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131.
Zak Mesyan James D. Mitchell Michał Morayne Yann H. Péresse 《Mathematical Logic Quarterly》2012,58(6):424-433
Let $\mathbb {N}^\mathbb {N}Let $\mathbb {N}^\mathbb {N}$ be the semigroup of all mappings on the natural numbers $\mathbb {N}$, and let U and V be subsets of $\mathbb {N}^\mathbb {N}$. We write U?V if there exists a countable subset C of $\mathbb {N}^\mathbb {N}$ such that U is contained in the subsemigroup generated by V and C. We give several results about the structure of the preorder ?. In particular, we show that a certain statement about this preorder is equivalent to the Continuum Hypothesis. The preorder ? is analogous to one introduced by Bergman and Shelah on subgroups of the symmetric group on $\mathbb {N}$. The results in this paper suggest that the preorder on subsemigroups of $\mathbb {N}^\mathbb {N}$ is much more complicated than that on subgroups of the symmetric group. 相似文献
132.
The consequences for particle classification of the Volovich hypothesis that spacetime geometry is non-archimedean at the
Planck scale are explored. The multiplier groups and universal topological central extensions of the p-adic Poincaré and Galilean groups are determined.
The text was submitted by the author in English. 相似文献
133.
Valerio Lucarini 《Journal of statistical physics》2008,131(3):543-558
We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the
non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions
entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders
of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results
are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the
establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time
response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for
optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality
for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and
model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations
to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations.
In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response
theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved
in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and
Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation
theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations,
K-K relations might be robust tools for the definition of a self-consistent theory of climate change. 相似文献
134.
论假设检验中的两类错误 总被引:9,自引:1,他引:8
蔡越江.论假设检验中的两类错误.本文从假设检验的两个例子谈起,指出备择假设也是影响接区域的。接着论述了假设检验中的两类错误之间的关系。最后讨论如何同时控制两类错误。 相似文献
135.
W. Duke 《Compositio Mathematica》2003,136(1):103-115
Assuming the generalized Riemann hypothesis (GRH) and Artin conjecture for Artin L-functions, we prove that there exists a totally real number field of any fixed degree (>1) with an arbitrarily large discriminant whose normal closure has the full symmetric group as Galois group and whose class number is essentially as large as possible. One ingredient is an unconditional construction of totally real fields with small regulators. Another is the existence of Artin L-functions with large special values. Assuming the GRH and Artin conjecture it is shown that there exist an Artin L-functions with arbitrarily large conductor whose value at s=1 is extremal and whose associated Galois representation has a fixed image, which is an arbitrary nontrivial finite irreducible subgroup of GL(n, ) with property Gal
T
. 相似文献
136.
Xiaodong Zheng 《Proceedings of the American Mathematical Society》1998,126(12):3669-3679
Confidence interval construction for parameters of lattice distributions is considered. By using saddlepoint formulas and bootstrap calibration, we obtain relatively short intervals and bounds with coverage errors, in contrast with and coverage errors for normal theory intervals and bounds when the population distribution is absolutely continuous. Closed form solutions are also provided for the cases of binomial and Poisson distributions. The method is illustrated by some simulation results.
137.
Mohammad Azad Igor Chikalov Shahid Hussain Mikhail Moshkov Beata Zielosko 《Entropy (Basel, Switzerland)》2021,23(12)
Conventional decision trees use queries each of which is based on one attribute. In this study, we also examine decision trees that handle additional queries based on hypotheses. This kind of query is similar to the equivalence queries considered in exact learning. Earlier, we designed dynamic programming algorithms for the computation of the minimum depth and the minimum number of internal nodes in decision trees that have hypotheses. Modification of these algorithms considered in the present paper permits us to build decision trees with hypotheses that are optimal relative to the depth or relative to the number of the internal nodes. We compare the length and coverage of decision rules extracted from optimal decision trees with hypotheses and decision rules extracted from optimal conventional decision trees to choose the ones that are preferable as a tool for the representation of information. To this end, we conduct computer experiments on various decision tables from the UCI Machine Learning Repository. In addition, we also consider decision tables for randomly generated Boolean functions. The collected results show that the decision rules derived from decision trees with hypotheses in many cases are better than the rules extracted from conventional decision trees. 相似文献
138.
PENG Huan-Wu 《理论物理通讯》2005,43(1):81-88
Taking Dirac's large number hypothesis as true, we have shown [Commun. Theor. Phys. (Beijing, China) 42 (2004) 703] the inconsistency of applying Einstein's theory of general
relativity with fixed gravitation constant G to cosmology, and
a modified theory for varying G is found, which reduces to Einstein's theory outside the gravitating body for phenomena of short duration in small distances, thereby agrees with all the
crucial tests formerly supporting Einstein's theory. The modified
theory, when applied to the usual homogeneous cosmological model,
gives rise to a variable cosmological tensor term determined by the derivatives of G, in place of the cosmological constant term usually introduced ad hoc. Without any free
parameter the theoretical Hubble's relation obtained from the modified theory seems not in contradiction to observations, as Dr. Wang's preliminary analysis of the recent data indicates
[Commun. Theor. Phys. (Beijing, China) 42 (2004) 703]. As a complement to Commun. Theor. Phys. (Beijing, China) 42 (2004) 703 we shall study in this paper the modification of electromagnetism due to Dirac's large number hypothesis in more detail to show that the approximation of geometric optics still
leads to null geodesics for the path of light, and that the general
relation between the luminosity distance and the proper geometric
distance is still valid in our theory as in Einstein's theory, and
give the equations for homogeneous cosmological model involving
matter plus electromagnetic radiation. Finally we consider the
impact of the modification to quantum mechanics and statistical
mechanics, and arrive at a systematic theory of evolving natural
constants including Planck's ħ as well as Boltzmann's kB by finding out their cosmologically combined counterparts with factors of appropriate powers of G that may remain truly constant to cosmologically long time. 相似文献
139.
§ 1.Introduction WearegivenkindependentWishartdensitiesofthe (p +q)× (p +q)randomsymmetricpositivedefinitematricesG1,… ,Gktobeg(Gi) =Kexp -12 trR- 1i Gi Gi12 (ni- q-p- 1) ,(1 )wherei=1 ,… ,k,andRidenotesthepopulationcorrelationmatrixofthei thpopulationandKasagenericletterdenote… 相似文献
140.
The concept of Heider balance, usually applied to interpersonal relations, is generalized here to opinions gathered in surveys. At first, we compare four algorithms, which drive a matrix dataset to a balanced state. The criterion is that the final state obtained with an algorithm should be as close as possible to the initial state. The result is that deterministic differential equations work better than their Monte Carlo counterparts. Next, we apply the winning algorithms to the matrix of correlations between opinions gathered in American states between 1974 and 1998. The results are interpreted in terms of the classic comfort hypothesis (E. Babbie, 2007). 相似文献