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3  Approximate Amenability of Segal Algebras II Alaghmandan, Mahmood
We prove that every proper Segal algebra of a SIN group is not
approximately amenable.


7  Characters on $C(X)$ Boulabiar, Karim
The precise condition on a completely regular space $X$ for every character on
$C(X) $ to be an evaluation at some point in $X$ is that $X$ be
realcompact. Usually, this classical result is obtained relying heavily on
involved (and even nonconstructive) extension arguments. This note provides a
direct proof that is accessible to a large audience.


9  Irreducible Tuples Without the Boundary Property Chavan, Sameer
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.


19  Compact Commutators of Rough Singular Integral Operators Chen, Jiecheng; Hu, Guoen
Let $b\in \mathrm{BMO}(\mathbb{R}^n)$ and $T_{\Omega}$ be the singular
integral operator with kernel $\frac{\Omega(x)}{x^n}$, where
$\Omega$ is homogeneous of degree zero, integrable and has mean
value zero on the unit sphere $S^{n1}$. In this paper, by Fourier
transform estimates and approximation to the operator $T_{\Omega}$
by integral operators with smooth kernels, it is proved that if
$b\in \mathrm{CMO}(\mathbb{R}^n)$ and $\Omega$ satisfies a certain
minimal size condition, then the commutator generated by $b$ and
$T_{\Omega}$ is a compact operator on $L^p(\mathbb{R}^n)$ for
appropriate index $p$. The associated maximal operator is also
considered.


30  On an Exponential Functional Inequality and its Distributional Version Chung, Jaeyoung
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 $S(x_1, \dots, x_n)=x_1+ \dots
+x_n$.


44  Orbits of Geometric Descent Daniilidis, A.; Drusvyatskiy, D.; Lewis, A. S.
We prove that quasiconvex functions always admit descent trajectories
bypassing all nonminimizing critical points.


51  Spectral Flows of Dilations of Fredholm Operators De Nitties, Giuseppe; SchulzBaldes, Hermann
Given an essentially unitary contraction and an arbitrary unitary
dilation of it, there is a naturally associated spectral flow which is
shown to be equal to the index of the operator. This result is
interpreted in terms of the $K$theory of an associated mapping
cone. It is then extended to connect $\mathbb{Z}_2$ indices of odd symmetric
Fredholm operators to a $\mathbb{Z}_2$valued spectral flow.


69  Correction to "Infinite Dimensional DeWitt Supergroups and Their Bodies" Fulp, Ronald Owen
The Theorem below is a correction to Theorem
3.5 in the article
entitled " Infinite Dimensional DeWitt Supergroups and Their
Bodies" published
in Canad. Math. Bull. Vol. 57 (2) 2014 pp. 283288. Only part
(iii) of that Theorem
requires correction. The proof of Theorem 3.5 in the original
article failed to separate
the proof of (ii) from the proof of (iii). The proof of (ii)
is complete once it is established
that $ad_a$ is quasinilpotent for each $a$ since it immediately
follows that $K$
is quasinilpotent. The proof of (iii) is not complete
in the original article. The revision appears as the proof of
(iii) of the revised Theorem below.


71  Limited Sets and Bibasic Sequences Ghenciu, Ioana
Bibasic sequences are used to study relative weak compactness
and relative norm compactness of limited sets.


80  The Equivariant Cohomology Rings of Peterson Varieties in All Lie
Types Harada, Megumi; Horiguchi, Tatsuya; Masuda, Mikiya
Let $G$ be a complex semisimple linear algebraic group and let
$Pet$ be the associated Peterson variety in the flag
variety $G/B$.
The main theorem of this note gives an efficient presentation
of the equivariant cohomology ring $H^*_S(Pet)$ of the
Peterson variety as a quotient of a polynomial ring by an ideal
$J$ generated by quadratic polynomials, in the spirit of the
Borel presentation of the cohomology of the flag variety. Here
the group $S \cong \mathbb{C}^*$ is a certain subgroup of a maximal
torus $T$ of $G$.
Our description of the ideal $J$ uses the Cartan matrix and is
uniform across Lie types. In our arguments we use the Monk formula
and Giambelli formula for the equivariant cohomology rings of
Peterson varieties for all Lie types, as obtained in the work
of Drellich. Our result generalizes a previous theorem of FukukawaHaradaMasuda,
which was only for Lie type $A$.


91  Essential Commutants of Semicrossed Products Hasegawa, Kei
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.


105  On Graphs Associated with Character Degrees and Conjugacy Class Sizes of Direct Products of Finite Groups HosseinZadeh, Samaneh; Iranmanesh, Ali; Hosseinzadeh, Mohammad Ali; Lewis, Mark L.
The prime vertex graph, $\Delta (X)$, and the common divisor graph,
$\Gamma (X)$, are two graphs that have been defined on a set of
positive integers $X$.
Some
properties of these graphs have been studied in the cases where either
$X$ is the set of character degrees of a group or $X$ is the set of
conjugacy class sizes of a group. In this paper, we gather some
results on these graphs arising in the context of direct product of
two groups.


110  Property T and Amenable Transformation Group $C^*$algebras Kamalov, F.
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 $C^*(X, G)$.


115  Weak Arithmetic Equivalence MantillaSoler, Guillermo
Inspired by the invariant of a number field given by its zeta
function, we define the notion of weak arithmetic equivalence and show
that under certain ramification hypotheses, this equivalence
determines the local root numbers of the number field. This is
analogous to a result of Rohrlich on the local root numbers of a
rational elliptic curve. Additionally, we prove that for tame
nontotally real number fields, the integral trace form is invariant
under arithmetic equivalence.


128  A Sharp Constant for the Bergman Projection Marković, Marijan
For the Bergman projection operator $P$ we prove that
\begin{equation*}
\P\colon L^1(B,d\lambda)\rightarrow B_1\ = \frac {(2n+1)!}{n!}.
\end{equation*}
Here $\lambda$ stands for the hyperbolic metric in the unit ball $B$ of
$\mathbb{C}^n$, and $B_1$ denotes the Besov space with an adequate
seminorm. We also consider a generalization of this result. This generalizes
some recent results due to Perälä.


134  On the Generalized AuslanderReiten Conjecture under Certain Ring Extensions Nasseh, Saeed
We show under some conditions that a Gorenstein ring $R$ satisfies the
Generalized AuslanderReiten Conjecture if and only if so does
$R[x]$. When $R$ is a local ring we prove the same result for some
localizations of $R[x]$.


144  Localization and Completeness in $L_2({\mathbb R})$ Olevskii, Victor
We give a necessary and sufficient condition for a sequence
to be a localization set for a determining average sampler.


150  Connections Between Metric Characterizations of Superreflexivity and the RadonNikodý Property for Dual Banach Spaces
Ostrovskii, Mikhail I.
Johnson and Schechtman (2009)
characterized superreflexivity in terms of finite diamond graphs.
The present author characterized the RadonNikodým property
(RNP) for dual spaces in terms of the infinite diamond. This
paper
is devoted to further study of relations between metric
characterizations of superreflexivity and the RNP for dual spaces.
The main result is that finite subsets of any set $M$ whose
embeddability characterizes the RNP for dual spaces, characterize
superreflexivity. It is also observed that the converse statement
does not hold, and that $M=\ell_2$ is a counterexample.


158  Corrigendum to "Chen Inequalities for Submanifolds of Real Space Forms with a Semisymmetric Nonmetric Connection" Özgür, Cihan; Mihai, Adela
We fix the coefficients in the inequality (4.1) in the Theorem 4.1(i) from
A. Mihai and C. zgür, "Chen inequalities for
submanifolds of real space forms with a semisymmetric nonmetric
connection" Canad. Math. Bull. 55 (2012), no. 3, 611622.


160  Some Normal Numbers Generated by Arithmetic Functions Pollack, Paul; Vandehey, Joseph
Let $g \geq 2$. A real number is said to be $g$normal if its base $g$ expansion contains every finite sequence of digits with the expected limiting frequency. Let $\phi$ denote Euler's totient function, let $\sigma$ be the sumofdivisors function, and let $\lambda$ be Carmichael's lambdafunction. We show that if $f$ is any function formed by composing $\phi$, $\sigma$, or $\lambda$, then the number
\[ 0. f(1) f(2) f(3) \dots \]
obtained by concatenating the base $g$ digits of successive $f$values is $g$normal. We also prove the same result if the inputs $1, 2, 3, \dots$ are replaced with the primes $2, 3, 5, \dots$. The proof is an adaptation of a method introduced by Copeland and Erdős in 1946 to prove the $10$normality of $0.235711131719\ldots$.


174  Periodic Solutions of Almost Linear Volterra Integrodynamic Equation on Periodic Time Scales Raffoul, Youssef N.
Using Krasnoselskii's fixed point theorem, we deduce
the existence of periodic solutions of nonlinear system of integrodynamic
equations on periodic time scales. These equations are
studied under a set of assumptions on the functions involved
in the
equations. The equations will be called almost linear when these
assumptions hold. The results of this papers are new for the
continuous and discrete time scales.


182  On Finite Groups with Dismantlable Subgroup Lattices Tărnăuceanu, Marius
In this note we study the finite groups whose subgroup
lattices are dismantlable.


188  Telescoping Estimates for Smooth Series Wirths, Karl Joachim
We derive telescoping majorants and minorants for some classes
of series and give applications of these results.


196  Dihedral Groups of order $2p$ of Automorphisms of Compact Riemann Surfaces of Genus $p1$ Yang, Qingjie; Zhong, Weiting
In this paper we prove that there is only one conjugacy class of
dihedral group of order $2p$ in the $2(p1)\times 2(p1)$ integral
symplectic group can be realized by an analytic automorphism
group
of compact connected Riemann surfaces of genus $p1$. A pair of
representative generators of the realizable class is also given.


207  Exact and Approximate Operator Parallelism Moslehian, Mohammad Sal; Zamani, Ali
Extending the notion of parallelism we introduce the concept of
approximate parallelism in normed spaces and then substantially
restrict ourselves to the setting of Hilbert space operators endowed
with the operator norm. We present several characterizations of the
exact and approximate operator parallelism in the algebra
$\mathbb{B}(\mathscr{H})$ of bounded linear operators acting on a
Hilbert space $\mathscr{H}$. Among other things, we investigate the
relationship between approximate parallelism and norm of inner
derivations on $\mathbb{B}(\mathscr{H})$. We also characterize the
parallel elements of a $C^*$algebra by using states. Finally we
utilize the linking algebra to give some equivalence assertions
regarding parallel elements in a Hilbert $C^*$module.


225  Characterizing Distinguished Pairs by Using Liftings of Irreducible Polynomials Aghigh, Kamal; Nikseresht, Azadeh
Let $v$ be a henselian valuation of any rank of a field
$K$ and $\overline{v}$ be the unique extension of $v$ to a
fixed algebraic closure $\overline{K}$ of $K$. In 2005, it was studied properties
of those pairs $(\theta,\alpha)$ of elements of $\overline{K}$
with $[K(\theta): K]\gt [K(\alpha): K]$ where $\alpha$ is an element
of smallest degree over $K$ such that
$$
\overline{v}(\theta\alpha)=\sup\{\overline{v}(\theta\beta)
\ \beta\in \overline{K}, \ [K(\beta): K]\lt [K(\theta): K]\}.
$$
Such pairs are referred to as distinguished pairs.
We use the concept of liftings of irreducible polynomials to give a
different characterization of distinguished pairs.


233  Affine Actions of $U_q(sl(2))$ on Polynomial Rings Bergen, Jeffrey
We classify the affine actions of $U_q(sl(2))$ on commutative
polynomial rings in $m \ge 1$ variables.
We show that, up to scalar multiplication, there are two possible
actions.
In addition, for each action, the subring of invariants is a
polynomial ring in either $m$ or $m1$ variables,
depending upon whether $q$ is or is not a root of $1$.


241  Isometries and Hermitian Operators on Zygmund Spaces Botelho, Fernanda
In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded.


250  Lifting Divisors on a Generic Chain of Loops Cartwright, Dustin; Jensen, David; Payne, Sam
Let $C$ be a curve over a complete valued field with infinite
residue field whose skeleton is a chain of loops with generic
edge lengths. We prove that
any divisor on the chain of loops that is rational over the value
group lifts to a divisor of the same rank on $C$, confirming
a conjecture of Cools,
Draisma, Robeva, and the third author.


263  Generalized Jordan Semiderivations in Prime Rings De Filippis, Vincenzo; Mamouni, Abdellah; Oukhtite, Lahcen
Let $R$ be a ring, $g$ an endomorphism of $R$.
The additive mapping $d\colon R\rightarrow R$ is called Jordan semiderivation of $R$, associated with $g$, if
$$d(x^2)=d(x)x+g(x)d(x)=d(x)g(x)+xd(x)\quad \text{and}\quad d(g(x))=g(d(x))$$
for all $x\in R$.
The additive mapping $F\colon R\rightarrow R$ is called generalized Jordan semiderivation of $R$, related to the Jordan semiderivation $d$ and endomorphism $g$, if
$$F(x^2)=F(x)x+g(x)d(x)=F(x)g(x)+xd(x)\quad \text{and}\quad F(g(x))=g(F(x))$$
for all $x\in R$.
In the present paper we prove that
if $R$ is a prime ring of characteristic different from $2$, $g$ an endomorphism of $R$, $d$ a Jordan semiderivation associated with $g$, $F$ a generalized Jordan semiderivation associated with $d$ and $g$,
then $F$ is a generalized semiderivation of $R$ and $d$ is a semiderivation of $R.$ Moreover, if $R$ is commutative then $F=d$.


271  On Domination of Zerodivisor Graphs of Matrix Rings Jafari, Sayyed Heidar; Jafari Rad, Nader
We study domination in zerodivisor graphs of matrix rings over a
commutative ring with $1$.


276  Injective Tauberian Operators on $L_1$ and Operators with Dense Range on $\ell_\infty$ Johnson, William; Nasseri, Amir Bahman; Schechtman, Gideon; Tkocz, Tomasz
There exist injective Tauberian operators on $L_1(0,1)$ that have
dense, nonclosed range. This gives injective, nonsurjective
operators on $\ell_\infty$ that have dense range. Consequently, there
are two quasicomplementary, noncomplementary subspaces of
$\ell_\infty$ that are isometric to $\ell_\infty$.


281  On the Relation of Real and Complex Lie Supergroups Kalus, Matthias
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.


285  Spectral Properties of a Family of Minimal Tori of Revolution in Fivedimensional Sphere Karpukhin, Mikhail
The normalized eigenvalues $\Lambda_i(M,g)$ of the LaplaceBeltrami
operator can be considered as functionals on the space of all
Riemannian metrics $g$ on a fixed surface $M$. In recent papers
several explicit examples of extremal metrics were provided.
These metrics are induced by minimal immersions of surfaces in
$\mathbb{S}^3$ or $\mathbb{S}^4$. In the present paper a family
of extremal metrics induced by minimal immersions in $\mathbb{S}^5$
is investigated.


297  Approximate Fixed Point Sequences of Nonlinear Semigroup in Metric Spaces Khamsi, M. A.
In this paper, we investigate the common
approximate fixed point sequences of nonexpansive semigroups of
nonlinear mappings $\{T_t\}_{t \geq 0}$, i.e., a family such that
$T_0(x)=x$, $T_{s+t}=T_s(T_t(x))$, where the domain is a metric space
$(M,d)$. In particular we prove that under suitable conditions, the
common approximate fixed point sequences set is the same as the common
approximate fixed point sequences set of two mappings from the family.
Then we use the Ishikawa iteration to construct a common approximate
fixed point sequence of nonexpansive semigroups of nonlinear
mappings.


306  On the Largest Dynamic Monopolies of Graphs with a Given Average Threshold Khoshkhah, Kaveh; Zaker, Manouchehr
Let $G$ be a graph and $\tau$ be an assignment of nonnegative
integer thresholds to the vertices of $G$. A subset of vertices,
$D$ is said to be a $\tau$dynamic monopoly, if $V(G)$ can be
partitioned into subsets $D_0, D_1, \ldots, D_k$ such that $D_0=D$
and for any $i\in \{0, \ldots, k1\}$, each vertex $v$ in $D_{i+1}$
has at least $\tau(v)$ neighbors in $D_0\cup \ldots \cup D_i$.
Denote the size of smallest $\tau$dynamic monopoly by $dyn_{\tau}(G)$
and the average of thresholds in $\tau$ by $\overline{\tau}$.
We show that the values of $dyn_{\tau}(G)$ over all assignments
$\tau$ with the same average threshold is a continuous set of
integers. For any positive number $t$, denote the maximum $dyn_{\tau}(G)$
taken over all threshold assignments $\tau$ with $\overline{\tau}\leq
t$, by $Ldyn_t(G)$. In fact, $Ldyn_t(G)$ shows the worstcase
value of a dynamic monopoly when the average threshold is a given
number $t$. We investigate under what conditions on $t$, there
exists an upper bound for $Ldyn_{t}(G)$ of the form $cG$, where
$c\lt 1$. Next, we show that $Ldyn_t(G)$ is coNPhard for planar
graphs but has polynomialtime solution for forests.


317  Coloring Fouruniform Hypergraphs on Nine Vertices Lewkowicz, Marek Kazimierz
Every 4uniform hypergraph on 9 vertices
with at most 25 edges has property B.
This gives the answer $m_9(4)=26$ to a question
raised in 1968 by Erdős.


320  Cover Product and Betti Polynomial of Graphs Llamas, Aurora; MartínezBernal, José
For disjoint graphs $G$ and $H$, with fixed
vertex covers
$C(G)$ and $C(H)$, their cover product is the graph $G
\circledast
H$ with vertex set
$V(G)\cup V(H)$ and edge set $E(G)\cup E(H)\cup\{\{i,j\}:i\in
C(G), j\in
C(H)\}$. We describe the graded Betti numbers of $G\circledast
H$ in terms of those of
$G$ and $H$. As applications we obtain: (i) For any positive
integer $k$ there
exists a connected bipartite graph $G$ such that $\operatorname{reg}
R/I(G)=\mu_S(G)+k$, where,
$I(G)$ denotes the edge ideal of $G$, $\operatorname{reg} R/I(G)$
is the CastelnuovoMumford
regularity of $R/I(G)$ and $\mu_S(G)$ is the induced or strong
matching number of
$G$; (ii) The graded Betti numbers of the complement of a tree
only depends upon
its number of vertices; (iii) The $h$vector of $R/I(G\circledast
H)$ is described in
terms of the $h$vectors of $R/I(G)$ and $R/I(H)$. Furthermore,
in a different
direction, we give a recursive formula for the graded Betti numbers
of chordal
bipartite graphs.


334  Countable Dense Homogeneity in Powers of Zerodimensional Definable Spaces Medini, Andrea
We show that, for a coanalytic subspace $X$ of $2^\omega$, the
countable dense homogeneity of $X^\omega$ is equivalent to $X$
being Polish. This strengthens a result of Hrušák and Zamora
Avilés. Then, inspired by results of HernándezGutiérrez,
Hrušák and van Mill, using a technique of Medvedev, we
construct a nonPolish subspace $X$ of $2^\omega$ such that $X^\omega$
is countable dense homogeneous. This gives the first $\mathsf{ZFC}$ answer
to a question of Hrušák and Zamora Avilés. Furthermore,
since our example is consistently analytic, the equivalence result
mentioned above is sharp. Our results also answer a question
of Medini and Milovich. Finally, we show that if every countable
subset of a zerodimensional separable metrizable space $X$ is
included in a Polish subspace of $X$ then $X^\omega$ is countable
dense homogeneous.


350  On Closed Ideals in a Certain Class of Algebras of Holomorphic Functions MerinoCruz, Héctor; Wawrzynczyk, Antoni
We recently introduced a weighted Banach algebra $\mathfrak{A}_G^n$ of
functions which are holomorphic on the unit disc $\mathbb{D}$, continuous
up to the boundary and of the class $C^{(n)}$ at all points where
the function $G$ does not vanish. Here, $G$ refers to a function
of the disc algebra without zeros on $\mathbb{D}$. Then we proved that
all closed ideals in $\mathfrak{A}_G^n$ with at most countable hull are
standard. In the present paper, on the assumption that $G$ is
an outer function in $C^{(n)}(\overline{\mathbb{D}})$ having infinite roots
in $\mathfrak{A}_G^n$ and countable zero set $h(G)$, we show that all the
closed ideals $I$ with hull containing $h(G)$ are standard.


356  Homological Planes in the Grothendieck Ring of Varieties Sebag, Julien
In this note, we identify, in the Grothendieck group of complex
varieties $K_0(\mathrm Var_\mathbf{C})$, the classes of $\mathbf{Q}$homological
planes. Precisely, we prove that a connected smooth affine complex
algebraic surface $X$ is a $\mathbf{Q}$homological plane if
and only if $[X]=[\mathbf{A}^2_\mathbf{C}]$ in the ring $K_0(\mathrm Var_\mathbf{C})$
and $\mathrm{Pic}(X)_\mathbf{Q}:=\mathrm{Pic}(X)\otimes_\mathbf{Z}\mathbf{Q}=0$.


363  Finite Semisimple Loop Algebras of Indecomposable $RA$ Loops Sharma, R. K.; Sidana, Swati
There are at the most seven classes of finite indecomposable $RA$ loops upto isomorphism. In this paper, we completely characterize the structure of the unit loop of loop algebras of these seven classes of loops over finite fields of characteristic greater than $2$.


374  A Short Note on the Continuous Rokhlin Property and the Universal Coefficient Theorem in $E$Theory Szabó, Gábor
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 $A^\alpha$.


381  The Schwarz Lemma at the Boundary of the Egg Domain $B_{p_1, p_2}$ in $\mathbb{C}^n$ Tang, Xiaomin; Liu, Taishun
Let $B_{p_1, p_2}=\{z\in\mathbb{C}^n:
z_1^{p_1}+z_2^{p_2}+\cdots+z_n^{p_2}\lt 1\}$
be an egg domain in $\mathbb{C}^n$. In this paper, we first
characterize the Kobayashi metric on $B_{p_1, p_2}\,(p_1\geq
1, p_2\geq 1)$,
and then establish a new type of the classical boundary Schwarz
lemma at $z_0\in\partial{B_{p_1, p_2}}$ for holomorphic selfmappings
of $B_{p_1, p_2}(p_1\geq 1, p_2\gt 1)$, where $z_0=(e^{i\theta},
0, \dots, 0)'$ and $\theta\in \mathbb{R}$.


393  On Stanley Depths of Certain Monomial Factor Algebras Tang, Zhongming
Let $S=K[x_1,\ldots,x_n]$
be the polynomial
ring in $n$variables over a field $K$ and $I$ a monomial ideal
of $S$. According to one standard primary decomposition of $I$,
we get a Stanley decomposition of the monomial factor algebra
$S/I$.
Using this Stanley decomposition, one can estimate the Stanley
depth of $S/I$. It is proved that
${\operatorname {sdepth}}_S(S/I)\geq{\operatorname {size}}_S(I)$. When $I$ is squarefree
and ${\operatorname {bigsize}}_S(I)\leq 2$, the Stanley conjecture holds
for
$S/I$, i.e., ${\operatorname {sdepth}}_S(S/I)\geq{\operatorname {depth}}_S(S/I)$.


402  On the Structure of Cuntz Semigroups in (Possibly) Nonunital C*algebras Tikuisis, Aaron Peter; Toms, Andrew
We examine the ranks of operators in semifinite $\mathrm{C}^*$algebras
as measured by their densely defined lower semicontinuous traces.
We first prove that a unital simple $\mathrm{C}^*$algebra whose
extreme tracial boundary is nonempty and finite contains positive
operators of every possible rank, independent of the property
of strict comparison. We then turn to nonunital simple algebras
and establish criteria that imply that the Cuntz semigroup is
recovered functorially from the Murrayvon Neumann semigroup
and the space of densely defined lower semicontinuous traces.
Finally, we prove that these criteria are satisfied by notnecessarilyunital
approximately subhomogeneous algebras of slow dimension growth.
Combined with results of the firstnamed author, this shows that
slow dimension growth coincides with $\mathcal Z$stability,
for approximately subhomogeneous algebras.


415  A Fixed Point Theorem and the Existence of a Haar Measure for Hypergroups Satisfying Conditions Related to Amenability Willson, Benjamin
In this paper we present a fixed point property for amenable
hypergroups which is analogous to Rickert's fixed point theorem
for semigroups. It equates the existence of a left invariant
mean on the space of weakly right uniformly continuous functions
to the existence of a fixed point for any action of the hypergroup.
Using this fixed point property, a certain class of hypergroups
are shown to have a left Haar measure.


423  Resultants of Chebyshev Polynomials: The First, Second, Third, and Fourth Kinds Yamagishi, Masakazu
We give an explicit formula for the resultant of Chebyshev polynomials of the
first, second, third, and fourth kinds.
We also compute the resultant of modified cyclotomic polynomials.


432  Secondorder Riesz Transforms and Maximal Inequalities Associated with Magnetic Schrödinger Operators Yang, Dachun; Yang, Sibei
Let $A:=(\nablai\vec{a})\cdot(\nablai\vec{a})+V$ be a
magnetic Schrödinger operator on $\mathbb{R}^n$,
where $\vec{a}:=(a_1,\dots, a_n)\in L^2_{\mathrm{loc}}(\mathbb{R}^n,\mathbb{R}^n)$
and $0\le V\in L^1_{\mathrm{loc}}(\mathbb{R}^n)$ satisfy some reverse
Hölder conditions.
Let $\varphi\colon \mathbb{R}^n\times[0,\infty)\to[0,\infty)$ be such that
$\varphi(x,\cdot)$ for any given $x\in\mathbb{R}^n$ is an Orlicz function,
$\varphi(\cdot,t)\in {\mathbb A}_{\infty}(\mathbb{R}^n)$ for all $t\in (0,\infty)$
(the class of uniformly Muckenhoupt weights) and its uniformly critical upper type index
$I(\varphi)\in(0,1]$. In this article, the authors prove that
secondorder Riesz transforms $VA^{1}$ and
$(\nablai\vec{a})^2A^{1}$ are bounded from the
MusielakOrliczHardy space $H_{\varphi,\,A}(\mathbb{R}^n)$, associated with $A$,
to the MusielakOrlicz space $L^{\varphi}(\mathbb{R}^n)$. Moreover, the authors
establish the boundedness of $VA^{1}$ on $H_{\varphi, A}(\mathbb{R}^n)$. As applications, some
maximal inequalities associated with $A$ in the scale of $H_{\varphi,
A}(\mathbb{R}^n)$ are obtained.


449  On the Graph of Divisibility of an Integral Domain Boynton, Jason Greene; Coykendall, Jim
It is well known that the factorization properties of a domain are reflected
in the structure of its group of divisibility. The main theme of this paper
is to introduce a topological/graphtheoretic point of view to the current
understanding of factorization in integral domains. We also show that
connectedness properties in the graph and topological space give rise to a
generalization of atomicity.


459  Hyperplanes in the Space of Convergent Sequences and Preduals of $\ell_1$ Casini, Emanuele; Miglierina, Enrico; Piasecki, Lukasz
The main aim of the present paper is to investigate various structural
properties
of hyperplanes of $c$, the Banach space of the convergent sequences.
In particular, we give an explicit formula for the projection
constants and we prove that an hyperplane of $c$ is isometric
to the whole space if and only if it is $1$complemented. Moreover,
we obtain the classification
of those hyperplanes for which their duals are isometric to
$\ell_{1}$ and we give a complete description of the preduals
of $\ell_{1}$ under the assumption that the standard basis of
$\ell_{1}$
is weak$^{*}$convergent.


471  Almost Sure Global Wellposedness for the Fractional Cubic Schrödinger Equation on Torus Demirbas, Seckin
In a previous paper, we proved that $1$d periodic fractional
Schrödinger equation with cubic nonlinearity is locally wellposed
in $H^s$ for $s\gt \frac{1\alpha}{2}$ and globally wellposed for
$s\gt \frac{10\alpha1}{12}$. In this paper we define an invariant
probability measure $\mu$ on $H^s$ for $s\lt \alpha\frac{1}{2}$,
so that for any $\epsilon\gt 0$ there is a set $\Omega\subset H^s$
such that $\mu(\Omega^c)\lt \epsilon$ and the equation is globally
wellposed for initial data in $\Omega$. We see that this fills
the gap between the local wellposedness and the global wellposedness
range in almost sure sense for $\frac{1\alpha}{2}\lt \alpha\frac{1}{2}$,
i.e. $\alpha\gt \frac{2}{3}$ in almost sure sense.


486  Inequalities for Partial Derivatives and their Applications Duc, Dinh Thanh; Nhan, Nguyen Du Vi; Xuan, Nguyen Tong
We present various weighted integral inequalities for partial
derivatives acting on products and compositions of functions
which are applied to establish some new Opialtype inequalities
involving functions of several independent variables. We also
demonstrate the usefulness of our results in the field of partial
differential equations.


497  Constructing Double Magma on Groups Using Commutation Operations Edmunds, Charles C.
A magma $(M,\star)$ is a nonempty set with a binary
operation. A double magma $(M, \star, \bullet)$ is a
nonempty set with two binary operations satisfying the
interchange law,
$(w \star x) \bullet (y\star z)=(w\bullet y)\star(x \bullet
z)$. We call a double magma proper if the two operations
are distinct and commutative if the operations are commutative.
A double semigroup, first introduced by Kock,
is a double magma for which both operations are associative.
Given a nontrivial group $G$ we define a system of two magma
$(G,\star,\bullet)$ using the commutator operations $x \star
y = [x,y](=x^{1}y^{1}xy)$ and $x\bullet y = [y,x]$. We show
that $(G,\star,\bullet)$ is a double magma if and only if $G$
satisfies the commutator laws $[x,y;x,z]=1$ and $[w,x;y,z]^{2}=1$.
We note that the first law defines the class of 3metabelian
groups. If both these laws hold in $G$, the double magma is proper
if and only if there exist $x_0,y_0 \in G$ for which $[x_0,y_0]^2
\not= 1$. This double magma is a double semigroup if and only
if $G$ is nilpotent of class two. We construct a specific example
of a proper double semigroup based on the dihedral group of order
16. In addition we comment on a similar construction for rings
using Lie commutators.


507  VMO Space Associated with Parabolic Sections and its Application Hsu, MingHsiu; Lee, MingYi
In this paper we define $VMO_\mathcal{P}$ space associated with
a family $\mathcal{P}$ of parabolic sections and show that the
dual of $VMO_\mathcal{P}$ is the Hardy space $H^1_\mathcal{P}$.
As an application, we prove that almost everywhere convergence
of a bounded sequence in $H^1_\mathcal{P}$ implies weak* convergence.


519  Refined Motivic Dimension Kang, SuJeong
We define a refined motivic dimension for an algebraic variety
by modifying the definition of motivic dimension by Arapura.
We apply this to check and recheck the generalized Hodge conjecture
for certain varieties, such as uniruled, rationally connected
varieties and a rational surface fibration.


530  Ricci Curvature Tensor and NonRiemannian Quantities Li, Benling; Shen, Zhongmin
There are several notions of Ricci curvature tensor
in Finsler geometry and spray geometry. One of them is defined by the
Hessian of the wellknown Ricci curvature.
In this paper we will introduce a new notion of Ricci curvature
tensor and discuss its relationship with the Ricci curvature and some
nonRiemannian quantities. By this Ricci curvature tensor, we shall
have a better understanding on these nonRiemannian quantities.


538  Minimal Non Self Dual Groups Li, Lili; Chen, Guiyun
A group $G$ is self dual if every
subgroup
of $G$ is isomorphic to a quotient of $G$ and every quotient
of $G$ is isomorphic to
a subgroup of $G$. It is minimal nonself dual if every
proper subgroup of $G$
is self dual but $G$ is not self dual. In this paper, the structure
of minimal nonself dual groups is determined.


548  Higher Moments of Fourier Coefficients of Cusp Forms Lü, Guangshi; Sankaranarayanan, Ayyadurai
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 $\lambda_f(n)$.


561  Plane Lorentzian and Fuchsian Hedgehogs MartinezMaure, Yves
Parts of the BrunnMinkowski theory can be extended to hedgehogs, which are
envelopes of families of affine hyperplanes parametrized by their Gauss map.
F. Fillastre introduced Fuchsian convex bodies, which are the
closed convex sets of LorentzMinkowski space that are globally invariant
under the action of a Fuchsian group. In this paper, we undertake a study of
plane Lorentzian and Fuchsian hedgehogs. In particular, we prove the
Fuchsian analogues of classical geometrical inequalities (analogues which
are reversed as compared to classical ones).


575  The Diffeomorphism Type of Canonical Integrations Of Poisson Tensors on Surfaces MartinezTorres, David
A surface $\Sigma$ endowed with a Poisson tensor
$\pi$ is known to admit
canonical integration, $\mathcal{G}(\pi)$,
which is a 4dimensional manifold with a (symplectic) Lie groupoid
structure.
In this short note we show that if $\pi$ is not an area
form on the 2sphere, then $\mathcal{G}(\pi)$ is diffeomorphic
to the cotangent bundle $T^*\Sigma$. This extends
results by the author and by Bonechi, Ciccoli, Staffolani, and Tarlini.


580  A Specialisation of the BumpFriedberg $L$function Matringe, Nadir
We study the restriction of the BumpFriedberg integrals to affine
lines $\{(s+\alpha,2s),s\in\mathbb{C}\}$.
It has a simple theory, very close to that of the Asai $L$function.
It is an integral representation of the product
$L(s+\alpha,\pi)L(2s,\Lambda^2,\pi)$ which we denote by $L^{lin}(s,\pi,\alpha)$
for this abstract, when $\pi$ is a cuspidal automorphic
representation of $GL(k,\mathbb{A})$ for
$\mathbb{A}$ the adeles of a number field. When $k$ is even, we show
that for a cuspidal automorphic representation $\pi$,
the partial $L$function $L^{lin,S}(s,\pi,\alpha)$ has a pole
at $1/2$, if and only if $\pi$ admits a (twisted) global
period, this gives a more direct proof of a
theorem of Jacquet and Friedberg, asserting
that $\pi$ has a twisted global period if and only if $L(\alpha+1/2,\pi)\neq
0$ and $L(1,\Lambda^2,\pi)=\infty$.
When $k$ is odd, the partial $L$function is holmorphic in a
neighbourhood of $Re(s)\geq 1/2$ when $Re(\alpha)$ is
$\geq 0$.


596  A Note on Planarity Stratification of Hurwitz Spaces Ongaro, Jared; Shapiro, Boris
One can easily show that any meromorphic function
on a complex closed Riemann surface can be represented as a
composition of a birational map of this surface to $\mathbb{CP}^2$ and
a projection of the image curve from an appropriate point
$p\in \mathbb{CP}^2$ to the pencil of lines through $p$. We introduce
a natural stratification of Hurwitz spaces according to the
minimal degree of a plane curve such that a given meromorphic
function can be represented in the above way and calculate the
dimensions of these strata. We observe that they are closely
related to a family of Severi varieties studied earlier by J. Harris,
Z. Ran and I. Tyomkin.


610  Path Decompositions of Kneser and Generalized Kneser Graphs Rodger, C. A.; Whitt, Thomas Richard III
Necessary and sufficient conditions are given for the existence
of a graph decomposition of the Kneser Graph $KG_{n,2}$ and of
the Generalized Kneser Graph $GKG_{n,3,1}$ into paths of length
three.


620  $L$functions for Quadratic Characters and Annihilation of Motivic Cohomology Groups Sands, Jonathan W.
Let $n$ be a positive even integer, and let $F$ be a totally real
number field and $L$ be an abelian Galois extension which is totally
real or CM.
Fix a finite set $S$ of primes of $F$ containing the infinite primes
and all those which ramify in
$L$, and let $S_L$ denote the primes of $L$ lying above those in
$S$. Then $\mathcal{O}_L^S$ denotes the ring of $S_L$integers of $L$.
Suppose that $\psi$ is a quadratic character of the Galois group of
$L$ over $F$. Under the assumption of the motivic Lichtenbaum
conjecture, we obtain a nontrivial annihilator of the motivic
cohomology group
$H_\mathcal{M}^2(\mathcal{O}_L^S,\mathbb{Z}(n))$ from the lead term of the Taylor series for the
$S$modified Artin $L$function $L_{L/F}^S(s,\psi)$ at $s=1n$.


632  Quantum Unique Ergodicity on Locally Symmetric Spaces: the Degenerate Lift Silberman, Lior
Given a measure $\bar\mu_\infty$ on a locally symmetric space $Y=\Gamma\backslash
G/K$,
obtained as a weak{*} limit of probability measures associated
to
eigenfunctions of the ring of invariant differential operators,
we
construct a measure $\bar\mu_\infty$ on the homogeneous space $X=\Gamma\backslash
G$
which lifts $\bar\mu_\infty$ and which is invariant by a connected subgroup
$A_{1}\subset A$ of positive dimension, where $G=NAK$ is an Iwasawa
decomposition. If the functions are, in addition, eigenfunctions
of
the Hecke operators, then $\bar\mu_\infty$ is also the limit of measures
associated
to Hecke eigenfunctions on $X$. This generalizes results of the
author
with A. Venkatesh in the case where the spectral parameters
stay
away from the walls of the Weyl chamber.


651  Ground State Solutions of NehariPankov Type for a Superlinear Hamiltonian Elliptic System on ${\mathbb{R}}^{N}$ Tang, Xianhua
This paper is concerned with the following
elliptic system of Hamiltonian type
\[
\left\{
\begin{array}{ll}
\triangle u+V(x)u=W_{v}(x, u, v), \ \ \ \ x\in {\mathbb{R}}^{N},
\\
\triangle v+V(x)v=W_{u}(x, u, v), \ \ \ \ x\in {\mathbb{R}}^{N},
\\
u, v\in H^{1}({\mathbb{R}}^{N}),
\end{array}
\right.
\]
where the potential $V$ is periodic and $0$ lies in a gap of
the spectrum of $\Delta+V$, $W(x, s, t)$ is
periodic in $x$ and superlinear in $s$ and $t$ at infinity.
We develop a direct approach to find ground
state solutions of NehariPankov type for the above system.
Especially, our method is applicable for the
case when
\[
W(x, u, v)=\sum_{i=1}^{k}\int_{0}^{\alpha_iu+\beta_iv}g_i(x,
t)t\mathrm{d}t
+\sum_{j=1}^{l}\int_{0}^{\sqrt{u^2+2b_juv+a_jv^2}}h_j(x,
t)t\mathrm{d}t,
\]
where $\alpha_i, \beta_i, a_j, b_j\in \mathbb{R}$ with $\alpha_i^2+\beta_i^2\ne
0$ and $a_j\gt b_j^2$, $g_i(x, t)$
and $h_j(x, t)$ are nondecreasing in $t\in \mathbb{R}^{+}$ for every
$x\in \mathbb{R}^N$ and $g_i(x, 0)=h_j(x, 0)=0$.


664  Betti Numbers and Flat Dimensions of Local Cohomology Modules Vahidi, Alireza
Assume that $R$ is a commutative Noetherian ring with nonzero
identity, $\mathfrak{a}$ is an ideal of $R$ and $X$ is an $R$module.
In this paper, we first study the finiteness of Betti numbers
of local cohomology modules $\operatorname{H}_\mathfrak{a}^i(X)$. Then we give some
inequalities between the Betti numbers of $X$ and those of its
local cohomology modules. Finally, we present many upper bounds
for the flat dimension of $X$ in terms of the flat dimensions
of its local cohomology modules and an upper bound for the flat
dimension of $\operatorname{H}_\mathfrak{a}^i(X)$ in terms of the flat dimensions of
the modules $\operatorname{H}_\mathfrak{a}^j(X)$, $j\not= i$, and that of $X$.


673  Local Heuristics and an Exact Formula for Abelian Surfaces Over Finite Fields Achter, Jeffrey; Williams, Cassandra
Consider a quartic $q$Weil polynomial $f$. Motivated by equidistribution
considerations, we define, for each prime $\ell$, a local factor
that
measures the relative frequency with which $f\bmod \ell$ occurs
as the
characteristic polynomial of a symplectic similitude over $\mathbb{F}_\ell$.
For a certain
class of polynomials, we show that the resulting infinite product
calculates the number of principally polarized abelian surfaces
over $\mathbb{F}_q$
with Weil polynomial $f$.


692  Sur les algèbres de Lie associées à une connexion Anona, F. M.; Randriambololondrantomalala, Princy; Ravelonirina, H. S. G.
Let $\Gamma$ be a connection on a smooth manifold
$M$, in this paper we give some properties of $\Gamma$ by studying
the corresponding Lie algebras. In particular, we compute the
first ChevalleyEilenberg cohomology space of the horizontal
vector fields Lie algebra on the tangent bundle of $M$, whose
the corresponding Lie derivative of $\Gamma$ is null, and of
the horizontal nullity curvature space.


704  On the Continued Fraction Expansion of Fixed Period in Finite Fields Benamar, H.; Chandoul, A.; Mkaouar, M.
The Chowla conjecture
states that,
if $t$ is any given
positive integer, there are infinitely many prime positive
integers $N$ such that $\operatorname{Per} (\sqrt{N})=t$, where
$\operatorname{Per} (\sqrt{N})$
is the period length of the continued fraction expansion for
$\sqrt{N}$.
C. Friesen proved
that, for any $k\in \mathbb{N}$, there are infinitely many
squarefree integers $N$, where the continued fraction expansion
of $\sqrt{N}$ has a fixed period. In this paper, we describe all
polynomials $Q\in \mathbb{F}_q[X] $ for which the continued fraction
expansion of $\sqrt {Q}$ has a fixed period, also we give a
lower
bound of the number of monic, nonsquares polynomials $Q$ such
that $\deg Q= 2d$ and $ Per \sqrt {Q}=t$.


713  On the Maximum Curvature of Closed Curves in Negatively Curved Manifolds Brendle, Simon; Chodosh, Otis
Motivated by Almgren's work on the isoperimetric inequality,
we prove a sharp inequality relating the length and maximum curvature
of a closed curve in a complete, simply connected manifold of
sectional curvature at most $1$. Moreover, if equality holds,
then the norm of the geodesic curvature is constant and the torsion
vanishes. The proof involves an application of the maximum principle
to a function defined on pairs of points.


723  Infinitely Many Rotationally Symmetric Solutions to a Class of Semilinear LaplaceBeltrami Equations on Spheres Castro, Alfonso; Fischer, Emily
We show that a class of semilinear LaplaceBeltrami equations
on the unit sphere
in $\mathbb{R}^n$ has infinitely many rotationally symmetric solutions.
The solutions to
these equations are the solutions to a two point boundary value
problem for a
singular ordinary differential equation. We prove the existence
of such solutions
using energy and phase plane analysis. We derive a
Pohozaevtype
identity
in
order to prove that the energy to an associated initial value
problem tends
to infinity as the energy at the singularity tends to infinity.
The nonlinearity is allowed to grow as fast as $s^{p1}s$ for
$s$ large
with $1 \lt p \lt (n+5)/(n3)$.


730  Vanishing of Massey Products and Brauer Groups Efrat, Ido; Matzri, Eliyahu
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, Mináċ, and Tân, to classical
results in the theory of central simple algebras.
For global fields, we prove a stronger form of the vanishing
property.


741  Homological Properties Relative to Injectively Resolving Subcategories Gao, Zenghui
Let $\mathcal{E}$ be an injectively resolving subcategory of
left $R$modules. A left $R$module $M$
(resp. right $R$module $N$) is called $\mathcal{E}$injective
(resp. $\mathcal{E}$flat)
if $\operatorname{Ext}_R^1(G,M)=0$ (resp. $\operatorname{Tor}_1^R(N,G)=0$)
for any $G\in\mathcal{E}$.
Let $\mathcal{E}$ be a covering subcategory.
We prove that a left $R$module $M$ is $\mathcal{E}$injective
if and only if $M$ is a direct sum
of an injective left $R$module and a reduced $\mathcal{E}$injective
left $R$module.
Suppose $\mathcal{F}$ is a preenveloping subcategory of right
$R$modules such that
$\mathcal{E}^+\subseteq\mathcal{F}$ and $\mathcal{F}^+\subseteq\mathcal{E}$.
It is shown that a finitely presented right $R$module $M$ is
$\mathcal{E}$flat if and only if
$M$ is a cokernel of an $\mathcal{F}$preenvelope of a right
$R$module.
In addition, we introduce and investigate the
$\mathcal{E}$injective and $\mathcal{E}$flat dimensions of
modules and rings. We also introduce $\mathcal{E}$(semi)hereditary
rings and $\mathcal{E}$von Neumann regular rings and characterize
them in terms of $\mathcal{E}$injective and $\mathcal{E}$flat
modules.


757  Embedding Theorem for Inhomogeneous Besov and TriebelLizorkin Spaces on RDspaces Han, Yanchang
In this article we prove the embedding theorem for inhomogeneous
Besov and TriebelLizorkin spaces on RDspaces.
The crucial idea is to use the geometric density condition
on the measure.


774  Character Sums over Bohr Sets Hanson, Brandon
We prove character sum estimates for additive Bohr subsets modulo
a prime.
These estimates are analogous to classical character sum bounds
of
PólyaVinogradov and Burgess. These estimates are applied to
obtain results on
recurrence mod $p$ by special elements.


787  Nonbranching RCD$(0,N)$ Geodesic Spaces with Small Linear Diameter Growth have Finitely Generated Fundamental Groups Kitabeppu, Yu; Lakzian, Sajjad
In this paper, we generalize the finite generation result of
Sormani
to nonbranching $RCD(0,N)$
geodesic spaces (and in particular, Alexandrov spaces) with full
support measures. This is a special case of the Milnor's Conjecture
for complete noncompact $RCD(0,N)$ spaces. One of the key tools
we use is the AbreschGromoll type excess estimates for nonsmooth
spaces obtained by GigliMosconi.


799  On $s$semipermutable or $s$quasinormally Embedded Subgroups of Finite Groups Kong, Qingjun; Guo, Xiuyun
Suppose that $G$ is a
finite group and $H$ is a subgroup of $G$. $H$ is said to be
$s$semipermutable in $G$ if $HG_{p}=G_{p}H$ for any Sylow
$p$subgroup $G_{p}$ of $G$ with $(p,H)=1$; $H$ is said to be
$s$quasinormally embedded in $G$ if for each prime $p$ dividing the
order of $H$, a Sylow $p$subgroup of $H$ is also a Sylow
$p$subgroup of some $s$quasinormal subgroup of $G$. We fix in
every noncyclic Sylow subgroup $P$ of $G$ some subgroup $D$
satisfying $1\lt D\lt P$ and study the structure of $G$ under the
assumption that every subgroup $H$ of $P$ with $H=D$ is either
$s$semipermutable or $s$quasinormally embedded in $G$.
Some recent results are generalized and unified.


808  On the Regularity of the Multisublinear Maximal Functions Liu, Feng; Wu, Huoxiong
This paper is concerned with the study of
the regularity for the multisublinear maximal operator. It is
proved that the multisublinear maximal operator is bounded on
firstorder Sobolev spaces. Moreover, two key pointwise
inequalities for the partial derivatives of the multisublinear
maximal functions are established. As an application, the
quasicontinuity on the multisublinear maximal function is also
obtained.


818  On the Limit Cycles of Linear Differential Systems with Homogeneous Nonlinearities Llibre, Jaume; Zhang, Xiang
We consider the class of polynomial differential systems of the
form
$\dot x= \lambda xy+P_n(x,y)$, $\dot y=x+\lambda y+ Q_n(x,y),$ where
$P_n$ and $Q_n$ are homogeneous polynomials of degree $n$. For
this
class of differential systems we summarize the known results
for the
existence of limit cycles, and we provide new results for their
nonexistence and existence.


824  Exact Morphism Category and Gorensteinprojective Representations Luo, XiuHua
Let $Q$ be a finite acyclic quiver, $J$ be an ideal of $kQ$ generated
by all arrows in $Q$, $A$ be a finitedimensional $k$algebra. The
category of all finitedimensional representations of $(Q, J^2)$ over
$A$ is denoted by $\operatorname{rep}(Q, J^2, A)$. In this paper, we
introduce the category $\operatorname{exa}(Q,J^2,A)$, which is a
subcategory of
$\operatorname{rep}{}(Q,J^2,A)$ of all exact representations.
The main result of this paper explicitly describes the Gorensteinprojective representations in $\operatorname{rep}{}(Q,J^2,A)$,
via the exact representations plus an extra condition.
As a corollary, $A$ is a selfinjective algebra, if
and only if the Gorensteinprojective representations are exactly the
exact representations of $(Q, J^2)$ over $A$.


835  Real Hypersurfaces in Complex TwoPlane Grassmannians with GTW Harmonic Curvature de Dios Pérez, Juan; Suh, Young Jin; Woo, Changhwa
We prove the nonexistence of Hopf real hypersurfaces in complex
twoplane Grassmannians with harmonic curvature with respect
to the generalized TanakaWebster connection if they satisfy
some further conditions.


846  A Computation with the ConnesThom Isomorphism Sundar, S.
Let $A \in M_{n}(\mathbb{R})$ be an invertible matrix. Consider
the semidirect product $\mathbb{R}^{n} \rtimes \mathbb{Z}$ where
the action of $\mathbb{Z}$ on $\mathbb{R}^{n}$ is induced by
the left multiplication by $A$. Let $(\alpha,\tau)$ be a strongly
continuous action of $\mathbb{R}^{n} \rtimes \mathbb{Z}$ on a
$C^{*}$algebra $B$ where $\alpha$ is a strongly continuous action
of $\mathbb{R}^{n}$ and $\tau$ is an automorphism. The map $\tau$
induces a map $\widetilde{\tau}$ on $B \rtimes_{\alpha} \mathbb{R}^{n}$.
We show that, at the $K$theory level, $\tau$ commutes with the
ConnesThom map if $\det(A)\gt 0$ and anticommutes if $\det(A)\lt 0$.
As an application, we recompute the $K$groups of the CuntzLi
algebra associated to an integer dilation matrix.


858  Ternary Quadratic Forms and Eta Quotients Williams, Kenneth S.
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
$\{16k+14\}_{k \geq 0}$, $\{64k+56\}_{k \geq 0}$, $\{256k+224\}_{k
\geq 0}$, $\{1024k+896\}_{k \geq 0}$, $\ldots$.


869  Variants of Korselt's Criterion Wright, Thomas
Under sufficiently strong assumptions about the first term in
an arithmetic progression, we prove that for any integer $a$,
there are infinitely many $n\in \mathbb N$ such that for each
prime factor $pn$, we have $pana$. This can be seen as a
generalization of Carmichael numbers, which are integers $n$
such that $p1n1$ for every $pn$.


877  Generating Some Symmetric Semiclassical Orthogonal Polynomials Zaatra, Mohamed
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.

