Adaptive multi-step piecewise interpolation reproducing kernel method for solving the nonlinear time-fractional partial differential equation arising from financial economics

This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)method which deals with this problem is very troublesome.This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first time.This method has three obvious advantages which are as follows.Firstly,the piecewise number is reduced.Secondly,the calculation accuracy is improved.Finally,the waste time caused by too many fragments is avoided.Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others.The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.

The Alternating Group Explicit Iterative Method for the Regularized Long-Wave Equation

An Alternating Group Explicit (AGE) iterative method with intrinsic parallelism is constructed based on an implicit scheme for the Regularized Long-Wave (RLW) equation. The method can be used for the iteration solution of a general tridiagonal system of equations with diagonal dominance. It is not only easy to implement, but also can directly carry out parallel computation. Convergence results are obtained by analysing the linear system. Numerical experiments show that the theory is accurate and the scheme is valid and reliable.

Rapid Springback Compensation for Age Forming Based on Quasi Newton Method

Iterative methods based on finite element simulation are effective approaches to design mold shape to compensate springback in sheet metal forming. However, convergence rate of iterative methods is difficult to improve greatly. To increase the springback compensate speed of designing age forming mold, process of calculating springback for a certain mold with finite element method is analyzed. Springback compensation is abstracted as finding a solution for a set of nonlinear functions and a springback compensation algorithm is presented on the basis of quasi Newton method. The accuracy of algorithm is verified by developing an ABAQUS secondary development program with MATLAB. Three rectangular integrated panels of dimensions 710 mmx750 mm integrated panels with intersected ribs of 10 mm are selected to perform case studies. The algorithm is used to compute mold contours for the panels with cylinder, sphere and saddle contours respectively and it takes 57%, 22% and 33% iterations as compared to that of displacement adjustment （DA） method. At the end of iterations, maximum deviations on the three panels are 0.618 4 mm, 0.624 1 mm and 0.342 0 mm that are smaller than the deviations determined by DA method （0.740 8 mm, 0.740 8 mm and 0.713 7 mm respectively）. In following experimental verification, mold contour for another integrated panel with 400 ram^380 mm size is designed by the algorithm. Then the panel is age formed in an autoclave and measured by a three dimensional digital measurement devise. Deviation between measuring results and the panel＇s design contour is less than 1 mm. Finally, the iterations with different mesh sizes （40 mm, 35 mm, 30 mm, 25 mm, 20 mm） in finite element models are compared and found no considerable difference. Another possible compensation method, Broyden-Fletcher-Shanmo method, is also presented based on the solving nonlinear fimctions idea. The Broyden-Fletcher-Shanmo method is employed to compute mold contour for the second panel. It only takes 50% iterations compared to that of DA. The proposed method can serve a faster mold contour compensation method for sheet metal forming.

Application of Multi-Step Differential Transform Method on Flow of a Second-Grade Fluid over a Stretching or Shrinking Sheet

In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization, discretization, or perturbation. It is a semi analytical-numerical technique that formulizes Taylor series in a very different manner. By applying the MDTM the interval of convergence for the series solution is increased. The MDTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. It is predicted that the MDTM can be applied to a wide range of engineering applications.

Facial Beautification Method Based on Age Evolution

This paper proposes a new facial beautification method using facial rejuvenation based on the age evolution. Traditional facial beautification methods only focus on the color of skin and deformation and do the transformation based on an experimental standard of beauty. Our method achieves the beauty effect by making facial image looks younger, which is different from traditional methods and is more reasonable than them. Firstly, we decompose the image into different layers and get a detail layer. Secondly, we get an age-related parameter： the standard deviation of the Gaussian distribution that the detail layer follows, and the support vector machine （SVM） regression is used to fit a function about the age and the standard deviation. Thirdly, we use this function to estimate the age of input image and generate a new detail layer with a new standard deviation which is calculated by decreasing the age. Lastly, we combine the original layers and the new detail layer to get a new face image. Experimental results show that this algo- rithm can make facial image become more beautiful by facial rejuvenation. The proposed method opens up a new way about facial beautification, and there are great potentials for applications.

Chaos control of gear system with elastomeric web based on multi-parameter multi-step method

This paper employs a multi-parameter multi-step chaos control method, which is built up on the OGY method, to stabilize desirable UPOs of a gear system with elastomeric web as a high-dimensional and non-hyperbolic chaotic system, and the analyses are carried out. Three types of relations between components of a certain control parameter combination are defined in a certain control process. Special emphasis is put on the comparison of control efficiencies of the multi-parameter multi-step method and single-parameter multi-step method. The numerical experiments show the ability to switch between different orbits and the method can be a good chaos control alternative since it provides a more effective UPOs stabilization of high-dimensional and non-hyperbolic chaotic systems than the single-parameter chaos control, and according to the relation between components of each parameter combination, the best combination for chaos control in a certain UPO stabilization process are obtained.

Factors Associated with the Use of Modern Contraceptive Methods by Women of Childbearing Age in Parakou in 2017

As in other countries of West Africa, Benin has a low rate of MCM utilization. The factors which lead to this low rate of use vary from one country to another. Purpose: The purpose of this work was to determine the factors associated with the use of modern contraceptive method (MCM) by women of childbearing age (WCBA) in Parakou in 2017. Materials and Methods: It was a cross-sectional and descriptive study with an analytical purpose among WCBA selected in households of the municipality of Parakou after a 2-degree cluster survey. Results: The WCBA’s average age was 29 ± 5.6 years old with extremes of 15 and 46 years. The modern contraceptive prevalence was 14.74%. Among WCBA, 57.14% had an average level of knowledge. The media were the main source of information (75.84%). Among them 34.39% never discussed the matter with their spouse;the latter were not in favor of contraception. The educational level, the perception of woman, the spouse’s favorable opinion, the discussion with the spouse, the level of knowledge of MCM and the knowledge of the existence of FP service were significantly associated with the use of MCM with p = 0.0000 after multivariate analysis. Conclusion: The level of MCM use still remains low. Any effort to increase the modern contraceptive prevalence should take into account its associated factors in order to optimize the use of MCM in the municipality of Parakou in 2017.

Improving Grain Yield of Indigenous Rice in Tidal Floodplain of Southern Bangladesh: Effect of Seedling Age and Transplanting Method

Rice production in the tidal floodplain of southern Bangladesh is constrained by uncontrolled water. In absence of high yielding varieties suitable for tidal floodplain, farmers grow low yielding indigenous cultivars of tall plant type. This paper reports the effect of agronomic management on the yield and yield components of an indigenous rice cultivar, Sadamota. The trial was conducted in 10 farmers’ plots located widely apart in two upazila (sub-districts)—Jhalakati and Rajapur. 45 d and 60 d old seedlings were transplanted either in rows at 40 cm × 20 cm spacing or following farmers’ traditional practice of random planting. Transplanting 60 d old seedlings produced 14% higher yield compared with 45 d old seedlings. Transplanting in rows also increased grain yield by 12%. The yield increase was associated with hill density, the number of effective tillers per hill and the number of spikelets per panicle.

Age trends and correlations of growth and wood properties in clone of Eucalyptus urophylla × E. grandis in Guangdong, China

We assessed growth traits and wood properties ofDH32-29, a clone of Eucalyptus urophylla x E. grandis, at age of two to six years in Guangdong in China. Analysis of variance of studied traits showed that there were significant differences （1% level） on all studied traits among ages except for wood basic density. Analysis of age trends of growth traits and wood properties revealed that rotation length of DH32-29 should be more than six years or longer. Phenotypic correlations among traits at individual ages indicated that correlations between growth traits were strongly positive. There was significant change in relationship between growth and wood basic density with increasing age, ranging from -0.03 to -0.54 at 2 and 5 year and 0.003 to 0.3 at 3, 4 and 6 year. Correlations between Pilodyn pin penetration and basic density measured on increment cores showed that Pilodyn could rank or group genotypes or sites into density classes, but failure to predict individual tree and individual clone.

Effect of Curing Age on Chloride Diffusion Coefficient of Recycled Aggregate Concrete Subjected to Compressive Stresses

The effect of curing age on chloride diffusion coefficient of recycled aggregate concrete subjected to different compressive stresses was investigated.A compression loading setup was both designed and fabricated.The chloride diffusion coefficients of recycled aggregate concrete under compressive stresses were measured by the rapid chloride ion migration(RCM)method.The experimental results show that the chloride diffusion coefficients of recycled aggregate concrete(RAC)under different compressive stress ratios generally decrease with the increase of curing age.For RAC subjected to the same compressive stress ratios,the chloride diffusion coefficients approximately have power functions with curing ages and the relationship models are proposed.Moreover,the influence of curing age on chloride diffusion coefficient firstly decreases and then increases as the compressive stress ratio increases.

Skeletochronological Study on Age Structure of a Chinese Endemic Frog(Rana omeimontis)

We used skeletochronology to estimate age structure of the Omei Wood Frog, Rana omeimontis, from southwestern China.Average age differed significantly between males and females.Age at sexual maturity in both males and females was 1 year. Longevity was 6 and 7 years for males and females, respectively. Average body size differed significantly between the sexes, with females being larger than males. A non-significant correlation between age and body size was found within each sex in this population. The ANCOVA analysis revealed that females also had larger body size than males when the effect of age was controlled.

Optimized Hybrid Block Adams Method for Solving First Order Ordinary Differential Equations

Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost.The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency.Hybrid block methods for instance are specifically used in numerical integration of initial value problems.In this paper,an optimized hybrid block Adams block method is designed for the solutions of linear and nonlinear first-order initial value problems in ordinary differential equations(ODEs).In deriving themethod,the Lagrange interpolation polynomial was employed based on some data points to replace the differential equation function and it was integrated over a specified interval.Furthermore,the convergence properties along with the region of stability of the method were examined.It was concluded that the newly derived method is convergent,consistent,and zero-stable.The method was also found to be A-stable implying that it covers the whole of the left/negative half plane.From the numerical computations of absolute errors carried out using the newly derived method,it was found that the method performed better than the ones with which we compared our results with.Themethod also showed its superiority over the existing methods in terms of stability and convergence.

Ponseti method treatment of neglected idiopathic clubfoot:Preliminary results of a multi-center study in Nigeria

AIM To evaluate the effectiveness of the Ponseti method for initial correction of neglected clubfoot cases in multiple centers throughout Nigeria.METHODS Patient charts were reviewed through the International Clubfoot Registry for 12 different Ponseti clubfoot treatment centers and 328 clubfeet(225 patients) met inclusion criteria. All patients were treated by the method described by Ponseti including manipulation and casting with percutaneous Achilles tenotomy as needed.RESULTS A painless plantigrade foot was obtained in 255 feet(78%) without the need for extensive soft tissue release and/or bony procedures.CONCLUSION We conclude that the Ponseti method is a safe, effective and low-cost treatment for initial correction of neglected idiopathic clubfoot presenting after walking age. Longterm follow-up will be required to assess outcomes.

A Comparison Study of Synkinematic Illite Isolation,Quantitative X-ray Powder Diffraction,and K-Ar Dating for Direct Fault Gouge Analyses

K-Ar dating of synkinematic illite is increasingly recognized as a central method to constrain the timing of shallow crustal faulting.Methods of efficient sample preparation and quantitative identification of illite polytypes are critical to acquiring K-Ar isotope data for authigenic clays.In this respect,we compared the commonly used clay size separation method through centrifugation with vacuum filtration technology,showing that the former is prone to extract fractions with finer particle sizes under similar conditions,thus improving the error in the authigenic end-member age.Additionally,we demonstrated that the side-packed mounting method for X-ray diffraction analysis can significantly enhance the randomness in powder samples,thus improving the quantification accuracy compared with the front-packed and back-packed methods.The validity of our quantification method was confirmed by comparing Profex■modeling patterns with a suite of synthetic mixtures of known compositions,yielding an average analytical error of 3%.Dating results of these artificial mixtures and the reference materials indicated that a large range in percentages of detrital illite and a sufficient amount of age data will produce reliable results for ages of both extrapolated end-members.However,if the range is limited,the extrapolated age close to those of datasets is still reliable.

A Study of the Rhenium-Osmium Geochronometry of Molybdenites

This study deals with the first application of the isotope dilution - inductively coupled plasma mass spectrometry in the rhenium-osmium geochronometry in China. The chemical separation procedure included decomposition of samples by means of alkali fusion, extraction of rhenium by acetone and extraction of osmium by distillation. The recovery of both elements in the entire process was more than 90% . The blanks of analyses were 0.07 ng for rhenium and 0.01 ng for 187Os. The mineralization ages of molybdenites from four molybdenum deposits in China were determined by using this method, with a precision (2σ)of about ±3% . These results agree satisfactorily with their geological backgrounds. The Re-Os method can directly determine ages of metal deposits and reflect the true ages more reliably than other dating methods that only determine the ages of country rocks from which mineralization ages are inferred. As many hydrothermal sulphide deposits usually contain molybdenites, this method has bright prospects of wide application.

THE STEP-TRANSITION OPERATORS FOR MULTI-STEP METHODS OF ODE'S

In this paper, we propose a new definition of symplectic multistep methods. This definition differs from the old ones in that it is given via the one step method defined directly on M which is corresponding to the m step scheme defined on M while the old definitions are given out by defining a corresponding one step method on M × M ×…× M = Mm with a set of new variables. The new definition gives out a steptransition operator g: M → M. Under our new definition, the Leap-frog method is symplectic only for linear Hamiltonian systems. The transition operator g will be constructed via continued fractions and rational approximations.

NON-EXISTENCE OF CONJUGATE-SYMPLECTIC MULTI-STEP METHODS OF ODD ORDER

We prove that any linear multi-step method G1^T of the form ∑k=0^mαkZk = T∑k=0^mβkJ^-1↓ΔH（Zk） with odd order u （u≥ 3） cannot be conjugate to a symplectic method G2^T of order w （w 〉 u） via any generalized linear multi-step method G3^T of the form ∑k=0^mαkZk = T∑k=0^mβkJ^-1↓ΔH（∑l=0^mγklZl）. We also give a necessary condition for this kind of generalized linear multi-step methods to be conjugate-symplectic. We also demonstrate that these results can be easily extended to the case when G3^T is a more general operator.

ON CONJUGATE SYMPLECTICITY OF MULTI-STEP METHODS

In this paper, we solve a problem on the existence of conjugate symplecticity of linear multi-step methods (LMSM), the negative result is obtained. [ABSTRACT FROM AUTHOR]

EXPANSIONS OF STEP-TRANSITION OPERATORS OF MULTI-STEP METHODS AND ORDER BARRIERS FOR DAHLQUIST PAIRS

Using least parameters, we expand the step-transition operator of any linear multi-step method （LMSM） up to O（τ^s＋5） with order s = 1 and rewrite the expansion of the steptransition operator for s = 2 （obtained by the second author in a former paper）. We prove that in the conjugate relation G3^λτ o G1^τ =G2^τ o G3^λτ with G1 being an LMSM,（1） theorder of G2 can not be higher than that of G1; （2） if G3 is also an LMSM and G2 is a symplectic B-series, then the orders of G1, G2 and G3 must be 2, 2 and 1 respectively.

The radio environment of the 21 Centimeter Array:RFI detection and mitigation

Detection and mitigation of radio frequency interference （RFI） is the first and also the key step for data processing in radio observations, especially for ongoing low frequency radio experiments towards the detection of the cosmic dawn and epoch of reionization （EoR）. In this paper we demonstrate the tech- nique and efficiency of RFI identification and mitigation for the 21 Centimeter Array （21CMA）, a radio interferometer dedicated to the statistical measurement of EoR. For terrestrial, man-made RFI, we concen- trate mainly on a statistical approach by identifying and then excising non-Gaussian signatures, in the sense that the extremely weak cosmic signal is actually buried under thermal and therefore Gaussian noise. We also introduce the so-called visibility correlation coefficient instead of conventional visibility, which allows a further suppression of rapidly time-varying RFI. Finally, we briefly discuss removals of the sky RFI, the leakage of sidelobes from off-field strong radio sources with time-invariant power and a featureless spec- trum. It turns out that state of the art technique should allow us to detect and mitigate RFI to a satisfactory level in present low frequency interferometer observations such as those acquired with the 21CMA, and the accuracy and efficiency can be greatly improved with the employment of low-cost, high-speed computing facilities for data acquisition and processing.