Freeness of adjoint linear systems on threefolds with terminal Gorenstein singularities or some quotient singularities

We generalize the result of Kawamata concerning the strong version of Fujita's freeness conjecture for smooth 3-folds to some singular cases, namely, Gorenstein terminal singularities and quotient singularities of type 1/r(1,1,1) and of type 1/r(1,1,-1). We generalize furthermore the result of that to projective threefolds with only canonical singularities for canonical and not terminal singularities. It turns out that the estimates in the first three cases are better than the one for the smooth case, which it is not in the fourth case. We also give explicit examples which show the estimate in the fourth case is necessarily worse than the one for the smooth case.Comment: 21 pages, Late

Gap conjecture for 3-dimensional canonical thresholds

We prove that the interval $(5/6, 1)$ contains no 3-dimensional canonical thresholds.Comment: 8 pages, latex, one reference is adde

Some remarks on A_1^{(1)} soliton cellular automata

In this short note, we describe the A_1^{(1)} soliton cellular automata as an evolution of a poset. This allows us to explain the conservation laws for the A_1^{(1)} soliton cellular automata, one given by Torii, Takahashi and Satsuma, and the other given by Fukuda, Okado and Yamada, in terms of the stack permutations of states in a very natural manner. As a biproduct, we can prove a conjectured formula relating these laws.Comment: 10 pages, LaTeX2

Connections and the Second Main Theorem for Holomorphic Curves

By means of $C^\infty$-connections we will prove a general second main theorem and some special ones for holomorphic curves. The method gives a geometric proof of H. Cartan's second main theorem in 1933. By applying the same method, we will prove some second main theorems in the case of the product space (\pone)^2 of the Riemann sphere.Comment: 21 page

Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions

We present a theoretical foundation for the Index theorem in naive and minimally doubled lattice fermions by studying the spectral flow of a Hermitean version of Dirac operators. We utilize the point splitting method to implement flavored mass terms, which play an important role in constructing proper Hermitean operators. We show the spectral flow correctly detects the index of the would-be zero modes which is determined by gauge field topology. Using the flavored mass terms, we present new types of overlap fermions from the naive fermion kernels, with a number of flavors that depends on the choice of the mass terms. We succeed to obtain a single-flavor naive overlap fermion which maintains hypercubic symmetry.Comment: 27 pages, 17 figures; references added, version accepted in JHE

Local Manipulation of Nuclear Spin in a Semiconductor Quantum Well

The shaping of nuclear spin polarization profiles and the induction of nuclear resonances are demonstrated within a parabolic quantum well using an externally applied gate voltage. Voltage control of the electron and hole wave functions results in nanometer-scale sheets of polarized nuclei positioned along the growth direction of the well. RF voltages across the gates induce resonant spin transitions of selected isotopes. This depolarizing effect depends strongly on the separation of electrons and holes, suggesting that a highly localized mechanism accounts for the observed behavior.Comment: 18 pages, 4 figure

Twisted Alexander polynomials and incompressible surfaces given by ideal points

We study incompressible surfaces constructed by Culler-Shalen theory in the context of twisted Alexander polynomials. For a $1$st cohomology class of a $3$-manifold the coefficients of twisted Alexander polynomials induce regular functions on the $SL_2(\mathbb{C})$-character variety. We prove that if an ideal point gives a Thurston norm minimizing non-separating surface dual to the cohomology class, then the regular function of the highest degree has a finite value at the ideal point.Comment: 10 pages, to appear in "The special issue for the 20th anniversary", the Journal of Mathematical Sciences, the University of Toky

Dixmier approximation and symmetric amenability for C*-algebras

We study some general properties of tracial C*-algebras. In the first part, we consider Dixmier type approximation theorem and characterize symmetric amenability for C*-algebras. In the second part, we consider continuous bundles of tracial von Neumann algebras and classify some of them.Comment: 19 pages; minor update (v2

The LpL^p boundedness of wave operators for Schr\"odinger operators with threshold singularities II. Even dimensional case

In this paper we consider the wave operators $W_{\pm}$ for a Schr\"odinger operator $H$ in ${\bf{R}}^n$ with $n\geq 4$ even and we discuss the $L^p$ boundedness of $W_{\pm}$ assuming a suitable decay at infinity of the potential $V$. The analysis heavily depends on the singularities of the resolvent for small energy, that is if 0-energy eigenstates exist. If such eigenstates do not exist $W_{\pm}: L^p \to L^p$ are bounded for $1 \leq p \leq \infty$ otherwise this is true for $\frac{n}{n-2} < p < \frac{n}{2}$. The extension to Sobolev space is discussed.Comment: 59 page

Local Zeta Functions for Non-degenerate Laurent Polynomials Over p-adic Fields

In this article, we study local zeta functions attached to Laurent polynomials over p-adic fields, which are non-degenerate with respect to their Newton polytopes at infinity. As an application we obtain asymptotic expansions for p-adic oscillatory integrals attached to Laurent polynomials. We show the existence of two different asymptotic expansions for p-adic oscillatory integrals, one when the absolute value of the parameter approaches infinity, the other when the absolute value of the parameter approaches zero. These two asymptotic expansions are controlled by the poles of twisted local zeta functions of Igusa type.Comment: The condition on the critical set on the mapping f considered in Section 2.5 of our article is not sufficient to assure the vanishing of the twisted local zeta functions (for almost all the characters) as we assert in Theorem 3.9. A new condition on the mapping f is provide