Criteria for the matrix equivalence of words

This paper investigates the criteria for deciding whether two words are matrix equivalent. Certain upper diagonal matrices, generally referred to as the Parikh matrices, have been widely investigated because of their usefulness in computing the numbers of subword occurrences and thereby characterizing words by numbers. However, apart from the binary alphabet, not much is known about the properties of the matrix equivalent words, that is, words possessing the same matrix. The paper investigates both the general criteria, as well as the criteria valid in natural special cases. An exhaustive solution is obtained for ternary alphabets.     

Transposition invariant words

We define an operation called transposition on words of fixed length. This operation arises naturally when the letters of a word are considered as entries of a matrix. Words that are invariant with respect to transposition are of special interest. It turns out that transposition invariant words have a simple interpretation by means of elementary group theory. This leads us to investigate some properties of the ring of integers modulo n$n$ and primitive roots. In particular, we show that there are infinitely many prime numbers p$p$ with a primitive root dividing p+1$p+1$ and infinitely many prime numbers p$p$ without a primitive root dividing p+1$p+1$. We also consider the orbit of a word under transposition.     

Calculation of sliding power loss in spur gear contacts

An engineering-level calculation model for sliding power loss in spur gear contacts is presented. Teeth contact through the line of action is modelled as a constantly changing roller contact whose radius, speed, and load can be calculated from the gear geometry under the given operating conditions. The gear mesh cycle is approximated by a large number of elastohydrodynamic contacts. A constant film thickness and a Hertzian pressure distribution are assumed in each contact. The model includes non-Newtonian lubricant behaviour together with temperature and mixed lubrication effects in contact. The numerical solver is reasonably fast in evaluating effectively the sliding power loss dependence on the essential gear and lubricant parameters. The features and behaviour trends of the calculated sliding power losses have a close similarity with published results obtained from measurements and experiment-based power loss models with mineral oil. The limiting shear stress of the lubricant is observed to have an essential role in the power loss behaviour especially at high loads.     

Morphological,mechanical, tribological,and thermal expansion properties of organoclay reinforced polyethylene composites

The morphological, mechanical, thermal, and tribological properties of high‐density polyethylene (HDPE) composites reinforced with organo‐modified nanoclay (3 and 6 wt%) were studied. A commercial maleic anhydride‐based polymeric compatibilizer (PEgMA) was used to improve the adhesion between the polyethylene and clay. Transmission electron microscopy (TEM) characterization of composites revealed that nanoclay exists mainly in a multilayered structure in the HDPE matrix. Mechanical testing of composites showed that Young's modulus and tensile strength increased with nanoclay content. Coefficients of the linear thermal expansion (CLTE) of HDPE–PEgMA–clay composites were slightly lower in the flow direction than those of HDPE–PEgMA. The tribological properties were measured in dry conditions against a steel counterface. The friction coefficient of the matrix was decreased by the addition of clay. Electron microscopic results suggested that the wear mechanism for HDPE and HDPE composites was mainly adhesive. Clay agglomerates were observed on the worn surfaces of the composites, which may partly explain decreased friction. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers     

Modeling of helical gear contact with tooth deflection

The majority of gear tribological studies are made on spur gears. However, helical gears are generally used in industry, and their contact behavior deserves more attention to establish a realistic base for detailed friction, wear and life studies. This study focuses on the modeling of helical gear contact with tooth deflection. A calculation model for helical gear contact analysis is introduced. Helical gear surface profiles are constructed from gear tool geometry by simulating the hobbing process. The model uses three-dimensional finite elements for the calculation of tooth deflection including tooth bending, shearing and tooth foundation flexibility. The model combines contact analysis with structural analysis to avoid large meshes. Tooth foundation flexibility was found to have an essential role in contact load sharing between the meshing teeth, whereas contact flexibility plays only a minor role. The capability of different local contact calculation methods was also studied.     

A DLL clock generator for a high speed A/D-converter with 1 ps jitter and skew calibrator with 1 ps precision in 0.35 μm CMOS

This paper presents a clock generator circuit for a high-speed analog-to-digital converter (ADC). A time-interleaved ADC requires accurate clocking for the converter fingers. The target ADC has 12 interleaved fingers each running at a speed of 166 MS/s, which corresponds to an equivalent sampling frequency of 2 GS/s. A delay-locked loop (DLL) based clock generator has been proposed to provide multiple clock signals for the converter. The DLL clock generator has been implemented with a 0.35 μm SiGe BiCMOS process (only MOS-transistor were used in DLL) by Austria Micro Systems and it occupies a 0.6 mm² silicon area. The measured jitter of the DLL is around 1 ps and the delay between phases can be adjusted using 1 ps precision.     

Enhanced magnetooptical response in dumbbell-like Ag-CoFe2O4 nanoparticle pairs

We study magnetooptical Faraday rotation in a colloidal solution of "dumbbell-like", physically conjoined nanoparticle pairs composed of a ferromagnetic (CoFe2O4) and a noble metal (Ag). We show that outside the CoFe2O4 interband dominated spectral regime, the coupled dumbbells show significantly enhanced magnetooptic response relative to single CoFe2O4 nanoparticles, derived from plasmonic contribution by the Ag nanoparticles.     

Fluctuations in small volumes of liquid 3He

We calculate fluctuation contributions to the thermodynamic properties in a small volume of liquid ³He. Functional integration techniques are employed to derive the fluctuation free-energy functional for temperatures just above the superfluid transition temperature and for zero temperature. Due to finite-size effects, the critical regime is estimated to be large enough to warrant an experimental observation of fluctuations. At zero temperature we find two kinds of quasicollective gapless excitations, which correspond to fluctuations of phase and rotations of the order parameter in spin space, respectively. These excitations result in a periodic time dependence of the pair correlation function. Finally, the experimental observability of the effects considered are contemplated.     

Mineral fillers in low density-polyethylene films

The use of fillers is an established method of modifying the properties of plastics. The recent increase in prices of plastic raw materials and the new developments in compounding technology have heightened the interest of the plastic industry in compounds of fillers and polyethylene. This article discusses briefly the literature dealing with the effect of fillers on the properties of polyethylene, and research carried out on the effects of different mineral fillers, talcs, micas, clays, wollastonite and dolomite on the many properties of low density polyethylene films. The fine grade talcs have proved to be better than the other fillers with respect to most film properties. The platy talcs decreased the oxygen permeability by as much as 80 percent and the water vapor transmission rate by as much as 70 percent. With talcs, clays and dolomite the yield strength increased but with all fillers the tensile strength at break weakened with increasing filler content. A low elongation at break and a low tearing, resistance indicate the brittleness of the films especially at high filler contents (over 30 wt percent). The coefficients of friction decreased considerably with all fillers and a significant improvement in printability was achieved. However, none of the fillers had more than a very minor effect on the heat sealability of low density polyethylene.