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Search: All articles in the CMB digital archive with keyword f

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401. 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 Itô equation with locally Lipschitz nonlinearites. An example of the equation is given.

Keywords:evolution equation, mild solution, non-Lipschitz drift, Ito integral
Category:60H20

402. 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 convergence
Categories:60H10, 60J60, 60J65, 60G44

403. 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 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 solution
Categories:34A45, 34K10

404. CMB 2010 (vol 53 pp. 438)

Chigogidze, A.; Nagórko, A.
Near-Homeomorphisms of Nöbeling Manifolds
We characterize maps between $n$-dimensional Nöbeling manifolds that can be approximated by homeomorphisms.

Keywords:n-dimensional Nöbeling manifold, Z-set unknotting, near-homeomorphism
Categories:55M10, 54F45

405. 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 projections
Categories:47A65, 47B15, 47B37

406. 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 relation
Category:46L99

407. 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 Schützenberger on evacuations of Young tableaux.

Keywords:Evacuation of Standard Young tableaux
Categories:05E10, 05A99

408. 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 equations
Categories:34K45, 34B37

409. 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 ordinals
Categories:54A25, 03E10, 03E75, 54A35

410. 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 continuity
Categories:47B38, 46E15, 46E40, 46H40, 47B33

411. 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 compactness
Categories:35Q53, 35B40, 35B41, 37L30

412. 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 number
Category:05C70

413. CMB 2009 (vol 53 pp. 133)

Moritoh, Shinya; Tomoeda, Kyoko
A Further Decay Estimate for the Dziubański-Hernández Wavelets
We give a further decay estimate for the Dziubański-Hernández 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 functions
Categories:42C40, 46E10

414. 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 curvature
Category:58E20

415. 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 points
Category:58A40

416. 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

417. 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 conjecture
Categories:11G09, 11G10

418. 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 Hardy–Littlewood 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

419. 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

420. 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 $(1-|z'|^2)^{\beta-\alpha}|u(z')|\ge\delta$, where $d(\cdot,\cdot)$ denotes the pseudo-distance on $D$.

Keywords:$\alpha$-Bloch function, multiplication operator
Categories:32A18, 30H05

421. 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

422. 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, hypersurface
Categories:14F05, 14J60, 14M15

423. CMB 2009 (vol 53 pp. 206)

Atçeken, Mehmet
Semi-Slant Submanifolds of an Almost Paracontact Metric Manifold
In this paper, we define and study the geometry of semi-slant submanifolds of an almost paracontact metric manifold. We give some characterizations for a submanifold to be semi-slant submanifold to be semi-slant product and obtain integrability conditions for the distributions involved in the definition of a semi-slant submanifold.

Keywords:paracontact metric manifold, slant distribution, semi-slant submanifold, semi-slant product
Categories:53C15, 53C25, 53C40

424. 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 \[ \prod_{n=1}^{\infty} \frac{(1-q^n)^5}{(1-q^{5n})} =1-5\sum_{n=1}^{\infty}\Big( \sum_{d \mid n} \qu{5}{d} d \Big) q^n \] and \[ q\prod_{n=1}^{\infty} \frac{(1-q^{5n})^5}{(1-q^{n})} =\sum_{n=1}^{\infty}\Big( \sum_{d \mid n} \qu{5}{n/d} d \Big) q^n. \] We give several more identities of this type.

Keywords:Power series expansions of certain infinite products
Categories:11E25, 11F11, 11F27, 30B10

425. CMB 2009 (vol 52 pp. 564)

Jin, Hai Lan; Doh, Jaekyung; Park, Jae Keol
Group Actions on Quasi-Baer Rings
A ring $R$ is called {\it quasi-Baer} if the right annihilator of every right ideal of $R$ is generated by an idempotent as a right ideal. We investigate the quasi-Baer 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
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