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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 solutionsCategories: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 sequenceCategories:13D45, 13D07, 13D25

353. CMB 2010 (vol 54 pp. 39)

Chapman, S. T.; García-Sánchez, 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, non-unique factorizationCategories: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 quasi-Baer and the right FI-extending 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 quasi-Baer 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 quasi-Baer 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 torsion-free Abelian group $G$ over a commutative semiprime quasi-continuous 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, $C^*$-algebraCategories: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 Hardy--Littlewood 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 kernelCategories: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, 6-dimension, Homogeneous, The 1st Chern Class, Einstein manifoldsCategories: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:One-dimensional SDEs, symmetric stable processes, nonnegative drift, time change, integral estimates, weak convergenceCategories:60H10, 60J60, 60J65, 60G44

358. CMB 2010 (vol 53 pp. 475)

 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 quasi-solutions 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, quasi-solutions, unique solutionCategories:34A45, 34K10

359. CMB 2010 (vol 53 pp. 438)

Chigogidze, A.; Nagórko, A.
 Near-Homeomorphisms of Nöbeling Manifolds We characterize maps between $n$-dimensional NÃ¶beling manifolds that can be approximated by homeomorphisms. Keywords:n-dimensional Nöbeling manifold, Z-set unknotting, near-homeomorphismCategories:55M10, 54F45

360. CMB 2010 (vol 53 pp. 398)

Botelho, Fernanda; Jamison, James
 Projections in the Convex Hull of Surjective Isometries We characterize those linear projections represented as a convex combination of two surjective isometries on standard Banach spaces of continuous functions with values in a strictly convex Banach space. Keywords:isometry, convex combination of isometries, generalized bi-circular projectionsCategories:47A65, 47B15, 47B37

361. CMB 2010 (vol 53 pp. 412)

Calvaruso, G.
 Einstein-Like Lorentz Metrics and Three-Dimensional Curvature Homogeneity of Order One We completely classify three-dimensional Lorentz manifolds, curvature homogeneous up to order one, equipped with Einstein-like metrics. New examples arise with respect to both homogeneous examples and three-dimensional Lorentz manifolds admitting a degenerate parallel null line field. Keywords:Lorentz manifolds, curvature homogeneity, Einstein-like metricsCategories:53C50, 53C20, 53C30

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, non-Lipschitz drift, Ito integralCategory:60H20

363. CMB 2010 (vol 53 pp. 256)

Fang, Xiaochun; Wang, Lin
 Equivalent Definitions of Infinite Positive Elements in Simple C*-algebras We prove the equivalence of three definitions given by different comparison relations for infiniteness of positive elements in simple $C^*$-algebras. Keywords:Infinite positive element, Comparison relationCategory:46L99

364. CMB 2010 (vol 53 pp. 453)

Desgroseilliers, Marc; Larose, Benoit; Malvenuto, Claudia; Vincent, Christelle
 Some Results on Two Conjectures of Schützenberger We present some partial results concerning two conjectures of SchÃ¼tzenberger on evacuations of Young tableaux. Keywords:Evacuation of Standard Young tableauxCategories:05E10, 05A99

365. CMB 2010 (vol 53 pp. 367)

Stamov, Gani Tr.
 Almost Periodicity and Lyapunov's Functions for Impulsive Functional Differential Equations with Infinite Delays This paper studies the existence and uniqueness of almost periodic solutions of nonlinear impulsive functional differential equations with infinite delay. The results obtained are based on the Lyapunov--Razumikhin method and on differential inequalities for piecewise continuous functions. Keywords:almost periodic solutions, impulsive functional differential equationsCategories:34K45, 34B37

366. CMB 2010 (vol 53 pp. 286)

Gorelic, Isaac
 Orders of π-Bases 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 π-base, point-countable π-base, free sequences, canonical form for ordinalsCategories:54A25, 03E10, 03E75, 54A35

367. CMB 2010 (vol 53 pp. 466)

Dubarbie, Luis
 Separating Maps between Spaces of Vector-Valued Absolutely Continuous Functions In this paper we give a description of separating or disjointness preserving linear bijections on spaces of vector-valued absolutely continuous functions defined on compact subsets of the real line. We obtain that they are continuous and biseparating in the finite-dimensional case. The infinite-dimensional case is also studied. Keywords:separating maps, disjointness preserving, vector-valued absolutely continuous functions, automatic continuityCategories: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 $(n-1)\cdot \operatorname{degree}(T(G/P))/n$. We prove that the restriction of the tangent bundle $\iota^*TG/P$ is semistable. Keywords:tangent bundle, homogeneous space, semistability, hypersurfaceCategories: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 integer-valued 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 non-empty 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 $\operatorname{bind}(G)\gt \frac{(a+b-1)(p-1)}{(a+1)p-(a+b)-bn+2} \quad\text{and}\quad p\geq \frac{(a+b-1)(a+b-2)}{a+1}+\frac{bn}{a}.$ Furthermore, it is shown that this result is best possible in some sense. Keywords:graph, $(g,f)$-factor, $(g,f,n)$-critical graph, binding numberCategory:05C70

370. CMB 2009 (vol 53 pp. 133)

Moritoh, Shinya; Tomoeda, Kyoko
 A Further Decay Estimate for the DziubaÅski-HernÃ¡ndez Wavelets We give a further decay estimate for the DziubaÅski-HernÃ¡ndez wavelets that are band-limited and have subexponential decay. This is done by constructing an appropriate bell function and using the Paley-Wiener theorem for ultradifferentiable functions. Keywords:wavelets, ultradifferentiable functionsCategories:42C40, 46E10

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, R-quadratic, flag curvatureCategory:58E20

372. CMB 2009 (vol 53 pp. 340)

Lusala, Tsasa; Śniatycki, Jędrzej; Watts, Jordan
 Regular Points of a Subcartesian Space We discuss properties of the regular part $S_{\operatorname{reg}}$ of a subcartesian space $S$. We show that $S_{\operatorname{reg}}$ is open and dense in $S$ and the restriction to $S_{\operatorname{reg}}$ of the tangent bundle space of $S$ is locally trivial. Keywords:differential structures, singular and regular pointsCategory:58A40

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 sequenceCategories: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 so-called asymptotic compactness property of the solution operator by energy equation approach. Keywords:global attractor, Fourier restriction norm, damping system, asymptotic compactnessCategories:35Q53, 35B40, 35B41, 37L30

375. CMB 2009 (vol 53 pp. 95)

Ghioca, Dragos
 Towards the Full Mordell-Lang 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, Mordell-Lang conjectureCategories:11G09, 11G10
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