On coming to power, Napoleon III was determined to create an imperial court which would project a powerful image of affluence and prosperity. One way of achieving this was through ostentatious court costume, with the added aim of stimulating demand for fabrics and trimmings and so helping to regenerate France's failing clothing and textile industries. Thousands of officials were provided with specially designed, elaborately braided uniforms, and the Empress played her part by wearing what she called her 'political outfits'1– voluminous, richly decorated dresses– to encourage luxury and consumption and help revive the clothing industry. Her example caught on as fashionable women vied with one another in the conspicuous consumption of ornate dress, and although Eugénie is said privately to have preferred simpler designs, the sumptuous dress code she imposed for her court receptions ensured a new lease of life for Lyons silk manufacturing. By the end of the Second Empire Paris was established as the fashion centre of the world.

During this period women's fashion changed at an ever-increasing speed. Skirts became fuller throughout the 1850s, supported at first by layers of petticoats made of stiff material such as the mixture of horsehair (crin) and linen (lin), which gave the crinoline its name. Waists were tightly laced to emphasise the skirts' flare, and as dresses grew more voluminous, technology came to the rescue with whalebone or steel skirt-hoops to support their weight.

The fall of Napoléon III's regime was widely regarded as a watershed in French history. ‘A new world is about to begin, another France’, Flaubert repeatedly told friends. The sense that an era had come to an abrupt end was further marked by the disastrous siege of Paris and the bloodshed of the Commune that followed. Those harrowing events inevitably provoked reflections on the period that had gone, and prompted attempts to reappraise the Second Empire.

Over that twenty-year period, much about France had changed almost beyond recognition. As we have seen, its embryonic railway system had developed into a complete network, linking France to its neighbours and bringing immense economic growth. Increasing industrialisation had drawn thousands of workers to cities which swelled to accommodate them, while an expanding Paris underwent its own major transformation under the direction of Haussmann. New industrially-produced fabrics and dyes and cheaper machine-made garments had revolutionised the way people dressed and made fashionable clothes available to a far wider range of the population, with the result that dress fashions themselves changed with ever-increasing speed. Eating habits, too, had undergone change: with famine a thing of the past, a far greater variety of foodstuffs and preparation methods were available, though industrial processing had brought with it new fears of food adulteration. From being the preserve of the few, photography had become available to all, and by creating an unprecedented visual record of people and places, it helped to shape the way the Second Empire would be seen by subsequent generations.

On the evening of 13 October 1892, at Pagani's Restaurant in London's West End, a small group of men gathered to celebrate the Rubáiyát of Omar Khayyám. At this inaugural meeting of the Omar Khayyám Club, and for years to come, the group came together to eat, drink heavily and praise the poet Omar Khayyám and his English translator Edward FitzGerald as ‘twin souls’, separated by time and place but united in the Rubáiyát text. The poem's mystique spread among friends and acquaintances, and eventually led to the formation of another group in Boston in 1900. This exclusive club welcomed a variety of male professionals, including artists, literati, scholars and political elites, who joined together not only in their admiration of the Rubáiyát but ‘on the basis of good fellowship as well as Oriental learning’.

On the surface, the Omar Khayyám Clubs, or O. K. Clubs, as they came to be known, sanctioned an escape from everyday life, a controlled environment where men could indulge in material pleasures, following what they saw as the Rubáiyát's hedonistic philosophy of living for the moment. On a deeper level, the Clubs became ritual spaces in which participants praised their own elite status as well as crafted and maintained a coveted identity through the vehicle of the Rubáiyát. FitzGerald's inauguration of the Rubáiyát in the West, the poem's delayed popular reception and its persistent connection to the East provide insight into the Clubbists' curious allegiance to a book of verse.

The studies brought together in this book are integral parts of a project developed over the past ten years. Many of them were published individually in various forms and forums, but the framework is the product of the accumulated work, and the pieces have been adapted to the comprehensive design. Since the overall “Contested Legacies” project has been a collaborative one, involving four workshops and a large conference, as documented in a number of collaborative publications, I am especially indebted to the many colleagues who made contributions to these events. None of the chapters of the present volume appear in these books. They do, however, variously draw on the following earlier publications: “Antifascism as Ideology: Review and Introduction,” in Habitus, Identität und die exilierten Dispositionen, ed. Anna Wessely, Karoly Kokai and Zoltan Peter, 139–159 (Budapest: Nemzeti Tankönyvkiado, 2008); “Erste Briefe. Zwischen Exil und Rückkehr,” Zeitschrift fürIdeengeschichte (May 2008): 79–107; “Le prime letteri dei refugees; una liquidazione dell'esperienza dell'esilio?” Memoria e Ricerca. Rivista di storia contemporanea 31 (Maggio/agosto 2009): 103–120; “Una ‘primera carta’ de Siegfried Kracauer,” in Siegfried Kracauer: un pensador más allá de las fronteras, ed. Carlos Eduardo J. Machado and Miguel Vedda, 171–178 (Buenos Aires: Gorla, 2010); “Negotiations: Learning from Three Frankfurt Schools,” in Fruits of Exile, ed. Richard Bodek and Simon Lewis (Charleston: University of South Carolina Press, 2009), and in German: “Ein unvollendetes Lehrstück: Meine Verhandlungen mit drei Frankfurter Schulen,” in Soziologie in Frankfurt. Eine Zwischenbilanz, ed. Felicia Herrschaft and Klaus Lichtblau, 257–281 (Berlin: VS Verlag, 2010);

It all started with Walsh functions, proposed by JL Walsh in 1922 (published in 1923). The orthonormal function set he introduced was very much dissimilar to then reigning sine-cosine functions, because it contained piecewise constant bi-valued component functions. Despite this novelty, the Walsh function attracted little attention at the time, much like its forerunner the Haar function (proposed in 1910).

However, amongst all other piecewise constant basis functions (in simple terms, staircase functions), the Walsh function suddenly became important in the mid-1960s because of its similarities, in essence, with the popular sine-cosine functions and its digital technology compatibility. This function set was a pioneer to generating the interest of researchers working in the area of communication engineering.

In the late 1980s and 1990s, orthogonal staircase functions, like the Walsh function and the block pulse function, encouraged many researchers in terms of successful applications befitting the digital age. However, the researchers, as always, kept on with zeal and vigour for better accuracy and faster computation, and this thriving attitude gave rise to many other orthogonal function sets useful for applications in the general area of systems and control. Yet compared to Walsh and block pulse functions, these new sets had to be satisfied with the back seat.

The orthogonal triangular function set is the result of such a quest, and this new function set has been applied to a few areas of control theory in this book.

Orthogonal properties [1] of familiar sine–cosine functions have been known for over two centuries; but the use of such functions to solve complex analytical problems was initiated by the work of the famous mathematician Baron Jean-Baptiste-Joseph Fourier [2]. Fourier introduced the idea that an arbitrary function, even the one defined by different equations in adjacent segments of its range, could nevertheless be represented by a single analytic expression. Although this idea encountered resistance at the time, it proved to be central to many later developments in mathematics, science, and engineering.

In many areas of electrical engineering the basis for any analysis is a system of sine–cosine functions. This is mainly due to the desirable properties of frequency domain representation of a large class of functions encountered in engineering design. In the fields of circuit analysis, control theory, communication, and the analysis of stochastic problems, examples are found extensively where the completeness and orthogonal properties of such a system lead to attractive solutions. But with the application of digital techniques in these areas, awareness for other more general complete systems of orthogonal functions has developed. This “new” class of functions, though not possessing some of the desirable properties of sine–cosine functions, has other advantages to be useful in many applications in the context of digital technology. Many members of this class of orthogonal functions are piecewise constant binary valued, and therefore indicated their possible suitability in the analysis and synthesis of systems leading to piecewise constant solutions.

ICTs and Social Change

The idea that ICTs are a unique technological intervention capable of challenging traditional barriers for social change and economic development continues to be the central pillar of ICT-based civil society initiatives in rural South Asia. Contrary to this widely held belief, the actual experience of many acclaimed developmental ICT projects provides grounds for reassessing the strategies and options of ICT deployment in rural spaces, given the fact that the application of information technology has not in itself led to any profound transformation of the social and economic milieu of marginalized communities. While major ICT-based projects, initiated by either the state or CSOs, are floundering due to the existence of formidable social and economic obstacles that they are unable to overcome, several new ICT-based projects are proliferating in rural South Asia. The attempt to usher in economic changes through providing access to net-based services and information has not had a significant impact on the rural economy in India. Besides, the potential for the organizational as well as technical innovations that lay at the base of these interventions, remoulding microlevel practices for generating sustained growth in incomes and jobs, appears to be rather limited and conditioned by the historically given the socioeconomic milieu in which they operate.

In India, one of the major claims made on behalf of these projects, besides their ability to redefine the economic contours of Indian villages, is their potential in engaging in social transformative action at the village level (Dugger 2000; Arunachalam 2002; Rajora 2002).

In this chapter, efforts have been made to solve integral equations [1] using orthogonal triangular function (TF) sets. It is well known that, in control system analysis and synthesis, integral equations play an important role and often the control problem surmises to solving one or several integral equations. The proposed TFs, when used in a fashion similar to that of block pulse functions (BPF) [2,3], yield a piecewise linear solution of dynamic systems with less integral squared error (ISE).

The main objectives of the present work are:

1. (i) To solve Fredholm integral equation of the second kind [1] via TFs and compare the results with its BPF domain solution.

2. (ii) To solve Volterra integral equation of the second kind [1] via TFs and compare the results with its BPF domain solution.

The theory of the proposed TF method has been developed and then supported by several examples. Results are also compared with BPF domain solution with respect to ISE.

Solution of integral equations was of interest to the scientific community that is apparent from the year of publication of Ref. 1. With the advent of Walsh [4], block pulse [2,3], and related functions, interest of the researchers took a new turn and they thrived for finding out techniques that were computationally more attractive using new family of orthogonal functions.