*Editors*: D. Bao (San Francisco,
SFSU), D. Blecher (Houston), Bernhard G. Bodmann (Houston), H. Brezis (Paris and Rutgers),
B. Dacorogna (Lausanne), K. Davidson (Waterloo), M. Dugas (Baylor), M.
Gehrke (LIAFA, Paris7), C. Hagopian (Sacramento), R. M. Hardt (Rice), Y. Hattori
(Matsue, Shimane), W. B. Johnson (College Station), M. Rojas (College Station),
Min Ru (Houston), S.W. Semmes (Rice).

*Managing Editor*: K. Kaiser (Houston)

Houston Journal of Mathematics

Contents

**Jacoby, Carol, ** Jacoby Consulting, Long Beach, California (cjacoby@jacobyconsulting.com), and **Loth, Peter, **Sacred Heart University, Fairfield, Connecticut (lothp@sacredheart.edu).

Z_{p}-modules
with partial decomposition bases in L^{δ}_{∞ω}, pp. 1007-1019.

ABSTRACT. We consider the class of mixed Z_{p}-modules
with partial decomposition bases. This class includes those modules classified by Ulm and
Warfield and is closed under L_{∞ω}-equivalence. In the context of
L_{∞ω}-equivalence, Jacoby defined invariants for this class and proved a
classification theorem. Here we examine this class relative to L^{δ}_{∞ω},
those formulas of quantifier rank ≤ some ordinal δ, defining invariants and
proving a classification theorem. This generalizes a result of Barwise and Eklof.

**Wagner Cortes,** Instituto de Matematica, Universidade Federal
do Rio Grande do Sul, 91509-900, Porto Alegre, RS, Brazil (cortes@mat.ufrgs.br)

Prime Goldie ideals in partial skew polynomial rings,
pp. 1021-1033

ABSTRACT. In this paper, we give necessary and sufficient conditions for all prime ideals of partial skew polynomial rings and partial skew Laurent polynomial rings to be right Goldie ideals. Moreover, we give an example to show that our results are not an easy generalization of the global case.

A note on essential extensions and submodules of generators, pp. 1035-1045.

ABSTRACT. This paper investigates when the class of progenerators of Mod-R is closed with respect to finitely generated essential extensions and essential submodules.

A non-commutative analog to E-rings, pp. 1047-1060.

ABSTRACT. Although E-rings are usually studied over commutative rings, they can be defined in a non-commutative setting too. The standard construction methods for E-rings use either the Black Box, colored trees or algebraically independent elements. This paper shows that they can be adapted to obtain E(R)-extension rings of a non-commutative ring R with out significant ring-theoretic restrictions on R beyond those necessary to avoid obvious counter-examples.

**Kowalczyk, Joanna**, Department of Mathematics, Institute of Mathematics, University of Rzeszow, Poland (jkowalcz@univ.rzeszow.pl), **Les, Edyta,** Department of Mathematics, Institute of Mathematics, University of Rzeszow, Poland (eles@univ.rzeszow.pl) and **Sokol, Janusz,** Department of Mathematics, Rzeszow University of Technology, Poland (jsokol@prz.edu.pl.

Radius problems in a certain subclass of close-to-convex functions, pp. 1061-1072.

ABSTRACT. Let K(s, γ) denote the class of all analytic
functions f in the unit disc U with the normalization
f(0)=f'(0)-1=0 and satisfying the condition
Re[zf'(z)/(g(z)g(-z))]>γ, in U, for some g , starlike of order 1/2. In this paper some basic
geometric properties for the class K(s,γ) are
investigated. Among others things, the radius of convexity for the class K(s, gamma) and the sharp upper and lower bounds
for |arg f'(z)| are determined.

Some congruences for trinomial coefficients, pp. 1073-1087.

ABSTRACT. We prove several congruences mod p

On the characterizations for compact composition operators on Bloch space over asmoothly bounded strictly pseudoconvex domain in C

ABSTRACT. Let D be a smoothly bounded strictly pseudoconvex domain in C

Equivariant loops of Hamiltonian diffeomorphisms, pp. 1101-1115.

ABSTRACT. We use Weinstein's homomorphism to detect non trivial loops of Hamiltonian diffeomorphism in the total space of a Hamiltonian fibration. In particular we detect a non-contractible loop in the group of Hamiltonian diffeomorphisms of a ruled surface.

Nadya Askaripour

On extension of holomorphic k-differentials on open Riemann surfaces, pp. 1117-1126.

ABSTRACT. Suppose X is a Riemann surface and C is a subset of X which is an open Riemann surface. We study the problem of extending a holomorphic k-differential on C to a holomorphic k-differential on X.

Classification of Möbius homogeneous hypersurfaces in a 5-dimensional sphere, pp. 1127-1146.

ABSTRACT. In this paper, we classify completely the Möbius homogeneous hypersurfaces in the 5-dimensional sphere S

**Alexi Quevedo Suárez, ** Facultad de Ciencias, Escuela de Matemáticas, Universidad Central de Venezuela, Caracas, Venezuela, (alexi.quevedo@ciens.ucv.ve).

Factorization of mixed operators, pp. 1147-1153.

ABSTRACT. Let T be an operator between Banach spaces that is, for example,
separable, Rosenthal, and decomposing. The real method of interpolation
of Lions-Peetre, for pairs, is used to prove that T factors through a
separable Banach space S that has no subspace isomorphic to l_{1} and whose dual S* has the Radon-Nikodým property. A technique to
produce such factorization spaces for ‘mixed operators’ is introduced.
For this, it is necessary first to prove that many mixed operator ideals possess the
‘strong property of interpolation’ for the real method of Lions-Peetre.

Normal Toeplitz and Hankel Operators with operator-valued symbols, pp. 1155-1181.

ABSTRACT. This paper mainly concerns the characterization of normal Toeplitz operators and normal Hankel operators with operator-valued symbols. We give complete characterizations of those operators and develop some more detailed analysis of normal Hankel operators with matrix-valued symbols.

We also prove that hyponormal Hankel operators with matrix-valued symbols are necessarily normal.

A reduction theory for operators in type I

ABSTRACT. In this paper we study the structures of operators in a type I

**Černý, Robert, **Department of Mathematical Analysis, Charles University,
Sokolovská 83, 186 00 Prague 8, Czech Republic
(rcerny@karlin.mff.cuni.cz), and
**Gurka, Petr, **Department of Mathematics, Czech University of Life Sciences Prague,
165 21 Prague 6, Czech Republic
(gurka@tf.czu.cz) and
Department of Mathematics, College of Polytechnics Jihlava,
Tolstého 16, 586 01 Jihlava, Czech Republic
(gurka@vspj.cz).

Moser-type inequalities for generalized Lorentz-Sobolev spaces pp. 1225-1269.

ABSTRACT. We give sharp constants concerning exponential
and multiple exponential inequalities corresponding to the limiting case of the
Sobolev inequalities in generalized Lorentz-Sobolev spaces of arbitrary order.
This is a natural extension of the result of S. Hencl (J. Funct. Anal., 204 (2003), No. 1, 196-227).
Notice that S. Hencl considers a different norm in the source space.

**Greiwe, Regina,** Department of Mathematics and Statistics, Auburn University,
Auburn, Alabama 36849 (greiwrm@auburn.edu), **Smith, Michel,** Department of Mathematics and Statistics, Auburn University, Auburn, Alabama 36849 (smith01@auburn.edu), and **Stone, Jennifer,** Lee Scott Academy, Auburn, AL, 36830 (jstone@lee-scott.org).

Every non-metric indecomposable
subcontinuum of the square of the lexicographic arc contains an arc, pp. 1271-1284.

ABSTRACT. We prove that if L is the lexicographic arc (the square disc with the
lexicographic order) then every non-metric indecomposable subcontinuum of the
topological product of L with itself contains an arc. A non-metric
indecomposable continuum which does not contain an arc is constructed in the
triple product of L to show that the theorem does not generalize to higher
dimensions. We construct an inverse limit on copies of L which does not embed in
the product of two copies of L.

**Buzyakova, Raushan, ** (Raushan_Buzyakova@yahoo.com) and ** Chigogidze, Alex, **Department of Mathematics,
College of Staten Island,
Staten Island, NY, 10314 (alex.chigogidze@csi.cuny.edu).

Periodic and fixed points of multivalued maps on Euclidean spaces, pp. 1285-1297.

ABSTRACT.
We show, in particular, that a multivalued map **f** from a closed
subspace X of R^{n} to exp_{k}R^{n} has a point of period exactly M
if and only if its continuous extension over β X to exp_{k}(β
R^{n}**)** has such a point. The result also holds if one replaces R^{n} by a locally compact Lindelof space of finite dimension.
We also show that if f is a colorable map from
a normal space X to the space K(X) of all compact subsets of X then its continuous
extension over β X to K(β X) is fixed-point free.

**Tall, Franklin D. **University of Toronto, Toronto, Canada (f.tall@utoronto.ca), and ** Usuba, Toshimichi, **Organization of Advanced Science and Technology, Kobe University, Rokko-dai 1-1, Nada, Kobe, 657-8501, Japan. (usuba@people.kobe-u.ac.jp).

Lindelöf spaces with small pseudocharacter and an analog of Borel's conjecture for subsets of [0, 1]^{ℵ1} , pp. 1299-1309.

ABSTRACT.
We improve results of Shelah, Tall, and Scheepers concerning the cardinality of Lindelof spaces with small pseudocharacter. We establish the consistency of an analog of Borel's Conjecture for subspaces of [0,1]^{ℵ1}.

**Jorge Bustamante**, Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla. Av. San Claudio y Río Verde, C. U., San Manuel, Puebla, Pue., México. C. P. 72570 (jbusta@fcfm.buap.mx), **Włodzimierz J. Charatonik**, Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409 (wcharat@mst.edu), and Raúl Escobedo, Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla. Av. San Claudio y Río Verde, C. U., San Manuel, Puebla, Pue., México. C. P. 72570 (escobedo@fcfm.buap.mx).

Planarity of Whitney levels, pp. 1311-1318.

ABSTRACT. First, we characterize all locally connected continua whose all
Whitney levels are planar. Second, we show by example that planarity
is not a (strong) Whitney reversible property. This answers a
question from Illanes-Nadler book [A. Illanes and S. B. Nadler, Jr., Hyperspaces: Fundamentals and
Recent Advances. Monographs and Textbooks in Pure and Applied
Mathematics, 216, New York: Marcel Dekker, Inc., 1999.]

**Michał Ryszard Wójcik,** Institute of Geography and Regional Development,
University of Wrocław
pl. Uniwersytecki 1, 50-137 Wrocław, Poland (michal.wojcik@uni.wroc.pl).

Continuity in terms of connectedness for functions on the line, pp. 1319-1324.

ABSTRACT. We show that a function from the real line into any space is continuous if and only if it has a connected locally connected graph. More precisely, a function from the real line whose graph is locally connected is continuous at precisely those points at which the function is bilaterally approachable. Alternatively, a function from the real line whose graph is connected is continuous at precisely those points where the graph is locally connected. In the second characterization, connected graph cannot be replaced with the Darboux property. A purely topological example with no set-theoretical arguments like transfinite induction and well-ordering of uncountable sets is given of a Darboux function with a zero-dimensional graph that is continuous on a dense set.

**V. Todorov,** Department of Mathematics, UACG, 1 H. Smirnenski
blvd., 1046 Sofia, Bulgaria (vtt-fte@uacg.bg) and **V. Valov**, Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay,
ON, P1B 8L7, Canada (veskov@nipissingu.ca).

Alexandroff type manifolds and homology manifolds, pp. 1325-1346.

ABSTRACT. We introduce and investigate a special type of metric continua. One of the results related to that class provides a partial answer of
the Bing-Borsuk problem whether any closed partition of a homogeneous metric ANR compactum of dimension n is cyclic in dimension n-1 .
Another result provides an analogue of the classical Mazurkiewicz theorem that no region of the Euclidean n -dimensional space can
be cut by a subset of dimension ≤ n-2. Concerning homology manifolds, it is shown that any arc-wise connected complete metric space, which is either
a homology n-manifold or a product of at least n metric spaces, is a Mazurkiewicz arc n -manifold.

A ladder of curvatures for hypersurfaces in the Euclidean ambient space, pp. 1347-1356.

ABSTRACT. We introduce a string of new curvature invariants of a hypersurface in the real (n+1)-dimensional space and we establish a ladder of inequalities involving these curvature invariants. There is an analogy between this series of inequalities and the classical ladder of power means for positive real numbers. To describe the natural geometric interpretation of our proposed construction we refer to B. Riemann's original idea of sectional curvature

The Cardinal cov(N), D-spaces and monotone normality, pp. 1357-1369.

ABSTRACT. We investigate a class of neighborhood assignments for Lindelöf spaces, which we called harmonious neighborhood assignments. We show that (1)If X is a Lindelöf space and N is a neighborhood assignment for X which has a closed discrete kernel, then N is harmonious; (2)If X is a Lindelöf space of cardinality less than cov(N), then every harmonious neighborhood assignment for X has a closed discrete kernel. We also strengthen a previous result on dual properties of monotonically normal spaces by proving that every neighborhood assignment for a monotonically normal space has a closed kernel which is homeomorphic to some subspace of an ordinal.