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.     

РЕАКЦИЯ (γ, р) НА ИНДИИ

Иамеряется энергети ческое и угловое расп ределение φотопрото нов из индия, облучаемого γ-квантами с энергией E_γ=17,6 Мэв u 14,8 Мзв. При сравнении энерге тического и углового распределения было о бнару-жено, что значительная час ть протонов образует ся при эвапорации и лишь около 3% прямым φо тоэφφектом. Из энергетического р аспределения найден ы энергии возбуждени я E _β ^* ядра¹¹⁴Cd, 3,8; 4,9; 5,6; 6,3 и. 7,6 Мэв.     

Effects of polymer–fiber interactions on rheology and flow behavior of suspensions of semi-flexible fibers in polymeric liquids

Rheological properties of suspensions of fibers in polymeric fluids are influenced by fiber–polymer interactions. In this paper, we investigate this influence from both experimental and modeling standpoints. In the experimental part of this investigation, we have changed the fiber–polymer interactions by treating the surface of the fibers. The resulting effects are observed using scanning electron microscopy and dynamic mechanical analysis techniques and quantified from the measurements of the viscosity in the start-up of shear flows and dynamic tests in the linear viscoelastic range region. The results are interpreted with the help of a mesoscopic rheological model developed for suspensions of fibers in viscoelastic fluids.     

Dominant matrices and max algebra

We study the class of so-called totally dominant matrices in the usual algebra and in the max algebra in which the sum is the maximum and the multiplication is usual. It turns out that this class coincides with the well known class of positive matrices having positive the determinants of all 2×2 submatrices. The closure of this class is closed not only with respect to the usual but also with respect to the max multiplication. Further properties analogous to those of totally positive matrices are proved and some connections to Monge matrices are mentioned.     

Further results on the least eigenvalue of connected graphs

In this paper, we identify within connected graphs of order n and size n+k (with and ) the graphs whose least eigenvalue is minimal. It is also observed that the same graphs have the largest spectral spread if n is large enough.     

On the Parameterization of Rational Ringed Surfaces and Rational Canal Surfaces

Ringed surfaces and canal surfaces are surfaces that contain a one-parameter family of circles. Ringed surfaces can be described by a radius function, a directrix curve and vector field along the directrix curve, which specifies the normals of the planes that contain the circles. In particular, the class of ringed surfaces includes canal surfaces, which can be obtained as the envelopes of a one-parameter family of spheres. Consequently, canal surfaces can be described by a spine curve and a radius function. We present parameterization algorithms for rational ringed surfaces and rational canal surfaces. It is shown that these algorithms may generate any rational parameterization of a ringed (or canal) surface with the property that one family of parameter lines consists of circles. These algorithms are used to obtain rational parameterizations for Darboux cyclides and to construct blends between pairs of canal surfaces and pairs of ringed surfaces.     

A bivariate INAR(1) time series model with geometric marginals

In this paper we introduce a simple bivariate integer-valued time series model with positively correlated geometric marginals based on the negative binomial thinning mechanism. Some properties of the model are considered. The unknown parameters of the model are estimated using the modified conditional least squares method.