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].

Forced Axial and Torsional Vibrations of a Shaft Line Using the Transfer Matrix Method Related to Solution Coefficients

This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the propeller and intermediate shafts, under the influence of propeller-induced static and variable hydrodynamic excitations are also studied. The transfer matrix method related to the constant coefficients of differential equation solutions is used. The advantage of the latter as compared with a well-known method of transfer matrix associated with state vector is the possibility of reducing the number of multiplied matrices when adjacent shaft segments have the same material properties and diameters. The results show that there is no risk of buckling and confirm that the strength of the shaft line depends on the value of the static tangential stresses which is the most important component of the stress tensor.

Prediction of Henry's constant in polymer solutions using PCOR equation of state coupled with an activity coefficient model

In this paper,the polymer chain of rotator(PCOR) equation of state(EOS) was used together with an EOS/G^E mixing rule(MHV1) and the Wilson's equation as an excess-Gibbs-energy model in the proposed approach to extend the capability and improve the accuracy of the PCOR EOS for predicting the Henry's constant of solutions containing polymers.The results of the proposed method compared with two equation of state(van der Waals and GC-Flory) and three activity coefficient models(UNIFAC,UNIFAC-FV and Entropic-FV) indicated that the PCOR EOS/Wilson's equation provided more accurate results.The interaction parameters of Wilson's equation were fitted with Henry's constant experimental data and the property parameters of PCOR,a and b,were fitted with experimental volume data(Tait equation).As a result,the present work provided a simple and useful model for prediction of Henry's constant for polymer solutions.

A Linear Interference Cancellation Multi-User Detector for Synchronous CDMA Communications

This paper describes a linear interference cancellation multi user detector for synchronous DS CDMA systems under the condition that all spread spectrum code waveforms have the constant cross correlating coefficients. The basic idea is to get the estimation for total multiple access interference (MAI) of all users using a reference code waveform, then subtract the total MAI from the received signal. The structure of such a detector is nearly similar to the conventional detector. The BER expression obtained in the paper shows significant performance improvement compared to the other detectors.

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.

Distribution Equilibrium of o-Phthalic Acid and trans-Butenedioic in Water and Di-n-butyl Phthalate

The organic dissolvent （di-n-butyl phthalate） needs to be washed by water to recycle itself in the process of recovering maleic anhydride by organic dissolvent. The design and optimization of the extraction process require the distribution coefficients of the organic solutes, o-phthalic acid and trans-butenedioic in water and di-n-butyl phthalate, on which the extraction efficiency depends. In this study, the distribution coefficients of o-phthalic acid and trans-butenedioic in water and all-n-butyl phthalate（DBP） at 298.15 K, 318.15 K and 333.15 K were determined respectively by acid-alkali titration. The dissociation constants of o-phthalic acid and trans-butenedioic at those temperatures were obtained by fitting the measured hydrogen-ion concentrations and the known solute concentrations in the aqueous solution containing the two organic solutes. Then the distribution constants were calculated. Both the distribution coefficients and the distribution constants increase along with the temperature increasing. And the distribution coefficients at 333. 15 K are large enough to ensure the efficiency of extraction process. In addition, the mutual solubility of water and all-n-butyl phthalate at 298.1.5 K, 318. 1.5 K and 333. 15 K was also measured respectively by High Performance Liquid Chromatography and Karl Fischer Watertitration, which was not more than 0. 5%（ mass fraction ）.

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.

Regularity Theorems for Elliptic and Hypoelliptic Operators via the Global Relation

In this paper we give a new proof regarding the regularity of solutions to hypoelliptic partial differential equations with constant coefficients. On the assumption of existence, we provide a spectral representation for the solution and use this spectral representation to deduce regularity results. By exploiting analyticity properties of the terms within the spectral representation, we are able to give simple estimates for the size of the derivatives of the solutions and interpret them in terms of Gevrey classes.