ON SHAPE-PRESERVING PROPERTIES AND SIMULTANEOUS APPROXIMATION OF STANCU OPERATOR

In the present paper, the shape-preserving properties and the monotonicity for convex functions of Stancu operator are given. Moreover, the simultaneous approximation problems of this operator are also considered.

Property Preservation of Petri Synthesis Net Based Representation for Embedded Systems

Embedded systems have numerous applications in everyday life.Petri-net-based representation for embedded systems(PRES+)is an important methodology for the modeling and analysis of these embedded systems.For a large complex embedded system,the state space explosion is a difficult problem for PRES+to model and analyze.The Petri net synthesis method allows one to bypass the state space explosion issue.To solve this problem,as well as model and analyze large complex systems,two synthesis methods for PRES+are presented in this paper.First,the property preservation of the synthesis shared transition set method is investigated.The property preservation of the synthesis shared transition subnet set method is then studied.An abstraction-synthesis-refinement representation method is proposed.Through this representation method,the synthesis shared transition set approach is used to investigate the property preservation of the synthesis shared transition subnet set operation.Under certain conditions,several important properties of these synthetic nets are preserved,namely reachability,timing,functionality,and liveness.An embedded control system model is used as an example to illustrate the effectiveness of these synthesis methods for PRES+.

Preservation Property of NBUCA Life Distributions

In this paper, some results of the NBUCA class of life distribution are obtained.The preservation properties of NBUCA aging properties under anti-star-shaped transformation are investigated. The preservation of NBUCA aging properties under general accelerated life model are studied as well.

Total Positivity of UE Spline Basis

A new geometric method to prove the total positivity of UE spline basis was proposed. UE spline basis is a kind of basis defined over algebraic-trigonometric unified space. UE spline basis shares most properties of the usual polynomial B-Splines. Total positivity is an important property for spline basis, it is highly related with shape preserving and variation diminishing properties. Knot inserted algorithm is the most useful algorithm for spline curves since many other useful properties are based on it. It is necessary to prove the total positivity of UE spline basis using knot inserted algorithm intuitively, not only enrich the UE spline basis theory, but also can be treated as supplement to the total positivity in algebraic sense. This approach also can be extended to other analogical bases.

BEST LIPSCHITZ CONSTANTS FOR THE BEZIER NETS AND BERNSTEIN POLYNOMIALS OVER A SIMPLEX

The present paper finds out that the geometric entity which characterizes the best Lipschitz constants for the Bezier nets and Bernstein polynomials over a simplex sigma is an angle Phi determined by sigma, and proves that (1) if f(x) is Lipschitz continuous over sigma, i.e., f(x) is an element of Lip(A)(alpha,sigma), then both the n-th Bezier net <(f)over cap (n)> and the n-th Bernstein polynomial B-n(f;x) corresponding to f(x) belong to Lip(B)(alpha,sigma) , where B = Asec(alpha)Phi; and (2) if n-th Bezier net <(f)over cap (n)> is an element of Lip(A)(alpha,sigma), then the elevation Bezier net <E(f)over cap (n)> and the corresponding Bernstein polynomial. B-n(f,;x) also belong to Lip(A)(alpha,sigma). Furthermore, the constant B = Asec(alpha)Phi, in case (1) is best in some sense.

Exponential Runge-Kutta Methods for the Multispecies Boltzmann Equation

This paper generalizes the exponential Runge-Kutta asymptotic preserving(AP)method developed in[G.Dimarco and L.Pareschi,SIAM Numer.Anal.,49(2011),pp.2057–2077]to compute the multi-species Boltzmann equation.Compared to the single species Boltzmann equation that the method was originally applied on,this set of equation presents a new difficulty that comes from the lack of local conservation laws due to the interaction between different species.Hence extra stiff nonlinear source terms need to be treated properly to maintain the accuracy and the AP property.The method we propose does not contain any nonlinear nonlocal implicit solver,and can capture the hydrodynamic limit with time step and mesh size independent of the Knudsen number.We prove the positivity and strong AP properties of the scheme,which are verified by two numerical examples.

A Gas-Kinetic Scheme for Collisional Vlasov-Poisson Equations in Cylindrical Coordinates

Many configurations in plasma physics are axisymmetric,it will be more convenient to depict them in cylindrical coordinates compared with Cartesian coordinates.In this paper,a gas-kinetic scheme for collisional Vlasov-Poisson equations in cylindrical coordinates is proposed,our algorithm is based on Strang splitting.The equation is divided into two parts,one is the kinetic transport-collision part solved by multiscale gas-kinetic scheme,and the other is the acceleration part solved by a Runge-Kutta solver.The asymptotic preserving property of whole algorithm is proved and it’s applied on the study of charge separation problem in plasma edge and 1D Z-pinch configuration.Numerical results show it can capture the process fromnon-equilibrium to equilibrium state by Coulomb collisions,and numerical accuracy is obtained.