The k-core of a graph G, Ck(G), is the maximal induced subgraph H ⊆ G such that δ(G) ≥ k, if it exists. For k > 0, the k-shell of a graph G is the subgraph of G induced by the edges contained in the k-core and not contained in the (k + 1)-core. The core number of a vertex is the largest value for k such that v ∈ Ck(G), and the maximum core number of a graph, Cb(G), is the maximum of the core numbers of the vertices of G. A graph G is k-monocore if Cb(G) = δ(G) = k. This paper discusses some basic results on the structure of k-cores and k-shells. In particular, an operation characterization of 2-monocore graphs is proven. Some applications of cores and shells to graph coloring and domination are considered.
We argue that the correction coefficients used to calculate Young’s modulus from resonant frequency of flexural vibration obtained by Štubňa and Trník (Journal of Mechanical Engineering - Strojniški vestnik. 52, 2006, p. 317) can be applied with very good precision only when Poisson’s ratio μ = 0.25 ± 0.05. We revise their results and propose more accurate correction coefficients for the first overtone and a prismatic sample with a square cross-section when their discrepancy is most evident. and V príspevku poukazujeme na to, že korekčné koeficienty, ktoré použili štubňa a trník na výpočet Youngovho modulu z rezonančnej frekvencie ohybových kmitov (Journal of Mechanical Engineering - strojniški vestnik. 52, 2006, p. 317), je možné použiť s veľmi dobrou presnosťou iba ak Poissonovo číslo μ = 0.25 ± 0.05. Po preskúmaní ich výsledkov navrhujeme presnejšie hodnoty korekčných koeficientov pre prvú vyššiu frekvenciu a hranolovú vzorku so štvorcovým prierezom, kedy je ich nesúlad najzjavnejší.
We analyzed several approaches dealing with the components of non-photochemical energy dissipation and introduced improved versions of the equations used to calculate this parameter. The usage of these formulae depends on the conditions of the sample (acclimation to dark or irradiation, presence or absence of the "actinic light"). The parameter known as "excess" cannot be used as a component of energy partitioning. In reality, this parameter reflects the differences between potential and actual quantum yields of photochemistry. and D. Kornyeyev, A. S. Holaday.
In this paper the author proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with variable exponent. As an application he proved the boundedness of certain sublinear operators on the weighted variable Lebesgue space. The proof of the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent does not contain any mistakes. But in the proof of the boundedness of certain sublinear operators on the weighted variable Lebesgue space Georgian colleagues discovered a small but significant error in my paper, which was published as R. A. Bandaliev, The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces, Czech. Math. J. 60 (2010), 327–337.
We compared photoinhibition sensitivity to high irradiance (HI) in wild-type barley (wt) and both its chlorina f104-nuclear gene mutant, that restricts chlorophyll (Chl) a and Chl b synthesis, and its f2-nuclear gene mutant, that inhibits all Chl b synthesis. Both Fv/Fm and ΦPS2 decreased more significantly in f2 than f104 and wt with duration of HI exposure. Chl degraded more rapidly in the f2 than in either f104 or wt. Most sensitivity to photoinhibition was exhibited for f2, whereas there was little difference in response to HI between the f104 and wt. The highest de-epoxidation (DES) value at every time point of exposure to HI was measured for f2, whereas the wt had the lowest value among the three strains. There were two lifetime components resolved for the conversion of violaxanthin (V) to zeaxanthin plus antheraxanthin (Z + A). The most rapid lifetime was around 6 min and the slower lifetime was >140 min, in both the mutants and wt. However, the wt and f104 both displayed larger amplitudes of both de-epoxidation lifetimes than f2. The difference between the final de-epoxidation state (DES = [Z + A]/[V + A + Z]) in the light compared to the dark expressed as ΔDES for wt, f104, and f2 was 0.630, 0.623, and 0.420, respectively. The slow lifetime component and overall larger ΔDES in the wt and f104 correlated with more photoprotection, as indicated by relatively higher Fv/Fm and ΦPS2, compared to the f2. Hence the photoprotection against photoinhibition has no relationship with the absolute DES value, but there is a strong relationship with de-epoxidation rate and relative extent or ΔDES. and Chang-Lian Peng ... [et al.].
The aim of this study was to find the principal parameters of surface tension of the blood and verify its possible correlation with some of the commonly assessed laboratory indicators that are affected by diseases with the expected possible changes in the surface tension of the blood. The surface tension of the blood was assessed in 150 patients. At the same time, the basic biochemical and hematological parameters were determined in these patients. The results have shown a close correlation between the surface blood tension and the activity of plasma gamma-glutamyltransferase. We assume that this relationship is based on the changes in concentration of bile acids in the blood during liver or bile duct afflictions., A. Kratochvíl, E. Hrnčíř., and Obsahuje bibliografii