1. CMB Online first
2. 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 

3. CMB 2017 (vol 60 pp. 436)
 Weng, Peixuan; Liu, Li

Globally Asymptotic Stability of a Delayed IntegroDifferential Equation with Nonlocal Diffusion
We study a population model with nonlocal diffusion, which
is a delayed integrodifferential equation with double nonlinearity
and two integrable kernels. By comparison method and analytical
technique, we obtain globally asymptotic stability of the zero
solution and the positive equilibrium. The results obtained
reveal that the globally asymptotic stability only depends on
the property of nonlinearity. As application, an example for
a population model with age structure is discussed at the end
of the article.
Keywords:integrodifferential equation, nonlocal diffusion, equilibrium, globally asymptotic stability, population model with age structure Categories:45J05, 35K57, 92D25 

4. CMB 2013 (vol 57 pp. 225)
 Adamaszek, Michał

Small Flag Complexes with Torsion
We classify flag complexes on at most $12$ vertices with torsion in
the first homology group. The result is moderately computeraided.
As a consequence we confirm a folklore conjecture that the smallest
poset whose order complex is homotopy equivalent to the real
projective plane (and also the smallest poset with torsion in the
first homology group) has exactly $13$ elements.
Keywords:clique complex, order complex, homology, torsion, minimal model Categories:55U10, 06A11, 55P40, 5504, 0504 

5. CMB 2011 (vol 55 pp. 632)
 Pigola, S.; Rimoldi, M.

Characterizations of Model Manifolds by Means of Certain Differential Systems
We prove metric rigidity for complete manifolds supporting solutions of
certain second order differential systems, thus extending classical works on a
characterization of spaceforms. Along the way, we also discover
new characterizations of spaceforms. We next generalize results concerning metric
rigidity via equations involving vector fields.
Keywords:metric rigidity, model manifolds, Obata's type theorems Category:53C20 

6. CMB 2011 (vol 55 pp. 487)
7. CMB 2008 (vol 51 pp. 146)
 Zhou, Xiaowen

SteppingStone Model with Circular Brownian Migration
In this paper we consider the steppingstone model on a circle with
circular Brownian migration. We first point out a connection between
Arratia flow on the circle and the marginal distribution of this
model. We then give a new representation for the steppingstone
model using Arratia flow and circular coalescing Brownian motion.
Such a representation enables us to carry out some explicit
computations. In particular, we find the distribution for the first
time when there is only one type
left across the circle.
Keywords:steppingstone model, circular coalescing Brownian motion, Arratia flow, duality, entrance law Categories:60G57, 60J65 

8. CMB 2001 (vol 44 pp. 459)
 Kahl, Thomas

LScatÃ©gorie algÃ©brique et attachement de cellules
Nous montrons que la Acat\'egorie d'un espace simplement connexe de
type fini est inf\'erieure ou \'egale \`a $n$ si et seulement si son
mod\`ele d'AdamsHilton est un r\'etracte homotopique d'une alg\`ebre
diff\'erentielle \`a $n$ \'etages. Nous en d\'eduisons que
l'invariant $\Acat$ augmente au plus de 1 lors de l'attachement
d'une cellule \`a un espace.
We show that the Acategory of a simply connected space of finite type
is less than or equal to $n$ if and only if its AdamsHilton model is
a homotopy retract of an $n$stage differential algebra. We deduce
from this that the invariant $\Acat$ increases by at most 1 when a
cell is attached to a space.
Keywords:LScategory, strong category, AdamsHilton models, cell attachments Categories:55M30, 18G55 
