Supply chain analysis under a price-discount incentive scheme for electric vehicles

We investigate an automobile supply chain where a manufacturer and a retailer serve heterogeneous consumers with electric vehicles (EVs) under a government’s price-discount incentive scheme that involves a price discount rate and a subsidy ceiling. We show that the subsidy ceiling is more effective in influencing the optimal wholesale pricing decision of the manufacturer with a higher unit production cost. However, the discount rate is more effective for the manufacturer with a lower unit production cost. Moreover, the expected sales are increasing in the discount rate but may be decreasing in the subsidy ceiling. Analytic results indicate that an effective incentive scheme should include both a discount rate and a subsidy ceiling. We also derive the necessary condition for the most effective discount rate and subsidy ceiling that maximize the expected sales of EVs, and obtain a unique discount rate and subsidy ceiling that most effectively improve the manufacturer’s incentive for EV production.     

Relaxation in nonconvex optimal control problems described by fractional differential equations

We consider the minimization problem of an integral functional with integrand that is not convex in the control on solutions of a control system described by fractional differential equation with mixed nonconvex constraints on the control. A relaxation problem is treated along with the original problem. It is proved that, under general assumptions, the relaxation problem has an optimal solution, and that for each optimal solution there is a minimizing sequence of the original problem that converges to the optimal solution with respect to the trajectory, the control, and the functional in appropriate topologies simultaneously.     

A globally convergent method for computing multiple vortices in a supersymmetric field theory

Computation of the solutions to the gauge field equations is known of great importance for the simulation of various particle physics systems. In this work, we establish a globally convergent iterative method for computing the multiple vortex solutions arising in a self-dual system of non-Abelian gauge field equations derived in a supersymmetric theory model. Using this method, we present a few numerical examples which demonstrate the effectiveness of the method and, at the same time, provide a concrete realization of the soliton-like behavior of the vortexlines concentrated around centers of vortices, which is believed to be essential for linear confinement in QCD.     

Generalized elementary functions

We use the theory of generalized linear differential equations to introduce new definitions of the exponential, hyperbolic and trigonometric functions. We derive some basic properties of these generalized functions, and show that the time scale elementary functions with Lebesgue integrable arguments represent a special case of our definitions.     

Mild solutions of non-autonomous second order problems with nonlocal initial conditions

In this paper we establish the existence of mild solutions for a non-autonomous abstract semi-linear second order differential equation submitted to nonlocal initial conditions. Our approach relies on the existence of an evolution operator for the corresponding linear equation and the properties of the Hausdorff measure of non-compactness.     

On super-linear Emden–Fowler type differential equations

We study the second order Emden–Fowler type differential equation

(a(t)|x^′|^αsgnx^′)^′+b(t)|x|^βsgnx=0${(a(t){\left|x^{\prime }\right|}^{\alpha }\mathrm{sgn}{x}^{\prime })}^{\prime }+b(t){|x|}^{\beta }\mathrm{sgn}x=0$

in the super-linear case α<β$\alpha <\beta$. Using a Hölder-type inequality, we resolve the open problem on the possible coexistence on three possible types of nononscillatory solutions (subdominant, intermediate, and dominant solutions). Jointly with this, sufficient conditions for the existence of globally positive intermediate solutions are established. Some of our results are new also for the Emden–Fowler equation.