Stereometry of compressed conoids and physical adequacy of q8 element bases

The paper considers new models of bases of serendipity finite elements (FE) Q8. The standard element Q8 has been used in the finite element method (FEM) for more than 50 years despite the physical inadequacy of the spectrum of equivalent nodal loads.In recent years, the library of serendipity finite elements has been significantly replen-ished with non-standard (alternative) models. The reasons for the inadequacy of the spectrum were identified and "recipes" were proposed to eliminate this shortcoming of standard serendipity models. New approaches to modeling bases with the help of hierarchical forms force to abandon conoids - linear surfaces that are associated with intermediate nodes of standard elements. According to the authors, these Catalan surfaces (1843) are insufficiently studied and deserve the attention of modern researchers. Therefore, research is being conducted today, and it is not necessary to give up conoids. The paper shows how by compressing the surface of the conoid it is possible to obtain a mathematically sound and physically adequate spectrum of nodal loads. It is interesting that such capabilities are embedded in trigonometric functions, the popularity of which in the FEM is growing steadily.The purpose of the research is to constructively prove the existence of mathematically substantiated and (most importantly) physically adequate models of serendipity elements Q8 with the help of trigonometric bases.Trigonometric models of the finite element Q8 once again confirmed that serendipity elements are an inexhaustible source of important and interesting information. It should be noted that today it is not necessary to give up conoids for the sake of physical adequacy of the model. Conoids are also of "historical" importance to FEM. The first bases of serendipity FEs were constructed from conoids (1968).Taylor's elegant method (1972) is also based on conoids. New results show that trigo-nometric bases are able to preserve conoids and ensure the physical adequacy of the models.

Identification of Preferences in Forced-Choice Conjoint Experiments: Reassessing the Quantity of Interest

Forced-choice conjoint experiments have become a standard element of the experimental toolbox in political science and sociology. Yet the literature has largely overlooked the fact that conjoint experiments are used for two distinct purposes: to uncover respondents' multidimensional preferences, and to estimate the causal effects of some attributes on a profile's selection probability in a multidimensional choice setting. This paper makes the argument that this distinction is both analytically and practically relevant, because the quantity of interest is contingent on the purpose of the study. The vast majority of social scientists relying on conjoint analyses, including most scholars interested in studying preferences, have adopted the average marginal component effect (AMCE) as their main quantity of interest. The paper shows that the AMCE is neither conceptually nor practically suited to explore respondents' preferences. Not only is it essentially a causal quantity conceptually at odds with the goal of describing patterns of preferences, but it also does generally not identify preferences, mixing them with compositional effects unrelated to preferences. This paper proposes a novel estimand—the average component preference (ACP)—designed to explore patterns of preferences, and it presents a method for estimating it.

A Protestant Purgatory? Visions of an Intermediate State in Eighteenth-century Scotland

The protestant afterlife is generally presented in binary terms, with departed souls going directly to either heaven or hell. However, the possible existence of an intermediate state for the dead was discussed by protestant theologians from the reformation onwards. This article traces the evolution of these debates in Scotland, with particular focus on the eighteenth century. The bishops Archibald Campbell, Thomas Rattray and George Innes produced tracts in support of the intermediate state. By the end of the century it had become a standard element of doctrine among the episcopalians, reflecting the formation of a more distinctive theological and liturgical identity, based on the teachings of the early church fathers. Presbyterians generally dismissed the idea as a papish conceit, but there were exceptions. Most notably, in the 1720s the minister William Ogilvie described a series of meetings with the ghost of Thomas Maxwell, Laird of Cool. His account framed the intermediate state as a sympathetic alternative to calvinist predestination, and spread to a wide audience when it was printed as a chapbook. As the episcopalian church declined and the Church of Scotland fragmented, there was greater scope for individuals to formulate their own theologies, potentially challenging traditional notions of what it meant to be a protestant.

EARLY REPRESENTATIONS OF FILIAL PIETY IN DYNASTIC HISTORIOGRAPHY: TEXTUAL HISTORY AND CONTENT OF HOU HAN SHU CHAPTER 39

Tales of filial piety became a standard element of the annals-biography style of historiography early on. Starting from the Song shu 宋書, almost every dynastic history contains a chapter that is devoted to filial men. An early—but often neglected—precursor is Chapter 39 of Fan Ye's 范曄 (398–446) Hou Han shu 後漢書. Inspired by his predecessor Hua Qiao 華嶠 (?–293), Fan inserted a chapter on filial men. The chapter was therefore compiled in times when the recommendation system of the Han and especially the recommendation as “filial and incorruptible” (xiaolian 孝廉) had lost influence. This paper tries to shed some light on its origins, form, and content, and attempts to distinguish the most common motives that were used to describe filial (xiao 孝) behavior in this early stage of its historiographical representation.