arXiv subjects

Keiichi Watanabe

Publications and source records attributed to Keiichi Watanabe.

23 records · Page 2Linked to original sources

arXiv2018

Higher-Order Program Verification via HFL Model Checking

There are two kinds of higher-order extensions of model checking: HORS model checking and HFL model checking. Whilst the former has been applied to automated verification of higher-order functional programs, applications of the latter have not been well studied. In the present paper, we show that various verification problems for functional programs, including may/must-reachability, trace properties, and linear-time temporal properties (and their negations), can be naturally reduced to (extended) HFL model checking. The reductions yield a sound and complete logical characterization of those program properties. Compared with the previous approaches based on HORS model checking, our approach provides a more uniform, streamlined method for higher-order program verification.

cs.PL↗

arXiv2017

Compressible-incompressible two-phase flows with phase transition: model problem

We study the compressible and incompressible two-phase flows separated by a sharp interface with a phase transition and a surface tension. In particular, we consider the problem in $\mathbb{R}^N$, and the Navier-Stokes-Korteweg equations is used in the upper domain and the Navier-Stokes equations is used in the lower domain. We prove the existence of $\mathcal{R}$-bounded solution operator families for a resolvent problem arising from its model problem. According to Shibata \cite{GS2014}, the regularity of $ρ_+$ is $W^1_q$ in space, but to solve the kinetic equation: $\mathbf{u}_Γ\cdot\mathbf{n}_t = [[ρ\mathbf{u}]]\cdot\mathbf{n}_t /[[ρ]]$ on $Γ_t$ we need $W^{2-1/q}_q$ regularity of $ρ_+$ on $Γ_t$, which means the regularity loss. Since the regularity of $ρ_+$ dominated by the Navier-Stokes-Korteweg equations is $W^3_q$ in space, we eliminate the problem by using the Navier-Stokes-Korteweg equations instead of the compressible Navier-Stokes equations.

math.AP↗

arXiv2012

A fundamental inequality between products of $x^p - 1$

We will show certain functional inequalities between some products of $x^p - 1$.

math.CA↗

arXiv2011

Isometries between groups of invertible elements in $C^{*}$-algebras

In this paper we describe all surjective isometries between open subgroups of the groups of invertible elements in unital $C^{*}$-algebras.

math.OA↗

arXiv2003

Integrally closed ideals in two-dimensional regular local rings are multiplier ideals

There has arisen in recent years a substantial theory of "multiplier ideals'' in commutative rings. These are integrally closed ideals with properties that lend themselves to highly interesting applications. But how special are they among integrally closed ideals in general? We show that in a two-dimensional regular local ring with algebraically closed residue field, there is in fact no difference between "multiplier" and "integrally closed" (or "complete.") However, among multiplier ideals arising from an integer multiplying constant (also known as adjoint ideals) the only simple complete ones primary for the maximal ideal are those of order one.

math.AC↗