Deformation of a nearly hemispherical conducting drop due to an electric field: theory and experiment

We consider, both theoretically and experimentally, the deformation due to an electric field of a pinned nearly-hemispherical static sessile drop of an ionic fluid with a high conductivity resting on the lower substrate of a parallel plate capacitor. Using both numerical and asymptotic approaches we find solutions to the coupled electrostatic and augmented Young–Laplace equations which agree very well with the experimental results. Our asymptotic solution for the drop interface extends previous work in two ways, namely to drops that have zero-field contact angles that are not exactly π/2 and to higher order in the applied electric field, and provides useful predictive equations for the changes in the height, contact angle and pressure as functions of the zero-field contact angle, drop radius, surface tension and applied electric field. The asymptotic solution requires some numerical computations, and so a surprisingly accurate approximate analytical asymptotic solution is also obtained

Powdery mildew resistance genes in vines: an opportunity to achieve a more sustainable viticulture

Grapevine (Vitis vinifera) is one of the main fruit crops worldwide. In 2020, the total surface area planted with vines was estimated at 7.3 million hectares. Diverse pathogens affect grapevine yield, fruit, and wine quality of which powdery mildew is the most important disease prior to harvest. Its causal agent is the biotrophic fungus Erysiphe necator, which generates a decrease in cluster weight, delays fruit ripening, and reduces photosynthetic and transpiration rates. In addition, powdery mildew induces metabolic reprogramming in its host, affecting primary metabolism. Most commercial grapevine cultivars are highly susceptible to powdery mildew; consequently, large quantities of fungicide are applied during the productive season. However, pesticides are associated with health problems, negative environmental impacts, and high costs for farmers. In paralleled, consumers are demanding more sustainable practices during food production. Therefore, new grapevine cultivars with genetic resistance to powdery mildew are needed for sustainable viticulture, while maintaining yield, fruit, and wine quality. Two main gene families confer resistance to powdery mildew in the Vitaceae, Run (Resistance to Uncinula necator) and Ren (Resistance to Erysiphe necator). This article reviews the powdery mildew resistance genes and loci and their use in grapevine breeding program

Leibniz and Peano. From binary number systems to machines|Leibniz e Peano Dalla numerazione binaria alle macchine

This paper presents some reflections on binary arithmetic and its applications by Gottfried Wilhelm Leibniz (1646-1716) and Giuseppe Peano (1858-1932). The topic is relevant both for the intrinsic historical, mathematical, philosophical, theological, and linguistic interests motivating its development, and for the social implications derived by the design and the realization of machines. In the light of Leibniz’s texts on dyadic between 1663 and 1705, we highlight the results that he obtained as well as the aims he did not achieve, both in the theoretical and in the applicative field. We also underline the ability of the German philosopher and mathematician to involve high-level experts, teachers, and academics from various countries in his projects on dyadic. With regard to Peano, we analyse the sources that between 1898 and 1903 brought him to deal with the history of the binary number system in the wake of Leibniz. Based on the examination of some unpublished manuscripts, we reconstruct his research and show how it culminates in the construction of a binary shorthand machine, in which mathematics, linguistics and technology merged together. For both authors, research in different cultural fields and their historical status constituted an important step in identifying and achieving their objectives

Mathematicians in Bologna 1861-1960

The organizing Committee of the (quadriennal) XIX Congress of Unione Matematica Italiana has delegated prof Salvatore Coen to edit the publication of a volume dedicated to those mathematicians who have been associated with Bologna University from 1861 to 1960. The general idea was that this volume had to consider the many illustrious scientific personages who have carried out their activity in various roles at Bologna\u2019s university (professors and students) during the first century after the unification of Italy. The objective was fully achieved, even exceeded. The work of preparation of the book has developed over a period of about two years. The published volume contains 23 different contributions, written by 28 different authors. The volume consists of about 550 pages. Most of the contributions are of a historical nature with a few being work in mathematical research in Bologna. The studied personalities are Ugo Amaldi, Eugenio Beltrami, Enrico Bompiani, Mario Burgatti Lamberto Cattabriga, Gianfranco Cimmino, Luigi Cremona, Federigo Enriques, Dario Graffi, Beppo Levi, Salvatore Pincherle, Bruno Pini, Beniamino Segre, Leonida Tonelli, Tullio Viola , Giuseppe Vitali and others. The topics covered are varied. We name a few: Non-Euclidean Geometry, Complex Analysis, Differential Geometry, Functional Analysis, Theory of Lie, Algebraic Geometry, Mechanics, , Calculus of Variations, Parabolic Potential theory, Philosophy of Science, Fractional Calculus, Measure Theory , Theory of Lie Groups, Difference Equations, Plane Curves and their Moduli, Linear Constant Coefficients Partial Differential Equations, Cimmino Integrals. New perspectives have appeared studying the work of E. Beltrami through the publication of new important unpublished correspondence. New studies on teacher training schools (Scuole di Magistero) by examining the work of Enriques in the school of Bologna; new studies also on the Italian Encyclopedia of Elementary Mathematics, The figures of F. Enriques and S. Pincherle are each examined by three different contributions

Egyptian Architecture and Mathematics

An analysis of the relationship between mathematics and architecture in ancient Egypt requires, first of all, an analysis of the terms involved in the discussion. Mathematics, mathematicians, architecture, and architect are modern terms that convey a range of meanings that may or may not find a precise correspondence in the ancient Egyptian culture. Textual, iconographic, and archaeological sources provide a significant amount of pieces of the puzzle representing the complex task of building a monument, and yet some important aspects still remain unclear. Mathematical knowledge was deeply intertwined with the architectural practice, but defining its nature and boundaries is not easy. The extant mathematical texts are schoolbooks and cast a relatively limited light on the way in which numbers and geometrical figures were used in the planning and building process; in particular, it is difficult to establish who decided the shape and the dimensions of the buildings and of their architectural elements. The overall impression is that building a monument was a collective enterprise, carried out by a long line of individuals, the majority of whom remained anonymous