This paper focuses on the 10-year period from 2000 to 2010, when foreign architects are said to have begun to become more active, and collects data mainly from literature surveys and on-site investigations related to that period. Based on this data, 1) it compiles a list of architectural works designed by foreign architects in China from 2000 to the present, and grasps an overall picture of the architectural activities of foreign architects. 2) It discusses the characteristics of the architectural activities of foreign architects by examining the designs of museums, theaters, exhibition facilities, etc., which are said to have a relatively large number of works by foreign architects.
This paper develops a companion paper intended to be read in conjunction with it, the terms used in this paper being defined as in that paper [1]. Herein, I investigate the role of the separation (SoP) and progression (PoP) of the Primary Polyhedra (PP) in the all-space-filling periodic arrays of polyhedra (the honeycombs), and their analogous morphology to the separation (SoF) and progression of faces (PoF) in the polyhedra (PP to PP within their class, and generically across classes). In previous research, I classify the honeycombs into three classes by symmetry. Here, I address Class III, and find 10 distinct forms (16 allowing reflections) in 3 clusters (Primary, Secondary, Tertiary) that are pervaded by the SoP and the PoP of two PPs of Class II of Polyhedra that are √3 compatible (in 4 cases being self-compatible), and are organized on that basis, where each honeycomb consists of two arrays of primary forms, one of which separates from contracted (〖PP〗_1 contiguous) to expanded (〖PP〗_1 separated), while the other progresses (morphs 〖PP〗_2→〖PP〗_3) while remaining contracted or expanded, where the overall honeycomb can be contracted (both 〖PP〗_1 and 〖PP〗_2), hybrid (〖PP〗_1/〖PP〗_2 contracted and 〖PP〗_2/〖PP〗_1 expanded), or fully expanded (both 〖PP〗_1 and 〖PP〗_2). Subsequent papers will address Class II of 4 distinct honeycombs, which may also be organized in somewhat similar manner, and Class I of one distinct honeycomb in contracted form, to clarify the morphology of the honeycombs.
Natural fiber-based mulching sheets are biodegradable and pose no risk of microplastic pollution. While single-fiber mulching sheets have been developed in previous studies, this research proposed hybrid mulching sheets using tomato stem residues and rice stalks. The results confirmed the feasibility of combining natural fibers from different genera and families for mulching sheet production. The hybrid mulching sheets exhibited densities ranging from 0.684 g/cm3 to 0.792 g/cm3. The tensile rupture stress of the hybrid mulching sheets ranged from 9.78 MPa to 14.87 MPa. The light-shielding ratio of the mulching sheets was over 99.9%. The mulching sheets made from tomato stem residues showed particularly high tensile rupture stress. These results highlight a sustainable approach to utilizing diverse agricultural residues, providing potential alternatives to conventional plastic mulching films.
The cubic schema—considered as a 3-frequency polar zonahedron (PZ_3)—based on the separation of faces (SoF) to account for the order of the regular and semi-regular polyhedra and tessellations that I have previously presented, unveils within each symmetry class a three-fold symmetry by gender of the Primary Polytopes (PPs). This 3-fold symmetry appears remarkably pervasive, rather than an artifact of the schema, and to logically precede the bilaterality of the developed schema. Analysis of the topological relationship of proximal, like principial faces allows matrices to be developed of their relationship according to the SoF, for separation from contiguous (adjoining; d=0) to separated (adjacent; d=1), for the three gendered cases of negative (−ve), neutral (ntrl), and positive (+ve) faces. These three cases can be considered simultaneously, while horizontal rotation of the 2.5D PZ_3 schema about the primary Verticial Polytope—Great Rhomb (VP−GR) vertical axis at 2π/3 intervals can provide convenient snapshots of the corresponding pairs of the separating facial PTs (d=0 to d=1) by gender. In this paper, I reformulate my previous α|β facial convention to α|ω, to newly define α and ω as the +ve and −ve faces, respectively, of the SR (Class II: SRCO), and for the ntrl faces, the edges of the PL^- and PL^+ (Class II: CB and OH), respectively. Together with the (Vesica Pisces) rhombic schema of the progression of faces (RSoF), and the remarkable and highly regular SoF phenomenon, this PZ_3 schema, together with its rotation, provides an adequate, readily accessible modelling of the morphology of the PPs of the 3D polyhedra and 2D tessellations by class; it demonstrates the importance of the inherent three-fold symmetry of that order, in which the interplay of three tripartite genders, while constrained by the bilateral complementarities of two polar genders and one neutral, appears fundamental to objectively describing the generic structural morphology in the evolution of form of the symmetry classes of the regular and semi-regular polytopes. Finally, I consider the limitations of that underlying 3-fold order, and question whether 3-fold order might be subsumed as a 2-step differentiation of 2-fold order, to account for the form–counterform complementarity that develops between the ntrl and the other 2 genders, within the ntrl, and between the −ve and +ve genders, with respect to the PPs and their faces. The imageability of the combination of the RSoF and SoF PZ_3 schema strongly recommends it to researchers and designers.
By using an asymptotic approach method, it has been shown that the Collatz Conjecture is true with a ratio 98.22% in all positive integers [6]. In this paper, we expand the range of numerical experiment and show that the Collatz Conjecture is true with a ratio 99.8216% in all positive integers.
