76. CMB 2014 (vol 57 pp. 485)
 Franc, Cameron; Mason, Geoffrey

Fourier Coefficients of Vectorvalued Modular Forms of Dimension $2$
We prove the following Theorem. Suppose that $F=(f_1, f_2)$ is a $2$dimensional vectorvalued modular form
on $\operatorname{SL}_2(\mathbb{Z})$ whose component functions $f_1, f_2$ have rational Fourier coefficients
with bounded denominators. Then $f_1$ and $f_2$ are classical modular forms on a congruence subgroup of the modular group.
Keywords:vectorvalued modular form, modular group, bounded denominators Categories:11F41, 11G99 

77. CMB 2014 (vol 58 pp. 30)
 Chung, Jaeyoung

On an Exponential Functional Inequality and its Distributional Version
Let $G$ be a group and $\mathbb K=\mathbb C$ or $\mathbb
R$.
In this article, as a generalization of the result of Albert
and Baker,
we investigate the behavior of bounded
and unbounded functions $f\colon G\to \mathbb K$ satisfying the inequality
$
\Biglf
\Bigl(\sum_{k=1}^n x_k
\Bigr)\prod_{k=1}^n f(x_k)
\Bigr\le \phi(x_2, \dots, x_n),\quad \forall\, x_1, \dots,
x_n\in G,
$
where $\phi\colon G^{n1}\to [0, \infty)$. Also, as a distributional
version of the above inequality we consider the stability of
the functional equation
\begin{equation*}
u\circ S  \overbrace{u\otimes \cdots \otimes u}^{n\text {times}}=0,
\end{equation*}
where $u$ is a Schwartz distribution or Gelfand hyperfunction,
$\circ$ and $\otimes$ are the pullback and tensor product of
distributions, respectively, and $S(x_1, \dots, x_n)=x_1+ \dots
+x_n$.
Keywords:distribution, exponential functional equation, Gelfand hyperfunction, stability Categories:46F99, 39B82 

78. CMB 2014 (vol 58 pp. 71)
 Ghenciu, Ioana

Limited Sets and Bibasic Sequences
Bibasic sequences are used to study relative weak compactness
and relative norm compactness of limited sets.
Keywords:limited sets, $L$sets, bibasic sequences, the DunfordPettis property Categories:46B20, 46B28, 28B05 

79. CMB 2014 (vol 57 pp. 780)
 Erzakova, Nina A.

Measures of Noncompactness in Regular Spaces
Previous results by the author on the connection
between three of measures
of noncompactness obtained for $L_p$, are extended
to regular spaces of measurable
functions.
An example of advantage
in some cases one of them in comparison with another is given.
Geometric characteristics of regular spaces are determined.
New theorems for $(k,\beta)$boundedness of partially additive
operators are proved.
Keywords:measure of noncompactness, condensing map, partially additive operator, regular space, ideal space Categories:47H08, 46E30, 47H99, 47G10 

80. CMB 2014 (vol 58 pp. 44)
81. CMB 2014 (vol 58 pp. 110)
 Kamalov, F.

Property T and Amenable Transformation Group $C^*$algebras
It is well known that a discrete group which is both amenable and
has Kazhdan's Property T must be finite. In this note we generalize
the above statement to the case of transformation groups. We show
that if $G$ is a discrete amenable group acting on a compact
Hausdorff space $X$, then the transformation group $C^*$algebra
$C^*(X, G)$ has Property T if and only if both $X$ and $G$ are finite. Our
approach does not rely on the use of tracial states on $C^*(X, G)$.
Keywords:Property T, $C^*$algebras, transformation group, amenable Categories:46L55, 46L05 

82. 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 

83. CMB 2014 (vol 57 pp. 431)
 Tagami, Keiji

The Rasmussen Invariant, Fourgenus and Threegenus of an Almost Positive Knot Are Equal
An oriented link is positive if it has a link diagram whose crossings are all positive.
An oriented link is almost positive if it is not positive and has a link diagram with exactly one negative crossing.
It is known that the Rasmussen invariant, $4$genus and $3$genus of a positive knot are equal.
In this paper, we prove that the Rasmussen invariant, $4$genus and $3$genus of an almost positive knot are equal.
Moreover, we determine the Rasmussen invariant of an almost positive knot in terms of its almost positive knot diagram.
As corollaries, we prove that all almost positive knots are not homogeneous, and there is no almost positive knot of $4$genus one.
Keywords:almost positive knot, fourgenus, Rasmussen invariant Categories:57M27, 57M25 

84. CMB 2014 (vol 57 pp. 765)
 da Silva, Rosângela Maria; Tenenblat, Keti

Helicoidal Minimal Surfaces in a Finsler Space of Randers Type
We consider the Finsler space $(\bar{M}^3, \bar{F})$ obtained by
perturbing the Euclidean metric of $\mathbb{R}^3$ by a rotation. It
is the open region of $\mathbb{R}^3$ bounded by a cylinder with a
Randers metric. Using the BusemannHausdorff volume form, we
obtain the differential equation that characterizes the helicoidal
minimal surfaces in $\bar{M}^3$. We prove that the helicoid is a
minimal surface in $\bar{M}^3$, only if the axis of the helicoid
is the axis of the cylinder. Moreover, we prove that, in the
Randers space $(\bar{M}^3, \bar{F})$, the only minimal
surfaces in the Bonnet family, with fixed axis $O\bar{x}^3$, are the catenoids
and the helicoids.
Keywords:minimal surfaces, helicoidal surfaces, Finsler space, Randers space Categories:53A10, 53B40 

85. CMB 2014 (vol 57 pp. 721)
 Bruillard, Paul; Galindo, César; Hong, SeungMoon; Kashina, Yevgenia; Naidu, Deepak; Natale, Sonia; Plavnik, Julia Yael; Rowell, Eric C.

Classification of Integral Modular Categories of FrobeniusPerron Dimension $pq^4$ and $p^2q^2$
We classify integral modular categories of dimension $pq^4$ and $p^2q^2$,
where
$p$ and $q$ are distinct primes. We show that such categories are always
grouptheoretical except for categories of dimension $4q^2$.
In these cases there are
wellknown examples of nongrouptheoretical categories, coming from
centers of
TambaraYamagami categories and quantum groups. We show that a
nongrouptheoretical integral modular category of dimension $4q^2$ is
equivalent to either one of these wellknown examples or is of dimension
$36$ and is twistequivalent to fusion categories arising from a
certain quantum group.
Keywords:modular categories, fusion categories Category:18D10 

86. CMB 2014 (vol 57 pp. 231)
 Bagherian, J.

On the Multiplicities of Characters in Table Algebras
In this paper we show that every module of a table algebra
can be considered as a faithful module of some quotient table
algebra.
Also we prove that every faithful module of a table algebra
determines a closed subset which is a cyclic group.
As a main result we give some information about multiplicities
of characters in table algebras.
Keywords:table algebra, faithful module, multiplicity of character Categories:20C99, 16G30 

87. CMB 2013 (vol 57 pp. 870)
 Parlier, Hugo

A Short Note on Short Pants
It is a theorem of Bers that any closed hyperbolic surface admits a pants decomposition consisting of curves of bounded length where the bound only depends on the topology of the surface. The question of the quantification of the optimal constants has been well studied and the best upper bounds to date are linear in genus, a theorem of Buser and SeppÃ¤lÃ¤. The goal of this note is to give a short proof of a linear upper bound which slightly improve the best known bound.
Keywords:hyperbolic surfaces, geodesics, pants decompositions Categories:30F10, 32G15, 53C22 

88. CMB 2013 (vol 57 pp. 845)
 Lei, Antonio

Factorisation of Twovariable $p$adic $L$functions
Let $f$ be a modular form which is nonordinary at $p$. Loeffler has
recently constructed four twovariable $p$adic $L$functions
associated to $f$. In the case where $a_p=0$, he showed that, as in
the onevariable case, Pollack's plus and minus splitting applies to
these new objects. In this article, we show that such a splitting can
be generalised to the case where $a_p\ne0$ using Sprung's logarithmic
matrix.
Keywords:modular forms, padic Lfunctions, supersingular primes Categories:11S40, 11S80 

89. CMB 2013 (vol 57 pp. 463)
 Bownik, Marcin; Jasper, John

Constructive Proof of Carpenter's Theorem
We give a constructive proof of Carpenter's Theorem due to Kadison.
Unlike the original proof our approach also yields the
real case of this theorem.
Keywords:diagonals of projections, the SchurHorn theorem, the Pythagorean theorem, the Carpenter theorem, spectral theory Categories:42C15, 47B15, 46C05 

90. CMB 2013 (vol 57 pp. 585)
 Lehec, Joseph

Short Probabilistic Proof of the BrascampLieb and Barthe Theorems
We give a short proof of the BrascampLieb theorem, which asserts that
a certain general form of Young's convolution inequality is saturated
by Gaussian functions. The argument is inspired by Borell's stochastic
proof of the PrÃ©kopaLeindler inequality and applies also to the
reversed BrascampLieb inequality, due to Barthe.
Keywords:functional inequalities, Brownian motion Categories:39B62, 60J65 

91. CMB 2013 (vol 57 pp. 526)
 Heil, Wolfgang; Wang, Dongxu

On $3$manifolds with Torus or Klein Bottle Category Two
A subset $W$ of a closed manifold $M$ is $K$contractible, where $K$
is a torus or Kleinbottle, if the inclusion $W\rightarrow M$ factors
homotopically through a map to $K$. The image of $\pi_1 (W)$ (for any
base point) is a subgroup of $\pi_1 (M)$ that is isomorphic to a
subgroup of a quotient group of $\pi_1 (K)$. Subsets of $M$ with this
latter property are called $\mathcal{G}_K$contractible. We obtain a
list of the closed $3$manifolds that can be covered by two open
$\mathcal{G}_K$contractible subsets. This is applied to obtain a list
of the possible closed prime $3$manifolds that can be covered by two
open $K$contractible subsets.
Keywords:LusternikSchnirelmann category, coverings of $3$manifolds by open $K$contractible sets Categories:57N10, 55M30, 57M27, 57N16 

92. CMB 2013 (vol 57 pp. 119)
93. CMB Online first


Leftorderable fundamental group and Dehn surgery on the knot $5_2$
We show that the resulting manifold by $r$surgery on the knot $5_2$, which is
the twobridge knot corresponding to the rational number $3/7$, has leftorderable
fundamental group if the slope $r$ satisfies $0\le r \le 4$.
Keywords:leftordering, Dehn surgery Categories:57M25, 06F15 

94. CMB Online first


Leftorderable fundamental group and Dehn surgery on the knot $5_2$
We show that the resulting manifold by $r$surgery on the knot $5_2$, which is
the twobridge knot corresponding to the rational number $3/7$, has leftorderable
fundamental group if the slope $r$ satisfies $0\le r \le 4$.
Keywords:leftordering, Dehn surgery Categories:57M25, 06F15 

95. CMB 2013 (vol 57 pp. 381)
 Łydka, Adrian

On Complex Explicit Formulae Connected with the MÃ¶bius Function of an Elliptic Curve
We study analytic properties function $m(z, E)$, which is defined on the upper halfplane as an integral from the shifted $L$function of an elliptic curve. We show that $m(z, E)$ analytically continues to a meromorphic function on the whole complex plane and satisfies certain functional equation. Moreover, we give explicit formula for $m(z, E)$ in the strip $\Im{z}\lt 2\pi$.
Keywords:Lfunction, MÃ¶bius function, explicit formulae, elliptic curve Categories:11M36, 11G40 

96. CMB 2013 (vol 57 pp. 439)
 Yang, YanHong

The Fixed Point Locus of the Verschiebung on $\mathcal{M}_X(2, 0)$ for Genus2 Curves $X$ in Charateristic $2$
We prove that for every ordinary genus$2$ curve $X$ over a finite
field $\kappa$ of characteristic $2$ with
$\textrm{Aut}(X/\kappa)=\mathbb{Z}/2\mathbb{Z} \times S_3$, there exist
$\textrm{SL}(2,\kappa[\![s]\!])$representations of $\pi_1(X)$ such
that the image of $\pi_1(\overline{X})$ is infinite. This result
produces a family of examples similar to Laszlo's counterexample
to de Jong's question regarding the finiteness of the geometric
monodromy of representations of the fundamental group.
Keywords:vector bundle, Frobenius pullback, representation, etale fundamental group Categories:14H60, 14D05, 14G15 

97. 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 

98. CMB 2013 (vol 57 pp. 310)
99. 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 

100. CMB 2013 (vol 57 pp. 506)
 Galindo, César

On Braided and Ribbon Unitary Fusion Categories
We prove that every braiding over a unitary fusion category is
unitary and every unitary braided fusion category admits a unique
unitary ribbon structure.
Keywords:fusion categories, braided categories, modular categories Categories:20F36, 16W30, 18D10 
