Vassilis J. Papantoniou and Kostas Petoumenos,  University of Patras, Department of Mathematics, GR-26500 Rion, Greece  (bipapant@math.upatras.gr, (copetoum@math.upatras.gr).
Biharmonic hypersurfaces of type M₂³ in E₂⁴, pp. 93-114.
ABSTRACT. An n-dimensional submanifold of index r of an m-dimensional pseudo-Euclidean space of index s is said to have harmonic mean curvature vector field, if the action of the Laplace operator (with respect to the induced pseudo-Riemannian metric) on the mean curvature vector field vanishes. Submanifolds with harmonic mean curvature vecror field are also known as biharmonic submanifolds. In the present paper, we use all possible canonical forms of the shape operator of a three dimensional hypersurface of index two in a four dimensional pseudo-Euclidean space of index two, and prove that every such a nondegenerate biharmonic hypersurface is minimal.

Yu Kawakami, Graduate School of Science and Engineering, Yamaguchi University, Yamaguchi, 753-8512, Japan (ykwkami@yamaguchi-u.ac.jp).
Value distribution of the hyperbolic Gauss maps for flat fronts in hyperbolic three-space, pp. 115-130.
ABSTRACT. We give an effective estimate for the totally ramified value number of the hyperbolic Gauss maps of complete flat fronts in the hyperbolic three-space. As a corollary, we give the upper bound for the number of exceptional values of them in some topological cases. Moreover, we obtain some new examples for this class.

Jincai Wang, School of Mathematical Sciences, Soochow University, P.R. China, 215006 (wwwanggj@163.com) and  Yi Chen, School of Mathematical Sciences, Soochow University, P.R. China, 215006.
Rotundity and uniform rotundity of Orlicz-Lorentz spaces with the Orlicz norm, pp. 131-151.
ABSTRACT.  In this article, we obtain criteria of rotundity and uniform rotundity of Orlicz-Lorentz spaces with the Orlicz norm. .

G. K. Eleftherakis, Department of Mathematics University of Athens, 157 84, Athens, Greece (gelefth@math.uoa.gr).
TRO equivalent algebras, pp. 153-175
ABSTRACT. In this work we study a new equivalence relation between w* closed algebras of operators on Hilbert spaces. The algebras A and B are called "TRO equivalent" if there exists a ternary ring of operators M (i.e. the set MM*M is contained in M) such that A is the w* closure of the span of the set M*BM and B is the w* closure of the span of the set MAM*. We prove that two reflexive algebras are TRO equivalent if and only if there exists a * isomorphism between the commutants of their diagonals mapping the invariant projection lattice of the first algebra onto the lattice of the second one.

Ian N. Deters, 871 Champagne Ave., Bowling Green, OH, 43402 (iandeters@iandeters.com) and Steven M. Seubert, Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, 43403-0221 (sseuber@bgsu.edu).
An application of entire function theory to the synthesis of diagonal operators on the space of entire functions, pp. 201-207.
ABSTRACT. In this paper, sufficient conditions are given for an operator acting on the space of entire functions having the monomials as eigenvectors to admit spectral synthesis, that is, for every closed invariant subspace of the operator to be the closed linear span of some collection of its eigenvectors.

Baudier, Florent, Université de Franche-Comté,25000 Besancon, France, Current Address: Université de Neuchâtel, 2000 Neuchâtel, Switzerland (florent.baudier@unine.ch).
Embeddings of proper metric spaces into Banach spaces, pp. 209-223.
ABSTRACT. We show that there exists a strong uniform embedding from any proper metric space into any Banach space without cotype. Then we prove a result concerning the Lipschitz embedding of locally finite subsets of script L_p-spaces. We use this locally finite result to construct a coarse bi-Lipschitz embedding for proper subsets of any script L_p-space into any Banach space X containing the l_pⁿ's. Finally using an argument of G. Schechtman we prove that for general proper metric spaces and for Banach spaces without cotype a converse statement holds. In particular X has no non-trivial cotype if and only if X contains a coarse Lipschitz copy of every locally finite metric space (with uniform constants).

Zunwei Fu, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China and Department of Mathematics, Linyi Normal University, Linyi 276005, P. R. China(zwfu@mail.bnu.edu.cn), Loukas Grafakos, Department of Mathematics, University of Missouri, Columbia, MO 65211, USA (grafakosl@missouri.edu), Shanzhen Lu, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China (lusz@bnu.edu.cn), Fayou Zhao (Corresponding author), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China; Department of Mathematics, University of Missouri, Columbia, MO 65211, USA (zhaofayou2008@yahoo.com.cn).
Sharp bounds for m-linear Hardy and Hilbert Operators, pp. 225-244.
ABSTRACT. The precise norms of m-linear Hardy operators and m-linear Hilbert operators on Lebesgue spaces with power weights are computed. Analogous results are also obtained for Morrey spaces and central Morrey spaces.

Paterson, Alan L. T., 3709 Bluefield Court, Clarksville, TN 37040 (apat1erson@gmail.com).
The stabilization theorem for proper groupoids, pp. 245-264.
ABSTRACT. The equivariant stabilization theorem for Hilbert (H-A)-modules under the action of a compact group was proved by G. G. Kasparov (who also obtained a corresponding result for the case of a non-compact group except that the isomorphism involved is not equivariant). An extension of this theorem (in the case A=C₀(Y)) to the case where a general locally compact group H acts properly on a locally compact space Y was established by N. C. Phillips. (A proof of the general case where A is an (H-C₀(Y))-algebra has been sketched in a paper of Kasparov and Skandalis.) The Phillips equivariant theorem involves the Hilbert (H,C₀(Y))-module C₀(Y,L²}H^∞). It can naturally be interpreted in terms of a stabilization theorem for proper groupoids, and the paper proves this theorem within the general, proper groupoid, context. The theorem has applications in equivariant KK-theory and groupoid index theory.

Mark S. Grinshpon, Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA (matmsg@langate.gsu.edu),  Peter A. Linnell, Department of Mathematics, Virginia Tech, Blacksburg VA 24061-0123, USA (plinnell@math.vt.edu), Michael J. Puls, Department of Mathematics, John Jay College--CUNY, 445 West 59th Street, New York, NY 10019, USA  (mpuls@jjay.cuny.edu).
Dimensions of l^p-cohomology groups, pp. 265-273.
ABSTRACT. Let G be an infinite discrete group of type FP_∞ and let p > 1 be a real number. We prove that the l^p-homology and cohomology groups of G are either 0 or infinite dimensional. We also show that the cardinality of the p-harmonic boundary of a finitely generated group is either 0, 1, or ∞.

Zhankui, Xiao, School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, P. R. China (zhkxiao@gmail.com)  and Feng, Wei, School of Mathematcs, Beijing Institute of Technology, Beijing, 100081, P. R. China (daoshuo@hotmail.com).
Jordan higher derivations on some operator algebras, pp. 275-293.
ABSTRACT. In this paper we mainly consider the question of whether any Jordan higher derivation on some operator algebras is a higher derivation. Let A be a torsion free algebra over a commutative ring R, D be the set of all Jordan higher derivations {d_n} on A, and G be the set of all sequences {g_n} of Jordan derivations on A. Then there is a one to one correspondence between D and G. It is shown via this correspondence that every Jordan higher derivation on some operator algebras is a higher derivation. The involved operator algebras include CSL algebras, reflexive algebras, nest algebras. At last, we describe local actions of Jordan higher derivations on nest algebras.

Bankston, Paul, Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI 53201 (paulb@mscs.mu.edu).  
Categoricity and topological graphs, pp. 295-310.
ABSTRACT. A lattice base for a topological space is a closed-set base that is also closed under finite unions and intersections. Let X be a topological graph; i.e., a union of finitely many points and arcs, with arcs joined only at end points. If Y is any locally connected metrizable compactum, and some lattice base for Y is elementarily equivalent (in the sense of model theory) to some lattice base for X, then Y is homeomorphic to X. This is a categoricity statement for topological graphs.

Liang-Xue  Peng,  College of Applied  Science,  Beijing University of Technology,  Beijing 100124,  China (pengliangxue@bjut.edu.cn).
A note on spaces of continuous step functions over LOTS, pp. 311-318.
ABSTRACT. Given a LOTS (linearly ordered topological space) L, the space T(L)=(T, Τ) is defined as follows. The underlying set is the subset T of cL that consists of all Dedekind sections as well as left endpoints of gaps of  L. That is, T(L) is the union of (cL\L) and the set of left endpoints of gaps of L. The base neighborhoods at points of (cL\ L) in Τ are those from the subspace topology on T, while all other points are declared isolated. We prove that if L is a LOTS and C_p(L, n+1) is Lindelöf then  T(L)ⁿ  and (dL)ⁿ are Lindelöf, where dL=cL\L and n is a natural number. This gives a positive answer to a question of Buzyakova (the question appears in Fund. Math. 192 (2006) 25-35). We also show that if L is a LOTS and T(L)ⁿ is Lindelöf for each natural number n then S_p (L, n) is Lindelöf for each natural number n, where S_p (L, n) is the subspace of  C_p (L, n), which consists of all step functions with finitely many steps and constant functions.

Carlson, Nathan, California Lutheran University, Thousand Oaks, CA 91360 (ncarlson@callutheran.edu), and Ridderbos, Guit-Jan, Technische Universiteit Delft, Delft, The Netherlands (G.F.Ridderbos@tudelft.nl).
On several cardinality bounds on power homogeneous spaces, pp. 311-332.
ABSTRACT. We show the cardinality of a homogeneous Hausdorff space X is not necessarily bounded by 2^L(X) , where k is the pi-character of X, by providing examples of sigma-compact, countably tight, homogeneous spaces of countable pi-character and arbitrary cardinality. We also generalize a closing-off argument of Pytkeev to show the cardinality of any power homogeneous Hausdorff space X is at most 2^{L(X)pct(X)t(X)}. This was previously shown to hold if X is also regular by G.J. Ridderbos. Another consequence of the generalization of Pytkeev's closing-off argument is the well-known cardinality bound 2^{L(X)t(X)psi(X)} for an arbitrary Hausdorff space X.