, using an invariance constraint from
our previous work.


175  Connections on a Parabolic Principal Bundle, II Biswas, Indranil
In Connections on a parabolic principal bundle over a curve, I
we defined connections on a parabolic
principal bundle. While connections on usual principal bundles are
defined as splittings of the Atiyah exact sequence, it was noted in
the above article that the Atiyah exact sequence does not generalize to
the parabolic principal bundles.
Here we show that a twisted version
of the Atiyah exact sequence generalizes to the context of
parabolic principal bundles. For usual principal bundles, giving a
splitting of this twisted Atiyah exact sequence is equivalent
to giving a splitting of the Atiyah exact sequence. Connections on
a parabolic principal bundle can be defined using the
generalization of the twisted Atiyah exact sequence.


186  Extension of the Riemann $\xi$Function's Logarithmic Derivative Positivity Region to Near the Critical Strip Broughan, Kevin A.
If $K$ is a number field with $n_k=[k:\mathbb{Q}]$, and $\xi_k$
the symmetrized
Dedekind zeta function of the field, the inequality
$$\Re\,{\frac{ \xi_k'(\sigma + {\rm i} t)}{\xi_k(\sigma
+ {\rm i} t)}} > \frac{ \xi_k'(\sigma)}{\xi_k(\sigma)}$$ for $t\neq 0$ is
shown
to be true for $\sigma\ge 1+ 8/n_k^\frac{1}{3}$ improving the result of
Lagarias where the constant in the inequality was 9. In the case $k=\mathbb{Q}$
the
inequality is extended to $\si\ge 1$ for all $t$ sufficiently large or small
and to the region $\si\ge 1+1/(\log t 5)$ for all $t\neq 0$. This
answers positively a question posed by Lagarias.


195  The Waring Problem with the Ramanujan $\tau$Function, II Garaev, M. Z.; Garcia, V. C.; Konyagin, S. V.
Let $\tau(n)$ be the Ramanujan $\tau$function. We prove that for
any integer $N$ with $N\ge 2$ the diophantine equation
$$\sum_{i=1}^{148000}\tau(n_i)=N$$ has a solution in positive
integers $n_1, n_2,\ldots, n_{148000}$ satisfying the condition
$$\max_{1\le i\le 148000}n_i\ll N^{2/11}e^{c\log N/\log\log
N},$$ for some absolute constant $c>0.$


200  Schubert Calculus on a Grassmann Algebra Gatto, Letterio; Santiago, Ta\'\i se
The ({\em classical}, {\em small quantum}, {\em equivariant})
cohomology ring of the grassmannian $G(k,n)$ is generated by
certain derivations operating on an exterior algebra of a free
module of rank $n$ ( Schubert calculus on a Grassmann
algebra). Our main result gives, in a unified way, a presentation
of all such cohomology rings in terms of generators and
relations. Using results of Laksov and Thorup, it also provides
a presentation of the universal
factorization algebra of a monic polynomial of degree $n$ into the
product of two monic polynomials, one of degree $k$.


213  DunfordPettis Properties and Spaces of Operators Ghenciu, Ioana; Lewis, Paul
J. Elton used an application of Ramsey theory to show that
if $X$ is an infinite dimensional Banach space,
then $c_0$ embeds in $X$, $\ell_1$ embeds in $X$, or there
is a subspace of $X$ that fails to have the DunfordPettis property.
Bessaga and Pelczynski showed that if $c_0$ embeds in $X^*$,
then $\ell_\infty$ embeds in $X^*$. Emmanuele and John showed
that if $c_0$ embeds in $K(X,Y)$, then $K(X,Y)$ is not
complemented in $L(X,Y)$. Classical results from Schauder basis theory
are used in a study of DunfordPettis sets and strong
DunfordPettis sets to extend each of the preceding theorems. The space
$L_{w^*}(X^* , Y)$ of $w^*w$ continuous operators is also studied.


224  Equations and Complexity for the DuboisEfroymson Dimension Theorem Ghiloni, Riccardo
Let $\R$ be a real closed field, let $X \subset \R^n$ be an
irreducible real algebraic set and let $Z$ be an algebraic subset of
$X$ of codimension $\geq 2$. Dubois and Efroymson proved the existence
of an irreducible algebraic subset of $X$ of codimension $1$
containing~$Z$. We improve this dimension theorem as follows. Indicate
by $\mu$ the minimum integer such that the ideal of polynomials in
$\R[x_1,\ldots,x_n]$ vanishing on $Z$ can be generated by polynomials
of degree $\leq \mu$. We prove the following two results:
\begin{inparaenum}[\rm(1)]
\item There
exists a polynomial $P \in \R[x_1,\ldots,x_n]$ of degree~$\leq \mu+1$
such that $X \cap P^{1}(0)$ is an irreducible algebraic subset of $X$
of codimension $1$ containing~$Z$.
\item Let $F$ be a polynomial in
$\R[x_1,\ldots,x_n]$ of degree~$d$ vanishing on $Z$. Suppose there
exists a nonsingular point $x$ of $X$ such that $F(x)=0$ and the
differential at $x$ of the restriction of $F$ to $X$ is nonzero. Then
there exists a polynomial $G \in \R[x_1,\ldots,x_n]$ of degree $\leq
\max\{d,\mu+1\}$ such that, for each $t \in (1,1) \setminus \{0\}$,
the set $\{x \in X \mid F(x)+tG(x)=0\}$ is an irreducible algebraic
subset of $X$ of codimension $1$ containing~$Z$.
\end{inparaenum} Result (1) and a
slightly different version of result~(2) are valid over any
algebraically closed field also.


237  Points of Small Height on Varieties Defined over a Function Field Ghioca, Dragos
We obtain a Bogomolov type of result for the affine space defined
over the algebraic closure of a function field of transcendence
degree $1$ over a finite field.


245  Involutions of RA Loops Goodaire, Edgar G.; Milies, César Polcino
Let $L$ be an RA loop, that is, a loop whose loop ring
over any coefficient ring $R$
is an alternative, but not associative, ring. Let
$\ell\mapsto\ell^\theta$ denote an involution on $L$ and extend
it linearly to the loop ring $RL$. An element $\alpha\in RL$ is
symmetric if $\alpha^\theta=\alpha$ and skewsymmetric
if $\alpha^\theta=\alpha$. In this paper, we show that
there exists an involution making
the symmetric elements of $RL$ commute if and only if
the characteristic of $R$ is $2$ or $\theta$ is the
canonical involution on $L$,
and an involution making the skewsymmetric elements of $RL$
commute if and only if
the characteristic of $R$ is $2$ or $4$.


257  Essential Surfaces in Graph Link Exteriors Ikeda, Toru
An irreducible graph manifold $M$ contains an essential torus if
it is not a special Seifert manifold.
Whether $M$ contains a closed essential surface of
negative Euler characteristic or not
depends on the difference of Seifert fibrations from the two sides
of a torus system which splits $M$ into Seifert manifolds.
However,
it is not easy to characterize geometrically the class of
irreducible graph manifolds which contain such surfaces.
This article studies this problem in the case of graph link exteriors.


267  Extensions of Rings Having McCoy Condition Ko\c{s}an, Muhammet Tamer
Let $R$ be an associative ring with unity.
Then $R$ is said to be a {\it right McCoy ring} when the equation
$f(x)g(x)=0$ (over $R[x]$), where $0\neq f(x),g(x) \in R[x]$,
implies that there exists a nonzero element $c\in R$ such that
$f(x)c=0$. In this paper, we characterize some basic ring
extensions of right McCoy rings and we prove that if $R$ is a
right McCoy ring, then $R[x]/(x^n)$ is
a right McCoy ring for any positive integer $n\geq 2$ .


273  Amalgamations of Categories MacDonald, John; Scull, Laura
We consider the pushout of embedding functors in $\Cat$, the
category of small categories.
We show that if the embedding functors satisfy a 3for2
property, then the induced functors to the pushout category are
also embeddings. The result follows from the connectedness of
certain associated slice categories. The condition is motivated
by a similar result for maps of semigroups. We show that our
theorem can be applied to groupoids and to inclusions of full
subcategories. We also give an example to show that the theorem
does not hold when the
property only holds for one of the inclusion functors, or when it
is weakened to a onesided condition.


285  Global Geometrical Coordinates on Falbel's CrossRatio Variety Parker, John R.; Platis, Ioannis D.
Falbel has shown that four pairwise distinct points on the boundary
of a
complex hyperbolic $2$space are completely determined, up to conjugation
in ${\rm PU}(2,1)$, by three complex crossratios satisfying two real
equations. We give global geometrical coordinates on the resulting
variety.


295  On Functions Whose Graph is a Hamel Basis, II P{\l}otka, Krzysztof
We say that a function $h \from \real \to \real$ is a Hamel function
($h \in \ham$) if $h$, considered as a subset of $\real^2$, is a Hamel
basis for $\real^2$. We show that $\A(\ham)\geq\omega$, i.e., for
every finite $F \subseteq \real^\real$ there exists $f\in\real^\real$
such that $f+F \subseteq \ham$. From the previous work of the author
it then follows that $\A(\ham)=\omega$.


303  A Comment on ``$\mathfrak{p} < \mathfrak{t}$'' Shelah, Saharon
Dealing with the cardinal invariants ${\mathfrak p}$ and
${\mathfrak t}$ of the continuum, we prove that
${\mathfrak m}={\mathfrak p} = \aleph_2\ \Rightarrow\ {\mathfrak t} =\aleph_2$.
In other words, if ${\bf MA}_{\aleph_1}$ (or a weak version of
this) holds, then (of course $\aleph_2\le {\mathfrak p}\le
{\mathfrak t}$ and) ${\mathfrak p}=\aleph_2\ \Rightarrow\
{\mathfrak p}={\mathfrak t}$. The proof is based on a criterion
for ${\mathfrak p}<{\mathfrak t}$.


315  Generic QuasiConvergence for Essentially Strongly OrderPreserving Semiflows Yi, Taishan; Zou, Xingfu
By employing the limit set
dichotomy for essentially strongly orderpreserving semiflows and
the assumption that limit sets have infima and suprema in the
state space, we prove a generic quasiconvergence principle
implying the existence of an open and dense set of stable
quasiconvergent points. We also apply this generic quasiconvergence principle
to a model for biochemical feedback in protein
synthesis and obtain some results about the model which are of theoretical
and realistic significance.


321  Photo CJM
No abstract.


323  Dedication: Ted Bisztriczky Böröczky, K.; Böröczky, K. J.; Fodor, F.; Harborth, H.; Kuperberg, W.
No abstract.


327  Geometric ``Floral'' Configurations Berman, Leah Wrenn; Bokowski, Jürgen; Grünbaum, Branko; Pisanski, Toma\v{z}
With an increase in size, configurations of points and lines
in the plane usually become complicated and hard to analyze.
The ``floral'' configurations we are introducing here represent
a new type that makes accessible and visually intelligible
even configurations of considerable size. This is achieved
by combining a large degree of symmetry with a hierarchical
construction. Depending on the details of the interdependence
of these aspects, there are several subtypes that are described
and investigated.


342  On the Xray Number of Almost Smooth Convex Bodies and of Convex Bodies of Constant Width Bezdek, K.; Kiss, Gy.
The Xray numbers of some classes of convex bodies are investigated.
In particular, we give a proof of the Xray Conjecture as well as
of the Illumination Conjecture for almost smooth convex bodies
of any dimension and for convex bodies of constant width of
dimensions $3$, $4$, $5$ and $6$.


349  On Projection Bodies of Order One Campi, Stefano; Gronchi, Paolo
The projection body of order one $\Pi_1K$ of a convex body $K$ in
$\R^n$ is the body whose support function is, up to a constant, the
average mean width of the orthogonal projections of $K$ onto
hyperplanes through the origin.


361  A Note on Covering by Convex Bodies Tóth, Gábor Fejes
A classical theorem of Rogers states
that for any convex body $K$ in $n$dimensional Euclidean space
there exists a covering of the space by translates of $K$ with
density not exceeding $n\log{n}+n\log\log{n}+5n$. Rogers' theorem
does not say anything about the structure of such a covering. We
show that for sufficiently large values of $n$ the same bound can
be attained by a covering which is the union of $O(\log{n})$
translates of a lattice arrangement of $K$.


366  A Class of Cellulated Spheres with NonPolytopal Symmetries Gévay, Gábor
We construct, for all $d\geq 4$, a cellulation of $\mathbb S^{d1}$.
We prove that these cellulations cannot be polytopal with maximal
combinatorial symmetry. Such nonrealizability phenomenon was first
described in dimension 4 by Bokowski, Ewald and Kleinschmidt, and,
to the knowledge of the author, until now there have not been any
known examples in higher dimensions. As a starting point for the
construction, we introduce a new class of (Wythoffian) uniform
polytopes, which we call duplexes. In proving our main result,
we use some tools that we developed earlier while studying perfect
polytopes. In particular, we prove perfectness of the duplexes;
furthermore, we prove and make use of the perfectness of another
new class of polytopes which we obtain by a variant of the socalled
$E$construction introduced by Eppstein, Kuperberg and Ziegler.


380  Successive Minima and Radii Henk, Martin; Cifre, Mar\'\i a A. Hernández
In this note we present inequalities relating the successive minima of an
$o$symmetric convex body and the successive inner and outer radii of the
body. These inequalities join known inequalities involving only either
the successive minima or the successive radii.


388  Transversals with Residue in Moderately Overlapping $T(k)$Families of Translates Heppes, Aladár
Let $K$ denote an oval, a centrally symmetric compact convex domain
with nonempty interior. A family of translates of $K$ is said to have
property $T(k)$ if for every subset of at most $k$ translates there
exists a common line transversal intersecting all of them. The integer
$k$ is the stabbing level of the family.
Two translates $K_i = K + c_i$ and $K_j = K + c_j$ are said to be
$\sigma$disjoint if $\sigma K + c_i$ and $\sigma K + c_j$ are disjoint.
A recent Hellytype result claims that for every
$\sigma > 0 $ there exists an integer $k(\sigma)$ such that if a
family of $\sigma$disjoint unit diameter discs has property $T(k) k
\geq k(\sigma)$, then there exists a straight line meeting all members
of the family. In the first part of the paper we give the extension of
this theorem to translates of an oval $K$. The asymptotic behavior of
$k(\sigma)$ for $\sigma \rightarrow 0$ is considered as well.


403  Shaken Rogers's Theorem for Homothetic Sections JerónimoCastro, J.; Montejano, L.; MoralesAmaya, E.
We shall prove the following shaken Rogers's theorem for
homothetic sections: Let $K$ and $L$ be strictly convex bodies and
suppose that for every plane $H$ through the origin we can choose
continuously sections of $K $ and $L$, parallel to $H$, which are
directly homothetic. Then $K$ and $L$ are directly homothetic.


407  On the BezdekPach Conjecture for Centrally Symmetric Convex Bodies Lángi, Zsolt; Naszódi, Márton
The BezdekPach conjecture asserts that the maximum number of
pairwise touching positive homothetic copies of a convex body in
$\Re^d$ is $2^d$. Nasz\'odi proved that the quantity in question is
not larger than $2^{d+1}$. We present an improvement to this result by
proving the upper bound $3\cdot2^{d1}$ for centrally symmetric
bodies. Bezdek and Brass introduced the onesided Hadwiger number of a
convex body. We extend this definition, prove an upper bound on the
resulting quantity, and show a connection with the problem of touching
homothetic bodies.


416  Hamiltonian Properties of Generalized Halin Graphs Malik, Shabnam; Qureshi, Ahmad Mahmood; Zamfirescu, Tudor
A Halin graph is a graph $H=T\cup C$, where $T$ is a tree with no
vertex of degree two, and $C$ is a cycle connecting the endvertices
of $T$ in the cyclic order determined by a plane embedding of $T$.
In this paper, we define classes of generalized Halin graphs, called
$k$Halin graphs, and investigate their Hamiltonian properties.


424  Covering Discs in Minkowski Planes Martini, Horst; Spirova, Margarita
We investigate the following version of the circle covering
problem in strictly convex (normed or) Minkowski planes: to cover
a circle of largest possible diameter by $k$ unit circles. In
particular, we study the cases $k=3$, $k=4$, and $k=7$. For $k=3$
and $k=4$, the diameters under consideration are described in
terms of sidelengths and circumradii of certain inscribed regular
triangles or quadrangles. This yields also simple explanations of
geometric meanings that the corresponding homothety ratios have.
It turns out that basic notions from Minkowski geometry play an
essential role in our proofs, namely Minkowskian bisectors,
$d$segments, and the monotonicity lemma.


435  Modular Reduction in Abstract Polytopes Monson, B.; Schulte, Egon
The paper studies modular reduction techniques for abstract regular
and chiral polytopes, with two purposes in mind:\ first, to survey the
literature about modular reduction in polytopes; and second, to apply
modular reduction, with moduli given by primes in $\mathbb{Z}[\tau]$
(with $\tau$ the golden ratio), to construct new regular $4$polytopes
of hyperbolic types $\{3,5,3\}$ and $\{5,3,5\}$ with automorphism
groups given by finite orthogonal groups.


451  Indecomposable Coverings Pach, János; Tardos, Gábor; Tóth, Géza
We prove that for every $k>1$, there exist $k$fold coverings of the
plane (i) with strips, (ii) with axisparallel rectangles, and
(iii) with homothets of any fixed concave quadrilateral, that cannot
be decomposed into two coverings. We also construct for every
$k>1$ a set of points $P$ and a family of disks $\cal D$ in the
plane, each containing at least $k$ elements of $P$, such that, no
matter how we color the points of $P$ with two colors,
there
exists a disk $D\in{\cal D}$ all of whose points are of the same
color.


464  Two Volume Product Inequalities and Their Applications Stancu, Alina
Let $K \subset {\mathbb{R}}^{n+1}$ be a convex body of class $C^2$
with everywhere positive Gauss curvature. We show that there exists
a positive number $\delta (K)$ such that for any $\delta \in (0,
\delta(K))$ we have $\Volu(K_{\delta})\cdot
\Volu((K_{\delta})^{\sstar}) \geq \Volu(K)\cdot \Volu(K^{\sstar}) \geq
\Volu(K^{\delta})\cdot \Volu((K^{\delta})^{\sstar})$, where $K_{\delta}$,
$K^{\delta}$ and $K^{\sstar}$ stand for the convex floating body, the
illumination body, and the polar of $K$, respectively. We derive a
few consequences of these inequalities.


481  Some Infinite Products of Ramanujan Type Alaca, Ay\c{s}e; Alaca, \c{S}aban; Williams, Kenneth S.
In his ``lost'' notebook, Ramanujan stated two results, which are equivalent to the identities
\[
\prod_{n=1}^{\infty} \frac{(1q^n)^5}{(1q^{5n})}
=15\sum_{n=1}^{\infty}\Big( \sum_{d \mid n} \qu{5}{d} d \Big) q^n
\]
and
\[
q\prod_{n=1}^{\infty} \frac{(1q^{5n})^5}{(1q^{n})}
=\sum_{n=1}^{\infty}\Big( \sum_{d \mid n} \qu{5}{n/d} d \Big) q^n.
\]
We give several more identities of this type.


493  A OneDimensional Family of $K3$ Surfaces with a $\Z_4$ Action Artebani, Michela
The minimal resolution of the degree four cyclic cover of the plane
branched along a GIT stable quartic is a $K3$ surface with a non
symplectic action of $\Z_4$. In this paper
we study the geometry of the onedimensional family of $K3$ surfaces
associated to the locus of plane quartics with five nodes.


511  The Irreducibility of Polynomials That Have One Large Coefficient and Take a Prime Value Bonciocat, Anca Iuliana; Bonciocat, Nicolae Ciprian
We use some classical estimates for polynomial roots to provide
several irreducibility criteria for polynomials with integer
coefficients that have one sufficiently large coefficient and take a
prime value.


521  The Parabolic LittlewoodPaley Operator with Hardy Space Kernels Chen, Yanping; Ding, Yong
In this paper, we give the $L^p$ boundedness for
a class of parabolic LittlewoodPaley $g$function with its kernel
function $\Omega$ is in the Hardy space $H^1(S^{n1})$.


535  A Note on Locally Nilpotent Derivations\\ and Variables of $k[X,Y,Z]$ Daigle, Daniel; Kaliman, Shulim
We strengthen certain results
concerning actions of $(\Comp,+)$ on $\Comp^{3}$
and embeddings of $\Comp^{2}$ in $\Comp^{3}$,
and show that these results are in fact valid
over any field of characteristic zero.


544  Intuitionistic Fuzzy $\gamma$Continuity Hanafy, I. M.
This paper introduces the concepts of
fuzzy $\gamma$open sets and fuzzy $\gamma$continuity
in intuitionistic fuzzy topological spaces. After defining the fundamental
concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological
spaces, we present intuitionistic fuzzy $\gamma$open sets and
intuitionistic fuzzy $\gamma$continuity and other results related
topological concepts.


555  Boundary Behavior of Solutions of the Helmholtz Equation Hirata, Kentaro
This paper is concerned with the boundary behavior of solutions of
the Helmholtz equation in $\mathbb{R}^\di$.
In particular, we give a Littlewoodtype theorem to show that
the approach region introduced by Kor\'anyi and Taylor (1983) is best possible.


564  Group Actions on QuasiBaer Rings Jin, Hai Lan; Doh, Jaekyung; Park, Jae Keol
A ring $R$ is called {\it quasiBaer} if the right
annihilator of every right ideal of $R$ is generated by an
idempotent as a right ideal. We investigate the quasiBaer
property of skew group rings and fixed rings under a finite group
action on a semiprime ring and their applications to
$C^*$algebras.
Various examples to illustrate and
delimit our results are provided.


583  Computing Polynomials of the Ramanujan $t_n$ Class Invariants Konstantinou, Elisavet; Kontogeorgis, Aristides
We compute the minimal polynomials of the Ramanujan values $t_n$,
where $n\equiv 11 \mod 24$, using the Shimura reciprocity law.
These polynomials can be used for defining the Hilbert class field
of the imaginary quadratic field $\mathbb{Q}(\sqrt{n})$ and have
much smaller coefficients than the Hilbert polynomials.


598  Numerical Semigroups That Are Not Intersections of $d$Squashed Semigroups Moreno, M. A.; Nicola, J.; Pardo, E.; Thomas, H.
We say that a numerical semigroup is $d$squashed if it can
be written in the form
$$ S=\frac 1 N \langle a_1,\dots,a_d \rangle \cap \mathbb{Z}$$
for $N,a_1,\dots,a_d$ positive integers with
$\gcd(a_1,\dots, a_d)=1$.
Rosales and Urbano have shown that a numerical semigroup is
2squashed if and only if it is proportionally modular.


613  Lipschitz Type Characterizations for Bergman Spaces Wulan, Hasi; Zhu, Kehe
We obtain new characterizations for Bergman spaces with standard
weights in terms of Lipschitz type conditions in the Euclidean,
hyperbolic, and pseudohyperbolic metrics. As a consequence, we
prove optimal embedding theorems when an analytic function
on the unit disk is symmetrically lifted to the bidisk.


627  On $L^{1}$Convergence of Fourier Series under the MVBV Condition Yu, Dan Sheng; Zhou, Ping; Zhou, Song Ping
Let $f\in L_{2\pi }$ be a realvalued even function with its Fourier series $%
\frac{a_{0}}{2}+\sum_{n=1}^{\infty }a_{n}\cos nx,$ and let
$S_{n}(f,x) ,\;n\geq 1,$ be the $n$th partial sum of the Fourier series. It
is well known that if the nonnegative sequence $\{a_{n}\}$ is decreasing and
$\lim_{n\rightarrow \infty }a_{n}=0$, then%
\begin{equation*}
\lim_{n\rightarrow \infty }\Vert fS_{n}(f)\Vert _{L}=0
\text{ if
and only if }\lim_{n\rightarrow \infty }a_{n}\log n=0.
\end{equation*}%
We weaken the monotone condition in this classical result to the socalled
mean value bounded variation (MVBV) condition. The generalization of the
above classical result in realvalued function space is presented as a
special case of the main result in this paper, which gives the $L^{1}$%
convergence of a function $f\in L_{2\pi }$ in complex space. We also give
results on $L^{1}$approximation of a function $f\in L_{2\pi }$ under the
MVBV condition.


637  Author Index  Index des auteurs 2009, for 2009  pour
No abstract.

