Professor Ján Jakubík nonagenarian

This issue of Mathematica Slovaca is in honour of Prof. Ján Jakubík’s 90th birthday. We present here a brief account of his research (to date) and a personal sketch of the gentleman.     

Combinatorial aspects of generalized complementary basic matrices

This paper extends some properties of the generalized complementary basic matrices, in particular, in a combinatorial direction. These include inheritance (such as for Alternating Sign Matrices), spectral, and sign pattern matrix (including sign nonsingularity) properties.     

Graphs with a Small Number of Nonnegative Eigenvalues

In this paper, by means of computer checking, all simple graphs with at most two nonnegative eigenvalues, and all minimal simple graphs with exactly two (respectively, three) nonnegative eigenvalues are determined. Received: April 5, 1996 / Revised: May 2, 1997     

Spectrophotometric study of the formation of ternary complexes of iron(III) with some triphenylmethane dyes and cationic surfactants

The optimum conditions have been found for the formation of the ternary complexes of iron(III) with Chrome Azurol S (CAS), Eriochrome Cyanine R, and Pyrocatechol Violet in the presence of cetyltrimethylammonium (CTA), cetylpyridinium, or tetradecyldimethyl-benzylammonium ions. The pH range of the complex formation is limited mainly by the pertinent hydrolysis constants of the metal ions. The maximum absorbances were obtained for excess R and cationic surfactants, ensuring the formation of complexes with the highest R:Fe molar ratio. The method based on the Fe-CAS-CTA system (ε = 1.32 × 10⁵ liter mol⁻¹ cm⁻¹ at 628 nm) is most sensitive and is recommended for the spectrophotometric determination of iron.     

Lower bounds of the Laplacian graph eigenvalues

In this paper we prove that all positive eigenvalues of the Laplacian of an arbitrary simple graph have some positive lower bounds. For a fixed integer k 1 we call a graph without isolated vertices k-minimal if its kth greatest Laplacian eigenvalue reaches this lower bound. We describe all 1-minimal and 2-minimal graphs and we prove that for every k 3 the path P_k+1 on k + 1 vertices is the unique k-minimal graph.     

Thin SiC<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> layers prepared by hybrid laser–magnetron deposition

Thin SiC _x films were fabricated by hybrid laser–magnetron deposition system. KrF excimer laser was used for deposition of carbon and magnetron at the same time for sputtering of Si species. Films were fabricated in argon/hydrogen ambient with and without additional RF discharge. The substrate temperature was changed up to 700°C. Films topology, crystallinity, composition, chemical bonds and optical emission spectra were studied. Films were smooth and amorphous. Films of thickness 400–1000 nm were fabricated. Adhesion moved from 8 to 14 N, depending on deposition conditions.     

РАСПРЕДЕЛЕНИЕ ЗВЕЗД, ОБУСЛОВЛЕННЫ Х КОСМИ ЧЕСКИМ ИЗЛУЧЕНИЕМ, В ЛДЕРНЫХ ЗМУЛЬСИЯХ

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On the star distribution, caused by the cosmic rays in nuclear emulsions

     

On the existence of bounded noncontinuable solutions

This paper presents necessary and sufficient conditions for an n ‐th order differential equation to have a non‐continuable solution with finite limits of its derivatives up to the order l at the right‐hand end point of the interval of its definition, l ≤ n – 2 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A mean value theorem on bounded symmetric domains

Let be a Cartan domain of rank and genus and , , the Berezin transform on ; the number can be interpreted as a certain invariant-mean-value of a function around . We show that a Lebesgue integrable function satisfying , , must be -harmonic. In a sense, this result is reminiscent of Delsarte's two-radius mean-value theorem for ordinary harmonic functions on the complex -space , but with the role of radius played by the quantity .

     

On bipartite graphs with small number of laplacian eigenvalues greater than two and three

All connected bipartite graphs with exactly two Laplacian eigenvalues greater than two are determined. Besides, all connected bipartite graphs with exactly one Laplacian eigenvalue greater than three are determined.