1. CMB Online first
 Moslehian, Mohammad Sal; Zamani, Ali

Characterizations of operator BirkhoffJames orthogonality
In this paper, we obtain some characterizations of the (strong)
BirkhoffJames orthogonality for elements of Hilbert $C^*$modules
and certain elements of $\mathbb{B}(\mathscr{H})$.
Moreover, we obtain a kind of Pythagorean relation for bounded
linear operators.
In addition, for $T\in \mathbb{B}(\mathscr{H})$ we prove that if the
norm attaining
set $\mathbb{M}_T$ is a unit sphere of some finite dimensional
subspace $\mathscr{H}_0$ of $\mathscr{H}$ and $\T\_{{{\mathscr{H}}_0}^\perp}
\lt \T\$, then for every $S\in\mathbb{B}(\mathscr{H})$, $T$ is the strong
BirkhoffJames orthogonal to $S$ if and only if there exists
a unit vector $\xi\in {\mathscr{H}}_0$ such that $\T\\xi =
T\xi$ and $S^*T\xi = 0$.
Finally, we introduce a new type of approximate orthogonality
and investigate this notion in the setting of inner product $C^*$modules.
Keywords:Hilbert $C^*$module, BirkhoffJames orthogonality, strong BirkhoffJames orthogonality, approximate orthogonality Categories:46L05, 46L08, 46B20 

2. 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 

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. 877)
 Zaatra, Mohamed

Generating Some Symmetric Semiclassical Orthogonal Polynomials
We show that if $v$ is a regular semiclassical form
(linear functional), then the symmetric form $u$ defined by the
relation
$x^{2}\sigma u = \lambda v$,
where $(\sigma f)(x)=f(x^{2})$ and the odd
moments of $u$ are $0$, is also
regular and semiclassical form for every
complex $\lambda $ except for a discrete set of numbers depending
on $v$. We give explicitly the threeterm recurrence relation
and the
structure relation coefficients of the orthogonal polynomials
sequence associated with $u$ and the class of the form $u$ knowing
that of $v$. We conclude with an illustrative example.
Keywords:orthogonal polynomials, quadratic decomposition, semiclassical forms, structure relation Categories:33C45, 42C05 

5. CMB 2011 (vol 55 pp. 418)
 Vinh, Le Anh

Maximal Sets of Pairwise Orthogonal Vectors in Finite Fields
Given a positive integer $n$, a finite field $\mathbb{F}_q$ of $q$ elements
($q$ odd), and a nondegenerate symmetric bilinear form $B$ on
$\mathbb{F}_q^n$, we determine the largest possible cardinality of pairwise
$B$orthogonal subsets $\mathcal{E} \subseteq \mathbb{F}_q^n$, that is, for
any two vectors $\mathbf{x}, \mathbf{y} \in \mathcal{E}$, one has $B
(\mathbf{x}, \mathbf{y}) = 0$.
Keywords:orthogonal sets, zerodistance sets Category:05B25 

6. CMB 2011 (vol 55 pp. 821)
 PerezGarcia, C.; Schikhof, W. H.

New Examples of NonArchimedean Banach Spaces and Applications
The study carried out in this paper about some new examples of
Banach spaces, consisting of certain valued fields extensions, is
a typical nonarchimedean feature. We determine whether these
extensions are of countable type, have $t$orthogonal bases, or are
reflexive.
As an application we construct, for a class of base fields, a norm
$\\cdot\$ on $c_0$, equivalent to the canonical supremum norm,
without nonzero vectors that are $\\cdot\$orthogonal and such
that there is a multiplication on $c_0$ making $(c_0,\\cdot\)$
into a valued field.
Keywords:nonarchimedean Banach spaces, valued field extensions, spaces of countable type, orthogonal bases Categories:46S10, 12J25 

7. CMB 2011 (vol 55 pp. 597)
 Osękowski, Adam

Sharp Inequalities for Differentially Subordinate Harmonic Functions and Martingales
We determine the best constants $C_{p,\infty}$ and $C_{1,p}$,
$1 < p < \infty$, for which the following holds. If $u$, $v$ are
orthogonal harmonic functions on a Euclidean domain such that $v$ is
differentially subordinate to $u$, then
$$ \v\_p \leq C_{p,\infty}
\u\_\infty,\quad
\v\_1 \leq C_{1,p} \u\_p.
$$
In particular, the inequalities are still sharp for the conjugate
harmonic functions on the unit disc of $\mathbb R^2$.
Sharp probabilistic versions of these estimates are also studied.
As an application, we establish a sharp version of the classical logarithmic inequality of Zygmund.
Keywords: harmonic function, conjugate harmonic functions, orthogonal harmonic functions, martingale, orthogonal martingales, norm inequality, optimal stopping problem Categories:31B05, 60G44, 60G40 

8. CMB 2011 (vol 55 pp. 767)
 Martini, Horst; Wu, Senlin

On Zindler Curves in Normed Planes
We extend the notion of Zindler curve from the Euclidean plane to
normed planes. A characterization of Zindler curves for general
normed planes is given, and the relation between Zindler curves and
curves of constant areahalving distances in such planes is
discussed.
Keywords:rc length, areahalving distance, Birkhoff orthogonality, convex curve, halving pair, halving distance, isosceles orthogonality, midpoint curve, Minkowski plane, normed plane, Zindler curve Categories:52A21, 52A10, 46C15 

9. CMB 2011 (vol 55 pp. 462)
 Campbell, Peter S.; Stokke, Anna

Hookcontent Formulae for Symplectic and Orthogonal Tableaux
By considering the specialisation
$s_{\lambda}(1,q,q^2,\dots,q^{n1})$ of
the Schur function, Stanley was able to describe a formula for the
number of semistandard Young tableaux of shape $\lambda$ in terms of
the contents and hook lengths of the boxes in the Young diagram.
Using specialisations of symplectic and orthogonal Schur functions,
we derive corresponding formulae,
first given by El Samra and King, for the number of semistandard
symplectic and orthogonal $\lambda$tableaux.
Keywords:symplectic tableaux, orthogonal tableaux, Schur function Categories:05E05, 05E10 

10. CMB 2009 (vol 52 pp. 95)
 Miranian, L.

Matrix Valued Orthogonal Polynomials on the Unit Circle: Some Extensions of the Classical Theory
In the work presented below the classical subject of orthogonal
polynomials on the unit
circle is discussed in the matrix setting. An explicit matrix
representation of the matrix valued orthogonal polynomials in terms of
the moments of the measure is presented. Classical recurrence
relations are revisited using the matrix representation of the
polynomials. The matrix expressions for the kernel polynomials and the
ChristoffelDarboux formulas are presented for the first time.
Keywords:Matrix valued orthogonal polynomials, unit circle, Schur complements, recurrence relations, kernel polynomials, ChristoffelDarboux Category:42C99 

11. CMB 2001 (vol 44 pp. 337)
 Vinet, Luc; Zhedanov, Alexei

Spectral Transformations of the Laurent Biorthogonal Polynomials, II. Pastro Polynomials
We continue to study the simplest closure conditions for chains of
spectral transformations of the Laurent biorthogonal polynomials
($\LBP$). It is shown that the 11periodic $q$closure condition
leads to the $\LBP$ introduced by Pastro. We introduce classes of
semiclassical and LaguerreHahn $\LBP$ associated to generic closure
conditions of the chain of spectral transformations.
Keywords:Laurent orthogonal polynomials, Pastro polynomials, spectral transformations Category:33D45 
