1. CMB Online first
 Franz, Matthias

Symmetric products of equivariantly formal spaces
Let \(X\) be a CW complex with a continuous action of a topological
group \(G\).
We show that if \(X\) is equivariantly formal for singular
cohomology
with coefficients in some field \(\Bbbk\), then so are all symmetric
products of \(X\)
and in fact all its \(\Gamma\)products.
In particular, symmetric products
of quasiprojective Mvarieties are again Mvarieties.
This generalizes a result by Biswas and D'Mello
about symmetric products of Mcurves.
We also discuss several related questions.
Keywords:symmetric product, equivariant formality, maximal variety, Gamma product Categories:55N91, 55S15, 14P25 

2. CMB Online first
3. CMB Online first
 Ding, Fan; Geiges, Hansjörg; Zhang, Guangjian

On subcritically Stein fillable 5manifolds
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.
Keywords:subcritically Stein fillable, 5manifold, almost contact structure, thickening Categories:53D35, 32Q28, 57M20, 57Q10, 57R17 

4. CMB Online first
 Jiang, Chunlan

Reduction to dimension two of local spectrum for $AH$ algebra with ideal property
A $C^{*}$algebra $A$ has the ideal property if any ideal
$I$ of $A$ is generated as a closed two sided ideal by the projections
inside the ideal. Suppose that the limit $C^{*}$algebra $A$
of inductive limit of direct sums of matrix algebras over spaces
with uniformly bounded dimension has ideal property. In this
paper we will prove that $A$ can be written as an inductive limit
of certain very special subhomogeneous algebras, namely, direct
sum of dimension drop interval algebras and matrix algebras over
2dimensional spaces with torsion $H^{2}$ groups.
Keywords:AH algebra, reduction, local spectrum, ideal property Category:46L35 

5. CMB Online first
 Gilligan, Bruce

Levi's problem for pseudoconvex homogeneous manifolds
Suppose $G$ is a connected complex Lie group and $H$ is a closed
complex subgroup.
Then there exists a closed complex subgroup $J$ of $G$ containing
$H$ such that
the fibration $\pi:G/H \to G/J$ is the holomorphic reduction
of $G/H$, i.e., $G/J$ is holomorphically
separable and ${\mathcal O}(G/H) \cong \pi^*{\mathcal O}(G/J)$.
In this paper we prove that if $G/H$ is pseudoconvex, i.e.,
if
$G/H$ admits a continuous plurisubharmonic exhaustion function,
then $G/J$ is Stein and $J/H$ has no nonconstant holomorphic
functions.
Keywords:complex homogeneous manifold, plurisubharmonic exhaustion function, holomorphic reduction, Stein manifold, Remmert reduction, Hirschowitz annihilator Categories:32M10, 32U10, 32A10, 32Q28 

6. 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 

7. CMB 2016 (vol 60 pp. 217)
 Wang, Yuanyi

Condition $C'_{\wedge}$ of Operator Spaces
In this paper, we study condition $C'_{\wedge}$ which is a
projective tensor product analogue of condition $C'$. We show
that
the finitedimensional OLLP operator spaces have condition
$C'_{\wedge}$ and $M_{n}$ $(n\gt 2)$ does not have that property.
Keywords:operator space, local theory, tensor product Category:46L07 

8. CMB 2016 (vol 59 pp. 813)
9. CMB 2016 (vol 59 pp. 705)
 Chen, Yichao; Yin, Xuluo

The Thickness of the Cartesian Product of Two Graphs
The thickness of a graph $G$ is the minimum number
of planar subgraphs whose union is $G.$ A
$t$minimal graph is a graph of thickness $t$ which contains
no proper subgraph of thickness $t.$ In this paper, upper and
lower bounds are obtained for the thickness, $t(G\Box H)$, of
the Cartesian
product of two graphs $G$ and $H$, in terms of the thickness
$t(G)$ and $t(H)$.
Furthermore, the thickness of the Cartesian product of two planar
graphs and of a $t$minimal graph and a planar graph are determined.
By using a new planar decomposition of the complete bipartite
graph $K_{4k,4k},$ the thickness of the Cartesian product of
two complete bipartite graphs $K_{n,n}$ and $K_{n,n}$ is also
given, for $n\neq 4k+1$.
Keywords:planar graph, thickness, Cartesian product, $t$minimal graph, complete bipartite graph Category:05C10 

10. CMB 2016 (vol 59 pp. 326)
11. CMB 2016 (vol 59 pp. 279)
12. CMB 2016 (vol 59 pp. 311)
 Ilten, Nathan; Teitler, Zach

Product Ranks of the $3\times 3$ Determinant and Permanent
We show that the product rank of the $3 \times 3$ determinant
$\det_3$ is $5$,
and the product rank of the $3 \times 3$ permanent
$\operatorname{perm}_3$
is $4$.
As a corollary, we obtain that the tensor rank of $\det_3$ is
$5$ and the tensor rank of $\operatorname{perm}_3$ is $4$.
We show moreover that the border product rank of $\operatorname{perm}_n$ is
larger than $n$ for any $n\geq 3$.
Keywords:product rank, tensor rank, determinant, permanent, Fano schemes Categories:15A21, 15A69, 14M12, 14N15 

13. CMB 2016 (vol 59 pp. 363)
 Li, Dan; Ma, Wanbiao

Dynamical Analysis of a StageStructured Model for Lyme Disease with Two Delays
In this paper, a
nonlinear stagestructured model for Lyme disease is considered.
The model is a system of differential equations with two time
delays. The basic reproductive rate, $R_0(\tau_1,\tau_2)$, is
derived. If $R_0(\tau_1,\tau_2)\lt 1$, then the boundary equilibrium
is globally asymptotically stable. If $R_0(\tau_1,\tau_2)\gt 1$,
then there exists
a unique positive equilibrium whose local asymptotical stability
and the existence of
Hopf bifurcations are established by analyzing the distribution
of the characteristic values.
An explicit algorithm for determining the direction of Hopf bifurcations
and the
stability of the bifurcating periodic solutions is derived by
using the normal form and
the center manifold theory. Some numerical simulations are performed
to confirm the correctness
of theoretical analysis. At last, some conclusions are given.
Keywords:Lyme disease, stagestructure, time delay, Lyapunov functional stability Hopf bifurcation. Category:34D20 

14. 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 

15. CMB 2015 (vol 58 pp. 858)
 Williams, Kenneth S.

Ternary Quadratic Forms and Eta Quotients
Let $\eta(z)$ $(z \in \mathbb{C},\;\operatorname{Im}(z)\gt 0)$
denote the Dedekind eta function. We use a recent producttosum
formula in conjunction with conditions for the nonrepresentability
of integers by certain ternary quadratic forms to give explicitly
10 eta quotients
\[
f(z):=\eta^{a(m_1)}(m_1 z)\cdots \eta^{{a(m_r)}}(m_r z)=\sum_{n=1}^{\infty}c(n)e^{2\pi
i nz},\quad z \in \mathbb{C},\;\operatorname{Im}(z)\gt 0,
\]
such that the Fourier coefficients $c(n)$ vanish for all positive
integers $n$ in each of infinitely many nonoverlapping arithmetic
progressions. For example, it is shown that for $f(z)=\eta^4(z)\eta^{9}(4z)\eta^{2}(8z)$
we have $c(n)=0$ for all $n$ in each of the arithmetic progressions
$\{16k+14\}_{k \geq 0}$, $\{64k+56\}_{k \geq 0}$, $\{256k+224\}_{k
\geq 0}$, $\{1024k+896\}_{k \geq 0}$, $\ldots$.
Keywords:Dedekind eta function, eta quotient, ternary quadratic forms, vanishing of Fourier coefficients, producttosum formula Categories:11F20, 11E20, 11E25 

16. CMB 2015 (vol 58 pp. 548)
 Lü, Guangshi; Sankaranarayanan, Ayyadurai

Higher Moments of Fourier Coefficients of Cusp Forms
Let $S_{k}(\Gamma)$ be the space of holomorphic cusp
forms of even integral weight $k$ for the full modular group
$SL(2, \mathbb{Z})$. Let
$\lambda_f(n)$, $\lambda_g(n)$, $\lambda_h(n)$ be the $n$th normalized
Fourier
coefficients of three distinct holomorphic primitive cusp forms
$f(z) \in S_{k_1}(\Gamma), g(z) \in S_{k_2}(\Gamma), h(z) \in
S_{k_3}(\Gamma)$ respectively.
In this paper we study the cancellations of sums related to arithmetic
functions, such as $\lambda_f(n)^4\lambda_g(n)^2$, $\lambda_g(n)^6$,
$\lambda_g(n)^2\lambda_h(n)^4$, and $\lambda_g(n^3)^2$ twisted
by
the arithmetic function $\lambda_f(n)$.
Keywords:Fourier coefficients of automorphic forms, Dirichlet series, triple product $L$function, Perron's formula Categories:11F30, 11F66 

17. CMB 2015 (vol 58 pp. 730)
 Efrat, Ido; Matzri, Eliyahu

Vanishing of Massey Products and Brauer Groups
Let $p$ be a prime number and $F$ a field containing a root of
unity of order $p$.
We relate recent results on vanishing of triple Massey products
in the mod$p$ Galois cohomology of $F$,
due to Hopkins, Wickelgren, MinÃ¡Ä, and TÃ¢n, to classical
results in the theory of central simple algebras.
For global fields, we prove a stronger form of the vanishing
property.
Keywords:Galois cohomology, Brauer groups, triple Massey products, global fields Categories:16K50, 11R34, 12G05, 12E30 

18. CMB 2015 (vol 58 pp. 374)
 Szabó, Gábor

A Short Note on the Continuous Rokhlin Property and the Universal Coefficient Theorem in $E$Theory
Let $G$ be a metrizable compact group, $A$ a separable $\mathrm{C}^*$algebra
and $\alpha\colon G\to\operatorname{Aut}(A)$ a strongly continuous action.
Provided that $\alpha$ satisfies the continuous Rokhlin property,
we show that the property of satisfying the UCT in $E$theory
passes from $A$ to the crossed product $\mathrm{C}^*$algebra $A\rtimes_\alpha
G$ and the fixed point algebra $A^\alpha$. This extends a similar
result by Gardella for $KK$theory in the case of unital
$\mathrm{C}^*$algebras,
but with a shorter and less technical proof. For circle actions
on separable, unital $\mathrm{C}^*$algebras with the continuous Rokhlin
property, we establish a connection between the $E$theory equivalence
class of $A$ and that of its fixed point algebra $A^\alpha$.
Keywords:Rokhlin property, UCT, KKtheory, Etheory, circle actions Categories:46L55, 19K35 

19. CMB 2015 (vol 58 pp. 281)
 Kalus, Matthias

On the Relation of Real and Complex Lie Supergroups
A complex Lie supergroup can be described as a real Lie supergroup
with integrable almost complex structure. The necessary and
sufficient conditions on an almost complex structure on a real
Lie supergroup for defining a complex Lie supergroup are deduced.
The classification of real Lie supergroups with such almost
complex
structures yields a new approach to the known classification
of complex Lie supergroups by complex HarishChandra superpairs.
A universal complexification of a real Lie supergroup is
constructed.
Keywords:Lie supergroup, almost complex structure, HarishChandra pair, universal complexification Categories:32C11, 58A50 

20. CMB 2014 (vol 58 pp. 91)
 Hasegawa, Kei

Essential Commutants of Semicrossed Products
Let $\alpha\colon G\curvearrowright M$ be a spatial action of countable
abelian group on a "spatial" von Neumann algebra $M$ and $S$ be its
unital subsemigroup with $G=S^{1}S$. We explicitly compute the
essential commutant and the essential fixedpoints, modulo the
Schatten $p$class or the compact operators, of the w$^*$semicrossed
product of $M$ by $S$ when $M'$ contains no nonzero compact
operators. We also prove a weaker result when $M$ is a von Neumann
algebra on a finite dimensional Hilbert space and
$(G,S)=(\mathbb{Z},\mathbb{Z}_+)$, which extends a famous result due
to Davidson (1977) for the classical analytic Toeplitz operators.
Keywords:essential commutant, semicrossed product Categories:47L65, 47A55 

21. CMB 2014 (vol 57 pp. 264)
 Dai, Li; Dong, Jingcheng

On Semisimple Hopf Algebras of Dimension $pq^n$
Let $p,q$ be prime numbers with $p^2\lt q$, $n\in \mathbb{N}$, and $H$ a
semisimple Hopf algebra of dimension $pq^n$ over an algebraically
closed field of characteristic $0$. This paper proves that $H$ must
possess one of the following structures: (1) $H$ is semisolvable;
(2) $H$ is a Radford biproduct $R\# kG$, where $kG$ is the group
algebra of group $G$ of order $p$, and $R$ is a semisimple YetterDrinfeld
Hopf algebra in ${}^{kG}_{kG}\mathcal{YD}$ of dimension $q^n$.
Keywords:semisimple Hopf algebra, semisolvability, Radford biproduct, Drinfeld double Category:16W30 

22. CMB 2013 (vol 57 pp. 375)
 López, S. C.; MuntanerBatle, ; RiusFont,

A Problem on Edgemagic Labelings of Cycles
Kotzig and Rosa defined in 1970 the concept of edgemagic labelings as
follows: let $G$ be a simple $(p,q)$graph (that is, a graph of order $p$
and size $q$ without loops or multiple edges). A bijective function $f:V(G)\cup
E(G)\rightarrow \{1,2,\ldots,p+q\}$ is an edgemagic labeling of $G$ if
$f(u)+f(uv)+f(v)=k$, for all $uv\in E(G)$. A graph that admits an edgemagic
labeling is called an edgemagic graph, and $k$ is called the magic sum
of the labeling. An old conjecture of Godbold and Slater sets that all
possible theoretical magic sums are attained for each cycle of order $n\ge
7$. Motivated by this conjecture, we prove that for all $n_0\in \mathbb{N}$,
there exists $n\in \mathbb{N}$, such that the cycle $C_n$ admits at least
$n_0$ edgemagic labelings with at least $n_0$ mutually distinct magic
sums. We do this by providing a lower bound for the number of magic sums
of the cycle $C_n$, depending on the sum of the exponents of the odd primes
appearing in the prime factorization of $n$.
Keywords:edgemagic, valence, $\otimes_h$product Category:05C78 

23. CMB 2013 (vol 57 pp. 245)
 Brodskiy, N.; Dydak, J.; Lang, U.

AssouadNagata Dimension of Wreath Products of Groups
Consider the wreath product $H\wr G$, where $H\ne 1$ is finite and $G$ is finitely generated.
We show that the AssouadNagata dimension $\dim_{AN}(H\wr G)$ of $H\wr G$
depends on the growth of $G$ as follows:
\par If the growth of $G$ is not bounded by a linear function, then $\dim_{AN}(H\wr G)=\infty$,
otherwise $\dim_{AN}(H\wr G)=\dim_{AN}(G)\leq 1$.
Keywords:AssouadNagata dimension, asymptotic dimension, wreath product, growth of groups Categories:54F45, 55M10, 54C65 

24. CMB 2013 (vol 57 pp. 401)
 Perrone, Domenico

Curvature of $K$contact SemiRiemannian Manifolds
In this paper we characterize $K$contact semiRiemannian manifolds
and Sasakian semiRiemannian manifolds in terms of
curvature. Moreover, we show that any conformally flat $K$contact
semiRiemannian manifold is Sasakian and of constant sectional
curvature $\kappa=\varepsilon$, where $\varepsilon =\pm 1$ denotes
the causal character of the Reeb vector field. Finally, we give some
results about the curvature of a $K$contact Lorentzian manifold.
Keywords:contact semiRiemannian structures, $K$contact structures, conformally flat manifolds, Einstein LorentzianSasaki manifolds Categories:53C50, 53C25, 53B30 

25. CMB 2013 (vol 57 pp. 821)
 Jeong, Imsoon; Kim, Seonhui; Suh, Young Jin

Real Hypersurfaces in Complex TwoPlane Grassmannians with Reeb Parallel Structure Jacobi Operator
In this paper we give a characterization of a real hypersurface of
Type~$(A)$ in complex twoplane Grassmannians ${ { {G_2({\mathbb
C}^{m+2})} } }$, which means a
tube over a totally geodesic $G_{2}(\mathbb C^{m+1})$ in
${G_2({\mathbb C}^{m+2})}$, by
the Reeb parallel structure Jacobi operator ${\nabla}_{\xi}R_{\xi}=0$.
Keywords:real hypersurfaces, complex twoplane Grassmannians, Hopf hypersurface, Reeb parallel, structure Jacobi operator Categories:53C40, 53C15 
