Inexact Uzawa algorithms for solving nonlinear saddle-point problems are proposed. A simple sufficient condition for the convergence of the inexact Uzawa algorithms is obtained. Numerical experiments show that the inexact Uzawa algorithms are convergent.

We consider the optimal proportional reinsurance from an insurer’s point of view to maximize the expected utility and minimize the value at risk. Under the general premium principle, we prove the existence and uniqueness of the optimal strategies and Pareto optimal solution, and give the relationship between the optimal strategies. Furthermore, we study the optimization problem with the variance premium principle. When the total claim sizes are normally distributed, explicit expressions for the optimal strategies and Pareto optimal solution are obtained. Finally, some numerical examples are presented to show the impact of the major model parameters on the optimal results.

In this note, we study deterministic and stochastic models for the spread of cholera. The deterministic model for the total number of cholera cases fits the observed total number of cholera cases in some recent outbreaks. The stochastic model for the total number of cholera cases leads to a binomial type distribution with a mean that agrees with the deterministic model.

It is shown that a simple deduction engine can be developed for a propositional logic that follows the normal rules of classical logic in symbolic form, but the description of what is known about a proposition uses two numeric state variables that conveniently describe unknown and inconsistent, as well as true and false. Partly true and partly false can be included in deductions. The multi-valued logic is easily understood as the state variables relate directly to true and false. The deduction engine provides a convenient standard method for handling multiple or complicated logical relations. It is particularly convenient when the deduction can start with different propositions being given initial values of true or false. It extends Horn clause based deduction for propositional logic to arbitrary clauses. The logic system used has potential applications in many areas. A comparison with propositional logic makes the paper self-contained.

This paper deals with the problem of discrete and distributed time-delay exponential stability for deterministic and uncertain stochastic high-order neural networks. The concept of a parameter weak coupling linear matrix inequality set (PWCLMIS) is developed. New results are derived in terms of PWCLMIS. Large mixed time delays can be obtained by using this approach. Furthermore, these results are more general than some previous existence results. Two numerical examples are given to show the merit of the approach.

A Chebyshev pseudo-spectral method for solving numerically linear and nonlinear fractional-order integro-differential equations of Volterra type is considered. The fractional derivative is described in the Caputo sense. The suggested method reduces these types of equations to the solution of linear or nonlinear algebraic equations. Special attention is given to study the convergence of the proposed method. Finally, some numerical examples are provided to show that this method is computationally efficient, and a comparison is made with existing results.

Scattering of membrane coupled gravity waves in deep water by partial vertical barriers is investigated by the recently developed expansion formulae for wave structure interaction problems. The horizontal thin membrane is considered to be under uniform tension and is covering the free surface. The analysis is based on the linearized theory of water waves, and by combining the kinematic and dynamic conditions at the membrane covered surface, one may derive a not so well-posed mixed boundary value problem for Laplace’s equation with third-order boundary condition. The flexible membrane is attached by a spring to the surface piercing barrier, giving suitable edge conditions for the unique solution. The boundary value problem has been converted into dual integral equations with kernels composed of trigonometric functions, which are then solved analytically. The important physical quantities such as reflection and transmission coefficients for both cases of submerged and surface piercing barriers are obtained analytically in terms of modified Bessel functions. It is found that complete reflection or transmission is possible at certain resonant frequencies for the incident membrane coupled waves. Numerical results are plotted and discussed for different values of the nondimensional membrane tension parameter.

The inadequacy of the traditional sliding mode variable structure (SMVS) control method for cruise missiles is addressed. An improved SMVS control method is developed, in which the reaching mode segment of the SMVS control is decomposed into an acceleration accessing segment, a speed keeping segment, and a deceleration buffer segment. A time-fuel optimal control problem is formulated as an optimal control problem involving a switched system with unknown switching times and subject to a continuous state inequality constraint. The new design method is developed based on a control parametrization, a time scaling transform and the constraint transcription method. A sequence of approximate optimal parameter selection problems is obtained with fixed switching time points and a canonical state inequality constraint. Each approximate optimal parameter selection problem can be solved effectively by using existing gradient-based optimization techniques. The convergence of these approximate optimal solutions to the true optimal solution is assured. Simulation results show that the proposed method is highly effective. The response speed of the missile under the control law obtained by the proposed method is improved significantly, while the elevator of the missile is constrained to operate within its permitted range.

We propose a new primal-dual interior-point algorithm based on a new kernel function for linear optimization problems. New search directions and proximity functions are proposed based on the kernel function. We show that the new algorithm has and iteration bounds for large-update and small-update methods, respectively, which are currently the best known bounds for such methods.

Steady magnetohydrodynamic flow of an incompressible micropolar fluid through a pipe of circular cross-section is studied by considering Hall and ionic effects. The fluid motion is due to a constant pressure gradient, and an external uniform magnetic field directed perpendicular to the flow direction is applied. Expressions for the velocity, microrotation, skin friction and flow rate are obtained. The effects of the micropolar parameter, magnetic parameter, Hall parameter and ion-slip parameter on the velocity, microrotation, skin friction and flow rate are discussed.

In this paper, using the framework of self-regularity, we propose a hybrid adaptive algorithm for the linear optimization problem. If the current iterates are far from a central path, the algorithm employs a self-regular search direction, otherwise the classical Newton search direction is employed. This feature of the algorithm allows us to prove a worst case iteration bound. Our result matches the best iteration bound obtained by the pure self-regular approach and improves on the worst case iteration bound of the classical algorithm.

In this study, Liénard equations in their general form are treated using the Adomian decomposition method. The special structure of the Liénard equation is exploited to obtain a numerically efficient algorithm suitable for solution by a computer program.