一类迁移方程逆问题的求解

迁移方程在原子核物理、气象预报和人口理论等方面具有广泛的应用，此类问题的逆问题更具有其实用性。作者在已有工作的基础上，应用奇异积分方程理论，给出了求解此类问题的具体表达式。     

Fractional Reaction-Diffusion Equations

In a series of papers, Saxena et al. (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen et al. (1999) for anomalous diffusion and del-Castillo-Negrete et al. (2003) for reaction-diffusion systems with Lévy flights. The solution has been developed in terms of the H-function in a compact form with the help of Laplace and Fourier transforms. Most of the results obtained are in a form suitable for numerical computation.     

附合网平差的基准与起始数据误差的影响

讨论在通用误差方程的基础上，已知数据用基准方程来给予体现，用秩亏平差的方式，解决独立网平差、特别是附合网平差的问题。用算例证明，基准方程平差附合网将达到传统附合网平差的目的且在某些方面优于传统平差。同时对起算数据误差的处理方式进行了探讨。     

不适定方程正则化算法的谱分解式

从观测方程系数矩阵的谱分解着手探讨不适宜方程的正则化算法。利用谱分解式阐明了正则化的主要作用是平滑对参数估值比较敏感的观测误差的高频分量，完整给出了最小二乘平差、秩亏平差和病态方程正则化解的谱分解公式，证明了正则化解参数估值偏离真值的二次范数的期望值与均方误差是等价的。     

A New Inversion Method of Sedimentary Strata For Deriving Double Parameters and Its Applications

The inverse problem of wave equation is the importance of study not only in seismic prospecting but also in applied mathematics. With the development of the research, the inverse methods of 1 - D wave equations have been trending towards the multiple parameters inversion . We have obtained an inverse method with double -parameter, in which medium density and wave velocity can be derived simultaneously. In this paper, to increase the inverse accuracy, the method is improved as follows. Firstly, the formula in which the Green Function is omitted are derived and used. Secondly, the regularizing method is reasonable used by choosing the stable function. With the new method, we may derive elastic parameter and medium density or medium density and wave velocity. Thus, lithology parameters for seismic prospecting may be obtained.After comparing the derived values from the new method with that from previous method, we obtain the new method through which substantially improve the derived accuracy . The new method has been applied to real depths inversion for sedimentary strata and volcanic rock strata in Chaoyanggou Terrace of Songliao Basin in eastern China. According to the inverse results,the gas - bearing beds are determlned.     

SCR Distribution Function in the Radial IMF Approximation

The transport of cosmic rays in the interplanetary medium is considered in terms of the kinetic equation describing the energetic particle scattering by magnetic irregularities and their focusing by the regular interplanetary magnetic field. The analytical expression for solar cosmic ray distribution function in the approximation of radial regular magnetic field is obtained and the evolution of energetic particle angular distribution is analyzed. The obtained results can be used for the analysis of ground-level enhancements of cosmic ray intensity.     

关于CAS FGOALS-f3-L模式中青藏高原地表温度偏差的归因分析

中国科学院全球海洋-大气-陆地耦合模式(FGOALS-f3-L)参加了耦合模式比较计划的第六阶段(CMIP6)试验,但是其对关键气候敏感地区青藏高原的地表温度的再现能力还不清楚.这项研究用再分析资料CFSR评估了FGOALS-f3-L模式对青藏高原地表温度的再现能力.结果表明,FGOALS-f3-L可以合理模拟整个高原上年平均地表温度的空间分布,但低估了整个高原上年平均地表温度.模拟的地表温度在整个高原上冬春季表现为冷偏差,夏秋季表现为暖偏差.基于地表能量平衡方程的进一步定量分析表明,地表反照率反馈(SAF)项极大地贡献了高原西部年平均,冬春季平均地表温度的冷偏差,而对高原东部是暖偏差贡献.与SAF项相比,地表感热项对地表温度偏差的贡献几乎相反,这大大抵消了SAF项引起的偏差.云辐射强迫项对高原东部的年平均和季节平均弱冷偏差有很大贡献.与高估的水蒸气含量有关的长波辐射项造成了夏秋季整个高原上大部分的暖偏差.该研究表明,提高FGOALS-f3-L中的陆面和云过程对降低高原上地表温度偏差至关重要.     

Seasonal temperatures from δ18O in recent Spanish tufa stromatolites: Equilibrium redux!

This study focuses on recent debate over the value of stable isotope‐based environmental proxies recorded in riverine tufa stromatolites. A twelve‐year record (1999 to 2012) of river‐bed tufa stromatolites in the River Piedra (north‐east Spain) was recovered in this study, along with a partly overlapping fifteen‐year record (1994 to 2009) of accumulations in a drainage pipe: both deposits formed in water with near identical physico/chemical parameters. Measured water temperature data and near‐constant δ ¹⁸O_water composition allowed selection of an ‘equilibrium’ palaeotemperature equation that best replicated actual temperatures. This study, as in some previous studies, found that just two published formulas for water temperature calculation from equilibrium calcite δ ¹⁸O compositions were appropriate for the River Piedra, where tufa deposition rates are high, with means between 5·6 mm and 10·8 mm in six months. The δ ¹⁸O_calcite in both the river and the pipe deposits essentially records the full actual seasonal water temperature range. Only the coldest times (water temperature <10°C), when calcite precipitation mass decreased to minimum, are likely to be unrepresented, an effect most noticeable in the pipe where depositional masses are smaller and below sample resolution. While kinetic effects on δ ¹⁸O_calcite‐based calculated water temperature cannot be ruled out, the good fit between measured water temperature and δ ¹⁸O_calcite‐calculated water temperature indicates that temperature is the principal control. Textural and deposition rate variability between the river and pipe settings are caused by differences in flow velocity and illumination. In the river, calcification of growing cyanobacterial mat occurred throughout the year, producing composite dense and porous laminae, whereas in the pipe, discontinuous cyanobacterial growth in winter promoted more abiogenic calcification. High‐resolution δ ¹⁸O_calcite data from synchronous pipe and river laminae show that reversals in water temperature occur within laminae, not at lamina boundaries, a pattern consistent with progressive increase in calcite precipitation rate as cyanobacterial growth re‐established in spring.     

Diagnostics of the shape and orientation of a rock failure zone based on electrical measurements as an inverse problem of geophysics

Exploration geophysics is concerned with the development of methods and techniques for remote search for mineral deposits, solution of various engineering and geological problems, mining monitoring, and diagnostics of zones of rock bursts and natural and technogenic tectonic earthquakes. In this paper, we consider the diagnostic problem of exploration geophysics related to the determination of the shape and inclination angle of a plane source of natural geoelectric field, which, under certain conditions, simulates a rock failure zone, e.g., during the preparation of rock bursts at the sites of developed mineral deposits. This approach may also be useful in determining the shape and size of ore shoots by electrical measurements on the ground surface. Evaluation of the parameters of a rock failure zone is required in the case of accumulation of multiple fractures having charges of the same sign before a catastrophic failure. This problem is formulated as a Fredholm-Urysohn integral equation of the first kind. The solution of the integral equation is sought using the Tikhonov regularization method of the second order.