Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar

This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for first-order automated reasoning. The main differences to SystemOnTPTP are the use of the Mizar language that is oriented towards human mathematicians (rather than the pure first-order logic used in SystemOnTPTP), and setting the service in the context of the large Mizar Mathematical Library of previous theorems,definitions, and proofs (rather than the isolated problems that are solved in SystemOnTPTP). These differences poses new challenges and new opportunities for automated reasoning and for proof presentation tools. This paper describes the overall structure of MizAR, and presents the automated reasoning systems and proof presentation tools that are combined to make MizAR a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial Intelligence and Symbolic Computation AISC 201

Some calculations on the ground and lowest-triplet state of the helium isoelectronic sequence with the nucleus in motion

The method described in the preceding paper for the solution of two-electron atoms, which was used to calculate the 1 1S and 2 3S states of helium and heliumlike atoms within the fixed-nucleus approximation, has been applied to the case where all three particles are in relative motion. The solutions in the present case automatically include the effects of the mass polarization term and are compared with the results obtained for the term by using first-order perturbation theory with the fixed-nucleus wave functions. The input data for a particular atom consist of the atomic number, as before, but now the corresponding mass of the nucleus must be given also. Nonrelativistic energies with the nuclear mass included in the calculation have been obtained for the 1 1S and 2 3S states for Z ranging from 1 to 10. The energy with the nucleus in motion can be expressed only to eight significant figures (SF's) given the accuracy with which the relevant physical constants are known at present. All the results given here are computed as if these constants were known to ten SF's so that errors not incurred due to rounding. Convergence of the energies to ten SF's for both the singlet and triplet state was reached with a matrix of size 444 for Z values from 2 to 10. Convergence for the H- ion was a little slower

Kink Chains from Instantons on a Torus

We describe how the procedure of calculating approximate solitons from instanton holonomies may be extended to the case of soliton crystals. It is shown how sine-Gordon kink chains may be obtained from CP1 instantons on a torus. These kink chains turn out to be remarkably accurate approximations to the true solutions. Some remarks on the relevance of this work to Skyrme crystals are also made.Comment: latex 17 pages, DAMTP 94-7

Sintered aluminium heat pipe (SAHP)

This work is the product of an ongoing PhD project in the School of the Built and Natural Environment of Northumbria University in collaboration with the University of Liverpool and Thermacore Europe Ltd. The achievements at the end of the first year are summarized. The main objective of the project is to develop an aluminum ammonia heat pipe with a sintered wick structure. Currently available ammonia heat pipes mainly use extruded axially grooved aluminum tubes as a capillary wick. There have been a few attempts of employing porous steel or nickel wicks in steel tubes with ammonia as the working fluid (Bai, Lin et al. 2009)although it is a common practice in loop heat pipes but there is no report of aluminum-ammonia heat pipes porous aluminium wick structures. The main barrier is the difficulty of sintering aluminum powders to manufacture porous wicks. So far during this project promising sintered aluminum heat pipe samples have been manufactured using the Selective Laser Melting (SLM) technique with various wick characteristics. This SLM method has proven to be capable of manufacturing very complicated wick structures with different thickness, porosity, permeability and pore sizes in different regions of a heat pipe. In addition the entire heat pipe including the end cap, outer tube wall, wick and the fill tube can be generated in a single process

Rapid Design and Manufacture of Ultralight Cellular Materials

This paper details the design, manufacture and testing of regular metallic lattice structures with unit cell sizes in the range 0.8mm to 5mm and truss elements of 100-500 µm in diameter [1]. The structures were manufactured using Selective Laser Melting (SLM) technology from 316L stainless steel. Compression tests have shown yield loadings of over 3.5kN despite being only 18mm by 18mm by 10mm in height, the results are favourably comparable to current commercially available metallic foams. Software has been developed that creates slice files without the use of CAD software or STL files and is capable of producing lattices within a volume defined by a STL file.Mechanical Engineerin

'Two Cultures' in the Study of Religion? - A Response to Håkan Rydving

No abstract available

Precise predictions for Λb→Λc\Lambda_b \to \Lambda_c semileptonic decays

We calculate the $\Lambda_b \to \Lambda_c \ell \nu$ form factors and decay rates for all possible $b\to c \ell\bar\nu$ four-Fermi interactions beyond the Standard Model, including nonzero charged lepton masses and terms up to order $\alpha_s\, \Lambda_\text{QCD}/m_{c,b}$ and $\Lambda_\text{QCD}^2/m_c^2$ in the heavy quark effective theory. At this order, we obtain model independent predictions for semileptonic $\Lambda_b \to \Lambda_c$ decays in terms of only two unknown sub-subleading Isgur-Wise functions, which can be determined from fitting LHCb and lattice QCD data. We thus obtain model independent results for $\Lambda_b\to \Lambda_c\ell\bar\nu$ decays, including predictions for the ratio $R(\Lambda_c) = {\cal B}(\Lambda_b\to \Lambda_c \tau\bar\nu) / {\cal B}(\Lambda_b\to \Lambda_c \mu\bar\nu)$ in the presence of new physics, that are more precise than prior results in the literature, and systematically improvable with better data on the decays with $\mu$ (or $e$) in the final state. We also explore tests of factorization in $\Lambda_b \to \Lambda_c\pi$ decays, and emphasize the importance of measuring at LHCb the double differential rate $d^2\Gamma(\Lambda_b\to\Lambda_c\ell\bar\nu) / (d q^2\, d\cos\theta)$, in addition to the $q^2$ spectrum.Comment: 30 pages, 7 figures, 1 tabl