351. CMB 2010 (vol 53 pp. 674)
 Kristály, Alexandru; Papageorgiou, Nikolaos S.; Varga, Csaba

Multiple Solutions for a Class of Neumann Elliptic Problems on Compact Riemannian Manifolds with Boundary
We study a semilinear elliptic problem on a compact Riemannian
manifold with boundary, subject to an inhomogeneous Neumann
boundary condition. Under various hypotheses on the nonlinear
terms, depending on their behaviour in the origin and infinity, we
prove multiplicity of solutions by using variational arguments.
Keywords:Riemannian manifold with boundary, Neumann problem, sublinearity at infinity, multiple solutions Categories:58J05, 35P30 

352. CMB 2010 (vol 53 pp. 667)
 Khashyarmanesh, Kazem

On the Endomorphism Rings of Local Cohomology Modules
Let $R$ be a commutative Noetherian ring and $\mathfrak{a}$ a proper ideal
of $R$. We show that if $n:=\operatorname{grade}_R\mathfrak{a}$, then
$\operatorname{End}_R(H^n_\mathfrak{a}(R))\cong \operatorname{Ext}_R^n(H^n_\mathfrak{a}(R),R)$. We also
prove that, for a nonnegative integer $n$ such that
$H^i_\mathfrak{a}(R)=0$ for every $i\neq n$, if $\operatorname{Ext}_R^i(R_z,R)=0$ for
all $i >0$ and $z \in \mathfrak{a}$, then
$\operatorname{End}_R(H^n_\mathfrak{a}(R))$ is a homomorphic
image of $R$, where $R_z$ is the ring of fractions of $R$ with
respect to a multiplicatively closed subset $\{z^j \mid j \geqslant
0 \}$ of $R$. Moreover, if $\operatorname{Hom}_R(R_z,R)=0$ for all $z
\in \mathfrak{a}$,
then $\mu_{H^n_\mathfrak{a}(R)}$ is an isomorphism, where $\mu_{H^n_\mathfrak{a}(R)}$
is the canonical ring homomorphism $R \rightarrow \operatorname{End}_R(H^n_\mathfrak{a}(R))$.
Keywords:local cohomology module, endomorphism ring, Matlis dual functor, filter regular sequence Categories:13D45, 13D07, 13D25 

353. CMB 2010 (vol 54 pp. 39)
 Chapman, S. T.; GarcíaSánchez, P. A.; Llena, D.; Marshall, J.

Elements in a Numerical Semigroup with Factorizations of the Same Length
Questions concerning the lengths of factorizations into irreducible
elements in numerical monoids
have gained much attention in the recent literature. In this note,
we show that a numerical monoid has an element with two different
irreducible factorizations of the same length if and only if its
embedding dimension is greater than
two. We find formulas in embedding dimension three for the smallest
element with two different irreducible factorizations of the same
length and the largest element whose different irreducible
factorizations all have distinct lengths. We show that these
formulas do not naturally extend to higher embedding
dimensions.
Keywords:numerical monoid, numerical semigroup, nonunique factorization Categories:20M14, 20D60, 11B75 

354. CMB 2010 (vol 53 pp. 587)
 Birkenmeier, Gary F.; Park, Jae Keol; Rizvi, S. Tariq

Hulls of Ring Extensions
We investigate the behavior of the quasiBaer and the
right FIextending right ring hulls under various ring extensions
including group ring extensions, full and triangular matrix ring
extensions, and infinite matrix ring extensions. As a consequence,
we show that for semiprime rings $R$ and $S$, if $R$ and $S$ are
Morita equivalent, then so are the quasiBaer right ring hulls
$\widehat{Q}_{\mathfrak{qB}}(R)$ and $\widehat{Q}_{\mathfrak{qB}}(S)$ of
$R$ and $S$, respectively. As an application, we prove that if
unital $C^*$algebras $A$ and $B$ are Morita equivalent as rings,
then the bounded central closure of $A$ and that of $B$ are
strongly Morita equivalent as $C^*$algebras. Our results show
that the quasiBaer property is always preserved by infinite
matrix rings, unlike the Baer property. Moreover, we give an
affirmative answer to an open question of Goel and Jain for the
commutative group ring $A[G]$ of a torsionfree Abelian group $G$
over a commutative semiprime quasicontinuous ring $A$. Examples
that illustrate and delimit the results of this paper are provided.
Keywords:(FI)extending, Morita equivalent, ring of quotients, essential overring, (quasi)Baer ring, ring hull, u.p.monoid, $C^*$algebra Categories:16N60, 16D90, 16S99, 16S50, 46L05 

355. CMB 2010 (vol 53 pp. 491)
 Jizheng, Huang; Liu, Heping

The Weak Type (1,1) Estimates of Maximal Functions on the Laguerre Hypergroup
In this paper, we discuss various maximal functions on the Laguerre hypergroup $\mathbf{K}$ including the heat maximal function, the Poisson maximal function, and the HardyLittlewood maximal function which is consistent with the structure of hypergroup of $\mathbf{K}$. We shall establish the weak type $(1,1)$ estimates for these maximal functions. The $L^p$ estimates for $p>1$ follow from the interpolation. Some applications are included.
Keywords:Laguerre hypergroup, maximal function, heat kernel, Poisson kernel Categories:42B25, 43A62 

356. CMB 2010 (vol 53 pp. 564)
 Watanabe, Yoshiyuki; Suh, Young Jin

On $6$Dimensional Nearly KÃ¤hler Manifolds
In this paper we give a sufficient condition for a complete, simply connected, and strict nearly KÃ¤hler manifold of dimension 6 to be a homogeneous nearly KÃ¤hler manifold. This result was announced in a previous paper by the first author.
Keywords:Nearly KÃ¤hler manifold, 6dimension, Homogeneous, The 1st Chern Class, Einstein manifolds Categories:53C40, 53C15 

357. CMB 2010 (vol 53 pp. 503)
 Kurenok, V. P.

The Time Change Method and SDEs with Nonnegative Drift
Using the time change method we show how to construct a solution to the stochastic equation $dX_t=b(X_{t})dZ_t+a(X_t)dt$ with a nonnegative drift $a$ provided there exists a solution to the auxililary equation $dL_t=[a^{1/\alpha}b](L_{t})d\bar Z_t+dt$ where $Z, \bar Z$ are two symmetric stable processes of the same index $\alpha\in(0,2]$. This approach allows us to prove the existence of solutions for both stochastic equations for the values $0<\alpha<1$ and only measurable coefficients $a$ and $b$ satisfying some conditions of boundedness. The existence proof for the auxililary equation uses the method of integral estimates in the sense of Krylov.
Keywords:Onedimensional SDEs, symmetric stable processes, nonnegative drift, time change, integral estimates, weak convergence Categories:60H10, 60J60, 60J65, 60G44 

358. CMB 2010 (vol 53 pp. 475)
 Jankowski, Tadeusz

Nonlinear Multipoint Boundary Value Problems for Second Order Differential Equations
In this paper we shall discuss nonlinear multipoint boundary value problems for second order differential equations when deviating arguments depend on the unknown solution. Sufficient conditions under which such problems have extremal and quasisolutions are given. The problem of when a unique solution exists is also investigated. To obtain existence results, a monotone iterative technique is used. Two examples are added to verify theoretical results.
Keywords:second order differential equations, deviated arguments, nonlinear boundary conditions, extremal solutions, quasisolutions, unique solution Categories:34A45, 34K10 

359. CMB 2010 (vol 53 pp. 438)
360. CMB 2010 (vol 53 pp. 398)
361. CMB 2010 (vol 53 pp. 412)
362. CMB 2010 (vol 53 pp. 526)
 Milian, Anna

On Some Stochastic Perturbations of Semilinear Evolution Equations
We consider semilinear evolution equations with some locally Lipschitz nonlinearities, perturbed by Banach space valued, continuous, and adapted stochastic process. We show that under some assumptions there exists a solution to the equation. Using the result we show that there exists a mild, continuous, global solution to a semilinear ItÃ´ equation with locally Lipschitz nonlinearites. An example of the equation is given.
Keywords:evolution equation, mild solution, nonLipschitz drift, Ito integral Category:60H20 

363. CMB 2010 (vol 53 pp. 256)
364. CMB 2010 (vol 53 pp. 453)
365. CMB 2010 (vol 53 pp. 367)
366. CMB 2010 (vol 53 pp. 286)
 Gorelic, Isaac

Orders of πBases
We extend the scope of B. Shapirovskii's results on the order of $\pi$bases in compact spaces and answer some questions of V. Tkachuk.
Keywords:Shapirovskii πbase, pointcountable πbase, free sequences, canonical form for ordinals Categories:54A25, 03E10, 03E75, 54A35 

367. 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 

368. 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 

369. 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 

370. CMB 2009 (vol 53 pp. 133)
371. 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 

372. CMB 2009 (vol 53 pp. 340)
373. 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 

374. 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 

375. 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 
