An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota

We sketch the outlines of Gian Carlo Rota's interaction with the ideas that Hermann Grassmann developed in his Ausdehnungslehre of 1844 and 1862, as adapted and explained by Giuseppe Peano in 1888. This leads us past what Rota variously called 'Grassmann-Cayley algebra', or 'Peano spaces', to the Whitney algebra of a matroid, and finally to a resolution of the question "What, really, was Grassmann's regressive product?". This final question is the subject of ongoing joint work with Andrea Brini, Francesco Regonati, and William Schmitt. The present paper was presented at the conference "The Digital Footprint of Gian-Carlo Rota: Marbles, Boxes and Philosophy" in Milano on 17 Feb 2009. It will appear in proceedings of that conference, to be published by Springer Verlag.Comment: 28 page

The linear mirror for solar energy exploitation

We describe a simple two-dimensional array of plane mirrors operated by only two motors, which collects efficiently Sun light in order to produce electrical power at about the cost of oil. The system preserves the merits of previous state-of-the-art solar power plants but is simpler and by far less expensive. A first prototype has been operated at the Physics Department of the University of Udine providing a power of 0.56 kW per m2 of mirror surface in mid November

On-the-fly Uniformization of Time-Inhomogeneous Infinite Markov Population Models

This paper presents an on-the-fly uniformization technique for the analysis of time-inhomogeneous Markov population models. This technique is applicable to models with infinite state spaces and unbounded rates, which are, for instance, encountered in the realm of biochemical reaction networks. To deal with the infinite state space, we dynamically maintain a finite subset of the states where most of the probability mass is located. This approach yields an underapproximation of the original, infinite system. We present experimental results to show the applicability of our technique

Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle dies with instantaneous rate $\mu_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics

Design and construction of new central and forward muon counters for CDF II

New scintillation counters have been designed and constructed for the CDF upgrade in order to complete the muon coverage of the central CDF detector, and to extend this coverage to larger pseudorapidity. A novel light collection technique using wavelength shifting fibers, together with high quality polystyrene-based scintillator resulted in compact counters with good and stable light collection efficiency over lengths extending up to 320 cm. Their design and construction is described and results of their initial performance are reported.Comment: 20 pages, 15 figure

Spectral properties of zero temperature dynamics in a model of a compacting granular column

The compacting of a column of grains has been studied using a one-dimensional Ising model with long range directed interactions in which down and up spins represent orientations of the grain having or not having an associated void. When the column is not shaken (zero 'temperature') the motion becomes highly constrained and under most circumstances we find that the generator of the stochastic dynamics assumes an unusual form: many eigenvalues become degenerate, but the associated multi-dimensional invariant spaces have but a single eigenvector. There is no spectral expansion and a Jordan form must be used. Many properties of the dynamics are established here analytically; some are not. General issues associated with the Jordan form are also taken up.Comment: 34 pages, 4 figures, 3 table

Precise Critical Exponents for the Basic Contact Process

We calculated some of the critical exponents of the directed percolation universality class through exact numerical diagonalisations of the master operator of the one-dimensional basic contact process. Perusal of the power method together with finite-size scaling allowed us to achieve a high degree of accuracy in our estimates with relatively little computational effort. A simple reasoning leading to the appropriate choice of the microscopic time scale for time-dependent simulations of Markov chains within the so called quantum chain formulation is discussed. Our approach is applicable to any stochastic process with a finite number of absorbing states.Comment: LaTeX 2.09, 9 pages, 1 figur

Устройство для перемещения датчиков в магнитном поле малогабаритного бетатрона

Рассматривается возможность увеличения точности измерений характеристик магнитного поля посредством более точной установки датчиков в исследуемой точке

Ethyl 1-(2-hy­droxy­eth­yl)-2-p-tolyl-1H-benzimidazole-5-carboxyl­ate

The asymmetric unit of the title compound, C19H20N2O3, contains two mol­ecules (A and B) with slightly different orientations of the ethyl groups with respect to the attached carboxyl­ate groups. Intra­molecular C—H⋯O hydrogen bonds generate S(8) ring motifs in both mol­ecules A and B. In each mol­ecule, the benzimidazole ring system is essentially planar, with maximum deviations of 0.023 (1) and 0.020 (1) Å, respectively, for mol­ecules A and B. The dihedral angle between the benzimidazole ring system and the phenyl ring is 37.34 (5)° for mol­ecule A and 42.42 (5)° for mol­ecule B. In the crystal, O—H⋯N and C—H⋯O hydrogen bonds link the mol­ecules into [100] columns with a cross-section of two-mol­ecule by two-mol­ecule wide, and further stabilization is provided by weak C—H⋯π and π–π inter­actions [centroid separations = 3.5207 (7) and 3.6314 (8) Å]

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017