*Editors*: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao
(Houston), H. Brezis (Paris), J. Damon (Chapel Hill), K. Davidson (Waterloo), C.
Hagopian (Sacramento), R. M. Hardt (Rice), J. Hausen (Houston), J. A. Johnson
(Houston), J. Nagata (Osaka), V. I. Paulsen (Houston), G. Pisier (College
Station and Paris), S. W. Semmes (Rice)
*Managing Editor*: K. Kaiser (Houston)

Houston Journal of Mathematics

*Contents*

**D.D. Anderson, **Department of Mathematics, The University of Iowa, Iowa
City, Iowa 52242-1419, U.S.A.
(dan-anderson@uiowa.edu) and
**Tiberiu Dumitrescu, **Facultatea de Matematică, Universitatea Bucureşti, 14
Academiei Str., Bucharest, RO 70109, Romania
(tiberiu@al.math.unibuc.ro).

Half Condensed Domains,
pp. 929-936.

ABSTRACT.
An integral domain *D* is condensed (resp., strongly condensed) if for each
pair of ideals *I*, *J* of *D*,
*IJ*={*ij* ; *i* in *I*, *j* in *J*} (resp.,
*IJ=iJ* for some *i* in *I* or *IJ =Ij* for some *j* in *
J*). In this paper we introduce and study the two related notions of a half
condensed domain and a strongly half condensed domain. An integral domain *D*
is half condensed if whenever a nonzero *z* is in *IJ* with *I*, *
J* ideals of *D*, there exist *I'*, *J'* (invertible) ideals
of *D* such that *I'* is a subset of *I*, *J'* is a subset
of *J*, and *zD=I'J'*. And *D* is strongly half condensed if
whenever *I*, *J* are nonzero ideals of *D*,
*IJ=I*_{1}*J* for some invertible ideal *I*_{1}
that is a subset of *I* or
*IJ=IJ*_{1} for some invertible ideal *J*_{1}
that is a subset of *J*.

**John Harding ** and **Guram Bezhanishvili, **Department of
Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003-0001,
USA (jharding@nmsu.edu), (gbezhani@nmsu.edu).

MacNeille Completions of
Heyting Algebras, pp. 937-952.

ABSTRACT.
In this note we provide a topological description of the MacNeille completion
of a Heyting algebra similar to the description of the MacNeille completion of a
Boolean algebra in terms of regular open sets of its Stone space. We also show
that the only varieties of Heyting algebras that are closed under MacNeille
completions are the trivial variety, the variety of all Boolean algebras, and
the variety of all Heyting algebras.

**Amir Khosravi, **Faculty of Mathematical Sciences and Computer
Engineering, University For Teacher Education, 599 Taleghani Ave., Tehran 15614,
IRAN, and **Behrooz Khosravi, ** Dept. of Pure Math., Faculty of Math. and
Computer Science, Amirkabir University of Technolog (Tehran Polytechnic),
424, Hafez Ave., Tehran 15914, IRAN
(khosravibbb@yahoo.com).

A New Characterization of Some
Alternating and Symmetric Groups (II), pp. 953-967.

ABSTRACT.
The order of every finite group G can be expressed as a product of coprime
positive integers m_{1},...,m_{t} such that the set of prime
numbers divided m_{i} is a connected component of the prime graph of G.
The integers m_{1},...,m_{t} are called the order components of
G. Order components of a finite group are introduced in Chen (J. Algebra 15
(1996) 184).

There exist some characterizations about alternating and symmetric groups. Some
non-abelian simple groups are known to be uniquely determined by their order
components. In this paper, we suppose that p=2^{a} x^{b}+1>5 be
a prime number, where a,b>0 are positive integers and x>3 is an odd prime
number. Then by using the classification of finite simple groups, we proved that
A_{p}, A_{p+1}, A_{p+2}, S_{p}, S_{p+1},
are also uniquely determined by their order components. As corollaries of these
results, the validity of a conjecture of J. G. Thompson and a conjecture of W.
Shi and J. Bi both on A_{n}, where n=p, p+1 or p+2 are obtained. Also we
generalize these conjectures for the groups S_{n}, where n=p, p+1.

**Coffman, Adam, **Indiana University - Purdue University Fort Wayne, Fort
Wayne, IN 46805
(http://www.ipfw.edu/math/Coffman/).

Analytic Normal Form for CR
Singular Surfaces in
**C**^{3},
pp. 969-996.

ABSTRACT.
A real analytic surface inside complex 3-space with an isolated, non-degenerate
complex tangent is shown to be holomorphically equivalent to a fixed real
algebraic variety. The analyticity of the normalizing transformation is proved
using a rapid convergence argument. Real surfaces in higher dimensions are also
shown to have an algebraic normal form.

**Hao Fang, ** Courant Institute of Mathematical Sciences, New York
University, New York 10012, USA and **Changyou Wang, **
Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA
(cywang@ms.uky.edu).

On the Mean Curvature Flow for σ_{k}-Convex
Hypersurfaces,
pp. 997-1007.

ABSTRACT.
We obtain estimates on both size and dimensions of the singular set at the first
blow-up time of the mean curvature flow of hypersurfaces whose initial data is σ_{k}-convex.

**Erdem, Sadettin,
** Middle East Technical University, 06531 Ankara, Turkey.
(saerdem@fef.sdu.edu.tr ) or ( serdem@metu.edu.tr ).

J-Pseudo Harmonic Morphisms, Some
Subclasses And Their Liftings To Tangent Bundles,
pp. 1009-1038.

ABSTRACT.
New subclasses of J- pseudo harmonic morphisms F of a (semi-) Rumanian manifold
( M, g) into a metric (para-) f-manifold (N,h,J ) are introduced, namely;
nearly, quasi, semi homothetic harmonic maps. On the way, some characterizations
of its tension field of F are given. Also liftings of J-pseudo harmonic
morphisms F to the tangent bundles TM and TN, with various type of lifted metric
(para-) f-structures are considered. Finally, some supporting examples are
provided.

**Garcia-Ferreira, S.,** Instituto de Matemáticas (UNAM), Apartado Postal
61-3, Xangari, 58089, Morelia, Michoacán, México (sgarcia@matmor.unam.mx), **
Sakai, S.,** Department of Mathematics, Kanagawa University, Yokohama
221-8686, Japan (sakaim01@kanagawa-u.ac.jp), and
**Sanchis, M.,** Departament de Matemátiques, Universitat Jaume I, Campus Riu
Sec, 12071, Castelló, Spain (sanchis@mat.uji.es).

Free topological groups over ω_{μ}-metrizable
spaces , pp 1039-1053.

ABSTRACT.
Let be an uncountable regular cardinal. For a Tychonoff space X, we let A(X) and
F(X) be the free Abelian topological group and the free topological group over
X, respectively. In this paper, we establish the next equivalences.

Theorem. Let X be a space. The following are equivalent.

1. (X,U_{X}) is an -metrizable uniform space, where is the universal
uniformity on X.

2. A(X) is topologically orderable and χ(A(X)) =ω_{μ} .

3. The derived set is ω_{μ}-compact and X is ω_{μ}-metrizable.

Theorem. Let X be a non-discrete space. Then, the following are equivalent.

1. X is ω_{μ}-compact and ω_{μ}-metrizable.

2. (X,U_{X}) is ω_{μ}-metrizable and X is ω_{μ}-compact.

3. F(X) is topologically orderable and χ(F(X)) =ω_{μ} .

We also prove that an ω_{μ}-metrizable uniform space (X,U) is a
retract of its uniform free Abelian group A(X,U) and of its uniform free group
F(X,U).

**Naotsugu Chinen,** University of Tsukuba, Ibraki 305-8571, Japan
(naochin@math.tsukuba.ac.jp).

Sets of all ω-limit points for
one-dimensional maps, pp. 1055-1068.

ABSTRACT.
Let f be a continuous map from a graph G to itself and m the maximum of orders
of all points of G. The main result of this paper is that a point c in G lies in
the limit set of some point of G if and only if every open neighborhood of c
contains at least (m + 1) points of some trajectory. This shows that every set
of all limit points for every graph map satisfies the analogue to the Birkhoff
theorem. But, the above does not holds for one-dimensional maps.

**J.J. Charatonik,** Instituto de Matematicas, UNAM, Cd. Universitaria,
04510 Mexico, D.F., Mexico (jjc@matem.unam.mx), **W.J. Charatonik,**
Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla,
MO 65409-0020, U.S.A. (wjcharat@umr.edu) and **J.R. Prajs,** Department of
Mathematics, Idaho State University, Pocatello, ID 83209, U.S.A. (prajs@isu.edu)

Atriodic absolute retracts
for hereditarily unicoherent continua, pp. 1069-1087.

ABSTRACT.
Let X be an absolute retract for the class of hereditarily unicoherent continua
that contains no simple triod. In the paper we prove that (a) X is atriodic; (b)
X is either an arc or an indecomposable continuum having only arcs as its proper
subcontinua; (c) if X is either tree-like or circle-like, then it is arc-like.

**Jonathan Hatch, **Department of Mathematical Sciences, University of
Delaware, Newark, DE 19716 (hatch@math.udel.edu).

On a characterization of W-sets,
pp. 1089-1101.

ABSTRACT.
A proper subcontinuum H of a continuum X is said to be a W-set provided for each
continuous surjective function f from a continuum Y onto X, there exists a
subcontinuum C of Y that maps entirely onto H. Descriptions, definitions, and
results concerning two new types of W-sets are given, as well as a new
characterization of W-sets.

**Louis Block**, Department of Mathematics, University of Florida,
Gainesville, FL 32611-8105,
(block@math.ufl.edu) and
**James Keesling**, Department of Mathematics, University of Florida,
Gainesville, FL 32611-8105,
(jek@math.ufl.edu).

Topological Entropy and Adding
Machine Maps, pp. 1103-1113.

ABSTRACT.
We prove two theorems which extend known theorems concerning periodic orbits and
topological entropy in one-dimensional dynamics. Our first result may be
described as follows. Given a sequence of prime numbers, we form the
corresponding adding machine map (also called the odometer map). We then
determine the infimum of the topological entropies of all continuous maps of the
interval which contain a copy of the given adding machine map. Our second result
deals with the following question. Suppose we are given a closed subset of the
interval and a continuous map of this closed subset to itself. How do we extend
the given map to a map of the entire interval which has the smallest possible
entropy?

**Gady Kozma, **
Faculty of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel
(gadykozma@hotmail.com), (gadyk@wisdom.weizmann.ac.il).

On removing one point from a
compact space, pp. 1115-1126.

ABSTRACT.
If B is a compact space such that after removing one point x it is still
Lindelof, then any power of B satisfies that after removing one point (namely
the point all whose coordinates are x) it is still star-Lindelof. If after
removing one point B is still compact, then any power of B, after removing one
point is still discretely star-Linedlof. In particular, this gives new examples
of Tychonoff, discretely star-Lindelof spaces with unlimited extent.

**R. Lowen **and **S. Verwulgen, **
Department of Mathematics, University of Antwerp, Antwerp 2020, Belgium
(rlow@ruca.ua.ac.be), (vwulgen@ruca.ua.ac.be).

Approach Vector Spaces, pp.
1127-1142.

ABSTRACT.
In this paper we determine what properties an approach structure has to fulfil
for it to concord well with a vector space structure. Not surprisingly these
conditions are more subtle than those for a topology. That the conditions we
impose are the right ones follows mainly from the good categorical relationship
among the different categories which play an important role in this setting,
namely topological vector spaces, completely regular spaces, metrizable vector
spaces and of course approach vector spaces.

**Boulabiar, Karim , ** IPEST, University of Carthage, BP 51, 2070-La
Marsa, Tunisia 42101
(karim.boulabiar@ipest.rnu.tn).

Order Bounded Separating
Linear Maps on Φ-Algebras, pp.1143-1155.

ABSTRACT.
A Φ-algebra is an Archimedean lattice ordered algebra with a weak order unit.
Let be *A*
and *B* be Φ -algebras and let *T* be a separating linear map from *
A* into *B*, that is, *T* is a linear map such that *T(f)T(g)*
= 0 in *B* whenever *fg
*= 0 in *A*. It is proven by an order theoretical and purely algebraic
method that there exist a 'weight' element *w* in *B* and a positive
algebra homomorphism *S* from *A* into the maximal ring of quotients *
Q(B)* of *B* such that *T(f) = wS(f)* holds for all *f*
in *A*. Both real and complex cases are considered. This result generalizes
the following theorem proved by W. Arendt in his paper [Spectral properties of
Lamperti operators, *Indiana Univ. J. Math*., **32** (1983), 199-215].
Let *C(X)* and *C(Y)* be the Φ-algebras of all scalar-valued
continuous functions on compact Hausdorff topological spaces *X* and *Y*,
respectively. Then for every separating linear map
*T* from *C(X)* into *C(Y)* there exist a 'weight' function *w*
in *C(Y)* and a function *h* from *Y* into *X* (continuous
on the cozero set of *w*) such that *T(f)(y) = w(y)f(h(y))* holds for
all *f* in *C(X)* and *y* in *Y*.

**B.E. Forrest ** and **L.W. Marcoux, **Department of Pure
Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
(beforres@math.uwaterloo.ca) , (LWMarcoux@math.uwaterloo.ca).

Second Order Cohomology of
Triangular Banach Algebras, pp. 1157-1176.

ABSTRACT.
Explicit calculations of the various cohomology groups of a Banach algebra *I*
are often very difficult to obtain. In this paper, we will present an elementary
method to describe the second cohomology group H^{2}(*I *,*I*)
for a class of algebras called triangular Banach algebras. The techniques are
then illustrated through a number of examples.

**Zhai Fahui,** Institute of Mathematics, Institute of Qingdao Chemical
Technology, Qingdao 266042 , P.R. China, (fahuiz@163.com).

The Closures of (u+k)-Orbits of
Class Essentially Normal Operators, pp. 1177-1194.

ABSTRACT.
Let A , B be simply connected analytic cauchy domains, B be a subset of the
closure of A , u and v be measures on the boundary of A and B* which are assumed
to be equivalent to arc length measures, respectively. M(A , u) and M(B*, v) are
the multiplication operators on Hardy spaces of functions on the simply
connected cauchy domain A and the simply connected cauchy domain B* ,
respectively. In this paper, we describe the closure of (u+k)-oribt of direct
sum of the finitely direct sum M(A , u) with the finitely direct sum M(B*, v)*,
furthermore, if A=D={z: |z|<1}, we also describe the closure of (u+k)-oribt of
finitely direct sum of a class essentially normal operator models.

**Leo Livshits, **
Department of Mathematics and Computer Science, Colby College, Waterville, ME
04901 (llivshi@colby.edu), **Sing-Cheong Ong, **
Department of Mathematics, Central Michigan University, Mount Pleasant, MI 48859
(ong1s@cmich.edu ) and **Sheng-Wang Wang** Department of Mathematics, Nanjing
Audit Institute, Nanjing 210029, China (wang2598@nju.edu.cn).

Schur Algebras Over Function
Algebras, pp. 1195-1217.

ABSTRACT.
The authors generalize results of L. Livshits, S.-C. Ong and S. W. Wang, *
Banach Space Duality in Absolute Schur Algebras, *Integral Equations and
Operator Theory. Vol. 41 (2001) 343-359.

**Hem Raj Joshi, **Department of Math and CS, Xavier University
Cincinnati, OH 45207-4441 (joshi@xavier.edu) and **Suzanne Lenhart, **
Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300
(lenhart@math.utk.edu).

Solving a Parabolic
Identification Problem by Optimal Control Methods, pp. 1219-1242.

ABSTRACT.
An unknown coefficient of the interaction term of a parabolic system with a
Neumann boundary condition in a multi-dimensional bounded domain is identified.
The solution of the system represents the concentrations of prey and predator
populations. Given partial (perhaps noisy) observations of a true solution in a
subdomain, we seek to ``identify" the coefficient of the interaction term using
an optimal control technique, involving Tikhonov's regularization. The existence
and uniqueness of the optimal control approximating the desired coefficient are
obtained, an optimality system is derived, the identification problem is
discussed and an example illustrating how to find a solution numerically is
presented.