*Editors*: D. Bao (San Francisco, SFSU), D. Blecher
(Houston), B. G. Bodmann (Houston), H. Brezis (Paris and Rutgers),
B. Dacorogna (Lausanne), K. Davidson (Waterloo), 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*

Eilenberg theorems for many-sorted formations, pp. 321-369.

ABSTRACT. A theorem of Eilenberg establishes that there exists a bijection between the set of all varieties of regular languages and the set of all varieties of finite monoids. In this article after defining, for a fixed set of sorts S and a fixed S-sorted signature Σ, the concepts of formation of congruences with respect to Σ and of formation of Σ-algebras, we prove that the algebraic lattices of all Σ-congruence formations and of all Σ-algebra formations are isomorphic, which is an Eilenberg’s type theorem. Moreover, under a suitable condition on the free Σ-algebras and after defining the concepts of formation of congruences of finite index with respect to Σ, of formation of finite Σ-algebras, and of formation of regular languages with respect to Σ, we prove that the algebraic lattices of all Σ-finite index congruence formations, of all Σ-finite algebra formations, and of all Σ-regular language formations are isomorphic, which is also an Eilenberg’s type theorem.

Some bounds for the genus of a class of graphs arising from rings, pp. 371-384.

ABSTRACT. Let R be a commutative ring with nonzero identity and denote its Jacobson radical by J(R). The Jacobson graph of R is the graph in which the vertex set is R \ J(R), and two distinct vertices x and y are adjacent if and only if 1-xy is not a unit in R. In this paper, some bounds for the genus of Jacobson graphs are obtained. As an application, all commutative Artinian rings with nonzero identity whose Jacobson graphs are toroidal is classified up to isomorphism by a similar result for finite case. Finally, we obtain an isomorphism relation between two Jacobson graphs.

New sufficient conditions for strong starlikeness, pp. 385-393.

ABSTRACT. This paper determines new sufficient conditions for strong starlikeness and some related properties. The proof rests on several genetralizations and corollaries from Nunokawa's lemma, On the Order of Strongly Starlikeness of Strongly Convex Functions, Proc. Japan Acad. 69, Ser. A (1993) 234-237.

Deviations and spreads of holomorphic curves of finite lower order, pp. 395-411.

ABSTRACT. In this paper, we consider the relation between the number of maximum modulus points, spread and growth of a holomorphic curve. We use the method of I. I. Marchenko and E. Ciechanowicz to generalize their results of meromorphic functions to holomorphic curves.

The Weierstrass ℘-function as a distribution on a complex torus, and its Fourier Series, pp. 413-429.

ABSTRACT. We treat the Weierstrass ℘-function associated to a lattice in the complex plane as a principal value distribution on the quotient torus and compute its Fourier coefficients. The computation of these coefficients for nonzero frequencies is straightforward, but quite pretty. The "constant term" is more mysterious. It leads to a non-absolutely convergent doubly infinite series. This can be regarded as a version of an Eisenstein series, though as we discuss in Section 4 it differs from the "Eisenstein summation" of the series, as treated in Weil's monograph on elliptic functions. Material from Section 3 on the Fourier series of elliptic functions arising from the Weierstrass zeta function leads to a formula connecting our sum with the Eisenstein series treated in Weil's text, and thereby yields a rapidly convergent approximation to the constant term.

Entire solutions of certain types of nonlinear differential equations, pp. 431-437.

ABSTRACT. By utilizing classical Laguerre's theorem, we can resolve the entire solutions of nonlinear differential equations of the form: f(z)f''(z)=(p

On exact transcendental meromorphic solutions of nonlinear complex differential equations, pp. 439-453.

ABSTRACT. In this paper, we will deal with the existence and the form of transcendental meromorphic solutions of nonlinear differential equation f

A global version of a classical result of Joachimsthal, pp. 455-467.

ABSTRACT. A classical result attributed to Joachimsthal in 1846 states that if two surfaces intersect with constant angle along a line of curvature of one surface, then the curve of intersection is also a line of curvature of the other surface. In this note we prove the following global analogue of this result. Suppose that two closed convex surfaces intersect with constant angle along a curve that is not umbilic in either surface. We prove that the principal foliations of the two surfaces along the curve are either both orientable, or both non-orientable. We prove this by characterizing the constant angle intersection of two surfaces in Euclidean 3-space as the intersection of a Lagrangian surface and a foliated hypersurface in the space of oriented lines, endowed with its canonical neutral Kähler structure. This establishes a relationship between the principal directions of the two surfaces along the intersection curve in Euclidean space. A winding number argument yields the result. The method of proof is motivated by topology and, in particular, the slice problem for curves in the boundary of a 4-manifold.

The properties of extremal surfaces in Ahlfors' theory of covering surfaces, pp. 469-495.

ABSTRACT. Ahlfors' second fundamental theorem in Ahlfors' theory of covering surfaces claims that for each fixed set E

A converse of the characterization of operator geometric means, pp. 497-508.

ABSTRACT. In this paper, we used the closed convex hull of unitary orbit of positive operators and completely positive linear maps to investigate reverse of the characterization of operator geometric means by positive block matrices.

Algebras of disjointness preserving operatcors on Banach lattices, pp. 509-524.

ABSTRACT. Let A be an algebra of disjointness preserving operators on a Banach lattice X. We shall characterize the set of all nilpotent operators in A and we will deduce that if A is semiprime (i.e., with no nonzero nilpotent elements) then A is automatically commutative. This will lead us to show that if A is semiprime then A has an isometrically-isomorphic copy in the center of some Banach lattice.

Topological freeness for *-commuting covering maps, pp. 525-551.

ABSTRACT. We prove a close connection between *-commutativity and independence of group endomorphisms as considered by Cuntz-Vershik. This motivates the study of a family of *-commuting surjective local homeomorphisms of a compact Hausdorff space. Inspired by Ledrappier's shift, we describe interesting new examples related to cellular automata. To every such family we associate a universal C*-algebra that we then identify as the Cuntz-Nica-Pimsner algebra of a product system of Hilbert bimodules. This allows us to extend a result of Meier-Carlsen and Silvestrov which yields an application for irreversible algebraic dynamical systems.

The algebras of bounded operators on the Tsirelson and Baernstein spaces are not Grothendieck spaces, pp. 553-566.

ABSTRACT. We present two new examples of reflexive Banach spaces X for which the associated Banach algebra B(X) of bounded operators on X is not a Grothendieck space, namely X = T (the Tsirelson space) and X = B

Bounds on integral means of Bergman projections and their derivatives, pp. 567-588.

ABSTRACT. We bound integral means of the Bergman projection of a function in terms of integral means of the original function. As an application of these results, we bound certain weighted Bergman space norms of derivatives of Bergman projections in terms of weighted L

Existence of solutions for a nonhomogeneous semilinear fractional Laplacian problems, pp. 589-599.

ABSTRACT. In this paper we give existence results for a nonhomogeneous semilinear fractional laplacian problems with local coercivity in euclidean bounded domains using variational methods.

Zero-dimensional spaces homeomorphic to their Cartesian squares, pp. 601-608.

ABSTRACT. We show that there exists uncountably many zero-dimensional compact metric spaces homeomorphic to their cartesian squares as well as their n-fold symmetric products.

Endpoints of nondegenerate hereditarily decomposable chainable continua, pp. 609-624.

ABSTRACT. We show that a nondegenerate hereditarily decomposable chainable continuum must have a pair of opposite endpoints and use this result to investigate more on endpoints of such continua.

Some properties of bounded sets in certain topological spaces, pp. 625-646.

ABSTRACT. In the first part of this article we give some sufficient conditions under which a bounded set in a topological space (paratopological group) X is strongly bounded in X (p-bounded in X for every p∈ω