Homotopy perturbation method for linear programming problems

In this paper, He’s homotopy perturbation method (HPM) is applied for solving linear programming (LP) problems. This paper shows that some recent findings about this topic cannot be applied for all cases. Furthermore, we provide the correct application of HPM for LP problems. The proposed method has a simple and graceful structure. Finally, a numerical example is displayed to illustrate the proposed method.     

Solvability of the boundary value problem for stationary magnetohydrodynamic equations under mixed boundary conditions for the magnetic field

The global solvability of the boundary value problem for stationary magnetohydrodynamic equations under the Dirichlet boundary condition for the velocity and mixed boundary conditions for the magnetic field is proved.     

Effect of a plant fortifier (Boundary) on pests and predators of greenhouse vegetable crops

Boundary, a plant fortifier composed of extracts of Sophora flavescens Aiton and brown algae, was tested for control of the leaf miner Tuta absoluta (Meyrick) on tomato (three trials) and of the red spider mite Tetranychus urticae Koch on eggplant (one trial) and for side effects on the whitefly predator Macrolophus pygmaeus (Kambur) (two trials) on tomato and on the thrips predators Orius laevigatus (Fieber) and Amblyseius swirskii Athias-Henriot (two trials) on pepper, all in cold greenhouses in South Italy. Control rates for T. absoluta were moderate (40–70%) in the autumn crop but very high and comparable to those for emamectin benzoate in the spring crops (96–100%). Boundary compared well with abamectin against T. urticae, with near complete control. M. pygmaeus was moderately injured in late autumn, but not in early autumn. At the tested application rate and predator population density Boundary was safe for O. laevigatus and A. swirskii.     

Ferric Phosphate Hydroxide Microstructures Affect Their Magnetic Properties

Uniformly sized and shape-controlled nanoparticles are important due to their applications in catalysis, electrochemistry, ion exchange, molecular adsorption, and electronics. Several ferric phosphate hydroxide (Fe₄(OH)₃(PO₄)₃) microstructures were successfully prepared under hydrothermal conditions. Using controlled variations in the reaction conditions, such as reaction time, temperature, and amount of hexadecyltrimethylammonium bromide (CTAB), the crystals can be grown as almost perfect hyperbranched microcrystals at 180 °C (without CTAB) or relatively monodisperse particles at 220 °C (with CTAB). The large hyperbranched structure of Fe₄(OH)₃(PO₄)₃ with a size of ∼19 μm forms with the “fractal growth rule” and shows many branches. More importantly, the magnetic properties of these materials are directly correlated to their size and micro/nanostructure morphology. Interestingly, the blocking temperature (T_B) shows a dependence on size and shape, and a smaller size resulted in a lower T_B. These crystals are good examples that prove that physical and chemical properties of nano/microstructured materials are related to their structures, and the precise control of the morphology of such functional materials could allow for the control of their performance.     

Free boundary minimal hypersurfaces with spherical boundary

We first prove that a compact embedded minimal annulus in meeting two concentric spheres perpendicularly along the boundaries is part of a plane. We also prove that an embedded minimal hypersurface lying outside of a ball is part of either a catenoid or a hyperplane if it is perpendicular to the sphere along the boundary and has only one end that is asymptotic to either a catenoid if , or a hyperplane if .     

Blow‐up of the smooth solutions to the compressible Navier–Stokes equations

In this paper, we will firstly extend the results about Jiu, Wang, and Xin (JDE, 2015, 259, 2981–3003). We prove that any smooth solution of compressible fluid will blow up without any restriction about the specific heat ratio γ. Then we prove the blow‐up of smooth solution of compressible Navier–Stokes equations in half space with Navier‐slip boundary. The main ideal is constructing the differential inequality. Copyright © 2017 John Wiley & Sons, Ltd.     

On mechanical waves and Doppler shifts from moving boundaries

We investigate the propagation of infinitesimal harmonic mechanical waves emitted from a boundary with variable velocity and arriving at a stationary observer. In the classical Doppler effect, X_s(t)=vt is the location of the source with constant velocity v. In the present work, however, we consider a source co‐located with a moving boundary x=X_s(t), where X_s(t) can have an arbitrary functional form. For ‘slowly moving’ boundaries (i.e., ones for which the timescale set by the mechanical motion is large in comparison to the inverse of the frequency of the emitted wave), we present a multiple‐scale asymptotic analysis of the moving boundary problem for the linear wave equation. We obtain a closed‐form leading‐order (with respect to the latter small parameter) solution and show that the variable velocity of the boundary results not only in frequency modulation but also in amplitude modulation of the received signal. Consequently, our results extend the applicability of two basic tenets of the theory of a moving source on a stationary domain, specifically that (i) for non‐uniform boundary motion can be inserted in place of the constant velocity v in the classical Doppler formula and (ii) that the non‐uniform boundary motion introduces variability in the amplitude of the wave. The specific examples of decelerating and oscillatory boundary motion are worked out and illustrated. Copyright © 2017 John Wiley & Sons, Ltd.     

A nonhomogeneous boundary value problem for the Kuramoto–Sivashinsky equation in a quarter plane

We study the initial boundary value problem for the one‐dimensional Kuramoto–Sivashinsky equation posed in a half line with nonhomogeneous boundary conditions. Through the analysis of the boundary integral operator, and applying the known results of the Cauchy problem of the Kuramoto–Sivashinsky equation posed on the whole line , the initial boundary value problem of the Kuramoto–Sivashinsky equation is shown to be globally well‐posed in Sobolev space for any s >?2. Copyright © 2017 John Wiley & Sons, Ltd.     

Well‐posedness of initial boundary value problems on longitudinal impact on a composite linear viscoelastic bar

We investigate the correctness of the initial boundary value problem of longitudinal impact on a piecewise‐homogeneous semi‐infinite bar consisting of a semi‐infinite elastic part and finite length visco‐elastic part whose hereditary properties are described by linear integral relations with an arbitrary difference kernel. Introducing nonstationary regularization in boundary conditions and in the contact conditions, the well‐posedness of the considered problem is proved. Copyright © 2017 John Wiley & Sons, Ltd.     

General decay of solutions of a wave equation with memory term and acoustic boundary condition

In this paper, the global solvability to the mixed problem involving the wave equation with memory term and acoustic boundary conditions for non‐locally reacting boundary is considered. Moreover, the general decay of the energy functionality is established by the techniques of Messaoudi. Copyright © 2016 John Wiley & Sons, Ltd.