In this paper, a new approach to a characterization of solvability of a nonlinear nonsmooth multiobjective programming problem with inequality constraints is introduced. A family of η-approximated vector optimization problems is constructed by a modification of the objective and the constraint functions in the original nonsmooth multiobjective programming problem. The connection between (weak) efficient points in the original nonsmooth multiobjective programming problem and its equivalent η-approximated vector optimization problems is established under V-invexity. It turns out that, in most cases, solvability of a nonlinear nonsmooth multiobjective programming problem can be characterized by solvability of differentiable vector optimization problems.

We describe a simple deterministic model for the dispersion of particulate ash which has been ejected into the atmosphere by a volcanic eruption. In our model the atmosphere is divided into a series of horizontal layers within which the physical parameters involved are constant. This is an effective way to allow for the changing behaviour of the particulate ash and atmospheric flow with height whilst retaining simplicity. From our model we construct an analytical expression for the final deposit which could be incorporated within hazard assessment projections. In particular we show how to allow for variation with height of dispersion (caused by turbulence due to the wind) and settling speed (affected by the agglomeration and fragmentation of particles).

In this paper, by using the Leggett–Williams fixed point theorem, we prove the existence of three nonnegative solutions to second-order nonlinear impulsive differential equations with a three-point boundary value problem.

Families of vortex equilibria, with constant vorticity, in steady flow past a flat plate are computed numerically. An equilibrium configuration, which can be thought of as a desingularized point vortex, involves a single symmetric vortex patch located wholly on one side of the plate. Given that the outermost edge of the vortex is unit distance from the plate, the equilibria depend on three parameters: the length of the plate, circulation about the plate, and the distance of the innermost edge of the vortex from the plate. Families in which there is zero circulation about the plate and for which the Kutta condition at the plate ends is satisfied are both considered. Properties such as vortex area, lift and free-stream speed are computed. Time-dependent numerical simulations are used to investigate the stability of the computed steady solutions.

By means of a symbolic calculus for finding solutions of difference equations, we derive explicit eigenvalues, eigenvectors and inverses for tridiagonal Toeplitz matrices with four perturbed corners.

Quintic B-spline collocation schemes for numerical solution of the regularized long wave (RLW) equation have been proposed. The schemes are based on the Crank–Nicolson formulation for time integration and quintic B-spline functions for space integration. The quintic B-spline collocation method over finite intervals is also applied to the time-split RLW equation and space-split RLW equation. After stability analysis is applied to all the schemes, the results of the three algorithms are compared by studying the propagation of the solitary wave, interaction of two solitary waves and wave undulation.

In this paper a smoothed particle hydrodynamics (SPH) method is introduced for simulating two-dimensional incompressible non-Newtonian fluid flows, and the non-Newtonian effects in the flow of a fluid which can be modelled by generalized Newtonian constitutive equations are investigated. Two viscoplastic models including Bingham-plastic and power-law models are considered along with the Newtonian model. The governing equations include the conservation of mass and momentum equations in a pseudo-compressible form. The spatial discretization of these equations is achieved by using the SPH method. The temporal discretization algorithm is a fully explicit two-step predictor–corrector scheme. In the prediction step, an intermediate velocity field is obtained using a forward scheme in time without enforcing incompressibility. The correction step consists of solving a pressure Poisson equation to satisfy incompressibility by providing a trade-off between the pressure and density variables. The performance of the proposed scheme is evaluated by studying a benchmark problem including flow of viscoplastic fluids in a lid-driven cavity. Both Newtonian and non-Newtonian cases are investigated and the results are compared with available numerical data. It was shown that in all cases the method is stable and the results are in very good agreement with available data.

A sharp L2 inequality of Ostrowski type is established, which provides a generalization of some previous results and gives some other interesting results as special cases. Applications in numerical integration are also given.

In this paper we introduce a set of orthonormal functions, , where ϕn[r] is composed of a sine function and a sigmoidal transformation γr of order r>0. Based on the proposed functions ϕn[r] named by sigmoidal sine functions, we consider a series expansion of a function on the interval [−1,1] and the related convergence analysis. Furthermore, we extend the sigmoidal transformation to the whole real line ℝ and then, by reconstructing the existing sigmoidal cosine functions ψn[r] and the presented functions ϕn[r], we develop two kinds of 2-periodic series expansions on ℝ. Superiority of the presented sigmoidal-type series in approximating a function by the partial sum is demonstrated by numerical examples.