Fast computation of Bernoulli, Tangent and Secant numbers

We consider the computation of Bernoulli, Tangent (zag), and Secant (zig or Euler) numbers. In particular, we give asymptotically fast algorithms for computing the first n such numbers in O(n^2.(log n)^(2+o(1))) bit-operations. We also give very short in-place algorithms for computing the first n Tangent or Secant numbers in O(n^2) integer operations. These algorithms are extremely simple, and fast for moderate values of n. They are faster and use less space than the algorithms of Atkinson (for Tangent and Secant numbers) and Akiyama and Tanigawa (for Bernoulli numbers).Comment: 16 pages. To appear in Computational and Analytical Mathematics (associated with the May 2011 workshop in honour of Jonathan Borwein's 60th birthday). For further information, see http://maths.anu.edu.au/~brent/pub/pub242.htm

Palpable Hits: Popular Music Forms and Teaching Early Modern Poetry

Recent pedagogical scholarship has engaged strenuously with the use of YouTube and other online platforms in the literature classroom. Stephen O’Neill, for one, champions video-sharing and similar media “in the interests of fostering various experiential, collaborative and peer-learning scenarios,” especially in tandem with the “array of Shakespeare content, which can potentially illuminate and deepen [learners’] understanding of the text and its diverse contexts” (190). In this essay, I discuss the advantages of sharing for this purpose online materials that have been developed by artists, instructors, students, and others—specifically, materials with a musical orientation. Along the way, I shall explain my own strategies in developing particular types of “Shakespeare content” that students have found useful in coming to terms with aspects of Shakespeare’s literary craft and that students have used as springboards for their own creative responses to his work. In describing this educational exchange, I make no claim about being “the only begetter” of student projects; as O’Neill notes, most of our students today are “digital natives,” quite at home with such widespread online practices as video remix and mashup (190). However, I have observed that setting 16th- and 17th-century texts (including, of course, Shakespeare’s) to popular music forms can elicit specifically musical responses from students and that an instructor’s willingness to share materials online can encourage students to bring video-sharing and other digital practices more richly into an educational setting that might initially have seemed unfriendly to such interventions

Effects of physical parameters in mashing on lautering performance

This thesis investigates performance parameters of unit operations in the brewery. It describes effects of the parameters temperature and agitation during mashing on mash properties. Mainly two properties are influenced by these parameters, the viscosity and the particle size distribution in the fines. It could be shown that both factors have significant influence on filterability of mash. In pilot scale and laboratory trials particle size effects in mash were investigated systematically. The importance of fine particles for lautering performance could be confirmed and quantified. The precipitation and aggregation of fine particles with increasing temperatures in the mash could be monitored for the first time. It could be shown that this parameter is not malt dependent. Mashes from different malts react in the same way. In laboratory trials it could be proved that the particle size parameter is more important than viscosity for filterability of mash. The parameters described above have been quantified and correlated with mash filtration parameters. This work provided a basis for the development of a computer model which describes mash separation in a lauter tun

Structure-mechanics relationships of collagen fibrils in the Osteogenesis Imperfecta Mouse model

The collagen molecule, which is the building block of collagen fibrils, is a triple helix of two α1(I) chains and one α2(I) chain. However, in the severe mouse model of osteogenesis imperfecta (OIM), deletion of the COL1A2 gene results in the substitution of the α2(I) chain by one α1(I) chain. As this substitution severely impairs the structure and mechanics of collagen-rich tissues at the tissue and organ level, the main aim of this study was to investigate how the structure and mechanics are altered in OIM collagen fibrils. Comparing results from atomic force microscopy imaging and cantilever-based nanoindentation on collagen fibrils from OIM and wild-type (WT) animals, we found a 33% lower indentation modulus in OIM when air-dried (bound water present) and an almost fivefold higher indentation modulus in OIM collagen fibrils when fully hydrated (bound and unbound water present) in phosphate-buffered saline solution (PBS) compared with WT collagen fibrils. These mechanical changes were accompanied by an impaired swelling upon hydration within PBS. Our experimental and atomistic simulation results show how the structure and mechanics are altered at the individual collagen fibril level as a result of collagen gene mutation in OIM. We envisage that the combination of experimental and modelling approaches could allow mechanical phenotyping at the collagen fibril level of virtually any alteration of collagen structure or chemistry.United States. Dept. of Defense. Presidential Early Career Award for Scientists and EngineersNational Science Foundation (U.S.) (CAREER Award

Current State of the Electrodynamic Dust Shield for Mitigation

The Electrodynamic Dust Shield (EDS) has been developed as a means to lift, transport and remove dust from surfaces for over 18 years in the Electrostatics and Surface Physics Laboratory at NASA Kennedy Space Center. Resent advances in the technology have allowed large-scale EDSs to be fabricated using roll-to-roll techniques for quick efficient processing. The aim of the current research is to demonstrate the 3-dimensional (3-D) version of the EDS and its applicability to various surfaces of interest throughout the Artemis program that require dust mitigation. The conventional two dimensional (2-D) EDS has been comprised of interdigitated electrodes across a surface of alternating polarity to setup non-uniform electric fields in the location of interest for which the particles need to be removed. The 2-D system can be designed to accommodate various phases. For example, the two phase EDS is comprised of two electrodes 180 out of phase, while the 3-phase EDS is 120 out of phase with the adjacent leg. 4-phase EDS configurations are also possible but for each square wave a high voltage signal is applied to each leg

Electrostatic Characterization of Lunar Dust Simulants

Lunar dust can jeopardize exploration activities due to its ability to cling to most surfaces. In this paper, we report on our measurements of the electrostatic properties of the lunar soil simulants. Methods have been developed to measure the volume resistivity, dielectric constant, chargeability, and charge decay of lunar soil. While the first two parameters have been measured in the past [Olhoeft 1974], the last two have never been measured directly on the lunar regolith or on any of the Apollo samples. Measurements of the electrical properties of the lunar samples are being performed in an attempt to answer important problems that must be solved for the development of an effective dust mitigation technology, namely, how much charge can accumulate on the dust and how long does the charge remain on surfaces. The measurements will help develop coatings that are compatible with the intrinsic electrostatic properties of the lunar regolith

Germanium Detector with Internal Amplification for Investigation of Rare Processes

Device of new type is suggested - germanium detector with internal amplification. Such detector having effective threshold about 10 eV opens up fresh opportunity for investigation of dark matter, measurement of neutrino magnetic moment, of neutrino coherent scattering at nuclei and for study of solar neutrino problem. Construction of germanium detector with internal amplification and perspectives of its use are described.Comment: 13 pages, latex, 3 figures, report at NANP-99, International Conference on Non-Accelerator Physics, Dubna, Russia, June 29- July 3, 1999. To be published in the Proceeding

Temperature-controlled interlayer exchange coupling in strong/weak ferromagnetic multilayers: a thermo-magnetic Curie-switch

We investigate a novel type of interlayer exchange coupling based on driving a strong/weak/strong ferromagnetic tri-layer through the Curie point of the weakly ferromagnetic spacer, with the exchange coupling between the strongly ferromagnetic outer layers that can be switched, on and off, or varied continuously in magnitude by controlling the temperature of the material. We use Ni-Cu alloy of varied composition as the spacer material and model the effects of proximity-induced magnetism and the interlayer exchange coupling through the spacer from first principles, taking into account not only thermal spin-disorder but also the dependence of the atomic moment of Ni on the nearest-neighbor concentration of the non-magnetic Cu. We propose and demonstrate a gradient-composition spacer, with a lower Ni-concentration at the interfaces, for greatly improved effective-exchange uniformity and significantly improved thermo-magnetic switching in the structure. The reported magnetic multilayer materials can form the base for a variety of novel magnetic devices, such as sensors, oscillators, and memory elements based on thermo-magnetic Curie-switching in the device.Comment: 15 pages, 5 figure