A Chebotarev Theorem for finite homogeneous extensions of shifts

We derive a Chebotarev Theorem for finite homogeneous extensions of shifts of finite type. These extensions are of the form :X×G/H→X×G/H where (x,gH)=(σx, α(x)gH), for some finite groupG and subgroupH. Given a σ-closed orbit τ, the periods of the -closed orbits covering τ define a partition of the integer |G/H|. The theorem then gives us an asymptotic formula for the number of closed orbits with respect to the various partitions of the integer |G/H|. We apply our theorem to the case of a finite extension and of an automorphism extension of shifts of finite type. We also give a further application to ‘automorphism extensions’ of hyperbolic toral automorphisms. Financially supported by Universiti Kebangsaan Malaysia     

10-GHz Optical Comb in L-Band Region With Brillouin/Erbium-Doped Fibre Laser

A multiwavelength Brillouin/erbium fibre laser (BEFL) which operates in the long wavelength (L-band) region is demonstrated for potential applications in an L-band wavelength division multiplexing (WDM) communication system. The laser configuration consists of a long erbium-doped fibre to enable L-band amplification where two 3-dB couplers take a portion of the generated BEFL signal and re-inject it into the single mode fibre to seed a cascaded BEFL line in the same direction as the first BEFL line. A stable and strong laser comb of up to five lines with 10-GHz spacing has been obtained with a Brillouin pump (BP) of 9.2 mW and a 980 nm pump of 92 mW. The BEFL has shown a broad tuning range with a tuning characteristic for line #1 which is flat over a range greater than 9.9 nm.     

Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems

This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the system are explored and discussed via several numerical simulations. This system displays complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. Besides, by means of adapting certain controlled constants, it is shown that this system possesses a three-variable offset boosting system. In conformity with the performed simulations, it also turns out that the resultant hidden attractors can be distributively ordered in a grid of three dimensions, a lattice of two dimensions, a line of one dimension, and even arbitrariness in the phase space. Through considering the Caputo fractional-order operator in all performed simulations, phase portraits in two- and three-dimensional projections, Lyapunov exponents, and the bifurcation diagrams are numerically reported in this work as beneficial exit results.     

Enhanced Directed Random Walk for the Identification of Breast Cancer Prognostic Markers from Multiclass Expression Data

Artificial intelligence in healthcare can potentially identify the probability of contracting a particular disease more accurately. There are five common molecular subtypes of breast cancer: luminal A, luminal B, basal, ERBB2, and normal-like. Previous investigations showed that pathway-based microarray analysis could help in the identification of prognostic markers from gene expressions. For example, directed random walk (DRW) can infer a greater reproducibility power of the pathway activity between two classes of samples with a higher classification accuracy. However, most of the existing methods (including DRW) ignored the characteristics of different cancer subtypes and considered all of the pathways to contribute equally to the analysis. Therefore, an enhanced DRW (eDRW+) is proposed to identify breast cancer prognostic markers from multiclass expression data. An improved weight strategy using one-way ANOVA (F-test) and pathway selection based on the greatest reproducibility power is proposed in eDRW+. The experimental results show that the eDRW+ exceeds other methods in terms of AUC. Besides this, the eDRW+ identifies 294 gene markers and 45 pathway markers from the breast cancer datasets with better AUC. Therefore, the prognostic markers (pathway markers and gene markers) can identify drug targets and look for cancer subtypes with clinically distinct outcomes.     

A Review on Effects of Lubricant Formulations on Tribological Performance and Boundary Lubrication Mechanisms of Non-Doped DLC/DLC Contacts

Tribological efficiency of industrial applications involving boundary lubrication regime can be improved to an appreciable extent by the deposition of hard coatings on interacting surfaces. Among such coatings, diamond-like carbon (DLC) coatings are considered to be one of the most suitable ones for the said role. DLC coatings possess a unique combination of physical, chemical, and material properties due to which they can help in minimizing friction-induced energy and material losses even under starved lubrication conditions. Since commercial lubricants are optimized for steel surfaces, therefore, a lot of experimental investigations were carried out to analyze the tribological compatibility of these lubricants with various DLC coatings. However, there is still a lack of understanding about how DLC coatings interact with conventional lubricant additives. Some researchers reported tribologically beneficial interactions between DLC coatings and formulated lubricants while others observed no such behavior. To address these inconsistencies, there is a need to rearrange the published data in a more apprehensible and organized manner with a special emphasis on the mechanisms responsible for a particular tribological behavior. In this way, it can be determined whether synergistic or antagonistic correlation exists between a particular DLC-lubricant combination and research on DLC coatings can be continued in a logical way. In this article, most widely investigated non-doped DLC coatings (ta-C, a-C:H, a-C, and ta-C:H) are tribologically analyzed. Average values of friction and wear coefficients are calculated for various DLC-lubricant combinations using already published data and compared to quantify the effectiveness of a particular lubricant additive in enhancing tribological characteristics of symmetrical non-doped DLC contacts. Moreover, tribological performance parameters of non-doped DLC coatings are compared with those of doped-DLC coatings to understand differences in their tribological behavior in combination with additives.     

Abundant Exact Traveling Wave Solutions of Generalized Bretherton Equation via Improved (G′/G)-Expansion Method

In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves.     

Transparent and flexible field emission display device based on single‐walled carbon nanotubes

A fully transparent and flexible field emission device (FED) has been demonstrated. Single‐walled carbon nanotubes (SWCNTs) coated on arylite substrate were used as electron emitters for the FED and a novel metavanadate phosphor coated on the SWCNTs/arylite film was used as transparent and flexible screen. The SWCNTs/arylite based emitters and the SWCNTs/arylite/metal‐vanadate‐based phosphor showed a transmittance value of 92.6% and 54%, respectively. The assembled device also showed satisfactory transparency and flexibility as well as producing significant current. Metavanadate phosphor is considered to be an excellent candidate due to its superior luminescence properties and easy fabrication onto transparent and flexible conductive substrate at room temperature while retaining reasonable transparency of the substrate. Thus, its transparency and flexibility will open the door to next‐generation FEDs. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of 60Co γ-irradiation on structural and optical properties of thin films of Ga10Se80Hg10

Thin films of Ga₁₀Se₈₀Hg₁₀ have been deposited onto a chemically cleaned Al₂O₃ substrates by thermal evaporation technique under vacuum. The investigated thin films are irradiated by ⁶⁰Co γ-rays in the dose range of 50–150 kGy. X-ray diffraction patterns of the investigated thin films confirm the preferred crystallite growth occurs in the tetragonal phase structure. It also shows, the average crystallite size increases after γ-exposure, which indicates the crystallinity of the material increases after γ-irradiation. These results were further supported by surface morphological analysis carried out by scanning electron microscope and atomic force microscope which also shows the crystallinity of the material increases with increasing the γ-irradiation dose. The optical transmission spectra of the thin films at normal incidence were investigated in the spectral range from 190 to 1100 nm. Using the transmission spectra, the optical constants like refractive index (n) and extinction coefficient (k) were calculated based on Swanepoel’s method. The optical band gap (E_g) was also estimated using Tauc’s extrapolation procedure. The optical analysis shows: the value of optical band gap of investigated thin films decreases and the corresponding absorption coefficient increases continuously with increasing dose of γ-irradiation.     

Performance improvement of spectral amplitude coding-optical code division multiple access systems using NAND detection with enhanced double weight code

The bit-error rate (BER) performance of the spectral amplitude coding-optical code division multiple access (SACOCDMA) system has been investigated by using NAND subtraction detection technique with enhanced double weight (EDW) code. The EDW code is the enhanced version of double weight (DW) code family where the code weight is any odd number and greater than one with ideal cross-correlation. In order to evaluate the performance of the system, we used mathematical analysis extensively along with the simulation experiment. The evaluation results obtained using the NAND subtraction detection technique was compared with those obtained using the complementary detection technique for the same number of active users. The comparison results revealed that the BER performance of the system using NAND subtraction detection technique has greatly been improved as compared to the complementary technique.     

Characterization of small-signal intensity modulation of single-mode fiber grating Fabry-Perot laser source

A comprehensive study on the small-signal intensity modulation (IM) characteristics of a fiber grating Fabry-Perot (FGFP) laser is numerically investigated. The effect of external optical feedback (OFB), temperature, injection current, cavity volume, nonlinear gain compression factor, and fiber grating (FG) parameters on IM characteristics are presented. The temperature dependence (TD) of IM is calculated according to the TD of laser cavity parameters instead of using the well-known Parkove relationship. It has been shown that the optimum external fiber length (L _ext) is 3.1 cm. The optimum range of working temperature for FGFP laser is between 23 to 27 °C. We also show that by increasing the laser injection current from 10 to 60 mA, the IM peak amplitude decreased from 6.3 to 0.2 dB and the relaxation-oscillation frequency (ROF) is shifted from 1.2 GHz towards higher frequency of 5.48 GHz. In addition, the AR coating reflectivity and gain compression factor have no significant effect on the IM. The study indicates that a stable operation and excellent modulation characteristic can be obtained after optimization process.