7,585 research outputs found
An explicit trace formula of Jacquet-Zagier type for Hilbert modular forms
We give an exact formula of the average of adjoint -functions of
holomorphic Hilbert cusp forms with a fixed weight and a square-free level,
which is a generalization of Zagier's formula known for the case of elliptic
cusp forms on . As an application, we prove that the
Satake parameters of Hilbert cusp forms with a fixed weight and with growing
square-free levels are equidistributed in an ensemble constructed by values of
the adjoint -functions
Clemens-Schmid exact sequence in characteristic p
For a semistable family of varieties over a curve in characteristic , we
prove the existence of a "Clemens-Schmid type" long exact sequence for the
-adic cohomology. The cohomology groups appearing in such a long exact
sequence are defined locall
Existence of Hilbert cusp forms with non-vanishing -values
We give a derivative version of the relative trace formula on PGL(2) studied
in our previous work, and obtain a formula of an average of central values
(derivatives) of automorphic -functions for Hilbert cusp forms. As an
application, we prove existence of Hilbert cusp forms with non-vanishing
central values (derivatives) such that the absolute degrees of their Hecke
fields are sufficiently large
Rebalancing Static Super-Replications
This paper proposes a trading strategy that dynamically rebalances static super-replicating portfolios, which is very useful for both investment and hedging strategies. In order to investigate general properties of the strategy, we derive the Doob-Meyer decomposition for the value process without any specifications of models under the continuous processes of the underlying variables. In particular, we find that the increasing part of the decomposition characterizes the performance of the strategy. Also, we obtain more concrete features for cross-currency and one-touch options based on our general framework. Moreover, numerical examples for cross-currency options demonstrate the effectiveness of our strategy for investment and hedging.
Convergence study and optimal weight functions of an explicit particle method for the incompressible Navier--Stokes equations
To increase the reliability of simulations by particle methods for
incompressible viscous flow problems, convergence studies and improvements of
accuracy are considered for a fully explicit particle method for incompressible
Navier--Stokes equations. The explicit particle method is based on a penalty
problem, which converges theoretically to the incompressible Navier--Stokes
equations, and is discretized in space by generalized approximate operators
defined as a wider class of approximate operators than those of the smoothed
particle hydrodynamics (SPH) and moving particle semi-implicit (MPS) methods.
By considering an analytical derivation of the explicit particle method and
truncation error estimates of the generalized approximate operators, sufficient
conditions of convergence are conjectured.Under these conditions, the
convergence of the explicit particle method is confirmed by numerically
comparing errors between exact and approximate solutions. Moreover, by focusing
on the truncation errors of the generalized approximate operators, an optimal
weight function is derived by reducing the truncation errors over general
particle distributions. The effectiveness of the generalized approximate
operators with the optimal weight functions is confirmed using numerical
results of truncation errors and driven cavity flow. As an application for flow
problems with free surface effects, the explicit particle method is applied to
a dam break flow.Comment: 27 pages, 13 figure
UV-shielding ceramic nanoparticles synthesised by mechanochemcial processing
ZnO, TiO2 and CeO2 are known as UV-shielding ceramic materials that have advantages over organic UV absorbers for their photo-stability and non-hazardous nature to human bodies. However, they normally cause low transparency in the visible-light range due to light scattering by large particles, which is undesirable for many transparent UV-blocking applications in cosmetic and plastic industries. Light-scattering efficiency of particles can be drastically reduced by decreasing the particle sizes down below 100 nm. This paper reviews recent investigation on the synthesis of ZnO and CeO2 nanoparticles by mechanochemical processing. The resulting particles had a significantly low degree of agglomeration, having mean particle sizes of ~ 25 nm and ~ 10 nm, respectively. The aqueous suspensions of the nanoparticles showed strong absorption in the UV-light range and high transmittance in the visible-light range. Mechanochemical processing offers the possibility of industrial-scale production of transparent UV-shielding ceramic particles for many applications.<br /
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