Iteration

At first thought, iteration seems banal. It is about repeating the existing; nothing is changing.  But this special issue shows that, in an era obsessed with the new, it is often the repetition of the old that creates social change.  Iteration fosters persuasion.  It affords opportunities for critical and creative engagement with meaning, values and knowledge.  It invites collaboration, though its apparent simplicity often belies a tremendous amount of individual and collective labour involved in the practices of iteration.  Through its repetition of the existing, however, iteration also can be a mechanism for reproducing the status quo.  Its pervasiveness and banality naturalise power, and its mimetic qualities shrink spaces for critical distance and care.

The editors of this special issue have brought together a delightful and fascinating diversity of articles focused on iteration in cultural production in the digital age.  We hop across geographies to examine lockdown diaries, artists’ books, socialist memes, fake news, the design of social media platforms and artificial intelligence, activism, film, social media forum moderation, news website reader comments and more.  Iterating through the collection, across its many disciplines, is a commitment to theorising through empirical evidence, to explaining with critique, and to providing pathways to praxis.  These characteristics of this special issue, and the many concepts and arguments it puts forward, make this collection of work exceptionally rich material for seeing iteration and how it shapes the world we live in today, as well as the world we want it to be.

In this preface, I take a media sociology approach to show how iteration can be usefully understood as collaborative communication for change.  I see this understanding of iteration, whose ascendancy is related to the ascendancy of computer science, as baked into the form of communication technologies – and thus as shaping the kinds of iteration that are possible when we use these technologies.  This understanding also prompts us to focus on the connection between iteration and social change.  To explore how this works, I analytically slow down the practice of iteration to show that it is a communication practice of transmission.  That transmission practice is itself constituted of cognate communication practices – the reception, evaluation and production of knowledge – in which visibility and persuasion are key.  In the latter parts of the preface, I illustrate this through the example of witnessing as iteration, as the high-stakes nature of witnessing make it a canary in the coalmine, more generally, for mediated communication in the digital age.  I show how breaking the witnessing practice down into its various parts allows us to see how power enters and inflects who and what are iterated, when – and who and what are not.  Thinking critically with iteration and against unequal power relations, the praxis this preface suggests is one – much in line with the rest of this special issue – of explaining how iteration might move the grassroots towards their goals.

In this paper, we discuss some applications of exciting fields like Mathematics, Statistics, Medical, Biological Sciences, Engineering, Economics etc. We show their real-life applications both theoretically and analytically considering some phenomena of the nature. We mainly focused on some applications of dynamical system in real life cases known as chaos, iteration, fractal geometry, Mandelbrot and Julia sets. We derive some mathematical formula concerning dynamical systems. Necessary programs are considered for all cases. We use Mathematica and MATLAB to perform programming.

Multi-stage counter current solid-liquid extraction usually results in a high concentration of soluble components (= solutes) in the extract (so in a high recovery % R), and in a low concentration of solutes in the discarded spent solids (so in a low loss % F).
This Excel file estimates the required number of counter current extraction stages N and the related mass of solvent V, the % solute recovery R and the solute mass% yTOTAL in the extract, the % solute loss F and the solute mass% xN  in the discarded spent solids.
In a counter current extraction installation, the solid product and the solvent move in opposite directions. The "fresh" solid product starts in extraction stage 1, moves to extraction stage 2, then to stage 3, .... and so to the last stage N. In each consecutive stage, the solid product will be a bit more depleted by the solvent, which moves in the opposite direction. After passing through the last stage N, the (almost) completely depleted solid will be discarded. The "fresh" solvent, however, enters in that last extraction stage (N), moves to extraction stage N-1, then to stage N-2, ... and so to stage 1. In each consecutive counter current stage, the solutes concentration in the solvent increases. After passing through stage 1, the then heavily loaded solvent is removed from the installation as the “extract”.
If a solid product considerably swells or shrinks during extraction, process design requires tedious stage-to-stage mass balances, or graphical calculations. This Excel document, however, uses simplified Kremser equations: it assumes a constant mass L of the solid product throughout the installation, and also a constant mass V of the solution. Thus this document should be applied only for solid products which do NOT swell, NOR shrink during extraction; or for solid products which have been pre-soaked (= swollen) PRIOR to extraction.
Some 5 worked examples explain how to use the Excel worksheets. Each example has also been solved by manually applying the Kremser graphs and the Kremser equations.

This Excel spreadsheet calculates the required sterilization time of canned solid foods, by applying Pham's (1987; 1990) formula method. The spreadsheet can also find the heat process value F of such foods.
Pham's original equations have been extended, to enable calculation of the microbial spoilage rate and of the nutrient retention. All equations used are listed in the calculation section of this spreadsheet.
Findings by Pham are compared and contrasted to those of C.R. Stumbo's heat processing model (1973): the calculated sterilization times Pt, heat process values F, microbial spoilage rates, and nutrient retention were found to be very similar.
Important differences between Pham and Stumbo, however, are: 1) Pham's equations were primarily developed for conduction-heating, solid canned foods; Stumbo's model can also be used for canned convection-heated, liquid products. 2) Pham developed equations for processes in which the heating (fh) and cooling (fc) rates can differ; Stumbo assumes equal heating and cooling rates: fh = fc.
Pham (1987) stated that some of his calculations have to be solved by trial and error. In this spreadsheet such iterations, indicated by pink cells, can easily be solved by Excel's tool Goal Seek. An instruction on how to use Goal Seek has been added.
Six worked examples are included, which may be of help in understanding the use of this spreadsheet. The worked examples are also applied for model validation, and to compare Pham's findings with Stumbo's results.

Cross flow solid-liquid extraction is a relatively simple unit operation, used for leaching, for extraction, for decontamination, or for washing of solid (food) materials.
“Cross flow” means that the solid to be extracted, will be mixed with fresh solvent, drained, mixed with new (= fresh) solvent again, drained, etc. The required number of solid-liquid contacts N (= number of extraction stages), the % R of all solubles present recovered (in the extract), the solubles concentration YTOTAL mass% in the mixture of all extracts, and the loss % F of all solubles initially present, but lost with the discarded spent solid, can be estimated by this Excel file.
The Kremser-Southers-Brown equations and graph are at the basis of all calculations.
Some 5 worked examples explain in detail how to use the Excel file. For reference purposes, each worked example has also been solved by using both the Kremser graph and the Kremser equations.
Often solid foods such as tea leaves, will swell during extraction. In such cases, the input values in both the Excel file and in the Kremser equations/graph, should be based on the mass and composition of the swollen solid product. This is outlined in Examples 4 and 5. Worked example 3, adapted from Earle (2004), has been used to validate the calculation results of this document: the Kremser equations in this Excel file produced almost identical results as were reported by Earle.

This paper explores the tacit practice of walking as a craft that already exists in the design process of the architect. Made explicit, and with the help of mapping, walking may offer a powerful tool for the architect to participate more actively in the project of social change. The benefits of walking and mapping are examined and some suggestions are offered on how to bring them together. Walking the line becomes drawing the line in an interactive and iterative cycle. Recordings of a site by a designer entail a range of activity types, from personal observations, interviews or casual conversations with project stake-holders, to interpreting existing maps and research data. The recordings that result between site, body and architect's studio aim to contribute to an engaged practice; a practice that remains true to the multi-modal nature of architecture that brings together the various crafts that go into making buildings. This practice of recording responds to the various and often conflicting social and material, visible and invisible, realities of a given context. The designer's approach to recording and understanding information at the start of a project, and the way this process is crafted, will frame and determine the direction, and level of social responsiveness, of the eventual design. The paper sets out walking types and mapping techniques presented as the craft of walking and mapping. This process involves the iterative process of drawing, which entails recording, understanding and projecting as interconnected actions of the designer. It is hoped that if the recording stages of the design process explicitly engage and reveal the lived realities of the site, the design will stand a better chance of resonating with its users in a meaningful way.

— SS is an algorithm for efficient searching of an element from the list. Basically it uses modified binary search algorithm. That modification makes searching much more efficient as compare to simple binary search algorithm. That modification is rather then checking only middle position, SS is checking lower and high position as well. By checking three position simultaneously in the one iteration, the speed of searching an searching is increased than regular binary search algorithm.

This paper is concerned with a compact finite difference method for solving systems of two-dimensional reaction–diffusion equations. This method has the accuracy of fourth-order in both space and time. The existence and uniqueness of the finite difference solution are investigated by the method of upper and lower solutions, without any monotone requirement on the nonlinear term. Three monotone iterative algorithms

Abstract: The article examines Polish translations of the Derridian term différance. Polish philosophical discourse uses the following renditions of différance: róż (ni (c) oś) ć by Bogdan Banasiak, różNICa by Tadeusz Sławek, gra-na-zwłokę-o-różnicę by Stanisław Cichowicz and the most popular: różnia by Joanna Skoczylas. Should a mistake be deliberately committed in Polish, as it was done in the original? Or should it be corrected, and if so–how to explain the correction?

Is it possible to conceive two perfectly identical objects? Is identity even possible without individuality? How would a perfectly symmetrical universe be? The current philosophical debate on identity, and in particular on the necessity of the Leibniz's principle of the identity of indiscernibles, is complex and multi-faceted. Recent works have indicated that the problem becomes increasingly complex if we apply it to mathematical objects. Is it possible to speak of ‘identity’ for numbers? How can we identify numbers?
Drawing on philosophical accounts on identity and individuality in contemporary metaphysics (analytic and continental), this book explores a new path. The author argues that an identity without individuality is possible. By means of a critique of the idea of the identity of indiscernibles, the book formulates the concept of 'manifold identity', through the concept of 'iteration'. Iteration is a specific transgression of the identity of indiscernibles arising from the collision of two forms of identity: qualitative identity and numerical identity. Nonetheless, a pair of perfectly identical objects is still a paradox, a contradiction.
The first thesis of the book is that iteration is a paraconsistent and dialethetical logical structure, which allows for true contradiction. The author applies recent works in non-standard logic and dialetheism (Priest, Routley, Berto) to illustrate how we can make sense of the idea that objects can be perfectly identical but discernible.
The second thesis of the book is that iteration is the basis of enumerability and computability. A 'computable object' is an object constructed on the basis of an iterative logic. It is possible to re-interpret all the primary concepts of computability theory through the logic of iteration.

In this article, I explore the paradoxes of language, cultural difference, and law in Hopi jurisprudence. In it, I analyze the metapragmatic “talk about courtroom talk,” whereby actors frame court discourse in shifting relations to Hopi cultural distinctiveness and sovereignty, exemplifying how language mediates the cultural politics of Hopi law. I thus argue for a reconsideration of the usual binaries of indigenous identity—in which claims to cultural distinctiveness are either libratory or reifying, autochthonous or other determined—suggesting that a sharper picture of cultural politics takes these antinomies together as the ironic dialectics constituting the emergent “edge” of indigenous governance today.

In this paper I will present the use of fractal geometry to design tile motifs. A fractal is a geometric figure that combines the several characteristics among others: its parts have the same form as the whole, fragmented, and formation by iteration. The concept of fractals has been spread over all fields of sciences, technology, and art. This paper aims to provide an algorithm to creating motifs of tile algorithm for create the tile motif consists of base, iteration, coloration and duplication. In order to help the reader better understand the algorithm, I will present some script using Matlab. We describe a mathematically based algorithm that can fill a spatial region with sequence of randomly placed which may be transformed copies of one motif or several motifs. By using this algorithm, I can produce thousand variety of aesthetically pleasing tile motifs, of which we show a number of examples.

In this paper, we discuss some applications of exciting fields like Mathematics, Statistics, Medical, Biological Sciences, Engineering, Economics etc. We show their real life applications both theoretically and analytically considering some phenomena of the nature. We mainly focused on some applications of dynamical system in real life cases known as chaos, iteration, fractal geometry, Mandelbrot and Julia sets .We derive some mathematical formula concerning dynamical systems. Necessary programs are considered for all cases. We use Mathematica and MatLab to perform programming.Dynamical Systems considering some popular.

The starting point of this article is an old question asked by Feferman in his paper on Hancock's conjecture [6] about the strength of . This theory is obtained from the well-known theory ID1 by restricting fixed point induction to formulas that contain fixed point constants only positively. The techniques used to perform the proof-theoretic analysis of also permit to analyze its transfinitely iterated variants . Thus, we eventually know that