On copulas and their diagonals

We formulate the necessary and sufficient conditions for a function δ:[0,1]→[0,1] to be the diagonal section of a multivariate absolutely continuous copula. Moreover we provide some simple analytic formulas for copulas having given diagonal section or given distribution functions of order statistics.     

Characterization of catalysts obtained from rapidly quenched alloy precursors by electrochemical/chemical processes of material degradation—selected examples

Rapidly quenched amorphous alloys—containing metallic or metalloid elements—are precursors for selective catalysts of many technically important reactions. To increase their activity, various methods of material degradation occurring at the surface and in the bulk of the rapidly quenched alloys have been used for promoting the catalytic performance of such materials. The modifications of the structure, composition, and morphology of the substrate proved to be efficient in transforming inactive metal alloy precursors into active and selective catalysts for hydrogenation, and dehydrogenation of organic compounds, as well as for other processes like steam reforming of methanol. This article presents several examples of characterization of such catalysts and discusses their selectivity and activity in a connection with physical and chemical properties of their surfaces. Moreover, it is shown that scanning electron microscopy, Auger electron spectroscopy, scanning Auger microscopy, and energy dispersive spectrometry allowed the local changes occurring during the activation process to be identified and their implications for catalytic function to be considered.     

Application of Green's functions for analysis of transient thermal states in electronic circuits

This paper presents an approach to the modelling of transient thermal states in electronic circuits using an analytical solution of the heat equation. Fully three-dimensional analytical time dependent solutions are determined with the help of Green's functions. The solution method is illustrated in detail on a practical example, where the results of transient thermal simulations of a real hybrid circuit are compared with infrared measurements.     

Ion sensitive field effect transistor modelling for multidomain simulation purposes

The proper design and simulation of modern electronic microsystems oriented towards environment monitoring requires accurate models of various ambient sensors. In particular, this paper presents a comprehensive model of an ion sensitive field effect transistor (ISFET). The model can be employed straightforwardly for simulations at device, circuit or system level.First, the model was validated with electrical measurements and simulations of real structures performed for different ion concentration and temperature values. Then, the ISFET sensor model was employed for mixed-signal simulations in VHDL-AMS, when the analysis of a microsystem consisting of the ISFET sensor and a sigma-delta analogue-to-digital converter was carried out. Additionally, the presence of other ions than hydrogen in the measured solution was also taken into account in the simulations.     

Assessment of the Superheater Ash Fouling Using a Numerical Model of the Superheater

ABSTRACT

Superheaters are high-temperature cross-flow heat exchangers. Steam flows inside the tubes, and the flue gas outside in a direction perpendicular to the axes of the tubes. However, they differ very substantially from the other heat exchangers operating at low temperatures. Superheaters are characterized by complex flow system and high tube walls temperature. Superheaters are among the most exposed to damaging pressure elements of steam boilers. Damage to the superheater causes about 40% of emergency shutdowns of boilers. The paper presents the boiler superheater model with distributed parameters, which is used to determine on-line the degree of superheater fouling by ash.     

Framework influence of erbium doped oxyfluoride glasses on their optical properties

Glasses of different matrix (phosphate, borate, silicate and lead-silicate) were studied for their optical properties. The effect of Er dopant on transmittance and luminescence properties was presented. The significant “red shift” and “blue shift” of UV edge absorption were discussed based on the changes in the framework of the borate and phosphate glasses, respectively. It was showed that the integral intensity of the two main optical absorption transitions monotonically increases with the order: phosphate < borate < silicate < lead-silicate. Ellipsometric measurement was applied to obtain the refractive index of the glasses. The correlation between the shift of edge absorption and the change of refractive index was presented. Effect of glassy matrix on luminescence of Er³⁺ was discussed.     

High and low spin energy states of the Tb 4f5d configuration in BaF2

In this paper we present results of detailed spectroscopic studies of Tb³⁺ luminescence from BaF₂:0.075 mol% Tb performed at Superlumi station of Hasylab, DESY, Hamburg and at Institute of Physics, N. Copernicus University, Torun, Poland (IF UMK Torun).We have measured UV/VUV excitation spectra of the dominant blue Tb³⁺ luminescence and emission spectra under excitation into various bands found from the excitation spectra. The excitation spectra are dominated by the two well known broad bands due to the parity and spin-allowed (SA) 4f⁸ → 4f⁷5d transitions. The higher energy triple t-band and unresolved single e-band at lower energies are widely separated (10 Dq about 16,500 cm⁻¹) reflecting the single d-electron energy in the high symmetry cubic crystal field with a relatively low contribution from the low symmetry component.In addition to these bands we have also detected a number of weaker bands at lower energy sides of both dominant SA bands. While the structured band with components at 252.8, 252.3, 250.4 and 248.4 nm clearly corresponds to the SF (spin-forbidden) band found earlier in LiYF₄:Tb, the bands at 183, 178 and 172 nm have been never, to the best of our knowledge, reported before. We present arguments that these new bands are the SF counterparts of the triple SA t-band at about 158 nm. The d-f exchange energies for d(e) and d(t) electrons are different at 7779 and 8245 cm⁻¹, respectively.Although the energy levels corresponding to the identified high and low spin (HS and LS) states of the 4f⁷5d configuration are, in BaF₂, well separated, there are no SA nor SF transitions generating d-f emission in BaF₂:Tb. This is because the numerous 4f⁸ energy levels intercept the excitation energy from 4f⁷5d levels leading to the well known blue and green Tb³⁺ 4f⁸ emissions.