We prove that every smooth divisor in $\mathbb {P}^1\times \mathbb {P}^1\times \mathbb {P}^2$ of degree $(1,1,2)$ is K-stable.

We show that the generic fiber of a family $f:X\rightarrow S$ of smooth $\mathbb{A}^{1}$-ruled affine surfaces always carries an $\mathbb{A}^{1}$-fibration, possibly after a finite extension of the base $S$. In the particular case where the general fibers of the family are irrational surfaces, we establish that up to shrinking $S$, such a family actually factors through an $\mathbb{A}^{1}$-fibration $\unicode[STIX]{x1D70C}:X\rightarrow Y$ over a certain $S$-scheme $Y\rightarrow S$ induced by the MRC-fibration of a relative smooth projective model of $X$ over $S$. For affine threefolds $X$ equipped with a fibration $f:X\rightarrow B$ by irrational $\mathbb{A}^{1}$-ruled surfaces over a smooth curve $B$, the induced $\mathbb{A}^{1}$-fibration $\unicode[STIX]{x1D70C}:X\rightarrow Y$ can also be recovered from a relative minimal model program applied to a smooth projective model of $X$ over $B$.

Medium scale integrated circuits with 108 CNT-TFTs have been fabricated using CNTs grown by plasma enhanced chemical vapor deposition (PECVD) which has the advantage of preferential growth of CNTs with semiconducting behavior in the FET current–voltage characteristics. High-speed operation with a switching time of 0.51 μs/gate, which is highest in the CNT-TFT integrated circuits to our knowledge, was demonstrated by a 53-stage ring oscillator. Characterization of CNT-TFTs using scanning probe microscopy has also been performed. The island-like structure in the electrical properties of the CNT network was observed even in a high-density CNT network in the subthreshold regime. This was explained by the decrease of the effective number of CNTs which contribute the electrical conduction.

The Nagata automorphism is a kind of complicated automorphism on the affine 3-space . For a long time, it remained unknown whether or not the Nagata automorphism is tame until Shestakov and Umirbaev at last proved that it is not tame in 2004, by purely algebraic methods (e.g. Poisson algebra). In this paper, we consider a certain necessary condition for a given automorphism on to be tame from the point of view of the Sarkisov program established by Corti. Furthermore, by using it, we shall give a new algebro-geometric proof of the non-tameness of the Nagata automorphism.

The technologies utilizing Fluorinated Silicon Oxide (FSG, k=3.6) and Hydrogen Silsesquioxane (HSQ, k=3.0) have been established for 0.25-μm and 0.18-μm generation ULSIs. However, low-k materials for the next generation ULSIs, which have a dielectric constant of less than 3.0, have not become mature yet. In this paper, we review process integration issues in applying FSG and HSQ, and describe integration results and device performance using Fluorinated Amorphous Carbon (a-C:F, k=2.5) as one of the promising low-k materials for the next generation ULSIs.

The technologies utilizing Fluorinated Silicon Oxide (FSG, k=3.6) and Hydrogen Silsesquioxane (HSQ, k=3.0) have been established for 0.25-µm and 0.1 8-µm generation ULSIs. However, low-k materials for the next generation ULSIs, which have a dielectric constant of less than 3.0, have not become mature yet. In this paper, we review process integration issues in applying FSG and HSQ, and describe integration results and device performance using Fluorinated Amorphous Carbon (a-C:F, k=2.5) as one of the promising low-k materials for the next generation ULSIs.