In this paper, a unified formula of a series of rogue wave solutions for the standard (1+1)-dimensional nonlinear Schrödinger equation is obtained through exp-function method. Further, by means of an appropriate transformation and previously obtained solutions, rogue wave solutions of the variable coefficient Schrödinger equation are also obtained. Two free functions of time 𝑡 and several arbitrary parameters are involved to generate a large number of wave structures.

On the basis of second mean-value theorem (SMVT) for integrals, a discretization method is proposed with the aim of representing the expectation value of a function with respect to a probability density function in terms of the discrete probability theory. This approach is applied to the continuous Rényi entropy, and it is established that a discrete probability distribution can be associated to it in a very natural way. The probability density functions for the linear superposition of two coherent states is used for developing a representative example.

Quantum information technology largely relies on a sophisticated and fragile resource, called quantum entanglement, which exhibits a highly nontrivial manifestation of the coherent superposition of the states of composite quantum systems. In this paper, we study the interaction between the general and even coherent fields with moving and stationary two two-level atoms. In this regard, this paper investigates the von Neumann entropy and the atoms–field tangle as a measure of entanglement between the general and even coherent fields with the two atoms. Also, the entanglement between the two atoms using concurrence and negativity during time evolution is discussed. This paper examines the effects of multiphoton transitions and initial state setting on the entanglement for the system under consideration. Finally, the results demonstrate an important phenomenon such as the sudden death and birth of entanglement when the two atoms are initially in entangled states.

A new solution of Einstein's vacuum field equations is discovered which appears as a generalization of the well-known Ozsváth–Schücking solution and explains its source of curvature which has otherwise remained hidden. Curiously, the new solution has a vanishing Kretschmann scalar and is singularity-free despite being curved. The discovery of the new solution is facilitated by a new insight which reveals that it is always possible to define the source of curvature in a vacuum solution in terms of some dimensional parameters. As the parameters vanish, so does the curvature. The new insight also helps to make the vacuum solutions the Machian solutions.

In this paper, variable coefficient Benny equation (also called the KdV Burgers–Kuramoto equation) has been considered. By using the Painlevé analysis and Lie group analysis methods, the Painlevé properties and symmetries have been studied. Some solutions of the reduced ODEs are obtained.

In the present work, it is shown that an asymptotically flat spherical black hole can have a nontrivial signature of any field, for an exterior observer, if the energy–momentum tensor of the corresponding field is either trace-free or if the trace falls off at least as rapidly as the inverse cube of the radial distance. In the absence of a general `No Hair Theorem', this result can provide a characterization of the fields leading to a black hole hair.

This paper studies the global synchronization of non-autonomous, time-delay, chaotic power systems via linear state-error feedback control. The frequency domain criterion and the LMI criterion are proposed and applied to design the coupling matrix. Some algebraic criteria via a single-variable linear coupling are derived and formulated in simple algebraic inequalities. The effectiveness of the new criteria is illustrated with numerical examples.

In this paper, a hierarchy of nonisospectral equations with variable coefficients is derived from the compatibility condition of Toda spectral problem and its time evolution. In order to solve the derived Toda lattice hierarchy, the inverse scattering transformation is utilized. As a result, new and more general exact solutions are obtained. It is shown that the inverse scattering transformation can be generalized to solve some other nonisospectral lattice hierarchies with variable coefficients.

A workspace modelling technique, that achieves real-time detection of closeness of robot to workspace object, has been developed by additional physics attribute attachment to workspace. Physics phenomena suiting the realistic work conditions have been identified and a computational model for emulating the phenomenon has been developed. Need for building sensitivity to dynamics in the model has also been addressed. Model building and algorithms for embedding the model in workspace comprising complex object shapes have been studied in detail. Applications like fast execution in real-time scenarios, design of data structure for realistic implementation and the problem of attaining functionality without new sensor addition to telerobots working in radioactive environment are addressed.

The anisotropy of fission fragment angular distribution, evaporation residue crosssection and the fission cross-section were calculated for ¹⁹⁷Tl formed in ¹⁶O+¹⁸¹Ta reactions in the framework of the modified statistical model and the results were compared with the experimental data. The effects of temperature and projection of spin about the symmetry axis 𝐾 have been considered for calculating potential energy surfaces and fission widths. It was shown that in the framework of the modified statistical model, by choosing appropriate values for the temperature coefficient of the effective potential, 𝛼, and scaling factor of the fission-barrier height, 𝑟_s, one can satisfactorily reproduce the above-mentioned experimental data. It was also shown that the appropriate values of these parameters for ¹⁹⁷Tl are 𝛼 = 0.0185 ± 0.0050 MeV^-2 and 𝑟_s = 1.0006 ± 0.0020.

The presence of trapped ions in electron storage rings causes considerable degradation in the performances of the beam, such as increase in beam size, reduction in beam lifetime, shifting of betatron tune, beam instabilities etc. This paper discusses the effects of ion trapping and its mitigation in Indus-2 electron storage ring. Ion-induced instability generating partial beam loss is one of the main barriers in higher beam current accumulation in any electron storage ring. Though there are several techniques to clear the ions from the electron beam path, in Indus-2, it is addressed mainly by filling the storage ring in partial bunch filling pattern. In order to improve the electron beam performance and to mitigate the ion-related problem, a suitable bunch filling pattern has been determined. The theoretical prediction and the result of optimal bunch filling pattern are presented in this paper.

A 2.2 kJ plasma focus device was analysed as an electron beam and an X-ray source that operates with argon gas refilled at a specific pressure. Time-resolved X-ray signals were observed using an array of PIN diode detectors, and the electron beam energy was detected using a scintillator-assisted photomultiplier tube. The resultant X-rays were investigated by plasma focus discharge for pressures ranging from 1.5 mbar to 2.0 mbar. This range corresponded to the significant values of X-ray yields and electron beam energies from the argon plasma. The electron temperature of argon plasma at an optimum pressure range was achieved by an indirect method using five-channel BPX65 PIN diodes of aluminum foils with different thicknesses. X-ray yield, electron beam energy, and electron temperature of argon plasma were achieved at 1.5–2.0 mbar because of the strong bombardment of the energetic electron beam.

In this paper, we have developed a mathematical model to predict the behaviour of gate capacitance and threshold voltage with nanoscale variation of oxide thickness in AlInN/GaN and AlGaN/GaN metal oxide semiconductor high electron mobility transistor (MOSHEMT). The results obtained from the model are compared with the TCAD simulation results to validate the model. It is observed that AlInN/GaN MOSHEMT has an advantage of significant decrease in gate capacitance up to 0.0079 pF/𝜇m² with increase in oxide thickness up to 5 nm as compared to conventional AlGaN/GaN MOSHEMT. This decrease in gate capacitance in AlInN/GaN MOSHEMT reduces the propagation delay and hence improves the RF performance of the device.

Superconductivity in perovskite, BaKBiO, is studied in the Bardeen–Cooper–Schrieffer (BCS) model, with three-square-well potentials. Components of the new coupling are: the attractive acoustic phonon–electron, optical phonon–electron and repulsive Coulomb interactions. With these in the BCS pairing Hamiltonian, expressions for the superconducting transition temperature and isotope effect exponent are obtained. Results of our analysis are consistent with experiments. Contributions of interactions to system properties are exhibited and analysed. Acoustic phonon–electron and optical phonon–electron interactions have near-identical elevation of transition temperature, holding out possible explanations for high-𝑇_𝑐. Contrastingly, optical phonon–electron and Coulomb couplings cause debilitation of isotope exponent, a possible explanation for low isotope exponent in the cuprates and other high-𝑇_𝑐 systems. It is found that BCS electron–phonon coupling appears synonymous with acoustic phonon–electron coupling.

In this work, we present the effect of refractive index of an embedding medium, core and shell having various sizes of metallic nanoshells on the surface plasmon resonance (SPR) properties in the spherical dielectric–metal core–shell nanoparticles based on the quasistatic approaches and Mie theory. For the metallic nanoshell with dimensions comparable to the wavelength of light, the quasistatic approximation shows good agreement with the Mie theory results. However, for large nanoparticles the quasistatic approximation is not appropriate and Mie theory illustrates SPR due to dipole and quadrupole in extinction cross-section. The typical cross-section calculations show two peaks that related to inner and outer surfaces. The dimensional dependence of optical constant in the Drude model leads to a decrease in plasma absorption in metal core–shell. By increasing the shell radius and therefore increasing the metal content the SPR at the outer surface shifts to higher energy and the weaker peak (at inner surface) shifts to lower energy. Also, depending on the metal shell materials SPR occurs in different energy regions and therefore can be tuned the SP frequency at higher energy by changing the shell materials. In addition, SPR frequency is sensitive to variation in refractive index of the environment of core-shell.

As we read the paper by Jianqi Zhang and Huan Xu, Pramana – J. Phys. 72, 547 (2009), two issues became clear, that warranted writing this comment. First, the switch, which is the main building block of the devices, and which is used to route the signal, does not work as explained in Section 4.1. Accordingly, the optical router does not work as explained, either. In addition, the half adder does not work as explained and a completely different Truth Table is obtained. The full adder is left to the reader as an exercise. Secondly, the previously published work, which is closely related to the work reported, was not referenced or discussed. In the following paragraphs we discuss each issue in some detail to give the authors the opportunity to better explain their work and clear such issues.