544 research outputs found
On unbalanced Boolean functions with best correlation immunity
It is known that the order of correlation immunity of a nonconstant
unbalanced Boolean function in variables cannot exceed ; moreover,
it is if and only if the function corresponds to an equitable
-partition of the -cube with an eigenvalue of the quotient matrix.
The known series of such functions have proportion , , or of
the number of ones and zeros. We prove that if a nonconstant unbalanced Boolean
function attains the correlation-immunity bound and has ratio of the
number of ones and zeros, then is divisible by . In particular, this
proves the nonexistence of equitable partitions for an infinite series of
putative quotient matrices. We also establish that there are exactly
equivalence classes of the equitable partitions of the -cube with quotient
matrix and classes, with . These
parameters correspond to the Boolean functions in variables with
correlation immunity and proportion and , respectively (the case
remains unsolved). This also implies the characterization of the
orthogonal arrays OA and OA.Comment: v3: final; title changed; revised; OA(512,11,2,6) discusse
Some results on the Wiener index related to the \v{S}olt\'{e}s problem of graphs
The Wiener index, , of a connected graph is the sum of distances
between its vertices. In 2021, Akhmejanova et al. posed the problem of finding
graphs with large . It is shown that there is a graph with for any
integer . In particular, there is a regular graph of even degree with
this property for any odd . The proposed approach allows to construct
new families of graphs with when the order of
increases.Comment: 9 pages, 3 tables, 7 figure
Політичні еліти: основи концептуалізації
Воробйов В. А. Політичні еліти: основи концептуалізації / В. А.Воробйов // Людина, суспільство, політика: актуальні виклики сучасності: матеріали міжнародної науково-практичної конференції (м. Одеса, 22-23 травня 2014 р.) / за загальною редакцією д.ю.н., професора В.М. Дрьоміна. – м. Одеса : Національний університет «Одеська юридична академія», 2014. – С. 44-46
Characteristics of water and ion exchange of Elodea nuttallii cells at high concentrations of lanthanides
© 2016 Elsevier LtdChanges of diffusive permeability of membranes of Elodea nuttallii cells following a short-term (60 min) treatment with high concentrations of lanthanides were recorded by the 1H NMR-diffusometry and conductometry methods. The 1-h infiltration of segments of Elodea nuttallii internodes in 10 mM solutions of nitrates of La, Nd and Lu resulted in the increased leakage of electrolytes from cells, but has no effect on a water diffusive permeability of membranes. In samples subjected to a 30 min pretreatment with a water channel inhibitor HgCl2 the water diffusive permeability of membranes (Pd) drops down under the influence of lanthanides, as well as an outcome of electrolytes. To explain the observed effects the change of spontaneous curvature of membrane lipid layer has been taken into consideration. The interaction of lanthanides with lipids of plasmalemma leads to the negative spontaneous curvature of lipid layer at which membrane channels are unclosed. Blocking of the ionic and water channels by mercury ions compensate the effect of change of spontaneous curvature of lipid layer
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