Comments on a numerical method for solving Boolean equations

A recent paper in this journal, by Abdel-Gawad, Atiya, and Darwish, presents a method of solving a system Boolean equations using the polynomial algebra invented by George Boole in 1854. The authors do not mention Boole, however, or the modern applications of this algebra. Their method entails reduction of the given system to a triangular system, which is solved by back-substitution. We show that the solutions of the triangular system include all those of the given system, but may include others that do not satisfy the given system.     

Pulsed electromagnetic heating of microparticles

The application of pulsed heating by a laser beam to determine the thermal properties of microparticles is explored. Two problems are analyzed : (i) spatially uniform heating of the surface of an absorbing microsphere, and (ii) non-uniform surface heating based on Mie theory computations of the electromagnetic energy source. A parametric study shows that the spatially uniform heating model is sufficient when the thermal conductivity of the microparticle is sufficiently large or the Biot number is sufficiently low, but a more rigorous model is needed to predict the temperature distribution with the microsphere for lower thermal conductivity materials. The resulting analytical solutions are compared with previously published experiments involving infrared heating of single spherocarb particles and are shown to be in good agreement with time-dependent surface temperature measurements.     

Polynomials,radial basis functions and multilayer perceptron neural network methods in local geoid determination with GPS/levelling

The means for determining reference surfaces when using satellite-based positioning techniques differs from the way they are determined using classical terrestrial positioning techniques. The height of any point on earth, as determined by a global positioning system (GPS), is based on the World Geodetic System of 1984 datum, but when using classical terrestrial measurements this height is based on the geoid. However, GPS-derived ellipsoidal heights must initially be transformed into orthometric heights for practical applications. We use geoid models developed with geoid heights for the height transformation, because orthometric height determination methods using classical techniques require time and manpower. In this study, the performances of polynomials, radial basis functions (RBFs) and multilayer perceptron (MLP) neural network algorithms used in local geoid surface modelling were evaluated in the study area. Upon analysis of statistical results, the artificial neural network method was observed to give better results than the other two methods.     

Computational problems in the theory of finite fields

We give a survey of selected topics in the theory of finite fields with emphasis on computational aspects including recent advances and open problems.Dedicated to Professor G. E. Wall     

Stability and coefficients properites of polynomials of linear discrete systems

In this paper, by examining the coefficients of a given polynomial, we derive sufficient conditions for the zeros of the polynomial to be either inside the unit disk in the complex plane or at least one zero not inside the unit disk. The results are easily verifiable and provide handy ways of checking. Most results are proved using either Rouché's Theorem or fundamental mathematical ideas. Some of the results are extensions of known coefficient properties found in the literature.     

Polynomial Chaos Decomposition for the Simulation of Non-Gaussian Nonstationary Stochastic Processes

A method is developed for representing and synthesizing random processes that have been specified by their two-point correlation function and their nonstationary marginal probability density functions. The target process is represented as a polynomial transformation of an appropriate Gaussian process. The target correlation structure is decomposed according to the Karhunen–Loève expansion of the underlying Gaussian process. A sequence of polynomial transformations in this process is then used to match the one-point marginal probability density functions. The method results in a representation of a stochastic process that is particularly well suited for implementation with the spectral stochastic finite element method as well as for general purpose simulation of realizations of these processes.     

LIWER ESTIMATES FOR A GENERALIZED SUMS OF LEBESGUE FUNCTION TYPE

1IntroductionI,etX:={x,,*,k=l,2,..',n,n=1,2,..-}beandtriangularmatrixofnodeswith(1)(X,=X,,O=)-1<.T,,,<.Tn,C-'..r.,,<1(=X,,;) 1=X'. 1),n=1,2,-..Putingarethecorrcspondlngfundan1cntalpolynon1ialsoftheI,agranginterpoilation,isthelebesguefunction,andforanyfixednonnegat1veintegersandtiscalledthesumofI,ebesguefuncti0ntype.Tostateourresultweneedtointroducesomeothernotation-Foreachn,n=1,2,';define1相似文献   

Approximation With Taylor Matching At The Origin

Robust techniques for best approximation by polynomials matching up to given order the Taylor series at {0} are given. Much cheaper robust techniques giving near best results in favorable cases are also given for the same problems. A heuristic technique for matching only the function value at {0} when it is an error extremum is put on a sound theoretical basis and offers possibilities of making rounding error and analytic error cancel, thus reducing their effect.     

两种添加剂对石蜡针入度的影响

对于一般的 q- 1维正规单纯形利益区域和多重线性多项式模型 ,利用n(≤ q)阶多重线性多项式的最优设计 ,采用了极端顶点设计及棱中心设计方案 ,选用 16个实验数据 ,建立石蜡在两种添加剂的作用下针入度性质的 3阶多重线性多项式的针入度拟合方程 :f(x1,x2 ,x3 ) =- 172 .5 9+5 96 8.91x1- 5 830 .5 7x21+2 5 0 4 .4 4x3 1- 32 .4 9x2 。并对其协同效应、对抗效应和可加效应以及变化趋势进行了研究 ,结果表明 :动物蜡添加剂对石蜡针入度的影响不显著 ,而植物蜡添加剂对石蜡针入度的影响显著 ,并可以利用拟合方程对添加剂作用于石蜡的针入度的物理特性进行预测。这一结果对石蜡新产品的研究具有参考价值。