Adaptive iterative regularization schemes for two‐dimensional integral‐algebraic systems

The main idea of this paper is to utilize the adaptive iterative schemes based on regularization techniques for moderately ill‐posed problems that are obtained by a system of linear two‐dimensional Volterra integral equations with a singular matrix in the leading part. These problems may arise in the modeling of certain heat conduction processes as well as in the dynamic simulation packages such as compressible flow through a plant piping network. Owing to the ill‐posed nature of the first kind Volterra equation that appears in the system, we will focus on the two families of regularization algorithms, ie, the Landweber and Lavrentiev type methods, where we treat both the exact and perturbed data. Our aim is to work directly with the original Volterra equations without any kind of reduction. Two fast iterative algorithms with reasonable computational complexity are developed. Numerical experiments on a few test problems are used to illustrate the validity and efficiency of the proposed iterative methods in comparison with the classical regularization methods.     

Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case

We have developed a stochastic mathematical formulation for designing a network of multi-product supply chains comprising several capacitated production facilities, distribution centres and retailers in markets under uncertainty. This model considers demand-side and supply-side uncertainties simultaneously, which makes it more realistic in comparison to models in the existing literature. In this model, we consider a discrete set as potential locations of distribution centres and retailing outlets and investigate the impact of strategic facility location decisions on the operational inventory and shipment decisions of the supply chain. We use a path-based formulation that helps us to consider supply-side uncertainties that are possible disruptions in manufacturers, distribution centres and their connecting links. The resultant model, which incorporates the cut-set concept in reliability theory and also the robust optimisation concept, is a mixed integer nonlinear problem. To solve the model to attain global optimality, we have created a transformation based on the piecewise linearisation method. Finally, we illustrate the model outputs and discuss the results through several numerical examples, including a real-life case study from the agri-food industry.     

The hyper-Zagreb index and some graph operations

Let G be a simple connected graph. The Hyper-Zagreb index is defined as \(\textit{HM}(G)=\sum _{uv\in E_{G}}(d_{G}(u)+d_{G}(v))^2\). In this paper some exact expressions for the hyper-Zagreb index of graph operations containing cartesian product and join of n graphs, splice, link and chain of graphs will be presented. We also apply these results to some graphs to chemical and general interest, such as \(C_4\) nanotube, rectangular grid, prism, complete n-partite graph.     

Structure and electronic properties of native and defected gallium nitride nanotubes

Structure and electronic properties of GaN nanotubes (GaNNTs) are investigated by using ab initio density functional theory. By full optimization, the optimized structures (bond-lengths and angles between them) of zigzag GaNNTs (n,0) and armchair GaNNTs (n,n) (4<n<11) are calculated. The difference between nitrogen ring diameter and gallium ring diameter (buckling distance) and semiconducting energy gap in term of diameter for zigzag and armchair GaNNTs have also been calculated. We found that buckling distance decreases by increasing nanotube diameter. Furthermore, we have investigated the effects of nitrogen and gallium vacancies on structure and electronic properties of zigzag GaNNT (5,0) using spin dependent density functional theory. By calculating the formation energy, we found that N vacancy in GaNNT (5,0) is more favorable than Ga vacancy. The nitrogen vacancy in zigzag GaNNT induces a 1.0μB magnetization and makes a polarized structure. We have shown that in polarized GaNNT a flat band near the Fermi energy splits to occupied spin up and unoccupied spin down levels.     

Cosmic string in the BTZ black hole background with time-dependent tension

In this Letter, we study the equation of circular loops with time-dependent tension in the BTZ black hole background. We obtain various cases where cosmic string loops finally collapse to form black holes. Also, we study effect of the BTZ black hole mass and angular momentum on the evolution of cosmic string loops. We find the critical values of initial radii as a limit for the cosmic string loops collapsing to form black holes.     

Dynamical Calculation of Θ+ Mass and Decay width in the Quark Model

In this paper we study the mass splitting and the decay width of pentaquark (Θ⁺) at the ground states in the framework of flux tube, quark delocalization and color screening model. We consider the pentaquark as diquark-triquark configuration and obtained closer values of mass splitting and the decay width of Θ⁺ to the experimental data.     

Time-Dependent Density of Modified Cosmic Chaplygin Gas with Variable Cosmological Constant in Non-Flat Universe

In this paper we study modified cosmic Chaplygin cosmology with non-zero cosmological constant in non-flat Universe. By using well-known forms of scale factor we obtain time-dependent dark energy density by numerical analysis of non-linear differential equation and fitting curves. We use observational data to fix solution and discuss about stability of our system. First of all we consider cosmological constant as a constant in Einstein equation, and then study possibility of variable cosmological constant.     

Accurate estimation of Brillouin frequency shift in Brillouin optical time domain analysis sensors using cross correlation

Current methods of estimating the Brillouin frequency shift in Brillouin optical time domain analysis sensors are based on curve-fitting techniques. These techniques apply the same weight to all portions of the curve and dutifully fit into the peak and noisy ends of the curve. This makes them very sensitive to noise, initialization of fitting parameters, symmetry, and start and stop frequencies. We introduce a method based on the cross-correlation technique to estimate the central frequency of noisy Lorentzian curves, which is more robust to noise and free from initial settings of fitting parameters.     

A novel 2-D six-parameter power-law distribution for free vibration and vibrational displacements of two-dimensional functionally graded fiber-reinforced curved panels

As a first endeavor, the three-dimensional free vibration and vibrational displacements characteristics of two-dimensional functionally graded fiber-reinforced (2-D FGFR) curved panels with different boundary conditions are presented. This paper presents a novel 2-D six-parameter power-law distribution for fiber volume fractions of 2-D FGFR that gives designers a powerful tool for design flexible of structures under multi-functional requirements. Various material profiles in two radial and axial directions can be illustrated using the six-parameter power-law distribution. The study is carried out based on the three-dimensional, linear and small strain elasticity theory. In this work, orthotropic panel is assumed to be simply supported at one pair of opposite edges and arbitrary boundary conditions at the other edges such that trigonometric functions expansion can be used to satisfy the boundary conditions precisely at simply supported edges. The 2-D generalized differential quadrature method (GDQM) as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made with the available solutions for FGM curved panels. Results indicate by using the 2-D six-parameter power-law distribution, it is possible to study the influence of different kinds of two-directional material profiles including symmetric and classic on the natural frequencies and modal displacements of a 2-D FGFR panel. Furthermore, maximum amplitude and uniformity of modal displacements distributions can be modified to a required manner by selecting suitable different parameters of 2-D power-law distribution and several various volume fractions profiles in two directions.