Results 151 to 160 of about 211 (181)
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Liouville Integrable System and Associated Integrable Coupling
Communications in Theoretical Physics, 2009Liouville integrable discrete integrable system is derived based on discrete isospectral problem. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses bi-Hamiltonian structure. Finally, integrable couplings of the obtained system is given by means of semi-direct sums of Lie algebras.
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Unitary Integration of Quantum Liouville-Bloch Equations
Physical Review Letters, 1998Summary: The Liouville-Bloch equation for a general spin in time-dependent external fields is solved as a unitary product of exponential operators. Operator noncommutativity is explicitly handled so as to leave behind a set of first-order differential equations for classical functions of time.
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Integral operators of Sturm-Liouville type
Integral Equations and Operator Theory, 2000This paper extends the class of integral equations whose solutions are known to be finitely generated to include equations of Sturm-Liouville type. The authors obtain an explicit expression for the resolvent operator from two particular solutions, in a form amenable to the use of approximation techniques having an explicit error bound available without
Porter, D., Stirling, D. S. G.
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
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The Riemann-Liouville integral
Es wird eine Schar von Banachräumen \(C^{\nu}[0,1]\), \(\nu\geq 0\), als Bild des Riemann-Liouville Integrals konstruiert. Für \(\nu\) nicht ganz sind die \(C^{\nu}\) echte Unterräume der Räume Hölderstetiger Funktionen der Ordnung \(\nu\). Für die Dualräume wird eine Art Rieszscher Darstellungssatz bewiesen.openaire +2 more sources
SIMPLE GENERALIZATION OF LIOUVILLE INTEGRABILITY
Nonlinearity, Integrability and All That, 2000M. GIORDANO, G. MARMO, A. SIMONI
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Riemann-Liouville Differential and Integral Operators
2010This chapter begins with the definition of fractional integral operators in the sense of Riemann and Liouville and with an investigation of their fundamental properties. Based on these integral operators we then introduce the Riemann-Liouville differential operators and discuss their behaviour. Moreover we analyze how the differential operators and the
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