1. CMB Online first
 Chen, Wengu; Ge, Huanmin

A sharp bound on RIC in generalized orthogonal matching pursuit
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.
Keywords:sensing matrix, generalized orthogonal matching pursuit, restricted isometry constant, sparse signal Categories:65D15, 65J22, 68W40 

2. CMB 2016 (vol 60 pp. 350)
 Ma, Yumei

Isometry on Linear $n$Gquasi Normed Spaces
This paper generalizes the Aleksandrov problem: the MazurUlam
theorem on $n$Gquasi normed spaces. It proves that a one$n$distance
preserving mapping is an $n$isometry if and only if it has the
zero$n$Gquasi preserving property, and two kinds of $n$isometries
on $n$Gquasi normed space are equivalent; we generalize the
Benz theorem to nnormed spaces with no restrictions on the dimension
of spaces.
Keywords:$n$Gquasi norm, MazurUlam theorem, Aleksandrov problem, $n$isometry, $n$0distance Categories:46B20, 46B04, 51K05 

3. CMB 2016 (vol 59 pp. 234)
 Beardon, Alan F.

Nondiscrete Frieze Groups
The classification of Euclidean frieze groups into seven conjugacy
classes is well known, and many articles on recreational mathematics
contain frieze patterns that illustrate these classes. However,
it is
only possible to draw these patterns because the subgroup of
translations that leave the pattern invariant is (by definition)
cyclic, and hence discrete. In this paper we classify the conjugacy
classes of frieze groups that contain a nondiscrete subgroup of
translations, and clearly these groups cannot be represented
pictorially in any practical way. In addition, this discussion
sheds
light on why there are only seven conjugacy classes in the classical
case.
Keywords:frieze groups, isometry groups Categories:51M04, 51N30, 20E45 

4. CMB 2014 (vol 58 pp. 9)
 Chavan, Sameer

Irreducible Tuples Without the Boundary Property
We examine spectral behavior of irreducible tuples which do not
admit boundary property. In particular, we prove under some mild
assumption that the spectral radius of such an $m$tuple $(T_1,
\dots, T_m)$ must be the operator norm of $T^*_1T_1 + \cdots +
T^*_mT_m$. We use this simple observation to ensure boundary
property for an irreducible, essentially normal joint $q$isometry provided it
is not a joint isometry.
We further exhibit a family of
reproducing Hilbert $\mathbb{C}[z_1, \dots, z_m]$modules (of which
the DruryArveson Hilbert module is a prototype) with the property that any
two nested unitarily equivalent submodules are indeed equal.
Keywords:boundary representations, subnormal, joint pisometry Categories:47A13, 46E22 

5. CMB 2011 (vol 54 pp. 680)
 JiménezVargas, A.; VillegasVallecillos, Moisés

$2$Local Isometries on Spaces of Lipschitz Functions
Let $(X,d)$ be a metric space, and let $\mathop{\textrm{Lip}}(X)$ denote the Banach
space of all scalarvalued bounded Lipschitz functions $f$ on $X$
endowed with one of the natural norms
$
\ f\ =\max \{\ f\ _\infty ,L(f)\}$ or $\f\ =\
f\ _\infty +L(f),
$
where $L(f)$ is the
Lipschitz constant of $f.$ It is said that the isometry
group of $\mathop{\textrm{Lip}}(X)$ is canonical if every
surjective linear isometry of
$\mathop{\textrm{Lip}}(X) $ is induced by a surjective isometry of $X$.
In this paper
we prove that if $X$ is bounded separable and the isometry group of
$\mathop{\textrm{Lip}}(X)$ is canonical, then every $2$local isometry
of $\mathop{\textrm{Lip}}(X)$ is
a surjective linear isometry. Furthermore, we give a complete
description of all $2$local isometries of $\mathop{\textrm{Lip}}(X)$ when $X$ is
bounded.
Keywords:isometry, local isometry, Lipschitz function Categories:46B04, 46J10, 46E15 

6. CMB 2010 (vol 53 pp. 398)