The article presents a survey of the so-called noun-verb transitions – which are traditionally labeled as huóyòng or “live usage” – in the Shījīng, and touches upon the more general issue of word-class flexibility in old varieties of Chinese. It is based on a theoretical platform elaborated in my previous study, which itself drew on the corpus of Classical Chinese prose. An application of the theory on the Shījīng thus constitutes an extension of this material by reference to data from Pre-Classical poetry, which enables us to observe both similarities and possible differences between the two periods and styles of the language. Instances of well-established patterns are summarized in a list and supplemented by a brief commentary; much space is, on the other hand, dedicated to less predictable derivations, which deserve closer attention and call for a more detailed investigation. Special attention is paid also to the role of metaphor and metonymy in the respective processes. The analysis reveals the complexity and fine-grained stratification of the phenomenon at issue, tests and proves the usefulness of the system of interpretative instruments proposed earlier, and invites further exploration in relation to the role and distribution of noun-verb huóyòng in this canonical book.
For integers $m > r \geq0$, Brietzke (2008) defined the $(m,r)$-central coefficients of an infinite lower triangular matrix $G=(d, h)=(d_{n,k})_{n,k \in\mathbb{N}}$ as $ d_{mn+r,(m-1)n+r}$, with $n=0,1,2,\cdots$, and the $(m,r)$-central coefficient triangle of $G$ as $G^{(m,r)} = (d_{mn+r,(m-1)n+k+r})_{n,k \in\mathbb{N}}. $ It is known that the $(m,r)$-central coefficient triangles of any Riordan array are also Riordan arrays. In this paper, for a Riordan array $G=(d,h)$ with $h(0)=0$ and $d(0), h'(0)\not= 0$, we obtain the generating function of its $(m,r)$-central coefficients and give an explicit representation for the $(m,r)$-central Riordan array $G^{(m,r)}$ in terms of the Riordan array $G$. Meanwhile, the algebraic structures of the $(m,r)$-central Riordan arrays are also investigated, such as their decompositions, their inverses, and their recessive expressions in terms of $m$ and $r$. As applications, we determine the $(m,r)$-central Riordan arrays of the Pascal matrix and other Riordan arrays, from which numerous identities are constructed by a uniform approach., Sheng-Liang Yang, Yan-Xue Xu, Tian-Xiao He., and Obsahuje bibliografii
It is known that a ring $R$ is left Noetherian if and only if every left $R$-module has an injective (pre)cover. We show that $(1)$ if $R$ is a right $n$-coherent ring, then every right $R$-module has an $(n,d)$-injective (pre)cover; $(2)$ if $R$ is a ring such that every $(n,0)$-injective right $R$-module is $n$-pure extending, and if every right $R$-module has an $(n,0)$-injective cover, then $R$ is right $n$-coherent. As applications of these results, we give some characterizations of $(n,d)$-rings, von Neumann regular rings and semisimple rings.
In the present paper we are concerned with convergence in $\mu $-density and $\mu $-statistical convergence of sequences of functions defined on a subset $D$ of real numbers, where $\mu $ is a finitely additive measure. Particularly, we introduce the concepts of $\mu $-statistical uniform convergence and $\mu $-statistical pointwise convergence, and observe that $\mu $-statistical uniform convergence inherits the basic properties of uniform convergence.
Let $R$ be a ring and $M$ a right $R$-module. $M$ is called $ \oplus $-cofinitely supplemented if every submodule $N$ of $M$ with $\frac{M}{N}$ finitely generated has a supplement that is a direct summand of $M$. In this paper various properties of the $\oplus $-cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of $\oplus $-cofinitely supplemented modules is $\oplus $-cofinitely supplemented. (2) A ring $R$ is semiperfect if and only if every free $R$-module is $\oplus $-cofinitely supplemented. In addition, if $M$ has the summand sum property, then $M$ is $\oplus $-cofinitely supplemented iff every maximal submodule has a supplement that is a direct summand of $M$.
A sign pattern $A$ is a $\pm $ sign pattern if $A$ has no zero entries. $A$ allows orthogonality if there exists a real orthogonal matrix $B$ whose sign pattern equals $A$. Some sufficient conditions are given for a sign pattern matrix to allow orthogonality, and a complete characterization is given for $\pm $ sign patterns with $n-1 \le N_-(A) \le n+1$ to allow orthogonality.
We prove a separable reduction theorem for $\sigma $-porosity of Suslin sets. In particular, if $A$ is a Suslin subset in a Banach space $X$, then each separable subspace of $X$ can be enlarged to a separable subspace $V$ such that $A$ is $\sigma $-porous in $X$ if and only if $A\cap V$ is $\sigma $-porous in $V$. Such a result is proved for several types of $\sigma $-porosity. The proof is done using the method of elementary submodels, hence the results can be combined with other separable reduction theorems. As an application we extend a theorem of L. Zajíček on differentiability of Lipschitz functions on separable Asplund spaces to the nonseparable setting.
In [1], Jakubík showed that the class of $\sigma $-interpolation lattice-ordered groups forms a radical class, but left open the question of whether the class forms a torsion class. In this paper, we show that this class does indeed form a torsion class.