%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "1.02",
%%%     date            = "05 August 2004",
%%%     time            = "11:08:11 MDT",
%%%     filename        = "canmathbull.bib",
%%%     address         = "University of Utah
%%%                        Department of Mathematics, 110 LCB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone       = "+1 801 581 5254",
%%%     FAX             = "+1 801 581 4148",
%%%     URL             = "http://www.math.utah.edu/~beebe",
%%%     checksum        = "27683 1840 9126 79656",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at ieee.org (Internet)",
%%%     codetable       = "ISO/ASCII",
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%%%                        math{\'e}matiques, Canadian Mathematical
%%%                        Bulletin",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of the Bulletin
%%%                        canadien de math{\'e}matiques = Canadian
%%%                        Mathematical Bulletin (CODEN CMBUA3, ISSN
%%%                        0008-4395), published by the Canadian
%%%                        Mathematical Society = Soci{\'e}t{\'e}
%%%                        canadienne de math{\'e}matiques.
%%%
%%%                        Publication began with Volume 1, Number 1, in
%%%                        1958.  The journal was published irregularly
%%%                        from 1958 to 1969, and since then, appears
%%%                        quarterly.
%%%
%%%                        Articles may be published in either English
%%%                        or French, and English abstracts are provided
%%%                        for articles in French.
%%%
%%%                        The journal has a World-Wide Web site at
%%%
%%%                            http://www.camel.math.ca/CMS/CMB/
%%%
%%%                        with publication data starting with volume 40
%%%                        (1997).  Electronic full text of articles is
%%%                        available to qualified subscribers, and for
%%%                        older issues, to anyone.
%%%
%%%                        For entries since 1990, entries in this
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%%%                        computer program that converts the journal
%%%                        metadata from the journal's Editorial Office
%%%                        to BibTeX form, ensuring that the entries
%%%                        exactly match the published articles.
%%%
%%%                        At version 1.02, the year coverage looked
%%%                        like this:
%%%
%%%                             1999 (  57)
%%%
%%%                             Article:         57
%%%
%%%                             Total entries:   57
%%%
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%%----------------------------------------------------------------------
%% Acknowledgement abbreviations:

}

@String{ack-nhfb = "Nelson H. F. Beebe, University of Utah, Department
                 of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake
                 City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1
                 801 581 4148, e-mail: \path|beebe@math.utah.edu|,
                 \path|beebe@acm.org|, \path|beebe@ieee.org| (Internet),
                 URL: \path|http://www.math.utah.edu/~beebe/|"}

%%----------------------------------------------------------------------
%% Journal abbreviations:

}

@String{j-CAN-MATH-BULL = "Bulletin canadien de math{\'e}matiques =
                 Canadian Mathematical Bulletin"}

%%----------------------------------------------------------------------
%% Bibliography entries:

}

@Article{Beauzamy:1999:HRP,
  author =       "Bernard Beauzamy",
  title =        "How the Roots of a Polynomial Vary with Its
                 Coefficients: {A} Local Quantitative Result",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "3--12",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "30C10",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "A well-known result, due to Ostrowski, states that if
                 $\Vert P-Q \Vert_2< \varepsilon$, then the roots
                 $(x_j)$ of $P$ and $(y_j)$ of $Q$ satisfy $|x_j
                 -y_j|\le C n \varepsilon^{1/n}$, where $n$ is the
                 degree of $P$ and $Q$. Though there are cases where
                 this estimate is sharp, it can still be made more
                 precise in general, in two ways: first by using
                 Bombieri's norm instead of the classical $l_1$ or $l_2$
                 norms, and second by taking into account the
                 multiplicity of each root. For instance, if $x$ is a
                 simple root of $P$, we show that $|x-y|< C \varepsilon$
                 instead of $\varepsilon^{1/n}$. The proof uses the
                 properties of Bombieri's scalar product and Walsh
                 Contraction Principle.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "30C10",
  journalabbrev = "CMB",
  refnum =       "7281",
}


@Article{Brendle:1999:DPS,
  author =       "J{\"o}rg Brendle",
  title =        "{Dow}'s Principle and ${Q}$-Sets",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "13--24",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "03E05 03E35 54A35",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "A $Q$-set is a set of reals every subset of which is a
                 relative $G_\delta$. We investigate the combinatorics
                 of $Q$-sets and discuss a question of Miller and Zhou
                 on the size $\qq$ of the smallest set of reals which is
                 not a $Q$-set. We show in particular that various
                 natural lower bounds for $\qq$ are consistently
                 strictly smaller than $\qq$.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "03E05 03E35 54A35",
  journalabbrev = "CMB",
  keywords =     "almost disjoint family; almost disjointness principle;
                 cardinal invariants of the continuum; Dow's principle;
                 iterated forcing; $\MA$($\sigma$-centered);
                 pseudointersection number; $Q$-set",
  refnum =       "7276",
}


@Article{Brown:1999:SCD,
  author =       "Tom C. Brown and Ronald L. Graham and Bruce M.
                 Landman",
  title =        "On the Set of Common Differences in {van der
                 Waerden}'s Theorem on Arithmetic Progressions",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "25--36",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "11B25; 05D10",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Analogues of van der Waerden's theorem on arithmetic
                 progressions are considered where the family of all
                 arithmetic progressions, $\AP$, is replaced by some
                 subfamily of $\AP$. Specifically, we want to know for
                 which sets $A$, of positive integers, the following
                 statement holds: for all positive integers $r$ and $k$,
                 there exists a positive integer $n= w'(k,r)$ such that
                 for every $r$-coloring of $[1,n]$ there exists a
                 monochromatic $k$-term arithmetic progression whose
                 common difference belongs to $A$. We will call any
                 subset of the positive integers that has the above
                 property {\em large}. A set having this property for a
                 specific fixed $r$ will be called {\em $r$-large}. We
                 give some necessary conditions for a set to be large,
                 including the fact that every large set must contain an
                 infinite number of multiples of each positive integer.
                 Also, no large set $\{a_{n}: n=1,2,\dots\}$ can have
                 $\liminf\limits_{n \rightarrow \infty}
                 \frac{a_{n+1}}{a_{n}} > 1$. Sufficient conditions for a
                 set to be large are also given. We show that any set
                 containing $n$-cubes for arbitrarily large $n$, is a
                 large set. Results involving the connection between the
                 notions of ``large'' and ``2-large'' are given. Several
                 open questions and a conjecture are presented.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "11B25",
  ams-subject-secondary = "05D10",
  journalabbrev = "CMB",
  refnum =       "7227",
}


@Article{Christensen:1999:OCR,
  author =       "Ole Christensen",
  title =        "Operators with Closed Range, Pseudo-Inverses, and
                 Perturbation of Frames for a Subspace",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "37--45",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "42C15",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Recent work of Ding and Huang shows that if we perturb
                 a bounded operator (between Hilbert spaces) which has
                 closed range, then the perturbed operator again has
                 closed range. We extend this result by introducing a
                 weaker perturbation condition, and our result is then
                 used to prove a theorem about the stability of frames
                 for a subspace.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "42C15",
  journalabbrev = "CMB",
  refnum =       "7262",
}


@Article{Dijkstra:1999:GPT,
  author =       "Jan J. Dijkstra",
  title =        "Generic Partial Two-Point Sets Are Extendable",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "46--51",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "57N05",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "It is shown that under $\ZFC$ almost all planar
                 compacta that meet every line in at most two points are
                 subsets of sets that meet every line in exactly two
                 points. This result was previously obtained by the
                 author jointly with K.~Kunen and J.~van~Mill under the
                 assumption that Martin's Axiom is valid.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "57N05",
  journalabbrev = "CMB",
  refnum =       "7290",
}


@Article{Edmonds:1999:ECB,
  author =       "Allan L. Edmonds",
  title =        "Embedding Coverings in Bundles",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "52--55",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "57M10, 55R25, 55S40, 57N35",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "If $V\to X$ is a vector bundle of fiber dimension $k$
                 and $Y\to X$ is a finite sheeted covering map of degree
                 $d$, the implications for the Euler class $e(V)$ in
                 $H^k(X)$ of $V$ implied by the existence of an
                 embedding $Y\to V$ lifting the covering map are
                 explored. In particular it is proved that $dd'e(V)=0$
                 where $d'$ is a certain divisor of $d-1$, and often
                 $d'=1$.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "57M10, 55R25, 55S40, 57N35",
  journalabbrev = "CMB",
  refnum =       "7277",
}


@Article{Elbert:1999:SFZ,
  author =       "\'Arp\'ad Elbert and Panayiotis D. Siafarikas",
  title =        "On the Square of the First Zero of the {Bessel}
                 Function ${J}_\nu(z)$",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "56--67",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "33A40",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Let $j_{\nu,1}$ be the smallest (first) positive zero
                 of the Bessel function $J_{\nu}(z)$, $\nu>-1$, which
                 becomes zero when $\nu$ approaches $-1$. Then
                 $j_{\nu,1}^{2}$ can be continued analytically to
                 $-2<\nu<-1$, where it takes on negative values. We show
                 that $j_{\nu,1}^{2}$ is a convex function of $\nu$ in
                 the interval $-2<\nu\leq 0$, as an addition to an old
                 result [\'A.~Elbert and A.~Laforgia, SIAM J. Math.
                 Anal. {\bf 15}(1984), 206--212], stating this convexity
                 for $\nu>0$. Also the monotonicity properties of the
                 functions $\frac{j_{\nu,1}^{2}}{4 (\nu+1)}$,
                 $\frac{j_{\nu,1}^{2}}{4(\nu+1)\sqrt{\nu+2}}$ are
                 determined. Our approach is based on the series
                 expansion of Bessel function $J_{\nu}(z)$ and it turned
                 out to be effective, especially when $-2<\nu<-1$.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "33A40",
  journalabbrev = "CMB",
  refnum =       "7139",
}


@Article{Gittenberger:1999:MSD,
  author =       "Bernhard Gittenberger and J{\"o}rg M. Thuswaldner",
  title =        "The Moments of the Sum-Of-Digits Function in Number
                 Fields",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "68--77",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "11A63; 11N60",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "We consider the asymptotic behavior of the moments of
                 the sum-of-digits function of canonical number systems
                 in number fields. Using Delange's method we obtain the
                 main term and smaller order terms which contain
                 periodic fluctuations.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "11A63",
  ams-subject-secondary = "11N60",
  journalabbrev = "CMB",
  refnum =       "7263",
}


@Article{Gonzalez:1999:FJP,
  author =       "Josep Gonz\'alez",
  title =        "{Fermat Jacobians} of Prime Degree over Finite
                 Fields",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "78--86",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "11G20; 14H40",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "We study the splitting of Fermat Jacobians of prime
                 degree $\ell$ over an algebraic closure of a finite
                 field of characteristic $p$ not equal to $\ell$. We
                 prove that their decomposition is determined by the
                 residue degree of $p$ in the cyclotomic field of the
                 $\ell$-th roots of unity. We provide a numerical
                 criterion that allows to compute the absolutely simple
                 subvarieties and their multiplicity in the Fermat
                 Jacobian.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "11G20",
  ams-subject-secondary = "14H40",
  journalabbrev = "CMB",
  refnum =       "7275",
}


@Article{Kittaneh:1999:SNI,
  author =       "Fuad Kittaneh",
  title =        "Some norm inequalities for operators",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "87--96",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "47A30, 47B10, 47B15, 47B20",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Let $A_i$, $B_i$ and $X_i$ $(i=1, 2, \dots, n)$ be
                 operators on a separable Hilbert space. It is shown
                 that if $f$ and $g$ are nonnegative continuous
                 functions on $[0,\infty)$ which satisfy the relation
                 $f(t)g(t) =t$ for all $t$ in $[0,\infty)$, then $$
                 \Biglvert \,\Bigl|\sum^n_{i=1} A^*_i X_i B_i \Bigr|^r
                 \,\Bigrvert^2 \leq \Biglvert \Bigl( \sum^n_{i=1} A^*_i
                 f (|X^*_i|)^2 A_i \Bigr)^r \Bigrvert \, \Biglvert
                 \Bigl( \sum^n_{i=1} B^*_i g (|X_i|)^2 B_i \Bigr)^r
                 \Bigrvert $$ for every $r>0$ and for every unitarily
                 invariant norm. This result improves some known
                 Cauchy-Schwarz type inequalities. Norm inequalities
                 related to the arithmetic-geometric mean inequality and
                 the classical Heinz inequalities are also obtained.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "47A30, 47B10, 47B15, 47B20",
  journalabbrev = "CMB",
  keywords =     "arithmetic-geometric mean inequality; Cauchy-Schwarz
                 inequality; Heinz inequality; positive operator;
                 Unitarily invariant norm",
  refnum =       "7284",
}


@Article{Nikolskaia:1999:IVP,
  author =       "Ludmila Nikolskaia",
  title =        "Instabilit\'e de vecteurs propres d'op\'erateurs
                 lin\'eaires",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "104--117",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "47A10, 46B15",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "We consider some geometric properties of eigenvectors
                 of linear operators on infinite dimensional Hilbert
                 space. It is proved that the property of a family of
                 vectors $(x_n)$ to be eigenvectors $Tx_n= \lambda_n
                 x_n$ ($\lambda_n \noteq \lambda_k$ for $n\noteq k$) of
                 a bounded operator $T$ (admissibility property) is very
                 instable with respect to additive and linear
                 perturbations. For instance, (1)~for the sequence
                 $(x_n+\epsilon_n v_n)_{n\geq k(\epsilon)}$ to be
                 admissible for every admissible $(x_n)$ and for a
                 suitable choice of small numbers $\epsilon_n\noteq 0$
                 it is necessary and sufficient that the perturbation
                 sequence be eventually scalar: there exist $\gamma_n\in
                 \C$ such that $v_n= \gamma_n v_{k}$ for $n\geq k$
                 (Theorem~2); (2)~for a bounded operator $A$ to
                 transform admissible families $(x_n)$ into admissible
                 families $(Ax_n)$ it is necessary and sufficient that
                 $A$ be left invertible (Theorem~4).",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "47A10, 46B15",
  journalabbrev = "CMB",
  keywords =     "eigenvectors; minimal families; reproducing kernels",
  refnum =       "7282",
}


@Article{Rao:1999:PWN,
  author =       "T. S. S. R. K. Rao",
  title =        "Points of Weak$^\ast$-Norm Continuity in the Unit Ball
                 of the Space ${\WC}({K},{X})^\ast$",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "118--124",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "46B20, 46E40",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "For a compact Hausdorff space with a dense set of
                 isolated points, we give a complete description of
                 points of weak$^\ast$-norm continuity in the dual unit
                 ball of the space of Banach space valued functions that
                 are continuous when the range has the weak topology. As
                 an application we give a complete description of points
                 of weak-norm continuity of the unit ball of the space
                 of vector measures when the underlying Banach space has
                 the Radon-Nikodym property.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "46B20, 46E40",
  journalabbrev = "CMB",
  keywords =     "$M$-ideals; Points of weak$^\ast$-norm continuity;
                 space of vector valued weakly continuous functions",
  refnum =       "7280",
}


@Article{Smith:1999:MVI,
  author =       "Larry Smith",
  title =        "Modular Vector Invariants of Cyclic Permutation
                 Representations",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "125--128",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "13A50",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Vector invariants of finite groups (see the
                 introduction for an explanation of the terminology)
                 have often been used to illustrate the difficulties of
                 invariant theory in the modular case: see, \eg.,
                 \cite{Ber}, \cite{norway}, \cite{fossum}, \cite{MmeB},
                 \cite{poly} and \cite{survey}. It is therefore all the
                 more surprising that the {\it unpleasant} properties of
                 these invariants may be derived from two unexpected,
                 and remarkable, {\it nice} properties: namely for
                 vector permutation invariants of the cyclic group
                 $\mathbb{Z}/p$ of prime order in characteristic $p$ the
                 image of the transfer homomorphism $\Tr^{\mathbb{Z}/p}
                 \colon \mathbb{F}[V] \lra \mathbb{F}[V]^{\mathbb{Z}/p}$
                 is a prime ideal, and the quotient algebra
                 $\mathbb{F}[V]^{\mathbb{Z}/p}/ \Im
                 (\Tr^{\mathbb{Z}/p})$ is a polynomial algebra on the
                 top Chern classes of the action.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "13A50",
  journalabbrev = "CMB",
  keywords =     "polynomial invariants of finite groups",
  refnum =       "7271",
}


@Article{Baker:1999:HOA,
  author =       "Andrew Baker",
  title =        "{Hecke} Operations and the {Adams} ${E}_2$-Term Based
                 on Elliptic Cohomology",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "129--138",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "55N20, 55N22, 55T15; 11F11, 11F25",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Hecke operators are used to investigate part of the
                 $\E_2$-term of the Adams spectral sequence based on
                 elliptic homology. The main result is a derivation of
                 $\Ext^1$ which combines use of classical Hecke
                 operators and $p$-adic Hecke operators due to Serre.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "55N20, 55N22, 55T15",
  ams-subject-secondary = "11F11, 11F25",
  journalabbrev = "CMB",
  keywords =     "Adams spectral sequence; elliptic cohomology; Hecke
                 operators",
  refnum =       "7326",
}


@Article{Bonet:1999:ENW,
  author =       "Jos\'e Bonet and Pawe{\l} Doma\'nski and Mikael
                 Lindstr{\"o}m",
  title =        "Essential Norm and Weak Compactness of Composition
                 Operators on Weighted {Banach} Spaces of Analytic
                 Functions",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "139--148",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "47B38; 30D55, 46E15",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Every weakly compact composition operator between
                 weighted Banach spaces $H_v^{\infty}$ of analytic
                 functions with weighted sup-norms is compact. Lower and
                 upper estimates of the essential norm of continuous
                 composition operators are obtained. The norms of the
                 point evaluation functionals on the Banach space
                 $H_v^{\infty}$ are also estimated, thus permitting to
                 get new characterizations of compact composition
                 operators between these spaces.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "47B38",
  ams-subject-secondary = "30D55, 46E15",
  journalabbrev = "CMB",
  keywords =     "compact operator; composition operator; weakly compact
                 operator; weighted Banach spaces of holomorphic
                 functions",
  refnum =       "7306",
}


@Article{Boyer:1999:NFD,
  author =       "S. Boyer and X. Zhang",
  title =        "A Note on Finite {Dehn} Fillings",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "149--154",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "57M25, 57R65",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Let $M$ be a compact, connected, orientable 3-manifold
                 whose boundary is a torus and whose interior admits a
                 complete hyperbolic metric of finite volume. In this
                 paper we show that if the minimal Culler-Shalen norm of
                 a non-zero class in $H_1(\partial M)$ is larger than
                 $8$, then the finite surgery conjecture holds for $M$.
                 This means that there are at most $5$ Dehn fillings of
                 $M$ which can yield manifolds having cyclic or finite
                 fundamental groups and the distance between any slopes
                 yielding such manifolds is at most $3$.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "57M25, 57R65",
  journalabbrev = "CMB",
  refnum =       "7337",
}


@Article{Campbell:1999:NCM,
  author =       "H. E. A. Campbell and A. V. Geramita and I. P. Hughes
                 and R. J. Shank and D. L. Wehlau",
  title =        "Non--{Cohen-Macaulay} Vector Invariants and a
                 {Noether} Bound for a {Gorenstein} Ring of Invariants",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "155--161",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "13A50",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "This paper contains two essentially independent
                 results in the invariant theory of finite groups. First
                 we prove that, for any faithful representation of a
                 non-trivial $p$-group over a field of characteristic
                 $p$, the ring of vector invariants of $m$ copies of
                 that representation is not \comac\ for $m\geq 3$. In
                 the second section of the paper we use Poincar\'e
                 series methods to produce upper bounds for the degrees
                 of the generators for the ring of invariants as long as
                 that ring is Gorenstein. We prove that, for a finite
                 non-trivial group $G$ and a faithful representation of
                 dimension $n$ with $n>1$, if the ring of invariants is
                 Gorenstein then the ring is generated in degrees less
                 than or equal to $n(|G|-1)$. If the ring of invariants
                 is a hypersurface, the upper bound can be improved to
                 $|G|$.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "13A50",
  journalabbrev = "CMB",
  refnum =       "7304",
}


@Article{Cobos:1999:LSC,
  author =       "Fernando Cobos and Thomas K{\"u}hn",
  title =        "{Lorentz-Schatten} Classes and Pointwise Domination of
                 Matrices",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "162--168",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "47B10",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "We investigate pointwise domination property in
                 operator spaces generated by Lorentz sequence spaces.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "47B10",
  journalabbrev = "CMB",
  refnum =       "7309",
}


@Article{Ding:1999:HKL,
  author =       "Hongming Ding",
  title =        "Heat Kernels of {Lorentz} Cones",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "169--173",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "35K05, 43A85; 35K15, 80A20",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "We obtain an explicit formula for heat kernels of
                 Lorentz cones, a family of classical symmetric cones.
                 By this formula, the heat kernel of a Lorentz cone is
                 expressed by a function of time $t$ and two eigenvalues
                 of an element in the cone. We obtain also upper and
                 lower bounds for the heat kernels of Lorentz cones.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "35K05, 43A85",
  ams-subject-secondary = "35K15, 80A20",
  journalabbrev = "CMB",
  keywords =     "eigenvalues; heat equation; heat kernel; Jordan
                 algebra; Laplace-Beltrami operator; Lorentz cone;
                 symmetric cone",
  refnum =       "7315",
}


@Article{Ferrero:1999:RC,
  author =       "Miguel Ferrero and Alveri Sant'Ana",
  title =        "Rings With Comparability",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "174--183",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "16U99; 16P40, 16D14, 16N60",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "The class of rings studied in this paper properly
                 contains the class of right distributive rings which
                 have at least one completely prime ideal in the
                 Jacobson radical. Amongst other results we study prime
                 and semiprime ideals, right noetherian rings with
                 comparability and prove a structure theorem for rings
                 with comparability. Several examples are also given.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "16U99",
  ams-subject-secondary = "16P40, 16D14, 16N60",
  journalabbrev = "CMB",
  refnum =       "7332",
}


@Article{Fiorito:1999:AMS,
  author =       "Giovanni Fiorito",
  title =        "On Arithmetic Means of Sequences Generated by a
                 Periodic Function",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "184--189",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "40A05",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "In this paper we prove the convergence of arithmetic
                 means of sequences generated by a periodic function
                 $\varphi (x) $, moreover if $\varphi (x) $ satisfies a
                 suitable symmetry condition, we prove that their limit
                 is $\varphi (0) $. Applications of previous results are
                 given to study other means of sequences and the
                 behaviour of a class of recursive series.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "40A05",
  journalabbrev = "CMB",
  refnum =       "7292",
}


@Article{Gilmer:1999:TQF,
  author =       "Patrick M. Gilmer",
  title =        "Topological Quantum Field Theory and Strong Shift
                 Equivalence",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "190--197",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "57R99, 57M99, 54H20",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Given a TQFT in dimension $d+1,$ and an infinite
                 cyclic covering of a closed $(d+1)$-dimensional
                 manifold $M$, we define an invariant taking values in a
                 strong shift equivalence class of matrices. The notion
                 of strong shift equivalence originated in R.~Williams'
                 work in symbolic dynamics. The Turaev-Viro module
                 associated to a TQFT and an infinite cyclic covering is
                 then given by the Jordan form of this matrix away from
                 zero. This invariant is also defined if the boundary of
                 $M$ has an $S^1$ factor and the infinite cyclic cover
                 of the boundary is standard. We define a variant of a
                 TQFT associated to a finite group $G$ which has been
                 studied by Quinn. In this way, we recover a link
                 invariant due to D.~Silver and S.~Williams. We also
                 obtain a variation on the Silver-Williams invariant, by
                 using the TQFT associated to $G$ in its unmodified
                 form.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "57R99, 57M99, 54H20",
  journalabbrev = "CMB",
  keywords =     "knot; link; shift equivalence; symbolic dynamics;
                 TQFT",
  refnum =       "7308",
}


@Article{Guadalupe:1999:CAD,
  author =       "Jos\'e J. Guadalupe and Mario P\'erez and Juan L.
                 Varona",
  title =        "Commutators and Analytic Dependence of
                 {Fourier-Bessel} Series on $(0,\infty)$",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "198--208",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "42C10",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "In this paper we study the boundedness of the
                 commutators $[b, S_n]$ where $b$ is a $\BMO$ function
                 and $S_n$ denotes the $n$-th partial sum of the
                 Fourier-Bessel series on $(0,\infty)$. Perturbing the
                 measure by $\exp(2b)$ we obtain that certain operators
                 related to $S_n$ depend analytically on the functional
                 parameter $b$.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "42C10",
  journalabbrev = "CMB",
  keywords =     "$A_p$ weights; BMO; commutators; Fourier-Bessel
                 series",
  refnum =       "7346",
}


@Article{Lanteri:1999:AVB,
  author =       "Antonio Lanteri and Hidetoshi Maeda",
  title =        "Ample Vector Bundles of Curve Genus One",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "209--213",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "14J60; 14F05, 14J40",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "We investigate the pairs $(X,\cE)$ consisting of a
                 smooth complex projective variety $X$ of dimension $n$
                 and an ample vector bundle $\cE$ of rank $n-1$ on $X$
                 such that $\cE$ has a section whose zero locus is a
                 smooth elliptic curve.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "14J60",
  ams-subject-secondary = "14F05, 14J40",
  journalabbrev = "CMB",
  refnum =       "7295",
}


@Article{Paeng:1999:CRS,
  author =       "Seong-Hun Paeng and Jong-Gug Yun",
  title =        "Conjugate Radius and Sphere Theorem",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "214--220",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "53C20, 53C21",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Bessa [Be] proved that for given $n$ and $i_0$, there
                 exists an $\varepsilon(n,i_0)>0$ depending on $n,i_0$
                 such that if $M$ admits a metric $g$ satisfying
                 $\Ric_{(M,g)} \ge n-1$, $\inj_{(M,g)} \ge i_0>0$ and
                 $\diam_{(M,g)} \ge \pi-\varepsilon$, then $M$ is
                 diffeomorphic to the standard sphere. In this note, we
                 improve this result by replacing a lower bound on the
                 injectivity radius with a lower bound of the conjugate
                 radius.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "53C20, 53C21",
  journalabbrev = "CMB",
  keywords =     "conjugate radius; Ricci curvature",
  refnum =       "7335",
}


@Article{Peide:1999:BMS,
  author =       "Liu Peide and Eero Saksman and Hans-Olav Tylli",
  title =        "Boundedness of the $q$-Mean-Square Operator on
                 Vector-Valued Analytic Martingales",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "221--230",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "46B20; 60G46",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "We study boundedness properties of the $q$-mean-square
                 operator $S^{(q)}$ on $E$-valued analytic martingales,
                 where $E$ is a complex quasi-Banach space and $2 \leq q
                 < \infty$. We establish that a.s. finiteness of
                 $S^{(q)}$ for every bounded $E$-valued analytic
                 martingale implies strong $(p,p)$-type estimates for
                 $S^{(q)}$ and all $p\in (0,\infty)$. Our results yield
                 new characterizations (in terms of analytic and
                 stochastic properties of the function $S^{(q)}$) of the
                 complex spaces $E$ that admit an equivalent
                 $q$-uniformly PL-convex quasi-norm. We also obtain a
                 vector-valued extension (and a characterization) of
                 part of an observation due to Bourgain and Davis
                 concerning the $L^p$-boundedness of the usual
                 square-function on scalar-valued analytic
                 martingales.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "46B20",
  ams-subject-secondary = "60G46",
  journalabbrev = "CMB",
  refnum =       "7322",
}


@Article{Rush:1999:GIR,
  author =       "David E. Rush",
  title =        "Generating Ideals in Rings of Integer-Valued
                 Polynomials",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "231--236",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "13B25, 13F20, 13F05",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Let $R$ be a one-dimensional locally analytically
                 irreducible Noetherian domain with finite residue
                 fields. In this note it is shown that if $I$ is a
                 finitely generated ideal of the ring $\Int(R)$ of
                 integer-valued polynomials such that for each $x \in R$
                 the ideal $I(x) =\{f(x) \mid f \in I\}$ is strongly
                 $n$-generated, $n \geq 2$, then $I$ is $n$-generated,
                 and some variations of this result.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "13B25, 13F20, 13F05",
  journalabbrev = "CMB",
  refnum =       "7305",
}


@Article{Thompson:1999:BDA,
  author =       "A. C. Thompson",
  title =        "On {Benson}'s Definition of Area in {Minkowski}
                 Space",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "237--247",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "52A21; 52A38",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Let $(X, \norm)$ be a Minkowski space (finite
                 dimensional Banach space) with unit ball $B$. Various
                 definitions of surface area are possible in $X$. Here
                 we explore the one given by Benson \cite{ben1},
                 \cite{ben2}. In particular, we show that this
                 definition is convex and give details about the nature
                 of the solution to the isoperimetric problem.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "52A21",
  ams-subject-secondary = "52A38",
  journalabbrev = "CMB",
  refnum =       "7342",
}


@Article{Weber:1999:CBC,
  author =       "Christian Weber",
  title =        "The Classification of ${\Pin}_4$-Bundles over a
                 $4$-Complex",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "2",
  pages =        "248--256",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "55N25, 55R10, 57S15",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "In this paper we show that the Lie-group $\Pin_4$ is
                 isomorphic to the semidirect product $(\SU_2\times
                 \SU_2)\timesv \Z/2$ where $\Z/2$ operates by flipping
                 the factors. Using this structure theorem we prove a
                 classification theorem for $\Pin_4$-bundles over a
                 finite $4$-complex $X$.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "55N25, 55R10, 57S15",
  journalabbrev = "CMB",
  refnum =       "7109",
}


@Article{Austin:1999:HKA,
  author =       "David Austin and Dale Rolfsen",
  title =        "Homotopy of Knots and the {Alexander} Polynomial",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "257--262",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "57N10; 57M05, 57M25, 57N65",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Any knot in a 3-dimensional homology sphere is
                 homotopic to a knot with trivial Alexander
                 polynomial.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "57N10",
  ams-subject-secondary = "57M05, 57M25, 57N65",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7407",
}


@Article{Choie:1999:MTM,
  author =       "Youngju Choie and Min Ho Lee",
  title =        "{Mellin} Transforms of Mixed Cusp Forms",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "263--273",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "11F12, 11F66, 11M06; 14K05",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "We define generalized Mellin transforms of mixed cusp
                 forms, show their convergence, and prove that the
                 function obtained by such a Mellin transform of a mixed
                 cusp form satisfies a certain functional equation. We
                 also prove that a mixed cusp form can be identified
                 with a holomorphic form of the highest degree on an
                 elliptic variety.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "11F12, 11F66, 11M06",
  ams-subject-secondary = "14K05",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7347",
}


@Article{Dadarlat:1999:BMN,
  author =       "Marius D\u{a}d\u{a}rlat and S\o ren Eilers",
  title =        "The {Bockstein} Map is Necessary",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "274--284",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "46L35, 46L80, 19K14",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "We construct two non-isomorphic nuclear, stably
                 finite, real rank zero $C^\ast$-algebras $E$ and $E'$
                 for which there is an isomorphism of ordered groups
                 $\Theta\colon \bigoplus_{n \ge 0} K_\bullet(E;\ZZ/n)
                 \to \bigoplus_{n \ge 0} K_\bullet(E';\ZZ/n)$ which is
                 compatible with all the coefficient transformations.
                 The $C^\ast$-algebras $E$ and $E'$ are not isomorphic
                 since there is no $\Theta$ as above which is also
                 compatible with the Bockstein operations. By tensoring
                 with Cuntz's algebra $\OO_\infty$ one obtains a pair of
                 non-isomorphic, real rank zero, purely infinite
                 $C^\ast$-algebras with similar properties.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "46L35, 46L80, 19K14",
  journalabbrev = "CMB",
  keywords =     "Bockstein maps; $C^\ast$-algebras; classification;
                 $K$-theory; natural transformations; purely infinite;
                 real rank zero; torsion coefficients",
  language =     "English",
  refnum =       "7417",
}


@Article{Deng:1999:KSO,
  author =       "Peiming Deng",
  title =        "On {Kloosterman} Sums with Oscillating Coefficients",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "285--290",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "10G10",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "In this paper we prove: for any positive integers $a$
                 and $q$ with $(a,q) =1$, we have uniformly $$
                 \sum_{\substack{n \leq N \\ (n,q) = 1, \,n\on \equiv 1
                 (\mod q)}} \mu (n) e \left( \frac{a\on}{q} \right) \ll
                 Nd (q) \left\{ \frac{\log^{\frac52} N}{q^{\frac12}} +
                 \frac{q^{\frac15} \log^{\frac{13}5} N}{N^{\frac15}}
                 \right\}. $$ This improves the previous bound obtained
                 by D.~Hajela, A.~Pollington and B.~Smith~\cite{5}.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "10G10",
  journalabbrev = "CMB",
  keywords =     "estimate; Kloosterman sums; oscillating coefficients",
  language =     "English",
  refnum =       "7344",
}


@Article{Grubb:1999:SQM,
  author =       "D. J. Grubb and Tim LaBerge",
  title =        "Spaces of Quasi-Measures",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "291--297",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "28C15",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "We give a direct proof that the space of Baire
                 quasi-measures on a completely regular space (or the
                 space of Borel quasi-measures on a normal space) is
                 compact Hausdorff. We show that it is possible for the
                 space of Borel quasi-measures on a non-normal space to
                 be non-compact. This result also provides an example of
                 a Baire quasi-measure that has no extension to a Borel
                 quasi-measure. Finally, we give a concise proof of the
                 Wheeler-Shakmatov theorem, which states that if $X$ is
                 normal and $\dim(X) \le 1$, then every quasi-measure on
                 $X$ extends to a measure.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "28C15",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7323",
}


@Article{Jespers:1999:SAM,
  author =       "Eric Jespers and Jan Okni\'nski",
  title =        "Semigroup Algebras and Maximal Orders",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "298--306",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "16S36, 16H05; 20M25",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "We describe contracted semigroup algebras of Malcev
                 nilpotent semigroups that are prime Noetherian maximal
                 orders.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "16S36, 16H05",
  ams-subject-secondary = "20M25",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7455",
}


@Article{Kapovich:1999:MSS,
  author =       "Michael Kapovich and John J. Millson",
  title =        "On the Moduli Space of a Spherical Polygonal Linkage",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "307--320",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "14D20; 14P05",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "We give a ``wall-crossing'' formula for computing the
                 topology of the moduli space of a closed $n$-gon
                 linkage on $\mathbb{S}^2$. We do this by determining
                 the Morse theory of the function $\rho_n$ on the moduli
                 space of $n$-gon linkages which is given by the length
                 of the last side---the length of the last side is
                 allowed to vary, the first $(n - 1)$ side-lengths are
                 fixed. We obtain a Morse function on the $(n -
                 2)$-torus with level sets moduli spaces of $n$-gon
                 linkages. The critical points of $\rho_n$ are the
                 linkages which are contained in a great circle. We give
                 a formula for the signature of the Hessian of $\rho_n$
                 at such a linkage in terms of the number of back-tracks
                 and the winding number. We use our formula to determine
                 the moduli spaces of all regular pentagonal spherical
                 linkages.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "14D20",
  ams-subject-secondary = "14P05",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7359",
}


@Article{Kikuchi:1999:AOM,
  author =       "Masato Kikuchi",
  title =        "Averaging Operators and Martingale Inequalities in
                 Rearrangement Invariant Function Spaces",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "321--334",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "60G44, 60G46, 46E30",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "We shall study some connection between averaging
                 operators and martingale inequalities in rearrangement
                 invariant function spaces. In Section~2 the equivalence
                 between Shimogaki's theorem and some martingale
                 inequalities will be established, and in Section~3 the
                 equivalence between Boyd's theorem and martingale
                 inequalities with change of probability measure will be
                 established.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "60G44, 60G46, 46E30",
  journalabbrev = "CMB",
  keywords =     "martingale inequalities; rearrangement invariant
                 function spaces",
  language =     "English",
  refnum =       "7354",
}


@Article{Kim:1999:CSS,
  author =       "Goansu Kim and C. T. Yang",
  title =        "Cyclic Subgroup Separability of {HNN}-Extensions with
                 Cyclic Associated Subgroups",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "335--343",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "20E26, 20E06, 20F10",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "We derive a necessary and sufficient condition for
                 HNN-extensions of cyclic subgroup separable groups with
                 cyclic associated subgroups to be cyclic subgroup
                 separable. Applying this, we explicitly characterize
                 the residual finiteness and the cyclic subgroup
                 separability of HNN-extensions of abelian groups with
                 cyclic associated subgroups. We also consider these
                 residual properties of HNN-extensions of nilpotent
                 groups with cyclic associated subgroups.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "20E26, 20E06, 20F10",
  journalabbrev = "CMB",
  keywords =     "cyclic subgroup separable $(\pi_c)$; HNN-extension;
                 nilpotent groups; residually finite",
  language =     "English",
  refnum =       "7107",
}


@Article{Koldobsky:1999:PDD,
  author =       "Alexander Koldobsky",
  title =        "Positive Definite Distributions and Subspaces of
                 ${L}_p$ With Applications to Stable Processes",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "344--353",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "42A82, 46B04, 46F12, 60E07",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "We define embedding of an $n$-dimensional normed space
                 into $L_{-p}$, $0<p<n$ by extending analytically with
                 respect to $p$ the corresponding property of the
                 classical $L_p$-spaces. The well-known connection
                 between embeddings into $L_p$ and positive definite
                 functions is extended to the case of negative $p$ by
                 showing that a normed space embeds in $L_{-p}$ if and
                 only if $\|x\|^{-p}$ is a positive definite
                 distribution. We show that the technique of embedding
                 in $L_{-p}$ can be applied to stable processes in some
                 situations where standard methods do not work. As an
                 example, we prove inequalities of correlation type for
                 the expectations of norms of stable vectors. In
                 particular, for every $p\in [n-3,n)$,
                 $\mathbb{E}(\max_{i=1,\dots,n} |X_i|^{-p}) \ge
                 \mathbb{E}(\max_{i=1,\dots,n} |Y_i|^{-p})$, where
                 $X_1,\dots,X_n$ and $Y_1,\dots,Y_n$ are jointly
                 $q$-stable symmetric random variables, $0<q\le 2$, so
                 that, for some $k\in \mathbb{N}$, $1\le k <n$, the
                 vectors $(X_1,\dots,X_k)$ and $(X_{k+1},\dots,X_n)$
                 have the same distributions as $(Y_1,\dots,Y_k)$ and
                 $(Y_{k+1},\dots,Y_n)$, respectively, but $Y_i$ and
                 $Y_j$ are independent for every choice of $1\le i\le
                 k$, $k+1\le j\le n$.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "42A82, 46B04, 46F12, 60E07",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7367",
}


@Article{Marshall:1999:RHR,
  author =       "Murray A. Marshall",
  title =        "A Real Holomorphy Ring without the {Schm{\"u}dgen}
                 Property",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "354--358",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "12D15, 14P10; 44A60",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "A preordering $T$ is constructed in the polynomial
                 ring $A = \R [t_1,t_2, \dots]$ (countably many
                 variables) with the following two properties: (1)~~For
                 each $f \in A$ there exists an integer $N$ such that
                 $-N \le f(P) \le N$ holds for all $P \in \Sper_T(A)$.
                 (2)~~For all $f \in A$, if $N+f, N-f \in T$ for some
                 integer $N$, then $f \in \R$. This is in sharp contrast
                 with the Schm{\"u}dgen-W{\"o}rmann result that for any
                 preordering $T$ in a finitely generated $\R$-algebra
                 $A$, if property~(1) holds, then for any $f \in A$, $f
                 > 0$ on $\Sper_T(A) \Rightarrow f \in T$. Also,
                 adjoining to $A$ the square roots of the generators of
                 $T$ yields a larger ring $C$ with these same two
                 properties but with $\Sigma C^2$ (the set of sums of
                 squares) as the preordering.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "12D15, 14P10",
  ams-subject-secondary = "44A60",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7312",
}


@Article{Martin:1999:GRB,
  author =       "W. J. Martin and D. R. Stinson",
  title =        "A Generalized {Rao} Bound for Ordered Orthogonal
                 Arrays and $(t,m,s)$-Nets",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "359--370",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "05B15; 65C99",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "In this paper, we provide a generalization of the
                 classical Rao bound for orthogonal arrays, which can be
                 applied to ordered orthogonal arrays and
                 $(t,m,s)$-nets. Application of our new bound leads to
                 improvements in many parameter situations to the
                 strongest bounds (\ie, necessary conditions) for
                 existence of these objects.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "05B15",
  ams-subject-secondary = "65C99",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7286",
}


@Article{Marubayashi:1999:PPI,
  author =       "H. Marubayashi and A. Ueda",
  title =        "Prime and Primary Ideals in a {Pr{\"u}fer} Order in a
                 Simple {Artinian} Ring with Finite Dimension over its
                 Center",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "371--379",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "16H05; 16L30",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Let $Q$ be a simple Artinian ring with finite
                 dimension over its center. An order $R$ in $Q$ is said
                 to be {\it Pr{\"u}fer\/} if any one-sided $R$-ideal is
                 a progenerator. We study prime and primary ideals of a
                 Pr{\"u}fer order under the condition that the center is
                 Pr{\"u}fer. Also we characterize branched and
                 unbranched prime ideals of a Pr{\"u}fer order.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "16H05",
  ams-subject-secondary = "16L30",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7104",
}


@Article{Nurmela:1999:ABO,
  author =       "Kari J. Nurmela and Patric R. J. {\"O}sterg{\aa}rd and
                 Rainer aus dem Spring",
  title =        "Asymptotic Behavior of Optimal Circle Packings in a
                 Square",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "380--385",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "52C15",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "A lower bound on the number of points that can be
                 placed in a square of side $\sigma$ such that no two
                 points are within unit distance from each other is
                 proven. The result is constructive, and the series of
                 packings obtained contains many conjecturally optimal
                 packings.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "52C15",
  journalabbrev = "CMB",
  keywords =     "asymptotic bound; circle packing",
  language =     "English",
  refnum =       "7135",
}


@Article{Polat:1999:MS,
  author =       "Norbert Polat",
  title =        "Minimal Separators",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "386--392",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "05C40",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "A separator of a connected graph $G$ is a set of
                 vertices whose removal disconnects $G$. In this paper
                 we give various conditions for a separator to contain a
                 minimal one. In particular we prove that every
                 separator of a connected graph that has no thick end,
                 or which is of bounded degree, contains a minimal
                 separator.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "05C40",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7093",
}


@Article{Savin:1999:CSR,
  author =       "Gordan Savin",
  title =        "A Class of Supercuspidal Representations of
                 ${G}_2(k)$",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "393--400",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "22E35, 22E50; 11F70",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Let $H$ be an exceptional, adjoint group of type $E_6$
                 and split rank 2, over a $p$-adic field $k$. In this
                 article we discuss the restriction of the minimal
                 representation of $H$ to a dual pair
                 $\PD^{\times}\times G_2(k)$, where $D$ is a division
                 algebra of dimension 9 over $k$. In particular, we
                 discover an interesting class of supercuspidal
                 representations of $G_2(k)$.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "22E35, 22E50",
  ams-subject-secondary = "11F70",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7379",
}


@Article{Swain:1999:LDP,
  author =       "Gordon A. Swain and Philip S. Blau",
  title =        "{Lie} Derivations in Prime Rings With Involution",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "401--411",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "16W10, 16N60, 16W25",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Let $R$ be a non-GPI prime ring with involution and
                 characteristic $\neq 2,3$. Let $K$ denote the skew
                 elements of $R$, and $C$ denote the extended centroid
                 of $R$. Let $\delta$ be a Lie derivation of $K$ into
                 itself. Then $\delta=\rho+\epsilon$ where $\epsilon$ is
                 an additive map into the skew elements of the extended
                 centroid of $R$ which is zero on $[K,K]$, and $\rho$
                 can be extended to an ordinary derivation of $\langle
                 K\rangle$ into $RC$, the central closure.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "16W10, 16N60, 16W25",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7352",
}


@Article{Tai:1999:PD,
  author =       "Yung-Sheng Tai",
  title =        "{Peirce} Domains",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "3",
  pages =        "412--416",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "17C27",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "A theorem of Kor\'anyi and Wolf displays any Hermitian
                 symmetric domain as a Siegel domain of the third kind
                 over any of its boundary components. In this paper we
                 give a simple proof that an analogous realization holds
                 for any self-adjoint homogeneous cone.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "17C27",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7429",
}


@Article{Aziz-Ul-Auzeem:1999:SPR,
  author =       "Abdul Aziz-Ul-Auzeem and B. A. Zarger",
  title =        "Some Properties of Rational Functions with Prescribed
                 Poles",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "4",
  pages =        "417--426",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "26D07",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Let $P(z)$ be a polynomial of degree not exceeding $n$
                 and let $W(z) = \prod^n_{j=1}(z-a_j)$ where $|a_j|> 1$,
                 $j =1,2,\dots, n$. If the rational function $r(z) =
                 P(z)/W(z)$ does not vanish in $|z| < k$, then for $k=1$
                 it is known that $$ |r'(z)| \leq \frac{1}{2} |B'(z)|
                 \Sup_{|z|=1} |r(z)| $$ where $B(Z) = W^\ast(z)/W(z)$
                 and $W^\ast (z) = z^n \overline {W(1/\bar z)}$. In the
                 paper we consider the case when $k>1$ and obtain a
                 sharp result. We also show that $$ \Sup_{|z|=1}
                 \biggl\{ \biggl| \frac{r'(z)}{B'(z)} \biggr| +\biggr|
                 \frac{\bigl(r^\ast (z)\bigr)'}{B'(z)} \biggr| \biggr\}
                 = \Sup_{|z|=1} |r(z)| $$ where $r^\ast (z) = B(z)
                 \overline{r(1/\bar z)}$, and as a consequence of this
                 result, we present a generalization of a theorem of
                 O'Hara and Rodriguez for self-inversive polynomials.
                 Finally, we establish a similar result when supremum is
                 replaced by infimum for a rational function which has
                 all its zeros in the unit circle.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "26D07",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7053",
}


@Article{Berndt:1999:RMI,
  author =       "Bruce C. Berndt and Heng Huat Chan",
  title =        "{Ramanujan} and the Modular $j$-Invariant",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "4",
  pages =        "427--440",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "33C05, 33E05, 11R20, 11R29",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "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.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "33C05, 33E05, 11R20, 11R29",
  journalabbrev = "CMB",
  keywords =     "Hilbert class fields; modular functions; the Borweins'
                 cubic theta-functions",
  language =     "English",
  refnum =       "7376",
}


@Article{Berrizbeitia:1999:PBR,
  author =       "P. Berrizbeitia and P. D. T. A. Elliott",
  title =        "Product Bases for the Rationals",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "4",
  pages =        "441--444",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "11N99; 11N05",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "A sequence of positive rationals generates a subgroup
                 of finite index in the multiplicative positive
                 rationals, and group product representations by the
                 sequence need only a bounded number of terms, if and
                 only if certain related sequences have densities
                 uniformly bounded from below.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "11N99",
  ams-subject-secondary = "11N05",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7242",
}


@Article{Bochnak:1999:SMR,
  author =       "J. Bochnak and W. Kucharz",
  title =        "Smooth Maps and Real Algebraic Morphisms",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "4",
  pages =        "445--451",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "14P05, 14P25",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Let $X$ be a compact nonsingular real algebraic
                 variety and let $Y$ be either the blowup of
                 $\mathbb{P}^n(\mathbb{R})$ along a linear subspace or a
                 nonsingular hypersurface of $\mathbb{P}^m(\mathbb{R})
                 \times \mathbb{P}^n(\mathbb{R})$ of bidegree $(1,1)$.
                 It is proved that a $\mathcal{C}^\infty$ map $f \colon
                 X \rightarrow Y$ can be approximated by regular maps if
                 and only if $f^* \bigl( H^1(Y, \mathbb{Z}/2) \bigr)
                 \subseteq H^1_{\alg} (X,\mathbb{Z}/2)$, where
                 $H^1_{\alg} (X,\mathbb{Z}/2)$ is the subgroup of $H^1
                 (X, \mathbb{Z}/2)$ generated by the cohomology classes
                 of algebraic hypersurfaces in $X$. This follows from
                 another result on maps into generalized flag
                 varieties.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "14P05, 14P25",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7345",
}


@Article{Bradley:1999:FRO,
  author =       "Sean Bradley",
  title =        "Finite Rank Operators in Certain Algebras",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "4",
  pages =        "452--462",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "47D30, 47A15, 47A10",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Let $\Alg(\l)$ be the algebra of all bounded linear
                 operators on a normed linear space $\x$ leaving
                 invariant each member of the complete lattice of closed
                 subspaces $\l$. We discuss when the subalgebra of
                 finite rank operators in $\Alg(\l)$ is non-zero, and
                 give an example which shows this subalgebra may be zero
                 even for finite lattices. We then give a necessary and
                 sufficient lattice condition for decomposing a finite
                 rank operator $F$ into a sum of a rank one operator and
                 an operator whose range is smaller than that of $F$,
                 each of which lies in $\Alg(\l)$. This unifies results
                 of Erdos, Longstaff, Lambrou, and Spanoudakis. Finally,
                 we use the existence of finite rank operators in
                 certain algebras to characterize the spectra of Riesz
                 operators (generalizing results of Ringrose and Clauss)
                 and compute the Jacobson radical for closed algebras of
                 Riesz operators and $\Alg(\l)$ for various types of
                 lattices.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "47D30, 47A15, 47A10",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7050",
}


@Article{Hofmann:1999:GCC,
  author =       "Steve Hofmann and Xinwei Li and Dachun Yang",
  title =        "A Generalized Characterization of Commutators of
                 Parabolic Singular Integrals",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "4",
  pages =        "463--477",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "42B20",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "Let $x=(x_1, \dots, x_n)\in\rz$ and $\dz_\lz
                 x=(\lz^{\az_1}x_1, \dots,\lz^{\az_n}x_n)$, where
                 $\lz>0$ and $1\le \az_1\le\cdots \le\az_n$. Denote
                 $|\az|=\az_1+\cdots+\az_n$. We characterize those
                 functions $A(x)$ for which the parabolic Calder\'on
                 commutator $$ T_{A}f(x)\equiv \pv \int_{\mathbb{R}^n}
                 K(x-y)[A(x)-A(y)]f(y)\,dy $$ is bounded on
                 $L^2(\mathbb{R}^n)$, where $K(\dz_\lz
                 x)=\lz^{-|\az|-1}K(x)$, $K$ is smooth away from the
                 origin and satisfies a certain cancellation property.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "42B20",
  journalabbrev = "CMB",
  keywords =     "commutator; homogeneous space; parabolic $\BMO$
                 Sobolev space; parabolic singular integral; symbol;
                 T1-theorem",
  language =     "English",
  refnum =       "6920",
}


@Article{Pruss:1999:RMA,
  author =       "Alexander R. Pruss",
  title =        "A Remark On the {Moser-Aubin} Inequality For Axially
                 Symmetric Functions On the Sphere",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "4",
  pages =        "478--485",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "26D15; 58G30",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "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.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "26D15",
  ams-subject-secondary = "58G30",
  journalabbrev = "CMB",
  keywords =     "axially symmetric functions; borderline Sobolev
                 inequalities; Moser inequality",
  language =     "English",
  refnum =       "7057",
}


@Article{Sawyer:1999:SF,
  author =       "P. Sawyer",
  title =        "Spherical Functions on ${\SO}_0(p,q)/{\SO}(p)\times
                 {\SO}(q)$",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "4",
  pages =        "486--498",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "33C55; 17B20, 53C35",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "An integral formula is derived for the spherical
                 functions on the symmetric space $G/K=\break
                 \SO_0(p,q)/\SO(p)\times \SO(q)$. This formula allows us
                 to state some results about the analytic continuation
                 of the spherical functions to a tubular neighbourhood
                 of the subalgebra $\a$ of the abelian part in the
                 decomposition $G=KAK$. The corresponding result is then
                 obtained for the heat kernel of the symmetric space
                 $\SO_0(p,q)/\SO (p)\times\SO (q)$ using the Plancherel
                 formula.\par In the Conclusion, we discuss how this
                 analytic continuation can be a helpful tool to study
                 the growth of the heat kernel.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "33C55",
  ams-subject-secondary = "17B20, 53C35",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7214",
}


@Article{Zaharia:1999:CSI,
  author =       "Alexandru Zaharia",
  title =        "Characterizations of Simple Isolated Line
                 Singularities",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "4",
  pages =        "499--506",
  year =         "1999",
  CODEN =        "CMBUA3",
  ISSN =         "0008-4395",
  MRclass =      "32S25; 14B05",
  bibdate =      "Thu Dec 9 08:25:40 MST 1999",
  abstract =     "A line singularity is a function germ $f\colon(\CC
                 ^{n+1},0) \lra\CC$ with a smooth $1$-dimensional
                 critical set $\Sigma=\{(x,y)\in \CC\times \CC^n \mid
                 y=0\}$. An isolated line singularity is defined by the
                 condition that for every $x \neq 0$, the germ of $f$ at
                 $(x,0)$ is equivalent to $y_1^2 +\cdots+y_n ^2$. Simple
                 isolated line singularities were classified by Dirk
                 Siersma and are analogous of the famous $A-D-E$
                 singularities. We give two new characterizations of
                 simple isolated line singularities.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "32S25",
  ams-subject-secondary = "14B05",
  journalabbrev = "CMB",
  language =     "English",
  refnum =       "7401",
}
