Leopardi “Everything Is Evil”

Giacomo Leopardi, a major Italian poet of the nineteenth century, was also an expert in evil to whom Schopenhauer referred as a “spiritual brother.” Leopardi wrote: “Everything is evil. That is to say, everything that is, is evil; that each thing exists is an evil; each thing exists only for an evil end; existence is an evil.” These and other thoughts are collected in the Zibaldone, a massive collage of heterogeneous writings published posthumously. Leopardi’s pessimism assumes a polished form in his literary writings, such as Dialogue between Nature and an Islander (1824)—an invective against nature and the suffering of creatures within it. In his last lyric, Broom, or the flower of the desert (1836), Leopardi points to the redeeming power of poetry and to human solidarity as placing at least temporary limits on the scope of evil

On Kronecker Quotients

Leopardi introduced the notion of a Kronecker quotient in [Paul Leopardi. A generalized FFT for Clifford algebras. Bulletin of the Belgian Mathematical Society, 11:663--688, 2005.]. This article considers the basic properties that a Kronecker quotient should satisfy and additional properties which may be satisfied. A class of Kronecker quotients for which these properties have a natural description is completely characterized. Two examples of types of Kronecker quotients are described.Comment: Published article available at http://www.math.technion.ac.il/iic/ela/27.htm

Leopardi sulle tracce di Montaigne

Il saggio esplora le tracce della presenza di Montaigne in Leopardi, il quale cita l'autore francese soltanto sei volte in tutta la sua opera. Si identificano innanzitutto le letture che possono aver fatto conoscere Montaigne al giovane Leopardi. Si passa poi all'analisi dei luoghi zibaldoniani, in cui è citato, escludendo l'ultimo, cui sarà dedicato un altro contributo.This essay explores the traces of Montaigne's presence in Leopardi, who mentions the French author only six times. First of all, the essay identifies some of the texts through which the young Leopardi may have heard of Montaigne. Secondly, it analyses all the passages in the Zibaldone where Leopardi mentions "Montaigne" (or "Montagna"), with the exception of the last, which is the subject of another essay

Twin bent functions, strongly regular Cayley graphs, and Hurwitz-Radon theory

The real monomial representations of Clifford algebras give rise to two sequences of bent functions. For each of these sequences, the corresponding Cayley graphs are strongly regular graphs, and the corresponding sequences of strongly regular graph parameters coincide. Even so, the corresponding graphs in the two sequences are not isomorphic, except in the first 3 cases. The proof of this non-isomorphism is a simple consequence of a theorem of Radon.Comment: 13 pages. Addressed one reviewer's questions in the Discussion section, including more references. Resubmitted to JACODES Math, with updated affiliation (I am now an Honorary Fellow of the University of Melbourne

Twin bent functions and Clifford algebras

This paper examines a pair of bent functions on $\mathbb{Z}_2^{2m}$ and their relationship to a necessary condition for the existence of an automorphism of an edge-coloured graph whose colours are defined by the properties of a canonical basis for the real representation of the Clifford algebra $\mathbb{R}_{m,m}.$ Some other necessary conditions are also briefly examined.Comment: 11 pages. Preprint edited so that theorem numbers, etc. match those in the published book chapter. Final post-submission paragraph added to Section 6. in "Algebraic Design Theory and Hadamard Matrices: ADTHM, Lethbridge, Alberta, Canada, July 2014", Charles J. Colbourn (editor), pp. 189-199, 201

The map of Johannes Quintinus Haeduus and its derivatives

The first known map of the Maltese islands was drawn in the latter part of the fifteenth century, but the first printed map was that published in 1536 in Lyons by Johannes Quintinus. Being rather primitive, it did not serve as a model for other maps beyond the 16th century. However, as it was important in the time frame of Maltese cartography, it was reproduced by other cartographers, namely, in Frankfurt in 1600, in 1725 in Leiden, and around 1800 as a loose sheet probably in Malta. Of the 16th-century Malta maps, those by Antonio Lafreri (1551) and Matteo Perez d'Aleccio (1582) remained the basic maps for the next two centuries.peer-reviewe

Leopardi in the footsteps of Montaigne

L'article explora els rastres de la presència de Montaigne en Leopardi, el qual cita l'autor francès només sis vegades en tota la seva obra. S'identifiquen en primer lloc les lectures que poden haver fet conèixer Montaigne al jove Leopardi. Després s'analitzen els passatges del Zibaldone en què se cita Montaigne, tret del darrer, al qual es dedicarà una altra aportació.This essay explores the traces of Montaigne’s presence in Leopardi, who mentions the French author only six times. First of all, the essay identifies some of the texts through which the young Leopardi may have heard of Montaigne. Secondly, it analyzes all the passages in the Zibaldone where Leopardi mentions “Montaigne” (or “Montagna”), with the exception of the last, which is the subject of another essay.El artículo explora los rastros de la presencia de Montaigne en Leopardi, quien cita al autor francés solo seis veces en toda su obra. Se identifican en primer lugar las lecturas por las que el joven Leopardi pudo haber conocido a Montaigne. Luego se pasa a analizar los pasajes del Zibaldone donde se cita a Montaigne, excluyendo el último, al cual se le dedicará otra aportación.Il saggio esplora le tracce della presenza di Montaigne in Leopardi, il quale cita l'autore francese soltanto sei volte in tutta la sua opera. Si identificano innanzitutto le letture che possono aver fatto conoscere Montaigne al giovane Leopardi. Si passa poi all'analisi dei luoghi zibaldoniani in cui Montaigne è citato, escludendo l'ultimo, cui sarà dedicato un altro contributo

Optimal polynomial meshes and Caratheodory-Tchakaloff submeshes on the sphere

Using the notion of Dubiner distance, we give an elementary proof of the fact that good covering point configurations on the 2-sphere are optimal polynomial meshes. From these we extract Caratheodory-Tchakaloff (CATCH) submeshes for compressed Least Squares fitting

The abstract Hodge-Dirac operator and its stable discretization

This paper adapts the techniques of finite element exterior calculus to study and discretize the abstract Hodge-Dirac operator, which is a square root of the abstract Hodge-Laplace operator considered by Arnold, Falk, and Winther [Bull. Amer. Math. Soc. 47 (2010), 281-354]. Dirac-type operators are central to the field of Clifford analysis, where recently there has been considerable interest in their discretization. We prove a priori stability and convergence estimates, and show that several of the results in finite element exterior calculus can be recovered as corollaries of these new estimates.Comment: 21 pages, 1 figure; v2: minor revision