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...     

Exact upper bounds for the number of the polynomials with given discriminants

We generalize the result of Davenport on the sum of absolute values of discriminants of integer polynomials of degree three. For the first time, we find the exact upper bound for the number of polynomials with given discriminant in the class of cubic polynomials of bounded height for the whole interval of values of discriminants.     

Structural and magnetic properties of nanocrystalline bismuth manganite obtained by mechanochemical synthesis

We have studied the formation of BiMnO3 (BMO) nanocrystalline perovskite powder produced by high-energy milling of the constituent oxides. The crystal structure and the amount of crystalline and amorphous phases in the powder as a function of the milling time were determined with XRPD using Rietveld refinement. BMO perovskite formed directly from highly activated nano-sized constituent oxides after 240 min of milling and subsequently grew during prolonged milling. The morphology, structure, and chemical composition of the powder were investigated by SEM and TEM. A clear ferromagnetic transition was observed at T _C ~66 K for a sample milled for 240 min and increased with milling time. The magnetic hysteresis behavior is similar to that of a soft ferromagnet. The magnetic properties of the obtained BMO powders were found to change as a function of milling time in a manner consistent with variations in the nanocomposite microstructure.     

Positivity and matrix semigroups

We study various aspects of how certain positivity assumptions on complex matrix semigroups affect their structure. Our main result is that every irreducible group of complex matrices with nonnegative diagonal entries is simultaneously similar to a group of weighted permutations. We also consider the corresponding question for semigroups and discuss the effect of the assumption that a fixed linear functional has nonnegative values when restricted to a given semigroup.     

On Semitransitive Collections of Operators

A collection F of operators on a vector space V is said to be semitransitive if for every pair of nonzero vectors x and y in V there exists a member T of F such that either Tx = y or Ty = x (or both). We study semitransitive algebras and semigroups of operators. One of the main results is that if the underlying field is algebraically closed, then every semitransitive algebra of operators on a space of dimension n contains a nilpotent element of index n. Among other results on semitransitive semigroups, we show that if the rank of nonzero members of such a semigroup acting on an n-dimensional space is a constant k, then k divides n.     

Extremal property of some surfaces in n-dimensional Euclidean space

A surface Γ=(f ₁(X₁,..., x_m),...,f _n(x₁,..., x_m)) is said to be extremal if for almost all points of Γ the inequality $$\parallel a_1 f_1 (x_1 , \ldots ,x_m ) + \ldots + a_n f_n (x_1 , \ldots ,x_m )\parallel< H^{ - n - \varepsilon } ,$$ , where H=max(¦a _i¦) (i=1, 2, ..., n), has only a finite number of solutions in the integersa ₁, ...,a _n. In this note we prove, for a specific relationship between m and n and a functional condition on the functionsf ₁, ...,f _n, the extremality of a class of surfaces in n-dimensional Euclidean space.     

Electronic nose screening of limonene release from multicomponent essential oils encapsulated in pectin gels

Multicomponent essential oils Tagetes Minuta and Poleo as well as pure limonene were encapsulated in Tween doped-high methoxylated pectin gels. Optical microscopy reveals that the obtained gels containing limonene consisted in a highly heterogeneous oil-in-water emulsion stabilised by the gelled medium. The influence of limonene encapsulation in pectin gelation kinetics and the gel structural properties were followed by dynamic rheological measurements. An electronic nose device developed in our laboratory was used to follow the flavour release of the three systems in order to discriminate the samples according to the main components released to the headspace. PCA and Neural Network Analysis allowed us to discriminate Tagetes Minuta from Poleo due to the difference in their limonene content. It is remarkable that the fingerprints of encapsulated complex mixtures differ from those obtained for the non-encapsulated oils, showing a preferential release of some components. In the case of limonene, the effect of the encapsulated concentration on the detected odour was also studied.     

A multipoint problem with multiple nodes for linear hyperbolic equations

We establish conditions for the unique solvability of a multipoint (with respect to the time coordinate) problem with multiple nodes for linear hyperbolic equations with constant coefficients in the class of functions periodic in the space variable. We prove metric statements concerning lower bounds of small denominators that appear in the course of construction of a solution of the problem. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 10, pp. 1311–1316, October, 1999.     

Fluorescent Dimers of Merocyanine 540 (MC540) in the Gel Phase of Phosphatidylcholine Liposomes

Abstract— Fluorescence emission from merocyanine 540 (MC540) dimers was observed in dipalmitoylphosphatidylcholine (DPPC) vesicles. This unusual behavior was observed only for vesicles in the gel-phase state. No dimer fluorescence was observed either in monopalmitoylphosphati-dylcholine (C₁₆PC) micelles or in liquid-crystalline DPPC vesicles, indicating that dimer fluorescence efficiency increases in highly packed interfaces. The excitonic theory of Kasha was used to interpret the spectral features. The overall fluorescence quantum yield (φ_r) decreases with decreasing lipid: probe ratio, not only because of the presence of a weakly fluorescent dimer that absorbs a high fraction of the total absorbed light but also due to quenching of monomer emission. This suggests the existence of probe domains. The dimer fluorescence quantum yields (φ_m) were estimated in DPPC large unilamellar vesicles (LUV) and DPPC multilamellar vesicles. The dependence of φ_r with probe concentration is compatible with values of φ_m lower than 0.05. The dimerization equilibrium of MC540 in C₁₆PC micelles and DPPC-LUV was also studied. Apparent dimerization equilibrium constants, K_dapp and dimer absorption spectrum were calculated in C₁₆PC micelles for the first time. The dimerization equilibrium constant in DPPC-LUV was calculated and discussed in terms of the fraction of volume occupied by the lipid phase.     

New estimates for the number of integer polynomials with given discriminants

Lithuanian Mathematical Journal - In this paper, we propose a new method of upper bounds for the number of integer polynomials of the fourth degree with a given discriminant. By direct calculation...