*Editors*: D. Bao (San Francisco, SFSU), D. Blecher
(Houston), B. G. Bodmann (Houston), H. Brezis (Paris and Rutgers),
B. Dacorogna (Lausanne), M. Dugas (Baylor), M.
Gehrke (LIAFA, Paris7), C. Hagopian (Sacramento), A. Haynes (Houston), 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 Editors*: B. G. Bodmann and K. Kaiser (Houston)

Houston Journal of Mathematics

*Contents*

Commuting automorphisms of the group consisting of the unit upper triangular matrices, pp. 647-658.

ABSTRACT. Let G be a group, an automorphism h of G is called a commuting automorphism, if for all x in G, h(x) commutes with x. Let Un(K) be the group consisting of all unit upper triangular matrices of order n over a field K with characteristic char(K) not equal to two. In this paper, we prove that if n is larger than 3, a map h on Un(K) is a commuting automorphism of Un(K) if and only if it is a central automorphism of Un(K). Moreover, the set of the commuting automorphisms of Un(K) is a normal subgroup of the automorphism group of Un(K).

Quasinormal families of meromorphic functions, pp. 659-668.

ABSTRACT. We discuss the quasinormal family of meromorphic functions and get a result that the derivatives of meromorphic functions converge to the omitted functions in the spherical metric. In addition, an example is also provided to show that the quasinormal order can be positive infinity.

A note on Fatou sets of solutions of complex linear differential equations, pp. 669-683.

ABSTRACT. We study the dynamical property and the growth of solutions of f''+A(z)f=F(z), where A(z) is an entire function of finite order, and F(z) is an entire function of order of growth less than that of A(z). On the one hand, some conditions on A(z) guaranteeing every non-trivial solution of the equation is of infinite lower order are obtained. On the other hand, we prove that the entire solutions of the equation have no Baker wandering domain.

Para-Blaschke isoparametric spacelike hypersurfaces in Lorentzian space forms, pp. 685-706.

ABSTRACT. Let M

A new representation of tubular surfaces, pp. 707-720.

ABSTRACT. Assume we are given a polynomial curve in 3D Euclidean space. The basic idea behind the proposed frame is that the new binormal vector is computed by using the cross product of the first and the highest order derivatives of the curve. We call this new frame as Frenet-like curve frame or for short, Flc-frame. This new frame is proposed to decrease the number of singular points where we cannot define the Frenet frame. Surprisingly, it has been noticed that the proposed frame also decreases the undesirable rotation around the tangent vector of the curve. In addition, we introduce three new curvatures of a polynomial space curve. Then, we give the geometric interpretation of the new curvatures. Finally, we derive the parametric equation of some tube surfaces generated by the Flc-frame.

Meromorphic functions and the Gauss map of complete minimal surfaces, pp. 721-729.

ABSTRACT. In this paper, we obtain a condition which guarantees the meromorphic function on the complex plane is the Gauss map of some complete minimal surface. In fact, we prove that if g

Boundary amenability of groups via ultrapowers, pp. 731-741.

ABSTRACT. We use C

Density-degree function for subsets of R

ABSTRACT. For all subsets

Unbounded quasitraces, stable finiteness and pure infiniteness, pp. 763-814.

ABSTRACT. We prove that if A is a sigma-unital exact C*-algebra of real rank zero, then every state on the zeroth K-group of A extends to a 2-quasitrace on A. This yields a generalisation of Rainone's work on pure infiniteness and stable finiteness of crossed products to the non-unital case. It also applies to k-graph algebras associated to row-finite k-graphs with no sources. We show that for a twisted C*-algebra of a cofinal k-graph with no sources, stable finiteness is independent of the twisting cocycle. We also study pure infiniteness of twisted higher rank graph C*-algebras.

Improvements of some operator inequalities involving positive linear maps via the Kantorovich constant, pp. 815-830.

ABSTRACT. In this paper, we present some operator inequalities involving positive linear maps that generalize and improve the derived results in some recent years. For instance, we prove some refinements of a reverse AM-GM operator inequality.

Matrix transformations on Lacunary Orlicz Sequence spaces and their Toeplitz duals, pp. 831-851.

ABSTRACT. In this paper we study some lacunary sequence spaces originated with infinite matrices and a sequence of Orlicz functions. We make an effort to study some algebraic and topological properties of these sequence spaces. Some inclusion relations between these spaces are also established. Furthermore, the β-,γ-duals and matrix transformation of these spaces are determined.

Multilinear fractional Calderon-Zygmund operators on weighted Hardy spaces, pp. 853-871.

ABSTRACT. We prove norm estimates for multilinear fractional integrals acting on weighted and variable Hardy spaces. In the weighted case we develop ideas we used for multilinear singular integrals (D.Cruz-Uribe, K.Moen, and H.V. Nguyen,

On a Schrödinger-Poisson system with singular term and critical growth, pp. 873-892.

ABSTRACT. In this work, we study the Schrödinger-Poisson system with singular and critical growth terms in a bounded domain. By using the variational method, the Brézis-Lieb(Proc. Amer. Math. Soc. 88 (1983)) and Brézis-Nirenberg (Comm. Pure Appl. Math. 36 (1983)) classical techniques, the existence and multiplicity of positive solutions are established.

Local networks for function spaces, pp. 893-923.

ABSTRACT. Let y be a point in a space Y, and suppose there is a countable family F of subsets of Y satisfying: whenever U is an open neighborhood of y, and y is in cl(A)\A for some subset A of Y, there is a D in F such that y ∈ D ⊆ U and D intersects A (respectively, D intersects A in an infinite set). Then we say F is a countable network (respectively, countable Pytkeev network) at y and that Y is (cn)

Characterizations of MCP and mcb spaces with maps, pp. 925-933.

ABSTRACT. This paper is a continuation of [Characterizations of some spaces with maps to ordered topological vector spaces, Houston J. Math., 43 (2017), 678-689] in which some characterizations of countably paracompact spaces and cb-spaces in terms of maps to ordered topological vector spaces were presented. In this paper, we shall generalize the corresponding results to MCP-spaces and mcb-spaces.

A dichotomy result for locally compact sober dcpos, pp. 935-951.

ABSTRACT. The second author proved in 1989 that each cartesian closed category of pointed domains and Scott-continuous functions is contained in either the category of Lawson-compact domains or that of L-domains, and this result eventually led to a classification of continuous domains with respect to cartesian closedness. In this paper, we generalise this result to the category LcS of pointed locally compact sober dcpos and Scott-continuous functions, and show that any cartesian closed full subcategory of LcS is contained in either the category of stably compact dcpos or that of L-dcpos. (Note that for domains Lawson-compactness and stable compactness are equivalent.) As we will show, this entails that any candidate for solving the Jung-Tix problem in LcS must be stably compact. To prove our dichotomy result, we first show that any dcpo with a core-compact function space must be meet-continuous; then we prove that a function space in LcS is meet-continuous only if either its input dcpo is coherent or its output dcpo has complete principal ideals.