非线性抛物积分微分方程的类Wilson非协调元分析

在半离散和全离散格式下讨论非线性抛物积分微分方程的类Wilson非协调有限元逼近.当问题的精确解u∈H3(Ω)/H4(Ω)时,利用该元的相容误差在能量模意义下可以达到O(h2)/O(h3)比其插值误差高一阶和二阶的特殊性质,再结合协调部分的高精度分析及插值后处理技术,并借助于双线性插值代替传统有限元分析中不可缺少的Ritz-Volterra投影导出了半离散格式下的O(h2)阶超逼近和超收敛结果.同时分别得到了向后Euler全离散格式下的超逼近性和Crank-Nicolson全离散格式下的最优误差估计.     

非线性sine-Gordon方程的各向异性线性元高精度分析新模式

在各向异性网格下,针对一类非线性sine-Gordon方程提出了线性三角形元新的高精度分析模式.基于该元的积分恒等式结果,导出了插值与Riesz投影之间的误差估计,再借助于插值后处理技术得到了在半离散和全离散格式下单独利用插值或Riesz投影所无法得到的超逼近和超收敛结果.最后,对一些常见的单元作了进一步探讨.     

非线性色散耗散波动方程双线性元的高精度分析

针对一类非线性色散耗散波动方程研究了双线性元逼近.基于该元的高精度分析和插值后处理技巧,对于半离散格式,在精确解的合理正则性假设下得到了H~11模意义下最优误差估计及超逼近性和超收敛结果.同时,通过构造一个新的外推格式,导出了具有三阶精度的外推解.最后,建立了一个全离散逼近格式及研究其解的超逼近性.     

电报方程的类Wilson非协调有限元分析

本文在矩形网格上讨论了半离散和全离散格式下电报方程的类Wilson非协调有限元逼近.利用该元在H1模意义下O(h2)阶的相容误差结果,平均值理论和关于时间t的导数转移技巧得到了超逼近性.进而,借助于插值后处理方法导出了超收敛结果.又由于该元在H1模意义下的相容误差可以达到O(h3)阶,构造了新的外推格式,给出了比传统误差估计高两阶的外推估计.最后,对于给出的全离散逼近格式得到了最优误差估计.     

拟线性双相滞热传导方程的双线性元高精度分析及外推

研究一类拟线性双相滞热传导方程的双线性有限元逼近,利用该元的Ritz投影和插值相结合的技巧,并结合高精度分析和插值后处理技术分别导出了半离散和全离散格式的超逼近和超收敛结果.同时通过构造合适的辅助问题,对半离散格式导出了具有三阶精度的外推解.     

非线性Benjamin-Bona-Mahony方程一个新的低阶混合元方法[英文]

基于双线性元和零阶R-T元, 建立了非线性Benjamin-Bona-Mahony (BBM)方程的一个新的低阶混合元方法. 借助积分恒等式技巧, 得到了一个对超逼近分析比较重要的误差估计. 对于半离散格式, 证明了解的存在性, 唯一性和稳定性, 然后得到了精确解~$u$在$H^1$模意义下和压力变量~ $\vec{p}=\nabla u_t$在 $L^2 $模意义下具有$O(h^2)$ 的超逼近和超收敛结果. 对于向后欧拉和 Crank-Nicolson 全离散格式, 分别探讨了解的稳定性, 且在对时间步长没有任何限制的前提下得到了超逼近结果.     

黏弹性方程的Wilson元收敛性分析

对一类黏弹性方程利用Wilson元提出新的半离散和全离散逼近格式.基于单元的性质,通过定义新的双线性型,在不需要外推和插值后处理技术的前提下,分别得到了比传统的H~1-范数更大的模意义下相应的O(h~2)阶和O(h~2+τ~2)阶的误差分析结果,正好比通常的关于Wilson元的误差估计高出一阶.这里,h,τ表示空间剖分参数和时间步长.     

四阶强阻尼非线性波动方程的Hermite型矩形混合有限元分析

讨论了四阶强阻尼非线性波动方程的Hermite型混合有限元方法,并证明了半离散格式下解的存在唯一性.基于该元积分恒等式结果,利用插值与Ritz投影之间的误差估计,可得到半离散格式下O(h~3)阶的超逼近性质,再借助于插值后处理技术导出整体超收敛.进而,通过构造一个新的金离散格式,得到了O(h~3+τ~2)的超逼近和超收敛结果.     

抛物方程的一个新混合元格式的高精度分析

借助双二次元及一阶Raviart-Thomas(R-T)元对抛物方程提出了一种新的协调混合有限元格式,导出了半离散及全离散格式下原始变量在H¹和L1和L²模意义下以及流量(?)在L2模意义下以及流量(?)在L²模意义下的超逼近结果.     

非线性粘弹性方程的EQrot1非协调有限元分析

针对非线性粘弹性方程,在半离散和全离散格式下给出EQrot1非协调有限元逼近.由于该单元的相容误差(O(h2)阶)比插值误差(O(h)阶)高一阶,可得到在H1模意义下的O(h2)阶超逼近结果,并利用插值后处理技术导出整体超收敛.进而,基于该单元的渐近展开式,构造新的插值后处理算子和外推格式,给出O(h4)阶的外推结果.最后,运用与以往文献不同的方法得到全离散逼近格式的最优误差估计.     

Boundary controllability for conservative PDEs

Boundary observability and controllability problems for evolution equations governed by PDEs have been greatly studied in the past years. However, the problems were studied on a case-by-case basis, only for some particular types of boundary controls, and, moreover, several unnatural restrictions concerning lower-order terms were used.Our goal here is to give a general approach for boundary controllability problems, which is valid for all evolution PDEs of hyperbolic or ultrahyperbolic type, all boundary controls for which the corresponding homogeneous problem is well-posed, and all well-posedness spaces for the homogeneous problem. The first example of such equations is the class of hyperbolic equations, but valid examples are also equations such as the Schroedinger equation and various models for the plate equation.This work is essentially based on some apriori estimates of Carleman's type obtained by the author in a previous paper [29].This research was partially supported by the National Science Foundation under Grant NSF-DMS-8903747.     

Study of the size-flux relation of pores and spots

Using the vector magnetic field data from the Huairou Solar Observing Station of National Astronomical Observatories, a statistical study on the size-flux relation of photospheric magnetic features without any assumption is given. The selected data here include mature sunspots, as well as protosunspot (with a partial penumbra) and pore. We studied not only their size-flux relations of pore, protosunspot and mature sunspot, but also that of umbra and penumbra of the mature sunspots. The size-flux relationship of mature sunspots and their umbra and penumbra is found to be in different indexes of power-law. No evident relations are found between size and flux of the pores and protosunspots. We found that there is a threshold of 1×1012 Wb or (3-4.03) × 107 km2 for the transition from a pore to a protospot. Such results may be useful for understanding the physical conditions and dynamical processes of magnetic flux tubes in solar plasma during sunspot's formation. In addition, their characteristic size is also given.     

了解积分——分割的艺术

求一个函数的黎曼积分,实际上就是一个分割、近似代替、求和、取极限的过程．分割是整个过程的初始点．本文以黎曼积分中的分割问题做背景知识,用通俗的语言,而不是严格的数学语言,介绍了分割的过程是如何实现的,应该注意哪些基本问题,整体与局部的联系,如何保证分割是我们期望的、有效的、均匀分割,以及对一个空间的或者集合的分割如何实现等,做了些许描述．为初学者在学习中并应用这样的方法时,应该如何思考问题,如何动手解决问题,进而如何创造新的知识,提供一个可以借鉴的途径．     

Moral responsibility for unprevented harm

That we are morally responsible for what we do willingly and knowingly is a commonplace. That our moral responsibility extends as far as to cover at least the intended consequences of our voluntary actions and perhaps also the ones we did not intend, but could or did foresee, is equally beyond dispute. But what about omissions? Are we, or can we be, (equally) morally responsible for the harm that has occured because we did not prevent it, even though we could have done so? Say, for all the enormous suffering, caused daily by famine, deprivation and curable diseases in the Third World countries?Moral intuitions and practices that one could consult in this matter seem to leave us in the dark. We regularly ascribe responsibility to people for harms resulting from their negligence or failure to fulfill professional duties. On the other hand, we tend to think that unless there is some evidence of the causal contribution that agents made to a harmful event and/or state, it is not really fair to blame it on them. And finally, to complicate things even more, most of us deny that omissions could effect anything (any change) in the world and consequently regard them as causally impotent (as well as possibly harmless).Most of the proposed solutions to this perplexing issue simply take negative moral responsibility for granted and then either try to revise our ordinary notion of causation accordingly or, alternatively, weaken the conditions for holding someone morally responsible. In the paper I present and defend the relative merits of the third approach, one sceptical of the notion of moral responsibility for the ‘outcomes’ of omissions. I try to show that for some identifiable core notion of moral responsibility and paradigmatic cases of omissions, the prospects for a happy marriage are rather slim.     

ParadisEO: A Framework for the Reusable Design of Parallel and Distributed Metaheuristics

In this paper, we present the ParadisEO white-box object-oriented framework dedicated to the reusable design of parallel and distributed metaheuristics (PDM). ParadisEO provides a broad range of features including evolutionary algorithms (EA), local searches (LS), the most common parallel and distributed models and hybridization mechanisms, etc. This high content and utility encourages its use at European level. ParadisEO is based on a clear conceptual separation of the solution methods from the problems they are intended to solve. This separation confers to the user a maximum code and design reuse. Furthermore, the fine-grained nature of the classes provided by the framework allow a higher flexibility compared to other frameworks. ParadisEO is of the rare frameworks that provide the most common parallel and distributed models. Their implementation is portable on distributed-memory machines as well as on shared-memory multiprocessors, as it uses standard libraries such as MPI, PVM and PThreads. The models can be exploited in a transparent way, one has just to instantiate their associated provided classes. Their experimentation on the radio network design real-world application demonstrate their efficiency.     

Cooperation when some players are incompatible

A situation with incompatibilities is defined to be a TU-game together with a graph whose arcs link pairs of incompatible players. In this paper we introduce an efficient and fair allocation rule which selects a payoff for every possible situation with incompatibilities (when the set of players is fixed), and prove that it is uniquely determined. Besides, we demonstrate that it is stable, study its relationship with the so-calledIR-Shapley value and show that it generalizes an earlier theory for simple games. Finally, the communication situations with incompatibilities are studied.We thank University of Santiago de Compostela and Xunta de Galicia for financial support through projects 60902.25064(5060) and XUGA20701B91.     

t-Extending Modules and t-Baer Modules

We introduce the notions of “t-extending modules,” and “t-Baer modules,” which are generalizations of extending modules. The second notion is also a generalization of nonsingular Baer modules. We show that a homomorphic image (hence a direct summand) of a t-extending module and a direct summand of a t-Baer module inherits the property. It is shown that a module M is t-extending if and only if M is t-Baer and t-cononsingular. The rings for which every free right module is t-extending are called right Σ-t-extending. The class of right Σ-t-extending rings properly contains the class of right Σ-extending rings. Among other equivalent conditions for such rings, it is shown that a ring R is right Σ-t-extending, if and only if, every right R-module is t-extending, if and only if, every right R-module is t-Baer, if and only if, every nonsingular right R-module is projective. Moreover, it is proved that for a ring R, every free right R-module is t-Baer if and only if Z ₂(R _R ) is a direct summand of R and every submodule of a direct product of nonsingular projective R-modules is projective.     

A game theoretical approach to sharing penalties and rewards in projects

This paper analyzes situations in which a project consisting of several activities is not realized according to plan. If the project is expedited, a reward arises. Analogously, a penalty arises if the project is delayed. This paper considers the case of arbitrary nondecreasing reward and penalty functions on the total expedition and delay, respectively. Attention is focused on how to divide the total reward (penalty) among the activities: the core of a corresponding cooperative project game determines a set of stable allocations of the total reward (penalty). In the definition of project games, surplus (cost) sharing mechanisms are used to take into account the specific characteristics of the reward (penalty) function at hand. It turns out that project games are related to bankruptcy and taxation games. This relation allows us to establish nonemptiness of the core of project games.     

Modelling of coupled heat and moisture transfer in porous construction materials

In this paper, a mathematical model is proposed for predicting air temperature and humidity in a two-room region. The model contains a coupled relationship between temperature and humidity within the constructions and can be solved by using the numerical method. However, the two-room region can be reduced to a single region when the region with no ventilation is considered, and then the room temperature and relative humidity can be obtained analytically. The solution obtained in this paper is verified by comparing with the result of the analytical method. It shows that the two results are in agreement. In addition, the proposed model can also be applied to simultaneously obtain the transient temperature and humidity of a two-room region for different porous construction materials.