Mauro Bologna - Böcker

This text describes how fractal phenomena, both deterministic and random, change over time, using the fractional calculus. The intent is to identify those characteristics of complex physical phenomena that require fractional derivatives or fractional integrals to describe how the process changes over time. The discussion emphasizes the properties of physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. In many cases, classic analytic function theory cannot serve for modeling complex phenomena; "Fractal Operators" shows how classes of less familiar functions, such as fractals, can serve as useful models in such cases. Because fractal functions, such as the Weierstrass function (long known not to have a derivative), do in fact have fractional derivatives, they can be cast as solutions to fractional differential equations. The traditional techniques for solving differential equations, including Fourier and Laplace transforms as well as Green's functions, can be generalized to fractional derivatives.Fractal Operators addresses a general strategy for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of various forms of transport in heterogeneous materials. This strategy builds on traditional approaches and explains why the historical techniques fail as phenomena become more and more complicated.

This text describes how fractal phenomena, both deterministic and random, change over time, using the fractional calculus. The intent is to identify those characteristics of complex physical phenomena that require fractional derivatives or fractional integrals to describe how the process changes over time. The discussion emphasizes the properties of physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory.In many cases, classic analytic function theory cannot serve for modeling complex phenomena; "Fractal Operators" shows how classes of less familiar functions, such as fractals, can serve as useful models in such cases. Because fractal functions, such as the Weierstrass function (long known not to have a derivative), do in fact have fractional derivatives, they can be cast as solutions to fractional differential equations. The traditional techniques for solving differential equations, including Fourier and Laplace transforms as well as Green's functions, can be generalized to fractional derivatives.Fractal Operators addresses a general strategy for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of various forms of transport in heterogeneous materials.This strategy builds on traditional approaches and explains why the historical techniques fail as phenomena become more and more complicated.

Biotargets of Cancer in Current Clinical Practice presents an updated and reasoned review of the current status of knowledge concerning the major cancer types with a special focus on the current biomarkers, genes involved and the potential future targets of innovative therapies.

Biotargets of Cancer in Current Clinical Practice presents an updated and reasoned review of the current status of knowledge concerning the major cancer types with a special focus on the current biomarkers, genes involved and the potential future targets of innovative therapies. The volume includes for each major cancer type, a comprehensive although concise discussion of epidemiology, affirmed and innovative biomarkers for diagnosis, and descriptions of the relevant genes for prognosis and (individualized) therapy through biotarget-specific new molecular treatments, with the latest information on the validation status of each novel biomarker. Individual chapters are dedicated to the major cancer types, plus a special chapter on metastasis. The present debate on patentability of genetic information applied to diagnostics and therapeutics of cancer is also discussed.