Class (philosophy)

About: Class (philosophy) is a research topic. Over the lifetime, 821 publications have been published within this topic receiving 28000 citations.

The Wedge Product and Analytic Geometry

Abstract: To do this, we show that it is possible to introduce simple ^-vectors?those of the form ax a A ak where ax,... , ak are vectors in some Rn?as geometric objects. In calculus or an introductory physics class, one sometimes hears a vector described as an equivalence class of directed line segments. It turns out that one can, in a similar way, define a simple /c-vector as an equivalence class of oriented parallelepipeds. We shall show that this geometric definition leads to the standard properties of exterior algebra. To illustrate the use and convenience of this machinery, we then generalize the triangle law of vector addition and the law of cosines to ft-simplexes and rederive the ft-dimensional versions of the parallelogram law and the Pythagorean theorem.

Radius and Differential Subordination Results for Starlikeness Associated with Limaçon Class

Abstract: In this study we investigate the sharp radius of starlikeness of subclasses of Ma and Minda class for the ratio of analytic functions which are related to limaçon functions. This survey is connected also to the first-order differential subordinations. In this context, we get the condition on β for which certain differential subordinations associated with limaçon functions imply Ma and Minda starlike functions. Simple corollaries are provided for certain examples of our results. Finally, we present several geometries related to our study.

Context dependence and procedural meaning : the semantics of definites

Abstract: This thesis argues that there is a theoretically interesting connection between members of the intuitive category of context-dependent expressions, including "we", "tall", "local", "every man", "the woman", "it", "those donkeys" and so on. A treatment of the linguistic meaning of these expressions will be proposed based on the idea that their use raises issues for the audience about the proper understanding of the utterances in which they occur. The proposal will be developed in terms of a semantics for questions, which draws on the idea that to know the meaning of a question is to know what would count as an answer. It can be summarised along similar lines: to know the meaning of a context-dependent expression is to know what properties or relations (of the appropriate type) it could be used to express. The framework in which this idea will be developed can account for why the expressions that are given this issue-based treatment can also be given dependent, bound readings. The class of definite expressions, including descriptions and pronouns, is analysed in detail. A quantificational approach, where the determiner is existential, is assumed for all forms of definiteness. In all cases, the restrictor is interpreted by an atomic definite concept. The audience's grasp of the properties which definite concepts express is the result of inferential processes which take the linguistic meaning of a definite expression as input. These processes are constrained by pragmatic principles. The analysis of context-dependent expressions is extended to account for dependent interpretations. A treatment of donkey sentences that accounts for their variable quantificational force is shown to follow naturally from the analysis. A pragmatic account of infelicitous uses of definites is provided and shown to compare favourably with that provided by dynamic semantic theories. Also, a novel treatment of plural definites is provided which accounts for their variable quantificational force.

A combination of Residual Distribution and the Active Flux formulations or a new class of schemes that can combine several writings of the same hyperbolic problem: application to the 1D Euler equations.

Abstract: We show how to combine in a natural way (i.e. without any test nor switch) the conservative and non conservative formulations of an hyperbolic system that has a conservative form. This is inspired from two different class of schemes: the Residual Distribution one \cite{MR4090481}, and the Active Flux formulations \cite{AF1, AF3, AF4,AF5,RoeAF}. The solution is globally continuous, and as in the active flux method, described by a combination of point values and average values. Unlike the "classical" active flux methods, the meaning of the pointwise and cella averaged degrees of freedom is different, and hence follow different form of PDEs: it is a conservative version of the cell average, and a possibly non conservative one for the points. This new class of scheme is proved to satisfy a Lax-Wendroff like theorem. We also develop a method to perform non linear stability. We illustrate the behaviour on several benchmarks, some quite challenging.