Effect of carbon nanotubes implantation on electrical properties of sisal fibre–epoxy composites

In this paper, the effects of carbon nanotubes (CNT) implantation and sisal fibre size on the electrical properties of sisal fibre-reinforced epoxy composites are reported. For this purpose, the epoxy composites reinforced with CNT-implanted sisal fibre of 5 mm and 10 mm lengths were prepared by hand moulding and samples characterized for their electrical properties, such as dielectric constant (ε′), dielectric dissipation factor (tan δ) and AC conductivity (σ_ac) at different temperatures and frequencies. It was observed that the dielectric constant increases with increase in temperature and decreases with increase in frequency from 500 Hz to 5 KHz. Interestingly, the sample having CNT-implanted sisal fibre of 5 mm length exhibited the highest value of dielectric constant than the one with length 10 mm. This is attributed to the increased surface area of sisal fibre and enhancement of the interfacial polarization. At a constant volume and a length of 5 mm of the fibres, the number of interfaces per unit volume element is high and results in a higher interfacial polarization. The interfaces decrease as the fibre length increases, and therefore, the value of ε′ decreases at 10 mm fibre length. The peak value of the dielectric constant decreases with increasing frequency. A continuous decrease in dissipation factor (tan δ) with increasing frequency for all samples was observed, while at lower temperatures, the values of tan δ remains approximately same. The AC conductivity for 5 mm length sisal epoxy composite and 10 mm length sisal fibre–epoxy composites is higher than that of pure epoxy at all the frequencies.     

Moment collapse in the Ce(Rh1−xOsx)3B2 system

The compound CeRh₃B₂ orders magnetically with a low saturation moment of about 0.4 micro_B per formula unit but a very high Curie temperature of 115 K. On replacing Rh with Os, it is observed that in the Ce(Rh_1?xOs_x)₃B₂ (0 ? x ? 0.167) series, both the magnetic moment and the Curie temperature decrease rapidly with increasing x. The compound CeRh_2.5Os_0.5B₂ (x = 0.167) does not appear to be ordered magnetically down to 5 K. This behavior is thought to arise from the changes in the hybridization of Ce 4f levels with sp type conduction electrons and/or with Rh and Os derived d bands.     

Exact solutions and conservation laws of Zakharov-Kuznetsov modified equal width equation with power law nonlinearity

This paper obtains solutions to the Zakharov-Kuznetsov modified equal width equation with power law nonlinearity. The Lie symmetry approach and the simplest equation method are used to obtain these solutions. Moreover, conservation laws are derived for the underlying equation by employing two approaches: the new conservation theorem and the multiplier method.     

Nonlinear breakup of a self-gravitating column

Using the method of strained coordinates, a weakly nonlinear theory of the breakup of a gravitating column is presented. It is shown that the self-gravitating column breaks into the main celestial bodies and their satellites whose dimensions are sensitive to the wavenumbers.     

Efficient power computation for r out of m runs rules schemes

In this article we develop a power computation code in the R language which provides an easy to use tool to researchers in designing Shewhart control charts. It enables researchers to use different existing and newly introduced sensitizing rules and runs rules schemes designed for Shewhart-type control charts for location and spread. The code provides researchers to compute the power for different options of r out of m rules/schemes. The code is flexible to apply for any sample size, false alarm rate, type of control limits (one- or two-sided), amount of shift in the process parameters and a variety of popular distributions for commonly used Shewhart-type control charts (i.e. ${\bar{{X}} ,R ,S}$ and S ² charts). These mentioned benefits of the developed functional code are only partially found in features of the existing software packages and these programs may be enhanced by adding the features of the developed code as a function in their libraries dealing with quality control charting.     

Traces of Permuting n-Additive Maps and Permuting n-Derivations of Rings

Let R be a prime ring with center Z(R). For a fixed positive integer n, a permuting n-additive map ${\Delta : R^n \to R}$ is known to be permuting n-derivation if ${\Delta(x_1, x_2, \ldots, x_i x'_{i},\ldots, x_n) = \Delta(x_1, x_2, \ldots, x_i, \ldots, x_n)x'_i + x_i \Delta(x_1, x_2, \ldots, x'_i, \ldots, x_n)}$ holds for all ${x_i, x'_i \in R}$ . A mapping ${\delta : R \to R}$ defined by δ(x) = Δ(x, x, . . . ,x) for all ${x \in R}$ is said to be the trace of Δ. In the present paper, we have proved that a ring R is commutative if there exists a permuting n-additive map ${\Delta : R^n \to R}$ such that ${xy + \delta(xy) = yx + \delta(yx), xy- \delta(xy) = yx - \delta(yx), xy - yx = \delta(x) \pm \delta(y)}$ and ${xy + yx = \delta(x) \pm \delta(y)}$ holds for all ${x, y \in R}$ . Further, we have proved that if R is a prime ring with suitable torsion restriction then R is commutative if there exist non-zero permuting n-derivations Δ₁ and Δ₂ from ${R^n \to R}$ such that Δ₁(δ ₂(x), x, . . . ,x) =  0 for all ${x \in R,}$ where δ ₂ is the trace of Δ₂. Finally, it is shown that in a prime ring R of suitable torsion restriction, if ${\Delta_1, \Delta_2 : R^n \longrightarrow R}$ are non-zero permuting n-derivations with traces δ ₁, δ ₂, respectively, and ${B : R^n \longrightarrow R}$ is a permuting n-additive map with trace f such that δ ₁ δ ₂(x) =  f(x) holds for all ${x \in R}$ , then R is commutative.     

On the pre-amplified linear cavity multi-wavelength Brillioun-erbium fiber laser with low SBS threshold highly nonlinear photonic crystal fiber

An efficient multi-wavelength Brillouin-erbium fiber laser utilizing low stimulated Brillouin scattering threshold highly nonlinear photonic crystal fiber (PCF) is presented. A Fabry-Perot pre-amplified Brillouin pump configuration was used which consists of 100 m PCF and 10 m erbium doped fiber (EDF). Up to 28 output channels with SNR of more than 20 dB could be generated with modest pump power.     

Dynamics of a Moving Two-Level Atom Under the Influence of Intrinsic Decoherence

We present a general and fascinating problem of quantum entanglement (QE) that is calculated with the help of quantum Fisher information (QFI) and von Neumann entropy (VNE) for moving two-level atomic systems. We calculate numerically the temporal evolution of the state vector of the entire system under the influence of intrinsic decoherence for a moving two-level atom. We demonstrate that the phase shifts of an estimator parameter, intrinsic decoherence, and the atomic motion play an important and prominent role during the time evolution of the atomic system. We observe that there is a monotonic relation between the atomic quantum Fisher information (QFI) and quantum entanglement (QE) in the absence of atomic motion. We also show that at the revival time the local maximum values of QFI decreases gradually. A periodic behavior of QFI is observed in the presence of atomic motion, which becomes more important and remarkable for two-level atomic systems. Moreover, the atomic quantum Fisher information and entanglement demonstrate an opposite response during the time evolution in the presence of atomic motion. We show that the evolution of entanglement is more susceptible to the intrinsic decoherence; a considerable change occurs in the degree of entanglement when the intrinsic decoherence parameter increases. Intrinsic decoherence in the atom–field interaction represses the nonclassical effects of the atomic systems. Both the entanglement and the quantum Fisher information saturate to their lower levels for longer time scales in the presence of intrinsic decoherence. For larger values of intrinsic decoherence, the sudden death of entanglement is observed.