351. CMB 2010 (vol 53 pp. 466)
 Dubarbie, Luis

Separating Maps between Spaces of VectorValued Absolutely Continuous Functions
In this paper we give a description of separating or disjointness preserving linear bijections on spaces of vectorvalued absolutely continuous functions defined on compact subsets of the real line. We obtain that they are continuous and biseparating in the finitedimensional case. The infinitedimensional case is also studied.
Keywords:separating maps, disjointness preserving, vectorvalued absolutely continuous functions, automatic continuity Categories:47B38, 46E15, 46E40, 46H40, 47B33 

352. CMB 2010 (vol 53 pp. 453)
353. CMB 2009 (vol 53 pp. 11)
 Burke, Maxim R.

Approximation and Interpolation by Entire Functions of Several Variables
Let $f\colon \mathbb R^n\to \mathbb R$ be $C^\infty$ and let $h\colon
\mathbb R^n\to\mathbb R$ be positive
and continuous. For any unbounded nondecreasing sequence $\{c_k\}$
of nonnegative real numbers and for any sequence without
accumulation points $\{x_m\}$ in $\mathbb R^n$, there exists an entire
function $g\colon\mathbb C^n\to\mathbb C$ taking real values on $\mathbb R^n$ such that
\begin{align*}
&g^{(\alpha)}(x)f^{(\alpha)}(x)\lt h(x), \quad x\ge c_k, \alpha\le k,
k=0,1,2,\dots,
\\
&g^{(\alpha)}(x_m)=f^{(\alpha)}(x_m), \quad x_m\ge c_k, \alpha\le k,
m,k=0,1,2,\dots.
\end{align*}
This is a version for functions of several variables of the
case $n=1$ due to L. Hoischen.
Keywords:entire function, complex approximation, interpolation, several complex variables Category:32A15 

354. CMB 2009 (vol 53 pp. 206)
 Atçeken, Mehmet

SemiSlant Submanifolds of an Almost Paracontact Metric Manifold
In this paper, we define and study the geometry of semislant submanifolds of an almost paracontact metric manifold. We give some characterizations for a submanifold to be semislant submanifold to be semislant product and obtain integrability conditions for the distributions involved in the definition of a semislant submanifold.
Keywords:paracontact metric manifold, slant distribution, semislant submanifold, semislant product Categories:53C15, 53C25, 53C40 

355. CMB 2009 (vol 53 pp. 218)
 Biswas, Indranil

Restriction of the Tangent Bundle of $G/P$ to a Hypersurface
Let P be a maximal proper parabolic subgroup of a connected simple linear algebraic group G, defined over $\mathbb C$, such that $n := \dim_{\mathbb C} G/P \geq 4$. Let $\iota \colon Z \hookrightarrow G/P$ be a reduced smooth hypersurface of degree at least $(n1)\cdot \operatorname{degree}(T(G/P))/n$. We prove that the restriction of the tangent bundle $\iota^*TG/P$ is semistable.
Keywords:tangent bundle, homogeneous space, semistability, hypersurface Categories:14F05, 14J60, 14M15 

356. CMB 2009 (vol 53 pp. 378)
 Zhou, Sizhong

A New Sufficient Condition for a Graph To Be $(g,f,n)$Critical
Let $G$ be a graph of order $p$, let $a$,
$b$, and $n$ be nonnegative integers with $1\leq a\lt b$, and let $g$
and $f$ be two integervalued functions defined on $V(G)$ such
that $a\leq g(x)\lt f(x)\leq b$ for all $x\in V(G)$. A $(g,f)$factor
of graph $G$ is a spanning subgraph $F$ of $G$ such
that $g(x)\leq d_F(x)\leq f(x)$ for each $x\in V(F)$. Then a graph
$G$ is called $(g,f,n)$critical if after deleting any $n$
vertices of $G$ the remaining graph of $G$ has a $(g,f)$factor.
The binding number $\operatorname{bind}(G)$ of $G$ is the minimum value of
${N_G(X)}/{X}$ taken over all nonempty subsets $X$ of
$V(G)$ such that $N_G(X)\neq V(G)$. In this paper, it is proved
that $G$ is a $(g,f,n)$critical graph if
\[
\operatorname{bind}(G)\gt \frac{(a+b1)(p1)}{(a+1)p(a+b)bn+2}
\quad\text{and}\quad p\geq
\frac{(a+b1)(a+b2)}{a+1}+\frac{bn}{a}.
\]
Furthermore, it is
shown that this
result is best possible in some sense.
Keywords:graph, $(g,f)$factor, $(g,f,n)$critical graph, binding number Category:05C70 

357. CMB 2009 (vol 53 pp. 133)
358. CMB 2009 (vol 53 pp. 122)
 Mo, Xiaohuan; Zhou, Linfeng

A Class of Finsler Metrics with Bounded Cartan Torsion
In this paper, we find a class of $(\alpha,\beta)$ metrics which have a bounded Cartan torsion. This class contains all Randers metrics. Furthermore, we give some applications and obtain two corollaries about curvature of this metrics.
Keywords:Finsler manifold, $(\alpha,\beta)$ metric, Cartan torsion, Rquadratic, flag curvature Category:58E20 

359. CMB 2009 (vol 53 pp. 340)
360. CMB 2009 (vol 53 pp. 118)
 Lewis, Paul

The Uncomplemented Spaces $W(X,Y)$ and $K(X,Y)$
Classical results of Kalton and techniques of Feder are used to study the complementation of the space $W(X, Y)$ of weakly compact operators and the space $K(X,Y)$ of compact operators in the space $L(X,Y)$ of all bounded linear maps from X to Y.
Keywords:spaces of operators, complemented subspace, weakly compact operator, basic sequence Categories:46B28, 46B15, 46B20 

361. CMB 2009 (vol 53 pp. 295)
 Guo, Boling; Huo, Zhaohui

The Global Attractor of a Damped, Forced Hirota Equation in $H^1$
The existence of the global attractor of a damped
forced Hirota equation in the phase space $H^1(\mathbb R)$ is proved. The
main idea is to establish the socalled asymptotic compactness
property of the solution operator by energy equation approach.
Keywords:global attractor, Fourier restriction norm, damping system, asymptotic compactness Categories:35Q53, 35B40, 35B41, 37L30 

362. CMB 2009 (vol 53 pp. 95)
 Ghioca, Dragos

Towards the Full MordellLang Conjecture for Drinfeld Modules
Let $\phi$ be a Drinfeld module of generic characteristic, and let X be a sufficiently generic affine subvariety of $\mathbb{G_a^g}$. We show that the intersection of X with a finite rank $\phi$submodule of $\mathbb{G_a^g}$ is finite.
Keywords:Drinfeld module, MordellLang conjecture Categories:11G09, 11G10 

363. CMB 2009 (vol 53 pp. 263)
 Feuto, Justin; Fofana, Ibrahim; Koua, Konin

Weighted Norm Inequalities for a Maximal Operator in Some Subspace of Amalgams
We give weighted norm inequalities for the maximal fractional operator $ \mathcal M_{q,\beta }$ of HardyÂLittlewood and the fractional integral $I_{\gamma}$. These inequalities are established between $(L^{q},L^{p}) ^{\alpha }(X,d,\mu )$ spaces (which are superspaces of Lebesgue spaces $L^{\alpha}(X,d,\mu)$ and subspaces of amalgams $(L^{q},L^{p})(X,d,\mu)$) and in the setting of space of homogeneous type $(X,d,\mu)$. The conditions on the weights are stated in terms of Orlicz norm.
Keywords:fractional maximal operator, fractional integral, space of homogeneous type Categories:42B35, 42B20, 42B25 

364. CMB 2009 (vol 53 pp. 58)
 Dąbrowski, Andrzej; Jędrzejak, Tomasz

Ranks in Families of Jacobian Varieties of Twisted Fermat Curves
In this paper, we prove that the unboundedness of ranks in families of Jacobian varieties of twisted Fermat curves is equivalent to the divergence of certain infinite series.
Keywords:Fermat curve, Jacobian variety, elliptic curve, canonical height Categories:11G10, 11G05, 11G50, 14G05, 11G30, 14H45, 14K15 

365. CMB 2009 (vol 53 pp. 23)
 Chen, Huaihui; Zhang, Minzhu

Boundedness From Below of Multiplication Operators Between $\alpha$Bloch Spaces
In this paper, the boundedness from below of multiplication
operators between $\alpha$Bloch spaces $\mathcal B^\alpha$, $\alpha\gt 0$, on the
unit disk $D$ is studied completely. For a bounded multiplication
operator $M_u\colon \mathcal B^\alpha\to\mathcal B^\beta$, defined by $M_uf=uf$ for
$f\in\mathcal B^\alpha$, we prove the following result:
(i) If $0\lt \beta\lt \alpha$, or
$0\lt \alpha\le1$ and $\alpha\lt \beta$, $M_u$ is not bounded below;
(ii) if $0\lt \alpha=\beta\le1$, $M_u$ is bounded below if and only if
$\liminf_{z\to\partial D}u(z)\gt 0$;
(iii) if $1\lt \alpha\le\beta$, $M_u$ is
bounded below if and only if there exist a $\delta\gt 0$ and a positive
$r\lt 1$ such that for every point $z\in D$ there is a point $z'\in
D$ with the property $d(z',z)\lt r$ and
$(1z'^2)^{\beta\alpha}u(z')\ge\delta$, where $d(\cdot,\cdot)$ denotes
the pseudodistance on $D$.
Keywords:$\alpha$Bloch function, multiplication operator Categories:32A18, 30H05 

366. CMB 2009 (vol 52 pp. 493)
 Artebani, Michela

A OneDimensional Family of $K3$ Surfaces with a $\Z_4$ Action
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.
Keywords:genus three curves, $K3$ surfaces Categories:14J28, 14J50, 14J10 

367. CMB 2009 (vol 52 pp. 564)
 Jin, Hai Lan; Doh, Jaekyung; Park, Jae Keol

Group Actions on QuasiBaer Rings
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.
Keywords:(quasi) Baer ring, fixed ring, skew group ring, $C^*$algebra, local multiplier algebra Categories:16S35, 16W22, 16S90, 16W20, 16U70 

368. CMB 2009 (vol 52 pp. 544)
 Hanafy, I. M.

Intuitionistic Fuzzy $\gamma$Continuity
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.
Keywords:intuitionistic fuzzy set, intuitionistic fuzzy point, intuitionistic fuzzy topological space, intuitionistic fuzzy $\gamma$open set, intuitionistic fuzzy $\gamma$\continuity, intuitionistic fuzzy $\gamma$closure ($\gamma$interior) Categories:54A40, 54A20, 54F99 

369. CMB 2009 (vol 52 pp. 535)
 Daigle, Daniel; Kaliman, Shulim

A Note on Locally Nilpotent Derivations\\ and Variables of $k[X,Y,Z]$
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.
Keywords:locally nilpotent derivations, group actions, polynomial automorphisms, variable, affine space Categories:14R10, 14R20, 14R25, 13N15 

370. CMB 2009 (vol 52 pp. 511)
371. CMB 2009 (vol 52 pp. 481)
 Alaca, Ay\c{s}e; Alaca, \c{S}aban; Williams, Kenneth S.

Some Infinite Products of Ramanujan Type
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.
Keywords:Power series expansions of certain infinite products Categories:11E25, 11F11, 11F27, 30B10 

372. CMB 2009 (vol 52 pp. 366)
 Gévay, Gábor

A Class of Cellulated Spheres with NonPolytopal Symmetries
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.
Keywords:CW sphere, polytopality, automorphism group, symmetry group, uniform polytope Categories:52B11, 52B15, 52B70 

373. CMB 2009 (vol 52 pp. 464)
 Stancu, Alina

Two Volume Product Inequalities and Their Applications
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.
Keywords:affine invariants, convex floating bodies, illumination bodies Categories:52A40, 52A38, 52A20 

374. CMB 2009 (vol 52 pp. 424)
 Martini, Horst; Spirova, Margarita

Covering Discs in Minkowski Planes
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.
Keywords:affine regular polygon, bisector, circle covering problem, circumradius, $d$segment, Minkowski plane, (strictly convex) normed plane Categories:46B20, 52A21, 52C15 

375. CMB 2009 (vol 52 pp. 388)
 Heppes, Aladár

Transversals with Residue in Moderately Overlapping $T(k)$Families of Translates
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.
Katchalski and Lewis proved the existence of a constant $r$ such that
for every pairwise disjoint family of translates of an oval $K$ with
property $T(3)$ a straight line can be found meeting all but at most
$r$ members of the family. In the second part of the paper
$\sigma$disjoint families of translates of $K$ are considered and the
relation of $\sigma$ and the residue $r$ is investigated. The
asymptotic behavior of $r(\sigma)$ for $\sigma \rightarrow 0$ is also
discussed.
Keywords:transversal, $\sigma$disjoint, $T(k)$family, Helly number, residue 
