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181.
Twin Paradox and the Logical Foundation of Relativity Theory 总被引:3,自引:0,他引:3
We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND. 相似文献
182.
Jerzy Król 《Foundations of Physics》2006,36(7):1070-1098
We analyse the proposition that the spacetime structure is modified at short distances or at high energies due to weakening of classical logic. The logic assigned to the regions of spacetime is intuitionistic logic of some topoi. Several cases of special topoi are considered. The quantum mechanical effects can be generated by such semi-classical spacetimes. The issues of: background independence and general relativity covariance, field theoretic renormalization of divergent expressions, the existence and definition of path integral measures, are briefly discussed in the proposal. The connection with some problems in foundations of mathematics and differential topology are also discussed. 相似文献
183.
184.
All-electron full-potential linearized augmented plane-wave calculations of the surface energy, work function, and interlayer spacings of close-packed metal surfaces are presented, in particular, for the free-electron-like metal surfaces, Mg(0 0 0 1) and Al(1 1 1), and for the transition metal surfaces, Ti(0 0 0 1), Cu(1 1 1), Pd(1 1 1), and Pt(1 1 1). We investigate the convergence of the surface energy as a function of the number of layers in the slab, using the Cu(1 1 1) surface as an example. The results show that the surface energy, as obtained using total energies of the slab and bulk from separate calculations, converges well with respect to the number of layers in the slab. Obviously, it is necessary that bulk and surface calculations are performed with the same high accuracy. Furthermore, we discuss the performance of the local-density and generalized gradient approximations for the exchange-correlation functional in describing the various surface properties. 相似文献
185.
Bram van Asch Henk Hollmann Henk van Tilborg 《Journal of Combinatorial Theory, Series A》2006,113(8):1594-1613
When Jack van Lint was appointed as full professor at the Eindhoven University of Technology at the age of 26 he combined a PhD in number theory with a very open scientific mind. It took a sabbatical visit to Bell Laboratories in 1966 to make him understand that a new and fascinating field of applied mathematics was emerging: discrete mathematics. It fascinated and inspired him for the rest of his life. When he passed away on September 28, 2004, he left behind a legacy of 18 books and 177 articles, covering many aspects of coding theory, combinatorics, and finite geometry.van Lint was also a strong international advocate of the role that discrete mathematics ought to play in modern applied mathematics curricula. Quite a few departments sought his advice. Years later, four different universities showed their appreciation by awarding him an honorary degree.This overview is an homage to van Lint's academic achievements and can serve as an introduction to his work for younger generations. 相似文献
186.
The decision problem for positively quantified formulae in the theory of linearly ordered Heyting algebras is known, as a special case of work of Kreisel, to be solvable; a simple solution is here presented, inspired by related ideas in Gödel-Dummett logic. 相似文献
187.
Density functional theory (DFT) slab calculations, mainly using the generalised gradient approximation, have been used to investigate the minimum energy structures of molecular SO2 and SO3 on Cu(1 1 1) and Ni(1 1 1) surfaces. On Ni(1 1 1) the optimal local adsorption structures are in close agreement with experimental results for both molecular species obtained using the X-ray standing wavefield technique, although for adsorbed SO2 the energetic difference between two alternative lateral positions of the lying-down molecule on the surface is marginally significant. On Cu(1 1 1) the results for adsorbed SO2, in particular, were sensitive to the DFT functional used in the calculations, but in all cases failed to reproduce the experimentally-established preference for adsorption with the molecular plane perpendicular to the surface. This result is discussed in the context of previously published DFT results for these species adsorbed on Cu(1 0 0). The optimal geometry found for SO3 on Cu(1 1 1) is similar to that on Ni(1 1 1), providing agreement with experiment regarding the molecular orientation but not the adsorption site. 相似文献
188.
Giuseppina Vannella 《Annali di Matematica Pura ed Applicata》2002,180(4):429-440
We consider a Neumann problem of the type -εΔu+F
′(u(x))=0 in an open bounded subset Ω of R
n
, where F is a real function which has exactly k maximum points.
Using Morse theory we find that, for ε suitably small, there are at least 2k nontrivial solutions of the problem and we give some qualitative information about them.
Received: October 30, 1999 Published online: December 19, 2001 相似文献
189.
D. Schütz 《K-Theory》2002,25(1):59-97
We use the one-parameter fixed-point theory of Geoghegan and Nicas to get information about the closed orbit structure of transverse gradient flows of closed 1-forms on a closed manifold M. We define a noncommutative zeta function in an object related to the first Hochschild homology group of the Novikov ring associated to the 1-form and relate it to the torsion of a natural chain homotopy equivalence between the Novikov complex and a completed simplicial chain complex of the universal cover of M. 相似文献
190.
Richard P. Fischer Arne W. Fliflet 《International Journal of Infrared and Millimeter Waves》2002,23(9):1297-1313
This paper presents the design and test of asymmetric quasioptical resonators for gyrotron applications, where most of the diffraction output coupling comes from the smaller of two mirrors. A computer code based on scalar diffraction theory is used to calculate the resonator losses and the electric field near the mirrors. Resonators with mirror separations approaching confocal have reduced side lobes in the diffraction patterns, which should allow for better power transmission and focusing. Cold tests have been performed at 94 and 141 GHz to measure the quality factor of the asymmetric resonators as a function of mirror separation and mirror misalignment. Typical resonator parameters include 65 cm mirror separation, 1-3% output coupling and 85% of the losses from the small mirror. A half-symmetric resonator with one flat and one curved mirror has also been investigated. The calculated values of Q are in reasonably good agreement with the cold test measurements. 相似文献