Harada (1971) argued some forty five years ago that the Japanese phenomenon called ``Nominative/Genitive Conversion'' (NGC) was undergoing a syntactic change, which was detected as idiolectal variations. Synchronically, Miyagawa (2011) argues that the NGC is not a free alternation but that more stative predicates are more likely to accept a Genitive subject. However, no one has ever proposed an argument that bridges the synchronic preference for ``stativity'' of the NGC and its diachronic syntactic change, which is characterized as ``stativization.'' In this article, we will show that the diachronic syntactic change has been in progress at least for the last 100 years. It will be shown that the semantic ``stativization'' is an epiphenomenon of the syntactic microparametric change which we refer to as ``clause shrinking,'' or a change in the syntactic size of the Genitive Subject Clause (GSC) from CP to TP to vP to VP/AP. Moreover, we will explain how such a drastic language change have actually influenced language acquisition for children who were born in different time periods, by integrating Kayne's (2000) microparametric syntax, Snyder's (2017) theory of competition between incompatible constructions, Lightfoot and Westergard's (2009) micro-cue analysis of language acquisition, Manzini and Wexler's (1987) Subset Principle, and Bošković (1997) Minimal Structure Principle.

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A finite subset X of the n-dimensional simplex is called a simplex t-design if the integral of any polynomial of degree at most t over the simplex is equal to the average value of the polynomial over the set X. Although these designs on a simplex are tightly connected to several other topics in mathematics, such as spherical designs, an explicit construction of such designs is not well-studied. In this paper, we will explicitly construct such designs using a union of sets consisting of elements whose coordinates are a cyclic permutation of a particular point. By choosing such a set, the conditions of a set to be a simplex t-design can be reduced to a system of t equations. Solving these system of equations, we managed to explicitly construct simplex 2-designs on a simplex of an arbitrary dimension.

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The discrete-time quantum walk (QW) is determined by a unitary matrix whose components are complex numbers. Konno (2015) extended the QW to the quaternionic quantum walk (QQW) whose components are quaternions and presented some properties of the QQW. Furthermore, Konno (2015) presented the question of whether or not the dynamics of a QQW is exactly the same as that of the corresponding QW. We give an answer to the problem by calculating the probability distribution and the weak limit density function of some classes of the QQW.

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