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101.
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
102.
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
103.
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
104.
Differential inequalities for polynomials generalizing the well-known Smirnov, Rahman, Schmeisser, and Bernstein inequalities are obtained.
相似文献105.
106.
Vanessa R. Machado Louis P. Sandjo Giovanni L. Pinheiro Milene H. Moraes Mario Steindel Moacir G. Pizzolatti 《Natural product research》2018,32(3):275-281
The natural product lupeol 1 was isolated from aerial parts of Vernonia scorpioides with satisfactory yield, which made it viable to be used as starting material in semisynthetic approach. Ten lupeol derivatives 2–11 were prepared by classical procedures. Including, five new esters derivatives 7–11, which were obtained by structural modifications in the isopropylidene fragment. All semisynthetic compounds and lupeol 1–11 were confirmed by 1H NMR, 13C NMR and HRMS. Their antiprotozoal activity was evaluated in vitro against L. amazonensis and T. cruzi. Derivative 6 showed the best antitrypanosomal activity (IC50 = 12.48 μg/mL) and the lowest cytotoxic derivative (CC50 = 161.50 μg/mL). The mechanism of action of the most active derivatives (4, 6 and 11) is not dependent from the enzyme trypanothione reductase. 相似文献
107.
The structure, chemical composition, and magnetic properties of electrochemically deposited nanocrystalline Co-Ni-Fe films
were investigated using a number of techniques. A high saturation magnetic induction up to B
s
= 21 kG was attained. An enhancement of the saturation magnetization compared to the ideal anticipated one was revealed,
which correlated with the nonlinear behavior of the structural phase composition and lattice parameters with the change of
the composition.
The text was submitted by the authors in English. 相似文献
108.
N. I. Golovina G. N. Nechiporenko G. G. Nemtsev G. P. Dolganova V. P. Roshchupkin D. B. Lempert G. B. Manelis 《Russian Journal of Applied Chemistry》2007,80(1):24-30
Methods for phase stabilization of ammonium nitrate were sought for in order to considerably expand the application area of this oxidizing agent in various-purpose self-combustible formulations, including that in a new generation of gas-generating formulations for automobile air bags. New methods for stabilization of ammonium nitrate were studied and, in particular, a search was made for organic compounds that can stabilize ammonium nitrate even at their low content. The mechanism of phase state stabilization of ammonium nitrate by compounds of this kind was examined. 相似文献
109.
In this study, stoichiometric protonation constants of L-tyrosine, L-cysteine, L-tryptophane, L-lysine, and L-histidine, and
their methyl and ethyl esters in water and ethanol–water mixtures of 30, 50, and 70% ethanol (v/v), were determined potentiometrically
using a combined pH electrode system calibrated as the concentration of hydrogen ion. Titrations were performed at 25∘C and the ionic strength of the medium was maintained at 0.10 mol⋅L−1 using sodium chloride. Protonation constants were calculated by using the BEST computer program. The effect of solvent composition
on the protonation constants is discussed. The log10 K2 values of esters generally decreased with increasing ethanol content. However, the log10 K1 values of the esters of L-tyrosine, L-cysteine, and L-tryptophane were found to increase with increasing ethanol content
in contrast those of L-lysine and L-histidine esters. 相似文献
110.
G. Panina 《Central European Journal of Mathematics》2003,1(2):157-168
All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible
with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples
of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual
polytope. 相似文献