Search results for "legend"
showing 10 items of 92 documents
Partial Stabilization of Input-Output Contact Systems on a Legendre Submanifold
2017
This technical note addresses the structure preserving stabilization by output feedback of conservative input-output contact systems, a class of input-output Hamiltonian systems defined on contact manifolds. In the first instance, achievable contact forms in closed-loop and the associated Legendre submanifolds are analysed. In the second instance the stability properties of a hyperbolic equilibrium point of a strict contact vector field are analysed and it is shown that the stable and unstable manifolds are Legendre submanifolds. In the third instance the consequences for the design of stable structure preserving output feedback are derived: in closed-loop one may achieve stability only rel…
Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function
2009
A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Helmholtz Green function are split into their half advanced+half retarded and half advanced-half retarded components. Closed form solutions are given for these components in terms of a Horn function and a Kampe de Feriet function, respectively. The systems of partial differential equations associated with these two-dimensional hypergeometric functions are used to construct a fourth-order ordinary differential equation which both components satisfy. A s…
Indefinite integrals involving the incomplete elliptic integrals of the first and second kinds
2016
ABSTRACTA substantial number of indefinite integrals are presented for the incomplete elliptic integrals of the first and second kinds. The number of new results presented is about three times the total number to be found in the current literature. These integrals were obtained with a Lagrangian method based on the differential equations which these functions obey. All results have been checked numerically with Mathematica. Similar results for the incomplete elliptic integral of the third kind will be presented separately.
Indefinite integrals involving the incomplete elliptic integral of the third kind
2016
ABSTRACTA substantial number of new indefinite integrals involving the incomplete elliptic integral of the third kind are presented, together with a few integrals for the other two kinds of incomplete elliptic integral. These have been derived using a Lagrangian method which is based on the differential equations which these functions satisfy. Techniques for obtaining new integrals are discussed, together with transformations of the governing differential equations. Integrals involving products combining elliptic integrals of different kinds are also presented.
El frau de l’alquimista en l’infern dantesc de Joan Pasqual i en la tradició medieval
2015
This article presents and analyses chapter XLVI from the Tractat de les penes particulars d’infern by Catalan franciscan friar Joan Pasqual, written soon after 1436. This chapter, “Del cercle de l’alquimia”, includes an exemplum which is doubly significant: on the one hand, it documents the alchemic legend in the Plantagenets’ court during the 14th and 15th centuries; on the other hand, and most importantly, it is a new testimony of two narrative motifs of Eastern origin: the fake alchemist and the king (Thompson, K.111.4; Tubach, 89), and the account-book of mistakes or fools (Thompson,J.1371). After introducing the medieval witnesses of these motifs, the alchemic legend of Ramon Llull and…
Approssimazioni alla “leggenda del legno della Croce” nell'Occitania medievale
2019
La leggenda del legno della croce è una delle storie apocrife più significative del medioevo religioso. Essa è il risultato di un lungo processo di stratificazione di racconti e motivi leggendari, e risulta declinata in versioni plurime, più o meno scorciate e interpolate. Il presente contributo indaga la diffusione della storia del lignum crucis nel contesto occitano. La scelta non è casuale; appare, anzi, necessaria. In effetti, come spesso è avvenuto per quella che può essere considerata un’appendice alla cosiddetta «eccezione narrativa» occitana, lo studio della letteratura religiosa del Midi necessita ancora di nuovi spunti d’indagine, trasversali e comparativi. Di questo soffrono anch…
New indefinite integrals from a method using Riccati equations
2018
ABSTRACTAn earlier method for obtaining indefinite integrals of special function from the second-order linear equations which define them has been reformulated in terms of Riccati equations, which ...
More indefinite integrals from Riccati equations
2019
ABSTRACTTwo new methods for obtaining indefinite integrals of a special function using Riccati equations are presented. One method uses quadratic fragments of the Riccati equation, the solutions of...
Kultalangalla kokonaiseksi
2019
Arvostelu teoksesta Nadeem Aslam: Kultainen legenda (The Golden Legend). Suom. Kirsi Luoma. 375 s. nonPeerReviewed
A Lagrangian method for deriving new indefinite integrals of special functions
2015
A new method is presented for obtaining indefinite integrals of common special functions. The approach is based on a Lagrangian formulation of the general homogeneous linear ordinary differential equation of second order. A general integral is derived which involves an arbitrary function, and therefore yields an infinite number of indefinite integrals for any special function which obeys such a differential equation. Techniques are presented to obtain the more interesting integrals generated by such an approach, and many integrals, both previously known and completely new are derived using the method. Sample results are given for Bessel functions, Airy functions, Legendre functions and hype…