Polynomial (chaos) approximation of maximum eigenvalue functions: efficiency and limitations

This paper is concerned with polynomial approximations of the spectral abscissa function (the supremum of the real parts of the eigenvalues) of a parameterized eigenvalue problem, which are closely related to polynomial chaos approximations if the parameters correspond to realizations of random variables. Unlike in existing works, we highlight the major role of the smoothness properties of the spectral abscissa function. Even if the matrices of the eigenvalue problem are analytic functions of the parameters, the spectral abscissa function may not be everywhere differentiable, even not everywhere Lipschitz continuous, which is related to multiple rightmost eigenvalues or rightmost eigenvalues with multiplicity higher than one. The presented analysis demonstrates that the smoothness properties heavily affect the approximation errors of the Galerkin and collocation-based polynomial approximations, and the numerical errors of the evaluation of coefficients with integration methods. A documentation of the experiments, conducted on the benchmark problems through the software Chebfun, is publicly available.Comment: This is a pre-print of an article published in Numerical Algorithms. The final authenticated version is available online at: https://doi.org/10.1007/s11075-018-00648-

Dante ghibellino. Note per una discussione

The essay proposes a chronlogical hypothesis which will clarify the diverse yet related moments of the request for the Black Guelfs' pardon in the canzone Tre donne, and the marked Ghibelline spirit which gives life to the eulogy of Frederick II and Manfredi in De vulgari eloquentia. Dante’s progressive estrangement from the Guelf viewpoint of his mentor Brunetto Latini is also considered as it leads to an openly pro-imperial stance that the Inferno neither denies nor hides, as some have indeed thought

Il canto XXX dell'Inferno

La lettura del XXX dell'Inferno mostra i legami stilistici e tematici tra questo canto e i precedenti VII e VIII (in particolare l'episodio di Filippo Argenti). Mostra l'importanza del contesto «canino» e generalmente bestiale entro il quale va collocato il latrato di Ecuba e l'importanza della sua funzione demitizzante nel momento che immette l'eredità classica nel mondo moderno. Del discorso di maestro Adamo, si rilevano gli echi complessi impliciti nel suo biblico esordio, e se ne analizzano le parole in chiave di «discours de la mauvaise foi» (seguendo una precisa indicazione della studiosa francese Claude Perrus). Dante si serve della zuffa tra i due personaggi per condannare lo sterile e pericoloso esercizio di falsificazione verbale costituito dall a tenzone.The reading of the XXX of Hell shows the stylistic and thematic links between that canto and the previous VII and VIII (particularly the episode of Filippo Argenti). It shows the significance of the «canine» and the generally brutal context in which the howling of Hecuba is placed and the importance of his demystifying function at the moment he releases the classical inheritance into the modern world. From the speech by Maestro Adamo, the complex echoes implicit in his Biblical debut point themselves out, and the words in the key of the «discours de la mauvaise foi» (following a precise indication from the French scholar Claude Perrus) are analysed within it. Dante used the fight between the two characters to condemn that sterile and dangerous exercise of verbal falsification constituted by the fight

Etica, estetica e politica del cibo in Petrarca

Il saggio considera l'insieme degli atteggiamenti di Petrarca nei confronti del cibo, testimoniati da una lunga serie di passi sparsi nella sua opera, e in particolare in alcune importanti lettere «Senili». Da questo esame risultano varie funzioni assegnate al discorso sull'alimentazione: quella oppositiva, che distingue tra gozzoviglia e moderazione, tra cibi artefatti e cibi naturali, tra sporcizia e pulizia, e infine, sul piano sociale e politico, tra lusso e corruzione da una parte, e modestia e virtù dall'altro; quella positiva, che associa la buona e semplice alimentazione naturale alla salute e alla vita tranquilla e solitaria; quella estetica, non meno importante delle altre, che fa del modo di nutrirsi un «test» particolarmente importante sulla civiltà e la buona educazione. Cibarsi, insomma, è per Petrarca un fatto assolutamente culturale, e con ciò egli chiaramente supera i dilemmi della morale cristiana, e pone per primo le basi per una riflessione moderna sull'argomento.The research considers the combined attitudes of Petrarch in comparison with food, attested by a long series of scattered steps in his work and, in particular, in some significant «Senile» letters. There are various functions resulting from this research, aimed at the discussion of nutrition: The opposing, which distinguishes between gluttony and moderate eating, artificial and natural foods, cleanliness and dirtiness -on both a social and political level, between luxury and depravation, on the one hand, and modesty and virtue, on the other. The positive, associates a good, simple natural diet with health and a peaceful, private life. The aesthetic, of no less importance than the others, tests eating habits, proven particularly important with regard to civilisation and good education. In short, for Petrarch, eating was a completely cultural event, with which one clearly overcame Christian moral dilemmas and which firmly stood by its foundations for a modern reflection on the debate

«Et havrà Barcellona il suo poeta». Benet Garret, il Cariteo

Il saggio considera lo sfondo storico e politico contro il quale va collocata la vita (1450 circa - 1514 circa) e l'opera del poeta di origine barcellonese Benet Garret, detto Cariteo, il quale fu constantemente fedele ai suoi re. Tutta la sua opera è segnata in profondità da questa esperienza e dà forma al vero e proprio mito della Napoli aragonese. Si esaminano inoltre le testimonianze dell'opera giunte sino a noi, per passare poi a considerare la struttura del canzioniere intitolato Endimione. L'amore per Luna e l'amore per i re aragonesi e quello per gli amici e quello per Napoli non sono, in essenza, cose diverse rispetto a quella che è, appunto, la struttura profonda del canzionere. Essa finisce per comprendere anche l'amore per la patria perduta, che constituisce l'ultimo e forse più struggente mito di Cariteo il quale, alla fine della propria vita, sogna di tornare a Barcellona per affidare alla città nella quale era nato la custodia dell'intero tesoro della sua esperienza poetica e umana.The thesis considers the historical and political background to the work of the Barcelona poet Benet Garret (1450 approx - 1514 approx) alias Cariteo, who was constantly faithful to his king. His work is deeply marked by this experience and relates the truth behind the myth of Aragonese Naples. Testimonies are taken toward an examination of committee work, in order to then consider the structure of the canzoniere or songbook entitled Endimione. Love for Luna, for the Aragonese king, for friends and for Naples is essentially the same thing in relation to the deep structure of the canzoniere. It terminates by also comprehending love for the lost patria that constitutes Cariteo's ultimate and perhaps most compelling myth, and expressing his lifelong dream of returning to Barcelona in order to entrust the treasure of his poetic and human experience to the city in which he was born

Spectrum-based stability analysis and stabilization of a class of time-periodic time delay systems

We develop an eigenvalue-based approach for the stability assessment and stabilization of linear systems with multiple delays and periodic coefficient matrices. Delays and period are assumed commensurate numbers, such that the Floquet multipliers can be characterized as eigenvalues of the monodromy operator and by the solutions of a finite-dimensional non-linear eigenvalue problem, where the evaluation of the characteristic matrix involves solving an initial value problem. We demonstrate that such a dual interpretation can be exploited in a two-stage approach for computing dominant Floquet multipliers, where global approximation is combined with local corrections. Correspondingly, we also propose two novel characterizations of left eigenvectors. Finally, from the nonlinear eigenvalue problem formulation, we derive computationally tractable expressions for derivatives of Floquet multipliers with respect to parameters, which are beneficial in the context of stability optimization. Several numerical examples show the efficacy and applicability of the presented results

PENERAPAN MODEL PEMBELAJARAN KOOPERATIF STUDENT TEAMS ACHIEVEMENT DIVISION (STAD) BERBANTUAN MEDIA ADOBE FLASH PROFESSIONAL CS6 PADA MATA PELAJARAN DASAR PERANCANGAN TEKNIK MESIN UNTUK MENINGKATKAN HASIL BELAJAR SISWA KELAS 10 TMI DI SMK NEGERI 1 JATIREJO – MOJOKERTO

Berdasarkan hasil refleksi yang dilakukan oleh peneliti dan guru di SMKN 1 Jatirejo didapatkan bahwa proses pembelajaran dengan model yang kurang efektif dapat menyebabkan respon siswa pasif sehingga hasil belajar siswa banyak yang belum tuntas. Dari permasalahan tersebut solusi yang dibutuhkan adalah penerapan model pembelajaran yang berpusat pada siswa. Penelitian ini bertujuan untuk menigkatkan kualitas pembelajaran dari segi efektivitas pembelajaran, respon siswa, dan hasil belajar menggunakan model pembelajaran STAD berbantuan media Adobe Flash Professional CS6 untuk mempermudah penyampaian materi dalam bentuk animasi dan video interaktif. Penelitian ini menggunakan metode Penelitian Tindakan Kelas (PTK) yang diterapkan pada kelas X TMI 1 pada mata pelajaran Dasar Perancangan Teknik Mesin. Data dikumpulkan dengan menggunakan teknik observasi, angket dan tes. Hasil penelitian ini menunjukkan adanya peningkatan pada efektivitas pembelajaran mendapatkan hasil dengan kategori sangat efektif, respon menunjukkan hasil dengan kategori sangat baik, dan hasil belajar siswa menunjukkan ketuntasan klasikal sebanyak 28 siswa hasil belajarnya tuntas. Kata kunci: STAD, Efektivitas Pembelajaran, Respon Siswa, Hasil belaja