口語英語における連結詞脱落に課せられた制約

口語英語において、文中に生起する定形の連結詞は脱落する傾向にある。この現象は、通常、簡潔さを求める情報伝達上の要請に起因すると考えられている。本論文は、コミュニケーション上の簡潔性が損なわれるような効果を持つ、連結詞脱落に課せられた形式的な制約が存在していることを示す。より具体的に述べると、本論文の主な目的は、文中に生起する定形の連結詞の分布が、口語英語において、少なくとも２種類の制約（すなわち、主語に関する制約と述部に関する制約）により規制されていることを論証することである。さらに、これらの制約をより一般的な原理から導出する可能性が論じられる。In spoken English, finite copulas at a sentence-medial position tend to be dropped. This phenomenon is usually considered to be due to communicative pressure for brevity. This article shows that there are formal constraints on the copula drop to the effect that communicative succinctness is undermined. More concretely, the main purpose of this article is to argue that the distribution of sentence-medial finite copulas in spoken English is regulated by at least two types of syntactic constraint, one being concerned with the subject and the other concerned with the predicate. Further possibilities are discussed to derive these constraints from more general principles.東京海洋大学学術研究院海事システム工学部門Department of Maritime Systems Engineering, Tokyo University of Marine Science and Technology (TUMSAT

The maximum forcing number of polyomino

The forcing number of a perfect matching $M$ of a graph $G$ is the cardinality of the smallest subset of $M$ that is contained in no other perfect matchings of $G$. For a planar embedding of a 2-connected bipartite planar graph $G$ which has a perfect matching, the concept of Clar number of hexagonal system had been extended by Abeledo and Atkinson as follows: a spanning subgraph $C$ of is called a Clar cover of $G$ if each of its components is either an even face or an edge, the maximum number of even faces in Clar covers of $G$ is called Clar number of $G$, and the Clar cover with the maximum number of even faces is called the maximum Clar cover. It was proved that if $G$ is a hexagonal system with a perfect matching $M$ and $K'$ is a set of hexagons in a maximum Clar cover of $G$, then $G-K'$ has a unique 1-factor. Using this result, Xu {\it et. at.} proved that the maximum forcing number of the elementary hexagonal system are equal to their Clar numbers, and then the maximum forcing number of the elementary hexagonal system can be computed in polynomial time. In this paper, we show that an elementary polyomino has a unique perfect matching when removing the set of tetragons from its maximum Clar cover. Thus the maximum forcing number of elementary polyomino equals to its Clar number and can be computed in polynomial time. Also, we have extended our result to the non-elementary polyomino and hexagonal system

Distinct trivial phases protected by a point-group symmetry in quantum spin chains

The ground state of the $S=1$ antiferromagnetic Heisenberg chain belongs to the Haldane phase -- a well known example of symmetry-protected topological phase. A staggered field applied to the $S=1$ antiferromagnetic chain breaks all the symmetries that protect the Haldane phase as a topological phase, reducing it to a trivial phase. That is, the Haldane phase is then connected adiabatically to an antiferromagnetic product state. Nevertheless, as long as the symmetry under site-centered inversion combined with a spin rotation is preserved, the phase is still distinct from another trivial phase. We demonstrate the existence of such distinct symmetry-protected trivial phases using a field-theoretical approach and numerical calculations. Furthermore, a general proof and a non-local order parameter are given in terms of an matrix-product state formulation.Comment: 5 pages, 1 figure, with 3 pages supplemental materia