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181.
G.E. Farr 《Discrete Mathematics》2019,342(5):1510-1519
This paper continues the study of combinatorial properties of binary functions — that is, functions such that , where is a finite set. Binary functions have previously been shown to admit families of transforms that generalise duality, including a trinity transform, and families of associated minor operations that generalise deletion and contraction, with both these families parameterised by the complex numbers. Binary function representations exist for graphs (via the indicator functions of their cutset spaces) and indeed arbitrary matroids (as shown by the author previously). In this paper, we characterise degenerate elements – analogues of loops and coloops – in binary functions, with respect to any set of minor operations from our complex-parameterised family. We then apply this to study the relationship between binary functions and Tutte’s alternating dimaps, which also support a trinity transform and three associated minor operations. It is shown that only the simplest alternating dimaps have binary representations of the form we consider, which seems to be the most direct type of representation. The question of whether there exist other, more sophisticated types of binary function representations for alternating dimaps is left open. 相似文献
182.
We consider the problem of estimating a large rank-one tensor u ⊗k ∈ (ℝn)⊗k , k ≥ 3 , in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio λ Bayes = O(1) above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Remarkably, no polynomial-time algorithm is known that achieved this goal unless λ ≥ Cn(k − 2)/4 , and even powerful semidefinite programming relaxations appear to fail for 1 ≪ λ ≪ n(k − 2)/4 . In order to elucidate this behavior, we consider the maximum likelihood estimator, which requires maximizing a degree-k homogeneous polynomial over the unit sphere in n dimensions. We compute the expected number of critical points and local maxima of this objective function and show that it is exponential in the dimensions n , and give exact formulas for the exponential growth rate. We show that (for λ larger than a constant) critical points are either very close to the unknown vector u or are confined in a band of width Θ(λ−1/(k − 1)) around the maximum circle that is orthogonal to u . For local maxima, this band shrinks to be of size Θ(λ−1/(k − 2)) . These “uninformative” local maxima are likely to cause the failure of optimization algorithms. © 2019 Wiley Periodicals, Inc. 相似文献
183.
Xiao Sun Li Zhang Yu Cao Jinhua Li Atanas G. Atanasov Linfang Huang 《Biomedical chromatography : BMC》2020,34(12):e4949
Balanophora involucrata J. D. Hooker has been known to possess potential anti-inflammatory and antibacterial activities; however, its antiviral activity has not been evaluated so far. In order to find new neuraminidase inhibitors (NAIs), the neuraminidase (NA) inhibition activity of different B. involucrata extracts was evaluated. In this study, an in vitro NA inhibition assay was performed to identify which extract of B. involucrata exhibits (maximal) inhibitory activity against NA. Ultra high performance liquid chromatography/quadrupole time-of-flight–tandem mass spectroscopy (MS/MS) and molecular docking techniques were used to identify the specific compounds responsible for the anti-influenza activity of the extract, and to explore the potential natural NAIs. The ethyl acetate extract of B. involucrata exhibited significant inhibitory activity against NA with 50% inhibitory concentration (IC50) value of 159.5 μg/mL. Twenty compounds were identified according to the MS/MS spectra; among them two compounds (quercitrin and phloridzin) showed obvious inhibitory activity against NA, with IC50 of 311.76 and 347.32 μmol/L, respectively. This study suggested that B. involucrata can be a potential natural source of NAIs and may be useful in the fight against ferocious influenza viruses. 相似文献
184.
Probing the Catalytic Activity of Reduced Graphene Oxide Decorated with Au Nanoparticles Triggered by Visible Light
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Dr. Jiale Wang Dr. Fabiane J. Trindade Caroline B. de Aquino Joana C. Pieretti Prof. Dr. Sergio H. Domingues Prof. Dr. Romulo A. Ando Prof. Dr. Pedro H. C. Camargo 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(27):9889-9894
Hybrid materials in which reduced graphene oxide (rGO) is decorated with Au nanoparticles (rGO–Au NPs) were obtained by the in situ reduction of GO and AuCl4?(aq) by ascorbic acid. On laser excitation, rGO could be oxidized as a result of the surface plasmon resonance (SPR) excitation in the Au NPs, which generates activated O2 through the transfer of SPR‐excited hot electrons to O2 molecules adsorbed from air. The SPR‐mediated catalytic oxidation of p‐aminothiophenol (PATP) to p,p′‐dimercaptoazobenzene (DMAB) was then employed as a model reaction to probe the effect of rGO as a support for Au NPs on their SPR‐mediated catalytic activities. The increased conversion of PATP to DMAB relative to individual Au NPs indicated that charge‐transfer processes from rGO to Au took place and contributed to improved SPR‐mediated activity. Since the transfer of electrons from Au to adsorbed O2 molecules is the crucial step for PATP oxidation, in addition to the SPR‐excited hot electrons of Au NPs, the transfer of electrons from rGO to Au contributed to increasing the electron density of Au above the Fermi level and thus the Au‐to‐O2 charge‐transfer process. 相似文献
185.
Differential inequalities for polynomials generalizing the well-known Smirnov, Rahman, Schmeisser, and Bernstein inequalities are obtained.
相似文献186.
Dr. Man-Bo Li Daniels Posevins Dr. Karl P. J. Gustafson Dr. Cheuk-Wai Tai Dr. Andrey Shchukarev Dr. Youai Qiu Dr. Jan-E. Bäckvall 《Chemistry (Weinheim an der Bergstrasse, Germany)》2019,25(1):210-215
A highly selective and efficient oxidative carbocyclization/borylation of enallenols catalyzed by palladium immobilized on amino-functionalized siliceous mesocellular foam (Pd-AmP-MCF) was developed for diastereoselective cyclobutenol synthesis. The heterogeneous palladium catalyst can be recovered and recycled without any observed loss of activity or selectivity. The high diastereoselectivity of the reaction is proposed to originate from a directing effect of the enallenol hydroxyl group. Optically pure cyclobutenol synthesis was achieved by the heterogeneous strategy by using chiral enallenol obtained from kinetic resolution. 相似文献
187.
188.
Journal of Structural Chemistry - An analysis is presented for the results obtained in the studies initiated by A. E. Shvelashivili, Corresponding Member, Academy of Sciences of Georgia, and... 相似文献
189.
Radiophysics and Quantum Electronics - We consider whether it is possible in principle to retrieve the key parameters of the mixed layer in the upper ocean (its thickness, bulk eddy viscosity and... 相似文献
190.