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sciscanpub.com

Since 1990s, there has been a change in focus in western language and gender scholarship from gender variations to discourses as sites of gender construction. Theoretically, this turn was inspired and supported by social constructionist and post-structuralist views on gender; methodologically, it was manifested largely by the transition from a preference for quantitative correlation analyses to that for localized qualitative analyses. Most discourse and gender studies could be seen as driven by two kinds of concerns, one on the production and circulation of gender norms, and the other on gender performance. The former is mainly taken up by critical discourse analysts, while the latter by researchers of different backgrounds, including social linguistics, CA, DP, CDA and FPDA. A comprehensive review of these studies can help scholars at home develop discourse and gender studies in Chinese contexts.

ijmttjournal.org

This paper presents new mathematical proofs on the correctness of the Collatz conjecture based on new unified formulas re-expressing this conjecture in a scalable algebraic form. We are proposing new precise formulas that enable expressing all natural numbers in the Collatz conjecture according to a unified methodology that allows scaling calculations on infinite numbers, and then we use these unified formulas to prove that all natural numbers are converging to the number one when we perform Collatz operations on them. In addition, we are presenting computational codes based on these algebraic formulas to provide computational results that guide the development of proofs. As a result, this paper is presenting twenty seven new theorems along detailed proofs, where the first seven theorems are proposing new unified formulas to re-express the values of numbers according to unified algebraic forms, whereas the other theorems are using these new formulas to demonstrate that all natural numbers are converging to the number “1” when we forward Collatz operations on them; whereas demonstrating that there is no divergency over these operations. We also use these formulas to demonstrate that all natural numbers create loops in infinity that may cause Collatz calculations to circulate in a ring of numbers. Furthermore, we demonstrate that the only ring of natural numbers that creates a loop for the Collatz conjecture is where we go from “1” to “4”, then calculations converge back to the number one. All theorems presented in this paper are developed according to an engineering methodology based on structuring unified formulas to re-express Collatz calculations along step-by-step proofs, which allow us to develop a breakthrough demonstrating the correctness of the Collatz conjecture, while providing new insights into the characteristics of prime numbers and their distribution.

ajops.com

An open access, peer-reviewed journal publishing original research on all aspects of plastic and reconstructive surgery.

ijmsc.org

IJMSC Insights offers a closer look at the latest research and the people behind it from the community of the International Journal of Multiple Sclerosis Care (IJMSC) and the Consortium of Multiple Sclerosis Centers (CMSC).

nuovarivistastorica.it

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mingyanjiaju.org

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tannlegetidende.no

Den norske tannlegeforenings Tidende Utgaver 2016