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1.
《Discrete Mathematics》2022,345(7):112898
The Hamming distance between two equal-length words u, v is the number of positions where u and v differ. The words u and v are said to be conjugates if there exist non-empty words such that and . The smallest value can take on is 0, when x and y commute. But, interestingly, the next smallest value can take on is 2 and not 1. In this paper, we consider conjugates and where . More specifically, we provide an efficient formula to count the number of length-n words over a k-letter alphabet that have a conjugate such that . We also provide efficient formulae for other quantities closely related to . Finally, we show that grows erratically: cubically for n prime, but exponentially for n even. 相似文献
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Benjamin Arras Ehsan Azmoodeh Guillaume Poly Yvik Swan 《Stochastic Processes and their Applications》2019,129(7):2341-2375
We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of . We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent. 相似文献
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We investigate cosmological dark energy models where the accelerated expansion of the universe is driven by a field with an anisotropic universe. The constraints on the parameters are obtained by maximum likelihood analysis using observational of 194 Type Ia supernovae(SNIa) and the most recent joint light-curve analysis(JLA) sample. In particular we reconstruct the dark energy equation of state parameter w(z) and the deceleration parameter q(z). We find that the best fit dynamical w(z) obtained from the 194 SNIa dataset does not cross the phantom divide line w(z) =-1 and remains above and close to w(z)≈-0.92 line for the whole redshift range 0 ≤ z ≤ 1.75 showing no evidence for phantom behavior. By applying the anisotropy effect on the ΛCDM model, the joint analysis indicates that ?_(σ0)= 0.0163 ± 0.03,with 194 SNIa, ?_(σ0)=-0.0032 ± 0.032 with 238 the SiFTO sample of JLA and ?_(σ0)= 0.011 ± 0.0117 with 1048 the SALT2 sample of Pantheon at 1σ′confidence interval. The analysis shows that by considering the anisotropy, it leads to more best fit parameters in all models with JLA SNe datasets. Furthermore, we use two statistical tests such as the usual χ_(min)~2/dof and p-test to compare two dark energy models with ΛCDM model. Finally we show that the presence of anisotropy is confirmed in mentioned models via SNIa dataset. 相似文献
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Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems. 相似文献
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In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum distances of these codes are determined and a recursive formula for the weight of a general codeword in these codes is given. 相似文献
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Direct Estimation of the Surface Location of Immobilized Functional Groups for Concerted Catalysis Using a Probe Molecule 下载免费PDF全文
Hiroto Noda Dr. Ken Motokura Prof. Dr. Yusuke Wakabayashi Kaori Sasaki Dr. Hiroo Tajiri Dr. Akimitsu Miyaji Dr. Sho Yamaguchi Prof. Dr. Toshihide Baba 《Chemistry (Weinheim an der Bergstrasse, Germany)》2016,22(15):5113-5117
The location of active sites during concerted catalysis by a metal complex and tertiary amine on a SiO2 surface is discussed based on the interaction between the functionalized SiO2 surface and a probe molecule, p‐formyl phenylboronic acid. The interactions of the probe molecule with the surface functionalities, diamine ligand, and tertiary amine, were analyzed by FT‐IR and solid‐state 13C and 11B MAS NMR. For the catalyst exhibiting high 1,4‐addition activity, the diamine ligand and tertiary amine base exist in closer proximity than in the catalyst with low activity. 相似文献
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