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3  Higher Dimensional Spaces of Functions on the Spectrum of a Uniform Algebra Basener, Richard F.
In this paper we introduce a nested family of spaces of continuous functions defined
on the spectrum of a uniform algebra. The smallest space in the family is the
uniform algebra itself. In the ``finite dimensional'' case, from some point on the
spaces will be the space of all continuous complexvalued functions on the
spectrum. These spaces are defined in terms of solutions to the nonlinear
CauchyRiemann equations as introduced by the author in 1976, so they are not
generally linear spaces of functions. However, these spaces do shed light on the
higher dimensional properties of a uniform algebra. In particular, these spaces are
directly related to the generalized Shilov boundary of the uniform algebra (as
defined by the author and, independently, by Sibony in the early 1970s).


11  van der Pol Expansions of LSeries Borwein, David; Borwein, Jonathan
We provide concise series representations for various
Lseries integrals. Different techniques are needed below and above
the abscissa of absolute convergence of the underlying Lseries.


24  Invariant Metrics with Nonnegative Curvature on Compact Lie Groups Brown, Nathan; Finck, Rachel; Spencer, Matthew; Tapp, Kristopher; Wu, Zhongtao
We classify the leftinvariant metrics with nonnegative sectional curvature on $\SO(3)$ and $U(2)$.


35  A Singular Critical Potential for the Schrödinger Operator Duyckaerts, Thomas
Consider a real potential $V$ on
$\RR^d$, $d\geq 2$, and the Schr\"odinger equation:
\begin{equation}
\tag{LS} \label{LS1} i\partial_t u +\Delta u Vu=0,\quad
u_{\restriction t=0}=u_0\in L^2.
\end{equation}
In this paper, we investigate the minimal local regularity of $V$
needed to get local in time dispersive estimates (such as local in
time Strichartz estimates or local smoothing effect with gain of
$1/2$ derivative) on solutions of \eqref{LS1}. Prior works
show some dispersive properties when $V$ (small at infinity) is in
$L^{d/2}$ or in spaces just a little larger but with a smallness
condition on $V$ (or at least on its negative part).


48  Tensor Square of the Minimal Representation of $O(p,q)$ Dvorsky, Alexander
In this paper, we study the tensor product $\pi=\sigma^{\min}\otimes
\sigma^{\min}$ of the minimal representation $\sigma^{\min}$ of $O(p,q)$ with
itself, and decompose $\pi$ into a direct integral of irreducible
representations. The decomposition is given in terms of the Plancherel measure
on a certain real hyperbolic space.


56  Simplicial Cohomology of Some Semigroup Algebras Gourdeau, F.; Pourabbas, A.; White, M. C.
In this paper, we investigate the higher simplicial cohomology
groups of the convolution algebra $\ell^1(S)$ for various semigroups
$S$. The classes of semigroups considered are semilattices, Clifford
semigroups, regular Rees semigroups and the additive semigroups of
integers greater than $a$ for some integer $a$. Our results are of
two types: in some cases, we show that some cohomology groups are $0$,
while in some other cases, we show that some cohomology groups are
Banach spaces.


71  Polynomials for Kloosterman Sums Gurak, S.
Fix an integer $m>1$, and set $\zeta_{m}=\exp(2\pi i/m)$. Let ${\bar x}$
denote the multiplicative inverse of $x$ modulo $m$. The Kloosterman
sums $R(d)=\sum_{x} \zeta_{m}^{x + d{\bar x}}$, $1 \leq d \leq
m$, $(d,m)=1$,
satisfy the polynomial
$$f_{m}(x) = \prod_{d} (xR(d)) = x^{\phi(m)} +c_{1}
x^{\phi(m)1} + \dots + c_{\phi(m)},$$
where the sum and product are taken over a complete system of reduced residues
modulo $m$. Here we give a natural factorization of $f_{m}(x)$, namely,
$$ f_{m}(x) = \prod_{\sigma} f_{m}^{(\sigma)}(x),$$
where $\sigma$ runs through the square classes of the group ${\bf Z}_{m}^{*}$
of reduced residues modulo $m$. Questions concerning the explicit
determination of the factors $f_{m}^{(\sigma)}(x)$ (or at least their
beginning coefficients), their reducibility over the rational field
${\bf Q}$ and duplication among the factors are studied. The treatment
is similar to what has been done for period polynomials for finite
fields.


85  Classification of Finite GroupFrames and SuperFrames Han, Deguang
Given a finite group $G$, we examine the classification of all
frame representations of $G$ and the classification of all
$G$frames, i.e., frames induced by group representations of $G$.
We show that the exact number of equivalence classes of $G$frames
and the exact number of frame representations can be explicitly
calculated. We also discuss how to calculate the largest number
$L$ such that there exists an $L$tuple of strongly disjoint
$G$frames.


97  Characterizations of Real Hypersurfaces in a Complex Space Form Kim, InBae; Kim, Ki Hyun; Sohn, Woon Ha
We study a real hypersurface $M$ in a complex space
form $\mn$, $c \neq 0$, whose shape operator and structure tensor
commute each other on the holomorphic distribution of $M$.


105  On Valuations, Places and Graded Rings Associated to $*$Orderings Klep, Igor
We study natural $*$valuations, $*$places and graded $*$rings
associated with $*$ordered rings.
We prove that the natural $*$valuation is always quasiOre and is
even quasicommutative (i.e., the corresponding graded $*$ring is
commutative), provided the ring contains an imaginary unit.
Furthermore, it is proved that the graded $*$ring is isomorphic
to a twisted semigroup algebra. Our results are applied to answer a question
of Cimpri\v c regarding $*$orderability of quantum
groups.


113  Hermitian Harmonic Maps into Convex Balls Li, ZhenYang; Zhang, Xi
In this paper, we consider Hermitian harmonic maps from
Hermitian manifolds into convex balls. We prove that there exist
no nontrivial Hermitian harmonic maps from closed Hermitian
manifolds into convex balls, and we use the heat flow method to
solve the Dirichlet problem for Hermitian harmonic maps when the
domain is a compact Hermitian manifold with nonempty boundary.


123  Simultaneous Approximation and Interpolation on Arakelian Sets Nikolov, Nikolai; Pflug, Peter
We extend results of P.~M. Gauthier, W. Hengartner and
A.~A. Nersesyan
on simultaneous approximation and interpolation
on Arakelian sets.


126  $\varphi$Dialgebras and a Class of Matrix ``Coquecigrues'' Ongay, Fausto
Starting with the Leibniz algebra defined by a $\varphi$dialgebra, we
construct examples of ``coquecigrues,'' in the sense of Loday, that is to
say, manifolds whose tangent structure at a distinguished point coincides
with that of the Leibniz algebra. We discuss some possible
implications and generalizations of this construction.


138  On the Structure of the Set of Symmetric Sequences in Orlicz Sequence Spaces Sari, Bünyamin
We study the structure of the sets of symmetric sequences and
spreading models of an Orlicz sequence space equipped with partial
order with respect to domination of bases. In the cases that these
sets are ``small'', some descriptions of the structure of these posets
are obtained.


149  On Quotients of NonArchimedean Köthe Spaces Śliwa, Wiesław
We show that there exists a nonarchimedean
Fr\'echetMontel space $W$ with a basis and with a continuous norm
such that any nonarchimedean Fr\'echet space of countable type is isomorphic
to a quotient of $W$. We also prove that any nonarchimedean nuclear
Fr\'echet space is isomorphic to a quotient of some nonarchimedean nuclear
Fr\'echet space with a basis and with a continuous norm.


158  A Note on Giuga's Conjecture Tipu, Vicentiu
Let $G(X)$ denote the number of positive composite integers $n$
satisfying $\sum_{j=1}^{n1}j^{n1}\equiv 1 \tmod{n}$.
Then $G(X)\ll X^{1/2}\log X$ for sufficiently large $X$.

