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131.
Andrej Dujella 《The Ramanujan Journal》2008,15(1):37-46
A set of m positive integers is called a Diophantine m-tuple if the product of any two of them is one less than a perfect square. It is known that there does not exist a Diophantine
sextuple and that there are only finitely many Diophantine quintuples. On the other hand, there are infinitely many Diophantine
m-tuples for m=2, 3 and 4.
In this paper, we derive asymptotic estimates for the number of Diophantine pairs, triples and quadruples with elements less
than given positive integer N.
The author was supported by the Ministry of Science and Technology, Republic of Croatia, grants 0037110 and 037-0372781-2821. 相似文献
132.
We are interested in the problem of scheduling orders for different product types in a facility with a number of machines
in parallel. Each order asks for certain amounts of various different product types which can be produced concurrently. Each
product type can be produced on a subset of the machines. Two extreme cases of machine environments are of interest. In the
first case, each product type can be produced on one and only one machine which is dedicated to that product type. In the
second case, all machines are identical and flexible; each product type can be produced by any one of the machines. Moreover,
when a machine in this case switches over from one product type to another, no setup is required. Each order has a release
date and a weight. Preemptions are not allowed. The objective is minimizing the total weighted completion time of the orders.
Even when all orders are available at time 0, both types of machine environments have been shown to be NP-hard for any fixed
number (≥2) of machines. This paper focuses on the design and analysis of approximation algorithms for these two machine environments.
We also present empirical comparisons of the various algorithms. The conclusions from the empirical analyses provide insights
into the trade-offs with regard to solution quality, speed, and memory space.
Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.
This research is supported by the National Science Foundation through grants DMI-0300156 and DMI-0245603. 相似文献
133.
S. Jain P. Buckley 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):133-136
Persistence is studied in a financial context by mapping the time
evolution of the values of the shares quoted on the London Financial
Times Stock Exchange 100 index (FTSE 100) onto Ising spins.
By following the time dependence
of the spins, we find evidence for power law decay of the proportion
of shares that remain either above or below their 'starting'
values. As a result, we estimate a persistence exponent for the
underlying financial market to be θf∼0.5. 相似文献
134.
The coherent potential approximation (CPA) within full counting statistics (FCS) formalism is shown to be a suitable method to investigate average electric conductance, shot noise as well as higher order cumulants in disordered systems. We develop a similar FCS-CPA formalism for phonon transport through disordered systems. As a byproduct, we derive relations among coefficients of different phonon current cumulants. We apply the FCS-CPA method to investigate phonon transport properties of graphene systems in the presence of disorders. For binary disorders as well as Anderson disorders, we calculate up to the 8-th phonon transmission moments and demonstrate that the numerical results of the FCS-CPA method agree very well with that of the brute force method. The benchmark shows that the FCS-CPA method achieves 20 times more speedup ratio. Collective features of phonon current cumulants are also revealed. 相似文献
135.
Xingbing Chao 《中国物理 B》2021,30(8):84212-084212
Owing to the unique feature that the signal and reference waves of self-interference digital holography (SIDH) contain the same spatial information from the same point of object, compared with conventional digital holography, the SIDH has the special spatial coherence properties. We present a statistical optics approach to analyzing the formation of cross-correlation image in SIDH. Our study reveals that the spatial coherence of illumination light can greatly influence the imaging characteristics of SIDH, and the impact extent of the spatial coherence depends substantially on the recording distance of hologram. The theoretical conclusions are supported well by numerical simulation and optical experiments. 相似文献
136.
WilliamJ. Griffiths Therese Koal Yuqin Wang Matthias Kohl DavidP. Enot Hans‐Peter Deigner 《Angewandte Chemie (International ed. in English)》2010,49(32):5426-5445
Metabolomics is a truly interdisciplinary field of science, which combines analytical chemistry, platform technology, mass spectrometry, and NMR spectroscopy with sophisticated data analysis. Applied to biomarker discovery, it includes aspects of pathobiochemistry, systems biology/medicine, and molecular diagnostics and requires bioinformatics and multivariate statistics. While successfully established in the screening of inborn errors in neonates, metabolomics is now widely used in the characterization and diagnostic research of an ever increasing number of diseases. In this Review we highlight important technical prerequisites as well as recent developments in metabolomics and metabolomics data analysis with special emphasis on their utility in biomarker identification and qualification, as well as targeted metabolomics by employing high‐throughput mass spectrometry. 相似文献
137.
It is shown that polarized light can be polarization squeezed only if it exhibits sub-Poissonian statistics with the Mandel's Q factor less than − 1/2. 相似文献
138.
The generalized Kullback-Leibler divergence (K-Ld) in Tsallis statistics [constrained by the additive duality of generalized statistics (dual generalized K-Ld)] is here reconciled with the theory of Bregman divergences for expectations defined by normal averages, within a measure-theoretic framework. Specifically, it is demonstrated that the dual generalized K-Ld is a scaled Bregman divergence. The Pythagorean theorem is derived from the minimum discrimination information principle using the dual generalized K-Ld as the measure of uncertainty, with constraints defined by normal averages. The minimization of the dual generalized K-Ld, with normal averages constraints, is shown to exhibit distinctly unique features. 相似文献
139.
General classical statistical uncertainty relation is deduced and generalized to quantum uncertainty relation. We give a general unification theory of the classical statistical and quantum uncertainty relations, and prove that the classical limit of quantum mechanics is just classical statistical mechanics. It is shown that the classical limit of the general quantum uncertainty relation is the general classical uncertainty relation. Also, some specific applications show that the obtained theory is self-consistent and coincides with those from physical experiments. 相似文献
140.
H. Babacan 《Physics letters. A》2011,375(3):360-362
A relation between the generalized partition function (Tsallis) and density of states is established by using the method of integral transform which enables reducing some integral equations into the algebraic equations. Inverse Mellin transformation of this equation gives the density of states. Similar relation is also hold the for standard partition function (Boltzmann-Gibbs) and the density of states. Using these relations, we recover the density of states for the classical ideal gas within both statistics. 相似文献