*Editors*: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao
(Houston), H. Brezis (Paris), K. Davidson (Waterloo), C. Hagopian (Sacramento),
R. M. Hardt (Rice), J. Hausen (Houston), J. A. Johnson (Houston), W. B. Johnson
(College Station), J. Nagata (Osaka), V. I. Paulsen (Houston), Min Ru (Houston),
S.W. Semmes (Rice)

*Managing Editor*: K. Kaiser (Houston)

**
Revised February 6, 2008. **

Houston Journal of Mathematics

**Brendan Goldsmith, **School of Mathematical
Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8 Ireland
(brendan.goldsmith@dit.ie) and
**Lutz Strüngmann, **Fachbereich 6, Mathematik, Universität
Duisburg-Essen, 45117 Essen, Germany
(lutz.struengmann@uni-essen.de).

Some transitivity results
for torsion abelian groups, pp. 941-957.

ABSTRACT.
We introduce a new class of fully transitive and transitive Abelian p-groups
and study the new concept of weak transitivity which is the missing link
between full transitivity and transitivity.

**L. Fuchs, **Department of Mathematics, Tulane University, New Orleans,
Louisiana 70118, USA, (fuchs@tulane.edu),

Large indecomposable modules
with many automorphisms, pp. 959-966.

ABSTRACT.
Over integral domains *R* admitting fully rigid systems of modules with *
R* as endomorphism rings, we construct indecomposable modules of cardinality
κ whose automorphism groups are as large as possible: they have cardinality 2^{κ}.
Here κ denotes any infinite cardinal with |R| ≤ κ.

We also show that over certain valuation domains there exist indecomposable
divisible torsion modules of arbitrarily large cardinalities κ whose
automorphism groups have cardinality 2^{κ}.

**Behrooz Khosravi,** Dept. of Pure Math., Faculty of Math. and Computer
Sci., Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez
Ave., Tehran 15914, IRAN; and Institute for Studies in Theoretical Physics
and Mathematics (IPM),
(khosravibbb@yahoo.com). and **Behnam Khosravi and Bahman Khosravi, **
Dept. of Math., Faculty of Math. Sci., Shahid Beheshti Univ., Evin, Tehran,
19838, IRAN .

Groups With the Same Prime Graph
as a CIT Simple Group, pp. 967-977.

ABSTRACT.
Let G be a finite group. The prime graph of G is the graph whose vertex set
is the set of all prime divisors of |G|, and two distinct primes p and q are
joined by an edge if and only if G contains an element of order pq. A group
M is called a CIT group or a C22 group if M is of even order and the
centralizer of any involution is a 2-group. In this paper we determine
finite groups G such that their prime graph is the same prime graph of M,
where M is a CIT simple group. As a consequence of this result, we prove
that if p>7 is a Mersenne prime or a Fermat prime, then PSL(2,p) is uniquely
determined by its prime graph. Also we prove a few results by using the main
theorem.

**Taylor, Michael E.,** University of North Carolina, Chapel
Hill, NC 27599 (met@math.unc.edu).

Scattering Length of Positive
Potentials, pp. 979-1003.

ABSTRACT. There is a notion of scattering length of a
positive function v on R^{n}, analogous to the notion of capacity of
a compact set K in R^{n}. Seminal work on this was done in papers of
M. Kac and J. Luttinger. This work played an important role in several
previous papers of the author on Schrodinger operators. Here we give a
systematic presentation of the fundamentals of the subject, and extend its
scope from R^{n} with n bigger than 2 to a natural class of complete
Riemannian manifolds, including two-dimensional cases. A central theme is
the relation of the scattering length of v to the spectral behavior of v
minus the Laplace operator.

**Juan de Dios Perez**, Universidad de Granada, Spain, (jdperez@ugr.es),
**Florentino G. Santos**, Universidad de Granada, Spain (florenti@ugr.es)
and **Young Jin Suh,** Kyungpook National University, Korea
(yjsuh@mail.knu.ac.kr).

Real hypersurfaces in nonflat complex
space forms with commuting structure Jacobi operator, pp. 1005-1009.

ABSTRACT. We prove the non existence of real
hypersurfaces in either complex projective spaces or complex hyperbolic spaces
whose structure Jacobi operator commutes with any other Jacobi operator.

**Borzellino, Joseph E., **California Polytechnic State University, San Luis
Obispo, CA 93407 (jborzell@calpoly.edu),
**Jordan-Squire, Christopher R., **Swarthmore College, Swarthmore, PA 19081
(cjordan1@swarthmore.edu), **
Petrics, Gregory C., **Dartmouth College, Hanover, NH 03755
(Gregory.Petrics@dartmouth. edu),
and **Sullivan, D. Mark, **University of Washington, Seattle, WA 98195
(msully@math.washington.edu).

Closed geodesics on orbifolds of
revolution., pp. 1011-1025.

ABSTRACT. Using the theory of geodesics on surfaces of
revolution, we show that any two-dimensional orbifold of revolution homeomorphic
to *S*^{2} must contain an infinite number of geometrically
distinct closed geodesics. Since any such orbifold of revolution can be regarded
as a topological two-sphere with metric singularities, we will have extended
Bangert's theorem on the existence of infinitely many closed geodesics on any
smooth Riemannian two-sphere. In addition, we give an example of a two-sphere
cone-manifold of revolution which possesses a single closed geodesic, thus
showing that Bangert's result does not hold in the wider class of closed
surfaces with cone manifold structures.

**Michał Ryszard Wojcik** and **
Michał Stanisław Wojcik, **Institute of Mathematics, Wroclaw University of
Technology, Wroclaw, Poland
(michal.ryszard.wojcik@gmail.com)**;**(michal.r.wojcik@pwr.wroc.pl)**.**

Characterization of continuity for
real valued functions in terms of connectedness, pp. 1027-1031.

ABSTRACT. In this paper we prove that for any
real-valued function defined on a connected topological space being
continuous is equivalent to having its graph connected coupled with the
complement of the graph being disconnected.

Concerning continua irreducible about finitely many points, pp. 1033-1046.

ABSTRACT. The purpose of this paper is to provide in a unified treatment a number of characterizations for continua and unicoherent continua that are irreducible about finitely many points, and for continua and unicoherent continua that are irreducible about

One of the main results, from which most of the others follow with relative ease, is that a continuum is irreducible about finitely many points if and only if every pairwise disjoint collection of nonseparating open subsets is finite. Alternate proofs for the classic results of Sorgenfrey are included in the development.

**M. de J. Lopez**, Facultad de Ciencias Fisico Matematicas, B. U. A. P.,
Ave. San Claudio y Rio Verde, Ciudad Universitaria, San Manuel Puebla, Pue. C.
P. 72570, MEXICO (mtoriz@fcfm.buap.mx),
**Sergio Macias**, Instituto de Matematicas, U. N. A. M., Circuito Exterior,
Ciudad Universitaria, M\'exico, D. F., C. P. 04510, MEXIC(macias@servidor.unam.mx).

Induced Maps on *n*-fold
Hyperspaces, pp. 1047-1057.

ABSTRACT. For a given map between continua we study the
induced maps between *n*-fold hyperspaces and between *n*-fold
hyperpsace suspensions.

Our results on *n*-fold hyperspaces extend some results that are known for
the induced maps between the hyperspace of subcontinua.

**Gala, Sadek,** University of Mostaganem, Department of Mathematics, Box
227, Mostaganem (27000), Algeria.
(sadek.gala@gmail.com).

The BMO-1 space and its application to
Schechter's inequality, pp. 1059-1066.
**(Access to this paper is unrestricted) **

EDITORIAL STATEMENT.
The managing editor has been informed that all of the material in this paper very closely parallels portions of the paper:
V.G. Maz'ya and J.E. Verbitsky, *Infinitesimal form boundedness and Trudinger's subordination for the Schrödinger operator*, Invent. Math. 162 (October 2005), no. 1, 81-136.

Moreover, modulo some minor changes in wording and notation, portions of Gala's paper are identical to corresponding sections in the manuscript of Maz'ya and Verbitsky.
The paper of Maz'ya and Verbitsky was posted June 2, 2004 on arXiv

http://arxiv.org/PS_cache/math/pdf/0406/0406050v1.pdf

but not cited by Gala.

HJM received Gala's manuscript on September 1, 2005 and, in view of the similarities of content and presentation, we sincerely regret the publication of this paper.

**Joiţa****,
Maria, **

Covariant completely
positive linear maps between locally C*-algebras, pp. 1067-1078.

ABSTRACT. We prove a covariant version of the
KSGNS (Kasparov,
Stinespring, Gel’fand,
Naimark, Segal) construction for completely
positive linear maps between locally C*-algebras.
As an application of this construction, we show that a covariant completely
positive linear map ρ from a locally C*-algebra A
to another locally C*-algebra B with
respect to a locally C*-dynamical system (
G, A,
α) extends
to a completely positive linear map on the crossed
product of G and A
by α.

**Sofi, M.A.**, Kashmir University, Srinagar-190006
(aminsofi@rediffmail.com).

Frechet-valued measures and
nuclearity, pp. 1079-1090.

ABSTRACT. The recognition of sequences localised inside
the range of a vector measure is an important theme in vector measure
theory. In a previous work, the author had characterized Banach spaces X in
which absolutely p-summable sequences in X (p>1) are contained inside the
range of an X-valued measure of bounded variation precisely as those having
(q)-Orlicz property (q being conjugate to p)- a property that characterizes
X as finite dimensional as long as p > 2. This motivates the natural
question of investigating this property in the setting of Frechet spaces
where it is shown to translate into nuclearity -in conformity with the
philosophy that nuclear Frechet spaces are better equipped to be called
infinite-dimensional variants of finite dimensional spaces than are the more
familiar Hilbert spaces. This result provides a strengthening of an earlier
result of Bonet and Madrigal, characterising nuclearity of a Frechet space X
with absolutely p- summable sequences in X being replaced by null sequences
in X. The paper concludes with another useful and more general version of
the said result in terms of (p,q)- summing multipliers.

**Magajna, Bojan,**
Department of Mathematics, University of Ljubljana, Jadranska 19, Ljubljana
1000, Slovenia
(Bojan.Magajna@fmf.uni-lj.si).

Injective cogenerators among
operator bimodules, pp. 1091-1115.

ABSTRACT. Given C*-algebras A and B acting cyclically on
Hilbert spaces H and K, respectively, we characterize completely isometric
A,B-bimodule maps from B(K,H) into operator A,B-bimodules. We determine
cogenerators in some classes of operator bimodules. For an injective
cogenerator X in a suitable category of operator A,B-bimodules we show: if
A, regarded as a C*-subalgebra of Al(X) (adjointable left multipliers on X),
is equal to its relative double commutant in Al(X), then A must be a
W*-algebra.

**Kucerovsky, Dan, **UNB-F, Fredericton, NB, Canada
(dan@math.unb.ca) and **Ng, P-W, **
Fields Institute, 222 College St., Toronto, Canada
(pwn@math.unb.ca).

On nonregular ideals in the
multipliers of a stable C*-algebra, pp. 1117-1130.

ABSTRACT. Let B be a unital, separable C*-algebra. Let Z be
the centre of B, and let X be the primitive ideal space of B. Suppose that X
contains infinitely many distinct points. Then the multipliers of the
stabilization of B have a proper, nonregular ideal (we define this concept in
the paper). Moreover, if X contains uncountably infinitely many points, then the
multipliers of the stabilization have uncountably many distinct, maximal,
proper, nonregular ideals. We also give results about Glimm ideals and
projections inside ideals of the multipliers of the stabilization

**Ilie, Monica,** Lakehead University, 955 Oliver Road, Thunder Bay, ON,
P7B 5E1, Canada (milie@lakeheadu.ca),
and **Spronk, Nico,** University of Waterloo, Waterloo, ON, N2L 3G1,
Canada (nspronk@uwaterloo.ca).

The algebra generated by
idempotents in a Fourier-Stieltjes algebra , pp. 1131-1145.

ABSTRACT.
We study the closed algebra B_{I}(G) generated by the idempotents in
the Fourier-Stieltjes algebra of a locally compact group G. We show that it
is a regular Banach algebra with computable spectrum G^{I}, which we
call the idempotent compactification of G. For any locally compact groups G
and H, we show that B_{I}(G) is completely isometrically isomorphic
to B_{I}(H) exactly when G/G_{e}= H/H_{e}, where G_{e}
and H_{e} are the connected components of the identities. We compute
some examples to illustrate our results.

**Blanchard, Etienne, **Institut de Mathématiques, Projet Algèbres
d’opérateurs (Plateau 7E), 175, rue du Chevaleret, F-75013 Paris, France,
(blanchar@math.jussieu.fr)
and **Wassermann, Simon, **Department of Mathematics, University of
Glasgow, Glasgow G12 8QW, United Kingdom
(asw@maths.gla.ac.uk)

Exact C*-Bundles, pp.
1147-1159.

ABSTRACT. Kirchberg and Wassermann showed that if A
is an exact continuous C*- bundle on a locally compact Hausdorff space X,
then for any other continuous C*-bundle B on X, the minimal tensor product
bundle amalgamated over C_{0}(X) of A and B is again continuous. In
this paper it is shown conversely that this property characterises the
continuous C*-bundles with exact bundle C*-algebra when the base space X has
no isolated points. For such X a corresponding result for the maximal tensor
product amalgamated over C_{0}(X) of C*-bundles on X is also shown
to hold, namely that the maximal tensor product amalgamated over C_{0}(X)
of A and B is continuous for all continuous C*-bundles B on X if and only if
A has nuclear bundle C*-algebra.

**Sarason, Donald,** University of California, Berkeley, CA 94720-3840
(sarason@math.berkeley.edu).

The Banach
algebra of slowly oscillating functions, pp. 1161-1182.

ABSTRACT. A complex-valued function on the nonnegative real
axis is said to be slowly oscillating if it is continuous, bounded, and
differs from each of its translates by a function that vanishes at infinity.
The family of such functions forms a commutative C*-algebra under the
supremum norm. This paper investigates the topology of the Gelfand space of
that algebra.

**Gao, Mingchu,** Louisiana College, Pineville, LA
71360, and College of Mathematics and Computer Science, Shanxi Normal
University, Linfen, Shanxi, China
(mingchug@yahoo.com).

Clifford algebras over Hilbert C*-Modules, pp. 1183-1214.

ABSTRACT. Clifford algebras of real Hilbert C*-modules with
orthonormal bases are introduced. It is showed that the C*-Clifford algebra
of a real Hilbert module over a real C*-algebra is *-isomorphic to the
spacial tensor product of the complexification C*-algebra and a UHF
C*-algebra. The von Neumann Clifford algebra of a real Hilbert module over a
von Neumann algebra is*-isomorphic to the von Neumann algebra tensor product
of the complexification von Neumann algebra and the hyper-finite type two
one factor.

**Miklyukov, Vladimir M.,** Department of Mathematics, Volgograd State
University, Universitetskii prospect 100, Volgograd 400062, Russia
(miklyuk@mail.ru), **Rasila, Antti,**
Helsinki University of Technology, Institute of Mathematics, P.O.Box 1100,
FIN-02015 TKK, Finland
(antti.rasila@tkk.fi), and **Vuorinen, Matti,** Department of
Mathematics, FIN-20014 University of Turku, Finland
(vuorinen@utu.fi).

Three sphres theorem for
p-harmonic functions,
pp.1215-1230.

ABSTRACT. Three spheres theorem type result is proved for
the p-harmonic functions defined on the complement of k-balls in the Euclidean
n-dimensional space.

**Kang, Y.H.,** University of Ulsan, Ulsan 680-749, Korea
(yonghann@math.ulsan.ac.kr), **
Lenhart, S.,** University of Tennessee, Knoxville, TN 37996-1330
(lenhart@math.utk.edu), and **
Protopopescu, V.,** Oak Ridge National Laboratory, Oak Ridge, Tennessee
37831-6364 (vvp@ornl.gov).

Optimal control of parameters and
input functions for nonlinear systems,
pp. 1231-1256.

ABSTRACT. We consider the optimal control problem for both parameters and
functions for general nonlinear systems. We show existence of optimal solution
and present necessary optimality conditions. We illustrate the approach on two
examples.