K. Bezdek and T. Odor proved the following statement in : If a covering ofE3 is a lattice packing of the convex compact bodyK with packing lattice Λ (K is a Λ-parallelotopes) then there exists such a 2-dimensional sublattice Λ′ of Λ which is covered by the set ∪(K+z∣z ∈ Λ′). (K ∪L(Λ′) is a Λ′-parallelotopes). We prove that the statement is not true in the case of the dimensionsn=6, 7, 8.
We give a weighted Hermite–Fejr type interpolation process on the half line. On suitable Laguerre nodes it converges for
continuous functions which fulfil a certain not too fast growing property at zero and infinity.
We give a weighted Hermite-Fejr-type interpolatory method on the real line, which is a positive operator on “good” matrices.
We give an example on “good” interpolatory matrix by weighted Fekete points. To prove the convergence theorem we need the
generalization of “Rodrigues’ property”.
The xeromesophilous loess grassland association,
, had been outlined seven years ago by the author (Horváth 2002). This first publication of the association provided a valid name for it, characterised the community by dominant, constant and typical species, as well as the abiotic conditions and attributes of small-scale spatial patterns. Based on these parameters, the new coenotaxon has been separated from xerophilous loess grassland association (
Zólyomi ex Soó 1964). Nevertheless, the prior description has to be considered incomplete, because it reported only the synthetic attributes of species occurrences in the surveyed stands of the community. In this paper, the description of the association is validated with offering a complete phytosociological table and selecting the holotype relevé. In addition, the author summarises the floristical, coenological and ecological characters of the association. It has to be considered as a well-distinguishable xeromesophilous coenotaxon of the Pannonian loess vegetation, stands of which constantly occur on northern or northeastern slopes. It has high nature conservancy values because many forest and forest-steppe species of the zonal forest-steppe vegetation of the Great Hungarian Plain could only survive within it.
In a Freud-type weighted (w) space, introducing another weight (v) with infinitely many roots, we give a complete and minimal system with respect to vw, by deleting infinitely many elements from the original orthonormal system with respect to w. The construction of the conjugate system implies an interpolation problem at infinitely many nodes. Besides the existence, we give some convergence properties of the solution.
Simultaneous TG, DTG, DTA measurements along with the continuous and selective monitoring of carbon monoxide, carbon dioxide and water evolved were carried out on K3[M(C2O4)3].3H2O-type transition metal complexes (whereM=Cr, Fe and Co). Based on the comparison of the recorded curves a detailed description of the decomposition mechanism was possible. In the case of the cobalt complex an exothermic process corresponding to modification of electron configuration is superimposed on the endothermic dehydration reaction.