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51.
Randall Dougherty Greg Hjorth 《Transactions of the American Mathematical Society》1999,351(5):1835-1844
We show that, for , the relation of -equivalence between infinite sequences of real numbers is Borel reducible to the relation of -equivalence (i.e., the Borel cardinality of the quotient is no larger than that of ), but not vice versa. The Borel reduction is constructed using variants of the triadic Koch snowflake curve; the nonreducibility in the other direction is proved by taking a putative Borel reduction, refining it to a reduction map that is not only continuous but `modular,' and using this nicer map to derive a contradiction.
52.
Greg Martin 《Transactions of the American Mathematical Society》1999,351(9):3641-3657
Every positive rational number has representations as Egyptian fractions (sums of reciprocals of distinct positive integers) with arbitrarily many terms and with arbitrarily large denominators. However, such representations normally use a very sparse subset of the positive integers up to the largest denominator. We show that for every positive rational there exist representations as Egyptian fractions whose largest denominator is at most and whose denominators form a positive proportion of the integers up to , for sufficiently large ; furthermore, the proportion is within a small factor of best possible. 相似文献
53.
A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary matrices delivers asymptotic freeness. In this paper we exhibit many other systems of random unitary matrices that, when used for conjugation, lead to freeness. We do so by first proving a general result asserting “asymptotic liberation” under quite mild conditions, and then we explain how to specialize these general results in a striking way by exploiting Hadamard matrices. In particular, we recover and generalize results of the second-named author and of Tulino, Caire, Shamai and Verdú. 相似文献
54.
Greg Orosi 《商业与工业应用随机模型》2015,31(4):515-527
In this work, we suggest a novel quadratic programming‐based algorithm to generate an arbitrage‐free call option surface. The empirical performance of the proposed method is evaluated using S&P 500 Index call options. Our results indicate that the proposed method provides a more precise fit to observed option prices than other alternative methodologies. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
55.
Consider a semigroup generated by matrices associated with an edge-coloring of a strongly connected, aperiodic digraph. We
call the semigroup Lie-solvable if the Lie algebra generated by its elements is solvable. We show that if the semigroup is
Lie-solvable then its kernel is a right group. Next, we study the Lie algebra generated by the kernel. Lie algebras generated
by two idempotents are analyzed in detail. We find that these have homomorphic images that are generalized quaternion algebras.
We show that if the kernel is not a direct product, then the Lie algebra generated by the kernel is not solvable by describing
the structure of these algebras. Finally, we discuss an infinite class of examples that are shown to always produce strongly
connected aperiodic digraphs having kernels that are not right groups. 相似文献
56.
Greg Friedman 《Proceedings of the American Mathematical Society》2004,132(10):3103-3109
Frame-spun knots are constructed by spinning a knot of lower dimension about a framed submanifold of . We show that all frame-spun knots are slice (null-cobordant).
57.
In Oman and Salminen [19], the authors introduce and study residually small rings, defined as follows: an infinite commutative ring R with identity is residually smallif for every r∈R?{0}, there exists an ideal Ir of R such that r?Ir and |R∕Ir|<|R|. The purpose of this note is to extend our study. In particular, we continue our investigation of residually small rings and then generalize this notion to modules. 相似文献
58.
According to a common line of criticism, Donald Davidson’s argument in “On the Very Idea of a Conceptual Scheme” is invalid because it moves illicitly from the relatively weak thesis that conceptual schemes cannot be incommensurable to the stronger thesis that the idea of a conceptual scheme itself is incoherent. I argue in this paper that such objections fail because they misunderstand the position that Davidson’s argument is intended to rule out. According to the “scheme-content dualism” Davidson targets, conceptual schemes differ only if they are incommensurable with one another. Thus, if Davidson has successfully shown the idea of incommensurability to be incoherent (as the critics in question grant), then he has shown “the very idea of a conceptual scheme” to be incoherent, as well. 相似文献
59.
60.
We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to solve hard problems. This experiment uses a particularly well-suited three quantum bit molecule and was made possible by introducing a technique that encodes general instances of the given optimization problem into an easily applicable Hamiltonian. Our results indicate an optimal run time of the adiabatic algorithm that agrees well with the prediction of a simple decoherence model. 相似文献