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The mixed mock modularity of a new -type function related to the Andrews-Gordon identities
No full textIn this paper we resolve a question by Bringmann, Lovejoy, and Rolen on a new vector-valued -type function. We obtain an expression for a corresponding family of Hecke--Appell-type sums in terms of mixed mock modular forms; that is, we express the sum in terms of Appell functions and theta functions. This -type function appears from considering the special polynomials related to generating functions for the partitions occurring in Gordon’s generalization of the Rogers--Ramanujan identities
Some Eichler-Selberg Trace Formulas
No full textThe Eichler-Selberg trace formulas express the traces of Hecke operators on a spaces of cusp forms in terms of weighted sums of Hurwitz-Kronecker class numbers. For cusp forms on Zagier proved these formulas by cleverly making use of the weight 3/2 nonholomorphic Eisenstein series he discovered in the 1970s. The holomorphic part of this form, its so-called {\it mock modular form}, is the generating function for these class numbers. In this expository note we revisit Zagier's method, and we show how to obtain such formulas for congruence subgroups, working out the details for and The trace formulas fall out naturally from the computation of the Rankin-Cohen brackets of Zagier's mock modular form with specific theta functions
Computation Against a Neighbour: Addressing Large-Scale Distribution and Adaptivity with Functional Programming and Scala
No full textRecent works in contexts like the Internet of Things (IoT) and large-scaleCyber-Physical Systems (CPS) propose the idea of programming distributedsystems by focussing on their global behaviour across space and time. In thisview, a potentially vast and heterogeneous set of devices is considered as an"aggregate" to be programmed as a whole, while abstracting away the details ofindividual behaviour and exchange of messages, which are expresseddeclaratively. One such a paradigm, known as aggregate programming, builds oncomputational models inspired by field-based coordination. Existing models suchas the field calculus capture interaction with neighbours by a so-called"neighbouring field" (a map from neighbours to values). This requires ad-hocmechanisms to smoothly compose with standard values, thus complicatingprogramming and introducing clutter in aggregate programs, libraries anddomain-specific languages (DSLs). To address this key issue we introduce thenovel notion of "computation against a neighbour", whereby the evaluation ofcertain subexpressions of the aggregate program are affected by recentcorresponding evaluations in neighbours. We capture this notion in theneighbours calculus (NC), a new field calculus variant which is shown tosmoothly support declarative specification of interaction with neighbours, andcorrespondingly facilitate the embedding of field computations as internal DSLsin common general-purpose programming languages -- as exemplified by a Scalaimplementation, called ScaFi. This paper formalises NC, thoroughly compares itwith respect to the classic field calculus, and shows its expressiveness bymeans of a case study in edge computing, developed in ScaFi
Maximality of moduli spaces of vector bundles on curves
No full textWe prove that moduli spaces of semistable vector bundles of coprime rank anddegree over a non-singular real projective curve are maximal real algebraicvarieties if and only if the base curve itself is maximal. This provides a newfamily of maximal varieties, with members of arbitrarily large dimension. Weprove the result by comparing the Betti numbers of the real locus to the Hodgenumbers of the complex locus and showing that moduli spaces of vector bundlesover a maximal curve actually satisfy a property which is stronger thanmaximality and that we call Hodge-expressivity. We also give a brief account onother varieties for which this property was already known
On the Usability of Available Digital Tools for Reconstructive TextualEditing
No full textThis article reviews some of the digital tools currently available for reconstructive textual editing. First the main idea of reconstructive textual editing is summarised, then its steps amenable to algorithmic description are compared to similar ones in evolutionary biology. The the unequal ability of its variants to be relationship revealing is an important difference between the two fields. Two Latin texts with a complicated transmission are then introduced and used as data to illustrate some available tools in praxi. The main focus is on stemma reconstruction. Some steps of the process can already be largely automated, especially collating texts. On the whole it is found that tree-constructing software is of little help in the case of the medical text Liber Aurelii, whereas it is somewhat more helpful for Plato of Tivoli’s translation of the Centiloquium. In a concluding part, the main problems for algorithmic approaches to the stemma are discussed: incomplete witnesses leading to only partly overlapping text samples, contamination in some witnesses, and rooting the automatically generated trees
On biharmonic functions on vector bundles
No full textThis paper is devoted to the investigation of harmonic and biharmonicfunctions on vector bundles equipped with spherically symmetric metrics. Wewill study the biharmonicity of vertical lifts of functions as well as-radial functions on vector bundle manifolds and, as a consequence, we willconstruct an infinite two-parameter family of proper biharmonic functions.Comment: 20 page
The second fundamental form of the moduli space of cubic threefolds in
No full textWe study the second fundamental form of the Siegel metric in restricted to the locus of intermediate Jacobians of cubic threefolds. We provethat the image of this second fundamental form, which is known to benon-trivial, is contained in the kernel of a suitable multiplication map. Someingredients are: the conic bundle structure of cubic threefolds, Prym theory,Gaussian maps and Jacobian ideals
Scarcity Concept in the contemporary mainstream economic science: an analysis of its ontological and epistemological ambiguity
No full textDifferent economic schools have studied the scarcity concept, reaching otherexplanations. Accordingly, the discussion underlines that for the Classical School ofPolitical Economy (CSPE), scarcity is considered an empirical fact in contrast to theMarginalist School, which instead finds it as a theoretical consequence derived from itsaxioms. Following both schools, the Marshallian theorists introduce an ontological andepistemological ambiguity about scarcity. With this background, the article will try toclarify the concept and characteristics of scarcity. It examines the concept from differentschools of economic thought, considering a new ontological and epistemological path.The article concludes by highlighting that the scarcity characteristics of mainstreameconomics neglect the sociocultural, historical, and political dimensions, making theconsideration to abolish them through social, political, and economic changes aproblematic and, at times, vain option
Well-Rounded ideal lattices of cyclic cubic and quartic fields
No full textIn this paper, we find criteria for when cyclic cubic and cyclic quarticfields have well-rounded ideal lattices. We show that every cyclic cubic fieldhas at least one well-rounded ideal. We also prove that there exist families ofcyclic quartic fields which have well-rounded ideals and explicitly constructtheir minimal bases. In addition, for a given prime number , if a cyclicquartic field has a unique prime ideal above , then we provide the necessaryand sufficient conditions for that ideal to be well-rounded. Moreover, incyclic quartic fields, we provide the prime decomposition of all odd primenumbers and construct an explicit integral basis for every prime ideal.Comment: 42 page
Le projet architectural à travers une pensée croisée entre l'art et la science
No full textL’enseignement de l’architecture se présente comme un carrefour d’échange interdisciplinaire, qui ne se base pas seulement sur le volet pratique, mais qui comporte une approche théorique faisant appel aux notions et références développées dans les cours théoriques. Il se présente ainsi comme un laboratoire de recherche et d’expérimentation sur l’architecture dans son écriture extérieure et intérieure en tant que discipline intégrant la forme et l’espace, développant des approches pédagogiques interactives et complémentaires. Le choix d’un dispositif pédagogique comme prétexte pour aborder l’interdisciplinarité dans le projet architectural devrait en conséquence être bien réfléchi avec un cheminement méthodologique ciblé qui permettrait d’explorer la synergie entre architecture et ingénierie, architecture et design de l’espace, architecture et sculpture, architecture et urbanisme. Faire intervenir les spécialistes tels que plasticien, ingénieur, historien, sociologue, conservateur du patrimoine et urbaniste dans la conception d’un projet architectural ne peut qu’enrichir les connaissances de l’apprenant et développer chez lui un esprit de collaboration et d’échange