2D multi-scale hybrid optimization method for geophysical inversion and its application

Local and global optimization methods are widely used in geophysical inversion but each has its own advantages and disadvantages. The combination of the two methods will make it possible to overcome their weaknesses. Based on the simulated annealing genetic algorithm （SAGA） and the simplex algorithm, an efficient and robust 2-D nonlinear method for seismic travel-time inversion is presented in this paper. First we do a global search over a large range by SAGA and then do a rapid local search using the simplex method. A multi-scale tomography method is adopted in order to reduce non-uniqueness. The velocity field is divided into different spatial scales and velocities at the grid nodes are taken as unknown parameters. The model is parameterized by a bi-cubic spline function. The finite-difference method is used to solve the forward problem while the hybrid method combining multi-scale SAGA and simplex algorithms is applied to the inverse problem. The algorithm has been applied to a numerical test and a travel-time perturbation test using an anomalous low-velocity body. For a practical example, it is used in the study of upper crustal velocity structure of the A＇nyemaqen suture zone at the north-east edge of the Qinghai-Tibet Plateau. The model test and practical application both prove that the method is effective and robust.

关于数据组带有导数的拟合问题

本文目的是将样条函数推广用于带有导数的拟合问题,拓广了

具不同变化规律的时间序列建模方法

本文对具不同变化规律的时间序列详细介绍了三种建模方法 :虚拟变量法 ,分段拟合法和样条函数法 。

非稳定法用张力样条计算模型拟合P－S曲线

本文分析了载荷试验数据处理的非稳定法高次多项式拟合不规则Ｐ－ｓ曲线的局限性，论述了张力样条函数计算模型拟合不规则Ｐ－ｓ曲线的可行性，借助工程实例说明该法为拟合Ｐ－ｓ曲线的较好模型。

凸轮机构反求设计中速度及加速度的计算

通过将解析法同数值法及三次插值样条函数相结合，提出了求盘形凸轮机构速度及加速度的半解析法。这种方法适合于凸轮机构的反求设计。

Method of Semi Analytic Perturbation Weighted Residuals for Nonlinear Bending of Shallow Shells

The semi? analytic perturbation weighted residuals method was used to solve the nonlinear bending problem of shallow shells, and the fifth order B spline was taken as trial function to seek an efficient method for nonlinear bending problem of shallow shells. The results from the present method are in good agreement with those derived from other methods. The present method is of higher accuracy, lower computing time and wider adaptability. In addition, the design of computer program is simple and it is easy to be programmed.

Positions and Widths of Anticrossings for Potassium Rydberg Stark States

The B-spline expansion technique is applied to study the anticrossings for potassium Rydberg states in a static electric field. The results of our calculation indicate that the antierossings are caused mainly by the core interaction or by the fine structure interaction. Our results for the positions and the widths of the anticrossings are in good agreement with experimental data.

Notes on the Scaling Function

Two properties are given in this paper about the scaling function: suppose Vj; j ∈ Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transform of φ is a continuous real function, compactly supported, then φ(0) ≠ 0 and when supp φ = [a1,b1]∪[a2,b2](b1 < a2,0 < a2), then we havea1 ≤ 0, 0 < b1, a1 < b2/2 ≤ b1, 2π < b2 - a1 ≤ 8π.

The Impacts of Permafrost Change on NPP and Implications:A Case of the Source Regions of Yangtze and Yellow Rivers

This paper studies the relationship between net primary productivity (NPP) and annual average air temperature (GT) at 0cm above ground in permafrost regions by using revised Chikugo NPP model,cubic spline interpolating functions,and non-linear regression methods.The source regions of the Yangtze and Yellow Rivers were selected as the research areas.Results illustrate that:(1) There is significant non-linear relationship between NPP and GT in various typical years;(2) The maximum value of NPP is 6.17,5.87,7.73,and 5.41 DM·t·hm-2 ·a-1 respectively,and the corresponding GT is 7.1,10.0,21.2,and 8.9 o C respectively in 1980,1990,2000 and 2007;(3) In 1980,the sensitivity of NPP to GT is higher than in 1990,2000 and 2007.This tendency shows that the NPP presents change from fluctuation to an adaptation process over time;(4) During 1980～2007,the accumulated NPP was reduced to 8.05,and the corresponding carrying capacity of theoretical livestock reduced by 11%;(5) The shape of the demonstration region of ecological compensation system,livelihood support system,and science appraisal system in the source regions of Yangtze and Yellow Rivers are an important research for increasing the adaptation capacity and balancing protection and development.

Improving cam profile design optimization based on classical splines and dynamic model

Cam profiles play an important part in the performance of cam mechanisms. Syntheses of cam profile designs and dynamics of cam designs are studied at first. Then, a cam profile design optimization model based on the six order classical spline and single DOF(degree of freedom) dynamic model of single-dwell cam mechanisms is developed. And dynamic constraints such as jumps and vibrations of followers are considered. This optimization model, with many advantages such as universalities of applications, conveniences to operations and good performances in improving kinematic and dynamic properties of cam mechanisms, is good except for the discontinuity of jerks at the end knots of cam profiles which will cause vibrations of cam systems. However, the optimization is improved by combining the six order classical spline with general polynomial spline which is the so-called "trade-offs". Finally, improved optimization is proven to have a better performance in designing cam profiles.

A B-spline active contour model based on finite element method

A B-spline active contour model based on finite element method is presented, into which the advantages of a B-spline active contour attributing to its fewer parameters and its smoothness is built accompanied with reduced computational complexity and better numerical stability resulted from the finite element method. In this model, a cubic B-spline segment is taken as an element, and the finite element method is adopted to solve the energy minimization problem of the B-spline active contour, thus to implement image segmentation. Experiment results verify that this method is efficient for B-spline active contour, which attains stable, accurate and faster convergence.

Climate-growth relationship stability of Picea crassifolia on an elevation gradient,Qilian Mountain,Northwest China

Climate affects Picea crassifolia growth and climate change will lead to changes in the climate–growth relationship(i.e., the "divergence" phenomenon). However, standardization methods can also change the understanding of such a relationship. We tested the stability of this relationship by considering several variables: 1) two periods(1952–1980 and 1981–2009), 2) three elevations(2700, 3000, and 3300 m), and 3) chronologies detrended using cubic splines with two different flexibilities. With increasing elevation, the climatic factor limiting the radial growth of Picea crassifolia shifted from precipitation to temperature. At the elevation of 2700 m, the relationship between radial growth and mean temperature of the previous December changed so that the more flexible spline had a greater precipitation signal. At the elevation of 3000 m, positive correlation of radial growth with mean temperature and precipitation in September of the previous year became more significant. At the elevation of 3300 m, positive correlation between radial growth and precipitation of the currentsummer and the previous spring and autumn was no longer significant, whereas the positive correlation between radial growth and temperature of the current spring and summer strengthened. The detrending with the most flexible spline enhanced the precipitation signal at 2700 m, while that with the least flexible spline enhanced the temperature signal at 3300 m. All results indicated that the divergence phenomenon was affected by the climatic signals in the chronologies and that it was most dependent on the detrending method. This suggests it is necessary to select a suitable spline bootstrap for studies of growth divergence phenomena.

Denoising of hyperspectral imagery by cubic smoothing spline in the wavelet domain

The acquired hyperspectral images （HSIs） are inherently attected by noise wlm Dano-varylng level, which cannot be removed easily by current approaches. In this study, a new denoising method is proposed for removing such kind of noise by smoothing spectral signals in the transformed multi- scale domain. Specifically, the proposed method includes three procedures： 1 ） applying a discrete wavelet transform （DWT） to each band; 2） performing cubic spline smoothing on each noisy coeffi- cient vector along the spectral axis; 3 ） reconstructing each band by an inverse DWT. In order to adapt to the band-varying noise statistics of HSIs, the noise covariance is estimated to control the smoothing degree at different spectra｜ positions. Generalized cross validation （GCV） is employed to choose the smoothing parameter during the optimization. The experimental results on simulated and real HSIs demonstrate that the proposed method can be well adapted to band-varying noise statistics of noisy HSIs and also can well preserve the spectral and spatial features.

B-Spline with Symplectic Algorithm Method for Solution of Time-Dependent Schrodinger Equations

A B-spline with the symplectic algorithm method for the solution of time-dependent Schrodinger equations （TDSEs） is introduced. The spatial part of the wavefunction is expanded by B-spline and the time evolution is given in a symplectic scheme. This method allows us to obtain a highly accurate and stable solution of TDSEs. The effectiveness and efficiency of this method is demonstrated by the high-order harmonic spectra of one-dimensional atoms in comparison with other references.

H_2^+-Like Impurities Confined by Spherical Quantum Dots:a Candidate for Charge Qubits

We have calculated the electron energy of the ground and lower excited states for H_2^+-like impurity statesconfined in finite spherical quantum dots in GaAs.Based on the characteristics of energy levels,we have proposed ascheme for realizing charge qubit composed by the the ground and the first excited states of this confined double donorsystem for the first time.In the proposed scheme the charge qubit is coded in terms of the located electronic states.

B-splines smoothed rejection sampling method and its applications in quasi-Monte Carlo integration

The rejection sampling method is one of the most popular methods used in Monte Carlo methods. It turns out that the standard rejection method is closely related to the problem of quasi-Monte Carlo integration of characteristic functions, whose accuracy may be lost due to the discontinuity of the characteristic functions. We proposed a B-splines smoothed rejection sampling method, which smoothed the characteristic function by B-splines smoothing technique without changing the integral quantity. Numerical experiments showed that the convergence rate of nearly O( N^-1 ) is regained by using the B-splines smoothed rejection method in importance sampling.

A novel contour design technique of super/hypersonic nozzle diverging section with sharing throat

A straightforward technique has been developed to quickly determine the wall contour of super/hypersonic nozzles working at multiply Mach number which share a common throat section.Mach number distribution along the centerline of the nozzle is specified in advance and divided into two sections,both of which are described by the b-spline function.The first section is shared by different exit Mach number nozzles.The nozzle contour is determined by the method of characteristics plus boundary layer correction.An example of this design method is employed to illustrate the technique with a computational fluid dynamics calculation.The simulation results indicate that desired Mach numbers are obtained at the nozzle exit,and the good flow quality is attained for different nozzles within δMa/Ma<±0.56% in the flow core region.This technique improves the design precision of the converging-diverging nozzle,cancels waves completely,and achieves nozzles with multiple Mach number exiting which share a common throat section.

Deformation Model Inferred from Focal Mechanisms in the Chinese Mainland and Its Adjacent Areas

We collect seismic moment tensors of the earthquakes occurring from 1900 to 2013 in and around the Chinese mainland and summarize the surface ruptures and displacements of 70 earthquakes with M S≥7. 0. We divide these large earthquakes into three types. Type A contains earthquakes with surface ruptures and displacements. Type B is earthquakes without displacements and Type C is those without any of this data. We simulate a triangular distribution of displacements for Type B and C. Then,we segment these large earthquakes by using their displacements and surface ruptures. Finally,kinematic models are determined from earthquake data and Bicubic Bessel spline functions. The results show that,first of all,the reasonability and spatial consistency of defined models are advanced.Strain rates have better continuity and are comparable with geologic and geodetic results in Himalaya thrust fault zones. The strain rates decrease in the Tarim basin and the Altun Tagh fault zones because of their low seismicity. The direction of compressional deformation in Gobi-Altay is changed from SE to NE and its extensional direction is changed from NE to NW. The extensional deformation in the Ordos block is diminished obviously. Secondly,earthquakes account for 30- 50% of expected motion of India relative to Eurasia determined from the NUVEL-1A model,with a missing component of 20 mm / a which may contain aseismic deformation such as fault creep and folds,the missing parts of earthquake data and elastic strain energy released by potential earthquakes.

THEORY AND METHOD FOR QUANTITATIVE COALFIELD EXPLORATION

The theoretical system of the quantitative coalfield exploration and the relevant quantitative evaluation system, as well as the mathematical models and quantitative indices and classification scheme have been preliminarily established on the basis of having quantitatively investigated and classified such basic problems in the coal exploration as the geological structure and coal seam variation, the exploration type, the density of exploration net, in the light of materials accumulated in China over the past forty years, under the theoretical guidance of modern coal geology, applied mathematics and mathematical geology by means of the computer technique.

Statistics and Correlation Properties of Diamagnetic High Rydberg Hydrogen Atom

The spectra of Rydberg hydrogen atom in magnetic fields have been calculated using linear variational method with B-splines basis functions [Acta Phys. Sin. 55 （2006） 3380]. Based on these calculations we have done some statistics analysis about the high Rydberg energy levels. The nearest-neighbor energy spacing distribution and the 3-statistics have been shown about diamagnetic Rydberg hydrogen atom with the magnetic field being 0.6 T and 6 T. The phenomena of multiply crossing, multiply anti-crossing, and the mixed of crossing and anti-crossing of energy levels have appeared in this paper. For both cases, in range of lower energy, the energy 1evel statistics properties close to Poisson distribution. With the increasing of the energy, the energy level statistics properties are away to Poisson distribution and tend to Wigner distribution step by step.