Stability Analysis and Performance Evaluation of Additive Mixed-Precision Runge-Kutta Methods

Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were previously proposed and analyzed.These specially designed methods use reduced precision for the implicit computations and full precision for the explicit computations.In this work,we analyze the stability properties of these methods and their sensitivity to the low-precision rounding errors,and demonstrate their performance in terms of accuracy and efficiency.We develop codes in FORTRAN and Julia to solve nonlinear systems of ODEs and PDEs using the mixed-precision additive Runge-Kutta(MP-ARK)methods.The convergence,accuracy,and runtime of these methods are explored.We show that for a given level of accuracy,suitably chosen MP-ARK methods may provide significant reductions in runtime.

Simultaneous Determination of Uranium and Thorium with Standard Dual-addition Method

dual-standard addition method was proposed and the principle of simultaneous determination for a interfering binary mixtures was discussed. The proposed procedure was applied to spectroscopic analyses for the simultaneous determination of uranium and thorium without prior separation. Various molar ratios of uranium/thorium, from 0.5∶1 to 10∶1, can be determined with satisfactory precision and accuracy. Uranium and thorium content in a phosphate ore and simulated sample were determined, the recoveries were 98.4%～102.5% for uranium and 96.8%～102.3% for thorium, the relative standard deviations (R.S.D) were 1.5%～2.3% for uranium and 2.1%～3.1% for thorium.

Study on extracting alumina from fly ash by compound additive activation method

According to the chemical and mineral composition characteristics of the fly ash,alumina can be extracted from fly ash through the calcining method by using sodium carbonate and calcium carbonate additives.The effects on leaching rate of alumina have been investigated. The results showed that the fly ash can be activated effectively and the leaching rate of alumina can be improved to more than 92% through this method. The best process parameters were the ratio of raw materials,i. e. the material weight ratio of fly ash,calcium carbonate and sodium carbonate was 1. 0∶1. 2∶0. 9. The activating temperature was 850℃-900℃,activating time was 3 h. This process has a potential application prospect and improves the value of comprehensive utilization of fly ash.

Ligand Size Effect on PdLn Oxidative Addition with Aryl Bromide： A DFT Study

The process and mechanism of the ligand volume controlled Pd（PR3）2 （PR3=PH3, PMe3, and PtBu3） oxidative addition with aryl bromide were investigated, using density functional theory method with the conductor-like screening model. Association pathway and dissocia-tion pathway were investigated by the comparison of several energies. The cleavage energy of Pd（PR3）2 complex was calculated, as well as the oxidative addition reaction barrier energy of Pd（PR3）n （n=1,2） with aryl bromide in N,N-dimethylformamide solvent. This study proved that the ligands volume possessed a great impact on the mechanism of oxidative addition： less bulky ligand palladium associated with aryl bromide via two donor ligands,but larger bulky ligand palladium coordinated via monoligand.

Quantification of trace amounts of impurities in high purity cobalt by high resolution inductively coupled plasma mass spectrometry

A An analytical method using high resolution inductively coupled plasma mass spectrometry （HR-ICP-MS） for rapid simultaneous determination of 24 elements （Be, Mg, A1, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Ga, Ge, As, Se, Mo, Ag, Cd, Sn Sb, Ba, Pt, Au, and Pb） in high purity cobalt was described. Sample digestions were performed in closed microwave vessels using HNO3 and HCI. The matrix effects because of the presence of excess HCI and Co were evaluated. The usefulness of high mass resolution for overcoming some spectral interference was demonstrated. The optimum conditions for the determination were tested and discussed. The standard addition method was employed for quantitative analysis. The detection limits were 0.016-1.50 ].tg·g^-1, the recovery ratios were 92.2%-111.2%, and the RSD was less than 3.6%. The method was accurate, quick, and convenient. It was applied to the determination of trace impurities in high purity cobalt with satisfactory results.

Determination of total sulfur in geothermal water by inductively coupled plasma-atomic emission spectrometry

Sulfur speciation and concentration in geothermal water are of great significance for the research and utilization of the water resources.In most situations,it is necessary to determine the total sulfur in geothermal water.In this study,the method was established for the determination of determining total sulfur content-the inductively coupled plasma-atomic emission spectrometry(ICP-AES),with the wavelength of 182.034 nm selected in spectral line of sulfur.It was identified that the optimal working conditions of the ICP-AES instrument were 1200 W for high frequency generator power 9 mm for vertical observation height,0.30 MPa atomizer pressure,and 50 r/min analytical pump speed.The matrix interference of the method was eliminated by the matrix matching method.Using this method,sulfur detection limit and minimum quantitative detection limit were 0.028 mg/L and 0.110 mg/L,respectively,whilst the linear range was 0.0-100.0 mg/L.The recovery rate of sample was between 90.67%and 108.7%,and the relative standard deviation(RSD)was between 0.36%and 2.14%.The method was used to analyze the actual samples and the results were basically consistent with the industry standard method.With high analysis efficiency,the method has low detection limit and minimum quantitative detection limit,wide linear range,good precision and accuracy,and provides an important detection method for the determination of total sulfur in geothermal water.

Application of artificial neural network to calculation of solitary wave run-up

The prediction of solitary wave run-up has important practical significance in coastal and ocean engineering, but the calculation precision is limited in the existing models. For improving the calculation precision, a solitary wave run-up calculation model was established based on artificial neural networks in this study. A back-propagation （BP） network with one hidden layer was adopted and modified with the additional momentum method and the auto-adjusting learning factor. The model was applied to calculation of solitary wave run-up. The correlation coefficients between the neural network model results and the experimental values was 0.996 5. By comparison with the correlation coefficient of 0.963 5, between the Synolakis formula calculation results and the experimental values, it is concluded that the neural network model is an effective method for calculation and analysis of solitary wave ran-up.

The constructive technique and its application in solving a nonlinear reaction diffusion equation

A mathematical technique based on the consideration of a nonlinear partial differential equation together with an additional condition in the form of an ordinary differential equation is employed to study a nonlinear reaction diffusion equation which describes a real process in physics and in chemistry. Several exact solutions for the equation are acquired under certain circumstances.

Eco-environmental susceptibility in Shangyi County,Northern Hebei Province,China

In this paper,the eco-environmental susceptibility of Shangyi County,Northern Hebei Province of China has been calculated by using the weighted-addition method based on expert's giv- ing a mark to each influencing factor according to their knowledge on the influence of all the factors on eco-environmental susceptibility.The eco-environmental classification and distribution map were reached based on the above results,its difference is mainly result from the physical conditions and human activity,however the value of eco-environmental susceptibility is only a relative index which can not completely reflect the quality of eco-environment.This work provided a basis for control- ling the further development of desertification.

Explicit Analytical Solutions of Radial Permeable Power Rate Flow

The research of different kinds of permeable non-Newtonian fluid flow is increasing day by day owing to the development of science,technology and production modes.It is most common to use power rate equation to describe such flows.However,this equation is nonlinear and very difficult to derive explicit exact analytical solutions.Generally,people can only derive approximate solutions with numerical methods.Recently,an advanced separating variables method which can derive exact analytical solutions easier is developed by Academician CAI Ruixian（the method of separating variables with addition）.It is assumed that the unknown variable may be indicated as the sum of one-dimensional functions rather than the product in the common method of separating variables.Such method is used to solve the radial permeable power rate flow unsteady nonlinear equations on account of making the process simple.Four concise（no special functions and infinite series） exact analytical solutions is derived with the new method about this flow to develop the theory of non-Newtonian permeable fluid,which are exponential solution,two-dimensional function with time and radius,logarithmic solution,and double logarithmic solution,respectively.In addition,the method of separating variables with addition is developed and applied instead of the conventional multiplication one.It is proven to be promising and encouraging by the deducing.The solutions yielded will be valuable to the theory of the permeable power rate flow and can be used as standard solutions to check numerical methods and their differencing schemes,grid generation ways,etc.They also can be used to verify the accuracy,convergency and stability of the numerical solutions and to develop the numerical computational approaches.

Modified attitude pursuit guidance law for low-cost missiles using strap-down seekers

Attitude pursuit guidance law is suitable for low cost missiles.A strap-down seeker is used to achieve this guidance law.The additional angles of attack or sideslip caused by wind and by control system are considered as two disturbing factors which make attitude pursuit law impossible.Therefore,general attitude pursuit guidance law did not account for this two disturbing factors,because with those disturbing factors,it is difficult to apply.To solve the problem,the principle of strap-down seeker detecting target is investigated,the mathematical control model is established,then a modified attitude pursuit guidance law which employs the angular correction for those two disturbing factors is presented.It is proved that the modified attitude pursuit guidance law is appropriated to both in the presence of the additional angle of attack or sideslip via the simulations with the mathematical control model and Monte-Carlo method.

Fast Determination of Phenanthrene in Soil by Gas Chroma- tography-Mass Spectrometry Using Chemometric Resolution and Standard Addition Method

A method for fast determination of the component in complex samples by using gas chromatography-mass spectrometry （GC-MS） was developed and used for quantitative analysis of phenanthrene in soils. In the method, window independent component analysis （WICA） was used for resolving the mass spectrum and non-negative im- mune algorithm （NNIA） was employed for obtaining the chromatographic profile. Therefore, spectral and chroma- tographic information of a specific component can be obtained from the measured GC-MS data of overlapping and high background. Six soil samples collected from different places were analyzed. The tedious pretreatments in pre- paring the samples and the elution in the separation were simplified for speeding up the analysis. Due to the com- plexity of the matrix, standard addition method was adopted for the final quantification. The applicability of the method was validated with a spiked sample and the results of the six samples are reasonable.

Effect of the chlortetracycline addition method on methane production from the anaerobic digestion of swine wastewater

Effects of antibiotic residues on methane production in anaerobic digestion are commonly studied using the following two antibiotic addition methods：（1） adding manure from animals that consume a diet containing antibiotics, and（2） adding antibiotic-free animal manure spiked with antibiotics. This study used chlortetracycline（CTC） as a model antibiotic to examine the effects of the antibiotic addition method on methane production in anaerobic digestion under two different swine wastewater concentrations（0.55 and 0.22 mg CTC/g dry manure）. The results showed that CTC degradation rate in which manure was directly added at 0.55 mg CTC/g（HSPIKE treatment） was lower than the control values and the rest of the treatment groups. Methane production from the HSPIKEtreatment was reduced（p 〈 0.05） by 12% during the whole experimental period and 15% during the first 7 days. The treatments had no significant effect on the pH and chemical oxygen demand value of the digesters, and the total nitrogen of the0.55 mg CTC/kg manure collected from mediated swine was significantly higher than the other values. Therefore, different methane production under different antibiotic addition methods might be explained by the microbial activity and the concentrations of antibiotic intermediate products and metabolites. Because the primary entry route of veterinary antibiotics into an anaerobic digester is by contaminated animal manure, the most appropriate method for studying antibiotic residue effects on methane production may be using manure from animals that are given a particular antibiotic, rather than adding the antibiotic directly to the anaerobic digester.

MATRIX ANALYSIS TO ADDITIVE SCHWARZ METHODS

Matrix analysis on additive Schwarz methods as preconditioners is given in this paper. Both cases of with and without coarse mesh are considered. It is pointed out that an advantage of matrix analysis is to obtain more exact upper hound. Our numerical tests access the estimations.

MATRIX ANALYSIS ON LEADING TERM OF CONDITION NUMBER FOR ADDITIVE SCHWARZ METHODS

It is well known the order of preconditioned matrix by using additive Schwarz methods. In order to estimate the resulted PCG iteration counts, the related leading term brfore the order is given in this paper.

A new method of binary addition scheme with massive use of non-linear material based system

The limitations in electronics in arithmetic, algebraic & logic processing are well known. Very high speed performance (above GHz) are not expected at all in conventional electronic mechanism. To achieve high speed performance we may think on the introduction of optics instead of electronics for information, processing and computing. Non-linear optical material is a successful candidate in this regard to play a major role in the optically controlled switching systems and therefore in all-optical parallel computation these materials can show a very good potential aspect. In this paper, we have proposed a new method of an optical half adder as well as full adder circuit for binary addition using non-linear and linear optical materials.

Concise synthesis of valuable chiral N-Boc-β-benzyl-β-amino acid via construction of chiral N-Boc-3-benzyl-5-oxoisoxazolidine through cross-metathesis/conjugate addition/oxidation

Valuable chiral N-Boc-β-benzyl-β-amino acid was concisely synthesized via construction of chiral NBoc-3-benzyl-5-oxoisoxazolidine through cross-metathesis/conjugate addition/oxidation.All of the starting materials for the synthesis of chiral N-Boc-β-benzyl-β-amino acid are cheap,and two-step short procedure make it easy for the rapid construction of various chiral β-arylmethyl-β-amino acids and important drugs,such as sitagliptin phosphate.