Poincaré on the Foundation of Geometry in the Understanding

This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study of groups of operations. In place of the established view I offer a revised view, according to which Poincaré held that axioms in geometry are in fact assertions about invariants of groups. Groups, as forms of the understanding, are prior in conception to the objects of geometry and afford the proper definition of those objects, according to Poincaré. Poincaré’s view therefore contrasts sharply with Kant’s foundation of geometry in a unique form of sensibility. According to my interpretation, axioms are not definitions in disguise because they themselves implicitly define their terms, but rather because they disguise the definitions which imply them

Local Simulation Algorithms for Coulomb Interaction

Long ranged electrostatic interactions are time consuming to calculate in molecular dynamics and Monte-Carlo simulations. We introduce an algorithmic framework for simulating charged particles which modifies the dynamics so as to allow equilibration using a local Hamiltonian. The method introduces an auxiliary field with constrained dynamics so that the equilibrium distribution is determined by the Coulomb interaction. We demonstrate the efficiency of the method by simulating a simple, charged lattice gas.Comment: Last figure changed to improve demonstration of numerical efficienc

Фізико-хімічна геотехнологія

Розглянуто принципові засади геотехнологічного видобування різнома- нітних корисних копалин. Викладено питання розкриття та підготовки родовищ за допомогою свердловинної розробки, проаналізовано способи буріння і кріп- лення геотехнологічних свердловин, а такж застосоване обладнання. Розкрито сутність технологічних процесів, які виконуються при диспергуванні гірських порід, розчиненні солей, вилуговуванні металів, підземній виплавці сірки і га- зифікації вугілля, видобуванні в’язкої нафти та сланцьового газу. Навчальний посібник призначений для студентів, які навчаються за спе- ціальністю «Розробка родовищ та видобування корисних копалин», а також для студентів інших спеціальностей гірничих вузів і факультетів та інженерно- технічних працівників підприємств і проектних організацій гірничовидобувних галузей промисловості України

Integrating phylogenomics, phylogenetics, morphometrics, relative genome size and ecological niche modelling disentangles the diversification of Eurasian Euphorbia seguieriana s. l. (Euphorbiaceae)

Next generation sequencing has revolutionised biology. Restriction-associated DNA sequencing (RADseq) has primarily been used to study infraspecific relationships but has also been applied in multi-species phylogenomic analyses. In this study, we used a combination of phylogenomic (with RADseq data) and phylogenetic (with sequences of the nuclear internal transcribed spacer, ITS) methods to explore relationships within the taxonomically intricate Euphorbia seguieriana s. l., one of the most widespread Euphorbia taxa inhabiting zonal and extrazonal steppes from Iberia to Central Asia. In the inferred phylogenies the southeastern Balkan and Anatolian populations were clearly separated, supporting the distinction of E. niciciana from E. seguieriana at the species level. Within E. seguieriana, the populations from the Caucasus, Iran, and easternmost Anatolia were sister to all other populations based on RADseq, making necessary the description of a new, morphologically divergent subspecies, E. seguieriana subsp. armeniaca. Conversely, additional studies are needed to understand the status of E. seguieriana subsp. hohenackeri, which is sympatric with E. seguieriana subsp. armeniaca. Niche analyses indicated that differences in the climatic niche between E. niciciana and E. seguieriana are relatively small compared with the climatic differences between the regions over which they are distributed. Contrary to previous believes, E. niciciana and E. seguieriana are allopatric and have likely diverged during the Pleistocene in two different glacial refugia as suggested by distribution modelling. Euphorbia niciciana nowadays has a submediterranean distribution, occupying habitats that are slightly warmer, moister, and less seasonal in temperature but more seasonal in precipitation than E. seguieriana, a characteristic species of continental steppes. Using flow cytometry, we demonstrate that the relative genome sizes of E. niciciana and E. seguieriana differ significantly. Additionally, multivariate morphometric analyses of 56 morphological characters indicated clear morphological divergence of the two species. Importantly, we also provide a revised taxonomic treatment including formal nomenclatural changes, an identification key and species descriptions. Our study demonstrates that an integrative approach, combining modern phylogenomic methods with traditional phylogenetic, cytogenetic, environmental and morphological analyses can result in satisfactorily resolved relationships in intricate groups of closely related species. Finally, phylogenetic inference using ITS sequences is still a useful tool for resolving relationships among the taxa at the species level, but the phylogenomic approach based on RADseq data certainly provides better resolution both among and within species.Austrian Science Fund Tiroler Wissenschaftsfond