26. CMB Online first
 Maican, Mario

Moduli of space sheaves with Hilbert polynomial $4m+1$
We investigate the moduli space of sheaves supported on space
curves of degree $4$ and having Euler characteristic $1$.
We give an elementary proof of the fact that this moduli space
consists of three irreducible components.
Keywords:moduli of sheaves, semistable sheaves Categories:14D20, 14D22 

27. CMB Online first
 Alhasanat, Ahmad; Ou, Chunhua

Periodic steadystate solutions of a liquid film model via a classical method
In this paper, periodic steadystate of a liquid film flowing
over a periodic uneven wall is investigated via a classical method.
Specifically, we analyze a longwave model that is valid at
the nearcritical Reynolds number. For the periodic wall surface,
we construct an iteration scheme in terms of an integral form
of the original steadystate problem. The uniform convergence
of the scheme is proved so that we can derive the existence and
the uniqueness, as well as the asymptotic formula, of the periodic
solutions.
Keywords:film flow, classical methods, asymptotic analysis Categories:34E05, 34E10, 34E15 

28. CMB Online first
29. CMB 2017 (vol 60 pp. 571)
30. CMB Online first
 Franz, Matthias

Symmetric products of equivariantly formal spaces
Let \(X\) be a CW complex with a continuous action of a topological
group \(G\).
We show that if \(X\) is equivariantly formal for singular
cohomology
with coefficients in some field \(\Bbbk\), then so are all symmetric
products of \(X\)
and in fact all its \(\Gamma\)products.
In particular, symmetric products
of quasiprojective Mvarieties are again Mvarieties.
This generalizes a result by Biswas and D'Mello
about symmetric products of Mcurves.
We also discuss several related questions.
Keywords:symmetric product, equivariant formality, maximal variety, Gamma product Categories:55N91, 55S15, 14P25 

31. CMB 2017 (vol 60 pp. 402)
 Shravan Kumar, N.

Invariant Means on a Class of von Neumann Algebras Related to Ultraspherical Hypergroups II
Let $K$ be an ultraspherical hypergroup associated to a locally
compact group $G$ and a spherical projector $\pi$ and let $VN(K)$
denote the dual of the Fourier algebra $A(K)$ corresponding to
$K.$ In this note, we show that the set of invariant means on
$VN(K)$ is singleton if and only if $K$ is discrete. Here $K$
need not be second countable. We also study invariant means on
the dual of the Fourier algebra $A_0(K),$ the closure of $A(K)$
in the $cb$multiplier norm. Finally, we consider generalized
translations and generalized invariant means.
Keywords:ultraspherical hypergroup, Fourier algebra, FourierStieltjes algebra, invariant mean, generalized translation, generalized invariant mean Categories:43A62, 46J10, 43A30, 20N20 

32. CMB Online first
 Wang, Lian Daniel

A Multiplier Theorem on Anisotropic Hardy Spaces
We present a multiplier theorem on anisotropic
Hardy spaces. When $m$ satisfies the anisotropic, pointwise Mihlin
condition, we obtain boundedness of the multiplier operator $T_m
: H_A^p (\mathbb R^n) \rightarrow H_A^p (\mathbb R^n)$, for the range of $p$
that depends on the eccentricities of the dilation $A$ and the
level of regularity of a multiplier symbol $m$. This extends
the classical multiplier theorem of Taibleson and Weiss.
Keywords:anisotropic Hardy space, multiplier, Fourier transform Categories:42B30, 42B25, 42B35 

33. CMB Online first
 Józiak, Paweł

Remarks on Hopf images and quantum permutation groups $S_n^+$
Motivated by a question of A. Skalski and P.M. SoÅtan (2016)
about inner faithfulness of the S. Curran's map of extending
a quantum increasing sequence to a quantum permutation, we revisit
the results and techniques of T. Banica and J. Bichon (2009)
and study some grouptheoretic properties of the quantum permutation
group on $4$ points. This enables us not only to answer the aforementioned
question in positive in case $n=4, k=2$, but also to classify
the automorphisms of $S_4^+$, describe all the embeddings $O_{1}(2)\subset
S_4^+$ and show that all the copies of $O_{1}(2)$ inside $S_4^+$
are conjugate. We then use these results to show that the converse
to the criterion we applied to answer the aforementioned question
is not valid.
Keywords:Hopf image, quantum permutation group, compact quantum group Categories:20G42, 81R50, 46L89, 16W35 

34. CMB Online first
 Gupta, Purvi

A realanalytic nonpolynomially convex isotropic torus with no attached discs
We show by means of an example in $\mathbb C^3$ that Gromov's
theorem on the presence of attached holomorphic discs for compact
Lagrangian manifolds is not true in the subcritical
realanalytic case, even in the absence of an obvious obstruction,
i.e, polynomial convexity.
Keywords:polynomial hull, isotropic submanifold, holomorphic disc Categories:32V40, 32E20, 53D12 

35. CMB Online first
 Takahashi, Tomokuni

Projective plane bundles over an elliptic curve
We calculate the dimension of cohomology groups for
the holomorphic tangent bundles of each isomorphism
class of the projective plane bundle over an elliptic curve.
As an application, we construct the families
of projective plane bundles, and prove that the families
are effectively parametrized and complete.
Keywords:projective plane bundle, vector bundle, elliptic curve, deformation, KodairaSpencer map Categories:14J10, 14J30, 14D15 

36. CMB Online first
 Zhang, GuoBao; Tian, Ge

Stability of Traveling Wavefronts for a TwoComponent Lattice Dynamical System Arising in Competition Models
In this paper, we study a twocomponent LotkaVolterra competition
system
on an onedimensional spatial lattice. By the method of the comparison
principle together with
the weighted energy, we prove that the traveling wavefronts with
large speed are exponentially asymptotically stable,
when the initial perturbation around the traveling wavefronts
decays
exponentially as $j+ct \rightarrow \infty$, where $j\in\mathbb{Z}$,
$t\gt 0$, but the initial perturbation
can be arbitrarily large on other locations. This partially answers
an open problem by J.S. Guo and C.H. Wu.
Keywords:lattice dynamical system, competition model, traveling wavefront, stability Categories:34A33, 34K20, 92D25 

37. CMB Online first
 Haralampidou, Marina; Oudadess, Mohamed; Palacios, Lourdes; Signoret, Carlos

A characterization of $C^{\ast}$normed algebras via positive functionals
We give a characterization of $C^{\ast}$normed algebras, among
certain involutive normed ones. This is done through the existence
of enough specific positive functionals. The same question is
also
examined in some non normed (topological) algebras.
Keywords:$C^{\ast}$normed algebra, $C^*$algebra, (pre)locally $C^*$algebra, pre$C^*$bornological algebra, positive functional, locally uniformly $A$convex algebra, perfect locally $m$convex algebra, $C^*$(resp. $^*$) subnormable algebra Categories:46H05, 46K05 

38. CMB Online first
 Tran, Anh T.; Yamaguchi, Yoshikazu

The asymptotics of the higher dimensional Reidemeister torsion for exceptional surgeries along twist knots
We determine the asymptotic behavior of the higher dimensional
Reidemeister torsion for
the graph manifolds obtained by exceptional surgeries along
twist knots.
We show that all irreducible
$\operatorname{SL}_2(\mathbb{C})$representations of the graph
manifold
are induced by irreducible metabelian representations of the
twist knot group.
We also give the set of the limits of the leading coefficients
in the higher dimensional Reidemeister torsion explicitly.
Keywords:Reidemeister torsion, graph manifold, asymptotic behavior, exceptional surgery Categories:57M27, 57M50 

39. CMB 2017 (vol 60 pp. 536)
40. CMB Online first
41. CMB Online first
 Koşan, Tamer; Sahinkaya, Serap; Zhou, Yiqiang

Additive maps on units of rings
Let $R$ be a ring. A map $f: R\rightarrow R$
is additive if $f(a+b)=f(a)+f(b)$ for all elements $a$ and $b$
of $R$.
Here a map $f: R\rightarrow R$ is called unitadditive if $f(u+v)=f(u)+f(v)$
for all units $u$ and $v$ of $R$. Motivated by a recent result
of Xu, Pei and Yi
showing that, for any field $F$, every
unitadditive map of ${\mathbb M}_n(F)$ is additive for all $n\ge
2$, this paper is about the question when every unitadditive
map of a ring is additive. It is proved that every unitadditive
map of a semilocal ring $R$ is additive if and only if either
$R$ has no homomorphic image isomorphic to $\mathbb Z_2$ or $R/J(R)\cong
\mathbb Z_2$ with $2=0$ in $R$. Consequently, for any semilocal
ring $R$, every unitadditive map of ${\mathbb M}_n(R)$ is additive
for all $n\ge 2$. These results are further extended to rings
$R$ such that $R/J(R)$ is a direct product of exchange rings
with primitive factors Artinian. A unitadditive map $f$ of a
ring $R$ is called unithomomorphic if $f(uv)=f(u)f(v)$ for all
units $u,v$ of $R$. As an application, the question of when every
unithomomorphic map of a ring is an endomorphism is addressed.
Keywords:additive map, unit, 2sum property, semilocal ring, exchange ring with primitive factors Artinian Categories:15A99, 16U60, 16L30 

42. CMB 2017 (vol 60 pp. 774)
 Jensen, Gerd; Pommerenke, Christian

On the Structure of the Schild Group in Relativity Theory
Alfred Schild has established conditions
that Lorentz transformations map worldvectors $(ct,x,y,z)$ with
integer coordinates onto vectors of the same kind. These transformations
are called integral Lorentz transformations.
The present paper contains supplements to
our earlier work
with a new focus on group theory. To relate the results to the
familiar matrix group nomenclature we associate Lorentz transformations
with matrices in $\mathrm{SL}(2,\mathbb{C})$. We consider the
lattice of subgroups of the group originated in Schild's paper
and obtain generating sets for the full group and its subgroups.
Keywords:Lorentz transformation, integer lattice, Gaussian integers, Schild group, subgroup Categories:22E43, 20H99, 83A05 

43. CMB Online first
 Bu, Shangquan; Cai, Gang

HÃ¶lder continuous solutions of degenerate differential equations with finite delay
Using known operatorvalued Fourier multiplier results on vectorvalued
HÃ¶lder continuous function spaces $C^\alpha (\mathbb R; X)$, we completely
characterize the $C^\alpha$wellposedness of the first order
degenerate differential equations with finite delay $(Mu)'(t)
= Au(t) + Fu_t + f(t)$ for $t\in\mathbb R$
by the boundedness of the $(M, F)$resolvent of $A$ under suitable
assumption on the delay operator $F$, where $A, M$ are closed
linear
operators on a Banach space $X$ satisfying $D(A)\cap D(M) \not=\{0\}$,
the delay operator $F$ is a bounded linear operator
from $C([r, 0]; X)$ to $X$ and $r \gt 0$ is fixed.
Keywords:wellposedness, degenerate differential equation, $\dot{C}^\alpha$multiplier, HÃ¶lder continuous function space Categories:34N05, 34G10, 47D06, 47A10, 34K30 

44. CMB Online first
 Ding, Fan; Geiges, Hansjörg; Zhang, Guangjian

On subcritically Stein fillable 5manifolds
We make some elementary observations concerning subcritically
Stein
fillable contact structures on $5$manifolds.
Specifically, we determine the diffeomorphism type of such
contact manifolds in the case the fundamental group is finite
cyclic,
and we show that on the $5$sphere the standard contact structure
is the unique subcritically fillable one. More generally,
it is shown that subcritically fillable contact structures
on simply connected $5$manifolds are determined by their
underlying almost contact structure. Along the way, we discuss
the
homotopy classification of almost contact structures.
Keywords:subcritically Stein fillable, 5manifold, almost contact structure, thickening Categories:53D35, 32Q28, 57M20, 57Q10, 57R17 

45. CMB Online first
46. CMB 2017 (vol 60 pp. 604)
 Louder, Larsen; Wilton, Henry

Stackings and the $W$cycles Conjecture
We prove Wise's $W$cycles conjecture: Consider a compact graph
$\Gamma'$ immersing into another graph $\Gamma$. For any immersed
cycle $\Lambda:S^1\to \Gamma$, we consider the map $\Lambda'$
from
the circular components $\mathbb{S}$ of the pullback to $\Gamma'$.
Unless
$\Lambda'$ is reducible, the degree of the covering map $\mathbb{S}\to
S^1$ is bounded above by minus the Euler characteristic of
$\Gamma'$. As a corollary, any finitely generated subgroup
of a
onerelator group has finitely generated Schur multiplier.
Keywords:free groups, onerelator groups, rightorderability Category:20F65 

47. CMB 2017 (vol 60 pp. 736)
 Gilligan, Bruce

Levi's Problem for Pseudoconvex Homogeneous Manifolds
Suppose $G$ is a connected complex Lie group and $H$ is a closed
complex subgroup.
Then there exists a closed complex subgroup $J$ of $G$ containing
$H$ such that
the fibration $\pi:G/H \to G/J$ is the holomorphic reduction
of $G/H$, i.e., $G/J$ is holomorphically
separable and ${\mathcal O}(G/H) \cong \pi^*{\mathcal O}(G/J)$.
In this paper we prove that if $G/H$ is pseudoconvex, i.e.,
if
$G/H$ admits a continuous plurisubharmonic exhaustion function,
then $G/J$ is Stein and $J/H$ has no nonconstant holomorphic
functions.
Keywords:complex homogeneous manifold, plurisubharmonic exhaustion function, holomorphic reduction, Stein manifold, Remmert reduction, Hirschowitz annihilator Categories:32M10, 32U10, 32A10, 32Q28 

48. CMB 2017 (vol 60 pp. 747)
 Huang, Yanhe; Sottile, Frank; Zelenko, Igor

Injectivity of Generalized Wronski Maps
We study linear projections on PlÃ¼cker space whose restriction
to the Grassmannian is a nontrivial branched
cover.
When an automorphism of the Grassmannian preserves the fibers,
we show that the Grassmannian is necessarily
of $m$dimensional linear subspaces in a symplectic vector
space of dimension $2m$, and the linear map is
the Lagrangian involution.
The Wronski map for a selfadjoint linear differential operator
and pole placement map for
symmetric linear systems are natural examples.
Keywords:Wronski map, PlÃ¼cker embedding, curves in Lagrangian Grassmannian, selfadjoint linear differential operator, symmetric linear control system, pole placement map Categories:14M15, 34A30, 93B55 

49. CMB Online first
 Li, Bao Qin

An Equivalent Form of Picard's Theorem and Beyond
This paper gives an equivalent form of Picard's
theorem via entire solutions of the functional equation $f^2+g^2=1$,
and then its improvements and applications to certain nonlinear
(ordinary and partial) differential equations.
Keywords:entire function, Picard's Theorem, functional equation, partial differential equation Categories:30D20, 32A15, 35F20 

50. CMB 2017 (vol 60 pp. 422)
 Tang, Xianhua

New Superquadratic Conditions for Asymptotically Periodic SchrÃ¶dinger Equations
This paper is dedicated to studying the
semilinear SchrÃ¶dinger equation
$$
\left\{
\begin{array}{ll}
\triangle u+V(x)u=f(x, u), \ \ \ \ x\in {\mathbf{R}}^{N},
\\
u\in H^{1}({\mathbf{R}}^{N}),
\end{array}
\right.
$$
where $f$ is a superlinear, subcritical nonlinearity. It focuses
on the case where
$V(x)=V_0(x)+V_1(x)$, $V_0\in C(\mathbf{R}^N)$, $V_0(x)$ is 1periodic
in each of $x_1, x_2, \ldots, x_N$ and
$\sup[\sigma(\triangle +V_0)\cap (\infty, 0)]\lt 0\lt \inf[\sigma(\triangle
+V_0)\cap (0, \infty)]$,
$V_1\in C(\mathbf{R}^N)$ and $\lim_{x\to\infty}V_1(x)=0$. A new superquadratic
condition is obtained,
which is weaker than some well known results.
Keywords:SchrÃ¶dinger equation, superlinear, asymptotically periodic, ground state solutions of NehariPankov type Categories:35J20, 35J60 
