Mathematical formalism on "Arabic Language DNA"

In this work we formalize new findings on formal Arabic language by constructing equivalence classes on letters depending on inversion principle. This equivalent relation furnishes a conjecture that Arabic language has a DNA-like inversion controller, called language DNA (LDNA) (Al-Rawajfeh, 2020, Ref [2]) and it can be even considered as a part of the full language DNA that can be discovered by more investigations similar to this work.

Rebels in Biblical and Chinese Texts: A Comparative Study on the Interplay of Myth and History

This study offers a new approach for studying biblical myth in two directions: first, by expanding the scope of investigation beyond the clearly mythological elements to other areas of biblical literature, and second, by drawing comparisons to classical Chinese literature. This article thus reconsiders the relationship between myth and history in both biblical and Chinese literature, while seeking to broaden the endeavor of the comparative method in biblical studies. Two examples are offered: (1) the story of Moses’s call narrative and his relationship with Aaron in Exodus in light of the story of Xiang Liang and Xiang Ji in the Shiji; (2) the story of Saul and David in 1 Samuel compared with the story of Dong Zhuo and Lü Bu in the Romance of the Three Kingdoms. Both comparisons demonstrate the operation of Claude Lévi-Strauss’s inversion principle. Conclusions regarding each of these literatures are presented separately, followed by cross-cultural insights and shared aspects in the study of myth, historiography, and religion.

Potential Vorticity and Balanced and Unbalanced Moisture

Atmospheric flows are often decomposed into balanced (low frequency) and unbalanced (high frequency) components. For a dry atmosphere, it is known that a single mode, the potential vorticity (PV), is enough to describe the balanced flow and determine its evolution. For a moist atmosphere with phase changes, on the other hand, balanced–unbalanced decompositions involve additional complexity. In this paper, we illustrate that additional balanced modes, beyond PV, arise from the moisture. To support and motivate the discussion, we consider balanced–unbalanced decompositions arising from a simplified Boussinesq numerical simulation and a hemispheric-sized channel simulation using the Weather Research and Forecasting (WRF) Model. One important role of the balanced moist modes is in the inversion principle that is used to recover the moist balanced flow: rather than traditional PV inversion that involves only the PV variable, it is PV-and-M inversion that is needed, involving M variables that describe the moist balanced modes. In examples of PV-and-M inversion, we show that one can decompose all significant atmospheric variables, including total water or water vapor, into balanced (vortical mode) and unbalanced (inertio-gravity wave) components. The moist inversion, thus, extends the traditional dry PV inversion to allow for moisture and phase changes. In addition, we illustrate that the moist balanced modes are essentially conserved quantities of the flow, and they act qualitatively as additional PV-like modes of the system that track balanced moisture.

Introduction

This chapter introduces the principles that guide the reading of Hume in this volume. (1) The Cover Principle: Hume is providing a cognitive science, not metaphysics, epistemology, or ethics. (2) The Skeptical Inversion Principle: Hume is a Pyrrhonian skeptic, and takes our practices to have no ground but custom. (3) The Centrality of Custom Principle: custom is the key to Hume’s account of normativity and of our epistemic and moral practices, and the term denotes both individual habit and social convention. (4) The nominalist Pseudo-idea Principle: Hume often takes us not to have the ideas we think we have, but rather to confuse customs for using words with ideas. (5) The Principle of the Uniformity of Method: Hume uses a consistent philosophical method throughout the Treatise.

Digital Approaches in Industrial Design

In the present paper the digital approaches in industrial design have been developed and described, which reveals interdisciplinary connections for solving the problems of universal design, and searches for new forms of industrial products and investigates new types of industrial design of industrial products. The inversion modeling approach in stages resembles the traditional one, however, to create a surface model, the data obtained by scanning a man-made layout or prototype on a three-dimensional scanner are used. Shaping is based on the results of three-dimensional scanning, i.e. the source data is a point field or a polygonal model. Suitable for modeling a body approaching the final stage of production or for restyling the existing body shape. This approach is more laborious than the traditional one, due to the fact that you need to create a layout or have a ready prototype available, spend time on scanning, however, the maximum approximation of body parameters to a real object or layout is achieved. Criteria for choosing the inversion principle of modeling: according to TK, as a source for design data, a plasticine model, the form is not fractal, does not require changes in time and space, but is a complex closed shell.

Antipodes of monoidal decomposition spaces

We introduce a notion of antipode for monoidal (complete) decomposition spaces, inducing a notion of weak antipode for their incidence bialgebras. In the connected case, this recovers the usual notion of antipode in Hopf algebras. In the non-connected case, it expresses an inversion principle of more limited scope, but still sufficient to compute the Möbius function as [Formula: see text], just as in Hopf algebras. At the level of decomposition spaces, the weak antipode takes the form of a formal difference of linear endofunctors [Formula: see text], and it is a refinement of the general Möbius inversion construction of Gálvez–Kock–Tonks, but exploiting the monoidal structure.

PURE LOGIC OF ITERATED FULL GROUND

This article develops the Pure Logic of Iterated Full Ground (plifg), a logic of ground that can deal with claims of the form “ϕ grounds that (ψ grounds θ)”—what we call iterated grounding claims. The core idea is that some truths Γ ground a truth ϕ when there is an explanatory argument (of a certain sort) from premisses Γ to conclusion ϕ. By developing a deductive system that distinguishes between explanatory and nonexplanatory arguments we can give introduction rules for operators for factive and nonfactive full ground, as well as for a propositional “identity” connective. Elimination rules are then found by using a proof-theoretic inversion principle.