1. CMB Online first
 Chen, Yichao; Gao, Xiaojian; Huang, Yuanqiu

Enumerating unlabelled embeddings of digraphs
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 $T_{2n+1}$.
Keywords:Eulerian digraph, directed embedding, unlabelled embedding Category:05C10 

2. 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 

3. CMB 2016 (vol 59 pp. 834)
 Liao, Fanghui; Liu, Zongguang

Some Properties of TriebelLizorkin and Besov Spaces Associated with Zygmund Dilations
In this paper, using CalderÃ³n's
reproducing formula and almost orthogonality estimates, we
prove the lifting property and the embedding theorem of the TriebelLizorkin
and Besov spaces associated with Zygmund dilations.
Keywords:TriebelLizorkin and Besov spaces, Riesz potential, CalderÃ³n's reproducing formula, almost orthogonality estimate, Zygmund dilation, embedding theorem Categories:42B20, 42B35 

4. CMB 2015 (vol 58 pp. 757)
5. CMB 2011 (vol 56 pp. 265)
 Chen, Yichao; Mansour, Toufik; Zou, Qian

Embedding Distributions of Generalized Fan Graphs
Total embedding distributions have been known for a few classes of graphs.
Chen, Gross, and Rieper
computed it for necklaces, closeend ladders and cobblestone
paths. Kwak and Shim computed it for bouquets of circles and
dipoles. In this paper, a splitting theorem is generalized
and the embedding distributions of
generalized fan graphs are obtained.
Keywords:total embedding distribution, splitting theorem, generalized fan graphs Category:05C10 

6. CMB 2008 (vol 51 pp. 140)
 Rossi, Julio D.

First Variations of the Best Sobolev Trace Constant with Respect to the Domain
In this paper we study the best constant of the Sobolev trace
embedding $H^{1}(\Omega)\to L^{2}(\partial\Omega)$, where $\Omega$
is a bounded smooth domain in $\RR^N$. We find a formula for the
first variation of the best constant with respect to the domain.
As a consequence, we prove that the ball is a critical domain when
we consider deformations that preserve volume.
Keywords:nonlinear boundary conditions, Sobolev trace embedding Categories:35J65, 35B33 

7. CMB 2006 (vol 49 pp. 82)
 Gogatishvili, Amiran; Pick, Luboš

Embeddings and Duality Theorem for Weak Classical Lorentz Spaces
We characterize the weight functions
$u,v,w$ on $(0,\infty)$ such that
$$
\left(\int_0^\infty f^{*}(t)^
qw(t)\,dt\right)^{1/q}
\leq
C \sup_{t\in(0,\infty)}f^{**}_u(t)v(t),
$$
where
$$
f^{**}_u(t):=\left(\int_{0}^{t}u(s)\,ds\right)^{1}
\int_{0}^{t}f^*(s)u(s)\,ds.
$$
As an application we present a~new simple characterization of
the associate space to the space $\Gamma^ \infty(v)$, determined by the
norm
$$
\f\_{\Gamma^ \infty(v)}=\sup_{t\in(0,\infty)}f^{**}(t)v(t),
$$
where
$$
f^{**}(t):=\frac1t\int_{0}^{t}f^*(s)\,ds.
$$
Keywords:Discretizing sequence, antidiscretization, classical Lorentz spaces, weak Lorentz spaces, embeddings, duality, Hardy's inequality Categories:26D10, 46E20 

8. CMB 2005 (vol 48 pp. 622)
 Vénéreau, Stéphane

Hyperplanes of the Form ${f_1(x,y)z_1+\dots+f_k(x,y)z_k+g(x,y)}$ Are Variables
The AbhyankarSathaye Embedded Hyperplane Problem asks whe\ther any
hypersurface of $\C^n$ isomorphic to $\C^{n1}$ is rectifiable, {\em
i.e.,}
equivalent to a linear hyperplane up to an automorphism of $\C^n$.
Generalizing the approach adopted by Kaliman, V\'en\'ereau, and
Zaidenberg which
consists in using almost nothing but the acyclicity of $\C^{n1}$, we solve
this problem for hypersurfaces given by polynomials of $\C[x,y,z_1,\dots, z_k]$
as in the title.
Keywords:variables, AbhyankarSathaye Embedding Problem Categories:14R10, 14R25 

9. CMB 2002 (vol 45 pp. 349)
 Coppens, Marc

Very Ample Linear Systems on BlowingsUp at General Points of Projective Spaces
Let $\mathbf{P}^n$ be the $n$dimensional projective space over some
algebraically closed field $k$ of characteristic $0$. For an integer
$t\geq 3$ consider the invertible sheaf $O(t)$ on $\mathbf{P}^n$ (Serre
twist of the structure sheaf). Let $N = \binom{t+n}{n}$, the
dimension of the space of global sections of $O(t)$, and let $k$ be an
integer satisfying $0\leq k\leq N  (2n+2)$. Let $P_1,\dots,P_k$
be general points on $\mathbf{P}^n$ and let $\pi \colon X \to
\mathbf{P}^n$ be the blowingup of $\mathbf{P}^n$ at those points.
Let $E_i = \pi^{1} (P_i)$ with $1\leq i\leq k$ be the exceptional
divisor. Then $M = \pi^* \bigl( O(t) \bigr) \otimes O_X (E_1 
\cdots E_k)$ is a very ample invertible sheaf on $X$.
Keywords:blowingup, projective space, very ample linear system, embeddings, Veronese map Categories:14E25, 14N05, 14N15 
