Porosity and the L p -conjecture

Recently, Abtahi, Nasr-Isfahani, and Rejali [1] have shown that if G is a locally compact but not compact topological group and p > 2, then there are two functions, f and g, such that the convolution f*g{f\star g} is equal to ∞ on some set of positive measure. In the paper we show the nonexistence of f*g{f\star g} on a set of positive measure for (f, g) from a complement of a σ-porous set.     

Functional Central Limit Theorem for Additive Functionals of <Emphasis Type="Italic">α</Emphasis>-stable Processes

Let β be a standard Brownian motion, let X be an α-stable process, and let f=[^(m)]f=\widehat \mu be the Fourier transform of a discrete measure. It is shown that weakly in C([0, + ∞ )),

Time irregularity of generalized Ornstein–Uhlenbeck processes

This Note is concerned with the properties of solutions to a linear evolution equation perturbed by a cylindrical Lévy process. It turns out that solutions, under rather weak requirements, do not have a càdlàg modification. Some natural open questions are also stated.     

On the completeness of a metric related to the Bergman metric

We study the completeness of a metric which is related to the Bergman metric of a bounded domain (sometimes called the Burbea metric or Fuks metric). We provide a criterion for its completeness in the spirit of the Kobayashi criterion for the completeness of the Bergman metric. In particular we prove that in hyperconvex domains our metric is complete.     

Growth order for the size of smallest hamiltonian chain saturated uniform hypergraphs

We say that a hypergraph H$H$ is hamiltonian chain saturated if H$H$ does not contain a hamiltonian chain but by adding any new edge we create a hamiltonian chain in H$H$. In this paper, for each k≥3$k\ge 3$, we establish the right order of magnitude n^k−1$n^{k-1}$ for the size of the smallest k$k$-uniform hamiltonian chain saturated hypergraph. This solves an open problem of G.Y. Katona.     

Correction to: Differences in the Efficiency of Separation of Analgesic Drugs by High-Performance Thin-Layer Chromatography with Similar Octadecyl Silica-Based Adsorbents

JPC – Journal of Planar Chromatography – Modern TLC -     

Ferromagnetic exchange coupling in phosphonato-bridged dinuclear copper(II) compound with monoethyl (pyridyn-2-ylmethyl)phosphonate ligand (2-mpmpe): Cu2(2-mpmpe)2(H2O)2(NO3)2

The interaction of diethyl (pyridyn-2-ylmethyl)phosphonate (2-pmpe) with Cu(NO₃)₂ · 6H₂O leads to a partial hydrolysis of the starting ligand and formation of the compound of the formula Cu₂(2-mpmpe)₂(H₂O)₂(NO₃)₂, where 2-mpmpe = monoethyl (pyridyn-2-ylmethyl)phosphonate. The crystal and molecular structure of a copper(II) compound was determined by single X-ray diffraction method. Its structure consists of five-coordinated in distorted square planar geometry (CuNO₄ chromophore) copper(II) ions doubly bridged by OPO from phosphonate. The Cu?Cu distance is 4.69 Å. The crystal packing is determined by the interdinuclear hydrogen bond system, which leads to a three-dimensional (3D) H-bonds network. The compound was characterized by infrared, ligand field, EPR spectroscopy, and magnetic studies. The magnetic properties of the title compound investigated over the 1.8–300 K, revealed the occurrence of a weak ferromagnetic coupling through phosphonate bridge (J = 1.86 cm⁻¹) and interdimer superexchange coupling through H-bond network (zJ′ = −0.17 cm⁻¹). Spectroscopic and magnetic properties are presented in the light of crystal structure.     

Investigation studies involving sound absorbing parameters of roadside screen panels subjected to aging in simulated conditions

The paper presents the results of investigation studies involving the impact of atmospheric factors on sound-absorbing parameters of roadside acoustic screen panels. The research studies comprised the aging test consisting of 1000 cycles in simulated conditions, sound absorption measurements and surface morphology tests, using the SEM scanning method. The simulation of aging consisted of 100 or 150 cycles at a time. Then, the panels were investigated in the reverberation chamber to define their sound-absorbing properties. The process was repeated until 1000 cycles were completed. Basing on the carried out tests, a statistical linear model was worked out which was used to estimate the value of a single number sound absorption coefficient after successive aging cycles. The optimality of the model was demonstrated by means of a statistical test confirming normal distribution of random residuals. For the research studies, we employed an innovative structural design of panels for which aging characteristics were obtained. Basing on the obtained results and on the statistical analysis, the prospects to maintain acoustic properties of the panels during their service life was estimated.