1.
Togliatti systems - Ilardi, Giovanna
We find some examples in $\mathbf{P}^5(\mathbf{C})$ of surfaces
satisfying Laplace equations. In particular, we study rational
surfaces in $\mathbf{P}^{5}(\mathbf{C})$ whose hyperplane
sections have genus one that satisfy a Laplace equation.
Then we study monomial Togliatti systems of cubics for variety
of dimension three, i.e. we find all the monomial examples
of three-folds satisfying Laplace equations.
2.
Microlocal analytic smoothing effects for operators of real principal type - Takuwa, Hideaki
We are interested in the microlocal smoothing effect for operators
of real principal type. On the initial value problem for
a dispersive evolution equation, we study the fact that the
sufficient decay of the initial data gives the smoothness
of the solution. We develop the theory of the FBI transform
in order to transform our operator of real principal type
into a simple operator of first order. Since the smoothing
effect is of global nature, our transformation is realized
globally along the bicharacteristics defined from the principal
symbol of the operator.
3.
Edge problems on configurations with model cones of different dimensions - Coriasco, Sandro; Schulze, Bert-Wolfgang
Elliptic equations on configurations $W = W_{1} \cup \dots
\cup W_{N}$ with edge $Y$ and components $W_{j}$ of different
dimension can be treated in the frame of pseudo-differential
analysis on manifolds with geometric singularities, here edges.
Starting from edge-degenerate operators on $W_{j}$, $j=1,\dots,N$,
we construct an algebra with extra `transmission' conditions
on $Y$ that satisfy an analogue of the Shapiro-Lopatinskij
condition. Ellipticity refers to a two-component symbolic
hierarchy with an interior and an edge part; the latter one
is operator-valued, operating on the union of different dimensional
model cones. We construct parametrices within our calculus,
where exchange of information between the various components
is encoded in Green and Mellin operators that are...
4.
Realization of hyperelliptic families with the hyperelliptic semistable monodromies - Ishizaka, Mizuho
Let $\Phi$ be an element of the mapping class group $\mathcal{M}_{g}$
of genus $g$ ($\geq 2$) such that $\Phi$ is the isotopy class
of a pseudo periodic map of negative twists. It is expected
that, for each $\Phi$ which commutes with a hyperelliptic
involution, there exists a hyperelliptic family whose monodromy
is the conjugacy class of $\Phi$ in the mapping class group.
In this paper, we give a partial solution for the conjecture
in the case where $\Phi$ is a semistable element.
5.
The dual Thurston norm and the geometry of closed 3-manifolds - Itoh, Mitsuhiro; Yamase, Takahisa
We investigate closed Riemannian 3-manifolds which satisfy
an extremal condition. Using monopole equations and considering
the action of the covering transformations, we decide the
geometric structure of such 3-manifolds. As a result, we
characterize the geometry of 3-manifolds with monopole classes
whose dual Thurston norm is equal to one.
6.
A note on compact solvmanifolds with Kähler structures - Hasegawa, Keizo
In this note we show that a compact solvmanifold admits a
Kähler structure if and only if it is a finite quotient
of a complex torus which has a structure of a complex torus
bundle over a complex torus. We can show in particular that
a compact solvmanifold of completely solvable type has a Kähler
structure if and only if it is a complex torus, which is known
as the Benson-Gordon's conjecture.
7.
Greenberg's theorem and equivalence problem on compact Riemann surfaces - Mizuta, Satoru; Namba, Makoto
Another proof of Greenberg's theorem on automorphism groups
of compact \mboxRiemann surfaces is given. Using the idea
of the proof, the equivalence problem for finite Galois coverings
of the compact projective line is answered affirmatively,
except special type of coverings.
8.
Curves in projective spaces and their index of regularity - Ballico, Edoardo
For all integers $n \ge 3$ we show the existence of many triples
$(d,g,\rho)$ such that there is a smooth non-degenerate curve
$C \subset \mathbf{P}^n$ with degree $d$, genus $g$ and index
of regularity $\rho$. The curve $C$ lies in a smooth $K3$
surface $S \subset \mathbf{P}^n$.
9.
Borsuk-Ulam type theorems on Stiefel manifolds - Inoue, Akira
In this paper, we study the degree of equivariant maps between
Stiefel manifolds by using cohomological index theory. As
applications, we have some Borsuk-Ulam type theorems on Stiefel
manifolds.
11.
Strongly real $2$-blocks and the Frobenius-Schur indicator - Murray, John
Let $G$ be a finite group, let $k$ be an algebraically closed
field of characteristic $2$ and let $\Omega:=\{g\in G\mid
g^2=1_G\}$. It is shown that for a block $B$ of $kG$, the
permutation module $k\Omega$ has a $B$-composition factor
if and only if the Frobenius-Schur indicator of the regular
character of $B$ is non-zero or equivalently if and only if
$B$ is real with a strongly real defect class.
12.
Exponential attractor for an adsorbate-induced phase transition model in non smooth domain - Takei, Yasuhiro; Efendiev, Messoud; Tsujikawa, Tohru; Yagi, Atsushi
We improve our preceding result obtained in Tsujikawa and
Yagi [10]. We construct the similar exponential attractors
to the same adsorbate-induced phase transition model as in
[10] but in a convex domain by using the compact smoothing
property of corresponding nonlinear semigroup. In [10], the
domain has been assumed to have $\mathcal{C}^{3}$ regularity
to ensure the squeezing property of semigroup.
13.
On some laws of iterated logarithm for Burgers turbulence with Brownian initial data based on the concave majorant - Isozaki, Yasuki
We study the shock structure and the asymptotic behaviour
of some flux across the origin in one-dimensional Burgers
turbulence, the entropy solution to the inviscid Burgers equation,
with random initial velocity for the uniformly distributed
particles on the positive half line. We assume, in contrast
to other works on Burgers turbulence, initially a vacuum state
on the negative half line. We also obtain some asymptotic
estimates for the concave majorant of Brownian motion.
14.
Infinitesimal deformations of the tangent bundle of a moduli space of vector bundles over a curve - Biswas, Indranil
Fix a line bundle $\xi$ on a connected smooth complex projective
curve $X$ of genus at least three. Let $\mathcal{N}$ denote
the moduli space of all stable vector bundles over $X$ of
rank $n$ and determinant $\xi$. We assume that $n\geq 3$ and
coprime to $\operatorname{degree}(\xi)$; If $\operatorname{genus}(X)\leq
4$, then we also assume that $n \geq 4$. We prove that $H^i(\mathcal{N},
\End(T\mathcal{N}\mkern2mu)) = H^i(X, \mathcal{O}_X)$ for
$i= 0,1$.
15.
Toric varieties whose canonical divisors are divisible by their dimensions - Fujino, Osamu
We totally classify the projective toric varieties whose
canonical divisors are divisible by their dimensions. In Appendix,
we show that Reid's toric Mori theory implies Mabuchi's characterization
of the projective space for toric varieties.
16.
Global small amplitude solutions to systems of nonlinear wave equations with multiple speeds - Katayama, Soichiro; Yokoyama, Kazuyoshi
We give a global existence theorem to systems of quasilinear
wave equations in three space dimensions, especially for the
multiple-speed cases. It covers a wide class of quadratic
nonlinearities which may depend on unknowns as well as their
first and second derivatives. Our proof is achieved through
total use of pointwise and $L^2$-estimates concerning unknowns
and their first and second derivatives.
17.
A category of spectral triples and discrete groups with length function - Bertozzini, Paolo; Conti, Roberto; Lewkeeratiyutkul, Wicharn
In the context of Connes' spectral triples, a suitable notion
of morphism is introduced. Discrete groups with length function
provide a natural example for our definitions. Connes' construction
of spectral triples for group algebras is a covariant functor
from the category of discrete groups with length functions
to that of spectral triples. Several interesting lines for
future study of the categorical properties of spectral triples
and their variants are suggested.
18.
The recurrence time for irrational rotations - Kim, Dong Han
Let $T$ be a measure preserving transformation on $X \subset
\mathbb{R}^d$ with a Borel measure $\mu$ and $R_E$ be the
first return time to a subset $E$. If $(X,\mu)$ has positive
pointwise dimension for almost every $x$, then for almost
every $x$ \[ \limsup_{r \to 0^+} \frac{\log R_{B(x,r)}(x)}{-\log
\mu(B(x,r))} \le 1, \] where $B(x,r)$ the the ball centered
at $x$ with radius $r$. But the above property does not hold
for the neighborhood of the `skewed' ball. Let $B(x,r;s)
= (x - r^s, x + r)$ be an interval for $s >0$. For arbitrary
$\alpha \ge 1$ and $\beta \ge 1$, there are uncountably many
irrational numbers whose rotation satisfy...
19.
An estimate of the ribbon number by the Jones polynomial - Mizuma, Yoko
For a ribbon knot we define the notion of its ribbon number.
In this paper we estimate the ribbon number for a ribbon knot
by using the Jones polynomial. As a corollary we determine
the ribbon number of the Kinoshita-Terasaka knot.
20.
Active sums II - Díaz-Barriga, Alejandro J.; González-Acuña, Francisco; Marmolejo, Francisco; Román, Leopoldo
We exhibit several finite groups that are not active sums
of cyclic subgroups. We show that this is the case for groups
with $H_{1}G$ of odd order and $H_{2}G$ of even order. As
particular examples of this we have the alternating groups
$A_n$ for $n\geq 4$, some special and some projective linear
groups. Our next set of examples consists of $p$-groups where
the normalizer and the centralizer of every element coincide.
We also have an example of a 2-group where the above conditions
are not satisfied; thus we had to devise an ad hoc argument.
We observe that the examples of $p$-groups given also provide
groups that are not molecular.
1.
