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71.
David S. Dummit Brett A. Tangedal Paul B. van Wamelen. 《Mathematics of Computation》2004,73(247):1525-1546
Systematic computation of Stark units over nontotally real base fields is carried out for the first time. Since the information provided by Stark's conjecture is significantly less in this situation than the information provided over totally real base fields, new techniques are required. Precomputing Stark units in relative quadratic extensions (where the conjecture is already known to hold) and coupling this information with the Fincke-Pohst algorithm applied to certain quadratic forms leads to a significant reduction in search time for finding Stark units in larger extensions (where the conjecture is still unproven). Stark's conjecture is verified in each case for these Stark units in larger extensions and explicit generating polynomials for abelian extensions over complex cubic base fields, including Hilbert class fields, are obtained from the minimal polynomials of these new Stark units.
72.
For solutions of (inviscid, forceless, one dimensional) Burgers equation with random initial condition, it is heuristically shown that a stationary Feller–Markov property (with respect to the space variable) at some time is conserved at later times, and an evolution equation is derived for the infinitesimal generator. Previously known explicit solutions such as Frachebourg–Martin's (white noise initial velocity) and Carraro–Duchon's Lévy process intrinsic-statistical solutions (including Brownian initial velocity) are recovered as special cases. 相似文献
73.
The thermal migration of cyclic and acyclic organoboranes were studied. In most cases, a stereoselective 1,2-dyotropic migration was observed, allowing the stereocontrol of three contiguous chiral centers. Scope and limitations of this thermal migration are presented. 相似文献
74.
The periodic precipitation pattern formation in gelatinous media is interpreted as a moving boundary problem. The time law,
spacing law and width law are revisited on the basis of the new scenario. The explicit dependence of the geometric structure
on the initial concentrations of the reactants is derived. Matalon—Packter law, which relates the spacing coefficient with
the initial concentrations is reformulated removing many ambiguities and impractical parameters. Experimental results are
discussed to establish the significance of moving boundary concept in the diffusion controlled pattern forming systems 相似文献
75.
76.
Jean-Pierre Changeux Alain Connes M. B. DeBevoise Jean Petitot Mark Anspach 《Mathematical Intelligencer》2005,27(4):48-56
Conclusion The debate between Jean-Pierre Changeux and Alain Connes is one of the most, interesting to take place in recent years. It
re-frames in a very up-to-date context a whole series of traditional and difficult questions from the standpoint of the knowledge
and experience of two of the leading protagonists of contemporary science. To the choice presented by the neurobiologist between
a Platonist ontology and a neurocognitive psychology of mathematical activity, the mathematician replies with a conception
that is objective (neither ontological nor psychological) of the thoroughly consistent universe of mathematical idealities.
It is indeed in this three-sided arena that the major difficulties play themselves out. One of the great virtues of the book
is to cast a spotlight on this confrontation. 相似文献
77.
C.P. Paul P. Ganesh S.K. Mishra P. Bhargava J. Negi A.K. Nath 《Optics & Laser Technology》2007,39(4):800-805
This paper presents an investigation of laser rapid manufacturing (LRM) for Inconel-625 components. LRM is an upcoming rapid manufacturing technology, it is similar to laser cladding at process level with different end applications. In general, laser-cladding technique is used to deposit materials on the substrate either to improve the surface properties or to refurbish the worn out parts, while LRM is capable of near-net shaping the components by layer-by-layer deposition of the material directly from CAD model. In the present study, a high-power continuous wave (CW) CO2 laser system, integrated with a co-axial powder-feeding system and a three-axis workstation were used. The effect of processing parameters during LRM of Inconel-625 was studied and the optimum set of parameters for the maximum deposition rate was established employing Orthogonal L9 array of Taguchi technique. Results indicated that the powder feed rate and the scan speed contributed about 56% and 26%, respectively to the deposition rate, while the influence of laser power was limited to 10% only. Fabricated components were subjected to non-destructive testing (like—ultrasonic testing, dye-penetrant testing), tensile testing, impact testing, metallographic examinations and micro-hardness measurement. The test results revealed defect-free material deposition with improved mechanical strength without sacrificing the ductility. 相似文献
78.
Jean E. Taylor 《Discrete and Computational Geometry》1991,6(1):225-262
We bound the number of plane segments in a crystalline minimal surface S in terms of its Euler characteristic, the number
of line segments in its boundary, and a factor determined by the Wulff shapeW of its surface energy function. A major technique in the proofs is to quantize the Gauss map ofS based on the Gauss map ofW. One thereby bounds the number of positive-curvature corners and the interior complexity ofS.
The support of the National Science Foundation and the Air Force Office of Scientific Research and the hospitality of Stanford
University, where this paper was extensively rewritten, are gratefully acknowledged. 相似文献
79.
Various types of LU-factorizations for nonsingular matrices, where L is a lower triangular matrix and U is an upper triangular matrix, are defined and characterized. These types of LU-factorizations are extended to the general m × n case. The more general conditions are considered in the light of the structures of [C.R. Johnson, D.D. Olesky, P. Van den Driessche, Inherited matrix entries: LU factorizations, SIAM J. Matrix Anal. Appl. 10 (1989) 99-104]. Applications to graphs and adjacency matrices are investigated. Conditions for the product of a lower and an upper triangular matrix to be the zero matrix are also obtained. 相似文献
80.