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3  Sweeping out properties of operator sequences Akcoglu, Mustafa A.; Ha, Dzung M.; Jones, Roger L.
Let $L_p=L_p(X,\mu)$, $1\leq p\leq\infty$, be the usual Banach
Spaces of real valued functions on a complete nonatomic
probability space. Let $(T_1,\ldots,T_{K})$ be
$L_2$contractions. Let $0<\varepsilon < \delta\leq1$. Call a
function $f$ a $\delta$spanning function if $\f\_2 = 1$ and if
$\T_kfQ_{k1}T_kf\_2\geq\delta$ for each $k=1,\ldots,K$, where
$Q_0=0$ and $Q_k$ is the orthogonal projection on the subspace spanned
by $(T_1f,\ldots,T_kf)$. Call a function $h$ a
$(\delta,\varepsilon)$sweeping function if $\h\_\infty\leq1$,
$\h\_1<\varepsilon$, and if
$\max_{1\leq k\leq K}T_kh>\delta\varepsilon$ on a set of
measure greater than $1\varepsilon$. The following is the main
technical result, which is obtained by elementary estimates. There
is an integer $K=K(\varepsilon,\delta)\geq1$ such that if $f$ is a
$\delta$spanning function, and if the joint distribution
of $(f,T_1f,\ldots,T_Kf)$ is normal, then $h=\bigl((f\wedge
M)\vee(M)\bigr)/M$
is a $(\delta,\varepsilon)$sweeping function, for some $M>0$.
Furthermore, if $T_k$s are the averages of operators induced by
the iterates of a measure preserving ergodic transformation, then a
similar result is true without requiring that the joint distribution
is normal. This gives the following theorem on a sequence $(T_i)$ of
these averages. Assume that for each $K\geq1$ there is a subsequence
$(T_{i_1},\ldots,T_{i_K})$ of length $K$, and a $\delta$spanning
function $f_K$ for this subsequence. Then for each $\varepsilon>0$
there is a function $h$,
$0\leq h\leq1$,
$\h\_1<\varepsilon$, such that $\limsup_iT_ih\geq\delta$ a.e..
Another application of the main result gives a refinement of a part
of Bourgain's ``Entropy Theorem'', resulting in a
different, self contained proof of that theorem.


24  Spatial branching processes and subordination Bertoin, Jean; Le Gall, JeanFrançois; Le Jan, Yves
We present a subordination theory for spatial branching processes. This
theory is developed in three different settings, first for branching Markov
processes, then for superprocesses and finally for the pathvalued process
called the {\it Brownian snake}. As a common feature of these three
situations, subordination can be used to generate new branching
mechanisms. As an application, we investigate the compact support
property for superprocesses with a general branching mechanism.


55  Normal Functions: $L^p$ Estimates Chen, Huaihui; Gauthier, Paul M.
For a meromorphic (or harmonic) function $f$, let us call the dilation
of $f$ at $z$ the ratio of the (spherical) metric at $f(z)$ and the
(hyperbolic) metric at $z$. Inequalities are known which estimate
the $\sup$ norm of the dilation in terms of its $L^p$ norm, for $p>2$,
while capitalizing on the symmetries of $f$. In the present paper
we weaken the hypothesis by showing that such estimates persist
even if the $L^p$ norms are taken only over the set of $z$ on which
$f$ takes values in a fixed spherical disk. Naturally, the bigger
the disk, the better the estimate. Also, We give estimates for
holomorphic functions without zeros and for harmonic functions in
the case that $p=2$.


74  Constrained approximation in Sobolev spaces Hu, Y. K.; Kopotun, K. A.; Yu, X. M.
Positive, copositive, onesided and intertwining (coonesided) polynomial
and spline approximations of functions $f\in\Wp^k\mll$ are considered.
Both uniform and pointwise estimates, which are exact in some sense, are
obtained.


100  Multiplication Invariant Subspaces of Hardy Spaces Lance, T. L.; Stessin, M. I.
This paper studies closed subspaces $L$
of the Hardy spaces $H^p$ which are $g$invariant ({\it i.e.},
$g\cdot L \subseteq L)$ where $g$ is inner, $g\neq 1$. If
$p=2$, the Wold decomposition theorem implies that there is
a countable ``$g$basis'' $f_1, f_2,\ldots$ of
$L$ in the sense that $L$ is a direct sum of spaces
$f_j\cdot H^2[g]$ where $H^2[g] = \{f\circ g \mid f\in H^2\}$.
The basis elements $f_j$ satisfy the
additional property that $\int_T f_j^2 g^k=0$,
$k=1,2,\ldots\,.$ We call such functions $g$$2$inner.
It also
follows that any $f\in H^2$ can be factored $f=h_{f,2}\cdot
(F_2\circ g)$ where $h_{f,2}$ is $g$$2$inner and $F$ is
outer, generalizing the classical Riesz factorization.
Using $L^p$ estimates for the canonical decomposition of
$H^2$, we find a factorization $f=h_{f,p} \cdot (F_p \circ
g)$ for $f\in H^p$. If $p\geq 1$ and $g$ is a finite
Blaschke product we obtain, for any $g$invariant
$L\subseteq H^p$, a finite $g$basis of $g$$p$inner
functions.


119  Automorphisms of the Lie algebras $W^*$ in characteristic $0$ Osborn, J. Marshall
No abstract.


133  Exterior powers of the adjoint representation Reeder, Mark
Exterior powers of the adjoint representation of a complex semisimple Lie
algebra are decomposed into irreducible representations, to varying
degrees of satisfaction.


160  The Classical Limit of Dynamics for Spaces Quantized by an Action of ${\Bbb R}^{\lowercase{d}}$ Rieffel, Marc A.
We have previously shown how to construct a deformation quantization
of any locally compact space on which a vector group acts. Within this
framework we show here that, for a natural class of Hamiltonians, the
quantum evolutions will have the classical evolution as their
classical limit.


175  Orthogonal Polynomials for a Family of Product Weight Functions on the Spheres Xu, Yuan
Based on the theory of spherical harmonics for measures invariant
under a finite reflection group developed by Dunkl recently, we study
orthogonal polynomials with respect to the weight functions
$x_1^{\alpha_1}\cdots x_d^{\alpha_d}$ on the unit sphere $S^{d1}$ in
$\RR^d$. The results include explicit formulae for orthonormal polynomials,
reproducing and Poisson kernel, as well as intertwining operator.


193  Classifying PL $5$manifolds by regular genus: the boundary case Casali, Maria Rita
In the present paper, we face the problem of classifying classes of
orientable PL $5$manifolds $M^5$ with $h \geq 1$ boundary components,
by making use of a combinatorial invariant called {\it regular genus}
${\cal G}(M^5)$. In particular, a complete classification up to
regular genus five is obtained:
$${\cal G}(M^5) = \gG \leq 5 \Longrightarrow M^5 \cong \#_{\varrho
 \gbG}(\bdo) \# \smo_{\gbG},$$
where $\gbG = {\cal G}(\partial M^5)$ denotes the regular genus of
the boundary $\partial M^5$ and $\smo_{\gbG}$ denotes the connected
sum of $h\geq 1$ orientable $5$dimensional handlebodies
$\cmo_{\alpha_i}$ of genus $\alpha_i\geq 0$
($i=1,\ldots, h$), so that $\sum_{i=1}^h \alpha_i = \gbG.$
\par
Moreover, we give the following characterizations of orientable PL
$5$manifolds $M^5$ with boundary satisfying particular conditions
related to the ``gap'' between ${\cal G}(M^5)$ and either
${\cal G}(\partial M^5)$ or the rank of their fundamental group
$\rk\bigl(\pi_1(M^5)\bigr)$:
$$\displaylines{{\cal G}(\partial M^5)= {\cal G}(M^5)
= \varrho \Longleftrightarrow M^5 \cong \smo_{\gG}\cr
{\cal G}(\partial M^5)= \gbG = {\cal G}(M^5)1 \Longleftrightarrow
M^5 \cong (\bdo) \# \smo_{\gbG}\cr
{\cal G}(\partial M^5)= \gbG = {\cal G}(M^5)2 \Longleftrightarrow
M^5 \cong \#_2 (\bdo) \# \smo_{\gbG}\cr
{\cal G}(M^5) = \rk\bigl(\pi_1(M^5)\bigr)= \varrho \Longleftrightarrow
M^5 \cong \#_{\gG  \gbG}(\bdo) \# \smo_{\gbG}.\cr}$$
\par
Further, the paper explains how the above results (together with
other known properties of regular genus of PL manifolds) may lead
to a combinatorial approach to $3$dimensional Poincar\'e Conjecture.


212  Differential equations defined by the sum of two quasihomogeneous vector fields Coll, B.; Gasull, A.; Prohens, R.
In this paper we prove, that under certain hypotheses,
the planar differential equation: $\dot x=X_1(x,y)+X_2(x,y)$,
$\dot y=Y_1(x,y)+Y_2(x,y)$, where $(X_i,Y_i)$, $i=1$, $2$, are
quasihomogeneous vector fields, has at most two limit cycles.
The main tools used in the proof are the generalized polar
coordinates, introduced by Lyapunov to study the stability of degenerate
critical points, and the analysis of the derivatives of the Poincar\'e
return map. Our results generalize those obtained for polynomial
systems with homogeneous nonlinearities.


232  Spectral theory for the Neumann Laplacian on planar domains with hornlike ends Edward, Julian
The spectral theory for the Neumann Laplacian on planar domains with
symmetric, hornlike ends is studied. For a large class of such domains,
it is proven that the Neumann Laplacian has no singular continuous
spectrum, and that the pure point spectrum consists of eigenvalues
of finite multiplicity which can accumulate only at $0$ or $\infty$.
The proof uses Mourre theory.


263  Determinantal forms for symplectic and orthogonal Schur functions Hamel, A. M.
Symplectic and orthogonal Schur functions can be defined
combinatorially in a manner similar to the classical Schur functions.
This paper demonstrates that they can also be expressed as determinants.
These determinants are generated using planar decompositions of tableaux
into strips and the equivalence of these determinants to symplectic or
orthogonal Schur functions is established by GesselViennot lattice path
techniques. Results for rational (also called {\it composite}) Schur functions
are also obtained.


283  The $2$rank of the class group of imaginary bicyclic biquadratic fields McCall, Thomas M.; Parry, Charles J.; Ranalli, Ramona R.
A formula is obtained for the rank of the $2$Sylow subgroup of the
ideal class group of imaginary bicyclic biquadratic fields. This
formula involves the number of primes that ramify in the field, the
ranks of the $2$Sylow subgroups of the ideal class groups of the
quadratic subfields and the rank of a $Z_2$matrix determined by
Legendre symbols involving pairs of ramified primes. As
applications, all subfields with both $2$class and class group
$Z_2 \times Z_2$ are determined. The final results assume the
completeness of D.~A.~Buell's list of imaginary fields with small
class numbers.


301  On some alternative characterizations of Riordan arrays Merlini, Donatella; Rogers, Douglas G.; Sprugnoli, Renzo; Verri, M. Cecilia
We give several new characterizations of Riordan Arrays, the most
important of which is: if $\{d_{n,k}\}_{n,k \in {\bf N}}$ is a lower
triangular array whose generic element $d_{n,k}$ linearly depends on
the elements in a welldefined though large area of the array, then
$\{d_{n,k}\}_{n,k \in {\bf N}}$ is Riordan. We also provide some
applications of these characterizations to the lattice path theory.


321  A complete convergence theorem for attractive reversible nearest particle systems Mountford, T. S.
In this paper we prove a complete convergence theorem for
attractive, reversible, supercritical nearest particle systems
satisfying a natural regularity condition. In particular this implies
that under these conditions there exist precisely two extremal
invariant measures. The result we prove is relevant to question seven
of Liggett (1985), Chapter~VII.


338  Local bifurcations of critical periods in the reduced Kukles system Rousseau, C.; Toni, B.
In this paper, we study the local bifurcations of critical periods
in the neighborhood of a nondegenerate centre of the reduced Kukles
system. We find at the same time the isochronous systems. We show
that at most three local critical periods bifurcate from the
ChristopherLloyd centres of finite order, at most
two from the linear isochrone and at most one critical period from the
nonlinear isochrone. Moreover, in all cases, there exist
perturbations which lead to the maximum number of critical
periods. We determine the isochrones, using the method of Darboux:
the linearizing transformation of an isochrone is derived from the
expression of the first integral.
Our approach is a combination of computational algebraic techniques
(Gr\"obner bases, theory of the resultant, Sturm's algorithm), the
theory of ideals of noetherian rings and the transversality theory
of algebraic curves.


359  Estimates for the heat kernel on $\SL (n,{\bf R})/\SO (n)$ Sawyer, P.
In \cite{Anker}, JeanPhilippe Anker conjectures an upper bound for the
heat kernel of a symmetric space of noncompact type. We show in this
paper that his prediction is verified for the space of positive
definite $n\times n$ real matrices.


373  Limit transitions for BC type multivariable orthogonal polynomials Stokman, Jasper V.; Koornwinder, Tom H.
Limit transitions will be derived between the five parameter
family of AskeyWilson polynomials, the four parameter family of
big $q$Jacobi polynomials and the three parameter family of little
$q$Jacobi polynomials in $n$ variables associated with root system $\BC$.
These limit transitions generalize the known hierarchy structure between
these families in the one variable case. Furthermore it will be proved
that these three families are $q$analogues of the three parameter
family of $\BC$ type Jacobi polynomials in $n$ variables. The limit
transitions will be derived by taking limits of $q$difference operators
which have these polynomials as eigenfunctions.


405  On Hurwitz constants for Fuchsian groups Vulakh, L. Ya.
Explicit bounds for the Hurwitz constants for general cofinite
Fuchsian groups have been found. It is shown that the bounds
obtained are exact for the Hecke groups and triangular groups with
signature $(0:2,p,q)$.


417  Characteristic cycles in Hermitian symmetric spaces Boe, Brian D.; Fu, Joseph H. G.
We give explicit combinatorial expresssions for the characteristic
cycles associated to certain canonical sheaves on Schubert varieties
$X$ in the classical Hermitian symmetric spaces: namely the
intersection homology sheaves $IH_X$ and the constant sheaves $\Bbb
C_X$. The three main cases of interest are the Hermitian symmetric
spaces for groups of type $A_n$ (the standard Grassmannian), $C_n$
(the Lagrangian Grassmannian) and $D_n$. In particular we find that
$CC(IH_X)$ is irreducible for all Schubert varieties $X$ if and only
if the associated Dynkin diagram is simply laced. The result for
Schubert varieties in the standard Grassmannian had been established
earlier by Bressler, Finkelberg and Lunts, while the computations in
the $C_n$ and $D_n$ cases are new.


468  Fine spectra and limit laws I. Firstorder laws Burris, Stanley; Sárközy, András
Using FefermanVaught techniques we show a certain property of the fine
spectrum of an admissible class of structures leads to a firstorder law.
The condition presented is best possible in the sense that if it is
violated then one can find an admissible class with the same fine
spectrum which does not have a firstorder law. We present three
conditions for verifying that the above property actually holds.
The first condition is that the count function of an admissible class
has regular variation with a certain uniformity of convergence. This
applies to a wide range of admissible classes, including those
satisfying Knopfmacher's Axiom A, and those satisfying Bateman
and Diamond's condition.
The second condition is similar to the first condition, but designed
to handle the discrete case, {\it i.e.}, when the sizes of the structures
in an admissible class $K$ are all powers of a single integer. It applies
when either the class of indecomposables or the whole class satisfies
Knopfmacher's Axiom A$^\#$.
The third condition is also for the discrete case, when there is a
uniform bound on the number of $K$indecomposables of any given size.


499  Gorenstein Witt rings II Fitzgerald, Robert W.
The abstract Witt rings which are Gorenstein have been classified
when the dimension is one and the classification problem for those of
dimension zero has been reduced to the case of socle degree three. Here we
classifiy the Gorenstein Witt rings of fields with dimension zero and
socle degree three. They are of elementary type.


520  Classical orthogonal polynomials as moments Ismail, Mourad E. H.; Stanton, Dennis
We show that the Meixner, Pollaczek, MeixnerPollaczek, the continuous
$q$ultraspherical polynomials and AlSalamChihara polynomials, in
certain normalization, are moments of probability measures. We use
this fact to derive bilinear and multilinear generating functions for
some of these polynomials. We also comment on the corresponding formulas
for the Charlier, Hermite and Laguerre polynomials.


543  Some summation theorems and transformations for $q$series Ismail, Mourad E. H.; Rahman, Mizan; Suslov, Sergei K.
We introduce a double sum extension of a very wellpoised series and
extend to this the transformations of Bailey and Sears as well as the
${}_6\f_5$ summation formula of F.~H.~Jackson and the $q$Dixon sum.
We also give $q$integral representations of the double sum.
Generalizations of the NassrallahRahman integral are also found.


568  A counterexample in $L^p$ approximation by harmonic functions Mateu, Joan
For ${n \over {n2}}\leq p<\infty$ we show that the
conditions $C_{2,q}(G\setminus \dox)=C_{2,q}(G \setminus
X)$ for all open sets $G$, $C_{2,q}$ denoting Bessel capacity, are not
sufficient to characterize the compact
sets $X$ with the property that each function harmonic on $\dox$
and in $L^p(X)$ is the limit in the $L^p$ norm of a sequence
of functions which are harmonic on neighbourhoods of $X$.


583  Summing up the dynamics of quadratic Hamiltonian systems with a center Pal, Janos; Schlomiuk, Dana
In this work we study the global geometry of planar quadratic
Hamiltonian systems with a center and we sum up the dynamics of
these systems in geometrical terms. For this we use the
algebrogeometric concept of multiplicity of intersection
$I_p(P,Q)$ of two complex projective curves $P(x,y,z) = 0$,
$Q(x,y,z) = 0$ at a point $p$ of the plane. This is a
convenient concept when studying polynomial systems and it
could be applied for the analysis of other classes of nonlinear
systems.


600  The Schreier technique for subalgebras of a free Lie algebra Rosset, Shmuel; Wasserman, Alon
In group theory Schreier's technique provides a basis for a
subgroup of a free group. In this paper an analogue is developed
for free Lie algebras. It hinges on the idea of cutting a Hall set
into two parts. Using it, we show that proper subalgebras of finite
codimension are not finitely generated and, following M.~Hall,
that a finitely generated subalgebra is a free factor of a
subalgebra of finite codimension.


617  On the zeros of some genus polynomials Stahl, Saul
In the genus polynomial of the graph $G$, the coefficient of $x^k$
is the number of distinct embeddings of the graph $G$ on the
oriented surface of genus $k$. It is shown that for several
infinite families of graphs all the zeros of the genus polynomial
are real and negative. This implies that their coefficients, which
constitute the genus distribution of the graph, are log concave and
therefore also unimodal. The geometric distribution of the zeros
of some of these polynomials is also investigated and some new
genus polynomials are presented.


641  Fine spectra and limit laws II Firstorder 01 laws. Burris, Stanley; Compton, Kevin; Odlyzko, Andrew; Richmond, Bruce
Using FefermanVaught techniques a condition on the fine
spectrum of an admissible class of structures is found
which leads to a firstorder 01 law.
The condition presented is best possible in the
sense that if it is violated then one can find an admissible
class with the same fine spectrum which does not have
a firstorder 01 law.
If the condition is satisfied (and hence we have a firstorder %% 01 law)


653  On $\lowercase{q}$Carleson measures for spaces of ${\cal M}$harmonic functions Cascante, Carme; Ortega, Joaquin M.
In this paper we study the $q$Carleson measures for a space $h_\alpha^p$
of ${\cal M}$harmonic potentials in the unit ball of $\C^n$, when
$q<p$. We obtain some computable sufficient conditions, and study the
relations among them.


675  Some adjunctiontheoretic properties of codimension two nonsingular subvarities of quadrics de Cataldo, Mark Andrea A.
We make precise the structure of the first two reduction morphisms
associated with codimension two nonsingular subvarieties
of nonsingular quadrics $\Q^n$, $n\geq 5$.
We give a coarse classification of the same class of subvarieties
when they are assumed not to be of loggeneraltype.}


696  Geodesic flow on ideal polyhedra Charitos, Charalambos; Tsapogas, Georgios
In this work we study the geodesic flow on $n$dimensional ideal polyhedra
and establish classical (for manifolds of negative curvature) results
concerning the distribution of closed orbits of the flow.


708  Density questions for the truncated matrix moment problem Duran, Antonio J.; LopezRodriguez, Pedro
For a truncated matrix moment problem, we describe in detail
the set of positive definite matrices of measures $\mu$ in $V_{2n}$ (this is
the set of solutions of the problem of degree $2n$) for which the polynomials
up to degree $n$ are dense in the corresponding space ${\cal L}^2(\mu)$.
These matrices of measures are exactly the extremal measures of the set $V_n$.


722  Galois module structure of the integers in wildly ramified $C_p\times C_p$ extensions Elder, G. Griffith; Madan, Manohar L.
Let $L/K$ be a finite Galois extension of local fields which are finite
extensions of $\bQ_p$, the field of $p$adic numbers. Let $\Gal (L/K)=G$,
and $\euO_L$ and $\bZ_p$ be the rings of integers in $L$ and $\bQ_p$,
respectively. And let $\euP_L$ denote the maximal ideal of $\euO_L$. We
determine, explicitly in terms of specific indecomposable $\bZ_p[G]$modules,
the $\bZ_p[G]$module structure of $\euO_L$ and $\euP_L$, for $L$, a
composite of two arithmetically disjoint, ramified cyclic extensions of
$K$, one of which is only weakly ramified in the sense of Erez \cite{erez}.


736  Dilations of one parameter Semigroups of positive Contractions on $L^{\lowercase {p}}$ spaces Fendler, Gero
It is proved in this note, that a strongly continuous semigroup of
(sub)positive contractions acting on an $L^p$space, for $1<p<\infty$
$p \not= 2$, can be dilated by a strongly continuous group of
(sub)positive isometries
in a manner analogous to the dilation M.~A.~Ak\c{c}oglu and
L.~Sucheston constructed for a discrete semigroup of
(sub)positive contractions. From this an improvement of a
von Neumann type estimation,
due to R.~R.~Coifman and G.~Weiss, on the transfer map
belonging to the semigroup is deduced.


749  Twisted HasseWeil $L$functions and the rank of MordellWeil groups Howe, Lawrence
Following a method outlined by Greenberg, root
number computations give a conjectural lower bound for the ranks of
certain MordellWeil groups of elliptic curves. More specifically,
for $\PQ_{n}$ a \pgl{{\bf Z}/p^{n}{\bf Z}}extension of ${\bf Q}$ and
$E$ an elliptic curve over {\bf Q}, define the motive $E \otimes
\rho$, where $\rho$ is any irreducible representation of
$\Gal (\PQ_{n}/{\bf Q})$. Under some restrictions, the root number in
the conjectural functional equation for the $L$function of $E
\otimes \rho$ is easily computible, and a `$1$' implies, by the
Birch and SwinnertonDyer conjecture, that $\rho$ is found in
$E(\PQ_{n}) \otimes {\bf C}$. Summing the dimensions of such $\rho$
gives a conjectural lower bound of
$$
p^{2n}  p^{2n  1}  p  1
$$
for the rank of $E(\PQ_{n})$.


772  Finite dimensional representations of $U_t\bigl(\rmsl (2)\bigr)$ at roots of unity Jie, Xiao
All finite dimensional indecomposable representations of
$U_t (\rmsl (2))$ at roots of $1$ are determined.


788  Trace functions in the ring of fractions of polycyclic group rings, II Lichtman, A. I.
We prove the existence of trace functions in the rings of fractions of
polycyclicbyfinite group rings or their homomorphic images. In
particular a trace function exists in the ring of fractions of $KH$,
where $H$ is a polycyclicbyfinite group and $\char K > N$, where
$N$ is a constant depending on $H$.


798  Boundedness of solutions of parabolic equations with anisotropic growth conditions Yu, Minqi; Lian, Xiting
In this paper, we consider the parabolic equation
with anisotropic growth conditions, and obtain some criteria on
boundedness of solutions, which generalize the corresponding results
for the isotropic case.


810  The Zero Distribution of Orthogonal Rational Functions on the Unit Circle Pan, K.
Rational functions orthogonal on the unit circle with prescribed
poles lying outside the unit circle are studied. We use the potential
theory to discuss the zeros distribution for the orthogonal rational
functions.


820  Sur l'intégrabilité des sousalgèbres de Lie en dimension infinie Robart, Thierry
Une des questions fondamentales de la th\'eorie des groupes de
Lie de dimension infinie concerne l'int\'egrabilit\'e des
sousalg\`ebres de Lie topologiques $\cal H$ de l'alg\`ebre
de Lie $\cal G$ d'un groupe de Lie $G$ de dimension infinie
au sens de Milnor. Par contraste avec ce qui se passe en
th\'eorie classique il peut exister des sousalg\`ebres de Lie
ferm\'ees $\cal H$ de $\cal G$ nonint\'egrables en un
sousgroupe de Lie. C'est le cas des alg\`ebres de Lie de champs
de vecteurs $C^{\infty}$ d'une vari\'et\'e compacte qui ne
d\'efinissent pas un feuilletage de Stefan. Heureusement cette
``imperfection" de la th\'eorie n'est pas partag\'ee par tous les
groupes de Lie int\'eressants. C'est ce que montre cet article
en exhibant une tr\`es large classe de groupes de Lie de
dimension infinie exempte de cette imperfection. Cela permet de
traiter compl\`etement le second probl\`eme fondamental de
Sophus Lie pour les groupes de jauge de la
physiquemath\'ematique et les groupes formels de
diff\'eomorphismes lisses de $\R^n$ qui fixent l'origine.


840  NonHermitian solutions of algebraic Riccati equation Rodman, Leiba
Nonhermitian solutions of algebraic matrix Riccati
equations (of the continuous and discrete types) are studied. Existence
is proved of nonhermitian solutions with given upper bounds of the
ranks of the skewhermitian parts, under the sign controllability
hypothesis.


855  Rational Classification of simple function space components for flag manifolds. Smith, Samuel Bruce
Let $M(X,Y)$ denote the space of all continous functions
between $X$ and $Y$ and $M_f(X,Y)$ the path component
corresponding to a given map $f: X\rightarrow Y.$ When $X$ and
$Y$ are classical flag manifolds, we prove the components of
$M(X,Y)$ corresponding to ``simple'' maps $f$ are classified
up to rational homotopy type by the dimension of the kernel of
$f$ in degree two
cohomology. In fact, these components are themselves all products
of flag manifolds and odd spheres.


865  Maps in locally orientable surfaces and integrals over real symmetric surfaces Goulden, I. P.; Jackson, D. M.
The genus series for maps is the generating series for the
number of rooted maps with a given number of vertices and
faces of each degree, and a given number of edges. It captures
topological information about surfaces, and appears in questions
arising in statistical mechanics, topology, group rings,
and certain aspects of free probability theory. An expression
has been given previously for the genus series for maps in
locally orientable surfaces in terms of zonal polynomials. The
purpose of this paper is to derive an integral representation
for the genus series. We then show how this can be used in
conjunction with integration techniques to determine the genus
series for monopoles in locally orientable surfaces. This
complements the analogous result for monopoles in orientable
surfaces previously obtained by Harer and Zagier. A conjecture,
subsequently proved by Okounkov, is given for the evaluation
of an expectation operator acting on the Jack symmetric function.
It specialises to known results for Schur functions and zonal
polynomials.


883  Proof of a conjecture of Goulden and Jackson Okounkov, Andrei
We prove an integration formula involving Jack polynomials
conjectured by I.~P.~Goulden and D.~M.~Jackson in connection with
enumeration of maps in surfaces.


887  Polynomials with $\{ 0, +1, 1\}$ coefficients and a root close to a given point Borwein, Peter; Pinner, Christopher
For a fixed algebraic number $\alpha$ we
discuss how closely $\alpha$ can be approximated by
a root of a $\{0,+1,1\}$ polynomial of given degree.
We show that the worst rate of approximation tends to
occur for roots of unity, particularly those of small degree.
For roots of unity these bounds depend on
the order of vanishing, $k$, of the polynomial at $\alpha$.
In particular we obtain the following. Let
${\cal B}_{N}$ denote the set of roots of all
$\{0,+1,1\}$ polynomials of degree at most $N$ and
${\cal B}_{N}(\alpha,k)$ the roots of those
polynomials that have a root of order at most $k$
at $\alpha$. For a Pisot number $\alpha$ in $(1,2]$
we show that
\[
\min_{\beta \in {\cal B}_{N}\setminus \{ \alpha \}} \alpha
\beta \asymp \frac{1}{\alpha^{N}},
\]
and for a root of unity $\alpha$ that
\[
\min_{\beta \in {\cal B}_{N}(\alpha,k)\setminus \{\alpha\}}
\alpha \beta\asymp \frac{1}{N^{(k+1) \left\lceil
\frac{1}{2}\phi (d)\right\rceil +1}}.
\]
We study in detail the case of $\alpha=1$, where, by far, the
best approximations are real.
We give fairly precise bounds on the closest real root to 1.
When $k=0$ or 1 we
can describe the extremal polynomials explicitly.


916  Quantization of the $4$dimensional nilpotent orbit of SL(3,$\mathbb{R}$) Brylinski, Ranee
We give a new geometric model for the quantization
of the 4dimensional conical (nilpotent) adjoint orbit
$O_\mathbb{R}$ of SL$(3,\mathbb{R})$. The space of quantization is the space of
holomorphic functions on $\mathbb{C}^2 \{ 0 \}$ which are square integrable
with respect to a signed measure defined by a Meijer $G$function.
We construct the quantization out a nonflat Kaehler structure on
$\mathbb{C}^2  \{ 0 \}$ (the universal cover of $O_\mathbb{R}$ ) with Kaehler potential
$\rho=z^4$.


944  Approximation by multiple refinable functions Jia, R. Q.; Riemenschneider, S. D.; Zhou, D. X.
We consider the shiftinvariant space,
$\bbbs(\Phi)$, generated by a set $\Phi=\{\phi_1,\ldots,\phi_r\}$
of compactly supported distributions on $\RR$ when the vector of
distributions $\phi:=(\phi_1,\ldots,\phi_r)^T$ satisfies a system
of refinement equations expressed in matrix form as
$$
\phi=\sum_{\alpha\in\ZZ}a(\alpha)\phi(2\,\cdot  \,\alpha)
$$
where $a$ is a finitely supported sequence of $r\times r$ matrices
of complex numbers. Such {\it multiple refinable functions} occur
naturally in the study of multiple wavelets.


963  Homomorphisms from $C(X)$ into $C^*$algebras Lin, Huaxin
Let $A$ be a simple $C^*$algebra
with real rank zero, stable rank one and weakly
unperforated $K_0(A)$ of countable rank. We show that
a monomorphism $\phi\colon C(S^2) \to A$ can be approximated
pointwise by homomorphisms from $C(S^2)$ into $A$ with
finite dimensional range if and only if certain index
vanishes. In particular, we show that every homomorphism
$\phi$ from $C(S^2)$ into a UHFalgebra can be approximated
pointwise by homomorphisms from $C(S^2)$ into the UHFalgebra
with finite dimensional range. As an application, we show
that if $A$ is a simple $C^*$algebra of real rank zero
and is an inductive limit of matrices over $C(S^2)$ then
$A$ is an AFalgebra. Similar results for tori are also
obtained. Classification of ${\bf Hom}\bigl(C(X),A\bigr)$
for lower dimensional spaces is also studied.


1010  A characterization of two weight norm inequalities for onesided operators of fractional type Lorente, Maria
In this paper we give a characterization of the pairs
of weights $(\w,v)$ such that $T$ maps $L^p(v)$ into
$L^q(\w)$, where $T$ is a general onesided operator
that includes as a particular case the Weyl fractional
integral. As an application we solve the following problem:
given a weight $v$, when is there a nontrivial weight
$\w$ such that $T$ maps $L^p(v)$ into $L^q(\w )$?


1034  Ray sequences of best rational approximants for $x^\alpha$ Saff, E. B.; Stahl, H.
The convergence behavior of best uniform rational
approximations $r^\ast_{mn}$ with numerator degree~$m$
and denominator degree~$n$ to the function $x^\alpha$,
$\alpha>0$, on $[1,1]$ is investigated. It is assumed
that the indices $(m,n)$ progress along a ray sequence in
the lower triangle of the Walsh table, {\it i.e.} the
sequence of indices $\{ (m,n)\}$ satisfies
$$
{m\over n}\rightarrow c\in [1, \infty)\quad\hbox{as } m+
n\rightarrow\infty.
$$
In addition to the convergence behavior, the asymptotic
distribution of poles and zeros of the approximants and the
distribution of the extreme points of the error function
$x^\alpha  r^\ast_{mn} (x)$ on $[1,1]$ will be studied.
The results will be compared with those for paradiagonal
sequences $(m=n+2[\alpha/2])$ and for sequences of best
polynomial approximants.


1066  Multiparameter Variational Eigenvalue Problems with Indefinite Nonlinearity Shibata, Tetsutaro
We consider the multiparameter nonlinear SturmLiouville problem
$$\displaylines{
u''(x)  \sum_{k=1}^m\mu_k u(x)^{p_k} + \sum_{k=m+1}^n
\mu_ku(x)^{p_k} = \lambda u(x)^q, \quad x \in I := (1,1), \cr
u(x) > 0, \quad x \in I, \cr
u(1) = u(1) = 0,\cr}$$
where $\mu = (\mu_1, \mu_2, \ldots, \mu_m, \mu_{m+1}, \ldots \mu_n)
\in \bar{R}_+^m \times R_+^{nm} \bigl(R_+ := (0, \infty)\bigr)$
and $\lambda \in R$ are parameters. We assume that
$$1 \le q \le p_1 < p_2 < \cdots < p_n < 2q + 3.$$
We shall establish an asymptotic formula of
variational eigenvalue $\lambda = \lambda(\mu,\alpha)$ obtained
by using LjusternikSchnirelman theory on general level set
$N_{\mu,\alpha} (\alpha > 0:$ parameter of level set).
Furthermore, we shall give the optimal condition of
$\{(\mu, \alpha)\}$, under which $\mu_i (m + 1 \le i \le n:
\hbox{\rm fixed})$ dominates the asymptotic behavior of
$\lambda(\mu,\alpha)$.


1089  Sets on which measurable functions are determined by their range Burke, Maxim R.; Ciesielski, Krzysztof
We study sets on which measurable realvalued functions on a
measurable space with negligibles are determined by their range.


1117  The von Neumann algebra $\VN(G)$ of a locally compact group and quotients of its subspaces Hu, Zhiguo
Let $\VN(G)$ be the von Neumann algebra of a locally
compact group $G$. We denote by $\mu$ the initial
ordinal with $\abs{\mu}$ equal to the smallest cardinality
of an open basis at the unit of $G$ and $X= \{\alpha;
\alpha < \mu \}$. We show that if $G$ is nondiscrete
then there exist an isometric $*$isomorphism $\kappa$
of $l^{\infty}(X)$ into $\VN(G)$ and a positive linear
mapping $\pi$ of $\VN(G)$ onto $l^{\infty}(X)$ such that
$\pi\circ\kappa = \id_{l^{\infty}(X)}$ and $\kappa$ and
$\pi$ have certain additional properties. Let $\UCB
(\hat{G})$ be the $C^{*}$algebra generated by
operators in $\VN(G)$ with compact support and
$F(\hat{G})$ the space of all $T \in \VN(G)$ such that
all topologically invariant means on $\VN(G)$ attain the
same value at $T$. The construction of the mapping $\pi$
leads to the conclusion that the quotient space $\UCB
(\hat{G})/F(\hat{G})\cap \UCB(\hat{G})$ has
$l^{\infty}(X)$ as a continuous linear image if $G$ is
nondiscrete. When $G$ is further assumed to be
nonmetrizable, it is shown that $\UCB(\hat{G})/F
(\hat{G})\cap \UCB(\hat{G})$ contains a linear
isomorphic copy of $l^{\infty}(X)$. Similar results are
also obtained for other quotient spaces.


1139  Majorations effectives pour l'équation de Fermat généralisée Kraus, Alain
Soient $A$, $B$ et $C$ trois entiers
non nuls premiers entre eux deux \`a deux, et $p$ un nombre premier.
Comme cons\'equence des travaux de A. Wiles et F. Diamond sur la
conjecture de TaniyamaWeil, on explicite une constante $f(A,B,C)$
telle que, sous certaines conditions portant sur $A$, $B$ et $C$,
l'\'equation $Ax^p+By^p+Cz^p=0$ n'a aucune solution non triviale
dans $\Z$, si $p$ est $>f(A,B,C)$. On d\'emontre par ailleurs,
sans condition suppl\'ementaire portant sur $A$, $B$ et $C$, que
cette \'equation n'a aucune solution non triviale dans $\Z$, si
$p$ divise $xyz$, et si $p$ est $>f(A,B,C)$.


1162  Isoperimetric inequalities on surfaces of constant curvature Ku, HsuTung; Ku, MeiChin; Zhang, XinMin
In this paper we introduce the concepts of hyperbolic and elliptic
areas and prove uncountably many new geometric isoperimetric
inequalities on the surfaces of constant curvature.


1188  Factorization in the invertible group of a $C^*$algebra Leen, Michael J.
In this paper we consider the following problem:
Given a unital \cs\ $A$ and a collection of elements $S$ in the
identity component of the invertible group of $A$, denoted \ino,
characterize the group of finite products of elements of $S$. The
particular $C^*$algebras studied in this paper are either
unital purely infinite simple or of the form \tenp, where $A$ is
any \cs\ and $K$ is the compact operators on an infinite dimensional
separable Hilbert space. The types of elements used in the
factorizations are unipotents ($1+$ nilpotent), positive invertibles
and symmetries ($s^2=1$). First we determine the groups of finite
products for each collection of elements in \tenp. Then we give
upper bounds on the number of factors needed in these cases. The main
result, which uses results for \tenp, is that for $A$ unital purely
infinite and simple, \ino\ is generated by each of these collections
of elements.


1206  Subalgebras which appear in quantum Iwasawa decompositions Letzter, Gail
Let $g$ be a semisimple Lie algebra. Quantum analogs of the
enveloping algebra of the fixed Lie subalgebra are introduced for
involutions corresponding to the negative of a diagram automorphism.
These subalgebras of the quantized enveloping algebra specialize to
their classical counterparts. They are used to form an Iwasawa type
decompostition and begin a study of quantum HarishChandra modules.


1224  Tensor products of analytic continuations of holomorphic discrete series Ørsted, Bent; Zhang, Genkai
We give the irreducible decomposition
of the tensor product of an analytic continuation of
the holomorphic discrete
series of $\SU(2, 2)$ with its conjugate.


1242  $1$complemented subspaces of spaces with $1$unconditional bases Randrianantoanina, Beata
We prove that if $X$ is a complex strictly monotone sequence
space with $1$un\con\di\tion\al basis, $Y \subseteq X$ has no bands
isometric to $\ell_2^2$ and $Y$ is the range of normone projection from
$X$, then $Y$ is a closed linear span a family of mutually
disjoint vectors in $X$.


1265  Hecke algebras and classgroup invariant Snaith, V. P.
Let $G$ be a finite group. To a set of subgroups of order two we associate
a $\mod 2$ Hecke algebra and construct a homomorphism, $\psi$, from its
units to the classgroup of ${\bf Z}[G]$. We show that this homomorphism
takes values in the subgroup, $D({\bf Z}[G])$. Alternative constructions of
Chinburg invariants arising from the Galois module structure of
higherdimensional algebraic $K$groups of rings of algebraic integers
often differ by elements in the image of $\psi$. As an application we show
that two such constructions coincide.


1281  Pieri's formula via explicit rational equivalence Sottile, Frank
Pieri's formula describes the intersection product of a Schubert
cycle by a special Schubert cycle on a Grassmannian.
We present a new geometric proof,
exhibiting an explicit chain of rational equivalences
from a suitable sum of distinct Schubert cycles
to the intersection of a Schubert cycle with a special
Schubert cycle. The geometry of these rational equivalences
indicates a link to a combinatorial proof of Pieri's formula using
Schensted insertion.


1299  The explicit solution of the $\bar\partial$Neumann problem in a nonisotropic Siegel domain Tie, Jingzhi
In this paper, we solve the $\dbar$Neumann problem
on $(0,q)$ forms, $0\leq q \leq n$, in the strictly
pseudoconvex nonisotropic Siegel domain:
\[
\cU=\left\{
\begin{array}{clc}
&\bz=(z_1,\ldots,z_n) \in \C^{n},\\
(\bz,z_{n+1}):&&\Im (z_{n+1}) > \sum_{j=1}^{n}a_j z_j^2 \\
&z_{n+1}\in \C;
\end{array}
\right\},
\]
where $a_j> 0$ for $j=1,2,\ldots, n$. The metric we
use is invariant under the action of the Heisenberg
group on the domain. The fundamental solution of the
related differential equation is derived via the
Laguerre calculus. We obtain an explicit formula for
the kernel of the Neumann operator. We also construct
the solution of the corresponding heat equation and
the fundamental solution of the Laplacian operator
on the Heisenberg group.


1323  Stable parallelizability of partially oriented flag manifolds II Sankaran, Parameswaran; Zvengrowski, Peter
In the first paper with the same title the authors
were able to determine all partially oriented flag
manifolds that are stably parallelizable or
parallelizable, apart from four infinite families
that were undecided. Here, using more delicate
techniques (mainly Ktheory), we settle these
previously undecided families and show that none of
the manifolds in them is stably parallelizable,
apart from one 30dimensional manifold which still
remains undecided.


1340  Author Index  Index des auteurs 1997, for 1997  pour
No abstract.

