Total <Emphasis Type="Italic">k</Emphasis>-domination in Cartesian product graphs

We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more detail, namely a problem that origins from a conjecture of Rényi and Erd?s (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem). This paper evolved from a plenary invited talk that the authors gave at the Joint Austrian-Hungarian Mathematical Conference 2015, August 25–27, 2015 in Gy?r (Hungary).     

Preparation and characterization of (Pebax 1657 + silica nanoparticle)/PVC mixed matrix composite membrane for CO<Subscript>2</Subscript>/N<Subscript>2</Subscript> separation

In this work, the films of poly(ether-block-amide) (Pebax 1657) and hydrophilic/hydrophobic silica nanoparticles (0–10 wt%) were coated on a poly(vinyl chloride) (PVC) ultrafiltration membrane to form new mixed matrix composite membranes (MMCMs) for CO₂/N₂ separation. The membranes were characterized by SEM, FTIR, DSC and XRD. Successful formation of a non-porous defect-free dense top layer with ~4 μm of thickness and also uniform dispersion of silica nanoparticles up to 8 wt% loading in Pebax matrix were confirmed by SEM images. The gas permeation results showed an increase in the permeance of all gases and an increase in ideal CO₂/N₂ selectivity with the increase in silica nanoparticle contents. Comparison between the incorporation of hydrophilic and hydrophobic silica nanoparticle into Pebax matrix revealed that the great enhancement of CO₂ solubility is the key factor for the performance improvement of Pebax + silica nanoparticle membranes. The best separation performance of the hydrophilic silica nanoparticle-incorporated Pebax/PVC membrane for pure gases (at 1 bar and 25 °C) was obtained with a CO₂ permeability of 124 barrer and an ideal CO₂/N₂ selectivity of 76, i.e., 63 and 35% higher than those of neat Pebax membrane, respectively. The corresponding values for hydrophobic silica nanoparticle-incorporated Pebax/PVC membrane were 107 barrer for CO₂ permeability and 61 for ideal CO₂/N₂ selectivity. Also the performances of MMCMs improved upon pressure increase (1–10 bar) owing to the shift in plasticizing effect of CO₂ towards the higher pressures. In addition, an increase in permeabilities with a decrease in ideal selectivity was observed upon temperature increase (25–50 °C) due to the intensification of chain mobility.     

Temperature tunable random laser using superconducting materials

We propose that spectral intensity of superconductor based random lasers can be made tunable by changing temperature. The two fluid model and wavelength dependent dispersion formula have been employed to describe the optical response of the superconducting materials. Random laser characteristics have been calculated using the one dimensional FDTD method. Our simulation results reveal that the emission spectrum can be manipulated through the ambient temperature of the system. It is observed that transition from metal phase to pure superconducting phase leads to the enhancement of the laser emission. Furthermore, spatial distribution of the fields in one dimensional disordered media is very sensitive to the system temperature.     

On Design of Parity Preserving Reversible Adder Circuits

In this paper novel parity preserving reversible logic blocks are presented and verified. Then, we present cost-effective parity preserving reversible implementations of Full Adder, 4:2 Compressor, Binary to BCD converter, and BCD adder using these blocks. The proposed parity preserving reversible BCD adder is designed by cascading the presented 4-digit parity preserving reversible Full Adder and a parity preserving reversible Binary to BCD Converter. In this design, instead of realizing the detection and correction unit, we design a Binary to BCD converter that its inputs are the output of parity preserving binary adder, and its output is a parity preserving BCD digit. In addition, several theorems on the numbers of garbage outputs, constant inputs, quantum cost and delay of the designs have been presented to show its optimality. In the presented circuits, the delay and the quantum cost are reduced by deriving designs based on the proposed parity preserving reversible blocks. The advantages of the proposed designs over the existing ones are quantitatively described and analysed. All the scales are in the Nano-metric area.     

Experimental and numerical study of residual stresses caused by cold expansion of adjacent holes

Cold expansion is a useful process for imposing compressive residual stresses around the holes in riveted and bolted connections. These stresses increase the fatigue life of holed parts. Distribution and amount of exerted residual stress dependent on various parameters as material, distance of adjacent holes, hole diameter, cold expansion ratio and plate thickness. In this study, experimental and numerical results for two different aluminum alloys and various holes distances are investigated and compared. Effects of mentioned parameters on the residual stress are studied.     

Carboxymethylated nanofibrillated cellulose: effect of monovalent electrolytes on the rheological properties

The effect of the ionic strength on the properties of a carboxymethylated nanofibrillated cellulose (NFC) system was investigated through rheological studies. It was shown that homogenization of pulp suspensions containing a high amount of a monovalent electrolyte leads to the production of NFC systems displaying a lower magnitude in the rheological response as compared with systems prepared at lower ionic strengths conditions. It was further shown that increasing the ionic strength of NFC suspensions after their manufacturing also results in a lowering of the rheological response. The decreased rheological response in the former case was postulated to be caused by a lowering of the delamination deficiency of the homogenization process, due to decreased swelling of the carboxymethylated pulp, caused by the screening of the charges. In the latter case (post-addition of the electrolyte), the lowering of the rheological response was postulated to be due to the compression of the electrostatic double layer, when the electrostatic repulsion between the charged fibrils diminished in the presence of the electrolyte.