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To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms.For instance, q-hypergeometric functions are now visually clear and easy to trace back to their hypergeometric parents. With this new notation it is also easy to see the connection between q-hypergeometric functions and the q-gamma function, something that until now has been overlooked. The book covers many topics on q-calculus, including special functions, combinatorics, and q-difference equations. Apart from a thorough review of the historical development of q-calculus, this book also presents the domains of modern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few.
Drawing on the authors' research work from the last ten years, Mathematical Inequalities: A Perspective gives readers a different viewpoint of the field. It discusses the importance of various mathematical inequalities in contemporary mathematics and how these inequalities are used in different applications, such as scientific modeling.The authors
This book traces the incorporation of Central Asia into the Soviet system, the region's path of development under socialism, and the vicissitudes of the economic and political collapse of socialism, before considering the trajectories of the new states as they chart their independent futures.
Despite advances in modern communication and the proliferation of information, there remain areas of the world about which little is known. One such place is Somalia. The informed public is aware of a political meltdown and consequent chaos there, but few comprehend the causes of this tragic crisis. This new edition covers Somalia's origin, history, culture, and language, as well as current economic and political issues. The alphabetical arrangement of this Dictionary, with a complete chronology, list of acronyms, and in-depth bibliography provide useful information about the country in a convenient format. A vital addition to reference collections supporting undergraduate and graduate programs on Africa and the Middle East, international relations, and economics- a useful fact-filled compendium for government and public libraries, NGO's, and other special libraries
This book covers new ground on the diffusion and transmission of geographical knowledge that occurred at critical junctures in the long history of the Silk Road. Much of twentieth-century scholarship on the Silk Road examined the ancient archaeological objects and medieval historical records found within each cultural area, while the consequences of long-distance interaction across Eurasia remained poorly studied. Here ample attention is given to the journeys that notions and objects undertook to transmit spatial values to other civilizations. In retracing the steps of four major circuits right across the many civilizations that shared the Silk Road, "The Journey of Maps and Images on the Silk Road" traces the ways in which maps and images surmounted spatial, historical and cultural divisions.
Commercially used for food flavorings, toiletry products, cosmetics, and perfumes, among others, citrus essential oil has recently been applied physiologically, like for chemoprevention against cancer and in aromatherapy. Citrus Essential Oils: Flavor and Fragrance presents an overview of citrus essential oils, covering the basics, methodology, and applications involved in recent topics of citrus essential oils research. The concepts, analytical methods, and properties of these oils are described and the chapters detail techniques for oil extraction, compositional analysis, functional properties, and industrial uses. This book is an unparalleled resource for food and flavor scientists and chemists.
Terrorism on the African continent is a complex and emotional topic. One of the primary reasons for this is that a historical introspection for any country, or its people, that has been confronted with a conflicting past can only be described as 'sensitive'. In addition to international developments and challenges, domestic circumstances predominately fuel domestic terrorism. It will therefore be a mistake to assess the threat of terrorism in any country in historic isolation. This is particularly true when one tries to assess and understand the 'renewed' threat of terrorism in Algeria, Morocco and Tunisia. This monograph will attempt to place the threat and implication of the name change an...
Winner of the 2003 Ohio Academy of History Outstanding Publication Award This revisionist study reevaluates the origins and foundation myths of the Faqaris and Qasimis, two rival factions that divided Egyptian society during the seventeenth and eighteenth centuries, when Egypt was the largest province in the Ottoman Empire. In answer to the enduring mystery surrounding the factions' origins, Jane Hathaway places their emergence within the generalized crisis that the Ottoman Empire—like much of the rest of the world—suffered during the early modern period, while uncovering a symbiosis between Ottoman Egypt and Yemen that was critical to their formation. In addition, she scrutinizes the factions' foundation myths, deconstructing their tropes and symbols to reveal their connections to much older popular narratives. Drawing on parallels from a wide array of cultures, she demonstrates with striking originality how rituals such as storytelling and public processions, as well as identifying colors and emblems, could serve to reinforce factional identity.
The first study of English historical plays about the Turks, using works in Greek, Arabic, and Turkish. Drawing on Bakhtin's concept of the dialogic, McJannet shows that instead of adverse authorial commentary playwrights such as Marlowe and Fulke Greville use dialogue and commentary to enhance the sultan's stature and mitigate his negative acts.