Ego in amorem inciderem ... et ego tristis spectator - Die Autobiographie des jülich-bergischen Rates Petrus Simonius Ritz (1562-1622)

Der vorliegende Beitrag stellt die 1604 verfasste und bislang unveröffentlichte Autobiographie des kurtrierischen, jülich-bergischen und nach dem Zerfall der Vereinigten Herzogtümer Jülich-Kleve-Berg pfalz-neuburgischen Rates Petrus Simonius Ritz (1562-1622) vor. Seit 1595 stand der Schreiber in jülich-bergischen Diensten und nahm bis zu seinem Tod an fast allen bedeutsamen Ereignissen der damals angespannten politischen Situation am Niederrhein teil. Bei Beachtung der Klischees, die Simonius in seiner Selbstdarstellung verwendet, dürfte die mitunter sehr detaillierte und aufmerksame Beschreibung seiner alltäglichen Wahrnehmungen den besonderen Wert der Aufzeichnungen ausmachen. Er erzählt von seinem Bildungsweg, von Heirat, Krankheit und dem Tode seiner ersten Frau, der anschließenden Wiederverheiratung und natürlich auch vom Alltag bei Hofe.

Krylov subspace approximations for the exponential Euler method: Error estimates and the harmonic Ritz approximant

We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error.

Analysis of vibration of clamped square plates by the Rayleigh-Ritz method with asymptotic solutions from a modified Bolotin method

Estimates of flexural frequencies of clamped square plates are initially obtained by the modified Bolotin's method. The mode shapes in “each direction” are then determined and the product functions of these mode shapes are used as admissible functions in the Rayleigh-Ritz method. The data for the first twenty eigenvalues in each of the three (four) symmetric groups obtained by the (i) Bolotin, (ii) Rayleigh and (iii) Rayleigh-Ritz methods are reported here. The Rayleigh estimates are found to be much closer to the true eigenvalues than the Bolotin estimates. The present product functions are found to be much superior to the conventional beam eigenmodes as admissible functions in the Rayleigh-Ritz method of analysis.

Stiff string approximations in Rayleigh-Ritz method for rotating beams

The governing differential equation of the rotating beam reduces to that of a stiff string when the centrifugal force is assumed as constant. The solution of the static homogeneous part of this equation is enhanced with a polynomial term and used in the Rayleighs method. Numerical experiments show better agreement with converged finite element solutions compared to polynomials. Using this as an estimate for the first mode shape, higher mode shape approximations are obtained using Gram-Schmidt orthogonalization. Estimates for the first five natural frequencies of uniform and tapered beams are obtained accurately using a very low order Rayleigh-Ritz approximation.

Petrus de Vinea, Summa dictaminis (1-157), Rythmi (157v-178).

Au f. 157, souscription rubriquée du 20 novembre 1384: "Explicit summa dictaminis magistri Petri de Vineis. Qui scripsit scribat, semper cum Domini vivat. Ffinito (sic) libro, referamus gratia Christo. Ffuit (sic) scriptum presens opus et completum, die qua computabatur vicesima mensis novembris, anno a Nativitate Domini M°CCC° octuagesimo quarto". Tout le ms. est de la même main.

Petrus Lombardus, Collectanea in epistolas Pauli.

Au contreplat sup. figure la signature de Claude Joly, suivie de la mention "nov. 1667". Ce ms. a appartenu à la bibliothèque du chapitre de la cathédrale Notre-Dame de Paris, dont il porte l'ex-libris "A la bibliotheque de l'Eglise de Paris" au contreplat sup. (XVIIe s.). Notre-Dame.