一类多维的非线性Schrdinger方程组的初边值问题

本文考虑一类具有耗散与磁场效应的多维非线性Schrdinger型方程组的初边值问题。使用积分估计(包括L~p—L~q估计)证明了整体解的存在性。     

The projection approach to the Fokker-Planck equation. I. Colored Gaussian noise

It is shown that the Fokker-Planck operator can be derived via a projection-perturbation approach, using the repartition of a more detailed operator into a perturbation ₁ and an unperturbed part ₀. The standard Fokker-Planck structure is recovered at the second order in ₁, whereas the perturbation terms of higher order are shown to provoke the breakdown of this structure. To get rid of these higher order terms, a key approximation, local linearization (LL), is made. In general, to evaluate at the second order in ₁ the exact expression of the diffusion coefficient which simulates the influence of a Gaussian noise with a finite correlation time, a resummation up to infinite order in must be carried out, leading to what other authors call the best Fokker-Planck approximation (BFPA). It is shown that, due to the role of terms of higher order in ₁, the BFPA leads to predictions on the equilibrium distributions that are reliable only up to the first order in t. The LL, on the contrary, in addition to making the influence of terms of higher order in ₁ vanish, results in a simple analytical expression for the term of second order that is formally coincident with the complete resummation over all the orders in t provided by the Fox theory. The corresponding diffusion coefficient in turn is shown to lead in the limiting case to exact results for the steady-state distributions. Therefore, over the whole range 0 the LL turns out to be an approximation much more accurate than the global linearization proposed by other authors for the same purpose of making the terms of higher order in ₁ vanish. In the short- region the LL leads to results virtually coincident with those of the BFPA. In the large- region the LL is a more accurate approximation than the BFPA itself. These theoretical arguments are supported by the results of both analog and digital simulation.     

ON THE ABRUPT CHANGE IN SOUTH ASIAN SUMMER MONSOON CLIMATE AND ITS SYNCHRONISM WITH THE GLOBAL RAPID WARMING

This paper has analysed the major characteristics of long-term variation, of summermonsoon climate in South Asia since 1888. An abrupt enhancement of summer monsoon inthe 1920s and its synchronism with the global rapid warming have been detected by theMann-Kendall Rank Statistic test. Based on diagnostic analysis on the atmospheric circulationover the monsoon region and the thermal conditions of both ocean and land during theperiod of abrupt change, it is found that the warming over land was stronger and earlierthan that over the ocean, which would enhance the land-sea thermal contrast and thereforebe favorable to the development of monsoon low and the disturbance in the monsoon flow.This may be a direct factor for the abrupt enhancement of summer monsoon.     

A conformational analysis method for understanding the energy landscapes of clusters.

A newly developed unbiased structural optimization method, named dynamic lattice searching (DLS), is proposed as an approach for conformational analysis of atomic/molecular clusters and used in understanding the energy landscape of large clusters. The structures of clusters are described in terms of the number of basic tetrahedron (BT) units they contain. We found that the hit numbers of different structural motifs in DLS runs is proportional to the number of BTs. A parameter T(max) is defined to limit the maximal number of atoms moved in a structural transition. Results show that T(max) is a key parameter for modulating the efficiency of the DLS method and has a great influence on the hit number of different motifs in DLS runs. Finally, the effect of potential range on the conformational distribution of the (Morse)(98) cluster is also discussed with different potential-range parameters.     

Global Forcing Number of Benzenoid Graphs

A global forcing set in a simple connected graph G with a perfect matching is any subset S of E(G) such that the restriction of the characteristic function of perfect matchings of G on S is an injection. The number of edges in a global forcing set of the smallest cardinality is called the global forcing number of G. In this paper we prove several results concerning global forcing sets and numbers of benzenoid graphs. In particular, we prove that all catacondensed benzenoids and catafused coronoids with n hexagons have the global forcing number equal to n, and that for pericondensed benzenoids the global forcing number is always strictly smaller than the number of hexagons.     

杂合型全局优化法优化水分子团簇结构

基于遗传算法、快速模拟退火及共轭梯度方法提出了一种快速的杂合型全局优化方法(fast hybrid global optimization algorithm, FHGOA),并将这一方法应用于TIP3P和TIPS2模型水分子团簇(H2O)n结构的优化.在进行TIP3P模型水分子团簇结构的优化过程中,发现了能量比文献值更低的团簇结构,且执行效率有较大提高.把该方法应用到优化TIPS2模型的水分子团簇,发现最优结构和采用TTM2-F模型优化的水分子团簇结构在n < 17时完全相同,为全表面结构;而在n=17、19、22时为单中心水分子笼状结构;在n=25、27时为双中心水分子笼状结构.说明随着团簇中水分子个数的增加,采用TIPS2和TTM2-F势能函数优化的团簇最优结构有相同的变化趋势.     

Resolution of global signals using ratio differential pulse polarograms: Determination of p-nitroaniline and p-nitrotoluene in their mixture

Ratio differential pulse polarograms obtained by dividing the multianalyte and single analyte signals are proposed as a tool for resolution of global signals and quantification of the analytes from a qualitatively known mixture by differential pulse polarography (DPP) and related electroanalytical techniques. The influences of shape and position of the resolving function (DP polarograms of individual analyte) on the efficiency of resolution are discussed on simulated and experimental results. The method is applied for the determination of p-nitroaniline (NA) and p-nitrotoluene (NT) from their mixture in N,N′-dimethylformamide solutions with 0.1 M tetrabutylammonium iodide as supporting electrolyte, using an external calibration diagram and internal standard addition methods. NA and NT give one-electron DP polarographic peaks with 93 mV of peak separation and, therefore, show significant overlapping which depends on the concentration ratio of NA and NT in the mixture. The method is especially suitable for quantification of one analyte in the presence of a large excess of another analyte, because by division the component in excess is removed and the pseudo-ratio DPP of the minor component is clearly revealed in a way which is not possible by deconvolution using polynomial division or deconvolution by Fourier transforms.     

基于CMIP6集合优化数据集的全球陆地极端气候变化预估

预估极端气候事件趋势能够降低其引起的灾害风险.该文基于CMIP6集合优化数据集EPTGODD-WHU,选取5个极端气候指数,即最高气温极大值(TXx)、最高气温极小值(TXn)、最低气温极大值(TNx)、最低气温极小值(TNn)和最大月降水量(PXx),并结合GIS分析手段,对2021—2100年SSP1-2.6、SSP2-4.5和SSP5-8.5情景下的全球陆地极端气温及降水进行预估.结果表明：1)相较于CMIP单一模式,EPTGODD-WHU数据集模拟性能显著提升,气温及降水的空间相关系数分别达到0.99和0.81.2) SSP5-8.5情景下,年最低气温和最高气温均上升明显,且这种上升趋势年内波动不大,地球陆地极寒地区将面临升温的风险,而赤道等极热地区将处于年内长时间酷热状态.3)六大洲在SSP5-8.5情景下的极端降水整体上升趋势最剧烈,但北美洲密西西比平原和滨海平原的地区在SSP5-8.5情景下在未来面临较高的旱灾风险.4)中国西南部地区的极端降水在三个情景下均呈稳定的增幅,且增幅高达60%,预示面临较高的洪灾风险.     

星载激光雷达GEDI数据林下地形反演性能验证

【目的】新一代天基测高系统全球生态系统动力学调查(GEDI)对森林观测及经营具有重要意义,为探究GEDI V2(GEDI第2版)数据反演林下地形的性能,利用机载雷达数据验证林下地形反演精度,并探究反演精度的影响因素。【方法】分别以美国西波拉森林与中国帽儿山森林为研究对象,利用G-liht及帽儿山高精度机载雷达数据验证GEDI V2数据在针叶林及针阔叶混交林下反演地形的性能,并分析不同光束强度、光斑时间、坡度及植被覆盖度对地形反演精度的影响。【结果】美国西波拉针叶林地区地形反演精度均方根误差(RMSE)为2.33 m,平均绝对误差(MAE)为1.48 m;帽儿山针阔叶混交林地区地形反演精度RMSE为4.49 m, MAE为3.33 m。随着坡度、植被覆盖度增大,两种森林类型地形反演精度均降低。【结论】GEDI V2数据反演针叶林林下地形精度要优于针阔叶混交林,强光束优于覆盖光束,湿润地区白天效果更优,干旱地区黑夜效果更优;平缓地区数据使用效果极好,陡峭地区精度降低;中低植被覆盖度区域地形反演精度较高,高植被覆盖区域地形测定性能有所下降。     

修正PRP共轭梯度方法求解无约束最优化问题

基于著名的PRP共轭梯度方法,利用CG_DESCENT共轭梯度方法的结构,本文提出了一种求解大规模无约束最优化问题的修正PRP共轭梯度方法。该方法在每一步迭代中均能够产生一个充分下降的搜索方向,且独立于任何线搜索条件。在标准Wolfe线搜索条件下,证明了修正PRP共轭梯度方法的全局收敛性和线性收敛速度。数值结果展示了修正PRP方法对给定的测试问题是非常有效的。