State-Space Formulation of Frequency Transformation for 2-D Digital Filters

科研費報告書収録論文(課題番号:15560314/研究代表者:川又政征/多次元ディジタルフィルタの最適設計とその画像・映像処理への応用

Characterization of the 4-canonical birationality of algebraic threefolds

In this article we present a 3-dimensional analogue of a well-known theorem of E. Bombieri (in 1973) which characterizes the bi-canonical birationality of surfaces of general type. Let $X$ be a projective minimal 3-fold of general type with $\mathbb{Q}$-factorial terminal singularities and the geometric genus $p_g(X)\ge 5$. We show that the 4-canonical map $\phi_4$ is {\it not} birational onto its image if and only if $X$ is birationally fibred by a family $\mathscr{C}$ of irreducible curves of geometric genus 2 with $K_X\cdot C_0=1$ where $C_0$ is a general irreducible member in $\mathscr{C}$.Comment: 25 pages, to appear in Mathematische Zeitschrif

Anti-Pluricanonical Systems On Q-Fano Threefolds

We investigate birationality of the anti-pluricanonical map $\phi_{-m}$, the rational map defined by the anti-pluricanonical system $|-mK|$, on $\mathbb{Q}$-Fano threefolds.Comment: 18 page

Quantum symmetries and exceptional collections

We study the interplay between discrete quantum symmetries at certain points in the moduli space of Calabi-Yau compactifications, and the associated identities that the geometric realization of D-brane monodromies must satisfy. We show that in a wide class of examples, both local and compact, the monodromy identities in question always follow from a single mathematical statement. One of the simplest examples is the Z_5 symmetry at the Gepner point of the quintic, and the associated D-brane monodromy identity

Three embeddings of the Klein simple group into the Cremona group of rank three

We study the action of the Klein simple group G consisting of 168 elements on two rational threefolds: the three-dimensional projective space and a smooth Fano threefold X of anticanonical degree 22 and index 1. We show that the Cremona group of rank three has at least three non-conjugate subgroups isomorphic to G. As a by-product, we prove that X admits a Kahler-Einstein metric, and we construct a smooth polarized K3 surface of degree 22 with an action of the group G.Comment: 43 page

A high fibered power of a family of varieties of general type dominates a variety of general type

We prove the following theorem: Fibered Power Theorem: Let X\rar B be a smooth family of positive dimensional varieties of general type, with $B$ irreducible. Then there exists an integer $n>0$, a positive dimensional variety of general type $W_n$, and a dominant rational map X^n_B \das W_n.Comment: Latex2e (in latex 2.09 compatibility mode). To get a fun-free version change the `FUN' variable to `n' on the second line (option dedicated to my friend Yuri Tschinkel). Postscript file with color illustration available on http://math.bu.edu/INDIVIDUAL/abrmovic/fibered.p

Interaction of Two Adjacent Structures Coupled by Inerter-based System considering Soil Conditions

The inerter-based systems have proven to be effective for vibration control of adjacent structures. The interaction through the soil medium between adjacent structures in urban areas is generally accepted. However, existing studies concerning the inerter-based adjacent structures are primarily based on the assumption of a fixed base, without considering the inevitable interaction. To address this issue, this study incorporated the soil effects into the theoretical analysis of adjacent structures interconnected by an inerter system, and correspondingly develops an optimal design framework for such system. Employing a classic discrete model for structures and soil, the interaction behavior between inerter-based adjacent structures and soil was extensively studied in a comparative analysis. Based on the revealed interaction phenomena, the need for considering the soil condition in the design of an inerter system for adjacent structures was addressed, and a performance-demand-based optimal design framework was developed. The results indicated that for inerter-based adjacent structures spaced closely, the coupled interaction effect of soil and structure requires careful consideration, especially in soft soil conditions. Owing to the soil effects, the inerter system exhibited a weakened effectiveness for displacement reduction. A larger inner deformation of the inerter system is required to meet the demand for energy dissipation. With consideration of the soil condition, the proposed design method can satisfy the pre-specified target displacement demands for adjacent structures, simultaneously optimizing the control cost as an economical solution