LIOUVILLE'S THEOREM FOR LPDO WITH CONSTANT COEFFICIENTS

In this note, the authors consider a class of linear partial differential operators P((?)) with constant coefficients and prove that the operator P((?)) has Liouville property if and only if the polynomial P(iξ) doesn't have roots in Rn\{0}.

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].

CONVERGENCE OF AN IMMERSED INTERFACE UPWIND SCHEME FOR LINEAR ADVECTION EQUATIONS WITH PIECEWISE CONSTANT COEFFICIENTS Ⅱ: SOME RELATED BINOMIAL COEFFICIENT INEQUALITIES

In this paper we give proof of three binomial coefficient inequalities. These inequalities are key ingredients in [Wen and Jin, J. Comput. Math. 26, （2008）, 1-22] to establish the L^1-error estimates for the upwind difference scheme to the linear advection equations with a piecewise constant wave speed and a general interface condition, which were further used to establish the L^1-error estimates for a Hamiltonian-preserving scheme developed in [Jin and Wen, Commun. Math. Sci. 3, （2005）, 285-315] to the Liouville equation with piecewise constant potentials [Wen and Jin, SIAM J. Numer. Anal. 46, （2008）, 2688-2714].

Bus Encoded LUT Multiplier for Portable Biomedical Therapeutic Devices

DSP operation in a Biomedical related therapeutic hardware need to beperformed with high accuracy and with high speed. Portable DSP hardware’s likepulse/heart beat detectors must perform with reduced operational power due to lack ofconventional power sources. This work proposes a hybrid biomedical hardware chip inwhich the speed and power utilization factors are greatly improved. Multipliers are thecore operational unit of any DSP SoC. This work proposes a LUT based unsignedmultiplication which is proven to be efficient in terms of high operating speed. For n bitinput multiplication n*n memory array of 2 n bit size is required to memorize all thepossible input and output combination. Various literature works claims to be achieve highspeed multiplication with reduced LUT size by integrating a barrel shifter mechanism.This paper work address this problem, by reworking the multiplier architecture with aparallel operating pre-processing unit which used to change the multiplier and multiplicandorder with respect to the number of computational addition and subtraction stages required.Along with LUT multiplier a low power bus encoding scheme is integrated to limit the powerconstraint of the on chip DSP unit. This paper address both the speed and power optimizationtechniques and tested with various FPGA device families.

Instability analysis and drag coefficient prediction on a swept RAE2822 wing with constant lift coefficient

Swept wing is widely used in civil aircraft,whose airfoil is chosen,designed and optimized to increase the cruise speed and decrease the drag coefficient.The parameters of swept wing,such as sweep angle and angle of attack,are determined according to the cruise lift coefficient requirement,and the drag coefficient is expected to be predicted accurately,which involves the instability characteristics and transition position of the flow.The pressure coefficient of the RAE2822 wing with given constant lift coefficient is obtained by solving the three-dimensional Navier-Stokes equation numerically,and then the mean flow is calculated by solving the boundary layer（BL） equation with spectral method.The cross-flow instability characteristic of boundary layer of swept wing in the windward and leeward is analyzed by linear stability theory（LST）,and the transition position is predicted by eNmethod.The drag coefficient is numerically predicted by introducing a laminar/turbulent indicator.A simple approach to calculate the lift coefficient of swept wing is proposed.It is found that there is a quantitative relationship between the angle of attack and sweep angle when the lift coefficient keeps constant;when the angle of attack is small,the flow on the leeward of the wing is stable.when the angle of attack is larger than 3°,the flow becomes unstable quickly;with the increase of sweep angle or angle of attack the disturbance on the windward becomes more unstable,leading to the moving forward of the transition position to the leading edge of the wing;the drag coefficient has two significant jumping growth due to the successive occurrence of transition in the windward and the leeward;the optimal range of sweep angle for civil aircraft is suggested.