Search results

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

 Expand all        Collapse all Results 76 - 100 of 375

76. CMB 2011 (vol 55 pp. 632)

Pigola, S.; Rimoldi, M.
 Characterizations of Model Manifolds by Means of Certain Differential Systems We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. Along the way, we also discover new characterizations of space-forms. We next generalize results concerning metric rigidity via equations involving vector fields. Keywords:metric rigidity, model manifolds, Obata's type theoremsCategory:53C20

77. CMB 2011 (vol 55 pp. 821)

Perez-Garcia, C.; Schikhof, W. H.
 New Examples of Non-Archimedean Banach Spaces and Applications The study carried out in this paper about some new examples of Banach spaces, consisting of certain valued fields extensions, is a typical non-archimedean feature. We determine whether these extensions are of countable type, have $t$-orthogonal bases, or are reflexive. As an application we construct, for a class of base fields, a norm $\|\cdot\|$ on $c_0$, equivalent to the canonical supremum norm, without non-zero vectors that are $\|\cdot\|$-orthogonal and such that there is a multiplication on $c_0$ making $(c_0,\|\cdot\|)$ into a valued field. Keywords:non-archimedean Banach spaces, valued field extensions, spaces of countable type, orthogonal basesCategories:46S10, 12J25

78. CMB 2011 (vol 56 pp. 136)

 On Constructing Ergodic Hyperfinite Equivalence Relations of Non-Product Type Product type equivalence relations are hyperfinite measured equivalence relations, which, up to orbit equivalence, are generated by product type odometer actions. We give a concrete example of a hyperfinite equivalence relation of non-product type, which is the tail equivalence on a Bratteli diagram. In order to show that the equivalence relation constructed is not of product type we will use a criterion called property A. This property, introduced by Krieger for non-singular transformations, is defined directly for hyperfinite equivalence relations in this paper. Keywords:property A, hyperfinite equivalence relation, non-product typeCategories:37A20, 37A35, 46L10

79. CMB 2011 (vol 55 pp. 523)

Iwase, Norio; Mimura, Mamoru; Oda, Nobuyuki; Yoon, Yeon Soo
 The Milnor-Stasheff Filtration on Spaces and Generalized Cyclic Maps The concept of $C_{k}$-spaces is introduced, situated at an intermediate stage between $H$-spaces and $T$-spaces. The $C_{k}$-space corresponds to the $k$-th Milnor-Stasheff filtration on spaces. It is proved that a space $X$ is a $C_{k}$-space if and only if the Gottlieb set $G(Z,X)=[Z,X]$ for any space $Z$ with ${\rm cat}\, Z\le k$, which generalizes the fact that $X$ is a $T$-space if and only if $G(\Sigma B,X)=[\Sigma B,X]$ for any space $B$. Some results on the $C_{k}$-space are generalized to the $C_{k}^{f}$-space for a map $f\colon A \to X$. Projective spaces, lens spaces and spaces with a few cells are studied as examples of $C_{k}$-spaces, and non-$C_{k}$-spaces. Keywords:Gottlieb sets for maps, L-S category, T-spacesCategories:55P45, 55P35

80. CMB 2011 (vol 56 pp. 31)

Ayuso, Fortuny P.
 Derivations and Valuation Rings A complete characterization of valuation rings closed for a holomorphic derivation is given, following an idea of Seidenberg, in dimension $2$. Keywords:singular holomorphic foliation, derivation, valuation, valuation ringCategories:32S65, 13F30, 13A18

81. CMB 2011 (vol 55 pp. 214)

Wang, Da-Bin
 Positive Solutions of Impulsive Dynamic System on Time Scales In this paper, some criteria for the existence of positive solutions of a class of systems of impulsive dynamic equations on time scales are obtained by using a fixed point theorem in cones. Keywords:time scale, positive solution, fixed point, impulsive dynamic equationCategories:39A10, 34B15

82. CMB 2011 (vol 56 pp. 80)

 Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity In this paper we study the existence of periodic solutions of a Volterra type integral equation with infinite heredity. Banach fixed point theorem, Krasnosel'skii's fixed point theorem, and a combination of Krasnosel'skii's and Schaefer's fixed point theorems are employed in the analysis. The combination theorem of Krasnosel'skii and Schaefer requires an a priori bound on all solutions. We employ Liapunov's direct method to obtain such an a priori bound. In the process, we compare these theorems in terms of assumptions and outcomes. Keywords:Volterra integral equation, periodic solutions, Liapunov's method, Krasnosel'skii's fixed point theorem, Schaefer's fixed point theoremCategories:45D05, 45J05

83. CMB 2011 (vol 55 pp. 555)

Michalowski, Nicholas; Rule, David J.; Staubach, Wolfgang
 Weighted $L^p$ Boundedness of Pseudodifferential Operators and Applications In this paper we prove weighted norm inequalities with weights in the $A_p$ classes, for pseudodifferential operators with symbols in the class ${S^{n(\rho -1)}_{\rho, \delta}}$ that fall outside the scope of CalderÃ³n-Zygmund theory. This is accomplished by controlling the sharp function of the pseudodifferential operator by Hardy-Littlewood type maximal functions. Our weighted norm inequalities also yield $L^{p}$ boundedness of commutators of functions of bounded mean oscillation with a wide class of operators in $\mathrm{OP}S^{m}_{\rho, \delta}$. Keywords:weighted norm inequality, pseudodifferential operator, commutator estimatesCategories:42B20, 42B25, 35S05, 47G30

84. CMB 2011 (vol 55 pp. 378)

 On Modules Whose Proper Homomorphic Images Are of Smaller Cardinality Let $R$ be a commutative ring with identity, and let $M$ be a unitary module over $R$. We call $M$ H-smaller (HS for short) if and only if $M$ is infinite and $|M/N|<|M|$ for every nonzero submodule $N$ of $M$. After a brief introduction, we show that there exist nontrivial examples of HS modules of arbitrarily large cardinality over Noetherian and non-Noetherian domains. We then prove the following result: suppose $M$ is faithful over $R$, $R$ is a domain (we will show that we can restrict to this case without loss of generality), and $K$ is the quotient field of $R$. If $M$ is HS over $R$, then $R$ is HS as a module over itself, $R\subseteq M\subseteq K$, and there exists a generating set $S$ for $M$ over $R$ with $|S|<|R|$. We use this result to generalize a problem posed by Kaplansky and conclude the paper by answering an open question on JÃ³nsson modules. Keywords:Noetherian ring, residually finite ring, cardinal number, continuum hypothesis, valuation ring, JÃ³nsson moduleCategories:13A99, 13C05, 13E05, 03E50

85. CMB 2011 (vol 55 pp. 697)

Borwein, Jonathan M.; Vanderwerff, Jon
 Constructions of Uniformly Convex Functions We give precise conditions under which the composition of a norm with a convex function yields a uniformly convex function on a Banach space. Various applications are given to functions of power type. The results are dualized to study uniform smoothness and several examples are provided. Keywords:convex function, uniformly convex function, uniformly smooth function, power type, Fenchel conjugate, composition, normCategories:52A41, 46G05, 46N10, 49J50, 90C25

86. CMB 2011 (vol 55 pp. 774)

Mollin, R. A.; Srinivasan, A.
 Pell Equations: Non-Principal Lagrange Criteria and Central Norms We provide a criterion for the central norm to be any value in the simple continued fraction expansion of $\sqrt{D}$ for any non-square integer $D>1$. We also provide a simple criterion for the solvability of the Pell equation $x^2-Dy^2=-1$ in terms of congruence conditions modulo $D$. Keywords:Pell's equation, continued fractions, central normsCategories:11D09, 11A55, 11R11, 11R29

87. CMB 2011 (vol 55 pp. 723)

Gigli, Nicola; Ohta, Shin-Ichi
 First Variation Formula in Wasserstein Spaces over Compact Alexandrov Spaces We extend results proved by the second author (Amer. J. Math., 2009) for nonnegatively curved Alexandrov spaces to general compact Alexandrov spaces $X$ with curvature bounded below. The gradient flow of a geodesically convex functional on the quadratic Wasserstein space $(\mathcal P(X),W_2)$ satisfies the evolution variational inequality. Moreover, the gradient flow enjoys uniqueness and contractivity. These results are obtained by proving a first variation formula for the Wasserstein distance. Keywords:Alexandrov spaces, Wasserstein spaces, first variation formula, gradient flowCategories:53C23, 28A35, 49Q20, 58A35

88. CMB 2011 (vol 55 pp. 597)

 Sharp Inequalities for Differentially Subordinate Harmonic Functions and Martingales We determine the best constants $C_{p,\infty}$ and $C_{1,p}$, $1 < p < \infty$, for which the following holds. If $u$, $v$ are orthogonal harmonic functions on a Euclidean domain such that $v$ is differentially subordinate to $u$, then $$\|v\|_p \leq C_{p,\infty} \|u\|_\infty,\quad \|v\|_1 \leq C_{1,p} \|u\|_p.$$ In particular, the inequalities are still sharp for the conjugate harmonic functions on the unit disc of $\mathbb R^2$. Sharp probabilistic versions of these estimates are also studied. As an application, we establish a sharp version of the classical logarithmic inequality of Zygmund. Keywords: harmonic function, conjugate harmonic functions, orthogonal harmonic functions, martingale, orthogonal martingales, norm inequality, optimal stopping problemCategories:31B05, 60G44, 60G40

89. CMB 2011 (vol 55 pp. 767)

Martini, Horst; Wu, Senlin
 On Zindler Curves in Normed Planes We extend the notion of Zindler curve from the Euclidean plane to normed planes. A characterization of Zindler curves for general normed planes is given, and the relation between Zindler curves and curves of constant area-halving distances in such planes is discussed. Keywords:rc length, area-halving distance, Birkhoff orthogonality, convex curve, halving pair, halving distance, isosceles orthogonality, midpoint curve, Minkowski plane, normed plane, Zindler curveCategories:52A21, 52A10, 46C15

90. CMB 2011 (vol 56 pp. 44)

Biswas, Indranil; Dey, Arijit
 Polystable Parabolic Principal $G$-Bundles and Hermitian-Einstein Connections We show that there is a bijective correspondence between the polystable parabolic principal $G$-bundles and solutions of the Hermitian-Einstein equation. Keywords:ramified principal bundle, parabolic principal bundle, Hitchin-Kobayashi correspondence, polystabilityCategories:32L04, 53C07

91. CMB 2011 (vol 55 pp. 487)

Deng, Xinghua; Moody, Robert V.
 Weighted Model Sets and their Higher Point-Correlations Examples of distinct weighted model sets with equal $2,3,4, 5$-point correlations are given. Keywords:model sets, correlations, diffractionCategories:52C23, 51P05, 74E15, 60G55

92. CMB 2011 (vol 55 pp. 462)

Campbell, Peter S.; Stokke, Anna
 Hook-content Formulae for Symplectic and Orthogonal Tableaux By considering the specialisation $s_{\lambda}(1,q,q^2,\dots,q^{n-1})$ of the Schur function, Stanley was able to describe a formula for the number of semistandard Young tableaux of shape $\lambda$ in terms of the contents and hook lengths of the boxes in the Young diagram. Using specialisations of symplectic and orthogonal Schur functions, we derive corresponding formulae, first given by El Samra and King, for the number of semistandard symplectic and orthogonal $\lambda$-tableaux. Keywords:symplectic tableaux, orthogonal tableaux, Schur functionCategories:05E05, 05E10

93. CMB 2011 (vol 55 pp. 611)

 Chen Inequalities for Submanifolds of Real Space Forms with a Semi-Symmetric Non-Metric Connection In this paper we prove Chen inequalities for submanifolds of real space forms endowed with a semi-symmetric non-metric connection, i.e., relations between the mean curvature associated with a semi-symmetric non-metric connection, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the ambient space. The equality cases are considered. Keywords:real space form, semi-symmetric non-metric connection, Ricci curvatureCategories:53C40, 53B05, 53B15

94. CMB 2011 (vol 55 pp. 509)

Gauthier, P. M.; Nestoridis, V.
 Domains of Injective Holomorphy A domain $\Omega$ is called a domain of injective holomorphy if there exists an injective holomorphic function $f\colon \Omega\rightarrow\mathbb{C}$ that is non-extendable. We give examples of domains that are domains of injective holomorphy and others that are not. In particular, every regular domain $(\overline\Omega^o=\Omega)$ is a domain of injective holomorphy, and every simply connected domain is a domain of injective holomorphy as well. Keywords:domains of holomorphyCategory:30Exx

95. CMB 2011 (vol 55 pp. 449)

Bahreini, Manijeh; Bator, Elizabeth; Ghenciu, Ioana
 Complemented Subspaces of Linear Bounded Operators We study the complementation of the space $W(X,Y)$ of weakly compact operators, the space $K(X,Y)$ of compact operators, the space $U(X,Y)$ of unconditionally converging operators, and the space $CC(X,Y)$ of completely continuous operators in the space $L(X,Y)$ of bounded linear operators from $X$ to $Y$. Feder proved that if $X$ is infinite-dimensional and $c_0 \hookrightarrow Y$, then $K(X,Y)$ is uncomplemented in $L(X,Y)$. Emmanuele and John showed that if $c_0 \hookrightarrow K(X,Y)$, then $K(X,Y)$ is uncomplemented in $L(X,Y)$. Bator and Lewis showed that if $X$ is not a Grothendieck space and $c_0 \hookrightarrow Y$, then $W(X,Y)$ is uncomplemented in $L(X,Y)$. In this paper, classical results of Kalton and separably determined operator ideals with property $(*)$ are used to obtain complementation results that yield these theorems as corollaries. Keywords:spaces of operators, complemented subspaces, compact operators, weakly compact operators, completely continuous operatorsCategories:46B20, 46B28

96. CMB 2011 (vol 54 pp. 654)

Forrest, Brian E.; Runde, Volker
 Norm One Idempotent $cb$-Multipliers with Applications to the Fourier Algebra in the $cb$-Multiplier Norm For a locally compact group $G$, let $A(G)$ be its Fourier algebra, let $M_{cb}A(G)$ denote the completely bounded multipliers of $A(G)$, and let $A_{\mathit{Mcb}}(G)$ stand for the closure of $A(G)$ in $M_{cb}A(G)$. We characterize the norm one idempotents in $M_{cb}A(G)$: the indicator function of a set $E \subset G$ is a norm one idempotent in $M_{cb}A(G)$ if and only if $E$ is a coset of an open subgroup of $G$. As applications, we describe the closed ideals of $A_{\mathit{Mcb}}(G)$ with an approximate identity bounded by $1$, and we characterize those $G$ for which $A_{\mathit{Mcb}}(G)$ is $1$-amenable in the sense of B. E. Johnson. (We can even slightly relax the norm bounds.) Keywords:amenability, bounded approximate identity, $cb$-multiplier norm, Fourier algebra, norm one idempotentCategories:43A22, 20E05, 43A30, 46J10, 46J40, 46L07, 47L25

97. CMB 2011 (vol 55 pp. 355)

Nhan, Nguyen Du Vi; Duc, Dinh Thanh
 Convolution Inequalities in $l_p$ Weighted Spaces Various weighted $l_p$-norm inequalities in convolutions are derived by a simple and general principle whose $l_2$ version was obtained by using the theory of reproducing kernels. Applications to the Riemann zeta function and a difference equation are also considered. Keywords:inequalities for sums, convolutionCategories:26D15, 44A35

98. CMB 2011 (vol 55 pp. 579)

Ndogmo, J. C.
 Casimir Operators and Nilpotent Radicals It is shown that a Lie algebra having a nilpotent radical has a fundamental set of invariants consisting of Casimir operators. A different proof is given in the well known special case of an abelian radical. A result relating the number of invariants to the dimension of the Cartan subalgebra is also established. Keywords:nilpotent radical, Casimir operators, algebraic Lie algebras, Cartan subalgebras, number of invariantsCategories:16W25, 17B45, 16S30

99. CMB 2011 (vol 55 pp. 319)

Jardine, J. F.
 The Verdier Hypercovering Theorem This note gives a simple cocycle-theoretic proof of the Verdier hypercovering theorem. This theorem approximates morphisms $[X,Y]$ in the homotopy category of simplicial sheaves or presheaves by simplicial homotopy classes of maps, in the case where $Y$ is locally fibrant. The statement proved in this paper is a generalization of the standard Verdier hypercovering result in that it is pointed (in a very broad sense) and there is no requirement for the source object $X$ to be locally fibrant. Keywords:simplicial presheaf, hypercover, cocycleCategories:14F35, 18G30, 55U35

100. CMB 2011 (vol 55 pp. 571)

Miller, A. R.; Paris, R. B.
 A Generalised Kummer-Type Transformation for the ${}_pF_p(x)$ Hypergeometric Function In a recent paper, Miller derived a Kummer-type transformation for the generalised hypergeometric function ${}_pF_p(x)$ when pairs of parameters differ by unity, by means of a reduction formula for a certain KampÃ© de FÃ©riet function. An alternative and simpler derivation of this transformation is obtained here by application of the well-known Kummer transformation for the confluent hypergeometric function corresponding to $p=1$. Keywords:generalised hypergeometric series, Kummer transformationCategories:33C15, 33C20
 Page Previous 1 ... 3 4 5 ... 15 Next