CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

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

  Expand all        Collapse all Results 376 - 400 of 425

376. CMB 2002 (vol 45 pp. 97)

Haas, Andrew
Invariant Measures and Natural Extensions
We study ergodic properties of a family of interval maps that are given as the fractional parts of certain real M\"obius transformations. Included are the maps that are exactly $n$-to-$1$, the classical Gauss map and the Renyi or backward continued fraction map. A new approach is presented for deriving explicit realizations of natural automorphic extensions and their invariant measures.

Keywords:Continued fractions, interval maps, invariant measures
Categories:11J70, 58F11, 58F03

377. CMB 2001 (vol 44 pp. 398)

Cardon, David A.; Ram Murty, M.
Exponents of Class Groups of Quadratic Function Fields over Finite Fields
We find a lower bound on the number of imaginary quadratic extensions of the function field $\F_q(T)$ whose class groups have an element of a fixed order. More precisely, let $q \geq 5$ be a power of an odd prime and let $g$ be a fixed positive integer $\geq 3$. There are $\gg q^{\ell (\frac{1}{2}+\frac{1}{g})}$ polynomials $D \in \F_q[T]$ with $\deg(D) \leq \ell$ such that the class groups of the quadratic extensions $\F_q(T,\sqrt{D})$ have an element of order~$g$.

Keywords:class number, quadratic function field
Categories:11R58, 11R29

378. CMB 2001 (vol 44 pp. 504)

Zhang, Yong
Weak Amenability of a Class of Banach Algebras
We show that, if a Banach algebra $\A$ is a left ideal in its second dual algebra and has a left bounded approximate identity, then the weak amenability of $\A$ implies the ($2m+1$)-weak amenability of $\A$ for all $m\geq 1$.

Keywords:$n$-weak amenability, left ideals, left bounded approximate identity
Categories:46H20, 46H10, 46H25

379. CMB 2001 (vol 44 pp. 323)

Schuman, Bertrand
Une classe d'hamiltoniens polynomiaux isochrones
Soit $H_0 = \frac{x^2+y^2}{2}$ un hamiltonien isochrone du plan $\Rset^2$. On met en \'evidence une classe d'hamiltoniens isochrones qui sont des perturbations polynomiales de $H_0$. On obtient alors une condition n\'ecessaire d'isochronisme, et un crit\`ere de choix pour les hamiltoniens isochrones. On voit ce r\'esultat comme \'etant une g\'en\'eralisation du caract\`ere isochrone des perturbations hamiltoniennes homog\`enes consid\'er\'ees dans [L], [P], [S]. Let $H_0 = \frac{x^2+y^2}{2}$ be an isochronous Hamiltonian of the plane $\Rset^2$. We obtain a necessary condition for a system to be isochronous. We can think of this result as a generalization of the isochronous behaviour of the homogeneous polynomial perturbation of the Hamiltonian $H_0$ considered in [L], [P], [S].

Keywords:Hamiltonian system, normal forms, resonance, linearization
Categories:34C20, 58F05, 58F22, 58F30

380. CMB 2001 (vol 44 pp. 376)

Zhang, Xi
A Note on $p$-Harmonic $1$-Forms on Complete Manifolds
In this paper we prove that there is no nontrivial $L^{q}$-integrably $p$-harmonic $1$-form on a complete manifold with nonnegatively Ricci curvature $(0
Keywords:$p$-harmonic, $1$-form, complete manifold, Sobolev inequality
Categories:58E20, 53C21

381. CMB 2001 (vol 44 pp. 337)

Vinet, Luc; Zhedanov, Alexei
Spectral Transformations of the Laurent Biorthogonal Polynomials, II. Pastro Polynomials
We continue to study the simplest closure conditions for chains of spectral transformations of the Laurent biorthogonal polynomials ($\LBP$). It is shown that the 1-1-periodic $q$-closure condition leads to the $\LBP$ introduced by Pastro. We introduce classes of semi-classical and Laguerre-Hahn $\LBP$ associated to generic closure conditions of the chain of spectral transformations.

Keywords:Laurent orthogonal polynomials, Pastro polynomials, spectral transformations
Category:33D45

382. CMB 2001 (vol 44 pp. 266)

Cencelj, M.; Dranishnikov, A. N.
Extension of Maps to Nilpotent Spaces
We show that every compactum has cohomological dimension $1$ with respect to a finitely generated nilpotent group $G$ whenever it has cohomological dimension $1$ with respect to the abelianization of $G$. This is applied to the extension theory to obtain a cohomological dimension theory condition for a finite-dimensional compactum $X$ for extendability of every map from a closed subset of $X$ into a nilpotent $\CW$-complex $M$ with finitely generated homotopy groups over all of $X$.

Keywords:cohomological dimension, extension of maps, nilpotent group, nilpotent space
Categories:55M10, 55S36, 54C20, 54F45

383. CMB 2001 (vol 44 pp. 210)

Leung, Man Chun
Growth Estimates on Positive Solutions of the Equation $\Delta u+K u^{\frac{n+2}{n-2}}=0$ in $\R^n$
We construct unbounded positive $C^2$-solutions of the equation $\Delta u + K u^{(n + 2)/(n - 2)} = 0$ in $\R^n$ (equipped with Euclidean metric $g_o$) such that $K$ is bounded between two positive numbers in $\R^n$, the conformal metric $g=u^{4/(n-2)}g_o$ is complete, and the volume growth of $g$ can be arbitrarily fast or reasonably slow according to the constructions. By imposing natural conditions on $u$, we obtain growth estimate on the $L^{2n/(n-2)}$-norm of the solution and show that it has slow decay.

Keywords:positive solution, conformal scalar curvature equation, growth estimate
Categories:35J60, 58G03

384. CMB 2001 (vol 44 pp. 129)

Currás-Bosch, Carlos
Linéarisation symplectique en dimension 2
In this paper the germ of neighborhood of a compact leaf in a Lagrangian foliation is symplectically classified when the compact leaf is $\bT^2$, the affine structure induced by the Lagrangian foliation on the leaf is complete, and the holonomy of $\bT^2$ in the foliation linearizes. The germ of neighborhood is classified by a function, depending on one transverse coordinate, this function is related to the affine structure of the nearly compact leaves.

Keywords:symplectic manifold, Lagrangian foliation, affine connection
Categories:53C12, 58F05

385. CMB 2001 (vol 44 pp. 126)

Zeron, E. Santillan
Each Copy of the Real Line in $\C^2$ is Removable
Around 1995, Professors Lupacciolu, Chirka and Stout showed that a closed subset of $\C^N$ ($N\geq 2$) is removable for holomorphic functions, if its topological dimension is less than or equal to $N-2$. Besides, they asked whether closed subsets of $\C^2$ homeomorphic to the real line (the simplest 1-dimensional sets) are removable for holomorphic functions. In this paper we propose a positive answer to that question.

Keywords:holomorphic function, removable set
Category:32D20

386. CMB 2001 (vol 44 pp. 97)

Ou, Zhiming M.; Williams, Kenneth S.
On the Density of Cyclic Quartic Fields
An asymptotic formula is obtained for the number of cyclic quartic fields over $Q$ with discriminant $\leq x$.

Keywords:cyclic quartic fields, density, discriminant
Categories:11R16, 11R29

387. CMB 2000 (vol 43 pp. 427)

Ivey, Thomas A.
Helices, Hasimoto Surfaces and Bäcklund Transformations
Travelling wave solutions to the vortex filament flow generated by elastica produce surfaces in $\R^3$ that carry mutually orthogonal foliations by geodesics and by helices. These surfaces are classified in the special cases where the helices are all congruent or are all generated by a single screw motion. The first case yields a new characterization for the B\"acklund transformation for constant torsion curves in $\R^3$, previously derived from the well-known transformation for pseudospherical surfaces. A similar investigation for surfaces in $H^3$ or $S^3$ leads to a new transformation for constant torsion curves in those spaces that is also derived from pseudospherical surfaces.

Keywords:surfaces, filament flow, Bäcklund transformations
Categories:53A05, 58F37, 52C42, 58A15

388. CMB 2000 (vol 43 pp. 496)

Xu, Yuan
Harmonic Polynomials Associated With Reflection Groups
We extend Maxwell's representation of harmonic polynomials to $h$-harmonics associated to a reflection invariant weight function $h_k$. Let $\CD_i$, $1\le i \le d$, be Dunkl's operators associated with a reflection group. For any homogeneous polynomial $P$ of degree $n$, we prove the polynomial $|\xb|^{2 \gamma +d-2+2n}P(\CD)\{1/|\xb|^{2 \gamma +d-2}\}$ is a $h$-harmonic polynomial of degree $n$, where $\gamma = \sum k_i$ and $\CD=(\CD_1,\ldots,\CD_d)$. The construction yields a basis for $h$-harmonics. We also discuss self-adjoint operators acting on the space of $h$-harmonics.

Keywords:$h$-harmonics, reflection group, Dunkl's operators
Categories:33C50, 33C45

389. CMB 2000 (vol 43 pp. 440)

Koufogiorgos, Themis; Tsichlias, Charalambos
On the Existence of a New Class of Contact Metric Manifolds
A new class of 3-dimensional contact metric manifolds is found. Moreover it is proved that there are no such manifolds in dimensions greater than 3.

Keywords:contact metric manifolds, generalized $(\kappa,\mu)$-contact metric manifolds
Categories:53C25, 53C15

390. CMB 2000 (vol 43 pp. 418)

Gong, Guihua; Jiang, Xinhui; Su, Hongbing
Obstructions to $\mathcal{Z}$-Stability for Unital Simple $C^*$-Algebras
Let $\cZ$ be the unital simple nuclear infinite dimensional $C^*$-algebra which has the same Elliott invariant as $\bbC$, introduced in \cite{JS}. A $C^*$-algebra is called $\cZ$-stable if $A \cong A \otimes \cZ$. In this note we give some necessary conditions for a unital simple $C^*$-algebra to be $\cZ$-stable.

Keywords:simple $C^*$-algebra, $\mathcal{Z}$-stability, weak (un)perforation in $K_0$ group, property $\Gamma$, finiteness
Category:46L05

391. CMB 2000 (vol 43 pp. 294)

Bracci, Filippo
Fixed Points of Commuting Holomorphic Maps Without Boundary Regularity
We identify a class of domains of $\C^n$ in which any two commuting holomorphic self-maps have a common fixed point.

Keywords:Holomorphic self-maps, commuting functions, fixed points, Wolff point, Julia's Lemma
Categories:32A10, 32A40, 32H15, 32A30

392. CMB 2000 (vol 43 pp. 362)

Kim, Hwankoo
Examples of Half-Factorial Domains
In this paper, we determine some sufficient conditions for an $A + XB[X]$ domain to be an HFD. As a consequence we give new examples of HFDs of the type $A + XB[X]$.

Keywords:atomic domain, HFD
Categories:13A05, 13B30, 13F15, 13G05

393. CMB 2000 (vol 43 pp. 330)

Hare, Kathryn E.
Maximal Operators and Cantor Sets
We consider maximal operators in the plane, defined by Cantor sets of directions, and show such operators are not bounded on $L^2$ if the Cantor set has positive Hausdorff dimension.

Keywords:maximal functions, Cantor set, lacunary set
Categories:42B25, 43A46

394. CMB 2000 (vol 43 pp. 268)

Bogley, W. A.; Gilbert, N. D.; Howie, James
Cockcroft Properties of Thompson's Group
In a study of the word problem for groups, R.~J.~Thompson considered a certain group $F$ of self-homeomorphisms of the Cantor set and showed, among other things, that $F$ is finitely presented. Using results of K.~S.~Brown and R.~Geoghegan, M.~N.~Dyer showed that $F$ is the fundamental group of a finite two-complex $Z^2$ having Euler characteristic one and which is {\em Cockcroft}, in the sense that each map of the two-sphere into $Z^2$ is homologically trivial. We show that no proper covering complex of $Z^2$ is Cockcroft. A general result on Cockcroft properties implies that no proper regular covering complex of any finite two-complex with fundamental group $F$ is Cockcroft.

Keywords:two-complex, covering space, Cockcroft two-complex, Thompson's group
Categories:57M20, 20F38, 57M10, 20F34

395. CMB 2000 (vol 43 pp. 3)

Adin, Ron; Blanc, David
Resolutions of Associative and Lie Algebras
Certain canonical resolutions are described for free associative and free Lie algebras in the category of non-associative algebras. These resolutions derive in both cases from geometric objects, which in turn reflect the combinatorics of suitable collections of leaf-labeled trees.

Keywords:resolutions, homology, Lie algebras, associative algebras, non-associative algebras, Jacobi identity, leaf-labeled trees, associahedron
Categories:18G10, 05C05, 16S10, 17B01, 17A50, 18G50

396. CMB 2000 (vol 43 pp. 60)

Farkas, Daniel R.; Linnell, Peter A.
Trivial Units in Group Rings
Let $G$ be an arbitrary group and let $U$ be a subgroup of the normalized units in $\mathbb{Z}G$. We show that if $U$ contains $G$ as a subgroup of finite index, then $U = G$. This result can be used to give an alternative proof of a recent result of Marciniak and Sehgal on units in the integral group ring of a crystallographic group.

Keywords:units, trace, finite conjugate subgroup
Categories:16S34, 16U60

397. CMB 2000 (vol 43 pp. 25)

Bounkhel, M.; Thibault, L.
Subdifferential Regularity of Directionally Lipschitzian Functions
Formulas for the Clarke subdifferential are always expressed in the form of inclusion. The equality form in these formulas generally requires the functions to be directionally regular. This paper studies the directional regularity of the general class of extended-real-valued functions that are directionally Lipschitzian. Connections with the concept of subdifferential regularity are also established.

Keywords:subdifferential regularity, directional regularity, directionally Lipschitzian functions
Categories:49J52, 58C20, 49J50, 90C26

398. CMB 2000 (vol 43 pp. 21)

Barnes, Bruce A.
The Commutant of an Abstract Backward Shift
A bounded linear operator $T$ on a Banach space $X$ is an abstract backward shift if the nullspace of $T$ is one dimensional, and the union of the null spaces of $T^k$ for all $k \geq 1$ is dense in $X$. In this paper it is shown that the commutant of an abstract backward shift is an integral domain. This result is used to derive properties of operators in the commutant.

Keywords:backward shift, commutant
Category:47A99

399. CMB 1999 (vol 42 pp. 478)

Pruss, Alexander R.
A Remark On the Moser-Aubin Inequality For Axially Symmetric Functions On the Sphere
Let $\scr S_r$ be the collection of all axially symmetric functions $f$ in the Sobolev space $H^1(\Sph^2)$ such that $\int_{\Sph^2} x_ie^{2f(\mathbf{x})} \, d\omega(\mathbf{x})$ vanishes for $i=1,2,3$. We prove that $$ \inf_{f\in \scr S_r} \frac12 \int_{\Sph^2} |\nabla f|^2 \, d\omega + 2\int_{\Sph^2} f \, d\omega- \log \int_{\Sph^2} e^{2f} \, d\omega > -\oo, $$ and that this infimum is attained. This complements recent work of Feldman, Froese, Ghoussoub and Gui on a conjecture of Chang and Yang concerning the Moser-Aubin inequality.

Keywords:Moser inequality, borderline Sobolev inequalities, axially symmetric functions
Categories:26D15, 58G30

400. CMB 1999 (vol 42 pp. 427)

Berndt, Bruce C.; Chan, Heng Huat
Ramanujan and the Modular $j$-Invariant
A new infinite product $t_n$ was introduced by S.~Ramanujan on the last page of his third notebook. In this paper, we prove Ramanujan's assertions about $t_n$ by establishing new connections between the modular $j$-invariant and Ramanujan's cubic theory of elliptic functions to alternative bases. We also show that for certain integers $n$, $t_n$ generates the Hilbert class field of $\mathbb{Q} (\sqrt{-n})$. This shows that $t_n$ is a new class invariant according to H.~Weber's definition of class invariants.

Keywords:modular functions, the Borweins' cubic theta-functions, Hilbert class fields
Categories:33C05, 33E05, 11R20, 11R29
Page
   1 ... 14 15 16 17    

© Canadian Mathematical Society, 2014 : https://cms.math.ca/