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Introduction To The Fractional Calculus Of Variations
This invaluable book provides a broad introduction to the fascinating and beautiful subject of Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non-conservative systems in mechanics. The inclusion of non-conservatism is extremely important from the point of view of applications. Forces that do not store energy are always present in real systems. They remove energy from the systems and, as a consequence, Noether's conservation laws cease to be valid. However, it is still possible to obtain the validity of Noether's principle using FCV. The new theory provides a more realistic approach to physics, allowing us to consider non-conservative systems in a na...
Voices of Freedom
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Quantum Variational Calculus
This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstractio...
Advanced Methods in the Fractional Calculus of Variations
This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler–Lagrange equations to include fractional derivatives. The dependence of Lagrangians on generalized fractional operators as well as on classical derivatives is considered along with still more general problems in which integer-order integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of...
In Gratitude for All the Gifts
In Gratitude for All the Gifts explores the literary and cultural links between the bestselling, Nobel Prize-winning Northern Irish poet Seamus Heaney and the preeminent Eastern European poets of the twentieth century, including fellow Nobel laureate Czeslaw Milosz and Zbigniew Herbert. Magdalena Kay opens new ground in comparative literary studies with her close analysis of Heaney's poetic work from the perspective of the English-speaking West's attraction, and especially Heane''s own attraction, to Eastern European poetry. While placing Milosz and Herbert in their cultural contexts and keeping an eye on the poems in their original Polish, this innovative and energetic study focuses on how Heaney encountered their work in translation. In Gratitude for All the Gifts thus allows us to see what happens when poetic forms, histories, and themes travel between countries and encourages us to understand cultural crossing not just thematically, but also in terms of form, voice, and aesthetic intent.
