Evaluation of education scenarios for acquiring digital competences of secondary school students in Slovenia

Central European Journal of Operations Research - Digital competences are among the most important competences in modern society, with the education system playing a key role in the acquisition of...     

Linearizability of d-webs, d ≥ 4, on two-dimensional manifolds

We find d − 2 relative differential invariants for a d-web, d ≥ 4, on a two-dimensional manifold and prove that their vanishing is necessary and sufficient for a d-web to be linearizable. If one writes the above invariants in terms of web functions f(x, y) and g ₄(x, y),..., g _d (x, y), then necessary and sufficient conditions for the linearizabilty of a d-web are two PDEs of the fourth order with respect to f and g ₄, and d − 4 PDEs of the second order with respect to f and g ₄,..., g _d . For d = 4, this result confirms Blaschke’s conjecture on the nature of conditions for the linearizabilty of a 4-web. We also give the Mathematica codes for testing 4- and d-webs (d > 4) for linearizability and examples of their usage.     

Comparison of the Temperature Effect on the π∗←n and π∗←π Electronic Transition Bands of NO<Subscript>3</Subscript><Superscript>−</Superscript>(aq)

The effect of temperature on the π∗←π transition band in the UV absorption spectrum of NO₃⁻(aq) centered at ≈200 nm was studied in the temperature range 10–70 ^∘C. The observed temperature independence of this band was in contrast to the significant influence of temperature on the nitrate π∗←n transition reported recently by us. However, taking into account the electronic states involved in both the transitions, it was concluded that this finding was in accordance with our previous assumption that interconversion between spectrally distinct (with respect to π∗←n band) nitrate species included the rupture/formation of hydrogen bond(s) in the hydration shell of the nitrate ion.     

Density functional study of the electric hyperfine interactions and the redox-structural correlations in the cofactor of nitrogenase. Analysis of general trends in (57)Fe isomer shifts

The influence of the interstitial atom, X, discovered in a recent crystallographic study of the MoFe protein of nitrogenase, on the electric hyperfine interactions of (57)Fe has been investigated with density functional theory. A semiempirical theory for the isomer shift, delta, is formulated and applied to the cofactor. The values of delta for the relevant redox states of the cofactor are predicted to be higher in the presence of X than in its absence. The analysis strongly suggests a [Mo(4+)4Fe(2+)3Fe(3+)] oxidation state for the S = 3/2 state M(N). Among C(4-), N(3-), and O(2-), oxide is found to be the least likely candidate for X. The analysis suggests that X should be present in the cofactor states M(OX) and M(R) as well as in the alternative nitrogenases. The calculations of the electric field gradients (EFGs) indicate that the small values for DeltaE(Q) in M(N) result from an extensive cancellation between valence and ligand contributions. X emerges from the analysis of the hyperfine interactions as an ionically bonded species. Its major effect is on the asymmetry parameters for the EFGs at the six equatorial sites, Fe(Eq). A spin-coupling scheme is proposed for the state [Mo(4+)4Fe(2+)3Fe(3+)] that is consistent with the measured (57)Fe A-tensors and DeltaE(Q) values for M(N) and identifies the unique site exhibiting the small A value with the terminal Fe site, Fe(T). The optimized structure of a cofactor model has been calculated for several oxidation states. The study reveals a contraction in the average Fe-Fe distance upon increasing the number of electrons stored in the cluster, in accord with extended X-ray absorption fine structure studies. The reliability of the adopted methodology for predicting redox-structural correlations is tested for cuboidal [4Fe-4S] clusters. The calculations reveal a systematic increase in the S...S sulfide distances, in quantitative agreement with the available data. These trends are rationalized by a simple electrostatic model.     

Transport in ceria electrolytes modified with sintering aids: effects on oxygen reduction kinetics

Small (2 mol%) cobalt oxide additions to ceria-gadolinia (CGO) materials considerably improve sinterability, making it possible to obtain ceramics with 95–99% density and sub-micrometre grain sizes at 1,170–1,370 K. The addition of Co causes a significant shift of the electrolytic domain to lower pO₂. This modification to the minor electronic conductivity of the electrolyte material has influence on the cathodic oxygen reduction reaction. The impedance technique is shown to provide information not only about polarisation resistance, but also about the active electrode area from analysis of the current constriction resistance. It is demonstrated that this current constriction resistance can be related to the minor electronic contributions to total conductivity in these materials. A simple imbedded grid approach gives control of the contact area allowing the properties of the electrolyte materials to be studied. A much lower polarisation resistance for the Co-containing CGO electrolyte is observed, which can be clearly attributed to an increased three-phase reaction area in the Co-containing material, as a consequence of elevated p-type conductivity.     

Thermal rearrangements of spiro[2.4]hepta-1,4,6-trienes

Thermolysis of spiro[2.4]hepta-1,4,6-triene (1a) at 50 degrees C yielded bicyclo[3.2.0]hepta-1,3,6-triene (5), which dimerized in two different fashions to form cyclobutanes. The 1,2-dimethyl and 1-propyl derivatives of 1a also rearranged at 50 degrees C, but at a faster rate, each yielding a pair of cyclobutane dimers. The structures of these symmetrical dimers were investigated by 1D and 2D NMR and NOE difference spectroscopy. Ab initio calculations indicated that the two strained olefins 1a and 5 had comparable energies about 50 kcal/mol lower than norborna-1(7),2,5-triene, which was thus excluded as a reaction intermediate.     

High-resolution four-dimensional 1H-13C NOE spectroscopy using methyl-TROSY, sparse data acquisition, and multidimensional decomposition

An approach for recording four-dimensional (4D) methyl (1)H-(13)C-(13)C-(1)H NOESY spectra with high resolution and sensitivity is presented and applied to Malate Synthase G (723 residues, 82 kDa). Sensitivity and resolution have been optimized using a highly deuterated, methyl-protonated sample in concert with methyl-TROSY, sparse data sampling in the three indirect dimensions, and 4D spectral reconstruction using multidimensional decomposition (MDD). A sparse data acquisition protocol is introduced that ensures that sufficiently long indirect acquisition times can be employed to exploit the decreased relaxation rates associated with methyl-TROSY, without increasing the duration of the 4D experiment beyond acceptable measurement times. In this manner, only a fraction ( approximately 30%) of the experimental data that would normally be needed to achieve a spectrum of high resolution is acquired. The reconstructed 4D spectrum is of similar resolution and sensitivity to three-dimensional (3D) (13)C-edited NOE spectra, is straightforward to analyze, and resolves ambiguities that emerge when 3D data sets only are considered.     

Off-resonance R(1rho) NMR studies of exchange dynamics in proteins with low spin-lock fields: an application to a Fyn SH3 domain

An (15)N NMR R(1rho) relaxation experiment is presented for the measurement of millisecond time scale exchange processes in proteins. On- and off-resonance R(1rho) relaxation profiles are recorded one residue at a time using a series of one-dimensional experiments in concert with selective Hartmann-Hahn polarization transfers. The experiment can be performed using low spin-lock field strengths (values as low as 25 Hz have been tested), with excellent alignment of magnetization along the effective field achieved. Additionally, suppression of the effects of cross-correlated relaxation between dipolar and chemical shift anisotropy interactions and (1)H-(15)N scalar coupled evolution is straightforward to implement, independent of the strength of the (15)N spin-locking field. The methodology is applied to study the folding of a G48M mutant of the Fyn SH3 domain that has been characterized previously by CPMG dispersion experiments. It is demonstrated through experiment that off-resonance R(1rho) data measured at a single magnetic field and one or more spin-lock field strengths, with amplitudes on the order of the rate of exchange, allow a complete characterization of a two-site exchange process. This is possible even in the case of slow exchange on the NMR time scale, where complementary approaches involving CPMG-based experiments fail. Advantages of this methodology in relation to other approaches are described.