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3  Periodic steadystate solutions of a liquid film model via a classical method Alhasanat, Ahmad; Ou, Chunhua
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.


16  Classification of simple weight modules over the Schrödinger algebra Bavula, V. V.; Lu, T.
A classification of simple weight modules over the Schrödinger
algebra is given. The Krull and the global dimensions are found
for the centralizer $C_{\mathcal{S}}(H)$ (and some of its prime factor
algebras) of the Cartan element $H$ in the universal enveloping
algebra $\mathcal{S}$ of the Schrödinger (Lie) algebra. The simple
$C_{\mathcal{S}}(H)$modules are classified. The Krull and the global
dimensions are found for some (prime) factor algebras of the
algebra $\mathcal{S}$ (over the centre). It is proved that some (prime)
factor algebras of $\mathcal{S}$ and $C_{\mathcal{S}}(H)$ are tensor homological/Krull
minimal.


40  A sharp bound on RIC in generalized orthogonal matching pursuit Chen, Wengu; Ge, Huanmin
Generalized orthogonal matching pursuit (gOMP) algorithm has
received much attention in recent years as a natural extension
of
orthogonal matching pursuit (OMP). It is used to recover sparse
signals in compressive sensing. In this paper, a new bound is
obtained for the exact reconstruction of every $K$sparse signal
via
the gOMP algorithm in the noiseless case. That is, if the restricted
isometry constant (RIC) $\delta_{NK+1}$ of the sensing matrix
$A$
satisfies $ \delta_{NK+1}\lt \frac{1}{\sqrt{\frac{K}{N}+1}}$, then
the
gOMP can perfectly recover every $K$sparse signal $x$ from $y=Ax$.
Furthermore, the bound is proved to be sharp.
In the noisy case, the above bound on RIC combining with an
extra condition on the minimum
magnitude of the nonzero components of $K$sparse signals can
guarantee
that the gOMP selects all of support indices of the $K$sparse
signals.


55  Enumerating unlabelled embeddings of digraphs Chen, Yichao; Gao, Xiaojian; Huang, Yuanqiu
A $2$cell embedding of an Eulerian digraph $D$
into a closed surface is said to be directed if the
boundary of each face is a directed closed walk in $D$. In this
paper, a method is developed with the purpose of enumerating
unlabelled embeddings for an Eulerian digraph. As an application,
we obtain explicit formulas for the number of unlabelled embeddings
of directed bouquets of cycles $B_n$, directed dipoles $OD_{2n}$
and for a class of regular tournaments $T_{2n+1}$.


70  Hilbert Transformation and Representation of the $ax+b$ Group Dang, Pei; Liu, Hua; Qian, Tao
In this paper we study the Hilbert transformations over
$L^2(\mathbb{R})$
and $L^2(\mathbb{T})$ from
the viewpoint of symmetry. For a linear operator over $L^2(\mathbb{R})$
commutative with the ax+b group we show that the operator is
of the form
$
\lambda I+\eta H,
$
where $I$ and $H$ are the identity operator and Hilbert transformation
respectively, and $\lambda,\eta$ are complex numbers. In the
related literature this result was proved through first invoking
the boundedness result of the operator, proved though a big
machinery.
In our setting the boundedness is a consequence of the boundedness
of the Hilbert transformation. The methodology that we use is
GelfandNaimark's representation of the ax+b group. Furthermore
we prove a similar result on the unit circle. Although there
does not exist a group like ax+b on the unit circle, we construct
a semigroup to play the same symmetry role for the Hilbert transformations
over the circle $L^2(\mathbb{T}).$


85  On subcritically Stein fillable 5manifolds Ding, Fan; Geiges, Hansjörg; Zhang, Guangjian
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.


97  On a singular integral of ChristJourné type with homogeneous kernel Ding, Yong; Lai, Xudong
In this paper, we prove that the following singular integral
defined by
$$T_{\Omega,a}f(x)=\operatorname{p.v.}\int_{\mathbb{R}^{d}}\frac{\Omega(xy)}{xy^d}\cdot m_{x,y}a\cdot
f(y)dy$$
is bounded on $L^p(\mathbb{R}^d)$ for $1\lt p\lt \infty$ and is of weak type
(1,1), where $\Omega\in L\log^+L(\mathbb{S}^{d1})$ and
$m_{x,y}a=:\int_0^1a(sx+(1s)y)ds$
with $a\in L^\infty(\mathbb{R}^d)$ satisfying some restricted conditions.


114  A characterization of $C^{\ast}$normed algebras via positive functionals Haralampidou, Marina; Oudadess, Mohamed; Palacios, Lourdes; Signoret, Carlos
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.


124  The Jordan Curve Theorem via Complex Analysis Hemasundar, Gollakota V. V.; Simha, R. R.
The aim of this article is to give a proof of the Jordan Curve
Theorem via complex analysis.


130  Additive maps on units of rings Koşan, Tamer; Sahinkaya, Serap; Zhou, Yiqiang
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.


142  An Equivalent Form of Picard's Theorem and Beyond Li, Bao Qin
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.


149  Global phase portraits for the Abel quadratic polynomial differential equations of second kind with $Z_2$symmetries Llibre, Jaume; Valls, Claudia
We provide normal forms and the global phase portraits on the
Poincaré disk for all Abel quadratic polynomial differential
equations of the second kind with $\mathbb Z_2$symmetries.


166  A moduletheoretic characterization of algebraic hypersurfaces MirandaNeto, Cleto B.
In this note we prove the following surprising characterization:
if
$X\subset {\mathbb A}^n$ is an (embedded, nonempty, proper)
algebraic variety defined over a
field $k$ of characteristic zero, then $X$ is a hypersurface
if and only if the module $T_{{\mathcal O}_{{\mathbb
A}^n}/k}(X)$ of logarithmic vector fields of
$X$ is a reflexive ${\mathcal
O}_{{\mathbb A}^n}$module. As a consequence of this result,
we derive that if $T_{{\mathcal O}_{{\mathbb A}^n}/k}(X)$ is a
free ${\mathcal
O}_{{\mathbb A}^n}$module, which is shown to be equivalent
to the freeness of the $t$th exterior power of $T_{{\mathcal O}_{{\mathbb
A}^n}/k}(X)$ for some (in fact, any) $t\leq n$, then necessarily
$X$ is a Saito free divisor.


174  A factorization result for classical and similitude groups Roche, Alan; Vinroot, C. Ryan
For most classical and similitude groups, we show that each element
can be written as a product of two transformations that
a) preserve or almost preserve the underlying form and b) whose
squares are certain scalar maps. This generalizes work of Wonenburger
and Vinroot.
As an application, we reprove and slightly extend a well known
result of Mœglin, Vignéras and Waldspurger on the existence
of automorphisms of $p$adic classical groups that take each
irreducible smooth representation to its dual.


191  The FeffermanStein type inequalities for strong and directional maximal operators in the plane Saito, Hiroki; Tanaka, Hitoshi
The FeffermanStein type inequalities
for strong maximal operator and directional maximal operator
are verified with an additional composition of the HardyLittlewood
maximal operator in the plane.


201  Projective plane bundles over an elliptic curve Takahashi, Tomokuni
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.


211  The asymptotics of the higher dimensional Reidemeister torsion for exceptional surgeries along twist knots Tran, Anh T.; Yamaguchi, Yoshikazu
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.

