*Editors*: G. Auchmuty (Houston), H. Brezis (Paris), S. S. Chern
(Berkeley), J. Damon (Chapel Hill), K. Davidson (Waterloo), L. C. Evans
(Berkeley), R. M. Hardt (Rice), J. A. Johnson (Houston), A. Lelek (Houston), J.
Nagata (Osaka), B. H. Neumann (Canberra), G. Pisier (College Station and Paris),
R. Scott (Houston), S. W. Semmes (Rice)
*Managing Editor*: K. Kaiser (Houston)

** Yoshio Agaoka,** Department of Mathematics, Faculty of Integrated Arts &
Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521, Japan
(agaoka@mis.hiroshima-u.ac.jp).

*A new example of higher order almost flat affine connections on the
three-dimensional sphere,
* pp.387-396

An error has been corrected in Vol. 24, No. 4, 1998.

ABSTRACT.
We give new examples of torsion free affine connections on the three-dimensional
sphere and Brieskorn manifolds with almost vanishing curvature, by considering a
class of left invariant affine connections on Lie groups. These examples
indicate a striking difference between "Riemannian" and "affine" category in
considering the concept "almost flatness".

**J. Llibre,
** Departament de Matemàtiques, Universitat Autònoma de Barcelona,
Bellaterra, 08193 Barcelona, Spain (jllibre@manwe.math.uab.es),
** J. Paraños,** Departamento de Anàlisi Matemàtica, Facultade de
Matemàticas, Universidade de Santiago de Compostela, 15706 Santiago de
Compostela, Spain, and
** J.A. Rodríguez,** Departamento de Matemàticas, Facultad de
Ciencias, Calvo Sotelo s/n, Universidad de Oviedo, 33007 Oviedo, Spain.

*Periods for Transversal Maps on Compact Manifolds with a Given Homology,*
pp. 397-407.

ABSTRACT.Let M be a compact differentiable
manifold such that its rational homology groups are either Q or 0. A
differentiable map f: from M into itself is called transversal if for all
m in N the graph of the m-th iterate of f intersects transversally the
diagonal of M x M at each point (x,x) such that x is a fixed point of the
m-iterate of f.. We study the set of periods of f by using the Lefschetz numbers
for periodic points.

** Rukimbira, Philippe, ** Florida International University, Miami, FL 33199
(rukim@fiu.edu).

* A characterization of flat contact metric Geometry,* pp.409-414.

ABSTRACT. Flat contact metrics exist only in dimension
3. Among the six isometry classes of flat closed 3-manifolds, one consists of
manifolds with trivial first de Rham cohomology. We prove that this particular
classe admits no flat contact metric by showing that a flat closed contact
3-manifold carries a nonsingular parallel vector field and thus has nontrivial
first de Rham cohomology.

**
Lei Fu,**
Institute of Mathematics, Nankai University, Tianjin 300071, China
(leifu@sun.nankai.edu.cn).

* An Analogue of Bernstein's Theorem, * pp. 415-419.

ABSTRACT. We prove the following analogue of
Bernstein's theorem: Let f(x,y) be a smooth function defined on the whole plane.
Then the graph of the gradient of f(x,y) is a minimal surface if and only if
f(x,y) is harmonic or a quadratic polynomial.

**Bejancu, Aurel, **Technical University of Iasi, 6600 Iasi, Romania,
(relu@math.tuiasi.ro),
**Hernández Encinas, Luis, **University of Salamanca, Paseo de Canalejas 169,
37008 Salamanca, Spain, (encinas@gugu.usal.es), and
**Muñoz Masqué, Jaime, **CSIC, Serrano 144, 28006 Madrid, Spain, (jaime@iec.csic.es).

*Invariant Differential Forms on the First Jet Prolongation of the Cotangent
Bundle, * pp.421-442.

ABSTRACT. The structure of the differential forms on J^{1}(T^{*}M)
which are invariant under the natural representacion of the gauge algebra of the
trivial principal bundle, MxU(1), and the structure of the horizontal forms on
the J^{1}(T^{*}M) which are invariant under the Lie algebra of
all infinitesimal automorphisms of MxU(1) are determined.

**D. Buhagiar, ** Department of Mathematics, Shimane University,
Matsue 690-8504, Japan (buhagiar@math.okayama-u.ac.jp) and **T. Miwa, **
Department of Mathematics, Shimane University, Matsue 690-8504, Japan
(miwa@riko.shimane-u.ac.jp).

*On Superparacompact and Lindelöf GO-Spaces,* pp. 443-457.

ABSTRACT.
In this paper we study some compact/paracompact type properties, namely weak
superparacompactness, superparacompactness and Lindelöfness. Particular
attention is given to GO-spaces. It is proved that a GO-space X is weakly
superparacompact if and only if every gap is a W-gap and every pseudogap is a
W-pseudogap. A characterization of Lindelöf GO-spaces involving C-(pseudo)gaps
is given. We also show that there is a 1--1 correspondence between
superparacompact (resp. Lindelöf) GO-d-extensions and preuniversal ODF (resp.
prelindelöf) GO-uniformities. Finally we give several examples corresponding to
the above results.

**C.E.M. Pearce, **Applied Mathematics Department, University of
Adelaide, Adelaide S.A. 5005, Australia (cpearce@maths.adelaide.edu.au), and **
J. Pecaric, ** **V. Simic, **Faculty of Textile Technology, University of
Zagreb, Pierottijeva 6, 41000 Zagreb, Croatia.

*Weighted Generalized Logarithmic Means,* pp. 459-465.

ABSTRACT.
An integral representation of Neuman is extended and used to suggest a
multidimensional weighted generalized logarithmic mean. Some inequalities are
established for such means. A number of known results appear as special cases.

**Chun-Lan Jiang,** Department of Mathematics, Jilin University, Chang Chun,
Jilin, People's Republic of China (cljiang@ns1.hebut.edu.cr), and **Pei Yuan
Wu,** Department of Applied Mathematics, National Chiao Tung University,
Hsinchu, Taiwan, Republic of China (pywu@cc.nctu.edu.tw).

*Sums of strongly irreducible operators,* pp. 467-481.

ABSTRACT.
In 1969, Radjavi proved that every (bounded linear) operator on a complex
separable Hilbert space is the sum of two irreducible operators.

In this paper, we consider the more refined problem whether every operator is
even the sum of two strongly irreducible operators. We are able to show that for
certain classes of operators this does have an affirmative answer. These classes
include those of finite-dimensional operators, triangular operators, multicyclic
operators and compact operators. In general, we can only show that every
operator is the sum of three strongly irreducible operators.

** R.L. Moore, ** and **T.T. Trent, ** Department of Mathematics,
University of Alabama, Tuscaloosa, AL 35487-0350 (rmoore@gp.as.ua.edu).

*Solving Operator Equations in Nest Algebras, * pp. 483-488.

ABSTRACT.
Let X and Y be operators on Hilbert space, and let *L* be a nest of
projections on the space. We consider the problem of finding an operator A in
Alg(*L*) such that A is Hilbert-Schmidt and such that AX = Y. A necessary
and sufficient condition involving X, Y, and the projections in the lattice is
found. We also indicate how the statements of the results can be modified so
that the main theorem is true for any commutative subspace lattice *L*.

**Robbins, D. A.**,** **Department of Mathematics, Trinity College,
Hartford, CT 06106 (david.robbins@mail.trincoll.edu).

*BSE Banach modules and bundles of Banach spaces,* pp. 489-505.

ABSTRACT.
In a recent paper [J. Funct. Anal. 125 (1994), 67-89], S.-E. Takahasi defined
the notion of a *BSE* Banach module over a commutative Banach algebra *A*
with bounded approximate identity. We show that the multiplier algebra *M(X)*
of *X* can be represented as a space of sections in a bundle of Banach
spaces, and we use bundle techniques to obtain shorter versions of various of
Takahasi's results on *C**-algebra modules and to answer several questions
which he raised.

**Ronald G. Douglas** Texas A & M University at College-Station,
TX (rgd@tamu.edu) and **Rongwei Yang** Texas A & M University at
College-Station, TX and Dept. of Mathematics, SUNY at Stonybrook, NY
(rwyang@math.tamu.edu)

*Quotient hardy Modules,* pp. 507-517.

ABSTRACT.
Suppose H^{2}(D^{n}) is the Hardy space over the unit polydisk D^{n},
and [h] is the closed submodule generated by a bounded holomorphic function h in
H^{infty}(D^{n}). The quotient H^{2}(D^{n})/[h]
is an A(D^{n}) module and the coordinate functions z_{1}, z_{2},
..., z_{n} act on H^{2}(D^{n})/[h] as bounded linear
operators. In this paper, we first make a study of the spectral properties of
these operators and reveal how these properties are related to the function h.
Then we will have a look at the analytic continuation problem. At last, we will
show a rigidity phenomenon of quotient Hardy modules.

**Zhuan Ye** Department of Mathematical Sciences Northern Illinois
University, DeKalb, IL 60115 USA (ye@math.niu.edu).

*A Unicity Theorem for Meromorphic Mappings,* pp. 519-531.

ABSTRACT.
We prove a unicity theorem of Nevanlinna for meromorphic mappings of C^{n}
into P^{m}.

**Lang, W. Christopher**, Indiana University Southeast, New Albany,
Indiana 47150
clang@ius.indiana.edu .

*Wavelet analysis on the Cantor dyadic group,* pp. 533-544.

Missing pictures can be found in Vol. 24, No. 4,
1998.

ABSTRACT.
Compactly supported orthogonal wavelets are built on the Cantor dyadic group
(the dyadic or 2-series local field). Necessary and sufficient conditions are
given on a trigonometric polynomial scaling filter for a multiresolution
analysis to result. A Lipschitz regularity condition is defined and an
unconditional
*L ^{p}*-convergence result is given for regular wavelet expansions
(

**James C. Alexander,** Department of Mathematics, University of Maryland
College Park, College Park, MD 20742-4015, USA (jca@math.umd.edu) and **Thomas
I. Seidman,** Department of Mathematics and Statistics, University of Maryland
Baltimore County, Baltimore, MD 21250, USA (seidman@math.umbc.edu).

* Sliding Modes in Intersecting Switching Surfaces, I: Blending,
* pp. 545-569.

ABSTRACT. When a flow, discontinuous across a
switching surface, points `inward' so one cannot leave, it induces a unique flow
within the surface, called the
*sliding mode*. When several such surfaces intersect, one would seek a
flow within the intersection, but some difficulties arise. We explore here the
extent of the ambiguity involved in this situation and then show that for a
certain form of `natural mechanism for implementation' (sigmoid blending) one
does indeed inherit, as a residual effect of this implementation, sufficient
information to characterize a well-defined sliding mode in the intersection of
two switching surfaces.