Clemens-Schmid exact sequence in characteristic p

For a semistable family of varieties over a curve in characteristic $p$, we prove the existence of a "Clemens-Schmid type" long exact sequence for the $p$-adic cohomology. The cohomology groups appearing in such a long exact sequence are defined locall

An explicit trace formula of Jacquet-Zagier type for Hilbert modular forms

We give an exact formula of the average of adjoint $L$-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 ${\rm SL}_2(\mathbb{Z})$. 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 $L$-functions

Existence of Hilbert cusp forms with non-vanishing LL-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 $L$-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 /