Two types of limit cycles of a resonant converter modelled by a three-dimensional system

In this paper, the long-run dynamics of a resonant converter is studied. The modelling of the resonant converter can be done using various approximations and the long-run dynamics of the two dimensional cases were earlier analysed. In this paper, we discuss results that can be extended to the three dimensional case. It seems that limit cycles describe the long-run dynamics in important situations in the three dimensional case, too. Our objective is to relate the limit cycles found previously in the two-dimensional case to those found now in the three dimensional approximation.     

CONVERGENCE OF AN IMMERSED INTERFACE UPWIND SCHEME FOR LINEAR ADVECTION EQUATIONS WITH PIECEWISE CONSTANT COEFFICIENTS I： L^1-ERROR ESTIMATES

We study the L^l-error estimates for the upwind scheme to the linear advection equations with a piecewise constant coefficients modeling linear waves crossing interfaces. Here the interface condition is immersed into the upwind scheme. We prove that, for initial data with a bounded variation, the numerical solution of the immersed interface upwind scheme converges in L^l-norm to the differential equation with the corresponding interface condition. We derive the one-halfth order L^l-error bounds with explicit coefficients following a technique used in [25]. We also use some inequalities on binomial coefficients proved in a consecutive paper [32].     

A parametric variational principle and residuality

We prove a parametric version of a smooth convex variational principle with constraints using a Baire category approach. We examine in depth the necessity of the assumptions of our variational principle by providing counterexamples.     

A computational analysis of multidimensional piecewise-linear models with applications to oil production optimization

Production optimization of gas-lifted oil wells under facility, routing and pressure constraints is a challenging problem, which has attracted the interest of operations engineers aiming to drive economic gains and scientists for its inherent complexity. The hardness of this problem rests on the non-linear characteristics of the multidimensional well-production and pressure-drop functions, as well as the discrete routing decisions. To this end, this work develops several formulations in Mixed-Integer Linear Programming (MILP) using multidimensional piecewise-linear models to approximate the non-linear functions with domains spliced in hypercubes and simplexes. Computational and simulation analyses were performed considering a synthetic but realistic oil field modeled with a multiphase-flow simulator. The purpose of the analyses was to assess the relative performance of the MILP formulations and their impact on the simulated oil production.     

Polynomial cases of the economic lot sizing problem with cost discounts

In this paper we study the economic lot sizing problem with cost discounts. In the economic lot sizing problem a facility faces known demands over a discrete finite horizon. At each period, the ordering cost function and the holding cost function are given and they can be different from period to period. There are no constraints on the quantity ordered in each period and backlogging is not allowed. The objective is to decide when and how much to order so as to minimize the total ordering and holding costs over the finite horizon without any shortages. We study two different cost discount functions. The modified all-unit discount cost function alternates increasing and flat sections, starting with a flat section that indicates a minimum charge for small quantities. While in general the economic lot sizing problem with modified all-unit discount cost function is known to be NP-hard, we assume that the cost functions do not vary from period to period and identify a polynomial case. Then we study the incremental discount cost function which is an increasing piecewise linear function with no flat sections. The efficiency of the solution algorithms follows from properties of the optimal solution. We computationally test the polynomial algorithms against the use of CPLEX.     

Asymptotics of Christoffel functions on arcs and curves

For a system of smooth Jordan curves and arcs asymptotics for Christoffel functions is established. A separate new method is developed to handle the upper and lower estimates. In the course to the upper bound a theorem of Widom on the norm of Chebyshev polynomials is generalized.     

Exact analytical inversion of TSK fuzzy systems with singleton and linear consequents

In literature, exact inversion methods for TSK fuzzy systems exist only for the systems with singleton consequents. These methods have binding limitations such as strong triangular partitioning, monotonic rule bases and/or invertibility check. These extra limitations lessen the modeling capabilities of the TSK fuzzy systems. In this study, an exact analytical inversion method for TSK fuzzy systems with singleton and linear consequents is presented. The only limitation of the proposed method is that the inversion variable should be represented by piecewise linear membership functions (PWL-MFs). In this case, the universe of discourse of the inversion variable is divided into specific regions in which only one linear piece exists for each PWL-MF at most. In the proposed method, the analytical formulation of TSK fuzzy system is expressed in terms of the inversion variable by using linear equations of PWL-MFs. Thus, the fuzzy system output in any region can be obtained by using the appropriate parameters of the linear equations of PWL-MFs defined within the related region. This expression provides a way to obtain linear and quadratic equations in terms of the inversion variable for TSK fuzzy systems with singleton and linear consequents, respectively. So, it becomes very easy to find exact inverse solutions for each region by using explicit analytical solutions for linear or quadratic equations. The proposed inversion method has been illustrated through simulation examples.     

Characterizations of K-smooth Spaces and K-strongly Smooth Spaces

Some necessary and sufficient conditions for a Banach space to be K-smooth or Kstrongly smooth are obtained.     

Nonlinear mappings associated with the generalized linear complementarity problem

We show that the Cottle—Dantzig generalized linear complementarity problem (GLCP) is equivalent to a nonlinear complementarity problem (NLCP), a piecewise linear system of equations (PLS), a multiple objective programming problem (MOP), and a variational inequalities problem (VIP). On the basis of these equivalences, we provide an algorithm for solving problem GLCP.Project partially supported by a grant from Oak Ridge Associated Universities, TN, USA.     

单位球面间的等距延拓

本文证明了在一定条件下赋范线性空间与其共轭空间的单位球面之间的等距算子可以延拓为全空间的实线性等距算子。进而,刻画了光滑的自反空间的单位球面到其共轭空间的单位球面上的等距算子。