一类奇异边值问题三解的存在性

利用Ｌｅｇｇｅｔｔ Ｗｉｌｌｉａｍｓ不动点定理,研究了一类含有ｐ Ｌａｐｌａｃｉａｎ算子的非线性奇异边值问题３个解的存在性,获得了这类方程存在３个解的充分条件．结果表明：如果非线性奇异项在其定义域内满足适当的条件,那么该问题必存在３个解．     

一类退化抛物型方程全局解的存在性与爆破

研究了一类具有一致Dirichlet边界条件的非线性退化抛物型方程组解的爆破和全局存在性，给出了解全局存在的一个充分必要条件。     

奇异Itô随机系统几个重要基础问题的研究进展

近年来,一类由Itô随机微分方程驱动的奇异随机系统因其在实际领域中的广泛应用而备受关注.然而,系统方程同时包含奇异矩阵和扩散矩阵,大大增加了分析问题的复杂性.本文首先概述了奇异Itô随机系统几个重要基础问题的研究进展,主要包括:系统方程解的存在条件、广义Itô公式、容许性定义及稳定性问题.同时针对不同文献对上述问题的研究结果提出了自己的观点.最后对以上基础问题研究待解决的问题进行了展望.     

奇异摄动系统的有限频段正实引理和界实引理

利用GKYP引理研究了奇异摄动系统的有限频段正实引理和界实引理,证明了全阶系统的有限频段正实性可以由快、慢子系统的有限频段正实性得到,同样可以证明奇异摄动系统的有限频段界实引理具有类似性质.最后作为应用,给出了一个两频域尺度模型降阶实现方案,表明了该方法的有效性.     

GRAPES全球奇异向量方法改进及试验分析

基于总能量模的奇异向量扰动常用于构造集合预报的初始条件。以建立GRAPES（Global and Regional Assimilation PrEdiction System）全球集合预报系统为目的,基于前期研发的GRAPES全球模式奇异向量方法,在GRAPES全球切线性模式和伴随模式2.0版的框架下,开展了引入线性化边界层方案来改善奇异向量结构,并提高奇异向量计算效率的研究。通过连续试验,从奇异向量的扰动能量结构、扰动能量谱及扰动空间分布等方面,综合分析改进GRAPES全球奇异向量的结构及演变特征。试验结果表明,改进后的GRAPES奇异向量方法有效抑制了之前扰动能量在近地面层不合理的快速增长,同时,奇异向量最优扰动的结构更客观地体现了中高纬度区域大气初始条件中的斜压不稳定扰动及其演变,如在初始时刻奇异向量扰动能量主要位于对流层中层,并呈现出随高度向西倾斜的大气斜压特征;经过线性化演变,扰动能量向较大水平尺度转移,并在垂直结构上表现出向对流层高层上传及向对流层低层下传的特征等。针对GRAPES奇异向量迭代求解中伴随模式计算耗时为主的情况,改进伴随模式中广义共轭余差方案的调用方式,并采用大内存存储法来提高其计算效率,进而将奇异向量总计算时间缩短了25%。总之,改进后的GRAPES奇异向量方法,可应用于构建面向业务应用的GRAPES全球集合预报系统。      

热力强迫的非线性奇异惯性重力内波与高原低涡的联系

利用相平面分析法,由非绝热大气运动方程组导出了与非线性惯性重力内波有关的KdV方程,然后用直接积分法得到两类有天气意义的孤立波解,重点分析了与青藏高原暖性低涡有联系的一类具有间断点的奇异孤立波解的特征,进而讨论了高原非绝热加热对高原低涡生成、移动及高原低涡暖心结构的作用。     

自忆预报模式中记忆特性的探讨

运用有限振幅斜压波的截谱方程对自忆模式中的的记忆性进行了理论探讨。推导了相应的自忆性方程,在给定记忆函数呈线性和指数衰减型时求出了它的解析解,并讨论了这些解的物理意义和预报含意;证明了零解自忆性方程与记忆函数形式无关。通过计算遗忘因子,对动力可预报性和回溯阶等问题进行了讨论,并指出可将其统一纳入大气记忆理论的框架中。     

一类奇异孤波解及其在高原低涡结构分析中的应用

文中利用相平面分析法 ,由非绝热大气运动方程组导出了与非线性重力内波有关的 Kd V方程 ,然后用直接积分法得到两类有意义的孤立波解 ,重点分析了一类具有间断点的奇异孤立波解的特征 ,初步建立了此波解与一类青藏高原暖性低涡的联系 ,讨论了高原加热和层结稳定度对高原低涡生成和移动的影响 ,并且从理论上论证了高原低涡具有与热带气旋类低涡( Tropical cyclone- like vortices)类似的涡眼和暖心结构     

基于总能量模的GRAPES全球模式奇异向量扰动研究

以发展基于奇异向量技术为初值扰动的GRAPES全球集合预报系统为目的,在GRAPES模式及其干动力框架下的切线性、伴随模式基础上开展了以总能量模为权重算子的奇异向量计算技术研究,建立奇异向量的计算求解模块,并通过奇异向量检验方法和切线性近似方法验证了奇异向量求解的正确性.通过对中高纬度的GRAPES奇异向量水平结构的线性演变分析,证实了在最优时间间隔内GRAPES奇异向量能够快速增长,并能描述中高纬度大气的斜压不稳定特征.分析在初始时刻和最优化时间间隔时刻的GRAPES奇异向量总能量及其分量(动能和势能)的垂直分布特征,发现在中高纬度区域,GRAPES奇异向量能够描述对流层不同层次的斜压不稳定增长特征.     

一类非线性蜕化抛物型方程的全局解的存在性和光滑性

本文主要考虑(E1)的全局解存在性和光滑性问题。主要结果:在(E1)的假设下,α0。有essup|u|≤c(T,||u_0||p) Q_(T,z)其中Q_(T,ε)=Ω_ε×(ε,T),Ω_ε={x∈Ω|dist{x,?Ω}>ε}。     

Splitting phenomenon of a higher-order shallow water theory associated with a longitudinal planetary waves

The Cauchy–Poisson free boundary problem associated with a nonstationary motion of a perfect incompressible fluid circulating around the equatorial plane of a planet is considered. It is shown that the corresponding theory of a higher-order shallow approximation admits two functionally independent systems, while the classical problem for the flat bottom admits only one system.     

一种新的统计回归模型及其建模方案

根据经典门限自回归模型的基本思想,引入半截多项式变换,导出了一种新的统计回归模型,并提出了相应的一整套建模方案。这种模型和建模方案的特点是:（1）解决了统计回归分析中逐段线性化模型的检验问题;（2）在确定统计回归模型中各待估参数和变量——包括门限变量、门限值、阶数、时滞和回归系数时显得十分方便、快捷。试验结果表明,根据此方案建立的统计回归模型具有较高的拟合和预报精度,同时具有良好的稳定性。     

A review of analytical models of sea‐ice growth

Abstract

The modelling of sea‐ice growth is a classical problem in geophysics, which has been traditionally treated as one‐dimensional, considering only the vertical heat transfer. The modelling work commenced in the 1800s with analytic methods. These are very effective tools for examining the sea‐ice growth problem, providing a clear insight into the physical mechanisms and producing simple first‐order approximations for the ice thickness in various conditions. This paper describes the physical problem of sea‐ice growth, presents an analytical modelling framework for the problem and provides analytic solutions for different environmental conditions.     

雹云识别的物元可拓模型及其效果检验

雹云识别是一个多参数的模式识别问题。应用物元可拓思想将单参数雹云识别的不相容性转化为相容性问题。通过构造雹云和雷雨云两类样本的经典物无降节域物元，根据计算出的待识别云体与两类样本云体之间的关联度大小，进行雹云识别。该方法用于成都地区雹云识别结果的正确率达85％以上。     

Application of the hybrid convection parameterization scheme HYMACS to different meteorological situations

Convection can cause severe precipitation events and is thus of major interest for quantitative precipitation forecasts. Due to its small horizontal scale convection usually has to be parameterized in numerical weather prediction (NWP) models as a subgrid scale phenomenon. Classical mass flux convection schemes assume grid box sizes much larger than the scale of the convective circulation. Thus, the convective mass transport is closed in the local grid column and no net mass transport occurs on the grid scale.In contemporary NWP models with grid sizes of a few kilometers, where convection is already partially resolved, the classical approach leads to a conceptual problem. This can be overcome by a hybrid mass flux convection scheme (HYMACS), in which only the small scale convective updrafts and downdrafts are parameterized, whereas the treatment of the larger scale environmental subsidence is left to the grid scale equations. Different to the classical schemes, HYMACS produces a net convective mass flux exerting pressure gradient forces to the grid scale model.We discuss real cases of different meteorological situations simulated with the operational weather forecast model COSMO of the German Meteorological Service as the hosting model of HYMACS. Precipitation and cloud top pressures simulated with HYMACS are compared with results from classical convection schemes and observational data from the DWD station network and the SEVIRI (MSG) satellite instrument.     

On the determination of the absolute velocity of steady flows of a baroclinic fluid with applications to ocean currents

The problem of determining the absolute velocity of marine currents, including its barotropic component, is revisited. A generalization of the classical Needler’s formula is discussed for a Boussinesq fluid and it is shown that the steady flow solution can be deduced from a variational principle that uses the constants of motion existing in the problem. A simple model of a steady flow is considered when the Bernoulli function consists of two terms. The first term is proportional to the square of Ertel’s potential vorticity and the second term is a quadratic function of the fluid buoyancy. This model is applied to mimic the circulation in the western Mediterranean Sea near the African coast. Alternatively, “potential temperature – salinity” coordinates are applied to construct the stream-tubes and infer the steady flow velocity in the simplest case of the Bernoulli function being proportional to the product of the above two variables.     

Polytropic atmospheres and the scaling of potential vorticity

Summary Potential vorticity P is in widespread use as a diagnostic in atmospheric dynamics. Here, we employ the concepts of polytropic change of state and polytropic temperature for investigating the problem of scaling potential vorticity. For many applications, it has proven useful to scale P with a dimensionless scale factor to remove its exponential increase with altitude. This scale factor may be derived from the assumption of a polytropic reference atmosphere which includes the classical scaling using isothermal reference atmospheres as a special case.     

顶点Pk覆盖问题的研究综述

顶点覆盖问题是经典的NP完全问题,在排序、计算机网络等现实生活中有许多的应用.近几年来,许多研究者开始探究它的推广形式——顶点P_k覆盖（VCP_k）问题,即寻找一个顶点子集,从拓扑结构图中删除后使得剩下的顶点导出的子图不包含P_k路,其中P_k是指包含k个顶点的路.本文简单介绍了VCP_k问题的应用背景,归纳了它在近似算法、精确算法、参数化算法3个方面的主要研究进展,并分析了一些主要的方法和技巧.在此基础上,对VCP_k问题及其相关问题的研究前景进行了展望.     

A new class of steady solutions of the barotropic vorticity equation

Early studies of the wind-driven ocean problem were concerned with finding steady solutions of the equations of motion, first by analytic, and later by numerical methods. The problem is characterized by an Ekman number (?) and a Rossby number (α). Prior to this study, steady solutions were confined to the ranges α, ? < < 1.In this work the problem is considered in a circular domain with lateral friction and a partial-slip boundary condition. Steady solutions are found analytically in the new regime α > 1. Furthermore, for large enough values of ?, steady solutions are determined numerically in the intermediate range between this high-α regime and the classical low-α regime. That is, for some values of ?, steady solutions can be found through all values of α. Numerical evidence suggests that below a critical value of ?, steady solutions in this intermediate range exist, but cease to be stable. Similar results have been obtained with bottom friction and with different boundary conditions.     

Climatic change as a topic in the classical Greek and Roman literature

A search was made of the classical Greek and Roman literature for references to climatic change, irrespective whether facts of observation or views. It was found that several scholars/scientists of the classical antiquity made pronouncements on the subject and their statements are either summarized or quoted verbatim in this paper. From the Greek literature we quote Plato, Aristotle and Theophrastus; Herodotus is also quoted for an indirect reference to the topic. From the Roman literature we cite the agricultural writer Columella and the scientist Pliny the Elder; actually, Columella quotes the distinguished writers on husbandry, the Sasernas, father and son.Aristotle's statement is relevant to a degree to the Mycenaean drought (~ 1200 B.C.) problem. The Columella-Saserna pronouncement relates to the astronomical theory of climatic change, while Theophrastus discusses man-made climatic changes.Appendix I gives a statistics of storms, as gleaned from the classical literature, covering approximately the months April–October. Further, it lists some pointers to the relative coolness of the era 850/800–400/300 B.C. in some areas of the Mediterranean. Appendix II offers a few examples for the usefulness of the ancient literature from the point of view of environmental data or events.Now visiting with the Department of Meteorology, The University of Helsinki, Helsinki, Finland.