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A clause complex consists of clauses, which are connected by component sharing relations and logic-semantic relations. Hence, clause-complex level structural transformations in translation are concerned with the expression adjustment of these two types of relations. In this paper, a formal scheme for tagging structural transformations in English-Chinese translation is designed. The annotation scheme include 3 steps operated on two grammatical levels: parsing an English clause complex into constructs and assembling construct translations on the clause complex level; translating constructs independently on the clause level. The assembling step involves 2 operations: performing operation functions and inserting Chinese words. The corpus annotation shows that it is feasible to divide structural transformations in English-Chinese translation into 2 levels. The corpus, which unfolds formally the operations of clause-complex level structural transformations, would help to improve the end-to-end translation of complicated sentences.

In this paper we show that it is possible to define a topology on the category of formal schemes over a ring of p-adic integers such that the left adjoint of the Greenberg Transform is a site cocontinuous functor when we equip the category of schemes over the residue field with the etale topology. We show furthermore that this topology allows us to give an isomorphism between the corresponding fundamental groups, and use this isomorphism to show that it is possible to geometrize the quasicharacters of a p-adic torus by a local system on a formal scheme over the ring of p-adic integers.

The Wright–Fisher model considers the effects of sampling for the distribution of alleles across discrete generations. Although the model is usually formulated for diploid populations, and some of the interesting effects occurring in generalizations depend on that diploidy, the formal scheme emerges already for haploid populations. In the basic version, with which we start here, there is a single genetic locus that can be occupied by different alleles, that is, alternative variants of a gene. In the haploid case, it is occupied by a single allele, whereas in the diploid case, there are two alleles at the locus. Biologically, diploidy expresses the fact that one allele is inherited from the mother and the other from the father. However, the distinction between female and male individuals is irrelevant for the basic model.

This chapter contains Raynaud’s characterization of rigid spaces in terms of formal scheme models. As an important technical tool admissible formal blowing-up is needed, which is explained in detail.

We introduce relative rigid spaces and, as an example, construct Raynaud’s universal Tate curve. Then, after a brief look at the Zariski–Riemann space, some advanced results on formal models of rigid spaces are reviewed.

Similarly as in arithmetic algebraic geometry, there is the notion of formal scheme models for rigid spaces. The theory of formal schemes is developed from scratch and basic properties are established.