Structural properties of graphs of diameter 2 with maximal repeats

It was shown using eigenvalue analysis by Erdös et al. that with the exception of C₄, there are no graphs of diameter 2, of maximum degree d and of order d², that is, one less than the Moore bound. These graphs belong to a class of regular graphs of diameter 2, and having certain interesting structural properties, which will be proved in this paper.     

Determination of Spectra of Functions

Boundaries of convex and compact spectra of functions on plane are fully described without passing to the complexification and the Fourier transform.     

TPR and XPS characterization of chromia–lanthana–zirconia catalyst prepared by impregnation and microwave plasma enhanced chemical vapour deposition methods

Chromia–lanthana–zirconia catalysts prepared by wet impregnation and microwave plasma enhanced chemical vapour deposition methods have been characterized by temperature-programmed reduction (TPR) and X-ray photoelectron spectroscopy (XPS). The impregnation procedure requires large amounts of solvent and calcination at high temperatures producing Cr⁶⁺ species. Unlike this, it is found that the microwave plasma enhanced chemical vapour deposition (PECVD) method predominantly produces Cr³⁺ species on zirconia-based supports. Moreover, it has been shown that the dispersion of chromium species deposited on zirconia-based support by the PECVD method is higher than the dispersion of those prepared by wet impregnation. Thus, the advantages of PECVD over the impregnation method consist in this case in preventing the use of large amounts of solvent and avoiding the primary formation of poisonous Cr⁶⁺ species as well as in enabling the deposition of chromium species with high dispersion on zirconia-based supports.     

Radiolysis of 1-naphthol in aqueous solutions

The effects of absorbed doses, initial pH and 1-naphthol concentration onto its radiolysis in aqueous sulphuric and hydrochloric acids by gamma rays from ⁶⁰Co were investigated. Under the experimental conditions, 1-naphthol degradation yields increased with increasing the absorbed doses (0.3–3.0 kGy) and with decreasing the initial 1-naphthol concentration (20–1 ppm). It was found out that the hydrated electrons did not play any significant roles in 1-naphthol radiolysis, as the degradation yields were higher at pH₀ ~ 0.46 compared to those at pH₀ ~ 2.0–5.0. The corresponding radiolytic yields G(−1-naphthol) were (6.13 ± 1.00)) × 10⁻² and (5.11 ± 0.22) × 10⁻² μmol/J in sulphuric acids, (15.61 ± 3.85) × 10⁻² and (4.76 ± 0.48) × 10⁻² μmol/J in hydrochloric acids. 1-Naphthol degradation rates could be described by the kinetic equations of pseudo-first-order reactions. An empirical relation between the observed reaction constants k _D and the initial 1-naphthol concentrations was established, enabling to predict the absorbed doses required for a given treatment efficiency. Three products of 1-naphthol degradation were revealed using an HPLC/UV procedure.     

Dimensional variance inequalities of Brascamp–Lieb type and a local approach to dimensional Prékopaʼs theorem

We give a new approach, inspired by Hörmander?s L²$L^2$-method, to weighted variance inequalities which extend results obtained by Bobkov and Ledoux. It provides in particular a local proof of the dimensional functional forms of the Brunn–Minkowski inequalities. We also present several applications of these variance inequalities, including reverse Hölder inequalities for convex functions, weighted Brascamp–Lieb inequalities and sharp weighted Poincaré inequalities for generalized Cauchy measures.     

Spectrum created by line defects in periodic structures

We study a Helmholtz‐type spectral problem related to the propagation of electromagnetic waves in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a three‐dimensional periodic medium; the defect is infinitely extended in one direction, but compactly supported in the remaining two. This perturbation introduces guided mode spectrum inside the band gaps of the fully periodic, unperturbed spectral problem. We will show that even small perturbations lead to additional spectrum in the spectral gaps of the unperturbed operator and investigate some properties of the spectrum that is created.