Editors: D. Bao (San Francisco, SFSU), S. Berhanu (Temple), D. Blecher
(Houston), B. G. Bodmann (Houston), H. Brezis (Paris and Rutgers),
B. Dacorogna (Lausanne), M.
Gehrke (LIAFA, Paris7), R. M. Hardt (Rice), S. Harvey (Rice), A. Haynes (Houston), Y. Hattori
(Matsue, Shimane), W. B. Johnson (College Station), M. Marsh (Sacramento), M. Rojas (College Station),
Min Ru (Houston), S.W. Semmes (Rice), D. Werner (FU Berlin).
Managing Editors: B. G. Bodmann and A. Haynes (Houston)
Houston Journal of Mathematics
Contents
Lei Tao, School of Mathematical Science, Guizhou Normal University, Guiyang, 550025,
P.R. China; School of Mathematics and Big Data, Guizhou Education University,
Guiyang, 550018, P. R. China (shidataolei@163.com), and Jianren Long, School of
Mathematical Science, Guizhou Normal University, Gui-yang, 550025, P.R. China
(longjianren2004@163.com).
On growth of solutions of complex differential equation concerning generalized Ozawa’s
problem, pp. 451–462.
ABSTRACT. The growth of solutions of linear differential equation f′′+A(z)f′+B(z)f = 0
is studied, where A(z) is a particular non-constant exponential sum with expression
A(z) = P(e−z) = ∑
j=1mAje−jz, B(z) is a non-constant polynomial with expression
B(z) = ∑
j=0nbjzj. Then every non-trivial solution of the equation is of infinite order,
which give a partial solution concerning generalized Ozawa’s problem.
Kesong Yan, School of Information and Statistics, Guangxi University of Finance and
Economics, Nanning, Guangxi, 530003, P.R.China (ksyan@mail.ustc.edu.cn),
Wen-Chiao Cheng, Department of Applied Mathematics, Chinese Culture University,
Yangmingshan, Taipei, Taiwan, 11114 (zwq2@ulive.pccu.edu.tw), and Fanping Zeng,
School of Information and Statistics, Guangxi University of Finance and Economics,
Nanning, Guangxi, 530003, P.R.China (fpzeng@gxu.edu.cn).
On the commutativity for partial pre-image entropy, pp. 463–478.
ABSTRACT. Yan and Zeng previously introduced the notion of entropy-like invariants
as an extension of the concept of point-wise pre-image entropy in [27]. The goal of this
paper is to utilize this concept and generalize to the case of a fixed sequence. Therefore,
such entropy-like quantity will exhibit as an invariant of topological conjugacy.
Some basic dynamical propositions are also discussed in the paper. Finally,
we also show that for any continuous maps T and S from a compact metric
space onto itself, the maps T ∘ S and S ∘ T have the same partial pre-image
entropy.
Takao Ohno, Faculty of Education, Oita University, Dannoharu Oita-city
870-1192, Japan (t-ohno@oita-u.ac.jp), and Tetsu Shimomura, Department of
Mathematics, Graduate School of Humanities and Social Sciences, Hiroshima University,
Higashi-Hiroshima 739-8524, Japan (tshimo@hiroshima-u.ac.jp).
Trudinger-type inequalities in Musielak-Orlicz spaces, pp. 479–497.
ABSTRACT. We are concerned with Trudinger-type inequalities for variable Riesz
potentials Jα(⋅),τf of functions in Musielak-Orlicz spaces LΦ(X) over bounded metric
measure spaces equipped with lower Ahlfors Q(x)-regular measures. As an application
and example we obtain Sobolev’s inequality for double phase functionals with variable
exponents.
Jeffrey Kuan, Texas A&M University, Department of Mathematics, Mailstop 3368,
College Station TX 77843–3368 (jkuanmath.tamu.edu), Mark Landry, Andrew Lin,
Andrew Park, and Zhengye Zhou.
Interacting particle systems with type D symmetry and duality, pp. 499–538.
ABSTRACT. We construct a two–class asymmetric interacting particle system with
𝒰q(𝔰𝔬6) or 𝒰q(𝔰𝔬8) symmetry, in which up to two particles may occupy a site if the two
particles have different class. The particles exhibit a drift, but there is no preference
given between first–class and second–class particles. The quantum group symmetry leads
to reversible measures and a self–duality for the particle system. Additionally, a new
method is developed to construct a symmetric interacting particle system from the
Casimir element of 𝔰𝔬2n.
A. Fovelle, Laboratoire de Mathématiques de Besançon, Université Bourgogne
Franche-Comté, 16 route de Gray, 25030 Besançon Cédex, Besançon, France
(audrey.fovelle@univ-fcomte.fr).
Hamming graphs and concentration properties in non-quasi-reflexive Banach spaces, pp.
539–579.
ABSTRACT. In this note, we study some concentration properties for Lipschitz maps
defined on Hamming graphs, as well as their stability under sums of Banach spaces. As
an application, we extend a result of Causey on the coarse Lipschitz structure of
quasi-reflexive spaces satisfying upper ℓp tree estimates to the setting of ℓp-sums
of such spaces. Our result provides us with a tool for constructing the first
examples of Banach spaces that are not quasi-reflexive but nevertheless admit
some concentration inequality. We also give a sufficient condition for a space
to be asymptotic-c0 in terms of a concentration property, as well as relevant
counterexamples.
Mikaël Pichot, McGill University, 805 Sherbrooke St W., Montréal, QC H3A 0B9,
Canada (mikael.pichot@mcgill.ca), and Erik Séguin, McGill University, 805
Sherbrooke St W., Montréal, QC H3A 0B9, Canada (erik.seguin@mail.mcgill.ca).
Positive definite maps on amenable groups, pp. 581–605.
ABSTRACT. We describe conditions that characterize amenability for groups in terms
of positive definite functions valued in a von Neumann algebra.
Minghui You, Mathematics Teaching and Research Section, Zhejiang
Institute of Mechanical and Electrical Engineering, Hangzhou 310053, China
(youminghui@zime.edu.cn).
On the general form of discrete Hilbert-type inequality, pp. 607–630.
ABSTRACT. In this paper, we first construct a general discrete kernel function with
several parameters, and then we establish a new discrete Hilbert-type inequality by
using the method of weight coefficient and Euler-Maclaurin summation formula.
Furthermore, the equivalent Hardy-type inequalities are also considered, and all
the constant factors in the newly obtained inequalities are proved to be the
best possible. At last, by assigning some specific functions to the new kernel,
and using techniques of real analysis and the numerical calculation function of
Matlab, some special Hilbert-type inequalities are established at the end of the
paper.
Michael Facci, Department of Mathematics, University of North Carolina, Chapel
Hill, NC 27599-3250 (mfacci@live.unc.edu), and Jason Metcalfe, Department
of Mathematics, University of North Carolina, Chapel Hill, NC 27599-3250
(metcalfe@email.unc.edu).
Global existence for quasilinear wave equations satisfying the null condition, pp.
631–653.
ABSTRACT. We explore the global existence of solutions to systems of quasilinear wave
equations satisfying the null condition when the initial data are sufficiently small. We
adapt an approach of Keel, Smith, and Sogge, which relies on integrated local energy
estimates and a weighted Sobolev estimate that yields decay in |x|, by using the
rp-weighted local energy estimates of Dafermos and Rodnianski. One advantage of
this approach is that all time-dependent vector fields can be avoided and the
proof can be readily adapted to address wave equations exterior to star-shaped
obstacles.
Meng Bao, School of Sciences and Arts, Suqian University, Suqian, 263800, P. R. China
(mengbao95213@163.com), Rongxin Shen, Department of Mathematics, Taizhou
University, Taizhou, Jiangsu 225300, P.R. China (srx20212021@163.com), and
Xiaoquan Xu, School of Mathematics and Statistics, Minnan Normal University,
Zhangzhou 363000, P. R. China (xiqxu2002@163.com).
A class of quotient spaces in strongly topological gyrogroups, pp. 655–676.
ABSTRACT. Quotient space is a class of the most important topological spaces in the
research of topology. In this paper, we show that if (G,τ,⊕) is a strongly topological
gyrogroup with a symmetric neighborhood base 𝒰 at 0 and H is an admissible
subgyrogroup generated from 𝒰, then G∕H is first-countable if and only if it is
metrizable. Moreover, if H is inner neutral and G∕H is Fréchet-Urysohn with an
ωω-base, then G∕H is first-countable. Therefore, we obtain that if H is inner
neutral, then G∕H is metrizable if and only if G∕H is Fréchet-Urysohn with an
ωω-base. Finally, it is shown that if H is inner neutral, πχ(G∕H) = χ(G∕H) and
πω(G∕H) = ω(G∕H).
Alejandro Ramírez-Páramo, Facultad de Ciencias de la Electrónica,
Benemérita Universidad Autónoma de Puebla, Av. San Claudio y Río
Verde, Ciudad Universitaria, San Manuel, Puebla, Pue., C.P. 72570, México
(alejandro.ramirez@correo.buap.mx), and Armando Romero-Morales, Instituto de
Física y Matemáticas, Universidad Tecnológica de la Mixteca, Carretera
a Acatlima, Km 2.5, Huajuapan de León, Oaxaca, C.P. 69000, México
(armando@mixteco.utm.mx).
Rothberger/Lindelöf-type star selection principles for hit-and-miss topology, pp.
677–689.
ABSTRACT. In this we characterize selection properties of the Rothberger and
Lindelöf type in the hyperspaces CL(X), 𝕂(X), 𝔽(X) and ℂ𝕊(X), endowed
with the hit-and-miss topology. To do so, we introduce several generic selection
properties.
Suhas Pandit, Indian Institute of Technology Madras, IIT PO. Chennai - 600 036,
Tamil Nadu, India (suhas@iitm.ac.in), and Selvakumar A, The Institute of
Mathematical Sciences, Chennai, IV Cross Road, CIT Campus, Taramani, Chennai - 600
113, Tamil Nadu, India (aselvammaths@gmail.com).
Embeddings of 4–manifolds in S2 × S4 and S2×S4 using bordered Lefschetz fibration,
pp. 691–723.
ABSTRACT. In this paper, we discuss co-dimension 2 bordered achiral Lefschetz
fibration (BALF) embeddings of bordered achiral Lefschetz fibrations over D2 of a
compact, connected, orientable 4–manifold with connected boundary into the trivial
BALF of 𝒟E(m) × D2 over D2, where 𝒟E(m) is the 2–disc bundle over S2 with the
Euler number m. Using this, we show that the double of a BALF admits a smooth
embedding in S2 ×S4 as well as in S2×S4. We also provide a huge collection of bordered
achiral Lefschetz fibrations which admit BALF embeddings into the trivial
Lefschetz fibration of D4 × D2 over D2. Finally, we discuss BALF embeddings of
non-orientable 4–manifolds X, where X does not admit 3– and 4–handles in the
handle decomposition, into the trivial Lefschetz fibration of 𝒟E(m) × D2 over
D2.